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href=/list/math/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> <dl id='articles'> <h3>New submissions (showing 117 of 117 entries)</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2503.16539" title="Abstract" id="2503.16539"> arXiv:2503.16539 </a> [<a href="/pdf/2503.16539" title="Download PDF" id="pdf-2503.16539" aria-labelledby="pdf-2503.16539">pdf</a>, <a href="https://arxiv.org/html/2503.16539v1" title="View HTML" id="html-2503.16539" aria-labelledby="html-2503.16539" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16539" title="Other formats" id="oth-2503.16539" aria-labelledby="oth-2503.16539">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Digital Twin Simulator of a Pastillation Process with Applications to Automatic Control based on Computer Vision </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gonz%C3%A1lez,+L+D">Leonardo D. Gonz谩lez</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Pulsipher,+J+L">Joshua L. Pulsipher</a> (2), <a href="https://arxiv.org/search/math?searchtype=author&query=Jiang,+S">Shengli Jiang</a> (3), <a href="https://arxiv.org/search/math?searchtype=author&query=Soderstrom,+T">Tyler Soderstrom</a> (4), <a href="https://arxiv.org/search/math?searchtype=author&query=Zavala,+V+M">Victor M. Zavala</a> (1) ((1) Department of Chemical &amp; Biological Engineering, University of Wisconsin-Madison, Madison, USA, (2) Department of Chemical Engineering, University of Waterloo, Waterloo, Canada, (3) Chemical &amp; Biological Engineering Department, Princeton University, Princeton, USA, (4) Advanced Process Control, ExxonMobil Technology and Engineering, Spring, USA)</div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Robotics (cs.RO) </div> <p class='mathjax'> We present a digital-twin simulator for a pastillation process. The simulation framework produces realistic thermal image data of the process that is used to train computer vision-based soft sensors based on convolutional neural networks (CNNs); the soft sensors produce output signals for temperature and product flow rate that enable real-time monitoring and feedback control. Pastillation technologies are high-throughput devices that are used in a broad range of industries; these processes face operational challenges such as real-time identification of clog locations (faults) in the rotating shell and the automatic, real-time adjustment of conveyor belt speed and operating conditions to stabilize output. The proposed simulator is able to capture this behavior and generates realistic data that can be used to benchmark different algorithms for image processing and different control architectures. We present a case study to illustrate the capabilities; the study explores behavior over a range of equipment sizes, clog locations, and clog duration. A feedback controller (tuned using Bayesian optimization) is used to adjust the conveyor belt speed based on the CNN output signal to achieve the desired process outputs. </p> </div> </dd> <dt> <a name='item2'>[2]</a> <a href ="/abs/2503.16555" title="Abstract" id="2503.16555"> arXiv:2503.16555 </a> [<a href="/pdf/2503.16555" title="Download PDF" id="pdf-2503.16555" aria-labelledby="pdf-2503.16555">pdf</a>, <a href="https://arxiv.org/html/2503.16555v1" title="View HTML" id="html-2503.16555" aria-labelledby="html-2503.16555" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16555" title="Other formats" id="oth-2503.16555" aria-labelledby="oth-2503.16555">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Natural Transformation between the Model Constructions of the Completeness and Compactness Theorems, Enhanced by Rigidity and 2-Categorical Strengthening </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Reizi,+B+J">Barreto Joaquim Reizi</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 26pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic (math.LO)</span>; Logic in Computer Science (cs.LO); Category Theory (math.CT) </div> <p class='mathjax'> In this paper we present a mathematically rigorous and constructive framework that unifies two canonical model constructions in classical first order logic. In particular, we define two functors F and G from the category of consistent first order theories to the category of models. The functor F is constructed via the Henkin method, which extends any given theory to a maximal consistent theory by means of a fixed enumeration and the systematic introduction of Henkin constants, and then constructs a term model by taking the quotient of the term algebra with respect to provable equality. The functor G is obtained through a canonical compactness based construction, using either a fixed ultraproduct or a saturation procedure, ensuring that the resulting model is unique up to isomorphism. <br>We prove the existence of a natural transformation eta from F to G such that each component is an isomorphism. Moreover, by leveraging the uniqueness of saturated (or prime) models in countable languages, we show that eta is rigid, meaning any other natural transformation between F and G must equal eta. Furthermore, we establish a strong natural equivalence between F and G in the two categorical sense, with eta and its inverse satisfying the required coherence conditions. <br>This unification not only deepens our understanding of the interplay between proof theory and model theory, but also opens new avenues for applications in automated theorem proving, formal verification, and the study of alternative logical systems. </p> </div> </dd> <dt> <a name='item3'>[3]</a> <a href ="/abs/2503.16570" title="Abstract" id="2503.16570"> arXiv:2503.16570 </a> [<a href="/pdf/2503.16570" title="Download PDF" id="pdf-2503.16570" aria-labelledby="pdf-2503.16570">pdf</a>, <a href="/format/2503.16570" title="Other formats" id="oth-2503.16570" aria-labelledby="oth-2503.16570">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Categorical Integration of Logical Connectives via Higher Category Theory </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Reizi,+B+J">Barreto Joaquim Reizi</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 120 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic (math.LO)</span>; Category Theory (math.CT) </div> <p class='mathjax'> This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the universal properties of logical operations such as negation, conjunction, disjunction, and implication are rigorously captured. Advanced techniques including pseudo-limits, pseudo-colimits, and strictification are employed to transform the resulting weak structure into a strict two-category, thereby simplifying composition rules and coherence verification without loss of semantic content. The framework is validated through detailed diagrammatic proofs and concrete examples, demonstrating its robustness and potential impact in areas such as type theory, programming language semantics, and formal verification. </p> </div> </dd> <dt> <a name='item4'>[4]</a> <a href ="/abs/2503.16590" title="Abstract" id="2503.16590"> arXiv:2503.16590 </a> [<a href="/pdf/2503.16590" title="Download PDF" id="pdf-2503.16590" aria-labelledby="pdf-2503.16590">pdf</a>, <a href="/format/2503.16590" title="Other formats" id="oth-2503.16590" aria-labelledby="oth-2503.16590">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Uniformly consistent proportion estimation for composite hypotheses via integral equations: "the case of location-shift families" </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Chen,+X">Xiongzhi Chen</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> expanded much results in <a href="https://arxiv.org/abs/1906.10246" data-arxiv-id="1906.10246" class="link-https">arXiv:1906.10246</a> on location-shift families, including concentration inequalities for 3 complicated empirical processes, how to deal with closed nulls, and two illustrations </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Statistics Theory (math.ST)</span> </div> <p class='mathjax'> We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means or medians of the random variables belonging to a non-empty, bounded interval; (ii) the means or medians of the random variables belonging to an unbounded interval that is not the whole real line. For each type of composite null hypotheses, uniformly consistent estimators of the proportion of false null hypotheses are constructed for random variables whose distributions are members of a Type I location-shift family. Further, uniformly consistent estimators of certain functions of a bounded null on the means or medians are provided for the random variables mentioned earlier; these functions are continuous and of bounded variation. The estimators are constructed via solutions to Lebesgue-Stieltjes integral equations and harmonic analysis, do not rely on a concept of p-value, and have various applications. </p> </div> </dd> <dt> <a name='item5'>[5]</a> <a href ="/abs/2503.16594" title="Abstract" id="2503.16594"> arXiv:2503.16594 </a> [<a href="/pdf/2503.16594" title="Download PDF" id="pdf-2503.16594" aria-labelledby="pdf-2503.16594">pdf</a>, <a href="https://arxiv.org/html/2503.16594v1" title="View HTML" id="html-2503.16594" aria-labelledby="html-2503.16594" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16594" title="Other formats" id="oth-2503.16594" aria-labelledby="oth-2503.16594">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Transformer-based Wireless Symbol Detection Over Fading Channels </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Fan,+L">Li Fan</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Yang,+J">Jing Yang</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Shen,+C">Cong Shen</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> arXiv admin note: substantial text overlap with <a href="https://arxiv.org/abs/2411.07600" data-arxiv-id="2411.07600" class="link-https">arXiv:2411.07600</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Information Theory (cs.IT)</span>; Machine Learning (cs.LG); Signal Processing (eess.SP); Machine Learning (stat.ML) </div> <p class='mathjax'> Pre-trained Transformers, through in-context learning (ICL), have demonstrated exceptional capabilities to adapt to new tasks using example prompts without model update. Transformer-based wireless receivers, where prompts consist of the pilot data in the form of transmitted and received signal pairs, have shown high detection accuracy when pilot data are abundant. However, pilot information is often costly and limited in practice. In this work, we propose the DEcision Feedback INcontExt Detection (DEFINED) solution as a new wireless receiver design, which bypasses channel estimation and directly performs symbol detection using the (sometimes extremely) limited pilot data. The key innovation in DEFINED is the proposed decision feedback mechanism in ICL, where we sequentially incorporate the detected symbols into the prompts as pseudo-labels to improve the detection for subsequent symbols. Furthermore, we proposed another detection method where we combine ICL with Semi-Supervised Learning (SSL) to extract information from both labeled and unlabeled data during inference, thus avoiding the errors propagated during the decision feedback process of the original DEFINED. Extensive experiments across a broad range of wireless communication settings demonstrate that a small Transformer trained with DEFINED or IC-SSL achieves significant performance improvements over conventional methods, in some cases only needing a single pilot pair to achieve similar performance of the latter with more than 4 pilot pairs. </p> </div> </dd> <dt> <a name='item6'>[6]</a> <a href ="/abs/2503.16617" title="Abstract" id="2503.16617"> arXiv:2503.16617 </a> [<a href="/pdf/2503.16617" title="Download PDF" id="pdf-2503.16617" aria-labelledby="pdf-2503.16617">pdf</a>, <a href="https://arxiv.org/html/2503.16617v1" title="View HTML" id="html-2503.16617" aria-labelledby="html-2503.16617" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16617" title="Other formats" id="oth-2503.16617" aria-labelledby="oth-2503.16617">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Concurrent Optimization of Satellite Phasing and Tasking for Cislunar Space Situational Awareness </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Patel,+M">Malav Patel</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tomita,+K">Kento Tomita</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ho,+K">Koki Ho</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages, 8 figures, submitted to 2024 AAS Conference </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> Recently, renewed interest in cislunar space spurred by private and public organizations has driven research for future infrastructure in the region. As Earth-Moon traffic increases amidst a growing space economy, monitoring architectures supporting this traffic must also develop. These are likely to be realized as constellations of patrol satellites surveying traffic between the Earth and the Moon. This work investigates the concurrent optimization of patrol satellite phasing and tasking to provide information-maximal coverage of traffic in periodic orbits. </p> </div> </dd> <dt> <a name='item7'>[7]</a> <a href ="/abs/2503.16618" title="Abstract" id="2503.16618"> arXiv:2503.16618 </a> [<a href="/pdf/2503.16618" title="Download PDF" id="pdf-2503.16618" aria-labelledby="pdf-2503.16618">pdf</a>, <a href="https://arxiv.org/html/2503.16618v1" title="View HTML" id="html-2503.16618" aria-labelledby="html-2503.16618" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16618" title="Other formats" id="oth-2503.16618" aria-labelledby="oth-2503.16618">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A note on Arveson's hyperrigidity and non-degenerate C*-correspondences </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Dessi,+J+A">Joseph A. Dessi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kakariadis,+E+T">Evgenios T.A. Kakariadis</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Paraskevas,+I+A">Ioannis Apollon Paraskevas</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 32 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Operator Algebras (math.OA)</span>; Functional Analysis (math.FA) </div> <p class='mathjax'> We revisit the results of Kim, and of Katsoulis and Ramsey concerning hyperrigidity for non-degenerate C*-correspondences. We show that the tensor algebra is hyperrigid, if and only if Katsura's ideal acts non-degenerately, if and only if Katsura's ideal acts non-degenerately under any representation. This gives a positive answer to the question of Katsoulis and Ramsey, showing that their necessary condition and their sufficient condition for hyperrigidity of the tensor algebra are equivalent. Non-degeneracy of the left action of Katsura's ideal was also shown by Kim to be equivalent to hyperrigidity for the selfadjoint operator space associated with the C*-correspondence, and our approach provides a simplified proof of this result as well. In the process we revisit Arveson's criterion connecting maximality with the unique extension property and hyperrigidity, in conjunction with the work of Salomon on generating sets. </p> </div> </dd> <dt> <a name='item8'>[8]</a> <a href ="/abs/2503.16619" title="Abstract" id="2503.16619"> arXiv:2503.16619 </a> [<a href="/pdf/2503.16619" title="Download PDF" id="pdf-2503.16619" aria-labelledby="pdf-2503.16619">pdf</a>, <a href="https://arxiv.org/html/2503.16619v1" title="View HTML" id="html-2503.16619" aria-labelledby="html-2503.16619" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16619" title="Other formats" id="oth-2503.16619" aria-labelledby="oth-2503.16619">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the Hodge and V-filtrations of mixed Hodge modules </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Davis,+D">Dougal Davis</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yang,+R">Ruijie Yang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 13 pages, comments are welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> In this note, we prove a filtered version of Beilinson-type formula for the V-filtration of Kashiwara and Malgrange for any D-module underlying a complex mixed Hodge module along a hypersurface, using Hodge filtrations on the localization. <br>We give some applications to the theory of higher multiplier and Hodge ideals. The main result is that the higher multiplier ideals can be deduced directly from the Hodge ideals by taking a suitable limit. As a corollary, we conclude that the Hodge ideals are left semi-continuous if and only if they coincide with the higher multiplier ideals. <br>In an appendix, we make some general observations about Hodge and higher multiplier ideals. We observe that results of Saito and Chen-Musta牛膬 give a birational formula for higher multiplier ideals, answering a question of Schnell and the second author, and that the Kodaira vanishing theorem for twisted Hodge modules gives a short proof of the vanishing theorem for Hodge ideals, strengthening a result of B. Chen. </p> </div> </dd> <dt> <a name='item9'>[9]</a> <a href ="/abs/2503.16626" title="Abstract" id="2503.16626"> arXiv:2503.16626 </a> [<a href="/pdf/2503.16626" title="Download PDF" id="pdf-2503.16626" aria-labelledby="pdf-2503.16626">pdf</a>, <a href="https://arxiv.org/html/2503.16626v1" title="View HTML" id="html-2503.16626" aria-labelledby="html-2503.16626" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16626" title="Other formats" id="oth-2503.16626" aria-labelledby="oth-2503.16626">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Continuous functions on limits of F-decomposable systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Manev,+T">Todor Manev</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span>; General Topology (math.GN) </div> <p class='mathjax'> We introduce the concept of F-decomposable systems, well-ordered inverse systems of Hausdorff compacta with fully closed bonding mappings. A continuous mapping between Hausdorff compacta is called fully closed if the intersection of the images of any two closed disjoint subsets is finite. We give a characterization of such systems in terms of a property of the continuous functions on their limit. When, moreover, the fibers of neighboring bonding mappings are metrizable, we call the limit of such a system an F_d-compact, a particular case of a Fedorchuk compact. The stated property allows us to obtain a locally uniformly rotund renorming on the space C(K), where K is an F_d-compact of countable spectral height. </p> </div> </dd> <dt> <a name='item10'>[10]</a> <a href ="/abs/2503.16633" title="Abstract" id="2503.16633"> arXiv:2503.16633 </a> [<a href="/pdf/2503.16633" title="Download PDF" id="pdf-2503.16633" aria-labelledby="pdf-2503.16633">pdf</a>, <a href="https://arxiv.org/html/2503.16633v1" title="View HTML" id="html-2503.16633" aria-labelledby="html-2503.16633" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16633" title="Other formats" id="oth-2503.16633" aria-labelledby="oth-2503.16633">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Functional limit theorems for Gaussian-fed queueing network in light and heavy traffic </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kriukov,+N">Nikolai Kriukov</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=D%C8%A9bicki,+K">Krzysztof D醛bicki</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mandjes,+M">Michel Mandjes</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 23 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We consider a queueing network operating under a strictly upper-triangular routing matrix with per column at most one non-negative entry. The root node is fed by a Gaussian process with stationary increments. Our aim is to characterize the distribution of the multivariate stationary workload process under a specific scaling of the queue's service rates. In the main results of this paper we identify, under mild conditions on the standard deviation function of the driving Gaussian process, in both light and heavy traffic parameterization, the limiting law of an appropriately scaled version (in both time and space) of the joint stationary workload process. In particular, we develop conditions under which specific queueing processes of the network effectively decouple, i.e., become independent in the limiting regime. </p> </div> </dd> <dt> <a name='item11'>[11]</a> <a href ="/abs/2503.16638" title="Abstract" id="2503.16638"> arXiv:2503.16638 </a> [<a href="/pdf/2503.16638" title="Download PDF" id="pdf-2503.16638" aria-labelledby="pdf-2503.16638">pdf</a>, <a href="https://arxiv.org/html/2503.16638v1" title="View HTML" id="html-2503.16638" aria-labelledby="html-2503.16638" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16638" title="Other formats" id="oth-2503.16638" aria-labelledby="oth-2503.16638">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Gradient sampling algorithm for subsmooth functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Boskos,+D">Dimitris Boskos</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Cort%C3%A9s,+J">Jorge Cort茅s</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mart%C3%ADnez,+S">Sonia Mart铆nez</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem, neither its values nor its gradients are available in closed form, which calls for approximation. Our approach hinges upon extending the so-called gradient sampling algorithm, which approximates the Clarke generalized gradient of the objective function at a point by sampling its derivative at nearby locations. This allows us to select descent directions around points where the function may fail to be differentiable and establish algorithm convergence to a stationary point from any initial condition. Our key contribution is to prove this convergence by alleviating the requirement on continuous differentiability of the objective function on an open set of full measure. We further provide assumptions under which a desired convex subset of the decision space is rendered attractive for the iterates of the algorithm. </p> </div> </dd> <dt> <a name='item12'>[12]</a> <a href ="/abs/2503.16641" title="Abstract" id="2503.16641"> arXiv:2503.16641 </a> [<a href="/pdf/2503.16641" title="Download PDF" id="pdf-2503.16641" aria-labelledby="pdf-2503.16641">pdf</a>, <a href="/format/2503.16641" title="Other formats" id="oth-2503.16641" aria-labelledby="oth-2503.16641">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Type C $K$-Stanley symmetric functions and Kra艣kiewicz-Hecke insertion </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Arroyo,+J">Joshua Arroyo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Hamaker,+Z">Zachary Hamaker</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Hawkes,+G">Graham Hawkes</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Pan,+J">Jianping Pan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 30 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> We study Type C $K$-Stanley symmetric functions, which are $K$-theoretic extensions of the Type C Stanley symmetric functions. They are indexed by signed permutations and can be used to enumerate reduced words via their expansion into Schur $Q$-functions, which are indexed by strict partitions. A combinatorial description of the Schur $Q$- coefficients is given by Kra艣kiewicz insertion. Similarly, their $K$-Stanley analogues are conjectured to expand positively into $GQ$'s, which are $K$-theory representatives for the Lagrangian Grassmannian introduced by Ikeda and Naruse also indexed by strict partitions. We introduce a $K$-theoretic analogue of Kra艣kiewicz insertion, which can be used to enumerate 0-Hecke expressions for signed permutations and gives a conjectural combinatorial rule for computing this $GQ$ expansion. <br>We show the Type C $K$-Stanleys for certain fully commutative signed permutations are skew $GQ$'s. Combined with a Pfaffian formula of Anderson's, this allows us to prove Lewis and Marberg's conjecture that $GQ$'s of (skew) rectangle shape are $GQ$'s of trapezoid shape. Combined with our previous conjecture, this also gives an explicit combinatorial description of the skew $GQ$ expansion into $GQ$'s. As a consequence, we obtain a conjecture for the product of two $GQ$ functions where one has trapezoid shape. </p> </div> </dd> <dt> <a name='item13'>[13]</a> <a href ="/abs/2503.16642" title="Abstract" id="2503.16642"> arXiv:2503.16642 </a> [<a href="/pdf/2503.16642" title="Download PDF" id="pdf-2503.16642" aria-labelledby="pdf-2503.16642">pdf</a>, <a href="https://arxiv.org/html/2503.16642v1" title="View HTML" id="html-2503.16642" aria-labelledby="html-2503.16642" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16642" title="Other formats" id="oth-2503.16642" aria-labelledby="oth-2503.16642">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Turing Instability Suppressed and Induced by Multiplicative Noise in Brusselator System </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Khan,+Q">Qasim Khan</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Suen,+A">Anthony Suen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tang,+B+Q">Bao Quoc Tang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 10 figures; Comments are welcome </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> The effect of multiplicative noise to the Turing instability of the Brusselator system is investigated. We show that when the noise acts on both of the concentrations with the same intensities, then the Turing instability is suppressed provided that the intensities are sufficiently large. This aligns with the stabilizing effect of multiplicative noise in partial differential equations. Utilizing the linearized system, we can quantify the magnitude of noise which stabilizes the system. On the other hand, when the noise is involving only one concentration, then the Turing instability can be triggered with suitable intensities. These are confirmed by numerical simulations. </p> </div> </dd> <dt> <a name='item14'>[14]</a> <a href ="/abs/2503.16651" title="Abstract" id="2503.16651"> arXiv:2503.16651 </a> [<a href="/pdf/2503.16651" title="Download PDF" id="pdf-2503.16651" aria-labelledby="pdf-2503.16651">pdf</a>, <a href="https://arxiv.org/html/2503.16651v1" title="View HTML" id="html-2503.16651" aria-labelledby="html-2503.16651" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16651" title="Other formats" id="oth-2503.16651" aria-labelledby="oth-2503.16651">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Fundamental Propositional Logic with Strict Implication </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Chen,+Z">Zhicheng Chen</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic (math.LO)</span> </div> <p class='mathjax'> ``Fundamental logic" is a non-classical logic recently introduced by Wesley Holliday. It has an elegant Fitch-style natural deduction system and, in a sense, it unifies orthologic and the $\{\land,\lor,\neg\}$-fragment of intuitionistic logic. In this paper, we incorporate strict implication into fundamental propositional logic (and a slightly weaker logic, respectively). We provide the axiomatization and prove the soundness and completeness theorems. </p> </div> </dd> <dt> <a name='item15'>[15]</a> <a href ="/abs/2503.16652" title="Abstract" id="2503.16652"> arXiv:2503.16652 </a> [<a href="/pdf/2503.16652" title="Download PDF" id="pdf-2503.16652" aria-labelledby="pdf-2503.16652">pdf</a>, <a href="https://arxiv.org/html/2503.16652v1" title="View HTML" id="html-2503.16652" aria-labelledby="html-2503.16652" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16652" title="Other formats" id="oth-2503.16652" aria-labelledby="oth-2503.16652">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Unified Column Generation and Elimination Method for Solving Large-Scale Set Partitioning Problems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ihara,+Y">Yasuyuki Ihara</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> The Set Partitioning Problem is a combinatorial optimization problem with wide-ranging applicability, used to model various real-world tasks such as facility location and crew scheduling. However, real-world applications often require solving large-scale instances that involve hundreds of thousands of variables. Although the conventional Column Generation method is popular for its computational efficiency, it lacks a guarantee for exact solutions. This paper proposes a novel solution method integrating relaxation of Column Generation conditions and automatic elimination of redundant columns, aimed at overcoming the limitations of conventional Column Generation methods in guaranteeing exact optimal solutions. Numerical experiments using actual bus route data reveal that while the traditional method achieves an exact solution rate of only about 3%, the proposed method attains a rate of approximately 99% and remarkably improves solution accuracy. </p> </div> </dd> <dt> <a name='item16'>[16]</a> <a href ="/abs/2503.16657" title="Abstract" id="2503.16657"> arXiv:2503.16657 </a> [<a href="/pdf/2503.16657" title="Download PDF" id="pdf-2503.16657" aria-labelledby="pdf-2503.16657">pdf</a>, <a href="https://arxiv.org/html/2503.16657v1" title="View HTML" id="html-2503.16657" aria-labelledby="html-2503.16657" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16657" title="Other formats" id="oth-2503.16657" aria-labelledby="oth-2503.16657">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Some contributions of Edoardo Ballico to Moduli spaces and their applications </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gasparim,+E">Elizabeth Gasparim</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> With a section written by W. Kucharz </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> This is a contribution to the Special Volume in Celebration of the 70th Birthday of Edoardo Ballico. <br>First, I describe how some results of Ballico on moduli of vector bundles and categories coherent sheaves were useful for solving problems in a variety of areas: Homological Mirror Symmetry, symplectic geometry, Hodge theory, mathematical physics, noncommutative geometry. <br>Second, I summarise some strong results of Ballico about the number of components of moduli scheme of sheaves and about the existence of singularities on moduli of vector bundles. <br>Third, the text includes a section written by Wojciech Kucharz, about the work of Ballico on moduli flexibility of real manifolds. </p> </div> </dd> <dt> <a name='item17'>[17]</a> <a href ="/abs/2503.16673" title="Abstract" id="2503.16673"> arXiv:2503.16673 </a> [<a href="/pdf/2503.16673" title="Download PDF" id="pdf-2503.16673" aria-labelledby="pdf-2503.16673">pdf</a>, <a href="https://arxiv.org/html/2503.16673v1" title="View HTML" id="html-2503.16673" aria-labelledby="html-2503.16673" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16673" title="Other formats" id="oth-2503.16673" aria-labelledby="oth-2503.16673">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Subgradient Method for System Identification with Non-Smooth Objectives </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Yalcin,+B">Baturalp Yalcin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lavaei,+J">Javad Lavaei</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 8 pages, 5 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Computational Complexity (cs.CC); Machine Learning (cs.LG); Systems and Control (eess.SY) </div> <p class='mathjax'> This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting where the optimization problems to be solved change over time as new measurements are taken, and we establish linear convergence results for both the best and Polyak step sizes after a burn-in period. Additionally, we characterize the asymptotic convergence of the best average sub-optimality gap under diminishing and constant step sizes. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth objectives. </p> </div> </dd> <dt> <a name='item18'>[18]</a> <a href ="/abs/2503.16677" title="Abstract" id="2503.16677"> arXiv:2503.16677 </a> [<a href="/pdf/2503.16677" title="Download PDF" id="pdf-2503.16677" aria-labelledby="pdf-2503.16677">pdf</a>, <a href="https://arxiv.org/html/2503.16677v1" title="View HTML" id="html-2503.16677" aria-labelledby="html-2503.16677" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16677" title="Other formats" id="oth-2503.16677" aria-labelledby="oth-2503.16677">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Leveraging Code Structure to Improve Soft Output for GRAND, GCD, OSD, and SCL </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Feng,+J">Jiewei Feng</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Duffy,+K+R">Ken R. Duffy</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=M%C3%A9dard,+M">Muriel M茅dard</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Information Theory (cs.IT)</span> </div> <p class='mathjax'> In addition to a proposed codeword, error correction decoders that provide blockwise soft output (SO) return an estimate of the likelihood that the decoding is correct. Following Forney, such estimates are traditionally only possible for list decoders where the soft output is the likelihood that a decoding is correct given it is assumed to be in the list. Recently, it has been established that Guessing Random Additive Noise Decoding (GRAND), Guessing Codeword Decoding (GCD), Ordered Statistics Decoding (OSD), and Successive Cancellation List (SCL) decoding can provide more accurate soft output, even without list decoding. Central to the improvement is a per-decoding estimate of the likelihood that a decoding has not been found that can be readily calculated during the decoding process. Here we explore how linear codebook constraints can be employed to further enhance the precision of such SO. We evaluate performance by adapting a forecasting statistic called the Brier Score. Results indicate that the SO generated by the approach is essentially as accurate as the maximum a posteriori estimate. </p> </div> </dd> <dt> <a name='item19'>[19]</a> <a href ="/abs/2503.16684" title="Abstract" id="2503.16684"> arXiv:2503.16684 </a> [<a href="/pdf/2503.16684" title="Download PDF" id="pdf-2503.16684" aria-labelledby="pdf-2503.16684">pdf</a>, <a href="https://arxiv.org/html/2503.16684v1" title="View HTML" id="html-2503.16684" aria-labelledby="html-2503.16684" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16684" title="Other formats" id="oth-2503.16684" aria-labelledby="oth-2503.16684">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Bridging Classical and Modern Approaches to Thales' Theorem </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=B%C5%82aszczyk,+P">Piotr B艂aszczyk</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Petiurenko,+A">Anna Petiurenko</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">History and Overview (math.HO)</span> </div> <p class='mathjax'> In this paper, we reconstruct Euclid's theory of similar triangles, as developed in Book VI of the \textit{Elements}, along with its 20th-century counterparts, formulated within the systems of Hilbert, Birkhoff, Borsuk and Szmielew, Millman and Parker, as well as Hartshorne. In the final sections, we present recent developments concerning non-Archimedean fields and mechanized proofs. Thales' theorem (VI.2) serves as the reference point in our comparisons. It forms the basis of Euclid's system and follows from VI.1 the only proposition within the theory of similar triangles that explicitly applies the definition of proportion. Instead of the ancient proportion, modern systems adopt the arithmetic of line segments or real numbers. Accordingly, they adopt other propositions from Euclid's Book VI, such as VI.4, VI.6, or VI.9, as a basis. In 搂\,10, we present a system that, while meeting modern criteria of rigor, reconstructs Euclid's theory and mimics its deductive structure, beginning with VI.1. This system extends to automated proofs of Euclid's propositions from Book VI. Systems relying on real numbers provide the foundation for trigonometry as applied in modern mathematics. In 搂\,9, we prove Thales' theorem in geometry over the hyperreal numbers. Just as Hilbert managed to prove Thales' theorem without referencing the Archimedean axiom, so do we by applying the arithmetic of the non-Archimedean field of hyperreal numbers. </p> </div> </dd> <dt> <a name='item20'>[20]</a> <a href ="/abs/2503.16688" title="Abstract" id="2503.16688"> arXiv:2503.16688 </a> [<a href="/pdf/2503.16688" title="Download PDF" id="pdf-2503.16688" aria-labelledby="pdf-2503.16688">pdf</a>, <a href="https://arxiv.org/html/2503.16688v1" title="View HTML" id="html-2503.16688" aria-labelledby="html-2503.16688" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16688" title="Other formats" id="oth-2503.16688" aria-labelledby="oth-2503.16688">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Random bipartite graphs with i.i.d. weights and applications to inhomogeneous random intersection graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Haig,+A">Alastair Haig</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+M">Minmin Wang</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection graph which has nontrivial clustering properties and inhomogeneous vertex degrees. We focus on the situation where the weights are themselves i.i.d. random variables. In the so-called moderate clustering regime, we identify three types of scaling limit for the large connected components in the graphs at criticality, depending on the tail behaviours of the weight distributions of both parts. </p> </div> </dd> <dt> <a name='item21'>[21]</a> <a href ="/abs/2503.16696" title="Abstract" id="2503.16696"> arXiv:2503.16696 </a> [<a href="/pdf/2503.16696" title="Download PDF" id="pdf-2503.16696" aria-labelledby="pdf-2503.16696">pdf</a>, <a href="https://arxiv.org/html/2503.16696v1" title="View HTML" id="html-2503.16696" aria-labelledby="html-2503.16696" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16696" title="Other formats" id="oth-2503.16696" aria-labelledby="oth-2503.16696">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Universal approximation property of neural stochastic differential equations </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kwossek,+A+P">Anna P. Kwossek</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Pr%C3%B6mel,+D+J">David J. Pr枚mel</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Teichmann,+J">Josef Teichmann</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 20 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Machine Learning (cs.LG); Functional Analysis (math.FA); Mathematical Finance (q-fin.MF); Machine Learning (stat.ML) </div> <p class='mathjax'> We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential equations can approximate general stochastic differential equations, both of It么 diffusion type, arbitrarily well. Moreover, quantitative error estimates are derived for stochastic differential equations with sufficiently regular coefficients. </p> </div> </dd> <dt> <a name='item22'>[22]</a> <a href ="/abs/2503.16697" title="Abstract" id="2503.16697"> arXiv:2503.16697 </a> [<a href="/pdf/2503.16697" title="Download PDF" id="pdf-2503.16697" aria-labelledby="pdf-2503.16697">pdf</a>, <a href="https://arxiv.org/html/2503.16697v1" title="View HTML" id="html-2503.16697" aria-labelledby="html-2503.16697" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16697" title="Other formats" id="oth-2503.16697" aria-labelledby="oth-2503.16697">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the solvability of the lie algebra $\mathrm{hh}^1(b)$ for blocks of finite groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Linckelmann,+M">Markus Linckelmann</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+J">Jialin Wang</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Representation Theory (math.RT)</span> </div> <p class='mathjax'> We give some criteria for the Lie algebra $\mathrm{HH}^1(B)$ to be solvable, where $B$ is a $p$-block of a finite group algebra, in terms of the action of an inertial quotient of $B$ on a defect group of $B$. </p> </div> </dd> <dt> <a name='item23'>[23]</a> <a href ="/abs/2503.16702" title="Abstract" id="2503.16702"> arXiv:2503.16702 </a> [<a href="/pdf/2503.16702" title="Download PDF" id="pdf-2503.16702" aria-labelledby="pdf-2503.16702">pdf</a>, <a href="https://arxiv.org/html/2503.16702v1" title="View HTML" id="html-2503.16702" aria-labelledby="html-2503.16702" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16702" title="Other formats" id="oth-2503.16702" aria-labelledby="oth-2503.16702">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Asymptotics for resolutions and smoothings of Calabi-Yau conifolds </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Benabida,+A+O">Abdou Oussama Benabida</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 45 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span>; Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Analysis of PDEs (math.AP) </div> <p class='mathjax'> We show that the Calabi--Yau metrics with isolated conical singularities of Hein--Sun admit polyhomogeneous expansions near their singularities. Moreover, we show that, under certain generic assumptions, natural families of smooth Calabi--Yau metrics on crepant resolutions and on polarized smoothings of conical Calabi--Yau manifolds degenerating to the initial conical Calabi--Yau metric admit polyhomogeneous expansions where the singularities are forming. The construction proceeds by performing weighted Melrose--type blow--ups and then gluing conical and scaled asymptotically conical Calabi--Yau metrics on the fibers, close to the blow--up's front face without compromising polyhomogeneity. This yields a polyhomogeneous family of K盲hler metrics that are approximately Calabi--Yau. Solving formally a complex Monge--Amp猫re equation, we obtain a polyhomogeneous family of K盲hler metrics with Ricci potential converging rapidly to zero as the family is degenerating. We can then conclude that the corresponding family of degenerating Calabi--Yau metrics is polyhomogeneous by using a fixed point argument. </p> </div> </dd> <dt> <a name='item24'>[24]</a> <a href ="/abs/2503.16713" title="Abstract" id="2503.16713"> arXiv:2503.16713 </a> [<a href="/pdf/2503.16713" title="Download PDF" id="pdf-2503.16713" aria-labelledby="pdf-2503.16713">pdf</a>, <a href="https://arxiv.org/html/2503.16713v1" title="View HTML" id="html-2503.16713" aria-labelledby="html-2503.16713" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16713" title="Other formats" id="oth-2503.16713" aria-labelledby="oth-2503.16713">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Optimal Matching Problem on the Boolean Cube </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Feng,+S">Shi Feng</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 27 pages, 0 figure </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We establish upper and lower bounds for the expected Wasserstein distance between the random empirical measure and the uniform measure on the Boolean cube. Our analysis leverages techniques from Fourier analysis, following the framework introduced in \cite{bobkov2021simple}, as well as methods from large deviations theory. </p> </div> </dd> <dt> <a name='item25'>[25]</a> <a href ="/abs/2503.16716" title="Abstract" id="2503.16716"> arXiv:2503.16716 </a> [<a href="/pdf/2503.16716" title="Download PDF" id="pdf-2503.16716" aria-labelledby="pdf-2503.16716">pdf</a>, <a href="https://arxiv.org/html/2503.16716v1" title="View HTML" id="html-2503.16716" aria-labelledby="html-2503.16716" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16716" title="Other formats" id="oth-2503.16716" aria-labelledby="oth-2503.16716">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On defect in finite extensions of valued fields </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=de+Souza,+C+H+S">Caio Henrique Silva de Souza</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Spivakovsky,+M">Mark Spivakovsky</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Commutative Algebra (math.AC)</span>; Algebraic Geometry (math.AG) </div> <p class='mathjax'> In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify defectless fields and study properties related to defect. In this paper we study the relations between the following properties of valued fields: simply defectless, immediate-defectless and algebraically maximal. The main result of the paper is an example of an algebraically maximal field that admits a simple defect extension. For this, we introduce the notion of quasi-finite elements in the generalized power series field $k\left(\left(t^\Gamma\right)\right)$. </p> </div> </dd> <dt> <a name='item26'>[26]</a> <a href ="/abs/2503.16717" title="Abstract" id="2503.16717"> arXiv:2503.16717 </a> [<a href="/pdf/2503.16717" title="Download PDF" id="pdf-2503.16717" aria-labelledby="pdf-2503.16717">pdf</a>, <a href="https://arxiv.org/html/2503.16717v1" title="View HTML" id="html-2503.16717" aria-labelledby="html-2503.16717" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16717" title="Other formats" id="oth-2503.16717" aria-labelledby="oth-2503.16717">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Random-sketching Techniques to Enhance the Numerically Stability of Block Orthogonalization Algorithms for s-step GMRES </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Yamazaki,+I">Ichitaro Yamazaki</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Higgins,+A+J">Andrew J. Higgins</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Boman,+E+G">Erik G. Boman</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Szyld,+D+B">Daniel B. Szyld</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 14 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span>; Distributed, Parallel, and Cluster Computing (cs.DC) </div> <p class='mathjax'> We integrate random sketching techniques into block orthogonalization schemes needed for s-step GMRES. The resulting block orthogonalization schemes generate the basis vectors whose overall orthogonality error is bounded by machine precision as long as each of the corresponding block vectors are numerically full rank. We implement these randomized block orthogonalization schemes using standard distributed-memory linear algebra kernels for s-step GMRES available in the Trilinos software packages. Our performance results on the Perlmutter supercomputer (with four NVIDIA A100 GPUs per node) demonstrate that these randomized techniques can enhance the numerical stability of the orthogonalization and overall solver, without a significant increase in the execution time. </p> </div> </dd> <dt> <a name='item27'>[27]</a> <a href ="/abs/2503.16722" title="Abstract" id="2503.16722"> arXiv:2503.16722 </a> [<a href="/pdf/2503.16722" title="Download PDF" id="pdf-2503.16722" aria-labelledby="pdf-2503.16722">pdf</a>, <a href="https://arxiv.org/html/2503.16722v1" title="View HTML" id="html-2503.16722" aria-labelledby="html-2503.16722" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16722" title="Other formats" id="oth-2503.16722" aria-labelledby="oth-2503.16722">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Cleanliness versus Specialness </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Jankiewicz,+K">Kasia Jankiewicz</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 6 pages, 4 figures. Comments are welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Group Theory (math.GR)</span> </div> <p class='mathjax'> We show that the fundamental group of a geometrically clean graph of finite rank free groups does not need to be virtually compact special, answering a question of Wise. This implies that the class of the virtually VH-clean graphs of finite rank free groups is a proper subclass of the class of virtually geometrically clean graphs of finite rank free groups. </p> </div> </dd> <dt> <a name='item28'>[28]</a> <a href ="/abs/2503.16723" title="Abstract" id="2503.16723"> arXiv:2503.16723 </a> [<a href="/pdf/2503.16723" title="Download PDF" id="pdf-2503.16723" aria-labelledby="pdf-2503.16723">pdf</a>, <a href="https://arxiv.org/html/2503.16723v1" title="View HTML" id="html-2503.16723" aria-labelledby="html-2503.16723" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16723" title="Other formats" id="oth-2503.16723" aria-labelledby="oth-2503.16723">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Divergence-free drifts decrease concentration </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Hess-Childs,+E">Elias Hess-Childs</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Raqu%C3%A9pas,+R">Renaud Raqu茅pas</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rowan,+K">Keefer Rowan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 24 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> We show that bounded divergence-free vector fields $u : [0,\infty) \times \mathbb{R}^d \to\mathbb{R}^d$ decrease the ''concentration'', quantified by the modulus of absolute continuity with respect to the Lebesgue measure, of solutions to the associated advection-diffusion equation when compared to solutions to the heat equation. In particular, for symmetric decreasing initial data, the solution to the advection-diffusion equation has (without a prefactor constant) larger variance, larger entropy, and smaller $L^p$ norms for all $p \in [1,\infty]$ than the solution to the heat equation. We also note that the same is not true on $\mathbb{T}^d$. </p> </div> </dd> <dt> <a name='item29'>[29]</a> <a href ="/abs/2503.16727" title="Abstract" id="2503.16727"> arXiv:2503.16727 </a> [<a href="/pdf/2503.16727" title="Download PDF" id="pdf-2503.16727" aria-labelledby="pdf-2503.16727">pdf</a>, <a href="https://arxiv.org/html/2503.16727v1" title="View HTML" id="html-2503.16727" aria-labelledby="html-2503.16727" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16727" title="Other formats" id="oth-2503.16727" aria-labelledby="oth-2503.16727">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A variational problem to calculate probabilities </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Reyna-Casta%C3%B1eda,+H+G">Hugo Guadalupe Reyna-Casta帽eda</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=de+los+%C3%81ngeles+Sandoval+Romero,+M">Mar铆a de los 脕ngeles Sandoval Romero</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18 pages, 5 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Functional Analysis (math.FA); Optimization and Control (math.OC) </div> <p class='mathjax'> In this paper, we prove the existence and uniqueness of the conditional expectation of an event $A$ given a $\sigma$-algebra $\mathcal{G}$ as a linear problem in the Lebesgue spaces $L^{p}$ associated with a probability space through the Riesz Representation Theorems. For the $L^{2}$ case, we state the Dirichlet's principle. Then, we extend this principle for specific values of $p$, framing the existence of the conditional expectation as a variational problem. We conclude with a proof of the law of total probability using these tools. </p> </div> </dd> <dt> <a name='item30'>[30]</a> <a href ="/abs/2503.16736" title="Abstract" id="2503.16736"> arXiv:2503.16736 </a> [<a href="/pdf/2503.16736" title="Download PDF" id="pdf-2503.16736" aria-labelledby="pdf-2503.16736">pdf</a>, <a href="https://arxiv.org/html/2503.16736v1" title="View HTML" id="html-2503.16736" aria-labelledby="html-2503.16736" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16736" title="Other formats" id="oth-2503.16736" aria-labelledby="oth-2503.16736">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The Betti Numbers of Kunz-Waldi Semigroups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gonz%C3%A1lez-S%C3%A1nchez,+M">Mario Gonz谩lez-S谩nchez</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Singh,+S">Srishti Singh</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Hema">Hema Srinivasan</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Commutative Algebra (math.AC)</span> </div> <p class='mathjax'> Given two coprime numbers $p<q$, KW semigroups contain $p,q$ and are contained in $\langle p,q,r \rangle$ where $2r= p,q, p+q$ whichever is even. These semigroups were first introduced by Kunz and Waldi. Kunz and Waldi proved that all $KW$ semigroups of embedding dimension $n\geq 4$ have Cohen-Macaulay type $n-1$ and first Betti number ${n \choose 2}$. In this paper, we characterize KW semigroups whose defining ideal is generated by the $2\times 2$ minors of a $2\times n$ matrix. In addition, we identify all KW semigroups that lie on the interior of the same face of the Kunz cone $\mathcal C_p$ as a KW semigroup with determinantal defining ideal. Thus, we provide an explicit formula for the Betti numbers of all those KW semigroups. </p> </div> </dd> <dt> <a name='item31'>[31]</a> <a href ="/abs/2503.16751" title="Abstract" id="2503.16751"> arXiv:2503.16751 </a> [<a href="/pdf/2503.16751" title="Download PDF" id="pdf-2503.16751" aria-labelledby="pdf-2503.16751">pdf</a>, <a href="https://arxiv.org/html/2503.16751v1" title="View HTML" id="html-2503.16751" aria-labelledby="html-2503.16751" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16751" title="Other formats" id="oth-2503.16751" aria-labelledby="oth-2503.16751">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> UAV-Relay Assisted RSMA Fluid Antenna System: Outage Probability Analysis </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Ghadi,+F+R">Farshad Rostami Ghadi</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Kaveh,+M">Masoud Kaveh</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Hernando-Gallego,+F">Francisco Hernando-Gallego</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Martin,+D">Diego Martin</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Wong,+K">Kai-Kit Wong</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Chae,+C">Chan-Byoung Chae</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Information Theory (cs.IT)</span>; Signal Processing (eess.SP) </div> <p class='mathjax'> This letter studies the impact of fluid antenna system (FAS) technology on the performance of unmanned aerial vehicle (UAV)-assisted multiuser communication networks. Specifically, we consider a scenario where a fixed-position antenna (FPA) base station (BS) serves K FAS-equipped users with the assistance of a UAV acting as an aerial relay. The BS employs rate-splitting multiple access (RSMA), while the UAV operates in half-duplex (HD) mode using the decode-and-forward (DF) strategy. For this system, we derive a compact analytical expression for the outage probability (OP) and its asymptotic behavior in the high signal-to-noise ratio (SNR) regime, leveraging the multivariate t-distribution. Our results show how deploying FAS at ground users (GUs) in UAV-aided communications improves overall system performance compared to using FPA GUs. </p> </div> </dd> <dt> <a name='item32'>[32]</a> <a href ="/abs/2503.16757" title="Abstract" id="2503.16757"> arXiv:2503.16757 </a> [<a href="/pdf/2503.16757" title="Download PDF" id="pdf-2503.16757" aria-labelledby="pdf-2503.16757">pdf</a>, <a href="https://arxiv.org/html/2503.16757v1" title="View HTML" id="html-2503.16757" aria-labelledby="html-2503.16757" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16757" title="Other formats" id="oth-2503.16757" aria-labelledby="oth-2503.16757">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Measure-expansive systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Morales,+C">C.A. Morales</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 16 pages. This is a copy of the original paper published on the IMPA Preprint server in 2011 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> We call a dynamical system on a measurable metric space {\em measure-expansive} if the probability of two orbits remain close each other for all time is negligible (i.e. zero). We extend results of expansive systems on compact metric spaces to the measure-expansive context. For instance, the measure-expansive homeomorphisms are characterized as those homeomorphisms $f$ for which the diagonal is almost invariant for $f\times f$ with respect to the product measure. In addition, the set of points with converging semi-orbits for such homeomorphisms have measure zero. In particular, the set of periodic orbits for these homeomorphisms is also of measure zero. We also prove that there are no measure-expansive homeomorphisms in the interval and, in the circle, they are the Denjoy ones. As an application we obtain probabilistic proofs of some result of expansive systems. We also present some analogous results for continuous maps. </p> </div> </dd> <dt> <a name='item33'>[33]</a> <a href ="/abs/2503.16758" title="Abstract" id="2503.16758"> arXiv:2503.16758 </a> [<a href="/pdf/2503.16758" title="Download PDF" id="pdf-2503.16758" aria-labelledby="pdf-2503.16758">pdf</a>, <a href="/format/2503.16758" title="Other formats" id="oth-2503.16758" aria-labelledby="oth-2503.16758">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Nonlinear stability of compressible vortex sheets in three-dimensional elastodynamics </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Chen,+R+M">Robin Ming Chen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Huang,+F">Feimin Huang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+D">Dehua Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yuan,+D">Difan Yuan</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> We investigate the nonlinear stability of compressible vortex sheet solutions for three-dimensional (3D) isentropic elastic flows. Building upon previous results on the weakly linear stability of elastic vortex sheets [19], we perform a detailed study of the roots of the Lopatinskii determinant and identify a geometric stability condition associated with the deformation gradient. We employ an upper triangularization technique that isolates the outgoing modes into a closed system, where they appear only at the leading order. This enables us to derive energy estimates despite derivative loss. The major novelty of our approach includes the following two key aspects: (1) For the 3D compressible Euler vortex sheets, the front symbol exhibits degenerate ellipticity in certain frequency directions, which makes it challenging to ensure the front's regularity using standard energy estimates. Our analysis reveals that the non-parallel structure of the deformation gradient tensor plays a crucial role in recovering ellipticity in the front symbol, thereby enhancing the regularity of the free interface. (2) Another significant challenge in 3D arises from the strong degeneracy caused by the collision of repeated roots and poles. Unlike in 2D, where such interactions are absent, we encounter a co-dimension one set in frequency space where a double root coincides with a double pole. To resolve this, we refine Coulombel's diagonalization framework [21] and construct a suitable transformation that reduces the degeneracy order of the Lopatinskii matrix, enabling the use of localized Garding-type estimates to control the characteristic components. Finally, we employ a Nash-Moser iteration scheme to establish the local existence and nonlinear stability of vortex sheets under small initial perturbations, showing stability within a subsonic regime. </p> </div> </dd> <dt> <a name='item34'>[34]</a> <a href ="/abs/2503.16763" title="Abstract" id="2503.16763"> arXiv:2503.16763 </a> [<a href="/pdf/2503.16763" title="Download PDF" id="pdf-2503.16763" aria-labelledby="pdf-2503.16763">pdf</a>, <a href="https://arxiv.org/html/2503.16763v1" title="View HTML" id="html-2503.16763" aria-labelledby="html-2503.16763" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16763" title="Other formats" id="oth-2503.16763" aria-labelledby="oth-2503.16763">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On uniqueness of free boundary minimal annuli in geodesic balls of $\mathbb{S}^3_+$ and $\mathbb{H}^3$ </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Lima,+C">C茅sar Lima</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span> </div> <p class='mathjax'> We consider $\Sigma$ an embedded free boundary minimal annulus in a geodesic ball in the round hemisphere $\mathbb{S}^3_+$ or in the hyperbolic space $\mathbb{H}^3$. Under the hypothesis of invariance due to an antipodal map on the geodesic ball and using the fact that this surface satisfies the Steklov problem with frequency, we prove that $\Sigma$ is congruent to a critical rotational annulus. </p> </div> </dd> <dt> <a name='item35'>[35]</a> <a href ="/abs/2503.16765" title="Abstract" id="2503.16765"> arXiv:2503.16765 </a> [<a href="/pdf/2503.16765" title="Download PDF" id="pdf-2503.16765" aria-labelledby="pdf-2503.16765">pdf</a>, <a href="https://arxiv.org/html/2503.16765v1" title="View HTML" id="html-2503.16765" aria-labelledby="html-2503.16765" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16765" title="Other formats" id="oth-2503.16765" aria-labelledby="oth-2503.16765">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A thermodynamically consistent phase-field model for mass transport with interfacial reaction and deformation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+Z">Zhaoyang Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Huang,+H">Huaxiong Huang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lin,+P">Ping Lin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Xu,+S">Shixin Xu</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> In this paper, a thermodynamically consistent phase-field model is proposed to describe the mass transport and reaction processes of multiple species in a fluid. A key feature of this model is that reactions between different species occur only at the interface, and may induce deformation of the interface. For the governing equations derived based on the energy variational method, we propose a structure-preserving numerical scheme that satisfies the mass conservation and energy dissipation laws at the discrete level. Furthermore, we carry out a rigorous error analysis of the time-discrete scheme for a simplified case. A series of numerical experiments are conducted to validate the effectiveness of the model as well as the accuracy and stability of the scheme. In particular, we simulate microvessels with straight and bifurcated structures to illustrate the risk of microaneurysm formation. </p> </div> </dd> <dt> <a name='item36'>[36]</a> <a href ="/abs/2503.16766" title="Abstract" id="2503.16766"> arXiv:2503.16766 </a> [<a href="/pdf/2503.16766" title="Download PDF" id="pdf-2503.16766" aria-labelledby="pdf-2503.16766">pdf</a>, <a href="https://arxiv.org/html/2503.16766v1" title="View HTML" id="html-2503.16766" aria-labelledby="html-2503.16766" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16766" title="Other formats" id="oth-2503.16766" aria-labelledby="oth-2503.16766">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Quantized volume comparison for Fano manifolds </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+K">Kewei Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> comments are welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> A result of Kento Fujita says that the volume of a K-semistable Fano manifold is bounded from above by the volume of the projective space. In this short note we establish quantized versions of Fujita's result. </p> </div> </dd> <dt> <a name='item37'>[37]</a> <a href ="/abs/2503.16770" title="Abstract" id="2503.16770"> arXiv:2503.16770 </a> [<a href="/pdf/2503.16770" title="Download PDF" id="pdf-2503.16770" aria-labelledby="pdf-2503.16770">pdf</a>, <a href="https://arxiv.org/html/2503.16770v1" title="View HTML" id="html-2503.16770" aria-labelledby="html-2503.16770" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16770" title="Other formats" id="oth-2503.16770" aria-labelledby="oth-2503.16770">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> An Improved Upper Bound on the Threshold Bias of the Oriented-cycle game </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Liebenau,+A">Anita Liebenau</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Saffidine,+A">Abdallah Saffidine</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yang,+J">Jeffrey Yang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages, 1 figure </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> We study the $b$-biased Oriented-cycle game where two players, OMaker and OBreaker, take turns directing the edges of $K_n$ (the complete graph on $n$ vertices). In each round, OMaker directs one previously undirected edge followed by OBreaker directing between one and $b$ previously undirected edges. The game ends once all edges have been directed, and OMaker wins if and only if the resulting tournament contains a directed cycle. Bollob谩s and Szab贸 asked the following question: what is the largest value of the bias $b$ for which OMaker has a winning strategy? Ben-Eliezer, Krivelevich and Sudakov proved that OMaker has a winning strategy for $b \leq n/2 - 2$. In the other direction, Clemens and Liebenau proved that OBreaker has a winning strategy for $b \geq 5n/6+2$. Inspired by their approach, we propose a significantly stronger strategy for OBreaker which we prove to be winning for $b \geq 0.7845n + O(1)$. </p> </div> </dd> <dt> <a name='item38'>[38]</a> <a href ="/abs/2503.16786" title="Abstract" id="2503.16786"> arXiv:2503.16786 </a> [<a href="/pdf/2503.16786" title="Download PDF" id="pdf-2503.16786" aria-labelledby="pdf-2503.16786">pdf</a>, <a href="https://arxiv.org/html/2503.16786v1" title="View HTML" id="html-2503.16786" aria-labelledby="html-2503.16786" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16786" title="Other formats" id="oth-2503.16786" aria-labelledby="oth-2503.16786">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Average Nikolskii factors for random trigonometric polynomials </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ling,+Y">Yun Ling</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Geng,+J">Jiaxin Geng</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Li,+J">Jiansong Li</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+H">Heping Wang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 17 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Classical Analysis and ODEs (math.CA)</span> </div> <p class='mathjax'> For $1\le p,q\le \infty$, the Nikolskii factor for a trigonometric polynomial $T_{\bf a}$ is defined by $$\mathcal N_{p,q}(T_{\bf a})=\frac{\|T_{\bf a}\|_{q}}{\|T_{\bf a}\|_{p}},\ \ T_{\bf a}(x)=a_{1}+\sum\limits^{n}_{k=1}(a_{2k}\sqrt{2}\cos kx+a_{2k+1}\sqrt{2}\sin kx).$$ We study this average Nikolskii factor for random trigonometric polynomials with independent $N(0,\sigma^{2})$ coefficients and obtain that the exact order. For $1\leq p<q<\infty$, the average Nikolskii factor is order degree to the 0, as compared to the degree $1/p-1/q$ worst case bound. We also give the generalization to random multivariate trigonometric polynomials. </p> </div> </dd> <dt> <a name='item39'>[39]</a> <a href ="/abs/2503.16790" title="Abstract" id="2503.16790"> arXiv:2503.16790 </a> [<a href="/pdf/2503.16790" title="Download PDF" id="pdf-2503.16790" aria-labelledby="pdf-2503.16790">pdf</a>, <a href="https://arxiv.org/html/2503.16790v1" title="View HTML" id="html-2503.16790" aria-labelledby="html-2503.16790" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16790" title="Other formats" id="oth-2503.16790" aria-labelledby="oth-2503.16790">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Fractal tiles induced by tent maps </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Scheicher,+K">Klaus Scheicher</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sirvent,+V+F">Victor F. Sirvent</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Surer,+P">Paul Surer</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> In the present article we introduce geometrical objects induced by the tent maps associated with special Pisot numbers that we call tent-tiles. They are compact subsets of the one-, two-, or three-dimensional Euclidean space, depending on the particular special Pisot number. Most of the tent-tiles have a fractal shape and we study the Hausdorff dimension of their boundary. Furthermore, we are concerned with tilings induced by tent-tiles. It turns out that tent-tiles give rise to two types of lattice tilings. In order to obtain these results we establish and exploit connections between tent-tiles and Rauzy fractals induced by substitutions and automorphisms of the free group. </p> </div> </dd> <dt> <a name='item40'>[40]</a> <a href ="/abs/2503.16792" title="Abstract" id="2503.16792"> arXiv:2503.16792 </a> [<a href="/pdf/2503.16792" title="Download PDF" id="pdf-2503.16792" aria-labelledby="pdf-2503.16792">pdf</a>, <a href="https://arxiv.org/html/2503.16792v1" title="View HTML" id="html-2503.16792" aria-labelledby="html-2503.16792" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16792" title="Other formats" id="oth-2503.16792" aria-labelledby="oth-2503.16792">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Numerical simulation of wormhole propagation with the mixed hybridized discontinuous Galerkin finite element method </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+J">Jiansong Zhang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhu,+J">Jiang Zhu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+Y">Yiming Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+Y">Yanyu Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Guo,+H">Hui Guo</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18pages, 2 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> The acid treatment of carbonate reservoirs is a widely employed technique for enhancing the productivity of oil and gas reservoirs. In this paper, we present a novel combined hybridized mixed discontinuous Galerkin (HMDG) finite element method to simulate the dissolution process near the wellbore, commonly referred to as the wormhole phenomenon. The primary contribution of this work lies in the application of hybridization techniques to both the pressure and concentration equations. Additionally, an upwind scheme is utilized to address convection-dominant scenarios, and a ``cut-off" operator is introduced to maintain the boundedness of porosity. Compared to traditional discontinuous Galerkin methods, the proposed approach results in a global system with fewer unknowns and sparser stencils, thereby significantly reducing computational costs. We analyze the existence and uniqueness of the new combined method and derive optimal error estimates using the developed technique. Numerical examples are provided to validate the theoretical analysis. </p> </div> </dd> <dt> <a name='item41'>[41]</a> <a href ="/abs/2503.16808" title="Abstract" id="2503.16808"> arXiv:2503.16808 </a> [<a href="/pdf/2503.16808" title="Download PDF" id="pdf-2503.16808" aria-labelledby="pdf-2503.16808">pdf</a>, <a href="/format/2503.16808" title="Other formats" id="oth-2503.16808" aria-labelledby="oth-2503.16808">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Gradient continuity for the parabolic $(1,\,p)$-Laplace system </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Tsubouchi,+S">Shuntaro Tsubouchi</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 55 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> This paper deals with the parabolic $(1,\,p)$-Laplace system, a parabolic system that involves the one-Laplace and $p$-Laplace operators with $p\in(1,\,\infty)$. We aim to prove that a spatial gradient is continuous in space and time. An external force term is treated under the optimal regularity assumption in the parabolic Lebesgue spaces. We also discuss a generalized parabolic system with the Uhlenbeck structure. A main difficulty is that the uniform ellipticity of the $(1,\,p)$-Laplace operator is violated on a facet, or the degenerate region of a spatial gradient. The gradient continuity is proved by showing local H枚lder continuity of a truncated gradient, whose support is far from the facet. This is rigorously demonstrated by considering approximate parabolic systems and deducing various regularity estimates for approximate solutions by classical methods such as De Giorgi's truncation, Moser's iteration, and freezing coefficient arguments. A weak maximum principle is also utilized when $p$ is not in the supercritical range. </p> </div> </dd> <dt> <a name='item42'>[42]</a> <a href ="/abs/2503.16813" title="Abstract" id="2503.16813"> arXiv:2503.16813 </a> [<a href="/pdf/2503.16813" title="Download PDF" id="pdf-2503.16813" aria-labelledby="pdf-2503.16813">pdf</a>, <a href="https://arxiv.org/html/2503.16813v1" title="View HTML" id="html-2503.16813" aria-labelledby="html-2503.16813" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16813" title="Other formats" id="oth-2503.16813" aria-labelledby="oth-2503.16813">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A note on the existence of self-similar profiles of the hydrodynamic formulation of the focusing nonlinear Schr枚dinger equation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cao-Labora,+G">Gonzalo Cao-Labora</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=G%C3%B3mez-Serrano,+J">Javier G贸mez-Serrano</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Shi,+J">Jia Shi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Staffilani,+G">Gigliola Staffilani</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages, 1 figure </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> After performing the Madelung transformation, the nonlinear Schr枚dinger equation is transformed into a hydrodynamic equation akin to the compressible Euler equations with a certain dissipation. In this short note, we construct self-similar solutions of such system in the focusing case for any mass supercritical exponent. To the best of our knowledge these solutions are new, and may formally arise as potential blow-up profiles of the focusing NLS equation. </p> </div> </dd> <dt> <a name='item43'>[43]</a> <a href ="/abs/2503.16821" title="Abstract" id="2503.16821"> arXiv:2503.16821 </a> [<a href="/pdf/2503.16821" title="Download PDF" id="pdf-2503.16821" aria-labelledby="pdf-2503.16821">pdf</a>, <a href="https://arxiv.org/html/2503.16821v1" title="View HTML" id="html-2503.16821" aria-labelledby="html-2503.16821" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16821" title="Other formats" id="oth-2503.16821" aria-labelledby="oth-2503.16821">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The graph zeta functions with respect to the group matrix of a finite group </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Miezaki,+T">Tsuyoshi Miezaki</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sato,+I">Iwao Sato</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 13 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> In this paper, we present formulas for the edge zeta function and the second weighted zeta function with respect to the group matrix of a finite abelian group $\Gamma $. Furthermore, we give another proof of Dedekind Theorem for the group determinant of $\Gamma $ by the decomposition formula for a matrix of a group covering of a digraph. Finally, we treat the weighted complexity of the complete graph with entries of the group matrix of $\Gamma $ as arc weights. </p> </div> </dd> <dt> <a name='item44'>[44]</a> <a href ="/abs/2503.16829" title="Abstract" id="2503.16829"> arXiv:2503.16829 </a> [<a href="/pdf/2503.16829" title="Download PDF" id="pdf-2503.16829" aria-labelledby="pdf-2503.16829">pdf</a>, <a href="https://arxiv.org/html/2503.16829v1" title="View HTML" id="html-2503.16829" aria-labelledby="html-2503.16829" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16829" title="Other formats" id="oth-2503.16829" aria-labelledby="oth-2503.16829">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+K">Kelei Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wei,+J">Juncheng Wei</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wu,+K">Ke Wu</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 36 pages; comments welcome </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Differential Geometry (math.DG) </div> <p class='mathjax'> We study properties of solutions to the fractional Allen-Cahn equation when $s\in (0, 1/2)$ and dimension $n\geq 2$. By applying the quantitative stratification principle developed by Naber and Valtorta, we obtain an optimal quantitative estimate on the transition set. As an application of this estimate, we improve the potential energy estimates of Cabre, Cinti, and Serra (2021), providing sharp versions for the fractional Allen-Cahn equation. Similarly, we obtain optimal perimeter estimates for stationary nonlocal minimal surfaces, extending previous results of Cinti, Serra, and Valdinoci (2019) from the stable case. </p> </div> </dd> <dt> <a name='item45'>[45]</a> <a href ="/abs/2503.16830" title="Abstract" id="2503.16830"> arXiv:2503.16830 </a> [<a href="/pdf/2503.16830" title="Download PDF" id="pdf-2503.16830" aria-labelledby="pdf-2503.16830">pdf</a>, <a href="https://arxiv.org/html/2503.16830v1" title="View HTML" id="html-2503.16830" aria-labelledby="html-2503.16830" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16830" title="Other formats" id="oth-2503.16830" aria-labelledby="oth-2503.16830">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Artin-Schreier-Witt extensions and ramification breaks </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Elder,+G+G">G. Griffith Elder</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Keating,+K">Kevin Keating</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span> </div> <p class='mathjax'> Let $K=k((t))$ be a local field of characteristic $p>0$, with perfect residue field $k$. Let $\vec{a}=(a_0,a_1,\dots,a_{n-1})\in W_n(K)$ be a Witt vector of length $n$. Artin-Schreier-Witt theory associates to $\vec{a}$ a cyclic extension $L/K$ of degree $p^i$ for some $i\le n$. Assume that the vector $\vec{a}$ is ``reduced'', and that $v_K(a_0)<0$; then $L/K$ is a totally ramified extension of degree $p^n$. In the case where $k$ is finite, Kanesaka-Sekiguchi and Thomas used class field theory to explicitly compute the upper ramification breaks of $L/K$ in terms of the valuations of the components of $\vec{a}$. In this note we use a direct method to show that these formulas remain valid when $k$ is an arbitrary perfect field. </p> </div> </dd> <dt> <a name='item46'>[46]</a> <a href ="/abs/2503.16839" title="Abstract" id="2503.16839"> arXiv:2503.16839 </a> [<a href="/pdf/2503.16839" title="Download PDF" id="pdf-2503.16839" aria-labelledby="pdf-2503.16839">pdf</a>, <a href="https://arxiv.org/html/2503.16839v1" title="View HTML" id="html-2503.16839" aria-labelledby="html-2503.16839" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16839" title="Other formats" id="oth-2503.16839" aria-labelledby="oth-2503.16839">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Minimum saturated graphs without $4$-cycles and $5$-cycles </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ma,+Y">Yue Ma</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 17 pages, 9 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> Given a family of graphs $\mathcal{F}$, a graph $G$ is said to be $\mathcal{F}$-saturated if $G$ does not contain a copy of $F$ as a subgraph for any $F\in\mathcal{F}$, but the addition of any edge $e\notin E(G)$ creates at least one copy of some $F\in\mathcal{F}$ within $G$. The minimum size of an $\mathcal{F}$-saturated graph on $n$ vertices is called the saturation number, denoted by $\mbox{sat}(n, \mathcal{F})$. Let $C_r$ be the cycle of length $r$. In this paper, we study on $\mbox{sat}(n, \mathcal{F})$ when $\mathcal{F}$ is a family of cycles. In particular, we determine that $\mbox{sat}(n, \{C_4,C_5\})=\lceil\frac{5n}{4}-\frac{3}{2}\rceil$ for any positive integer $n$. </p> </div> </dd> <dt> <a name='item47'>[47]</a> <a href ="/abs/2503.16845" title="Abstract" id="2503.16845"> arXiv:2503.16845 </a> [<a href="/pdf/2503.16845" title="Download PDF" id="pdf-2503.16845" aria-labelledby="pdf-2503.16845">pdf</a>, <a href="https://arxiv.org/html/2503.16845v1" title="View HTML" id="html-2503.16845" aria-labelledby="html-2503.16845" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16845" title="Other formats" id="oth-2503.16845" aria-labelledby="oth-2503.16845">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> One-Point Residual Feedback Algorithms for Distributed Online Convex and Non-convex Optimization </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+Y">Yaowen Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mo,+L">Lipo Mo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zuo,+M">Min Zuo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zheng,+Y">Yuanshi Zheng</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Systems and Control (eess.SY) </div> <p class='mathjax'> This paper mainly addresses the distributed online optimization problem where the local objective functions are assumed to be convex or non-convex. First, the distributed algorithms are proposed for the convex and non-convex situations, where the one-point residual feedback technology is introduced to estimate gradient of local objective functions. Then the regret bounds of the proposed algorithms are derived respectively under the assumption that the local objective functions are Lipschitz or smooth, which implies that the regrets are sublinear. Finally, we give two numerical examples of distributed convex optimization and distributed resources allocation problem to illustrate the effectiveness of the proposed algorithm. </p> </div> </dd> <dt> <a name='item48'>[48]</a> <a href ="/abs/2503.16859" title="Abstract" id="2503.16859"> arXiv:2503.16859 </a> [<a href="/pdf/2503.16859" title="Download PDF" id="pdf-2503.16859" aria-labelledby="pdf-2503.16859">pdf</a>, <a href="/format/2503.16859" title="Other formats" id="oth-2503.16859" aria-labelledby="oth-2503.16859">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Kato-Milne cohomology group over rational function fields in characteristic 2, I </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Laghribi,+A">Ahmed Laghribi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Maiti,+T">Trisha Maiti</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Commutative Algebra (math.AC)</span> </div> <p class='mathjax'> Let F be a field of characteristic 2. In this paper we determine the Kato-Milne cohomology of the rational function field F(x) in one variable x. This will be done by proving an analogue of the Milnor exact sequence [4] in the setting of Kato-Milne cohomology. As an application, we answer the open case of the norm theorem for Kato-Milne cohomology that concerns separable irreducible polynomials in many variables. This completes a result of Mukhija [17, Theorem A.3] that gives the norm theorem for inseparable polynomials. </p> </div> </dd> <dt> <a name='item49'>[49]</a> <a href ="/abs/2503.16869" title="Abstract" id="2503.16869"> arXiv:2503.16869 </a> [<a href="/pdf/2503.16869" title="Download PDF" id="pdf-2503.16869" aria-labelledby="pdf-2503.16869">pdf</a>, <a href="/format/2503.16869" title="Other formats" id="oth-2503.16869" aria-labelledby="oth-2503.16869">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Second Order Fully Nonlinear Mean Field Games with Degenerate Diffusions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bensoussan,+A">Alain Bensoussan</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Huang,+Z">Ziyu Huang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tang,+S">Shanjian Tang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yam,+S+C+P">Sheung Chi Phillip Yam</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Probability (math.PR) </div> <p class='mathjax'> In this article, we study the global-in-time well-posedness of second order mean field games (MFGs) with both nonlinear drift functions simultaneously depending on the state, distribution and control variables, and the diffusion term depending on both state and distribution. Besides, the diffusion term is allowed to be degenerate, unbounded and even nonlinear in the distribution, but it does not depend on the control. First, we establish the global well-posedness of the corresponding forward-backward stochastic differential equations (FBSDEs), which arise from the maximum principle under a so-called $\beta$-monotonicity commonly used in the optimal control theory. The $\beta$-monotonicity admits more interesting cases, as representative examples including but not limited to the displacement monotonicity, the small mean field effect condition or the Lasry-Lions monotonicity; and ensures the well-posedness result in diverse non-convex examples. In our settings, we pose assumptions directly on the drift and diffusion coefficients and the cost functionals, rather than indirectly on the Hamiltonian, to make the conditions more visible. Our probabilistic method tackles the nonlinear dynamics with a linear but infinite dimensional version, and together with our recently proposed cone property for the adjoint processes, following in an almost straightforward way the conventional approach to the classical stochastic control problem, we derive a sufficiently good regularity of the value functional, and finally show that it is the unique classical solution to the MFG master equation. Our results require fairly few conditions on the functional coefficients for solution of the MFG, and a bit more conditions -- which are least stringent in the contemporary literature -- for classical solution of the MFG master equation. </p> </div> </dd> <dt> <a name='item50'>[50]</a> <a href ="/abs/2503.16877" title="Abstract" id="2503.16877"> arXiv:2503.16877 </a> [<a href="/pdf/2503.16877" title="Download PDF" id="pdf-2503.16877" aria-labelledby="pdf-2503.16877">pdf</a>, <a href="https://arxiv.org/html/2503.16877v1" title="View HTML" id="html-2503.16877" aria-labelledby="html-2503.16877" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16877" title="Other formats" id="oth-2503.16877" aria-labelledby="oth-2503.16877">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Liang,+K">Kaiyi Liang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhu,+Y">Yuke Zhu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+J">Jiyu Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+Q">Qinghai Zhang</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> We propose a fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries on a Cartesian grid. We employ the ARMS technique to give an explicit and accurate representation of moving boundaries, and introduce a cell-merging technique to overcome discontinuities caused by topological changes in cut cells and the small cell problem. We use a polynomial interpolation technique base on poised lattice generation to achieve fourth-order spatial discretization, and use a fourth-order implicit-explicit Runge-Kutta scheme for time integration. Numerical tests are performed on various moving regions, with advection velocity both matching and differing from boundary velocity, which demonstrate the fourth-order accuracy of the proposed method. </p> </div> </dd> <dt> <a name='item51'>[51]</a> <a href ="/abs/2503.16878" title="Abstract" id="2503.16878"> arXiv:2503.16878 </a> [<a href="/pdf/2503.16878" title="Download PDF" id="pdf-2503.16878" aria-labelledby="pdf-2503.16878">pdf</a>, <a href="https://arxiv.org/html/2503.16878v1" title="View HTML" id="html-2503.16878" aria-labelledby="html-2503.16878" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16878" title="Other formats" id="oth-2503.16878" aria-labelledby="oth-2503.16878">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A central limit theorem and its application to the limiting distribution of volatility target index </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+X">Xuan Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Gauthier,+M">Michel Gauthier</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We study the limiting distribution of a volatility target index as the discretisation time step converges to zero. Two limit theorems (a strong law of large numbers and a central limit theorem) are established, and as an application, the exact limiting distribution is derived. We demonstrate that the volatility of the limiting distribution is consistently larger than the target volatility, and converges to the target volatility as the observation-window parameter $\lambda$ in the definition of the realised variance converges to $1$. Besides the exact formula for the drift and the volatility of the limiting distribution, their upper and lower bounds are derived. As a corollary of the exact limiting distribution, we obtain a vega conversion formula which converts the rho sensitivity of a financial derivative on the limiting diffusion to the vega sensitivity of the same financial derivative on the underlying of the volatility target index. </p> </div> </dd> <dt> <a name='item52'>[52]</a> <a href ="/abs/2503.16881" title="Abstract" id="2503.16881"> arXiv:2503.16881 </a> [<a href="/pdf/2503.16881" title="Download PDF" id="pdf-2503.16881" aria-labelledby="pdf-2503.16881">pdf</a>, <a href="https://arxiv.org/html/2503.16881v1" title="View HTML" id="html-2503.16881" aria-labelledby="html-2503.16881" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16881" title="Other formats" id="oth-2503.16881" aria-labelledby="oth-2503.16881">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Weak admissibility of exponentially twisted cohomology associated with some nondegenerate functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+P">Peijiang Liu</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> In this article, we study the filtered $\Phi$-modules canonically attached to the exponentially twisted cohomology associated with some nondegenerate functions. Inspired by $p$-adic Hodge theory, we conjecture that those filtered $\Phi$-modules are weakly admissible. We show that this expectation is correct under some assumptions using the theory of Adolphson and Sperber. </p> </div> </dd> <dt> <a name='item53'>[53]</a> <a href ="/abs/2503.16882" title="Abstract" id="2503.16882"> arXiv:2503.16882 </a> [<a href="/pdf/2503.16882" title="Download PDF" id="pdf-2503.16882" aria-labelledby="pdf-2503.16882">pdf</a>, <a href="https://arxiv.org/html/2503.16882v1" title="View HTML" id="html-2503.16882" aria-labelledby="html-2503.16882" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16882" title="Other formats" id="oth-2503.16882" aria-labelledby="oth-2503.16882">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Vertex Partitioning and $p$-Energy of Graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Akbari,+S">Saieed Akbari</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kumar,+H">Hitesh Kumar</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mohar,+B">Bojan Mohar</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Pragada,+S">Shivaramakrishna Pragada</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> For a Hermitian matrix $A$ of order $n$ with eigenvalues $\lambda_1(A)\ge \cdots\ge \lambda_n(A)$, define \[ \mathcal{E}_p^+(A)=\sum_{\lambda_i > 0} \lambda_i^p(A), \quad \mathcal{E}_p^-(A)=\sum_{\lambda_i<0} |\lambda_i(A)|^p,\] to be the positive and the negative $p$-energy of $A$, respectively. In this note, first we show that if $A=[A_{ij}]_{i,j=1}^k$, where $A_{ii}$ are square matrices, then \[ \mathcal{E}_p^+(A)\geq \sum_{i=1}^{k} \mathcal{E}_p^+(A_{ii}), \quad \mathcal{E}_p^-(A)\geq \sum_{i=1}^{k} \mathcal{E}_p^-(A_{ii}),\] for any real number $p\geq 1$. We then apply the previous inequality to establish lower bounds for $p$-energy of the adjacency matrix of graphs. </p> </div> </dd> <dt> <a name='item54'>[54]</a> <a href ="/abs/2503.16884" title="Abstract" id="2503.16884"> arXiv:2503.16884 </a> [<a href="/pdf/2503.16884" title="Download PDF" id="pdf-2503.16884" aria-labelledby="pdf-2503.16884">pdf</a>, <a href="https://arxiv.org/html/2503.16884v1" title="View HTML" id="html-2503.16884" aria-labelledby="html-2503.16884" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16884" title="Other formats" id="oth-2503.16884" aria-labelledby="oth-2503.16884">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Almost and quasi Leinster groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ple%C5%9Fca,+I">Iulia-C膬t膬lina Ple艧ca</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=T%C4%83rn%C4%83uceanu,+M">Marius T膬rn膬uceanu</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Accepted for publication in An. \c Stiin\c t. Univ. "Ovidius" Constan\c ta, Ser. Mat </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Group Theory (math.GR)</span> </div> <p class='mathjax'> In this paper, we study the parallelism between perfect numbers and Leinster groups and continue it by introducing the new concepts of almost and quasi Leinster groups which parallel almost and quasi perfect numbers. These are small deviations from perfect numbers; very few results and/or examples are known about them. <br>We investigate nilpotent almost-/quasi-/Leinster groups and find some examples and conditions for the existence of such groups for classes of non-nilpotent groups: ZM (Zassenhaus metacyclic) groups, dihedral generalised groups, generalised dyciclic groups and affine groups. </p> </div> </dd> <dt> <a name='item55'>[55]</a> <a href ="/abs/2503.16894" title="Abstract" id="2503.16894"> arXiv:2503.16894 </a> [<a href="/pdf/2503.16894" title="Download PDF" id="pdf-2503.16894" aria-labelledby="pdf-2503.16894">pdf</a>, <a href="https://arxiv.org/html/2503.16894v1" title="View HTML" id="html-2503.16894" aria-labelledby="html-2503.16894" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16894" title="Other formats" id="oth-2503.16894" aria-labelledby="oth-2503.16894">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Normalizer of Twisted Chevalley Groups over Commutative Rings </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Garge,+S+M">Shripad M. Garge</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Makadiya,+D+H">Deep H. Makadiya</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 12 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Group Theory (math.GR)</span> </div> <p class='mathjax'> Let $R$ be a commutative ring with unity. Consider the twisted Chevalley group $G_{\pi, \sigma} (\Phi, R)$ of type $\phi$ over $R$ and its elementary subgroup $E'_{\pi, \sigma} (\Phi, R)$. This paper investigates the normalizers of $E'_{\pi, \sigma}(\Phi, R)$ and $G_{\pi, \sigma}(\Phi, R)$ in the larger group $G_{\pi, \sigma}(\Phi, S)$, where $S$ is an extension ring of $R$. We establish that under certain conditions on $R$ these normalizers coincide. Moreover, in the case of adjoint type groups, we show that they are precisely equal to $G_{\pi, \sigma}(\Phi, R)$. </p> </div> </dd> <dt> <a name='item56'>[56]</a> <a href ="/abs/2503.16898" title="Abstract" id="2503.16898"> arXiv:2503.16898 </a> [<a href="/pdf/2503.16898" title="Download PDF" id="pdf-2503.16898" aria-labelledby="pdf-2503.16898">pdf</a>, <a href="https://arxiv.org/html/2503.16898v1" title="View HTML" id="html-2503.16898" aria-labelledby="html-2503.16898" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16898" title="Other formats" id="oth-2503.16898" aria-labelledby="oth-2503.16898">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Bernstein Theorems for Calibrated Submanifolds in $\mathbb{R}^7$ and $\mathbb{R}^8$ </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Lien,+C">Chun-Kai Lien</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tsai,+C">Chung-Jun Tsai</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 27 pages, 3 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span> </div> <p class='mathjax'> This paper explores the Bernstein problem of smooth maps $f:\mathbb{R}^4 \to \mathbb{R}^3$ whose graphs form coassociative submanifolds in $\mathbb{R}^7$. We establish a condition, expressed in terms of the second elementary symmetric polynomial of the map's slope, that ensures $f$ is affine. A corresponding result is also established for Cayley submanifolds in $\mathbb{R}^8$. </p> </div> </dd> <dt> <a name='item57'>[57]</a> <a href ="/abs/2503.16900" title="Abstract" id="2503.16900"> arXiv:2503.16900 </a> [<a href="/pdf/2503.16900" title="Download PDF" id="pdf-2503.16900" aria-labelledby="pdf-2503.16900">pdf</a>, <a href="https://arxiv.org/html/2503.16900v1" title="View HTML" id="html-2503.16900" aria-labelledby="html-2503.16900" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16900" title="Other formats" id="oth-2503.16900" aria-labelledby="oth-2503.16900">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Odd and even derivations, transposed Poisson superalgebra and 3-Lie superalgebra </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Abramov,+V">Viktor Abramov</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Sovetnikov,+N">Nikolai Sovetnikov</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; Commutative Algebra (math.AC) </div> <p class='mathjax'> One important example of a transposed Poisson algebra can be constructed by means of a commutative algebra and its derivation. This approach can be extended to superalgebras, that is, one can construct a transposed Poisson superalgebra given a commutative superalgebra and its even derivation. In this paper we show that including odd derivations in the framework of this approach requires introducing a new notion. It is a super vector space with two operations that satisfy the compatibility condition of transposed Poisson superalgebra. The first operation is determined by a left supermodule over commutative superalgebra and the second is a Jordan bracket. Then it is proved that the super vector space generated by an odd derivation of a commutative superalgebra satisfies all the requirements of introduced notion. We also show how to construct a 3-Lie superalgebra if we are given a transposed Poisson superalgebra and its even derivation. </p> </div> </dd> <dt> <a name='item58'>[58]</a> <a href ="/abs/2503.16902" title="Abstract" id="2503.16902"> arXiv:2503.16902 </a> [<a href="/pdf/2503.16902" title="Download PDF" id="pdf-2503.16902" aria-labelledby="pdf-2503.16902">pdf</a>, <a href="/format/2503.16902" title="Other formats" id="oth-2503.16902" aria-labelledby="oth-2503.16902">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Revisiting implicit variables in mathematical optimization: simplified modeling and a numerical evidence </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Mehlitz,+P">Patrick Mehlitz</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 43 pages, 5 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as explicit ones. Recently, it has been shown in terms of a comparatively complex model problem that this approach, generally, is theoretically disadvantageous as the surrogate problem typically suffers from the presence of artificial stationary points and the need for stronger constraint qualifications. The purpose of the present paper is twofold. First, it introduces a much simpler and easier accessible model problem which can be used to recapitulate and even broaden the aforementioned findings. Indeed, we will extend the analysis to two more classes of stationary points and the associated constraint qualifications. These theoretical results are accompanied by illustrative examples from cardinality-constrained, vanishing-constrained, and bilevel optimization. Second, the present paper illustrates, in terms of cardinality-constrained portfolio optimization problems, that treating implicit variables as explicit ones may also be disadvantageous from a numerical point of view. </p> </div> </dd> <dt> <a name='item59'>[59]</a> <a href ="/abs/2503.16912" title="Abstract" id="2503.16912"> arXiv:2503.16912 </a> [<a href="/pdf/2503.16912" title="Download PDF" id="pdf-2503.16912" aria-labelledby="pdf-2503.16912">pdf</a>, <a href="/format/2503.16912" title="Other formats" id="oth-2503.16912" aria-labelledby="oth-2503.16912">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Construction and sample path properties of diffusion house-moving between two curves </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ishitani,+K">Kensuke Ishitani</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Nishino,+S">Soma Nishino</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 37 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> The purpose of this paper is to introduce the construction of a stochastic process called ``diffusion house-moving'' and to explore its properties. We study the weak convergence of diffusion bridges conditioned to stay between two curves, and we refer to this limit as diffusion house-moving. Applying this weak convergence result, we give the sample path properties of diffusion house-moving. </p> </div> </dd> <dt> <a name='item60'>[60]</a> <a href ="/abs/2503.16919" title="Abstract" id="2503.16919"> arXiv:2503.16919 </a> [<a href="/pdf/2503.16919" title="Download PDF" id="pdf-2503.16919" aria-labelledby="pdf-2503.16919">pdf</a>, <a href="https://arxiv.org/html/2503.16919v1" title="View HTML" id="html-2503.16919" aria-labelledby="html-2503.16919" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16919" title="Other formats" id="oth-2503.16919" aria-labelledby="oth-2503.16919">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Gaussian Blahut-Arimoto Algorithm for Capacity Region Calculation of Gaussian Vector Broadcast Channels </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Jiao,+T">Tian Jiao</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Geng,+Y">Yanlin Geng</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Chu,+Y">Yonghui Chu</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=So,+A+M">Anthony Man-Cho So</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Yang,+Z">Zai Yang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 16 pages, 3 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Information Theory (cs.IT)</span> </div> <p class='mathjax'> This paper is concerned with the computation of the capacity region of a continuous, Gaussian vector broadcast channel (BC) with covariance matrix constraints. Since the decision variables of the corresponding optimization problem are Gaussian distributed, they can be characterized by a finite number of parameters. Consequently, we develop new Blahut-Arimoto (BA)-type algorithms that can compute the capacity without discretizing the channel. First, by exploiting projection and an approximation of the Lagrange multiplier, which are introduced to handle certain positive semidefinite constraints in the optimization formulation, we develop the Gaussian BA algorithm with projection (GBA-P). Then, we demonstrate that one of the subproblems arising from the alternating updates admits a closed-form solution. Based on this result, we propose the Gaussian BA algorithm with alternating updates (GBA-A) and establish its convergence guarantee. Furthermore, we extend the GBA-P algorithm to compute the capacity region of the Gaussian vector BC with both private and common messages. All the proposed algorithms are parameter-free. Lastly, we present numerical results to demonstrate the effectiveness of the proposed algorithms. </p> </div> </dd> <dt> <a name='item61'>[61]</a> <a href ="/abs/2503.16925" title="Abstract" id="2503.16925"> arXiv:2503.16925 </a> [<a href="/pdf/2503.16925" title="Download PDF" id="pdf-2503.16925" aria-labelledby="pdf-2503.16925">pdf</a>, <a href="https://arxiv.org/html/2503.16925v1" title="View HTML" id="html-2503.16925" aria-labelledby="html-2503.16925" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16925" title="Other formats" id="oth-2503.16925" aria-labelledby="oth-2503.16925">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> k-connectivity threshold for superpositions of Bernoulli random graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ardickas,+D">Daumilas Ardickas</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Bloznelis,+M">Mindaugas Bloznelis</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Vaicekauskas,+R">Rimantas Vaicekauskas</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 21 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> Let $G_1,\dots, G_m$ be independent identically distributed Bernoulli random subgraphs of the complete graph ${\cal K}_n$ having vertex sets of random sizes $X_1,\dots, X_m\in \{0,1,2,\dots\}$ and random edge densities $Q_1,\dots, Q_m\in [0,1]$. Assuming that each $G_i$ has a vertex of degree $1$ with positive probability, we establish the $k$-connectivity threshold as $n,m\to+\infty$ for the union $\cup_{i=1}^mG_i$ defined on the vertex set of ${\cal K}_n$. </p> </div> </dd> <dt> <a name='item62'>[62]</a> <a href ="/abs/2503.16933" title="Abstract" id="2503.16933"> arXiv:2503.16933 </a> [<a href="/pdf/2503.16933" title="Download PDF" id="pdf-2503.16933" aria-labelledby="pdf-2503.16933">pdf</a>, <a href="https://arxiv.org/html/2503.16933v1" title="View HTML" id="html-2503.16933" aria-labelledby="html-2503.16933" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16933" title="Other formats" id="oth-2503.16933" aria-labelledby="oth-2503.16933">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Wold-type decomposition for Doubly commuting two-isometries </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bhattacharjee,+M">Monojit Bhattacharjee</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Gupta,+R">Rajeev Gupta</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Venugopal,+V">Vidhya Venugopal</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 13 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> In this article, we prove that any pair of doubly commuting $2$-isometries on a Hilbert space has a Wold-type decomposition. Moreover, the analytic part of the pair is unitary equivalent to the pair of multiplication by coordinate function on a Dirichlet-type space on the bidisc. </p> </div> </dd> <dt> <a name='item63'>[63]</a> <a href ="/abs/2503.16936" title="Abstract" id="2503.16936"> arXiv:2503.16936 </a> [<a href="/pdf/2503.16936" title="Download PDF" id="pdf-2503.16936" aria-labelledby="pdf-2503.16936">pdf</a>, <a href="https://arxiv.org/html/2503.16936v1" title="View HTML" id="html-2503.16936" aria-labelledby="html-2503.16936" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16936" title="Other formats" id="oth-2503.16936" aria-labelledby="oth-2503.16936">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Hermitian metrics on complex non-K盲hler manifolds </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Angella,+D">Daniele Angella</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Dedicated to Professor Paul Gauduchon, on his 80th birthday. This survey expands the topic of a seminar given by the author at the Second International Conference on Differential Geometry in Fes in October 2024 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Complex Variables (math.CV)</span>; Differential Geometry (math.DG) </div> <p class='mathjax'> In this survey, we consider various analytic problems related to the geometry of the Chern connection on Hermitian manifolds, such as the existence of metrics with constant Chern-scalar curvature, generalizations of the K盲hler-Einstein condition to the non-K盲hler setting, and the convergence of the Chern-Ricci flow on compact complex surfaces. </p> </div> </dd> <dt> <a name='item64'>[64]</a> <a href ="/abs/2503.16940" title="Abstract" id="2503.16940"> arXiv:2503.16940 </a> [<a href="/pdf/2503.16940" title="Download PDF" id="pdf-2503.16940" aria-labelledby="pdf-2503.16940">pdf</a>, <a href="https://arxiv.org/html/2503.16940v1" title="View HTML" id="html-2503.16940" aria-labelledby="html-2503.16940" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16940" title="Other formats" id="oth-2503.16940" aria-labelledby="oth-2503.16940">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Magnetic ground states and the conformal class of a surface </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Colbois,+B">Bruno Colbois</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Provenzano,+L">Luigi Provenzano</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Savo,+A">Alessandro Savo</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span>; Spectral Theory (math.SP) </div> <p class='mathjax'> On a closed, orientable Riemannian surface $\Sigma_g$ of arbitrary genus $g\geq 1$ and Riemannian metric $h$ we study the magnetic Laplacian with magnetic potential given by a harmonic $1$-form $A$. Its lowest eigenvalue (magnetic ground state energy) is positive, unless $A$ represents an integral cohomology class. We isolate a countable set of ground state energies which we call $\textit{ground state spectrum}$ of the metric $h$. The main result of the paper is to show that the ground state spectrum determines the volume and the conformal class of the metric $h$. In particular, hyperbolic metrics are distinguished by their ground state spectrum. <br>We also compute the magnetic spectrum of flat tori and introduce some magnetic spectral invariants of $(\Sigma_g,h)$ which are conformal by definition and involve the geometry of what we call the Jacobian torus of $(\Sigma_g,h)$ (in Algebraic Geometry, the Jacobian variety of a Riemann surface). </p> </div> </dd> <dt> <a name='item65'>[65]</a> <a href ="/abs/2503.16952" title="Abstract" id="2503.16952"> arXiv:2503.16952 </a> [<a href="/pdf/2503.16952" title="Download PDF" id="pdf-2503.16952" aria-labelledby="pdf-2503.16952">pdf</a>, <a href="/format/2503.16952" title="Other formats" id="oth-2503.16952" aria-labelledby="oth-2503.16952">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Dimension-free estimates for discrete maximal functions and lattice points in high-dimensional spheres and balls with small radii </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Niksi%C5%84ski,+J">Jakub Niksi艅ski</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wr%C3%B3bel,+B">B艂a偶ej Wr贸bel</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 46 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Classical Analysis and ODEs (math.CA)</span>; Functional Analysis (math.FA) </div> <p class='mathjax'> We prove that the discrete Hardy-Littlewood maximal function associated with Euclidean spheres with small radii has dimension-free estimates on $\ell^p(\mathbb{Z}^d)$ for $p\in[2,\infty).$ This implies an analogous result for the Euclidean balls, thus making progress on a question of E.M. Stein from the mid 1990s. Our work provides the first dimension-free estimates for full discrete maximal functions related to spheres and balls without relying on comparisons with their continuous counterparts. An important part of our argument is a uniform (dimension-free) count of lattice points in high-dimensional spheres and balls with small radii. We also established a dimension-free estimate for a multi-parameter maximal function of a combinatorial nature, which is a new phenomenon and may be useful for studying similar problems in the future. </p> </div> </dd> <dt> <a name='item66'>[66]</a> <a href ="/abs/2503.16966" title="Abstract" id="2503.16966"> arXiv:2503.16966 </a> [<a href="/pdf/2503.16966" title="Download PDF" id="pdf-2503.16966" aria-labelledby="pdf-2503.16966">pdf</a>, <a href="https://arxiv.org/html/2503.16966v1" title="View HTML" id="html-2503.16966" aria-labelledby="html-2503.16966" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16966" title="Other formats" id="oth-2503.16966" aria-labelledby="oth-2503.16966">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A note on elliptic curves on toric surfaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Barash,+M+M">Michael M. Barash</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tyomkin,+I">Ilya Tyomkin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages. Comments are welcome </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> In this paper, we study the Severi varieties parametrizing integral curves of geometric genus one on polarized toric surfaces in characteristic zero and describe their irreducible components. We show that the irreducible components are in natural bijection with certain affine sublattices of the lattice of characters of the toric surface. The sublattices are described explicitly in terms of the polygon defining the polarization of the toric surface. </p> </div> </dd> <dt> <a name='item67'>[67]</a> <a href ="/abs/2503.16985" title="Abstract" id="2503.16985"> arXiv:2503.16985 </a> [<a href="/pdf/2503.16985" title="Download PDF" id="pdf-2503.16985" aria-labelledby="pdf-2503.16985">pdf</a>, <a href="https://arxiv.org/html/2503.16985v1" title="View HTML" id="html-2503.16985" aria-labelledby="html-2503.16985" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16985" title="Other formats" id="oth-2503.16985" aria-labelledby="oth-2503.16985">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> From Hyper Roughness to Jumps as $H \to -1/2$ </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Jaber,+E+A">Eduardo Abi Jaber</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Attal,+E">Elie Attal</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rosenbaum,+M">Mathieu Rosenbaum</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We investigate the weak limit of the hyper-rough square-root process as the Hurst index $H$ goes to $-1/2\,$. This limit corresponds to the fractional kernel $t^{H - 1 / 2}$ losing integrability. We establish the joint convergence of the couple $(X, M)\,$, where $X$ is the hyper-rough process and $M$ the associated martingale, to a fully correlated Inverse Gaussian L茅vy jump process. This unveils the existence of a continuum between hyper-rough continuous models and jump processes, as a function of the Hurst index. Since we prove a convergence of continuous to discontinuous processes, the usual Skorokhod $J_1$ topology is not suitable for our problem. Instead, we obtain the weak convergence in the Skorokhod $M_1$ topology for $X$ and in the non-Skorokhod $S$ topology for $M$. </p> </div> </dd> <dt> <a name='item68'>[68]</a> <a href ="/abs/2503.16987" title="Abstract" id="2503.16987"> arXiv:2503.16987 </a> [<a href="/pdf/2503.16987" title="Download PDF" id="pdf-2503.16987" aria-labelledby="pdf-2503.16987">pdf</a>, <a href="https://arxiv.org/html/2503.16987v1" title="View HTML" id="html-2503.16987" aria-labelledby="html-2503.16987" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16987" title="Other formats" id="oth-2503.16987" aria-labelledby="oth-2503.16987">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Roots of elements for groups over local fields </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kumar,+P">Parteek Kumar</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mandal,+A">Arunava Mandal</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span>; Group Theory (math.GR) </div> <p class='mathjax'> Let $\mathbb F$ be a local field and $G$ be a linear algebraic group defined over $\mathbb F$. For $k\in\mathbb N$, let $g\to g^k$ be the $k$-th power map $P_k$ on $G(\mathbb F)$. The purpose of this article is two-fold. First, we study the power map on real algebraic group. We characterise the density of the images of the power map $P_k$ on $G(\mathbb R)$ in terms of Cartan subgroups. Next we consider the linear algebraic group $G$ over non-Archimedean local field $\mathbb F$ with any characteristic. If the residual characteristic of $\mathbb F$ is $p$, and an element admits $p^k$-th root in $G(\mathbb F)$ for each $k$, then we prove that some power of the element is unipotent. In particular, we prove that an element $g\in G(\mathbb F)$ admits roots of all orders if and only if $g$ is contained in a one-parameter subgroup in $G(\mathbb F)$. Also, we extend these results to all linear algebraic groups over global fields. </p> </div> </dd> <dt> <a name='item69'>[69]</a> <a href ="/abs/2503.16990" title="Abstract" id="2503.16990"> arXiv:2503.16990 </a> [<a href="/pdf/2503.16990" title="Download PDF" id="pdf-2503.16990" aria-labelledby="pdf-2503.16990">pdf</a>, <a href="https://arxiv.org/html/2503.16990v1" title="View HTML" id="html-2503.16990" aria-labelledby="html-2503.16990" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16990" title="Other formats" id="oth-2503.16990" aria-labelledby="oth-2503.16990">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Preserving Lefschetz properties after extension of variables </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kling,+F+J">Filip Jonsson Kling</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 29 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Commutative Algebra (math.AC)</span> </div> <p class='mathjax'> Consider a standard graded artinian $k$-algebra $B$ and an extension of $B$ by a new variable, $A=B\otimes_k k[x]/(x^d)$ for some $d\geq 1$. We will show how maximal rank properties for powers of a general linear form on $A$ can be determined by maximal rank properties for different powers of general linear forms on $B$. This is then used to study Lefschetz properties of algebras that can be obtained via such extensions. In particular, it allows for a new proof that monomial complete intersections have the strong Lefschetz property over a field of characteristic zero. Moreover, it gives a recursive formula for the determinants that show up in that case. Finally, for algebras over a field of characteristic zero, we give a classification for what properties $B$ must have for all extensions $B\otimes_k k[x]/(x^d)$ to have the weak or the strong Lefschetz property. </p> </div> </dd> <dt> <a name='item70'>[70]</a> <a href ="/abs/2503.16995" title="Abstract" id="2503.16995"> arXiv:2503.16995 </a> [<a href="/pdf/2503.16995" title="Download PDF" id="pdf-2503.16995" aria-labelledby="pdf-2503.16995">pdf</a>, <a href="https://arxiv.org/html/2503.16995v1" title="View HTML" id="html-2503.16995" aria-labelledby="html-2503.16995" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16995" title="Other formats" id="oth-2503.16995" aria-labelledby="oth-2503.16995">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Painless Construction of Unconditional Bases for Anisotropic Modulation and Triebel-Lizorkin Type Spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Nielsen,+M">Morten Nielsen</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> We construct smooth localised orthonormal bases compatible with anisotropic Triebel-Lizorkin and Besov type spaces on $\mathbb{R}^d$. The construction is based on tensor products of so-called univariate brushlet functions that are based on local trigonometric bases in the frequency domain, and the construction is painless in the sense that all parameters for the construction are explicitly specified. It is shown that the associated decomposition system form unconditional bases for the full family of Triebel-Lizorkin and Besov type spaces, including for the so-called $\alpha$-modulation and $\alpha$-Triebel-Lizorkin spaces. In the second part of the paper we study nonlinear $m$-term approximation with the constructed bases, where direct Jackson and Bernstein inequalities for $m$-term approximation with the tensor brushlet system in $\alpha$-modulation and $\alpha$-Triebel-Lizorkin spaces are derived. The inverse Bernstein estimates rely heavily on the fact that the constructed system is non-redundant. </p> </div> </dd> <dt> <a name='item71'>[71]</a> <a href ="/abs/2503.17023" title="Abstract" id="2503.17023"> arXiv:2503.17023 </a> [<a href="/pdf/2503.17023" title="Download PDF" id="pdf-2503.17023" aria-labelledby="pdf-2503.17023">pdf</a>, <a href="https://arxiv.org/html/2503.17023v1" title="View HTML" id="html-2503.17023" aria-labelledby="html-2503.17023" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17023" title="Other formats" id="oth-2503.17023" aria-labelledby="oth-2503.17023">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A free boundary approach to the quasistatic evolution of debonding models </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Maggiorelli,+E">Eleonora Maggiorelli</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Riva,+F">Filippo Riva</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tolotti,+E+G">Edoardo Giovanni Tolotti</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existence of energetic solutions, based on global minimisers of a suitable functional together with an energy balance, is obtained within the natural class of open sets, improving and simplifying previous results known in literature. The proposed approach relies on an equivalent reformulation of the model in terms of the celebrated one-phase Bernoulli free boundary problem. This point of view allows performing the Minimizing Movements scheme in spaces of functions instead of the more complicated framework of sets. Nevertheless, in order to encompass irreversibility of the phenomenon, it remains crucial to keep track of the debonded region at each discrete time-step, thus actually resulting in a coupled algorithm. </p> </div> </dd> <dt> <a name='item72'>[72]</a> <a href ="/abs/2503.17045" title="Abstract" id="2503.17045"> arXiv:2503.17045 </a> [<a href="/pdf/2503.17045" title="Download PDF" id="pdf-2503.17045" aria-labelledby="pdf-2503.17045">pdf</a>, <a href="https://arxiv.org/html/2503.17045v1" title="View HTML" id="html-2503.17045" aria-labelledby="html-2503.17045" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17045" title="Other formats" id="oth-2503.17045" aria-labelledby="oth-2503.17045">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Multifractal formalism of Lyapunov exponents for fiber-bunched linear cocycles </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Mohammadpour,+R">Reza Mohammadpour</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Varandas,+P">Paulo Varandas</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> We develop a higher-dimensional extension of multifractal analysis for typical fiber-bunched linear cocycles. Our main result is a relative variational principle, which shows that the topological entropy of the level sets of Lyapunov exponents can be approximated by the metric entropy of ergodic measures fully concentrated on those level sets, addressing a question posed by Breuillard and Sert. We also establish a variational principle for the generalized singular value function. As an application to dynamically defined linear cocycles, we obtain a multifractal formalism for open sets of $C^{1+\alpha}$ repellers and Anosov diffeomorphisms. </p> </div> </dd> <dt> <a name='item73'>[73]</a> <a href ="/abs/2503.17049" title="Abstract" id="2503.17049"> arXiv:2503.17049 </a> [<a href="/pdf/2503.17049" title="Download PDF" id="pdf-2503.17049" aria-labelledby="pdf-2503.17049">pdf</a>, <a href="https://arxiv.org/html/2503.17049v1" title="View HTML" id="html-2503.17049" aria-labelledby="html-2503.17049" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17049" title="Other formats" id="oth-2503.17049" aria-labelledby="oth-2503.17049">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Optimal control on a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cavalleri,+G">Giulia Cavalleri</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Miranville,+A">Alain Miranville</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 30 pages. The keywords are: tumor growth models, lactate kinetics, mechanical effects, damage, optimal control, adjoint system, necessary optimality conditions </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Optimization and Control (math.OC) </div> <p class='mathjax'> In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, introduced in [G. Cavalleri, P. Colli, A. Miranville, E. Rocca, On a Brain Tumor Growth Model with Lactate Metabolism, Viscoelastic Effects, and Tissue Damage (2025)], couples a Fisher-Kolmogorov type equation for tumor cell density with a reaction-diffusion equation for the lactate, a quasi-static force balance governing the displacement, and a nonlinear differential inclusion for tissue damage. The control variables, representing chemotherapy and a lactate-targeting drug, influence tumor progression and treatment response. Starting from well-posedness, regularity, and continuous dependence results already established, we define a suitable cost functional and prove the existence of optimal controls. Then, we analyze the differentiability of the control-to-state operator and establish a necessary first-order condition for treatment optimality. </p> </div> </dd> <dt> <a name='item74'>[74]</a> <a href ="/abs/2503.17062" title="Abstract" id="2503.17062"> arXiv:2503.17062 </a> [<a href="/pdf/2503.17062" title="Download PDF" id="pdf-2503.17062" aria-labelledby="pdf-2503.17062">pdf</a>, <a href="https://arxiv.org/html/2503.17062v1" title="View HTML" id="html-2503.17062" aria-labelledby="html-2503.17062" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17062" title="Other formats" id="oth-2503.17062" aria-labelledby="oth-2503.17062">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Topologically independent sets in topological groups and vector spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Sp%C4%9Bv%C3%A1k,+J">Jan Sp臎v谩k</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Topology (math.GN)</span> </div> <p class='mathjax'> We study topological versions of an independent set in an abelian group and a linearly independent set in a vector space, a {\em topologically independent set} in a topological group and a {\em topologically linearly independent set} in a topological vector space. These counterparts of their algebraic versions are defined analogously and possess similar properties. <br>Let $\C^\times$ be the multiplicative group of the field of complex numbers with its usual topology. We prove that a subset $A$ of an arbitrary Tychonoff power of $\C^\times$ is topologically independent if and only if the topological subgroup $\hull{A}$ that it generates is the Tychonoff direct sum $\bigoplus_{a\in A}\hull{a}$. <br>This theorem substantially generalizes an earlier result of the author, who has proved this for Abelian precompact groups. <br>Further, we show that topologically independent and topologically linearly independent sets coincide in vector spaces with weak topologies, although they are different in general. <br>We characterize topologically linearly independent sets in vector spaces with weak topologies and normed spaces. In a weak topology, a set $A$ <br>is topologically linearly independent if and only if its linear span is the Tychonoff direct sum $\R^{(A)}$. In normed spaces $A$ is topologically linearly independent if and only if it is uniformly minimal. Thus, from the point of view of topological linear independence, the Tychonoff direct sums $\R^{(A)}$ and (linear spans of) uniformly minimal sets, which are closely related to bounded biorthogonal systems, are of the same essence. </p> </div> </dd> <dt> <a name='item75'>[75]</a> <a href ="/abs/2503.17066" title="Abstract" id="2503.17066"> arXiv:2503.17066 </a> [<a href="/pdf/2503.17066" title="Download PDF" id="pdf-2503.17066" aria-labelledby="pdf-2503.17066">pdf</a>, <a href="/format/2503.17066" title="Other formats" id="oth-2503.17066" aria-labelledby="oth-2503.17066">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Formation of condensations for non-radial solutions to 3-wave kinetic equations </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Staffilani,+G">Gigliola Staffilani</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tran,+M">Minh-Binh Tran</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> We consider in this work a $2$-dimensional $3$-wave kinetic equation describing the dynamics of the thermal cloud outside a Bose-Einstein Condensate. We construct global non-radial mild solutions for the equation. Those mild solutions are the summation of Dirac masses on circles. We prove that in each spatial direction, either Dirac masses at the origin, which are the so-called Bose-Einstein condensates, can be formed in finite time or the solutions converge to Bose-Einstein condensates as time evolves to infinity. We also describe a dynamics of the formation of the Bose-Einstein condensates latter case. In this case, on each direction, the solutions accumulate around circles close to the origin at growth rates at least linearly in time. </p> </div> </dd> <dt> <a name='item76'>[76]</a> <a href ="/abs/2503.17068" title="Abstract" id="2503.17068"> arXiv:2503.17068 </a> [<a href="/pdf/2503.17068" title="Download PDF" id="pdf-2503.17068" aria-labelledby="pdf-2503.17068">pdf</a>, <a href="/format/2503.17068" title="Other formats" id="oth-2503.17068" aria-labelledby="oth-2503.17068">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Weighted Heights and GIT Heights </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Shaska,+E">Elira Shaska</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Shaska,+T">Tony Shaska</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span>; Number Theory (math.NT) </div> <p class='mathjax'> This paper examines the relationship between GIT heights and weighted heights, exploring their definitions and applications to weighted projective spaces and binary forms. Drawing on prior weighted height frameworks, we relate them to Zhang's GIT height via the Veronese map, showing that for a semistable cycle Z in a weighted projective space over the algebraic closure of Q, the GIT height h(Z) equals L(Z) plus an Archimedean Chow metric term. For binary forms f in V_d, we define an invariant height H(f) with respect to the Chow metric and establish that the moduli weighted height L(xi(f)) of f's invariants equals H(f) plus the field degree times the Chow height h_Ch(f), linking arithmetic and moduli properties. </p> </div> </dd> <dt> <a name='item77'>[77]</a> <a href ="/abs/2503.17088" title="Abstract" id="2503.17088"> arXiv:2503.17088 </a> [<a href="/pdf/2503.17088" title="Download PDF" id="pdf-2503.17088" aria-labelledby="pdf-2503.17088">pdf</a>, <a href="https://arxiv.org/html/2503.17088v1" title="View HTML" id="html-2503.17088" aria-labelledby="html-2503.17088" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17088" title="Other formats" id="oth-2503.17088" aria-labelledby="oth-2503.17088">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Unsourced Random Access in MIMO Quasi-Static Rayleigh Fading Channels: Finite Blocklength and Scaling Law Analyses </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Gao,+J">Junyuan Gao</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Wu,+Y">Yongpeng Wu</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Caire,+G">Giuseppe Caire</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Yang,+W">Wei Yang</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Poor,+H+V">H. Vincent Poor</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Zhang,+W">Wenjun Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Accepted by IEEE Transactions on Information Theory </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Information Theory (cs.IT)</span> </div> <p class='mathjax'> This paper considers the unsourced random access (URA) problem with a random and unknown number of active users in multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channels. We derive non-asymptotic achievability bounds on the probability of incorrectly estimating the number of active users, and provide scaling laws on the gap between the estimated and true numbers of active users. We prove that the error probability reaches a plateau as the power $P$ and blocklength $n$ increase, whereas it decays exponentially with the number $L$ of receive antennas and eventually vanishes. Then, we explore the fundamental limits of URA by deriving non-asymptotic achievability bounds and converse bounds (including two single-user converse bounds and one multi-user ensemble converse bound) on the minimum energy-per-bit required by each active user to transmit $J$ bits with blocklength $n$ under misdetection and false-alarm constraints. Numerical results show that the extra required energy-per-bit due to the uncertainty in the number ${\rm{K}}_a$ of active users decreases as $L$ and $\mathbb{E}[{\rm{K}}_a]$ increase and the error requirement becomes milder. In the non-asymptotic regime, using codewords distributed on a sphere outperforms Gaussian random coding. Existing schemes are shown to exhibit a large gap to our bounds when the number of active users is large, calling for more advanced schemes that perform energy-efficiently in this case. In the asymptotic regime with $n\to\infty$, we establish scaling laws on the minimum required $P$ and $L$ to reliably support ${\rm{K}}_a$ active users as functions of $n$, which highlight the potential of MIMO in enabling low-cost communication and indicate that it is possible for the minimum required $P$ and $L$ to remain on the same order when the number of active users increases but stays below a threshold. </p> </div> </dd> <dt> <a name='item78'>[78]</a> <a href ="/abs/2503.17092" title="Abstract" id="2503.17092"> arXiv:2503.17092 </a> [<a href="/pdf/2503.17092" title="Download PDF" id="pdf-2503.17092" aria-labelledby="pdf-2503.17092">pdf</a>, <a href="https://arxiv.org/html/2503.17092v1" title="View HTML" id="html-2503.17092" aria-labelledby="html-2503.17092" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17092" title="Other formats" id="oth-2503.17092" aria-labelledby="oth-2503.17092">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Optimal Investment Portfolio of Thyristor- and IGBT-based Electrolysis Rectifiers in Utility-scale Renewable P2H Systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Zeng,+Y">Yangjun Zeng</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Qiu,+Y">Yiwei Qiu</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Xu,+L">Liuchao Xu</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Gu,+C">Chenjia Gu</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Zhou,+Y">Yi Zhou</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Li,+J">Jiarong Li</a> (2), <a href="https://arxiv.org/search/math?searchtype=author&query=Chen,+S">Shi Chen</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Zhou,+B">Buxiang Zhou</a> (1) ((1) College of Electrical Engineering, Sichuan University, (2) Harvard John A. Paulson School of Engineering and Applied Sciences)</div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Systems and Control (eess.SY) </div> <p class='mathjax'> Renewable power-to-hydrogen (ReP2H) systems require rectifiers to supply power to electrolyzers (ELZs). Two main types of rectifiers, insulated-gate bipolar transistor rectifiers (IGBT-Rs) and thyristor rectifiers (TRs), offer distinct tradeoffs. IGBT-Rs provide flexible reactive power control but are costly, whereas TRs are more affordable with lower power loss but consume a large amount of uncontrollable reactive power. A mixed configuration of rectifiers in utility-scale ReP2H systems could achieve an decent tradeoff and increase overall profitability. To explore this potential, this paper proposes an optimal investment portfolio model. First, we model and compare the active and reactive power characteristics of ELZs powered by TRs and IGBT-Rs. Second, we consider the investment of ELZs, rectifiers, and var resources and coordinate the operation of renewables, energy storage, var resources, and the on-off switching and load allocation of multiple ELZs. Subsequently, a two-stage stochastic programming (SP) model based on weighted information gap decision theory (W-IGDT) is developed to address the uncertainties of the renewable power and hydrogen price, and we apply the progressive hedging (PH) algorithm to accelerate its solution. Case studies demonstrate that optimal rectifier configurations increase revenue by at most 2.56% compared with using only TRs or IGBT-Rs, as well as those in existing projects. Under the optimal portfolio, reactive power compensation investment is nearly eliminated, with a preferred TR-to-IGBT-R ratio of 3:1. </p> </div> </dd> <dt> <a name='item79'>[79]</a> <a href ="/abs/2503.17100" title="Abstract" id="2503.17100"> arXiv:2503.17100 </a> [<a href="/pdf/2503.17100" title="Download PDF" id="pdf-2503.17100" aria-labelledby="pdf-2503.17100">pdf</a>, <a href="https://arxiv.org/html/2503.17100v1" title="View HTML" id="html-2503.17100" aria-labelledby="html-2503.17100" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17100" title="Other formats" id="oth-2503.17100" aria-labelledby="oth-2503.17100">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Social Optimization in Noncooperative Games under Central Regulation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Du,+K">Kaixin Du</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Meng,+M">Min Meng</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Li,+X">Xiuxian Li</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> This paper proposes a novel optimization problem building on noncooperative games under central regulation, which can be formulated as a bilevel structure. In the low-level, each player competes to minimize its own cost function that depends not only on the strategies of all players, but also on an intervention decision of the central regulator, while the central regulator located at the high-level attempts to achieve the social optimum, that is, to minimize the sum of cost functions of all players through an adjustable intervention decision. In this setting, under the intervention of the central regulator, the low-level players perform in a noncooperative game and aim to seek the Nash equilibrium, which indeed is related with the regulator's decision. Meanwhile, the objective of the regulator is to choose a decision such that the social cost, i.e., the sum of cost functions of all players is minimum. This formulated bilevel social optimization problem is proven to be constrained, nonconvex and nonsmooth. To address this intricate problem, an inexact zeroth-order algorithm is developed by virtue of the smoothing techniques, allowing for the Nash equilibrium of the low-level game to be computed in an inexact manner. Levering the properties of smoothing techniques, it is rigorously shown that the devised algorithm achieves a sublinear convergence rate for computing a stationary point of a related optimization problem with a smoothed objective. Moreover, the sublinear convergence rate in the scenario where the exact equilibrium of the low-level game is available is also discussed. Finally, numerical simulations are conducted to demonstrate the efficiency of theoretical findings. </p> </div> </dd> <dt> <a name='item80'>[80]</a> <a href ="/abs/2503.17112" title="Abstract" id="2503.17112"> arXiv:2503.17112 </a> [<a href="/pdf/2503.17112" title="Download PDF" id="pdf-2503.17112" aria-labelledby="pdf-2503.17112">pdf</a>, <a href="https://arxiv.org/html/2503.17112v1" title="View HTML" id="html-2503.17112" aria-labelledby="html-2503.17112" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17112" title="Other formats" id="oth-2503.17112" aria-labelledby="oth-2503.17112">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Separation Number and Treewidth, Revisited </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Houdrouge,+H">Hussein Houdrouge</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Miraftab,+B">Babak Miraftab</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Morin,+P">Pat Morin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages, 0 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span>; Discrete Mathematics (cs.DM) </div> <p class='mathjax'> We give a constructive proof of the fact that the treewidth of a graph $G$ is bounded by a linear function of the separation number of $G$. </p> </div> </dd> <dt> <a name='item81'>[81]</a> <a href ="/abs/2503.17120" title="Abstract" id="2503.17120"> arXiv:2503.17120 </a> [<a href="/pdf/2503.17120" title="Download PDF" id="pdf-2503.17120" aria-labelledby="pdf-2503.17120">pdf</a>, <a href="https://arxiv.org/html/2503.17120v1" title="View HTML" id="html-2503.17120" aria-labelledby="html-2503.17120" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17120" title="Other formats" id="oth-2503.17120" aria-labelledby="oth-2503.17120">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Orthogonality and domination in o-minimal expansions of ordered groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Guerrero,+P+a">Pablo and煤jar Guerrero</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Eleftheriou,+P+E">Pantelis E. Eleftheriou</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mennuni,+R">Rosario Mennuni</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic (math.LO)</span> </div> <p class='mathjax'> We analyse domination between invariant types in o-minimal expansions of ordered groups, showing that the domination poset decomposes as the direct product of two posets: the domination poset of an o-minimal expansion of a real closed field, and one derived from a linear o-minimal structure. We prove that if the Morley product is well-defined on the former poset, then the same holds for the poset computed in the whole structure. We establish our results by employing the `short closure' pregeometry ($\mathrm{scl}$) in semi-bounded o-minimal structures, showing that types of $\mathrm{scl}$-independent tuples are weakly orthogonal to types of short tuples. As an application we prove that, in an o-minimal expansion of an ordered group, every definable type is domination-equivalent to a product of 1-types. Furthermore, there are precisely two or four classes of definable types up to domination-equivalence, depending on whether a global field is definable or not. </p> </div> </dd> <dt> <a name='item82'>[82]</a> <a href ="/abs/2503.17127" title="Abstract" id="2503.17127"> arXiv:2503.17127 </a> [<a href="/pdf/2503.17127" title="Download PDF" id="pdf-2503.17127" aria-labelledby="pdf-2503.17127">pdf</a>, <a href="https://arxiv.org/html/2503.17127v1" title="View HTML" id="html-2503.17127" aria-labelledby="html-2503.17127" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17127" title="Other formats" id="oth-2503.17127" aria-labelledby="oth-2503.17127">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the Milnor fibres of initial forms of topologically equivalent holomorphic functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Sampaio,+J+E">Jos茅 Edson Sampaio</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span>; Complex Variables (math.CV) </div> <p class='mathjax'> Budur, Fernandes de Bobadilla, Le and Nguyen (2022) conjectured that if two germs of holomorphic functions are topologically equivalent, then the Milnor fibres of their initial forms are homotopy equivalent. In this note, we give affirmative answers to this conjecture in the case of plane curves. We show also that a positive answer to this conjecture implies in a positive answer to the famous Zariski multiplicity conjecture both in the case of right equivalence or in the case of hypersurfaces with isolated singularities. </p> </div> </dd> <dt> <a name='item83'>[83]</a> <a href ="/abs/2503.17130" title="Abstract" id="2503.17130"> arXiv:2503.17130 </a> [<a href="/pdf/2503.17130" title="Download PDF" id="pdf-2503.17130" aria-labelledby="pdf-2503.17130">pdf</a>, <a href="/format/2503.17130" title="Other formats" id="oth-2503.17130" aria-labelledby="oth-2503.17130">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Persistent cohomology operations and Gromov-Hausdorff estimates </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=M.Medina-Mardones,+A">Anibal M.Medina-Mardones</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhou,+L">Ling Zhou</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 32 pages, 3 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Topology (math.AT)</span> </div> <p class='mathjax'> We establish the foundations of the theory of persistent cohomology operations, derive decomposition formulas for wedge sums and products, and prove their Gromov-Hausdorff stability. We use these results to construct pairs of Riemannian pseudomanifolds for which the Gromov-Hausdorff estimates derived from persistent cohomology operations are strictly sharper than those obtained using persistent homology. </p> </div> </dd> <dt> <a name='item84'>[84]</a> <a href ="/abs/2503.17131" title="Abstract" id="2503.17131"> arXiv:2503.17131 </a> [<a href="/pdf/2503.17131" title="Download PDF" id="pdf-2503.17131" aria-labelledby="pdf-2503.17131">pdf</a>, <a href="https://arxiv.org/html/2503.17131v1" title="View HTML" id="html-2503.17131" aria-labelledby="html-2503.17131" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17131" title="Other formats" id="oth-2503.17131" aria-labelledby="oth-2503.17131">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The triconnected Kontsevich graph complex </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Willwacher,+T">Thomas Willwacher</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Algebra (math.QA)</span>; Algebraic Topology (math.AT) </div> <p class='mathjax'> We show that a smaller version of the Kontsevich graph complex spanned by triconnected graphs is quasi-isomorphic to the full Kontsevich graph complex. </p> </div> </dd> <dt> <a name='item85'>[85]</a> <a href ="/abs/2503.17145" title="Abstract" id="2503.17145"> arXiv:2503.17145 </a> [<a href="/pdf/2503.17145" title="Download PDF" id="pdf-2503.17145" aria-labelledby="pdf-2503.17145">pdf</a>, <a href="/format/2503.17145" title="Other formats" id="oth-2503.17145" aria-labelledby="oth-2503.17145">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Numerical Simulations of Fully Eulerian Fluid-Structure Contact Interaction using a Ghost-Penalty Cut Finite Element Approach </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Frei,+S">Stefan Frei</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Knoke,+T">Tobias Knoke</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Steinbach,+M+C">Marc C. Steinbach</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wenske,+A">Anne-Kathrin Wenske</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wick,+T">Thomas Wick</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 29 pages, 8 figures, 3 tables </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> In this work, we develop a cut-based unfitted finite element formulation for solving nonlinear, nonstationary fluid-structure interaction with contact in Eulerian coordinates. In the Eulerian description fluid flow modeled by the incompressible Navier-Stokes equations remains in Eulerian coordinates, while elastic solids are transformed from Lagrangian coordinates into the Eulerian system. A monolithic description is adopted. For the spatial discretization, we employ an unfitted finite element method with ghost penalties based on inf-sup stable finite elements. To handle contact, we use a relaxation of the contact condition in combination with a unified Nitsche approach that takes care implicitly of the switch between fluid-structure interaction and contact conditions. The temporal discretization is based on a backward Euler scheme with implicit extensions of solutions at the previous time step. The nonlinear system is solved with a semi-smooth Newton's method with line search. Our formulation, discretization and implementation are substantiated with an elastic falling ball that comes into contact with the bottom boundary, constituting a challenging state-of-the-art benchmark. </p> </div> </dd> <dt> <a name='item86'>[86]</a> <a href ="/abs/2503.17149" title="Abstract" id="2503.17149"> arXiv:2503.17149 </a> [<a href="/pdf/2503.17149" title="Download PDF" id="pdf-2503.17149" aria-labelledby="pdf-2503.17149">pdf</a>, <a href="https://arxiv.org/html/2503.17149v1" title="View HTML" id="html-2503.17149" aria-labelledby="html-2503.17149" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17149" title="Other formats" id="oth-2503.17149" aria-labelledby="oth-2503.17149">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A spectrum-level splitting of the $ku_\mathbb{R}$-cooperations algebra </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Li,+G">Guchuan Li</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Petersen,+S">Sarah Petersen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tatum,+E">Elizabeth Tatum</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Comments welcome </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Topology (math.AT)</span> </div> <p class='mathjax'> In the 1980's, Mahowald and Kane used integral Brown--Gitler spectra to decompose $ku \wedge ku$ as a sum of finitely generated $ku$-module spectra. This splitting, along with an analogous decomposition of $ko \wedge ko$ led to a great deal of progress in stable homotopy computations and understanding of $v_1$-periodicity in the stable homotopy groups of spheres. In this paper, we construct a $C_2$-equivariant lift of Mahowald and Kane's splitting of $ku \wedge ku$. We also give a description of the resulting $C_2$-equivariant splitting in terms of $C_2$-equivariant Adams covers and record an analogous splitting for $H\underline{\mathbb{Z}} \wedge H \underline{\mathbb{Z}}$. Similarly to the nonequivariant story, we expect the techniques of this paper to facilitate further $C_2$-equivariant stable homotopy computations and understanding of $v_1$-periodicity in $C_2$-equivariant stable stems. </p> </div> </dd> <dt> <a name='item87'>[87]</a> <a href ="/abs/2503.17152" title="Abstract" id="2503.17152"> arXiv:2503.17152 </a> [<a href="/pdf/2503.17152" title="Download PDF" id="pdf-2503.17152" aria-labelledby="pdf-2503.17152">pdf</a>, <a href="/format/2503.17152" title="Other formats" id="oth-2503.17152" aria-labelledby="oth-2503.17152">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Note on Mixed Cages of Girth 5 </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Araujo-Pardo,+G">Gabriela Araujo-Pardo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mendoza-Cadena,+L+M">Lydia Mirabel Mendoza-Cadena</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> A mixed regular graph is a graph where every vertex has $z$ incoming arcs, $z$ outgoing arcs, and $r$ edges; furthermore, if it has girth $g$, we say that the graph is a \emph{$[z,r;g]$-mixed graph}. A \emph{$[z,r;g]$-mixed cage} is a $[z,r;g]$-mixed graph with the smallest possible order. In this note, we give a family of $[z,q;5]$-mixed graphs for $q\geq 7$ power of prime and $q-1\leq 4z+R$ with $z\geq 1$ and $R \in \{1,\ldots,5\}$. This provides better upper bounds on the order of mixed cages until this moment. </p> </div> </dd> <dt> <a name='item88'>[88]</a> <a href ="/abs/2503.17159" title="Abstract" id="2503.17159"> arXiv:2503.17159 </a> [<a href="/pdf/2503.17159" title="Download PDF" id="pdf-2503.17159" aria-labelledby="pdf-2503.17159">pdf</a>, <a href="https://arxiv.org/html/2503.17159v1" title="View HTML" id="html-2503.17159" aria-labelledby="html-2503.17159" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17159" title="Other formats" id="oth-2503.17159" aria-labelledby="oth-2503.17159">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Bi-intuitionistic logics through the abstract algebraic logic lens </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Deakin,+J">Jonte Deakin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Shillito,+I">Ian Shillito</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic (math.LO)</span> </div> <p class='mathjax'> Since the discovery of critical mistakes in Rauszer's work on bi-intuitionistic logics, solid foundations for these have progressively been rebuilt. However, the algebraic treatment of these logics has not yet been tended to. We fill this gap by algebraically analysing the bi-intuitionistic logics wBIL and sBIL. Given that these logics are only distinguished as consequence relations, and not as sets of theorems (hence the conflation in Rauszer's work), the algebraic tools we use are tailored to the treatment of such relations. We mainly inspect these logics through the lens of abstract algebraic logic, but we also provide an alternative algebraic analysis of wBIL and sBIL as logic preserving degrees of truth and truth, respectively. Our results pertaining to wBIL and sBIL are formalised in the interactive theorem prover Rocq. </p> </div> </dd> <dt> <a name='item89'>[89]</a> <a href ="/abs/2503.17160" title="Abstract" id="2503.17160"> arXiv:2503.17160 </a> [<a href="/pdf/2503.17160" title="Download PDF" id="pdf-2503.17160" aria-labelledby="pdf-2503.17160">pdf</a>, <a href="https://arxiv.org/html/2503.17160v1" title="View HTML" id="html-2503.17160" aria-labelledby="html-2503.17160" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17160" title="Other formats" id="oth-2503.17160" aria-labelledby="oth-2503.17160">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Characterizing simplex graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Xie,+Y">Yan-Ting Xie</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Xu,+S">Shou-Jun Xu</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 12 pages, 4 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> The simplex graph $S(G)$ of a graph $G$ is defined as the graph whose vertices are the cliques of $G$ (including the empty set), with two vertices being adjacent if, as cliques of $G$, they differ in exactly one vertex. Simplex graphs form a subclass of median graphs and include many well-known families of graphs, such as gear graphs, Fibonacci cubes and Lucas cubes. <br>In this paper, we characterize simplex graphs from four different perspectives: the first focuses on a graph class associated with downwards-closed sets -- namely, the daisy cubes; the second identifies all forbidden partial cube-minors of simplex graphs; the third is from the perspective of the $\Theta$ equivalent classes; and the fourth explores the relationship between the maximum degree and the isometric dimension. Furthermore, very recently, Betre et al.\ [K. H. Betre, Y. X. Zhang, C. Edmond, Pure simplicial and clique complexes with a fixed number of facets, 2024, arXiv: <a href="https://arxiv.org/abs/2411.12945v1" data-arxiv-id="2411.12945v1" class="link-https">2411.12945v1</a>] proved that an abstract simplicial complex (i.e., an independence system) of a finite set can be represented to a clique complex of a graph if and only if it satisfies the Weak Median Property. As a corollary, we rederive this result by using the graph-theoretical method. </p> </div> </dd> <dt> <a name='item90'>[90]</a> <a href ="/abs/2503.17163" title="Abstract" id="2503.17163"> arXiv:2503.17163 </a> [<a href="/pdf/2503.17163" title="Download PDF" id="pdf-2503.17163" aria-labelledby="pdf-2503.17163">pdf</a>, <a href="https://arxiv.org/html/2503.17163v1" title="View HTML" id="html-2503.17163" aria-labelledby="html-2503.17163" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17163" title="Other formats" id="oth-2503.17163" aria-labelledby="oth-2503.17163">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Quantum geometric tensors from sub-bundle geometry </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Oancea,+M+A">Marius A. Oancea</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Mieling,+T+B">Thomas B. Mieling</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Palumbo,+G">Giandomenico Palumbo</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; Mesoscale and Nanoscale Physics (cond-mat.mes-hall); General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph) </div> <p class='mathjax'> The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. In this work, we use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. This construction is based on an arbitrary connection on a Hermitian vector bundle, which defines a notion of quantum state transport in parameter space, and a sub-bundle projector, which constrains the set of accessible quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by a generalization of the Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor, which contains an additional curvature contribution. To illustrate our results, we describe the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor, with its additional curvature contributions, is obtained in this case. As a concrete example, we consider Dirac fermions confined to a hyperbolic plane and demonstrate how spatial curvature influences the quantum geometry. This work sets the stage for further exploration of quantum systems in curved geometries, with applications in both high-energy physics and condensed matter systems. </p> </div> </dd> <dt> <a name='item91'>[91]</a> <a href ="/abs/2503.17176" title="Abstract" id="2503.17176"> arXiv:2503.17176 </a> [<a href="/pdf/2503.17176" title="Download PDF" id="pdf-2503.17176" aria-labelledby="pdf-2503.17176">pdf</a>, <a href="https://arxiv.org/html/2503.17176v1" title="View HTML" id="html-2503.17176" aria-labelledby="html-2503.17176" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17176" title="Other formats" id="oth-2503.17176" aria-labelledby="oth-2503.17176">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On high discrepancy $1$-factorizations of complete graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ai,+J">Jiangdong Ai</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=He,+F">Fankang He</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Im,+S">Seonghyuk Im</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lee,+H">Hyunwoo Lee</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> We proved that for every sufficiently large $n$, the complete graph $K_{2n}$ with an arbitrary edge signing $\sigma: E(K_{2n}) \to \{-1, +1\}$ admits a high discrepancy $1$-factor decomposition. That is, there exists a universal constant $c > 0$ such that every edge-signed $K_{2n}$ has a perfect matching decomposition $\{\psi_1, \ldots, \psi_{2n-1}\}$, where for each perfect matching $\psi_i$, the discrepancy $\lvert \frac{1}{n} \sum_{e\in E(\psi_i)} \sigma(e) \rvert$ is at least $c$. </p> </div> </dd> <dt> <a name='item92'>[92]</a> <a href ="/abs/2503.17177" title="Abstract" id="2503.17177"> arXiv:2503.17177 </a> [<a href="/pdf/2503.17177" title="Download PDF" id="pdf-2503.17177" aria-labelledby="pdf-2503.17177">pdf</a>, <a href="https://arxiv.org/html/2503.17177v1" title="View HTML" id="html-2503.17177" aria-labelledby="html-2503.17177" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17177" title="Other formats" id="oth-2503.17177" aria-labelledby="oth-2503.17177">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Isoperimetric bubbles in spaces with density $r^p + a$ </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gwynne,+M">Martyn Gwynne</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Cox,+S">Simon Cox</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 22 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> Least perimeter solutions for a region with fixed mass are sought in ${\mathbb{R}^d}$ on which a density function $\rho(r) = r^p+a$, with $p>0, a>0$, weights both perimeter and mass. On the real line ($d=1$) this is a single interval that includes the origin. For $p \le 1$ the isoperimetric interval has one end at the origin; for larger $p$ there is a critical value of $a$ above which the interval is symmetric about the origin. In the case $p=2$, for $d=2$ and $3$, the isoperimetric region is a circle or sphere, respectively, that includes the origin; the centre moves towards the origin as $a$ increases, with constant radius, and then remains centred on the origin for $a$ above the critical value as the radius decreases. </p> </div> </dd> <dt> <a name='item93'>[93]</a> <a href ="/abs/2503.17178" title="Abstract" id="2503.17178"> arXiv:2503.17178 </a> [<a href="/pdf/2503.17178" title="Download PDF" id="pdf-2503.17178" aria-labelledby="pdf-2503.17178">pdf</a>, <a href="https://arxiv.org/html/2503.17178v1" title="View HTML" id="html-2503.17178" aria-labelledby="html-2503.17178" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17178" title="Other formats" id="oth-2503.17178" aria-labelledby="oth-2503.17178">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Eigenvalue collisions for periodic matrix families associated with Ginibre matrices </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Vargas,+C">Carlos Vargas</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We study the eigenvalue collisions for certain families of matrices $$R(s,t) = \cos(s \pi / 2)C + \sin(s \pi / 2)U(t), \quad s,t \in [0,1]$$ where $C$ is a realization of a Ginibre random matrix and $U(t)$ is a $t$-periodic matrix with eigenvalues flowing along a parametrized curve. </p> </div> </dd> <dt> <a name='item94'>[94]</a> <a href ="/abs/2503.17187" title="Abstract" id="2503.17187"> arXiv:2503.17187 </a> [<a href="/pdf/2503.17187" title="Download PDF" id="pdf-2503.17187" aria-labelledby="pdf-2503.17187">pdf</a>, <a href="https://arxiv.org/html/2503.17187v1" title="View HTML" id="html-2503.17187" aria-labelledby="html-2503.17187" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17187" title="Other formats" id="oth-2503.17187" aria-labelledby="oth-2503.17187">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Hankel Determinants for Convolution of Power Series: An Extension of Cigler's Results </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+F">Feihu Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+Y">Ying Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+Y">Yingrui Zhang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+Z">Zihao Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> Cigler considered certain shifted Hankel determinants of convolution powers of Catalan numbers and conjectured identities for these determinants. Recently, Fulmek gave a bijective proof of Cigler's conjecture. Cigler then provided a computational proof. We extend Cigler's determinant identities to the convolution of general power series $F(x)$, where $F(x)$ satisfies a certain type of quadratic equation. As an application, we present the Hankel determinant identities of convolution powers of Motzkin numbers. </p> </div> </dd> <dt> <a name='item95'>[95]</a> <a href ="/abs/2503.17190" title="Abstract" id="2503.17190"> arXiv:2503.17190 </a> [<a href="/pdf/2503.17190" title="Download PDF" id="pdf-2503.17190" aria-labelledby="pdf-2503.17190">pdf</a>, <a href="https://arxiv.org/html/2503.17190v1" title="View HTML" id="html-2503.17190" aria-labelledby="html-2503.17190" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17190" title="Other formats" id="oth-2503.17190" aria-labelledby="oth-2503.17190">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Babu拧ka's paradox in a nonlinear bending model </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bartels,+S">S枚ren Bartels</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Bonito,+A">Andrea Bonito</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Hornung,+P">Peter Hornung</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Neunteufel,+M">Michael Neunteufel</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> The Babu拧ka or plate paradox concerns the failure of convergence when a domain with curved boundary is approximated by polygonal domains in linear bending problems with simple support boundary conditions. It can be explained via a boundary integral representation of the total Gaussian curvature that is part of the Kirchhoff--Love bending energy. It is shown that the paradox also occurs for a nonlinear bending-folding model which enforces vanishing Gaussian curvature. A simple remedy that is compatible with simplicial finite element methods to avoid wrong convergence is devised. </p> </div> </dd> <dt> <a name='item96'>[96]</a> <a href ="/abs/2503.17228" title="Abstract" id="2503.17228"> arXiv:2503.17228 </a> [<a href="/pdf/2503.17228" title="Download PDF" id="pdf-2503.17228" aria-labelledby="pdf-2503.17228">pdf</a>, <a href="https://arxiv.org/html/2503.17228v1" title="View HTML" id="html-2503.17228" aria-labelledby="html-2503.17228" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17228" title="Other formats" id="oth-2503.17228" aria-labelledby="oth-2503.17228">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Mean value of cubic $L$-funcitons with fixed genus </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Hong,+Z">Ziwei Hong</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Fang,+Z">Zhongqiu Fang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zheng,+Z">Zhiyong Zheng</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span> </div> <p class='mathjax'> We investigate the mean value of the first moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum <br>\begin{equation*} <br>\sum_{\substack{\chi\ primitive\ cubic\\ genus(\chi)=g}}L_q(\frac{1}{2}, \chi), <br>\end{equation*} where $L_q(s,\chi)$ denotes the $L$-function associated with primitive cubic character $\chi$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{7}{8}+\varepsilon)g}$. </p> </div> </dd> <dt> <a name='item97'>[97]</a> <a href ="/abs/2503.17232" title="Abstract" id="2503.17232"> arXiv:2503.17232 </a> [<a href="/pdf/2503.17232" title="Download PDF" id="pdf-2503.17232" aria-labelledby="pdf-2503.17232">pdf</a>, <a href="https://arxiv.org/html/2503.17232v1" title="View HTML" id="html-2503.17232" aria-labelledby="html-2503.17232" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17232" title="Other formats" id="oth-2503.17232" aria-labelledby="oth-2503.17232">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> High moments of 2d directed polymers up to quasi-criticality </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cosco,+C">Cl茅ment Cosco</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Nakajima,+S">Shuta Nakajima</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 39 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We consider two-dimensional directed polymers in random environment in the sub-critical regime and in the quasi-critical regime introduced recently by Caravenna, Cottini and Rossi, <a href="https://arxiv.org/abs/2307.02453v1" data-arxiv-id="2307.02453v1" class="link-https">arXiv:2307.02453v1</a>. For $q\leq q_N$ with $q_N\to\infty$ diverging at a suitable rate with the size of the system, we obtain upper bound estimates on the $q$-moment of the partition function for general environments. In the sub-critical regime, our results improve the $q_N$-threshold obtained for Gaussian environment in Cosco, Zeitouni, Comm. Math. Phys (2023). As a corollary, we derive large deviation estimates with a Gaussian rate function. </p> </div> </dd> <dt> <a name='item98'>[98]</a> <a href ="/abs/2503.17234" title="Abstract" id="2503.17234"> arXiv:2503.17234 </a> [<a href="/pdf/2503.17234" title="Download PDF" id="pdf-2503.17234" aria-labelledby="pdf-2503.17234">pdf</a>, <a href="https://arxiv.org/html/2503.17234v1" title="View HTML" id="html-2503.17234" aria-labelledby="html-2503.17234" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17234" title="Other formats" id="oth-2503.17234" aria-labelledby="oth-2503.17234">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> High Accuracy Techniques Based Adaptive Finite Element Methods for Elliptic PDEs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Xiao,+J">Jingjing Xiao</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+Y">Ying Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yi,+N">Nianyu Yi</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection refinement has been well established, in practical computations, the use of non-asymptotic exact of error estimator and the excessive number of adaptive iteration steps often lead to inefficiency of the adaptive algorithm. We propose an efficient adaptive finite element method based on high-accuracy techniques including the superconvergence recovery technique and high-quality mesh optimization. The centroidal Voronoi Delaunay triangulation mesh optimization is embedded in the mesh adaption to provide high-quality mesh, and then assure that the superconvergence property of the recovered gradient and the asymptotical exactness of the error estimator. A tailored adaptive strategy, which could generate high-quality meshes with a target number of vertices, is developed to ensure the adaptive computation process terminated within $7$ steps. The effectiveness and robustness of the adaptive algorithm is numerically demonstrated. </p> </div> </dd> <dt> <a name='item99'>[99]</a> <a href ="/abs/2503.17236" title="Abstract" id="2503.17236"> arXiv:2503.17236 </a> [<a href="/pdf/2503.17236" title="Download PDF" id="pdf-2503.17236" aria-labelledby="pdf-2503.17236">pdf</a>, <a href="https://arxiv.org/html/2503.17236v1" title="View HTML" id="html-2503.17236" aria-labelledby="html-2503.17236" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17236" title="Other formats" id="oth-2503.17236" aria-labelledby="oth-2503.17236">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The maximum of the two dimensional Gaussian directed polymer in the subcritical regime </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cosco,+C">Cl茅ment Cosco</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Nakajima,+S">Shuta Nakajima</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zeitouni,+O">Ofer Zeitouni</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 26 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We study the maximum $\phi_N^*$ of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an $\sqrt N \times \sqrt N$ box. We show that $\phi_N^*/\log N$ converges towards a constant $\sigma^*$, which we identify to be the same as for the maximum of a branching random walk with a slowly varying variance profile as studied in Fang-Zeitouni, J. Stat. Phys. 2012 and (in the context of the generalized random energy model) in Bovier-Kurkova, Ann. Inst. H. Poincare 2004. </p> </div> </dd> <dt> <a name='item100'>[100]</a> <a href ="/abs/2503.17255" title="Abstract" id="2503.17255"> arXiv:2503.17255 </a> [<a href="/pdf/2503.17255" title="Download PDF" id="pdf-2503.17255" aria-labelledby="pdf-2503.17255">pdf</a>, <a href="https://arxiv.org/html/2503.17255v1" title="View HTML" id="html-2503.17255" aria-labelledby="html-2503.17255" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17255" title="Other formats" id="oth-2503.17255" aria-labelledby="oth-2503.17255">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Perturbed Kullback-Leibler Deviation Bounds for Dirichlet Processes </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Perrault,+P">Pierre Perrault</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We present new and improved non-asymptotic deviation bounds for Dirichlet processes (DPs), formulated using the Kullback-Leibler (KL) divergence, which is known for its optimal characterization of the asymptotic behavior of DPs. Our method involves incorporating a controlled perturbation within the KL bound, effectively shifting the base distribution of the DP in the upper bound. Our proofs rely on two independent approaches. In the first, we use superadditivity techniques to convert asymptotic bounds into non-asymptotic ones via Fekete's lemma. In the second, we carefully reduce the problem to the Beta distribution case. Some of our results extend similar inequalities derived for the Beta distribution, as presented in [27]. </p> </div> </dd> <dt> <a name='item101'>[101]</a> <a href ="/abs/2503.17256" title="Abstract" id="2503.17256"> arXiv:2503.17256 </a> [<a href="/pdf/2503.17256" title="Download PDF" id="pdf-2503.17256" aria-labelledby="pdf-2503.17256">pdf</a>, <a href="https://arxiv.org/html/2503.17256v1" title="View HTML" id="html-2503.17256" aria-labelledby="html-2503.17256" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17256" title="Other formats" id="oth-2503.17256" aria-labelledby="oth-2503.17256">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Pullback parking functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Elder,+J">Jennifer Elder</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Harris,+P+E">Pamela E. Harris</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Koene,+L">Lybitina Koene</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lavene,+I">Ilana Lavene</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Martinez,+L">Lucy Martinez</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Oldham,+M">Molly Oldham</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 7 figures </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> American Journal of Combinatorics Vol. 4 (2025) 1--22 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> We introduce a generalization of parking functions in which cars are limited in their movement backwards and forwards by two nonnegative integer parameters $k$ and $\ell$, respectively. In this setting, there are $n$ spots on a one-way street and $m$ cars attempting to park in those spots, and $1\leq m\leq n$. We let $\alpha=(a_1,a_2,\ldots,a_m)\in[n]^m$ denote the parking preferences for the cars, which enter the street sequentially. Car $i$ drives to their preference $a_i$ and parks there if the spot is available. Otherwise, car $i$ checks up to $k$ spots behind their preference, parking in the first available spot it encounters if any. If no spots are available, or the car reaches the start of the street, then the car returns to its preference and attempts to park in the first spot it encounters among spots $a_i+1,a_i+2,\ldots,a_i+\ell$. If car $i$ fails to park, then parking ceases. If all cars are able to park given the preferences in $\alpha$, then $\alpha$ is called a $(k,\ell)$-pullback $(m,n)$-parking function. Our main result establishes counts for these parking functions in two ways: counting them based on their final parking outcome (the order in which the cars park on the street), and via a recursive formula. Specializing $\ell=n-1$, our result gives a new formula for the number of $k$-Naples $(m,n)$-parking functions and further specializing $m=n$ recovers a formula for the number of $k$-Naples parking functions given by Christensen et al. The specialization of $k=\ell=1$, gives a formula for the number of vacillating $(m,n)$-parking functions, a generalization of vacillating parking functions studied by Fang et al., and the $m=n$ result answers a problem posed by the authors. We conclude with a few directions for further study. </p> </div> </dd> <dt> <a name='item102'>[102]</a> <a href ="/abs/2503.17260" title="Abstract" id="2503.17260"> arXiv:2503.17260 </a> [<a href="/pdf/2503.17260" title="Download PDF" id="pdf-2503.17260" aria-labelledby="pdf-2503.17260">pdf</a>, <a href="https://arxiv.org/html/2503.17260v1" title="View HTML" id="html-2503.17260" aria-labelledby="html-2503.17260" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17260" title="Other formats" id="oth-2503.17260" aria-labelledby="oth-2503.17260">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Contact process for the spread of knowledge </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Lanchier,+N">Nicolas Lanchier</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mercer,+M">Max Mercer</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yun,+H">Hyunsik Yun</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages, 3 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> This paper is concerned with a natural variant of the contact process modeling the spread of knowledge on the integer lattice. Each site is characterized by its knowledge, measured by a real number ranging from 0 = ignorant to 1 = omniscient. Neighbors interact at rate $\lambda$, which results in both neighbors attempting to teach each other a fraction $\mu$ of their knowledge, and individuals die at rate one, which results in a new individual with no knowledge. Starting with a single omniscient site, our objective is to study whether the total amount of knowledge on the lattice converges to zero (extinction) or remains bounded away from zero (survival). The process dies out when $\lambda \leq \lambda_c$ and/or $\mu = 0$, where $\lambda_c$ denotes the critical value of the contact process. In contrast, we prove that, for all $\lambda > \lambda_c$, there is a unique phase transition in the direction of $\mu$, and for all $\mu > 0$, there is a unique phase transition in the direction of $\lambda$. Our proof of survival relies on block constructions showing more generally convergence of the knowledge to infinity, while our proof of extinction relies on martingale techniques showing more generally an exponential decay of the knowledge. </p> </div> </dd> <dt> <a name='item103'>[103]</a> <a href ="/abs/2503.17268" title="Abstract" id="2503.17268"> arXiv:2503.17268 </a> [<a href="/pdf/2503.17268" title="Download PDF" id="pdf-2503.17268" aria-labelledby="pdf-2503.17268">pdf</a>, <a href="https://arxiv.org/html/2503.17268v1" title="View HTML" id="html-2503.17268" aria-labelledby="html-2503.17268" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17268" title="Other formats" id="oth-2503.17268" aria-labelledby="oth-2503.17268">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Dimensional reduction of dynamical systems on graphons </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Eldo,+B+M">Bisna Mary Eldo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rakshit,+S">Sarbendu Rakshit</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Masuda,+N">Naoki Masuda</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 8 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> Dynamical systems on networks are inherently high-dimensional unless the number of nodes is extremely small. Dimension reduction methods for dynamical systems on networks aim to find a substantially lower-dimensional system that preserves key properties of the original dynamics such as bifurcation structure. A class of such methods proposed in network science research entails finding a one- (or low-) dimensional system that a particular weighted average of the state variables of all nodes in the network approximately obeys. We formulate and mathematically analyze this dimension reduction technique for dynamical systems on dense graphons, or the limiting, infinite-dimensional object of a sequence of graphs with an increasing number of nodes. We first theoretically justify the continuum limit for a nonlinear dynamical system of our interest, and the existence and uniqueness of the solution of graphon dynamical systems. We then derive the reduced one-dimensional system on graphons and prove its convergence properties. Finally, we perform numerical simulations for various graphons and dynamical system models to assess the accuracy of the one-dimensional approximation. </p> </div> </dd> <dt> <a name='item104'>[104]</a> <a href ="/abs/2503.17273" title="Abstract" id="2503.17273"> arXiv:2503.17273 </a> [<a href="/pdf/2503.17273" title="Download PDF" id="pdf-2503.17273" aria-labelledby="pdf-2503.17273">pdf</a>, <a href="https://arxiv.org/html/2503.17273v1" title="View HTML" id="html-2503.17273" aria-labelledby="html-2503.17273" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17273" title="Other formats" id="oth-2503.17273" aria-labelledby="oth-2503.17273">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Real subrank of order-three tensors </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Biaggi,+B">Benjamin Biaggi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Draisma,+J">Jan Draisma</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Eggleston,+S">Sarah Eggleston</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 14 pages; comments welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> We study the subrank of real order-three tensors and give an upper bound to the subrank of a real tensor given its complex subrank. Using similar arguments to those used by Bernardi-Blekherman-Ottaviani, we show that all subranks between the minimal typical subrank and the maximal typical subrank, which equals the generic subrank, are also typical. We then study small tensor formats with more than one typical subrank. In particular, we construct a $3 \times 3 \times 5$-tensor with subrank $2$ and show that the subrank of the $4 \times 4 \times 4$-quaternion multiplication tensor is $2$. Finally, we consider the tensor associated to componentwise complex multiplication in $\mathbb{C}^n$ and show that this tensor has real subrank $n$ - informally, no more than $n$ real scalar multiplications can be carried out using a device that does $n$ complex scalar multiplications. We also prove a version of this result for other real division algebras. </p> </div> </dd> <dt> <a name='item105'>[105]</a> <a href ="/abs/2503.17274" title="Abstract" id="2503.17274"> arXiv:2503.17274 </a> [<a href="/pdf/2503.17274" title="Download PDF" id="pdf-2503.17274" aria-labelledby="pdf-2503.17274">pdf</a>, <a href="/format/2503.17274" title="Other formats" id="oth-2503.17274" aria-labelledby="oth-2503.17274">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Composable Uncertainty in Symmetric Monoidal Categories for Design Problems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Furter,+M">Marius Furter</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Huang,+Y">Yujun Huang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zardini,+G">Gioele Zardini</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 22 pages, 2 figures, submitted to Applied Category Theory 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Category Theory (math.CT)</span>; Systems and Control (eess.SY) </div> <p class='mathjax'> Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging wires, or compact closed structures for feedback. A key example is the compact closed SMC of design problems (DP), which enables a compositional approach to co-design in engineering. However, in practice, the systems of interest may not be fully known. Recently, Markov categories have emerged as a powerful framework for modeling uncertain processes. In this work, we demonstrate how to integrate this perspective into the study of open systems while preserving consistency with the underlying SMC structure. To this end, we employ the change-of-base construction for enriched categories, replacing the morphisms of a symmetric monoidal $\mathcal{V}$-category $\mathcal{C}$ with parametric maps $A \to \mathcal{C}(X,Y)$ in a Markov category induced by a symmetric monoidal monad. This results in a symmetric monoidal 2-category $N_*\mathcal{C}$ with the same objects as $\mathcal{C}$ and reparametrization 2-cells. By choosing different monads, we capture various types of uncertainty. The category underlying $\mathcal{C}$ embeds into $N_*\mathcal{C}$ via a strict symmetric monoidal functor, allowing (co)monoidal and compact closed structures to be transferred. Applied to DP, this construction leads to categories of practical relevance, such as parametrized design problems for optimization, and parametrized distributions of design problems for decision theory and Bayesian learning. </p> </div> </dd> <dt> <a name='item106'>[106]</a> <a href ="/abs/2503.17277" title="Abstract" id="2503.17277"> arXiv:2503.17277 </a> [<a href="/pdf/2503.17277" title="Download PDF" id="pdf-2503.17277" aria-labelledby="pdf-2503.17277">pdf</a>, <a href="/format/2503.17277" title="Other formats" id="oth-2503.17277" aria-labelledby="oth-2503.17277">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Fraser,+R">Robert Fraser</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 16 Pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Classical Analysis and ODEs (math.CA)</span>; Number Theory (math.NT) </div> <p class='mathjax'> We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support measures whose Fourier transform decays to zero. </p> </div> </dd> <dt> <a name='item107'>[107]</a> <a href ="/abs/2503.17300" title="Abstract" id="2503.17300"> arXiv:2503.17300 </a> [<a href="/pdf/2503.17300" title="Download PDF" id="pdf-2503.17300" aria-labelledby="pdf-2503.17300">pdf</a>, <a href="https://arxiv.org/html/2503.17300v1" title="View HTML" id="html-2503.17300" aria-labelledby="html-2503.17300" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17300" title="Other formats" id="oth-2503.17300" aria-labelledby="oth-2503.17300">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Variational Tail Bounds for Norms of Random Vectors and Matrices </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bahmani,+S">Sohail Bahmani</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. We also propose a simplified version of the bound that parametrizes the ``aggregating'' distribution in the proposed variational bound by considering a certain pushforward of the Gaussian distribution. Furthermore, we show that the proposed method recovers some of the well-known bounds on norms of Gaussian random vectors, as well as a recent concentration inequality for the spectral norm of sum of independent and identically distributed positive semidefinite matrices. </p> </div> </dd> <dt> <a name='item108'>[108]</a> <a href ="/abs/2503.17312" title="Abstract" id="2503.17312"> arXiv:2503.17312 </a> [<a href="/pdf/2503.17312" title="Download PDF" id="pdf-2503.17312" aria-labelledby="pdf-2503.17312">pdf</a>, <a href="/format/2503.17312" title="Other formats" id="oth-2503.17312" aria-labelledby="oth-2503.17312">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Quasiconformal Maps between Bowditch Boundaries of Relatively Hyperbolic Groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Sardar,+R">Rana Sardar</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 25 pages, 9 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Geometric Topology (math.GT)</span> </div> <p class='mathjax'> Classifying groups up to quasi-isometry is a fundamental problem in geometric group theory. In the context of hyperbolic and relatively hyperbolic groups, one of the key invariants in this classification is the boundary at infinity. F. Paulin proved that two hyperbolic groups are quasi-isometric if and only if their Gromov boundaries are quasiconformally equivalent. In this article, we extend Paulin's result to relatively hyperbolic groups and their Bowditch boundaries. <br>A notion of quasiconformal map preserving the shadows of horoballs relative to a point at the Bowditch boundary is defined and we have shown that every coarsely cusp-preserving quasi-isometry between two relatively hyperbolic groups induces a shadow-preserving quasiconformal map between their Bowditch boundaries. Conversely, we have shown that if the Bowditch boundaries of two relatively hyperbolic groups are quasiconformally equivalent and the quasiconformal map coarsely preserves the shadows of horoballs relative to each boundary point, then the quasiconformal map induces a coarsely cusp-preserving quasi-isometry between those groups. </p> </div> </dd> <dt> <a name='item109'>[109]</a> <a href ="/abs/2503.17319" title="Abstract" id="2503.17319"> arXiv:2503.17319 </a> [<a href="/pdf/2503.17319" title="Download PDF" id="pdf-2503.17319" aria-labelledby="pdf-2503.17319">pdf</a>, <a href="/format/2503.17319" title="Other formats" id="oth-2503.17319" aria-labelledby="oth-2503.17319">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The algebraic internal groupoid model of Martin-L枚f type theory </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Hughes,+C">Calum Hughes</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 41 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Category Theory (math.CT)</span>; Logic (math.LO) </div> <p class='mathjax'> We extend the model structure on the category $\mathbf{Cat}(\mathcal{E})$ of internal categories studied by Everaert, Kieboom and Van der Linden to an algebraic model structure. Moreover, we show that it restricts to the category of internal groupoids. We show that in this case, the algebraic weak factorisation system that consists of the algebraic trivial cofibrations and algebraic fibrations forms a model of Martin-L枚f type theory. Taking $\mathcal{E} = \mathbf{Set}$ and forgetting the algebraic structure, this recovers Hofmann and Streicher's groupoid model of Martin-L枚f type theory. Finally, we are able to provide axioms on a $(2,1)$-category which ensure that it gives an algebraic model of Martin-L枚f type theory. </p> </div> </dd> <dt> <a name='item110'>[110]</a> <a href ="/abs/2503.17321" title="Abstract" id="2503.17321"> arXiv:2503.17321 </a> [<a href="/pdf/2503.17321" title="Download PDF" id="pdf-2503.17321" aria-labelledby="pdf-2503.17321">pdf</a>, <a href="https://arxiv.org/html/2503.17321v1" title="View HTML" id="html-2503.17321" aria-labelledby="html-2503.17321" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17321" title="Other formats" id="oth-2503.17321" aria-labelledby="oth-2503.17321">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Resolution of singularities for the dynamical mathematician </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Abramovich,+D">Dan Abramovich</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18 pages, 4 figures. These are lecture notes for a minicourse by the same title delivered at the CIRM conference "Foliations, birational geometry and applications", 3-7 February, 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> I begin by explaining to non-specialists why resolution of singularities in characteristic 0 works. Then I go into some ideas telling how it actually works. I finish with a brief discussion of related results on foliations. <br>I report on work with Andr茅 Belotto da Silva, Michael Temkin, and Jaros艂aw W艂odarczyk; any claim to originality is joint with them and appears in the paper [AdSTW25]. </p> </div> </dd> <dt> <a name='item111'>[111]</a> <a href ="/abs/2503.17326" title="Abstract" id="2503.17326"> arXiv:2503.17326 </a> [<a href="/pdf/2503.17326" title="Download PDF" id="pdf-2503.17326" aria-labelledby="pdf-2503.17326">pdf</a>, <a href="https://arxiv.org/html/2503.17326v1" title="View HTML" id="html-2503.17326" aria-labelledby="html-2503.17326" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17326" title="Other formats" id="oth-2503.17326" aria-labelledby="oth-2503.17326">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Action accessible and weakly action representable varieties of algebras </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Garc%C3%ADa-Mart%C3%ADnez,+X">Xabier Garc铆a-Mart铆nez</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mancini,+M">Manuel Mancini</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Category Theory (math.CT)</span> </div> <p class='mathjax'> The main goal of this article is to investigate the relationship between action accessibility and weak action representability in the context of varieties of non-associative algebras over a field. Specifically, using an argument of J. R. A. Gray in the setting of groups, we prove that the varieties of $k$-nilpotent Lie algebras ($k \geq 3$) and the varieties of $n$-solvable Lie algebras ($n \geq 2$) do not form weakly action representable categories. These are the first known examples of action accessible varieties of non-associative algebras that fail to be weakly action representable, establishing that a subvariety of a (weakly) action representable variety of non-associative algebras needs not be weakly action representable. Eventually, we refine J. R. A. Gray's result by proving that the varieties of $k$-nilpotent groups ($k \geq 3$) and that of $2$-solvable groups are not weakly action representable. </p> </div> </dd> <dt> <a name='item112'>[112]</a> <a href ="/abs/2503.17330" title="Abstract" id="2503.17330"> arXiv:2503.17330 </a> [<a href="/pdf/2503.17330" title="Download PDF" id="pdf-2503.17330" aria-labelledby="pdf-2503.17330">pdf</a>, <a href="https://arxiv.org/html/2503.17330v1" title="View HTML" id="html-2503.17330" aria-labelledby="html-2503.17330" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17330" title="Other formats" id="oth-2503.17330" aria-labelledby="oth-2503.17330">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Counting Frobenius Pseudoprimes </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Fiori,+A">Andrew Fiori</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Gheisari,+H">Hiva Gheisari</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span> </div> <p class='mathjax'> We generalize the work of Erdos-Pomerance and Fiori-Shallue on counting Frobenius pseudoprimes from the cases of degree one and two respectively to arbitrary degree. More specifically we provide formulas for counting the number of false witnesses for a number $n$ with respect to Grantham's Frobenius primality test. We also provide conditional assymptotic lower bounds on the average number of Frobenius pseudoprimes and assymptotic upper bounds on the same. </p> </div> </dd> <dt> <a name='item113'>[113]</a> <a href ="/abs/2503.17331" title="Abstract" id="2503.17331"> arXiv:2503.17331 </a> [<a href="/pdf/2503.17331" title="Download PDF" id="pdf-2503.17331" aria-labelledby="pdf-2503.17331">pdf</a>, <a href="https://arxiv.org/html/2503.17331v1" title="View HTML" id="html-2503.17331" aria-labelledby="html-2503.17331" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17331" title="Other formats" id="oth-2503.17331" aria-labelledby="oth-2503.17331">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Topological Data Analysis Framework for Quantifying Necrosis in Glioblastomas </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Tellez,+F">Francisco Tellez</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Torres-Giese,+E">Enrique Torres-Giese</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Topology (math.AT)</span>; Computer Vision and Pattern Recognition (cs.CV) </div> <p class='mathjax'> In this paper, we introduce a shape descriptor that we call "interior function". This is a Topological Data Analysis (TDA) based descriptor that refines previous descriptors for image analysis. Using this concept, we define subcomplex lacunarity, a new index that quantifies geometric characteristics of necrosis in tumors such as conglomeration. Building on this framework, we propose a set of indices to analyze necrotic morphology and construct a diagram that captures the distinct structural and geometric properties of necrotic regions in tumors. We present an application of this framework in the study of MRIs of Glioblastomas (GB). Using cluster analysis, we identify four distinct subtypes of Glioblastomas that reflect geometric properties of necrotic regions. </p> </div> </dd> <dt> <a name='item114'>[114]</a> <a href ="/abs/2503.17334" title="Abstract" id="2503.17334"> arXiv:2503.17334 </a> [<a href="/pdf/2503.17334" title="Download PDF" id="pdf-2503.17334" aria-labelledby="pdf-2503.17334">pdf</a>, <a href="https://arxiv.org/html/2503.17334v1" title="View HTML" id="html-2503.17334" aria-labelledby="html-2503.17334" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17334" title="Other formats" id="oth-2503.17334" aria-labelledby="oth-2503.17334">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On almost Gallai colourings in complete graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Grebennikov,+A">Alexandr Grebennikov</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mattos,+L">Let铆cia Mattos</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Szab%C3%B3,+T">Tibor Szab贸</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 23 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> For $t \in \mathbb{N}$, we say that a colouring of $E(K_n)$ is $\textit{almost}$ $t$-$\textit{Gallai}$ if no two rainbow $t$-cliques share an edge. Motivated by a lemma of Berkowitz on bounding the modulus of the characteristic function of clique counts in random graphs, we study the maximum number $\tau_t(n)$ of rainbow $t$-cliques in an almost $t$-Gallai colouring of $E(K_n)$. For every $t \ge 4$, we show that $n^{2-o(1)} \leq \tau_t(n) = o(n^2)$. For $t=3$, surprisingly, the behaviour is substantially different. Our main result establishes that $$\left ( \frac{1}{2}-o(1) \right ) n\log n \le \tau_3(n) = O\big (n^{\sqrt{2}\log n} \big ),$$ which gives the first non-trivial improvements over the simple lower and upper bounds. Our proof combines various applications of the probabilistic method and a generalisation of the edge-isoperimetric inequality for the hypercube. </p> </div> </dd> <dt> <a name='item115'>[115]</a> <a href ="/abs/2503.17337" title="Abstract" id="2503.17337"> arXiv:2503.17337 </a> [<a href="/pdf/2503.17337" title="Download PDF" id="pdf-2503.17337" aria-labelledby="pdf-2503.17337">pdf</a>, <a href="https://arxiv.org/html/2503.17337v1" title="View HTML" id="html-2503.17337" aria-labelledby="html-2503.17337" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17337" title="Other formats" id="oth-2503.17337" aria-labelledby="oth-2503.17337">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Distributional sectional curvature bounds for Riemannian metrics of low regularity </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Er%C3%B6s,+D">Darius Er枚s</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kunzinger,+M">Michael Kunzinger</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ohanyan,+A">Argam Ohanyan</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Vardabasso,+A">Alessio Vardabasso</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 21 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span>; Metric Geometry (math.MG) </div> <p class='mathjax'> Sectional curvature bounds are of central importance in the study of Riemannian mani\-folds, both in smooth differential geometry and in the generalized synthetic setting of Alexandrov spaces. Riemannian metrics along with metric spaces of bounded sectional curvature enjoy a variety of, oftentimes rigid, geometric properties. The purpose of this article is to introduce and discuss a new notion of sectional curvature bounds for manifolds equipped with continuous Riemannian metrics of Geroch--Traschen regularity, i.e., $H^1_{\mathrm{loc}} \cap C^0$, based on a distributional version of the classical formula. Our main result states that for $g \in C^1$, this new notion recovers the corresponding bound based on triangle comparison in the sense of Alexandrov. A weaker version of this statement is also proven for locally Lipschitz continuous metrics. </p> </div> </dd> <dt> <a name='item116'>[116]</a> <a href ="/abs/2503.17348" title="Abstract" id="2503.17348"> arXiv:2503.17348 </a> [<a href="/pdf/2503.17348" title="Download PDF" id="pdf-2503.17348" aria-labelledby="pdf-2503.17348">pdf</a>, <a href="https://arxiv.org/html/2503.17348v1" title="View HTML" id="html-2503.17348" aria-labelledby="html-2503.17348" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17348" title="Other formats" id="oth-2503.17348" aria-labelledby="oth-2503.17348">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Universality for catalytic equations and fully parked trees </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Contat,+A">Alice Contat</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Curien,+N">Nicolas Curien</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> are very welcome! 50 pages, 6 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Combinatorics (math.CO) </div> <p class='mathjax'> We show that critical parking trees conditioned to be fully parked converge in the scaling limits towards the Brownian growth-fragmentation tree, a self-similar Markov tree different from Aldous' Brownian tree recently introduced and studied by Bertoin, Curien and Riera. As a by-product of our study, we prove that positive non-linear polynomial equations involving a catalytic variable display a universal polynomial exponent $5/2$ at their singularity, confirming a conjecture by Chapuy, Schaeffer and Drmota & Hainzl. Compared to previous analytical works on the subject, our approach is probabilistic and exploits an underlying random walk hidden in the random tree model. </p> </div> </dd> <dt> <a name='item117'>[117]</a> <a href ="/abs/2503.17355" title="Abstract" id="2503.17355"> arXiv:2503.17355 </a> [<a href="/pdf/2503.17355" title="Download PDF" id="pdf-2503.17355" aria-labelledby="pdf-2503.17355">pdf</a>, <a href="https://arxiv.org/html/2503.17355v1" title="View HTML" id="html-2503.17355" aria-labelledby="html-2503.17355" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17355" title="Other formats" id="oth-2503.17355" aria-labelledby="oth-2503.17355">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Glivenko-Cantelli for $f$-divergence </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+H">Haoming Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lim,+L">Lek-Heng Lim</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 26 pages, 1 figure </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Statistics Theory (math.ST)</span>; Machine Learning (cs.LG) </div> <p class='mathjax'> We extend the celebrated Glivenko-Cantelli theorem, sometimes called the fundamental theorem of statistics, from its standard setting of total variation distance to all $f$-divergences. A key obstacle in this endeavor is to define $f$-divergence on a subcollection of a $\sigma$-algebra that forms a $\pi$-system but not a $\sigma$-subalgebra. This is a side contribution of our work. We will show that this notion of $f$-divergence on the $\pi$-system of rays preserves nearly all known properties of standard $f$-divergence, yields a novel integral representation of the Kolmogorov-Smirnov distance, and has a Glivenko-Cantelli theorem. </p> </div> </dd> </dl> <dl id='articles'> <h3>Cross submissions (showing 22 of 22 entries)</h3> <dt> <a name='item118'>[118]</a> <a href ="/abs/2503.11804" title="Abstract" id="2503.11804"> arXiv:2503.11804 </a> (cross-list from gr-qc) [<a href="/pdf/2503.11804" title="Download PDF" id="pdf-2503.11804" aria-labelledby="pdf-2503.11804">pdf</a>, <a href="https://arxiv.org/html/2503.11804v1" title="View HTML" id="html-2503.11804" aria-labelledby="html-2503.11804" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.11804" title="Other formats" id="oth-2503.11804" aria-labelledby="oth-2503.11804">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Hyperboloidal initial data without logarithmic singularities </div> <div class='list-authors'><a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Csuk%C3%A1s,+K">K谩roly Csuk谩s</a>, <a href="https://arxiv.org/search/gr-qc?searchtype=author&query=R%C3%A1cz,+I">Istv谩n R谩cz</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 30+5 pages, 3 figures, code and data on zenodo </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Relativity and Quantum Cosmology (gr-qc)</span>; Mathematical Physics (math-ph); Differential Geometry (math.DG) </div> <p class='mathjax'> Andersson and Chru艣ciel showed that generic asymptotically hyperboloidal initial data sets admit polyhomogeneous expansions, and that only a non-generic subclass of solutions of the conformal constraint equations is free of logarithmic singularities. The purpose of this work is twofold. First, within the evolutionary framework of the constraint equations, we show that the existence of a well-defined Bondi mass brings the asymptotically hyperboloidal initial data sets into a subclass whose Cauchy development guaranteed to admit a smooth boundary, by virtue of the results of Andersson and Chru艣ciel. Second, by generalizing a recent result of Beyer and Ritchie, we show that the existence of well-defined Bondi mass and angular momentum, together with some mild restrictions on the free data, implies that the generic solutions of the parabolic-hyperbolic form of the constraint equations are completely free of logarithmic singularities. We also provide numerical evidence to show that in the vicinity of Kerr, asymptotically hyperboloidal initial data without logarithmic singularities can indeed be constructed. </p> </div> </dd> <dt> <a name='item119'>[119]</a> <a href ="/abs/2503.16441" title="Abstract" id="2503.16441"> arXiv:2503.16441 </a> (cross-list from cs.RO) [<a href="/pdf/2503.16441" title="Download PDF" id="pdf-2503.16441" aria-labelledby="pdf-2503.16441">pdf</a>, <a href="https://arxiv.org/html/2503.16441v1" title="View HTML" id="html-2503.16441" aria-labelledby="html-2503.16441" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16441" title="Other formats" id="oth-2503.16441" aria-labelledby="oth-2503.16441">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Safe and Efficient Social Navigation through Explainable Safety Regions Based on Topological Features </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Toscano-Duran,+V">Victor Toscano-Duran</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Narteni,+S">Sara Narteni</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Carlevaro,+A">Alberto Carlevaro</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Gonzalez-Diaz,+R">Rocio Gonzalez-Diaz</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Mongelli,+M">Maurizio Mongelli</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Guzzi,+J">Jerome Guzzi</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Robotics (cs.RO)</span>; Artificial Intelligence (cs.AI); General Topology (math.GN) </div> <p class='mathjax'> The recent adoption of artificial intelligence (AI) in robotics has driven the development of algorithms that enable autonomous systems to adapt to complex social environments. In particular, safe and efficient social navigation is a key challenge, requiring AI not only to avoid collisions and deadlocks but also to interact intuitively and predictably with its surroundings. To date, methods based on probabilistic models and the generation of conformal safety regions have shown promising results in defining safety regions with a controlled margin of error, primarily relying on classification approaches and explicit rules to describe collision-free navigation conditions. <br>This work explores how topological features contribute to explainable safety regions in social navigation. Instead of using behavioral parameters, we leverage topological data analysis to classify and characterize different simulation behaviors. First, we apply global rule-based classification to distinguish between safe (collision-free) and unsafe scenarios based on topological properties. Then, we define safety regions, $S_\varepsilon$, in the topological feature space, ensuring a maximum classification error of $\varepsilon$. These regions are built with adjustable SVM classifiers and order statistics, providing robust decision boundaries. Local rules extracted from these regions enhance interpretability, keeping the decision-making process transparent. <br>Our approach initially separates simulations with and without collisions, outperforming methods that not incorporate topological features. It offers a deeper understanding of robot interactions within a navigable space. We further refine safety regions to ensure deadlock-free simulations and integrate both aspects to define a compliant simulation space that guarantees safe and efficient navigation. </p> </div> </dd> <dt> <a name='item120'>[120]</a> <a href ="/abs/2503.16580" title="Abstract" id="2503.16580"> arXiv:2503.16580 </a> (cross-list from stat.ML) [<a href="/pdf/2503.16580" title="Download PDF" id="pdf-2503.16580" aria-labelledby="pdf-2503.16580">pdf</a>, <a href="https://arxiv.org/html/2503.16580v1" title="View HTML" id="html-2503.16580" aria-labelledby="html-2503.16580" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16580" title="Other formats" id="oth-2503.16580" aria-labelledby="oth-2503.16580">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Procrustes Wasserstein Metric: A Modified Benamou-Brenier Approach with Applications to Latent Gaussian Distributions </div> <div class='list-authors'><a href="https://arxiv.org/search/stat?searchtype=author&query=Toukam,+K+M">Kevine Meugang Toukam</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (stat.ML)</span>; Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR); Applications (stat.AP) </div> <p class='mathjax'> We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This distance is defined by penalizing the action with a costless movement of the particle that does not change the direction and speed of its trajectory. We show that for Gaussian distribution resume to measuring the Euclidean distance between their ordered vector of eigenvalues and we show a direct application in recovering Latent Gaussian distributions. </p> </div> </dd> <dt> <a name='item121'>[121]</a> <a href ="/abs/2503.16589" title="Abstract" id="2503.16589"> arXiv:2503.16589 </a> (cross-list from cs.LG) [<a href="/pdf/2503.16589" title="Download PDF" id="pdf-2503.16589" aria-labelledby="pdf-2503.16589">pdf</a>, <a href="https://arxiv.org/html/2503.16589v1" title="View HTML" id="html-2503.16589" aria-labelledby="html-2503.16589" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16589" title="Other formats" id="oth-2503.16589" aria-labelledby="oth-2503.16589">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Statistical Analysis for Per-Instance Evaluation of Stochastic Optimizers: How Many Repeats Are Enough? </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Noori,+M">Moslem Noori</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Valiante,+E">Elisabetta Valiante</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Van+Vaerenbergh,+T">Thomas Van Vaerenbergh</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Mohseni,+M">Masoud Mohseni</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Rozada,+I">Ignacio Rozada</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Emerging Technologies (cs.ET); Statistics Theory (math.ST) </div> <p class='mathjax'> A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the problem. However, the accuracy of the estimated performance metrics depends on the number of runs and should be studied using statistical tools. We present a statistical analysis of the common metrics, and develop guidelines for experiment design to measure the optimizer's performance using these metrics to a high level of confidence and accuracy. To this end, we first discuss the confidence interval of the metrics and how they are related to the number of runs of an experiment. We then derive a lower bound on the number of repeats in order to guarantee achieving a given accuracy in the metrics. Using this bound, we propose an algorithm to adaptively adjust the number of repeats needed to ensure the accuracy of the evaluated metric. Our simulation results demonstrate the utility of our analysis and how it allows us to conduct reliable benchmarking as well as hyperparameter tuning and prevent us from drawing premature conclusions regarding the performance of stochastic optimizers. </p> </div> </dd> <dt> <a name='item122'>[122]</a> <a href ="/abs/2503.16604" title="Abstract" id="2503.16604"> arXiv:2503.16604 </a> (cross-list from quant-ph) [<a href="/pdf/2503.16604" title="Download PDF" id="pdf-2503.16604" aria-labelledby="pdf-2503.16604">pdf</a>, <a href="https://arxiv.org/html/2503.16604v1" title="View HTML" id="html-2503.16604" aria-labelledby="html-2503.16604" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16604" title="Other formats" id="oth-2503.16604" aria-labelledby="oth-2503.16604">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Isoperimetric Inequalities in Quantum Geometry </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Pai,+P">Praveen Pai</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Zhang,+F">Fan Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 6 pages, 2 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph) </div> <p class='mathjax'> We reveal strong and weak inequalities relating two fundamental macroscopic quantum geometric quantities, the quantum distance and Berry phase, for closed paths in the Hilbert space of wavefunctions. We recount the role of quantum geometry in various quantum problems and show that our findings place new bounds on important physical quantities. </p> </div> </dd> <dt> <a name='item123'>[123]</a> <a href ="/abs/2503.16737" title="Abstract" id="2503.16737"> arXiv:2503.16737 </a> (cross-list from stat.ML) [<a href="/pdf/2503.16737" title="Download PDF" id="pdf-2503.16737" aria-labelledby="pdf-2503.16737">pdf</a>, <a href="https://arxiv.org/html/2503.16737v1" title="View HTML" id="html-2503.16737" aria-labelledby="html-2503.16737" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16737" title="Other formats" id="oth-2503.16737" aria-labelledby="oth-2503.16737">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Optimal Nonlinear Online Learning under Sequential Price Competition via s-Concavity </div> <div class='list-authors'><a href="https://arxiv.org/search/stat?searchtype=author&query=Bracale,+D">Daniele Bracale</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Banerjee,+M">Moulinath Banerjee</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Shi,+C">Cong Shi</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Sun,+Y">Yuekai Sun</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (stat.ML)</span>; Machine Learning (cs.LG); Probability (math.PR); Statistics Theory (math.ST) </div> <p class='mathjax'> We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices and subsequently observe their respective demand that is unobservable to competitors. The demand function for each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. To address this challenge, we propose a semi-parametric least-squares estimation of the nonlinear mean function, which does not require sellers to communicate demand information. We show that when all sellers employ our policy, their prices converge at a rate of $O(T^{-1/7})$ to the Nash equilibrium prices that sellers would reach if they were fully informed. Each seller incurs a regret of $O(T^{5/7})$ relative to a dynamic benchmark policy. A theoretical contribution of our work is proving the existence of equilibrium under shape-constrained demand functions via the concept of $s$-concavity and establishing regret bounds of our proposed policy. Technically, we also establish new concentration results for the least squares estimator under shape constraints. Our findings offer significant insights into dynamic competition-aware pricing and contribute to the broader study of non-parametric learning in strategic decision-making. </p> </div> </dd> <dt> <a name='item124'>[124]</a> <a href ="/abs/2503.16743" title="Abstract" id="2503.16743"> arXiv:2503.16743 </a> (cross-list from cs.AI) [<a href="/pdf/2503.16743" title="Download PDF" id="pdf-2503.16743" aria-labelledby="pdf-2503.16743">pdf</a>, <a href="https://arxiv.org/html/2503.16743v1" title="View HTML" id="html-2503.16743" aria-labelledby="html-2503.16743" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16743" title="Other formats" id="oth-2503.16743" aria-labelledby="oth-2503.16743">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> SuperARC: A Test for General and Super Intelligence Based on First Principles of Recursion Theory and Algorithmic Probability </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Hern%C3%A1ndez-Espinosa,+A">Alberto Hern谩ndez-Espinosa</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Ozelim,+L">Luan Ozelim</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Abrah%C3%A3o,+F+S">Felipe S. Abrah茫o</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Zenil,+H">Hector Zenil</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 45 pages + Technical Supplementary Information, 71 pages total </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Artificial Intelligence (cs.AI)</span>; Information Theory (cs.IT) </div> <p class='mathjax'> We introduce an open-ended test grounded in algorithmic probability that can avoid benchmark contamination in the quantitative evaluation of frontier models in the context of their Artificial General Intelligence (AGI) and Superintelligence (ASI) claims. Unlike other tests, this test does not rely on statistical compression methods (such as GZIP or LZW), which are more closely related to Shannon entropy than to Kolmogorov complexity. The test challenges aspects related to features of intelligence of fundamental nature such as synthesis and model creation in the context of inverse problems (generating new knowledge from observation). We argue that metrics based on model abstraction and optimal Bayesian inference for planning can provide a robust framework for testing intelligence, including natural intelligence (human and animal), narrow AI, AGI, and ASI. Our results show no clear evidence of LLM convergence towards a defined level of intelligence, particularly AGI or ASI. We found that LLM model versions tend to be fragile and incremental, as new versions may perform worse than older ones, with progress largely driven by the size of training data. The results were compared with a hybrid neurosymbolic approach that theoretically guarantees model convergence from optimal inference based on the principles of algorithmic probability and Kolmogorov complexity. The method outperforms LLMs in a proof-of-concept on short binary sequences. Our findings confirm suspicions regarding the fundamental limitations of LLMs, exposing them as systems optimised for the perception of mastery over human language. Progress among different LLM versions from the same developers was found to be inconsistent and limited, particularly in the absence of a solid symbolic counterpart. </p> </div> </dd> <dt> <a name='item125'>[125]</a> <a href ="/abs/2503.16748" title="Abstract" id="2503.16748"> arXiv:2503.16748 </a> (cross-list from cond-mat.stat-mech) [<a href="/pdf/2503.16748" title="Download PDF" id="pdf-2503.16748" aria-labelledby="pdf-2503.16748">pdf</a>, <a href="https://arxiv.org/html/2503.16748v1" title="View HTML" id="html-2503.16748" aria-labelledby="html-2503.16748" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16748" title="Other formats" id="oth-2503.16748" aria-labelledby="oth-2503.16748">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Partition function for position-dependent mass systems from superestatistics </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Gomez,+I+S">Ignacio S. Gomez</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Santos,+M+G+A">Matheus Gabriel Alves Santos</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=de+Almeida+dos+Santos,+D">Daniela de Almeida dos Santos</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Thibes,+R">Ronaldo Thibes</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Statistical Mechanics (cond-mat.stat-mech)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> In this work, we show a connection between superstatistics and position-dependent mass (PDM) systems in the context of the canonical ensemble. The key point is to set the fluctuation distribution of the inverse temperature in terms od the system PDM. For PDMs associated to Tsallis and Kaniadakis nonextensive statistics, the pressure and entropy of the ideal gas result lower than the standard case but maintaining monotonic behavior. Gas of non-interacting harmonic oscillators provided with quadratic and exponential PDMs exhibit a behavior of standard ED harmonic oscillator gas and a linear specific heat respectively, the latter being consistent with Nernst's third law of thermodynamics. Thus, a combined PDM-superstatistics scenario offers an alternative way to study the effects of the inhomogeneities of PDM systems in their thermodynamics. </p> </div> </dd> <dt> <a name='item126'>[126]</a> <a href ="/abs/2503.16865" title="Abstract" id="2503.16865"> arXiv:2503.16865 </a> (cross-list from cs.LG) [<a href="/pdf/2503.16865" title="Download PDF" id="pdf-2503.16865" aria-labelledby="pdf-2503.16865">pdf</a>, <a href="https://arxiv.org/html/2503.16865v1" title="View HTML" id="html-2503.16865" aria-labelledby="html-2503.16865" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16865" title="Other formats" id="oth-2503.16865" aria-labelledby="oth-2503.16865">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Nonparametric Factor Analysis and Beyond </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Zheng,+Y">Yujia Zheng</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Liu,+Y">Yang Liu</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Yao,+J">Jiaxiong Yao</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Hu,+Y">Yingyao Hu</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Zhang,+K">Kun Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> AISTATS 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Statistics Theory (math.ST); Machine Learning (stat.ML) </div> <p class='mathjax'> Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or noiseless regimes. In contrast, we study the more general case where noise can take arbitrary forms, depend on latent variables, and be non-invertibly entangled within a nonlinear function. We propose a general framework for identifying latent variables in the nonparametric noisy settings. We first show that, under suitable conditions, the generative model is identifiable up to certain submanifold indeterminacies even in the presence of non-negligible noise. Furthermore, under the structural or distributional variability conditions, we prove that latent variables of the general nonlinear models are identifiable up to trivial indeterminacies. Based on the proposed theoretical framework, we have also developed corresponding estimation methods and validated them in various synthetic and real-world settings. Interestingly, our estimate of the true GDP growth from alternative measurements suggests more insightful information on the economies than official reports. We expect our framework to provide new insight into how both researchers and practitioners deal with latent variables in real-world scenarios. </p> </div> </dd> <dt> <a name='item127'>[127]</a> <a href ="/abs/2503.16917" title="Abstract" id="2503.16917"> arXiv:2503.16917 </a> (cross-list from cs.LG) [<a href="/pdf/2503.16917" title="Download PDF" id="pdf-2503.16917" aria-labelledby="pdf-2503.16917">pdf</a>, <a href="https://arxiv.org/html/2503.16917v1" title="View HTML" id="html-2503.16917" aria-labelledby="html-2503.16917" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16917" title="Other formats" id="oth-2503.16917" aria-labelledby="oth-2503.16917">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Malliavin-Bismut Score-based Diffusion Models </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Mirafzali,+E">Ehsan Mirafzali</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Gupta,+U">Utkarsh Gupta</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Wyrod,+P">Patrick Wyrod</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Proske,+F">Frank Proske</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Venturi,+D">Daniele Venturi</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Marinescu,+R">Razvan Marinescu</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Probability (math.PR) </div> <p class='mathjax'> We introduce a new framework that employs Malliavin calculus to derive explicit expressions for the score function -- i.e., the gradient of the log-density -- associated with solutions to stochastic differential equations (SDEs). Our approach integrates classical integration-by-parts techniques with modern tools, such as Bismut's formula and Malliavin calculus, to address linear and nonlinear SDEs. In doing so, we establish a rigorous connection between the Malliavin derivative, its adjoint (the Malliavin divergence or the Skorokhod integral), Bismut's formula, and diffusion generative models, thus providing a systematic method for computing $\nabla \log p_t(x)$. For the linear case, we present a detailed study proving that our formula is equivalent to the actual score function derived from the solution of the Fokker--Planck equation for linear SDEs. Additionally, we derive a closed-form expression for $\nabla \log p_t(x)$ for nonlinear SDEs with state-independent diffusion coefficients. These advancements provide fresh theoretical insights into the smoothness and structure of probability densities and practical implications for score-based generative modelling, including the design and analysis of new diffusion models. Moreover, our findings promote the adoption of the robust Malliavin calculus framework in machine learning research. These results directly apply to various pure and applied mathematics fields, such as generative modelling, the study of SDEs driven by fractional Brownian motion, and the Fokker--Planck equations associated with nonlinear SDEs. </p> </div> </dd> <dt> <a name='item128'>[128]</a> <a href ="/abs/2503.16977" title="Abstract" id="2503.16977"> arXiv:2503.16977 </a> (cross-list from quant-ph) [<a href="/pdf/2503.16977" title="Download PDF" id="pdf-2503.16977" aria-labelledby="pdf-2503.16977">pdf</a>, <a href="https://arxiv.org/html/2503.16977v1" title="View HTML" id="html-2503.16977" aria-labelledby="html-2503.16977" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16977" title="Other formats" id="oth-2503.16977" aria-labelledby="oth-2503.16977">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Parallel splitting method for large-scale quadratic programs </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Vandelli,+M">Matteo Vandelli</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Ferrari,+F">Francesco Ferrari</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Dragoni,+D">Daniele Dragoni</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 10 pages, 8 Figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; Optimization and Control (math.OC) </div> <p class='mathjax'> Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we introduce SPLIT, a general-purpose quantum-inspired framework for decomposing large-scale quadratic programs into smaller subproblems, which are then solved in parallel. SPLIT accounts for cross-interactions between subproblems, which are usually neglected in other decomposition techniques. The SPLIT framework can integrate generic subproblem solvers, ranging from standard branch-and-bound methods to quantum optimization algorithms. We demonstrate its effectiveness through comparisons with commercial solvers on the MaxCut and Antenna Placement Problems, with up to 20,000 decision variables. Our results show that SPLIT is capable of providing drastic reductions in computational time, while delivering high-quality solutions. In these regards, the proposed method is particularly suited for near real-time applications that require a solution within a strict time frame, or when the problem size exceeds the hardware limitations of dedicated devices, such as current quantum computers. </p> </div> </dd> <dt> <a name='item129'>[129]</a> <a href ="/abs/2503.17036" title="Abstract" id="2503.17036"> arXiv:2503.17036 </a> (cross-list from gr-qc) [<a href="/pdf/2503.17036" title="Download PDF" id="pdf-2503.17036" aria-labelledby="pdf-2503.17036">pdf</a>, <a href="https://arxiv.org/html/2503.17036v1" title="View HTML" id="html-2503.17036" aria-labelledby="html-2503.17036" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17036" title="Other formats" id="oth-2503.17036" aria-labelledby="oth-2503.17036">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> An asymptotic systems approach for the good-bad-ugly model with application to general relativity </div> <div class='list-authors'><a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Duarte,+M">Miguel Duarte</a>, <a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Feng,+J+C">Justin C. Feng</a>, <a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Gasper%C3%ADn,+E">Edgar Gasper铆n</a>, <a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Hilditch,+D">David Hilditch</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 17 pages, 1 figure </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Relativity and Quantum Cosmology (gr-qc)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> We employ an adapted version of H枚rmander's asymptotic systems method to show heuristically that the standard good-bad-ugly model admits formal polyhomogeneous asymptotic solutions near null infinity. In a related earlier approach, our heuristics were unable to capture potential leading order logarithmic terms appearing in the asymptotic solution of the good equation (the standard wave equation). Presently, we work with an improved method which overcomes this shortcoming, allowing the faithful treatment of a larger class of initial data in which such logarithmic terms are manifest. We then generalize this method to encompass models that include stratified null forms as sources and whose wave operators are built from an asymptotically flat metric. We then apply this result to the Einstein field equations in generalized harmonic gauge and compute the leading decay in~$R^{-1}$ of the Weyl scalars, where~$R$ is a suitably defined radial coordinate. We detect an obstruction to peeling, a decay statement on the Weyl scalars~$\Psi_n$ that is ensured by smoothness of null infinity. The leading order obstruction appears in~$\Psi_2$ and, in agreement with the literature, can only be suppressed by a careful choice of initial </p> </div> </dd> <dt> <a name='item130'>[130]</a> <a href ="/abs/2503.17103" title="Abstract" id="2503.17103"> arXiv:2503.17103 </a> (cross-list from q-fin.MF) [<a href="/pdf/2503.17103" title="Download PDF" id="pdf-2503.17103" aria-labelledby="pdf-2503.17103">pdf</a>, <a href="https://arxiv.org/html/2503.17103v1" title="View HTML" id="html-2503.17103" aria-labelledby="html-2503.17103" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17103" title="Other formats" id="oth-2503.17103" aria-labelledby="oth-2503.17103">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Martingale property and moment explosions in signature volatility models </div> <div class='list-authors'><a href="https://arxiv.org/search/q-fin?searchtype=author&query=Jaber,+E+A">Eduardo Abi Jaber</a>, <a href="https://arxiv.org/search/q-fin?searchtype=author&query=Gassiat,+P">Paul Gassiat</a>, <a href="https://arxiv.org/search/q-fin?searchtype=author&query=Sotnikov,+D">Dimitri Sotnikov</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Finance (q-fin.MF)</span>; Probability (math.PR) </div> <p class='mathjax'> We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of a time-extended Brownian motion. Excluding trivial cases, we demonstrate that the price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative. The proof involves a fine analysis of the explosion time of a signature stochastic differential equation. This result is of key practical relevance, as it highlights that, when used for approximation purposes, the linear combination of signature elements must be taken of odd order to preserve the martingale property. Once martingality is established, we also characterize the existence of higher moments of the price process in terms of a condition on a correlation parameter. </p> </div> </dd> <dt> <a name='item131'>[131]</a> <a href ="/abs/2503.17157" title="Abstract" id="2503.17157"> arXiv:2503.17157 </a> (cross-list from nlin.CD) [<a href="/pdf/2503.17157" title="Download PDF" id="pdf-2503.17157" aria-labelledby="pdf-2503.17157">pdf</a>, <a href="https://arxiv.org/html/2503.17157v1" title="View HTML" id="html-2503.17157" aria-labelledby="html-2503.17157" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17157" title="Other formats" id="oth-2503.17157" aria-labelledby="oth-2503.17157">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Ubiquitous order known as chaos </div> <div class='list-authors'><a href="https://arxiv.org/search/nlin?searchtype=author&query=Ovchinnikov,+I+V">Igor V. Ovchinnikov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> elsarticle cls </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Chaos, Solitons and Fractals 181 (2024) 114611 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Chaotic Dynamics (nlin.CD)</span>; Disordered Systems and Neural Networks (cond-mat.dis-nn); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) </div> <p class='mathjax'> A close relation has recently emerged between two of the most fundamental concepts in physics and mathematics: chaos and supersymmetry. In striking contrast to the semantics of the word 'chaos,' the true physical essence of this phenomenon now appears to be a spontaneous order associated with the breakdown of the topological supersymmetry (TS) hidden in all stochastic (partial) differential equations, i.e., in all systems from a broad domain ranging from cosmology to nanoscience. Among the low-hanging fruits of this new perspective, which can be called the supersymmetric theory of stochastic dynamics (STS), are theoretical explanations of 1/f noise and self-organized criticality. Central to STS is the physical meaning of TS breaking order parameter (OP). In this paper, we discuss that the OP is a field-theoretic embodiment of the 'butterfly effect' (BE) -- the infinitely long dynamical memory that is definitive of chaos. We stress that the formulation of the corresponding effective theory for the OP would mark the inception of the first consistent physical theory of the BE. Such a theory, potentially a valuable tool in solving chaos-related problems, would parallel the well-established and successful field theoretic descriptions of superconductivity, ferromagentism and other known orders arising from the spontaneous breakdown of various symmetries of nature. </p> </div> </dd> <dt> <a name='item132'>[132]</a> <a href ="/abs/2503.17179" title="Abstract" id="2503.17179"> arXiv:2503.17179 </a> (cross-list from stat.ME) [<a href="/pdf/2503.17179" title="Download PDF" id="pdf-2503.17179" aria-labelledby="pdf-2503.17179">pdf</a>, <a href="https://arxiv.org/html/2503.17179v1" title="View HTML" id="html-2503.17179" aria-labelledby="html-2503.17179" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17179" title="Other formats" id="oth-2503.17179" aria-labelledby="oth-2503.17179">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> An improved nonparametric test and sample size procedures for the randomized complete block designs </div> <div class='list-authors'><a href="https://arxiv.org/search/stat?searchtype=author&query=Jan,+S">Show-Li Jan</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Shieh,+G">Gwowen Shieh</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Methodology (stat.ME)</span>; Statistics Theory (math.ST) </div> <p class='mathjax'> The Friedman test has been extensively applied as a nonparametric alternative to the conventional F procedure for comparing treatment effects in randomized complete block designs. A chi-square distribution provides a convenient approximation to determining the critical values for the Friedman procedure in hypothesis testing. However, the chi-square approximation is generally conservative and the accuracy declines with increasing number of treatments. This paper describes an alternative transformation of the Friedman statistic along with an approximate F distribution that has the same numerator degrees of freedom as the ANOVA F test. Moreover, two approximate noncentral F distributions are presented for the proposed F-transformation under the alternative hypothesis of heterogeneous location shifts. Explicit power functions are derived when the underlying populations have the uniform, normal, Laplace, and exponential distributions. Theoretical examination and empirical assessment are presented to validate the advantages of the proposed approaches over the existing methods of the Friedman test. The developed test and power procedures are recommended due to their consistently acceptable Type I error rates and accurate power calculations for the location shift structures and population distributions considered here. </p> </div> </dd> <dt> <a name='item133'>[133]</a> <a href ="/abs/2503.17191" title="Abstract" id="2503.17191"> arXiv:2503.17191 </a> (cross-list from cs.LO) [<a href="/pdf/2503.17191" title="Download PDF" id="pdf-2503.17191" aria-labelledby="pdf-2503.17191">pdf</a>, <a href="https://arxiv.org/html/2503.17191v1" title="View HTML" id="html-2503.17191" aria-labelledby="html-2503.17191" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17191" title="Other formats" id="oth-2503.17191" aria-labelledby="oth-2503.17191">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Distributive Laws of Monadic Containers </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Purdy,+C">Chris Purdy</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Damato,+S">Stefania Damato</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages main text, 11 pages references and appendices </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic in Computer Science (cs.LO)</span>; Category Theory (math.CT); Logic (math.LO) </div> <p class='mathjax'> Containers are used to carve out a class of strictly positive data types in terms of shapes and positions. They can be interpreted via a fully-faithful functor into endofunctors on Set. Monadic containers are those containers whose interpretation as a Set functor carries a monad structure. The category of containers is closed under container composition and is a monoidal category, whereas monadic containers do not in general compose. <br>In this paper, we develop a characterisation of distributive laws of monadic containers. Distributive laws were introduced as a sufficient condition for the composition of the underlying functors of two monads to also carry a monad structure. Our development parallels Ahman and Uustalu's characterisation of distributive laws of directed containers, i.e. containers whose Set functor interpretation carries a comonad structure. Furthermore, by combining our work with theirs, we construct characterisations of mixed distributive laws (i.e. of directed containers over monadic containers and vice versa), thereby completing the 'zoo' of container characterisations of (co)monads and their distributive laws. <br>We have found these characterisations amenable to development of existence and uniqueness proofs of distributive laws, particularly in the mechanised setting of Cubical Agda, in which most of the theory of this paper has been formalised. </p> </div> </dd> <dt> <a name='item134'>[134]</a> <a href ="/abs/2503.17208" title="Abstract" id="2503.17208"> arXiv:2503.17208 </a> (cross-list from nlin.CD) [<a href="/pdf/2503.17208" title="Download PDF" id="pdf-2503.17208" aria-labelledby="pdf-2503.17208">pdf</a>, <a href="https://arxiv.org/html/2503.17208v1" title="View HTML" id="html-2503.17208" aria-labelledby="html-2503.17208" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17208" title="Other formats" id="oth-2503.17208" aria-labelledby="oth-2503.17208">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Hamiltonian Chaos: From Galactic Dynamics to Plasma Physics </div> <div class='list-authors'><a href="https://arxiv.org/search/nlin?searchtype=author&query=Moges,+H+T">Henok Tenaw Moges</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> PhD Thesis, 177 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Chaotic Dynamics (nlin.CD)</span>; Astrophysics of Galaxies (astro-ph.GA); Dynamical Systems (math.DS); Plasma Physics (physics.plasm-ph) </div> <p class='mathjax'> The primary focus of this thesis is the numerical investigation of chaos in Hamiltonian models describing charged particle orbits in plasma, star motions in barred galaxies, and orbits' diffusion in multidimensional maps. We systematically explore the interplay between magnetic and kinetic chaos in toroidal fusion plasmas, where non-axisymmetric perturbations disrupt smooth magnetic flux surfaces, generating complex particle trajectories. Using the Generalized Alignment Index (GALI) method, we efficiently quantify chaos, compare the behavior of magnetic field lines and particle orbits, visualize the radial distribution of chaotic regions, and offer GALI as a valuable tool for studying plasma physics dynamics. We also study the evolution of phase space structures in a 3D barred galactic potential, following successive 2D and 3D pitchfork and period-doubling bifurcations of periodic orbits. By employing the `color and rotation' technique to visualize the system's 4D Poincar茅 surface of sections, we reveal distinct structural patterns. We further investigate the long-term diffusion transport and chaos properties of single and coupled standard maps, focusing on parameters inducing anomalous diffusion through accelerator modes exhibiting ballistic transport. Using different ensembles of initial conditions in chaotic regions influenced by these modes, we examine asymptotic diffusion rates and time scales, identifying conditions suppressing anomalous transport and leading to long-term convergence to normal diffusion across coupled maps. Lastly, we perform the first comprehensive investigation into the GALI indices for various attractors in continuous and discrete-time dissipative systems, extending the method's application to non-Hamiltonian systems. A key aspect of our work involves analyzing and comparing GALIs' with Lyapunov Exponents for systems exhibiting hyperchaotic motion. </p> </div> </dd> <dt> <a name='item135'>[135]</a> <a href ="/abs/2503.17235" title="Abstract" id="2503.17235"> arXiv:2503.17235 </a> (cross-list from quant-ph) [<a href="/pdf/2503.17235" title="Download PDF" id="pdf-2503.17235" aria-labelledby="pdf-2503.17235">pdf</a>, <a href="https://arxiv.org/html/2503.17235v1" title="View HTML" id="html-2503.17235" aria-labelledby="html-2503.17235" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17235" title="Other formats" id="oth-2503.17235" aria-labelledby="oth-2503.17235">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Infinite-fold Quantum Advantage in Classical Correlation Sensing </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=N%C3%B6tzel,+J">Janis N枚tzel</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Munar-Vallespir,+P">Pere Munar-Vallespir</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> This work has been submitted to the IEEE for possible publication </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; Information Theory (cs.IT) </div> <p class='mathjax'> We study the hypothesis testing problem of detecting the presence of a thermal source emitting coherent quantum states towards an arbitrary but fixed number $K$ of detectors versus the situation where the detectors are presented uncorrelated thermal noise of the same average energy in the setting of asymmetric hypothesis testing. We compare two variations of this theme: In the first one the detectors perform heterodyne or homodyne detection and then transmit their measured results to a central processing unit with unlimited computational resources. In the second one the detectors are able to teleport the quantum states to the central unit, which acts on the received quantum states with unlimited quantum computational resources. We find that when the average received energy per detector goes to zero, the ratio of the error exponents goes to infinity, indicating an infinite-fold quantum advantage. </p> </div> </dd> <dt> <a name='item136'>[136]</a> <a href ="/abs/2503.17252" title="Abstract" id="2503.17252"> arXiv:2503.17252 </a> (cross-list from cs.LG) [<a href="/pdf/2503.17252" title="Download PDF" id="pdf-2503.17252" aria-labelledby="pdf-2503.17252">pdf</a>, <a href="https://arxiv.org/html/2503.17252v1" title="View HTML" id="html-2503.17252" aria-labelledby="html-2503.17252" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17252" title="Other formats" id="oth-2503.17252" aria-labelledby="oth-2503.17252">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On Privately Estimating a Single Parameter </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Asi,+H">Hilal Asi</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Duchi,+J+C">John C. Duchi</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Talwar,+K">Kunal Talwar</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 53 pages, 7 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Cryptography and Security (cs.CR); Statistics Theory (math.ST) </div> <p class='mathjax'> We investigate differentially private estimators for individual parameters within larger parametric models. While generic private estimators exist, the estimators we provide repose on new local notions of estimand stability, and these notions allow procedures that provide private certificates of their own stability. By leveraging these private certificates, we provide computationally and statistical efficient mechanisms that release private statistics that are, at least asymptotically in the sample size, essentially unimprovable: they achieve instance optimal bounds. Additionally, we investigate the practicality of the algorithms both in simulated data and in real-world data from the American Community Survey and US Census, highlighting scenarios in which the new procedures are successful and identifying areas for future work. </p> </div> </dd> <dt> <a name='item137'>[137]</a> <a href ="/abs/2503.17265" title="Abstract" id="2503.17265"> arXiv:2503.17265 </a> (cross-list from stat.ML) [<a href="/pdf/2503.17265" title="Download PDF" id="pdf-2503.17265" aria-labelledby="pdf-2503.17265">pdf</a>, <a href="https://arxiv.org/html/2503.17265v1" title="View HTML" id="html-2503.17265" aria-labelledby="html-2503.17265" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17265" title="Other formats" id="oth-2503.17265" aria-labelledby="oth-2503.17265">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Learning to Solve Related Linear Systems </div> <div class='list-authors'><a href="https://arxiv.org/search/stat?searchtype=author&query=Hegde,+D">Disha Hegde</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Cockayne,+J">Jon Cockayne</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (stat.ML)</span>; Machine Learning (cs.LG); Numerical Analysis (math.NA) </div> <p class='mathjax'> Solving multiple parametrised related systems is an essential component of many numerical tasks. Borrowing strength from the solved systems and learning will make this process faster. In this work, we propose a novel probabilistic linear solver over the parameter space. This leverages information from the solved linear systems in a regression setting to provide an efficient posterior mean and covariance. We advocate using this as companion regression model for the preconditioned conjugate gradient method, and discuss the favourable properties of the posterior mean and covariance as the initial guess and preconditioner. We also provide several design choices for this companion solver. Numerical experiments showcase the benefits of using our novel solver in a hyperparameter optimisation problem. </p> </div> </dd> <dt> <a name='item138'>[138]</a> <a href ="/abs/2503.17313" title="Abstract" id="2503.17313"> arXiv:2503.17313 </a> (cross-list from eess.SY) [<a href="/pdf/2503.17313" title="Download PDF" id="pdf-2503.17313" aria-labelledby="pdf-2503.17313">pdf</a>, <a href="https://arxiv.org/html/2503.17313v1" title="View HTML" id="html-2503.17313" aria-labelledby="html-2503.17313" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17313" title="Other formats" id="oth-2503.17313" aria-labelledby="oth-2503.17313">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Throughput Maximizing Takeoff Scheduling for eVTOL Vehicles in On-Demand Urban Air Mobility Systems </div> <div class='list-authors'><a href="https://arxiv.org/search/eess?searchtype=author&query=Pooladsanj,+M">Milad Pooladsanj</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Savla,+K">Ketan Savla</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Ioannou,+P+A">Petros A. Ioannou</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 14 pages, 12 figures, 2 tables </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Systems and Control (eess.SY)</span>; Optimization and Control (math.OC); Probability (math.PR) </div> <p class='mathjax'> Urban Air Mobility (UAM) offers a solution to current traffic congestion by using electric Vertical Takeoff and Landing (eVTOL) vehicles to provide on-demand air mobility in urban areas. Effective traffic management is crucial for efficient operation of UAM systems, especially for high-demand scenarios. In this paper, we present a centralized framework for conflict-free takeoff scheduling of eVTOLs in on-demand UAM systems. Specifically, we provide a scheduling policy, called VertiSync, which jointly schedules UAM vehicles for servicing trip requests and rebalancing, subject to safety margins and energy requirements. We characterize the system-level throughput of VertiSync, which determines the demand threshold at which the average waiting time transitions from being stable to being increasing over time. We show that the proposed policy maximizes throughput for sufficiently large fleet size and if the UAM network has a certain symmetry property. We demonstrate the performance of VertiSync through a case study for the city of Los Angeles, and show that it significantly reduces average passenger waiting time compared to a first-come first-serve scheduling policy. </p> </div> </dd> <dt> <a name='item139'>[139]</a> <a href ="/abs/2503.17357" title="Abstract" id="2503.17357"> arXiv:2503.17357 </a> (cross-list from hep-lat) [<a href="/pdf/2503.17357" title="Download PDF" id="pdf-2503.17357" aria-labelledby="pdf-2503.17357">pdf</a>, <a href="https://arxiv.org/html/2503.17357v1" title="View HTML" id="html-2503.17357" aria-labelledby="html-2503.17357" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.17357" title="Other formats" id="oth-2503.17357" aria-labelledby="oth-2503.17357">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Filtered Rayleigh-Ritz is all you need </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-lat?searchtype=author&query=Abbott,+R">Ryan Abbott</a>, <a href="https://arxiv.org/search/hep-lat?searchtype=author&query=Hackett,+D+C">Daniel C. Hackett</a>, <a href="https://arxiv.org/search/hep-lat?searchtype=author&query=Fleming,+G+T">George T. Fleming</a>, <a href="https://arxiv.org/search/hep-lat?searchtype=author&query=Pefkou,+D+A">Dimitra A. Pefkou</a>, <a href="https://arxiv.org/search/hep-lat?searchtype=author&query=Wagman,+M+L">Michael L. Wagman</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 22+7 pages, 0 figures, 1 table </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Lattice (hep-lat)</span>; Numerical Analysis (math.NA) </div> <p class='mathjax'> Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses. </p> </div> </dd> </dl> <dl id='articles'> <h3>Replacement submissions (showing 125 of 125 entries)</h3> <dt> <a name='item140'>[140]</a> <a href ="/abs/1703.07339" title="Abstract" id="1703.07339"> arXiv:1703.07339 </a> (replaced) [<a href="/pdf/1703.07339" title="Download PDF" id="pdf-1703.07339" aria-labelledby="pdf-1703.07339">pdf</a>, <a href="/format/1703.07339" title="Other formats" id="oth-1703.07339" aria-labelledby="oth-1703.07339">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Stochastic control on the half-line and applications to the optimal dividend/consumption problem </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Zawisza,+D">Dariusz Zawisza</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> The paper is not well written and contains numerous gaps and substantial flaws. Much of the material will be transferred to a new paper entitled "Stochastic exit-time control on the half-line over a finite horizon" </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Analysis of PDEs (math.AP); Probability (math.PR); Portfolio Management (q-fin.PM) </div> <p class='mathjax'> We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations has smooth solution. The aforementioned result is used to solve the optimal dividend and consumption problem. In the proof we use a fixed point type argument, with an operator which is based on the stochastic representation for a linear equation. </p> </div> </dd> <dt> <a name='item141'>[141]</a> <a href ="/abs/1804.01326" title="Abstract" id="1804.01326"> arXiv:1804.01326 </a> (replaced) [<a href="/pdf/1804.01326" title="Download PDF" id="pdf-1804.01326" aria-labelledby="pdf-1804.01326">pdf</a>, <a href="https://arxiv.org/html/1804.01326v2" title="View HTML" id="html-1804.01326" aria-labelledby="html-1804.01326" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/1804.01326" title="Other formats" id="oth-1804.01326" aria-labelledby="oth-1804.01326">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Purity in compactly generated derivators and t-structures with Grothendieck hearts </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Laking,+R">Rosanna Laking</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 25 pages. The following changes were made to v2: Corrected statement of third theorem in the introduction; changed acknowledgement to include thanks to Michal Hrbek; corrected statement and proof of Proposition 5.6; added counter-example of original statement in Example 5.7; added Example 5.16, which shows that Theorem 5.14 does not hold for partial cosilting objects in general </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Representation Theory (math.RT)</span>; Category Theory (math.CT) </div> <p class='mathjax'> We study t-structures with Grothendieck hearts on compactly generated triangulated categories $\mathcal{T}$ that are underlying categories of strong and stable derivators. This setting includes all algebraic compactly generated triangulated categories. We give an intrinsic characterisation of pure triangles and the definable subcategories of $\mathcal{T}$ in terms of directed homotopy colimits. For a left nondegenerate t-structure ${\bf t}=(\mathcal{U},\mathcal{V})$ on $\mathcal{T}$, we show that $\mathcal{V}$ is definable if and only if ${\bf t}$ is smashing and has a Grothendieck heart. Moreover, these conditions are equivalent to ${\bf t}$ being homotopically smashing and to ${\bf t}$ being cogenerated by a pure-injective partial cosilting object. Finally, we show that finiteness conditions on the heart of ${\bf t}$ are determined by purity conditions on the associated partial cosilting object. </p> </div> </dd> <dt> <a name='item142'>[142]</a> <a href ="/abs/1805.07311" title="Abstract" id="1805.07311"> arXiv:1805.07311 </a> (replaced) [<a href="/pdf/1805.07311" title="Download PDF" id="pdf-1805.07311" aria-labelledby="pdf-1805.07311">pdf</a>, <a href="https://arxiv.org/html/1805.07311v4" title="View HTML" id="html-1805.07311" aria-labelledby="html-1805.07311" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/1805.07311" title="Other formats" id="oth-1805.07311" aria-labelledby="oth-1805.07311">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Blended Conditional Gradients: the unconditioning of conditional gradients </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Braun,+G">G谩bor Braun</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Pokutta,+S">Sebastian Pokutta</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tu,+D">Dan Tu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wright,+S">Stephen Wright</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 33 pages + 12 figures; fixed typos in v4 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Computational Complexity (cs.CC); Machine Learning (cs.LG) </div> <p class='mathjax'> We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, combining the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps, different from away steps and pairwise steps, but still achieving linear convergence for strongly convex functions, along with good practical performance. Our approach retains all favorable properties of conditional gradient algorithms, notably avoidance of projections onto P and maintenance of iterates as sparse convex combinations of a limited number of extreme points of P. The algorithm is lazy, making use of inexpensive inexact solutions of the linear programming subproblem that characterizes the conditional gradient approach. It decreases measures of optimality (primal and dual gaps) rapidly, both in the number of iterations and in wall-clock time, outperforming even the lazy conditional gradient algorithms of [<a href="https://arxiv.org/abs/1410.8816" data-arxiv-id="1410.8816" class="link-https">arXiv:1410.8816</a>]. We also present a streamlined version of the algorithm for the probability simplex. </p> </div> </dd> <dt> <a name='item143'>[143]</a> <a href ="/abs/1908.10824" title="Abstract" id="1908.10824"> arXiv:1908.10824 </a> (replaced) [<a href="/pdf/1908.10824" title="Download PDF" id="pdf-1908.10824" aria-labelledby="pdf-1908.10824">pdf</a>, <a href="https://arxiv.org/html/1908.10824v2" title="View HTML" id="html-1908.10824" aria-labelledby="html-1908.10824" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/1908.10824" title="Other formats" id="oth-1908.10824" aria-labelledby="oth-1908.10824">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Almost Hermitian structures on tangent bundles </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Satoh,+H">Hiroyasu Satoh</a></div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Proceedings of the Eleventh International Workshop on Differential Geometry, 105-118, Kyungpook Nat. Univ., Taegu, 2007 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span> </div> <p class='mathjax'> In this article, we consider the almost Hermitian structure on $TM$ induced by a pair of a metric and an affine connection on $M$. We find the conditions under which $TM$ admits almost K盲hler structures, K盲hler structures and Einstein metrics, respectively. Moreover, we give two examples of K盲hler-Einstein structures on $TM$. </p> </div> </dd> <dt> <a name='item144'>[144]</a> <a href ="/abs/1910.05622" title="Abstract" id="1910.05622"> arXiv:1910.05622 </a> (replaced) [<a href="/pdf/1910.05622" title="Download PDF" id="pdf-1910.05622" aria-labelledby="pdf-1910.05622">pdf</a>, <a href="/format/1910.05622" title="Other formats" id="oth-1910.05622" aria-labelledby="oth-1910.05622">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> 3x + 1 Problem. Syracuse Conjecture </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Padilla,+V">Vicente Padilla</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 156 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Mathematics (math.GM)</span> </div> <p class='mathjax'> In this paper; we prove that all sequences can be broken up in cycles. Each cycle follows the same pattern: 1) Upward trajectory. Odd and even numbers alternate until the cycle reaches an upper bound 2) Downward trajectory. Two or more consecutive even numbers follow until it reaches another odd number. At this point, it's the beginning of the following cycle. Any sequence is evidently made of many consecutive cycles. In order to prove the conjecture, we build two sequences. The first sequence starts from any odd number. The sequence unfolds one cycle after the another. After each cycle, we build a second sequence that is built following a parallel path to the previous one, but adapting the last cycle to ensure it converges down to 1. In other words, their cycles have the same pattern of upward and downward steps except for the very last cycle. Finally, we prove that both sequences must be the same. Since the latter sequence converges to 1, so must the former. This document is a revision of the previous rev.12. There are significant changes that were made in order to make it easier to follow. The foundations of the demonstration remain the same. </p> </div> </dd> <dt> <a name='item145'>[145]</a> <a href ="/abs/2005.06222" title="Abstract" id="2005.06222"> arXiv:2005.06222 </a> (replaced) [<a href="/pdf/2005.06222" title="Download PDF" id="pdf-2005.06222" aria-labelledby="pdf-2005.06222">pdf</a>, <a href="https://arxiv.org/html/2005.06222v3" title="View HTML" id="html-2005.06222" aria-labelledby="html-2005.06222" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2005.06222" title="Other formats" id="oth-2005.06222" aria-labelledby="oth-2005.06222">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Enumerating partial linear transformations in a similarity class </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Arora,+A">Akansha Arora</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ram,+S">Samrith Ram</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages, 3 figures. One minor typo corrected in the main result </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> Let $V$ be a finite-dimensional vector space over the finite field ${\mathbb F}_q$ and suppose $W$ and $\widetilde{W}$ are subspaces of $V$. Two linear transformations $T:W\to V$ and $\widetilde{T}:\widetilde{W}\to V$ are said to be similar if there exists a linear isomorphism $S:V\to V$ with $SW=\widetilde{W}$ such that $S\circ T=\widetilde{T}\circ S $. Given a linear map $T$ defined on a subspace $W$ of $V$, we give an explicit formula for the number of linear maps that are similar to $T$. Our results extend a theorem of Philip Hall that settles the case $W=V$ where the above problem is equivalent to counting the number of square matrices over ${\mathbb F}_q$ in a conjugacy class. </p> </div> </dd> <dt> <a name='item146'>[146]</a> <a href ="/abs/2105.13355" title="Abstract" id="2105.13355"> arXiv:2105.13355 </a> (replaced) [<a href="/pdf/2105.13355" title="Download PDF" id="pdf-2105.13355" aria-labelledby="pdf-2105.13355">pdf</a>, <a href="https://arxiv.org/html/2105.13355v2" title="View HTML" id="html-2105.13355" aria-labelledby="html-2105.13355" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2105.13355" title="Other formats" id="oth-2105.13355" aria-labelledby="oth-2105.13355">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Besov regularity of non-linear parabolic PDEs on non-convex polyhedral domains </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Dahlke,+S">Stephan Dahlke</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Hansen,+M">Markus Hansen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Schneider,+C">Cornelia Schneider</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> arXiv admin note: substantial text overlap with <a href="https://arxiv.org/abs/2105.12796" data-arxiv-id="2105.12796" class="link-https">arXiv:2105.12796</a>; text overlap with <a href="https://arxiv.org/abs/1811.09428" data-arxiv-id="1811.09428" class="link-https">arXiv:1811.09428</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Numerical Analysis (math.NA) </div> <p class='mathjax'> This paper is concerned with the regularity of solutions to parabolic evolution equations. We consider semilinear problems on non-convex domains. Special attention is paid to the smoothness in the specific scale $B^r_{\tau,\tau}$, $\frac{1}{\tau}=\frac rd+ \frac 1p$ of Besov spaces. The regularity in these spaces determines the approximation order that can be achieved by adaptive and other nonlinear approximation schemes. We show that for all cases under consideration the Besov regularity is high enough to justify the use of adaptive algorithms. Our proofs are based on Schauder's fixed point theorem. </p> </div> </dd> <dt> <a name='item147'>[147]</a> <a href ="/abs/2204.07467" title="Abstract" id="2204.07467"> arXiv:2204.07467 </a> (replaced) [<a href="/pdf/2204.07467" title="Download PDF" id="pdf-2204.07467" aria-labelledby="pdf-2204.07467">pdf</a>, <a href="https://arxiv.org/html/2204.07467v2" title="View HTML" id="html-2204.07467" aria-labelledby="html-2204.07467" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2204.07467" title="Other formats" id="oth-2204.07467" aria-labelledby="oth-2204.07467">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Convergence of the Discrete Minimum Energy Path </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+X">Xuanyu Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Chen,+H">Huajie Chen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ortner,+C">Christoph Ortner</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> arXiv admin note: text overlap with <a href="https://arxiv.org/abs/2204.00984" data-arxiv-id="2204.00984" class="link-https">arXiv:2204.00984</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory. </p> </div> </dd> <dt> <a name='item148'>[148]</a> <a href ="/abs/2206.02759" title="Abstract" id="2206.02759"> arXiv:2206.02759 </a> (replaced) [<a href="/pdf/2206.02759" title="Download PDF" id="pdf-2206.02759" aria-labelledby="pdf-2206.02759">pdf</a>, <a href="/format/2206.02759" title="Other formats" id="oth-2206.02759" aria-labelledby="oth-2206.02759">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Polynomials with Lorentzian Signature, and Computing Permanents via Hyperbolic Programming </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Dey,+P">Papri Dey</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Theorem 42 is incorrect, and the concept of polynomials with Lorentzian signature has been further developed as K-Lorentzian polynomials in recent or follow-up papers </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span>; Combinatorics (math.CO) </div> <p class='mathjax'> We study the class of polynomials whose Hessians evaluated at any point of a closed convex cone have Lorentzian signature. This class is a generalization to the remarkable class of Lorentzian polynomials. We prove that hyperbolic polynomials and conic stable polynomials belong to this class, and the set of polynomials with Lorentzian signature is closed. Finally, we develop a method for computing permanents of nonsingular matrices which belong to a class that includes nonsingular $k$-locally singular matrices via hyperbolic programming. </p> </div> </dd> <dt> <a name='item149'>[149]</a> <a href ="/abs/2207.14197" title="Abstract" id="2207.14197"> arXiv:2207.14197 </a> (replaced) [<a href="/pdf/2207.14197" title="Download PDF" id="pdf-2207.14197" aria-labelledby="pdf-2207.14197">pdf</a>, <a href="https://arxiv.org/html/2207.14197v5" title="View HTML" id="html-2207.14197" aria-labelledby="html-2207.14197" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2207.14197" title="Other formats" id="oth-2207.14197" aria-labelledby="oth-2207.14197">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Diederich--Forn忙ss index and global regularity in the $\overline{\partial}$--Neumann problem: domains with comparable Levi eigenvalues </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+B">Bingyuan Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Straube,+E+J">Emil J. Straube</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 17 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Complex Variables (math.CV)</span> </div> <p class='mathjax'> Let $\Omega$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$. Let $1\leq q_{0}\leq (n-1)$. We show that if $q_{0}$--sums of eigenvalues of the Levi form are comparable, then if the Diederich--Forn忙ss index of $\Omega$ is $1$, the $\overline{\partial}$--Neumann operators $N_{q}$ and the Bergman projections $P_{q-1}$ are regular in Sobolev norms for $q_{0}\leq q\leq n$. In particular, for domains in $\mathbb{C}^{2}$, Diederich--Forn忙ss index $1$ implies global regularity in the $\overline{\partial}$--Neumann problem. </p> </div> </dd> <dt> <a name='item150'>[150]</a> <a href ="/abs/2208.06740" title="Abstract" id="2208.06740"> arXiv:2208.06740 </a> (replaced) [<a href="/pdf/2208.06740" title="Download PDF" id="pdf-2208.06740" aria-labelledby="pdf-2208.06740">pdf</a>, <a href="/format/2208.06740" title="Other formats" id="oth-2208.06740" aria-labelledby="oth-2208.06740">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Lipschitz decompositions of domains with bilaterally flat boundaries </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Krandel,+J">Jared Krandel</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Updated to accepted version. Accepted in Journal of the London Mathematical Society </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Classical Analysis and ODEs (math.CA)</span> </div> <p class='mathjax'> We study classes of domains in $\mathbb{R}^{d+1},\ d \geq 2$ with sufficiently flat boundaries that admit a decomposition or covering of bounded overlap by Lipschitz graph domains with controlled total surface area. This study is motivated by the following result proved by Peter Jones as a piece of his proof of the Analyst's Traveling Salesman Theorem in the complex plane: Any simply connected domain $\Omega\subseteq\mathbb{C}$ with finite boundary length $\mathcal{H}^1(\partial\Omega)$ can be decomposed into Lipschitz graph domains with total boundary length bounded above by $M\mathcal{H}^1(\partial\Omega)$ for some $M$ independent of $\Omega$. In this paper, we prove an analogous Lipschitz decomposition result in higher dimensions for domains with Reifenberg flat boundaries satisfying a uniform beta-squared sum bound. We use similar techniques to show that domains with general Reifenberg flat or uniformly rectifiable boundaries admit similar Lipschitz decompositions while allowing the constituent domains to have bounded overlaps rather than be disjoint. </p> </div> </dd> <dt> <a name='item151'>[151]</a> <a href ="/abs/2209.14790" title="Abstract" id="2209.14790"> arXiv:2209.14790 </a> (replaced) [<a href="/pdf/2209.14790" title="Download PDF" id="pdf-2209.14790" aria-labelledby="pdf-2209.14790">pdf</a>, <a href="/format/2209.14790" title="Other formats" id="oth-2209.14790" aria-labelledby="oth-2209.14790">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Sparse PCA With Multiple Components </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cory-Wright,+R">Ryan Cory-Wright</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Pauphilet,+J">Jean Pauphilet</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Updated version with improved algorithmics and a new section containing a generalization of the Gershgorin circle theorem; comments or suggestions welcome </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML) </div> <p class='mathjax'> Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves solving a sparsity and orthogonality constrained convex maximization problem, which is extremely computationally challenging. Most existing works address sparse PCA via methods-such as iteratively computing one sparse PC and deflating the covariance matrix-that do not guarantee the orthogonality, let alone the optimality, of the resulting solution when we seek multiple mutually orthogonal PCs. We challenge this status by reformulating the orthogonality conditions as rank constraints and optimizing over the sparsity and rank constraints simultaneously. We design tight semidefinite relaxations to supply high-quality upper bounds, which we strengthen via additional second-order cone inequalities when each PC's individual sparsity is specified. Further, we derive a combinatorial upper bound on the maximum amount of variance explained as a function of the support. We exploit these relaxations and bounds to propose exact methods and rounding mechanisms that, together, obtain solutions with a bound gap on the order of 0%-15% for real-world datasets with p = 100s or 1000s of features and r \in {2, 3} components. Numerically, our algorithms match (and sometimes surpass) the best performing methods in terms of fraction of variance explained and systematically return PCs that are sparse and orthogonal. In contrast, we find that existing methods like deflation return solutions that violate the orthogonality constraints, even when the data is generated according to sparse orthogonal PCs. Altogether, our approach solves sparse PCA problems with multiple components to certifiable (near) optimality in a practically tractable fashion. </p> </div> </dd> <dt> <a name='item152'>[152]</a> <a href ="/abs/2210.08939" title="Abstract" id="2210.08939"> arXiv:2210.08939 </a> (replaced) [<a href="/pdf/2210.08939" title="Download PDF" id="pdf-2210.08939" aria-labelledby="pdf-2210.08939">pdf</a>, <a href="https://arxiv.org/html/2210.08939v2" title="View HTML" id="html-2210.08939" aria-labelledby="html-2210.08939" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2210.08939" title="Other formats" id="oth-2210.08939" aria-labelledby="oth-2210.08939">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Blow-ups and the quantum spectrum of surfaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gyenge,+%C3%81">脕d谩m Gyenge</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Szab%C3%B3,+S">Szil谩rd Szab贸</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Numerous small corrections. 25 pages. Comments are welcome </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> We investigate the behaviour of the spectrum of the quantum (or Dubrovin) connection of smooth projective surfaces under blow-ups. Our main result is that for small values of the parameters, the quantum spectrum of such a surface is asymptotically the union of the quantum spectrum of a minimal model of the surface and a finite number of additional points located "close to infinity", that correspond bijectively to the exceptional divisors. This proves a conjecture of Kontsevich in the surface case. </p> </div> </dd> <dt> <a name='item153'>[153]</a> <a href ="/abs/2210.17282" title="Abstract" id="2210.17282"> arXiv:2210.17282 </a> (replaced) [<a href="/pdf/2210.17282" title="Download PDF" id="pdf-2210.17282" aria-labelledby="pdf-2210.17282">pdf</a>, <a href="https://arxiv.org/html/2210.17282v4" title="View HTML" id="html-2210.17282" aria-labelledby="html-2210.17282" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2210.17282" title="Other formats" id="oth-2210.17282" aria-labelledby="oth-2210.17282">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Quasi-projective varieties whose fundamental group is a free product of cyclic groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cogolludo-Agust%C3%ADn,+J+I">Jos茅 Ignacio Cogolludo-Agust铆n</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Elduque,+E">Eva Elduque</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 29 pages. To appear in Rev. Mat. Iberoam </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span>; Geometric Topology (math.GT) </div> <p class='mathjax'> In this work we study smooth complex quasi-projective surfaces whose fundamental group is a free product of cyclic groups. In particular, we prove the existence of an admissible map from the quasi-projective surface to a smooth complex quasi-projective curve. Associated with this result, we prove addition-deletion Lemmas for fibers of the admissible map which describe how these operations affect the fundamental group of the quasi-projective surface. Our methods also allow us to produce curves in smooth projective surfaces whose fundamental groups of their complements are free products of cyclic groups, generalizing classical results on $C_{p,q}$ curves and torus type projective sextics, and showing how general this phenomenon is. </p> </div> </dd> <dt> <a name='item154'>[154]</a> <a href ="/abs/2211.12747" title="Abstract" id="2211.12747"> arXiv:2211.12747 </a> (replaced) [<a href="/pdf/2211.12747" title="Download PDF" id="pdf-2211.12747" aria-labelledby="pdf-2211.12747">pdf</a>, <a href="/format/2211.12747" title="Other formats" id="oth-2211.12747" aria-labelledby="oth-2211.12747">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Beyond the broken tetrahedron </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Chen,+A+Y">August Y. Chen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sch%C3%BClke,+B">Bjarne Sch眉lke</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages, 5 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> Here we consider the hypergraph Tur谩n problem in uniformly dense hypergraphs as was suggested by Erd艖s and S贸s. Given a $3$-graph $F$, the uniform Tur谩n density $\pi_u(F)$ of $F$ is defined as the supremum over all $d\in[0,1]$ for which there is an $F$-free uniformly $d$-dense $3$-graph, where uniformly $d$-dense means that every linearly sized subhypergraph has density at least $d$. Recently, Glebov, Kr谩l', and Volec and, independently, Reiher, R枚dl, and Schacht proved that $\pi_u(K_4^{(3)-})=\frac{1}{4}$, solving a conjecture by Erd艖s and S贸s. Despite substantial attention, the uniform Tur谩n density is still only known for very few hypergraphs. In particular, the problem due to Erd艖s and S贸s to determine $\pi_u(K_4^{(3)})$ remains wide open. <br>In this work, we determine the uniform Tur谩n density of the $3$-graph on five vertices that is obtained from $K_4^{(3)-}$ by adding an additional vertex whose link forms a matching on the vertices of $K_4^{(3)-}$. Further, we point to two natural intermediate problems on the way to determining $\pi_u(K_4^{(3)})$, and solve the first of these. </p> </div> </dd> <dt> <a name='item155'>[155]</a> <a href ="/abs/2212.06450" title="Abstract" id="2212.06450"> arXiv:2212.06450 </a> (replaced) [<a href="/pdf/2212.06450" title="Download PDF" id="pdf-2212.06450" aria-labelledby="pdf-2212.06450">pdf</a>, <a href="https://arxiv.org/html/2212.06450v3" title="View HTML" id="html-2212.06450" aria-labelledby="html-2212.06450" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2212.06450" title="Other formats" id="oth-2212.06450" aria-labelledby="oth-2212.06450">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Infinite-dimensional genetic and evolution algebras generated by Gibbs measures </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Coletti,+C+F">Cristian F. Coletti</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=de+Lima,+L+R">Lucas R. de Lima</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Luiz,+D+A">Denis A. Luiz</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 26 pages, 4 figures; typos corrected, references added </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; Probability (math.PR); Rings and Algebras (math.RA) </div> <p class='mathjax'> Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields. Here, we consider that the algebras are determined by configurations of finite spins on a countable set with their associated Gibbs distributions. The model preserves properties of the finite-dimensional Gibbs algebras found in the literature and extend their results. We introduce infertility in the genetic dynamics when the configurations differ macroscopically. It induces a decomposition of the algebra into a direct sum of fertile ideals with genetic realization. <br>The proposed infinite-dimensional algebras are commutative, non-associative, with uncountable basis and zero divisors. The properties of Gibbs measures allow us to deal with the difficulties arising from the algebraic structure and obtain the results presented in this article. </p> </div> </dd> <dt> <a name='item156'>[156]</a> <a href ="/abs/2302.10579" title="Abstract" id="2302.10579"> arXiv:2302.10579 </a> (replaced) [<a href="/pdf/2302.10579" title="Download PDF" id="pdf-2302.10579" aria-labelledby="pdf-2302.10579">pdf</a>, <a href="/format/2302.10579" title="Other formats" id="oth-2302.10579" aria-labelledby="oth-2302.10579">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> An algebraic correspondence between stochastic differential equations and the Martin-Siggia-Rose formalism </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Bonicelli,+A">Alberto Bonicelli</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Dappiaggi,+C">Claudio Dappiaggi</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Drago,+N">Nicol貌 Drago</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 32 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; High Energy Physics - Theory (hep-th); Probability (math.PR) </div> <p class='mathjax'> In the realm of complex systems, dynamics is often modeled in terms of a non-linear, stochastic, ordinary differential equation (SDE) with either an additive or a multiplicative Gaussian white noise. In addition to a well-established collection of results proving existence and uniqueness of the solutions, it is of particular relevance the explicit computation of expectation values and correlation functions, since they encode the key physical information of the system under investigation. A pragmatically efficient way to dig out these quantities consists of the Martin-Siggia-Rose (MSR) formalism which establishes a correspondence between a large class of SDEs and suitably constructed field theories formulated by means of a path integral approach. Despite the effectiveness of this duality, there is no corresponding, mathematically rigorous proof of such correspondence. We address this issue using techniques proper of the algebraic approach to quantum field theories which is known to provide a valuable framework to discuss rigorously the path integral formulation of field theories as well as the solution theory both of ordinary and of partial, stochastic differential equations. In particular, working in this framework, we establish rigorously, albeit at the level of perturbation theory, a correspondence between correlation functions and expectation values computed either in the SDE or in the MSR formalism. </p> </div> </dd> <dt> <a name='item157'>[157]</a> <a href ="/abs/2304.01697" title="Abstract" id="2304.01697"> arXiv:2304.01697 </a> (replaced) [<a href="/pdf/2304.01697" title="Download PDF" id="pdf-2304.01697" aria-labelledby="pdf-2304.01697">pdf</a>, <a href="https://arxiv.org/html/2304.01697v2" title="View HTML" id="html-2304.01697" aria-labelledby="html-2304.01697" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2304.01697" title="Other formats" id="oth-2304.01697" aria-labelledby="oth-2304.01697">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Partially Hyperbolic Compact Complex Manifolds </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kasuya,+H">Hisashi Kasuya</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Popovici,+D">Dan Popovici</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 36 pages; to appear in Revista Matem谩tica Iberoamericana </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span>; Algebraic Geometry (math.AG); Complex Variables (math.CV) </div> <p class='mathjax'> We propose and investigate two types, the latter with two variants, of notions of partial hyperbolicity accounting for several classes of compact complex manifolds behaving hyperbolically in certain directions, defined by a vector subbundle of the holomorphic tangent bundle, but not necessarily in the other directions. A key role is played by certain entire holomorphic maps, possibly from a higher-dimensional space, into the given manifold $X$. The dimension of the origin $\C^p$ of these maps is allowed to be arbitrary, unlike both the classical $1$-dimensional case of entire curves and the $1$-codimensional case introduced in previous work of the second-named author with S. Marouani. The higher-dimensional generality necessitates the imposition of certain growth conditions, very different from those in Nevanlinna theory and those in works by de Th茅lin, Burns and Sibony on Ahlfors currents, on the entire holomorphic maps $f:\C^p\longrightarrow X$. The way to finding these growth conditions is revealed by certain special, possibly non-K盲hler, Hermitian metrics in the spirit of Gromov's K盲hler hyperbolicity theory but in a higher-dimensional context. We then study several classes of examples, prove implications among our partial hyperbolicity notions, give a sufficient criterion for the existence of an Ahlfors current and a sufficient criterion for partial hyperbolicity in terms of the signs of two curvature-like objects introduced recently by the second-named author. </p> </div> </dd> <dt> <a name='item158'>[158]</a> <a href ="/abs/2306.07359" title="Abstract" id="2306.07359"> arXiv:2306.07359 </a> (replaced) [<a href="/pdf/2306.07359" title="Download PDF" id="pdf-2306.07359" aria-labelledby="pdf-2306.07359">pdf</a>, <a href="/format/2306.07359" title="Other formats" id="oth-2306.07359" aria-labelledby="oth-2306.07359">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the topology of fiber-type curves: a Zariski pair of affine nodal curves </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cogolludo-Agust%C3%ADn,+J+I">Jos茅 Ignacio Cogolludo-Agust铆n</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Elduque,+E">Eva Elduque</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18 pages. Comments are welcome and greatly appreciated. V3: Improved exposition, added examples </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span>; Geometric Topology (math.GT) </div> <p class='mathjax'> In this paper we explore conditions for a curve in a smooth projective surface to have a free product of cyclic groups as the fundamental group of its complement. It is known that if the surface is $\mathbb P^2$, then such curves must be of fiber type, i.e. a finite union of fibers of an admissible map onto a complex curve. In this setting, we exhibit an infinite family of Zariski pairs of fiber-type curves, that is, pairs of plane projective fiber-type curves whose tubular neighborhoods are homeomorphic, but whose embeddings in $\mathbb P^2$ are not. This includes a Zariski pair of curves in $\mathbb C^2$ with only nodes as singularities (and the same singularities at infinity) whose complements have non-isomorphic fundamental groups, one of them being free. Our examples show that the position of nodes also affects the topology of the embedding of projective curves. Twisted Alexander polynomials with respect to finite $SU(2)$ representations show to be useful for this purpose, since all their abelian invariants are the same for both fundamental groups. </p> </div> </dd> <dt> <a name='item159'>[159]</a> <a href ="/abs/2306.07680" title="Abstract" id="2306.07680"> arXiv:2306.07680 </a> (replaced) [<a href="/pdf/2306.07680" title="Download PDF" id="pdf-2306.07680" aria-labelledby="pdf-2306.07680">pdf</a>, <a href="https://arxiv.org/html/2306.07680v2" title="View HTML" id="html-2306.07680" aria-labelledby="html-2306.07680" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2306.07680" title="Other formats" id="oth-2306.07680" aria-labelledby="oth-2306.07680">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Volterra-type inner derivations on Hardy spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Arroussi,+H">H. Arroussi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tong,+C">C. Tong</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Virtanen,+J+A">J. A. Virtanen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yuan,+Z">Z. Yuan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> To appear in Revista de la Real Academia de Ciencias Exactas, F铆sicas y Naturales. Serie A. Matematicas </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span>; Complex Variables (math.CV) </div> <p class='mathjax'> A classical result of Calkin [Ann. of Math. (2) 42 (1941), pp. 839-873] says that an inner derivation $S\mapsto [T,S] = TS-ST$ maps the algebra of bounded operators on a Hilbert space into the ideal of compact operators if and only if $T$ is a compact perturbation of the multiplication by a scalar. In general, an analogous statement fails for operators on Banach spaces. To complement Calkin's result, we characterize Volterra-type inner derivations on Hardy spaces using generalized area operators and compact intertwining relations for Volterra and composition operators. Further, we characterize the compact intertwining relations for multiplication and composition operators between Hardy and Bergman spaces. </p> </div> </dd> <dt> <a name='item160'>[160]</a> <a href ="/abs/2307.01685" title="Abstract" id="2307.01685"> arXiv:2307.01685 </a> (replaced) [<a href="/pdf/2307.01685" title="Download PDF" id="pdf-2307.01685" aria-labelledby="pdf-2307.01685">pdf</a>, <a href="https://arxiv.org/html/2307.01685v2" title="View HTML" id="html-2307.01685" aria-labelledby="html-2307.01685" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2307.01685" title="Other formats" id="oth-2307.01685" aria-labelledby="oth-2307.01685">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Topologically free actions and ideals in twisted Banach algebra crossed products </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bardadyn,+K">K. Bardadyn</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kwa%C5%9Bniewski,+B+K">B. K. Kwa艣niewski</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Accepted for publication (and already published online) by Proceedings of the Royal Society of Edinburgh. Small changes, e.g. notation for L^P-algebras changed </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span>; Operator Algebras (math.OA) </div> <p class='mathjax'> We generalize the influential $C^*$-algebraic result of Kawamura-Tomiyama and Archbold-Spielberg for crossed products of discrete transformation groups to the realm of Banach algebras and twisted actions. We prove that topological freeness is equivalent to the intersection property for all reduced twisted Banach algebra crossed products coming from subgroups, and in the untwisted case to a generalised intersection property for a full $L^p$-operator algebra crossed product for any $p\in [1,\infty]$. This gives efficient simplicity criteria for various Banach algebra crossed products. We also use it to identify the prime ideal space of some crossed products as the quasi-orbit space of the action. For amenable actions we prove that the full and reduced twisted $L^p$-operator algebras coincide. </p> </div> </dd> <dt> <a name='item161'>[161]</a> <a href ="/abs/2307.09179" title="Abstract" id="2307.09179"> arXiv:2307.09179 </a> (replaced) [<a href="/pdf/2307.09179" title="Download PDF" id="pdf-2307.09179" aria-labelledby="pdf-2307.09179">pdf</a>, <a href="https://arxiv.org/html/2307.09179v3" title="View HTML" id="html-2307.09179" aria-labelledby="html-2307.09179" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2307.09179" title="Other formats" id="oth-2307.09179" aria-labelledby="oth-2307.09179">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Combinatorics of Castelnuovo-Mumford Regularity of Binomial Edge Ideals </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=LaClair,+A">Adam LaClair</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Incorporated referee's suggestions into current version </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Commutative Algebra (math.AC)</span>; Combinatorics (math.CO) </div> <p class='mathjax'> Since the introduction of binomial edge ideals $J_{G}$ by Herzog et al. and independently Ohtani, there has been significant interest in relating algebraic invariants of the binomial edge ideal with combinatorial invariants of the underlying graph $G$. Here, we take up a question considered by Herzog and Rinaldo regarding Castelnuovo--Mumford regularity of block graphs. To this end, we introduce a new invariant $\nu(G)$ associated to any simple graph $G$, defined as the maximal total length of a certain collection of induced paths within $G$ subject to conditions on the induced subgraph. We prove that for any graph $G$, $\nu(G) \leq \text{reg}(J_{G})-1$, and that the length of a longest induced path of $G$ is less than or equal to $\nu(G)$; this refines an inequality of Matsuda and Murai. We then investigate the question: when is $\nu(G) = \text{reg}(J_{G})-1$? We prove that equality holds when $G$ is closed; this gives a new characterization of a result of Ene and Zarojanu, and when $G$ is bipartite and $J_{G}$ is Cohen-Macaulay; this gives a new characterization of a result of Jayanathan and Kumar. For a block graph $G$, we prove that $\nu(G)$ admits a combinatorial characterization independent of any auxiliary choices, and we prove that $\nu(G) = \text{reg}(J_{G})-1$. This gives $\text{reg}(J_{G})$ a combinatorial interpretation for block graphs, and thus answers the question of Herzog and Rinaldo. </p> </div> </dd> <dt> <a name='item162'>[162]</a> <a href ="/abs/2309.08117" title="Abstract" id="2309.08117"> arXiv:2309.08117 </a> (replaced) [<a href="/pdf/2309.08117" title="Download PDF" id="pdf-2309.08117" aria-labelledby="pdf-2309.08117">pdf</a>, <a href="https://arxiv.org/html/2309.08117v3" title="View HTML" id="html-2309.08117" aria-labelledby="html-2309.08117" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2309.08117" title="Other formats" id="oth-2309.08117" aria-labelledby="oth-2309.08117">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Discrete Differential Geometry for $C^{1,1}$ Hyperbolic Surfaces of Non-Constant Curvature </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Parkinson,+C">Christian Parkinson</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Venkataramani,+S+C">Shankar C. Venkataramani</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span> </div> <p class='mathjax'> We develop a discrete differential geometry for surfaces of non-constant negative curvature, which can be used to model various phenomena from the growth of flower petals to marine invertebrate swimming. Specifically, we derive and numerically integrate a version of the classical Lelieuvre formulas that apply to immersions of $C^{1,1}$ hyperbolic surfaces of non-constant curvature. In contrast to the constant curvature case, these formulas do not provide an explicit method for constructing an immersion but rather describe an immersion via an implicit set of equations. We propose an iterative method for resolving these equations. Because we are interested in scenarios where the curvature is a function of the intrinsic material coordinates, in particular, on the geodesic distance from an origin, we suggest a fast marching method for computing geodesic distance on manifolds. We apply our methods to generate surfaces of non-constant curvature and demonstrate how one can introduce branch points to account for the sort of multi-generational buckling and subwrinkling observed in many applications. </p> </div> </dd> <dt> <a name='item163'>[163]</a> <a href ="/abs/2309.11030" title="Abstract" id="2309.11030"> arXiv:2309.11030 </a> (replaced) [<a href="/pdf/2309.11030" title="Download PDF" id="pdf-2309.11030" aria-labelledby="pdf-2309.11030">pdf</a>, <a href="https://arxiv.org/html/2309.11030v2" title="View HTML" id="html-2309.11030" aria-labelledby="html-2309.11030" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2309.11030" title="Other formats" id="oth-2309.11030" aria-labelledby="oth-2309.11030">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Marquette,+I">Ian Marquette</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Zhang,+J">Junze Zhang</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Zhang,+Y">Yao-Zhong Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> To be appeared in Annals of Physics </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span> </div> <p class='mathjax'> The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions rely on explicit differential operator realisations and Marsden-Weinstein reductions. In this paper, we develop an algebraic approach based on the subalgebras of the 2D conformal algebra $\mathfrak{c}(2)$. This allows us to classify the centralisers of the enveloping algebra of the conformal algebra and construct the corresponding Hamiltonians with integrals in algebraic form. It is found that the symmetry algebras underlying these algebraic Hamiltonians are six-dimensional quadratic algebras. The Berezin brackets and commutation relations of the quadratic algebraic structures are closed without relying on explicit realisations or representations. We also give the Casimir invariants of the symmetry algebras. Our approach provides algebraic perspectives for the recent work by Fordy and Huang on the construction of superintegrable systems in the Darboux spaces. </p> </div> </dd> <dt> <a name='item164'>[164]</a> <a href ="/abs/2309.13694" title="Abstract" id="2309.13694"> arXiv:2309.13694 </a> (replaced) [<a href="/pdf/2309.13694" title="Download PDF" id="pdf-2309.13694" aria-labelledby="pdf-2309.13694">pdf</a>, <a href="https://arxiv.org/html/2309.13694v2" title="View HTML" id="html-2309.13694" aria-labelledby="html-2309.13694" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2309.13694" title="Other formats" id="oth-2309.13694" aria-labelledby="oth-2309.13694">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Large random intersection graphs inside the critical window and triangle counts </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+M">Minmin Wang</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We identify the scaling limit of random intersection graphs inside their critical windows. The limit graphs vary according to the clustering regimes, and coincide with the continuum Erdos--Renyi graph in two out of the three regimes. Our approach to the scaling limit relies upon the close connection of random intersection graphs with binomial bipartite graphs, as well as a graph exploration algorithm on the latter. This further allows us to prove limit theorems for the number of triangles in the large connected components of the graphs. </p> </div> </dd> <dt> <a name='item165'>[165]</a> <a href ="/abs/2310.10678" title="Abstract" id="2310.10678"> arXiv:2310.10678 </a> (replaced) [<a href="/pdf/2310.10678" title="Download PDF" id="pdf-2310.10678" aria-labelledby="pdf-2310.10678">pdf</a>, <a href="https://arxiv.org/html/2310.10678v3" title="View HTML" id="html-2310.10678" aria-labelledby="html-2310.10678" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2310.10678" title="Other formats" id="oth-2310.10678" aria-labelledby="oth-2310.10678">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Polar form of Dirac fields: implementing symmetries via Lie derivative </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Fabbri,+L">Luca Fabbri</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Vignolo,+S">Stefano Vignolo</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Cianci,+R">Roberto Cianci</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 10 pages </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Lett. Math. Phys. 114, 21 (2024) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span> </div> <p class='mathjax'> We consider the Lie derivative along Killing vector fields of the Dirac relativistic spinors: by using the polar decomposition we acquire the mean to study the implementation of symmetries on Dirac fields. Specifically, we will become able to examine under what conditions it is equivalent to impose a symmetry upon a spinor or only upon its observables. For one physical application, we discuss the role of the above analysis for the specific spherical symmetry, obtaining some no-go theorem regarding spinors and discussing the generality of our approach. </p> </div> </dd> <dt> <a name='item166'>[166]</a> <a href ="/abs/2310.13790" title="Abstract" id="2310.13790"> arXiv:2310.13790 </a> (replaced) [<a href="/pdf/2310.13790" title="Download PDF" id="pdf-2310.13790" aria-labelledby="pdf-2310.13790">pdf</a>, <a href="https://arxiv.org/html/2310.13790v2" title="View HTML" id="html-2310.13790" aria-labelledby="html-2310.13790" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2310.13790" title="Other formats" id="oth-2310.13790" aria-labelledby="oth-2310.13790">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Absolute calculus and prismatic crystals on cyclotomic rings </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gros,+M">Michel Gros</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Stum,+B+L">Bernard Le Stum</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Quir%C3%B3s,+A">Adolfo Quir贸s</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Improved notation. Relation with the theory of Wach modules made more transparent. Updated references </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> Let $p$ be a prime, $W$ the ring of Witt vectors of a perfect field $k$ of characteristic $p$ and $\zeta$ a primitive $p$th root of unity. We introduce a new notion of calculus over $W$ that we call absolute calculus. It may be seen as a singular version of the $q$-calculus used in previous work, in the sense that the role of the coordinate is now played by $q$ itself. We show that what we call a weakly nilpotent $\mathbb\Delta$-connection on a finite free module is equivalent to a prismatic vector bundle on $W[\zeta]$. As a corollary of a theorem of Bhatt and Scholze, we finally obtain that a $\mathbb\Delta$-connection with a frobenius structure on a finite free module is equivalent to a lattice in a crystalline representation. We also consider the case of de Rham prismatic crystals as well as Hodge-Tate prismatic crystals. </p> </div> </dd> <dt> <a name='item167'>[167]</a> <a href ="/abs/2312.10846" title="Abstract" id="2312.10846"> arXiv:2312.10846 </a> (replaced) [<a href="/pdf/2312.10846" title="Download PDF" id="pdf-2312.10846" aria-labelledby="pdf-2312.10846">pdf</a>, <a href="https://arxiv.org/html/2312.10846v2" title="View HTML" id="html-2312.10846" aria-labelledby="html-2312.10846" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2312.10846" title="Other formats" id="oth-2312.10846" aria-labelledby="oth-2312.10846">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Continuous biframes in Hilbert $C^{\ast}-$modules </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Lfounoune,+A">Abdellatif Lfounoune</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Karara,+A">Abdelilah Karara</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rossafi,+M">Mohamed Rossafi</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> arXiv admin note: text overlap with <a href="https://arxiv.org/abs/2309.07247" data-arxiv-id="2309.07247" class="link-https">arXiv:2309.07247</a> by other authors </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> In this paper, we will introduce the concept of a continuous biframe for Hilbert $ C^{\ast}- $modules. Then, we examine some characterizations of this biframe with the help of an invertible and adjointable operator is given. Moreover, we study continuous biframe Bessel multiplier and dual continuous biframe in Hilbert $ C^{\ast}- $modules. Also, we develop the concept of continuous biframes in the tensor product of two Hilbert $C^{\ast}$-modules over a unital $C^{\ast}$-algebra $\mathcal{A}$ and provide some properties of invertible transformed biframes and Bessel multipliers in the tensor product. </p> </div> </dd> <dt> <a name='item168'>[168]</a> <a href ="/abs/2312.12782" title="Abstract" id="2312.12782"> arXiv:2312.12782 </a> (replaced) [<a href="/pdf/2312.12782" title="Download PDF" id="pdf-2312.12782" aria-labelledby="pdf-2312.12782">pdf</a>, <a href="https://arxiv.org/html/2312.12782v4" title="View HTML" id="html-2312.12782" aria-labelledby="html-2312.12782" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2312.12782" title="Other formats" id="oth-2312.12782" aria-labelledby="oth-2312.12782">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Spectral gap bounds for reversible hybrid Gibbs chains </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Qin,+Q">Qian Qin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ju,+N">Nianqiao Ju</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+G">Guanyang Wang</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Statistics Theory (math.ST)</span>; Probability (math.PR) </div> <p class='mathjax'> Hybrid Gibbs samplers represent a prominent class of approximated Gibbs algorithms that utilize Markov chains to approximate conditional distributions, with the Metropolis-within-Gibbs algorithm standing out as a well-known example. Despite their widespread use in both statistical and non-statistical applications, little is known about their convergence properties. This article introduces novel methods for establishing bounds on the convergence rates of certain reversible hybrid Gibbs samplers. In particular, we examine the convergence characteristics of hybrid random-scan Gibbs algorithms. Our analysis reveals that the absolute spectral gap of a hybrid Gibbs chain can be bounded based on the absolute spectral gap of the exact Gibbs chain and the absolute spectral gaps of the Markov chains employed for conditional distribution approximations. We also provide a convergence bound of similar flavors for hybrid data augmentation algorithms, extending existing works on the topic. The general bounds are applied to three examples: a random-scan Metropolis-within-Gibbs sampler, random-scan Gibbs samplers with block updates, and a hybrid slice sampler. </p> </div> </dd> <dt> <a name='item169'>[169]</a> <a href ="/abs/2312.13446" title="Abstract" id="2312.13446"> arXiv:2312.13446 </a> (replaced) [<a href="/pdf/2312.13446" title="Download PDF" id="pdf-2312.13446" aria-labelledby="pdf-2312.13446">pdf</a>, <a href="https://arxiv.org/html/2312.13446v3" title="View HTML" id="html-2312.13446" aria-labelledby="html-2312.13446" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2312.13446" title="Other formats" id="oth-2312.13446" aria-labelledby="oth-2312.13446">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Low energy resolvent expansions in dimension two </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Christiansen,+T+J">T. J. Christiansen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Datchev,+K">K. Datchev</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 31 pages, 2 figures, expanded introduction compared to v1 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Mathematical Physics (math-ph); Spectral Theory (math.SP) </div> <p class='mathjax'> The behavior of the resolvent at low energies has implications for many kinds of asymptotics, including for the scattering matrix and phase, for the Dirichlet-to-Neumann map, and for wave evolution. In this paper we present a robust method, based in part on resolvent identity arguments following Vodev and boundary pairing arguments following Melrose, for deriving such expansions, and implement it in detail for compactly supported perturbations of the Laplacian on $\mathbb R^2$. We obtain precise results for general self-adjoint black box perturbations, in the sense of Sj枚strand--Zworski, and also for some non-self-adjoint ones. The most important terms are the most singular ones, and we compute them in detail, relating them to spaces of zero eigenvalues and resonances. </p> </div> </dd> <dt> <a name='item170'>[170]</a> <a href ="/abs/2312.14083" title="Abstract" id="2312.14083"> arXiv:2312.14083 </a> (replaced) [<a href="/pdf/2312.14083" title="Download PDF" id="pdf-2312.14083" aria-labelledby="pdf-2312.14083">pdf</a>, <a href="https://arxiv.org/html/2312.14083v2" title="View HTML" id="html-2312.14083" aria-labelledby="html-2312.14083" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2312.14083" title="Other formats" id="oth-2312.14083" aria-labelledby="oth-2312.14083">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Classical Namba forcing can have the weak countable approximation property </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Levine,+M">Maxwell Levine</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Revised version: The statements are the same as the submitted version, plus corrections from a helpful referee report </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic (math.LO)</span> </div> <p class='mathjax'> We show that it is consistent from an inaccessible cardinal that classical Namba forcing has the weak $\omega_1$-approximation property. In fact, this is the case if $\aleph_1$-preserving forcings do not add cofinal branches to $\aleph_1$-sized trees. The exact statement we obtain is similar to Hamkins' Key Lemma. It follows as a corollary that $\mathsf{MM}$ implies that there are stationarily many indestructibly weakly $\omega_1$-guessing models that are not internally unbounded. This answers a question of Cox and Krueger and partially answers another. Our result on $\mathsf{MM}$ gives a short proof of a weakening of Cox and Krueger's main result by removing their use of higher Namba forcings, but we find another application of their ideas by answering a question of Adolf, Apter, and Koepke on preservation of successive cardinals by singularizing forcings. </p> </div> </dd> <dt> <a name='item171'>[171]</a> <a href ="/abs/2401.12833" title="Abstract" id="2401.12833"> arXiv:2401.12833 </a> (replaced) [<a href="/pdf/2401.12833" title="Download PDF" id="pdf-2401.12833" aria-labelledby="pdf-2401.12833">pdf</a>, <a href="https://arxiv.org/html/2401.12833v2" title="View HTML" id="html-2401.12833" aria-labelledby="html-2401.12833" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2401.12833" title="Other formats" id="oth-2401.12833" aria-labelledby="oth-2401.12833">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Equivariant $K$-theory of even-dimensional complex quadrics </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Paul,+B">Bidhan Paul</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Topology (math.AT)</span>; K-Theory and Homology (math.KT) </div> <p class='mathjax'> The aim of this paper is to describe the torus equivariant $K$-ring of even-dimensional complex quadrics by studying the graph equivariant $K$-theory of their corresponding GKM graphs. This involves providing a presentation for its graph equivariant $K$- ring in terms of generators and relations. This parallels the description of the equivariant cohomology ring of even-dimensional complex quadrics due to Kuroki. </p> </div> </dd> <dt> <a name='item172'>[172]</a> <a href ="/abs/2401.17635" title="Abstract" id="2401.17635"> arXiv:2401.17635 </a> (replaced) [<a href="/pdf/2401.17635" title="Download PDF" id="pdf-2401.17635" aria-labelledby="pdf-2401.17635">pdf</a>, <a href="https://arxiv.org/html/2401.17635v2" title="View HTML" id="html-2401.17635" aria-labelledby="html-2401.17635" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2401.17635" title="Other formats" id="oth-2401.17635" aria-labelledby="oth-2401.17635">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Notes on symplectic squeezing in $T^* \mathbb T^n$ and spectra of Finsler dynamics </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Feng,+Q">Qi Feng</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+J">Jun Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Final version; add Theorem C about the tilde "thin" cylinder (in dimension 3); shorten the proof of Proposition 2.1 </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Math. Z. 310, 7 (2025) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Symplectic Geometry (math.SG)</span>; Dynamical Systems (math.DS) </div> <p class='mathjax'> In this paper, on the one hand, we prove that for $n \geq 2$ any subbundle of $T^* \mathbb T^n$ with bounded fibers symplectically embeds into a trivial subbundle of $T^* \mathbb T^n$ where the fiber is an irrational cylinder. This not only resolves an open problem in Gong-Xue's recent work (which was stated for the 4-dimension case, that is, $n =2$) and also generalizes to any higher-dimensional situation. The proof is based on some version of Dirichlet's approximation theorem. On the other hand, we generalize a main result in Gong-Xue's work mentioned above, showing that any topologically trivial Liouville diffeomorphism on $T^*M$ (for instance, a diffeomorphism induced by an isometry on $M$) does not change the full marked length spectrum of a Finsler metric $F$ on $M$, up to a lifting of the Finsler metric $F$ to the unit codisk bundle $D^*_FM$. The proof is based on persistence module theory. </p> </div> </dd> <dt> <a name='item173'>[173]</a> <a href ="/abs/2402.08036" title="Abstract" id="2402.08036"> arXiv:2402.08036 </a> (replaced) [<a href="/pdf/2402.08036" title="Download PDF" id="pdf-2402.08036" aria-labelledby="pdf-2402.08036">pdf</a>, <a href="https://arxiv.org/html/2402.08036v2" title="View HTML" id="html-2402.08036" aria-labelledby="html-2402.08036" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2402.08036" title="Other formats" id="oth-2402.08036" aria-labelledby="oth-2402.08036">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Conditional quantization for uniform distributions on line segments and regular polygons </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Biteng,+P">Pigar Biteng</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Caguiat,+M">Mathieu Caguiat</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Dominguez,+T">Tsianna Dominguez</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Roychowdhury,+M+K">Mrinal Kanti Roychowdhury</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this paper, we investigate the conditional quantization for the uniform distributions defined on the unit line segments and $m$-sided regular polygons, where $m\geq 3$, inscribed in a unit circle. </p> </div> </dd> <dt> <a name='item174'>[174]</a> <a href ="/abs/2403.07189" title="Abstract" id="2403.07189"> arXiv:2403.07189 </a> (replaced) [<a href="/pdf/2403.07189" title="Download PDF" id="pdf-2403.07189" aria-labelledby="pdf-2403.07189">pdf</a>, <a href="https://arxiv.org/html/2403.07189v2" title="View HTML" id="html-2403.07189" aria-labelledby="html-2403.07189" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.07189" title="Other formats" id="oth-2403.07189" aria-labelledby="oth-2403.07189">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A multiscale cavity method for sublinear-rank symmetric matrix factorization </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Barbier,+J">Jean Barbier</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Ko,+J">Justin Ko</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Rahman,+A+A">Anas A. Rahman</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 64 pages. Filled out proof details, with one step being more involved than initially thought and resulting in changes to the main theorem </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Information Theory (cs.IT)</span>; Disordered Systems and Neural Networks (cond-mat.dis-nn); Mathematical Physics (math-ph); Statistics Theory (math.ST) </div> <p class='mathjax'> We consider a statistical model for symmetric matrix factorization with additive Gaussian noise in the high-dimensional regime where the rank $M$ of the signal matrix to infer scales with its size $N$ as $M={\rm o}(\sqrt{\ln N})$. Allowing for an $N$-dependent rank offers new challenges and requires new methods. Working in the Bayes-optimal setting, we show that whenever the signal has i.i.d.~entries, the limiting mutual information between signal and data is given by a variational formula involving a rank-one replica symmetric potential. In other words, from the information-theoretic perspective, the case of a (slowly) growing rank is the same as when $M=1$ (namely, the standard spiked Wigner model). The proof is primarily based on a novel multiscale cavity method allowing for growing rank along with some information-theoretic identities on worst noise for the vector Gaussian channel. We believe that the cavity method developed here will play a role in the analysis of a broader class of inference and spin models where the degrees of freedom are large arrays instead of vectors. </p> </div> </dd> <dt> <a name='item175'>[175]</a> <a href ="/abs/2403.10992" title="Abstract" id="2403.10992"> arXiv:2403.10992 </a> (replaced) [<a href="/pdf/2403.10992" title="Download PDF" id="pdf-2403.10992" aria-labelledby="pdf-2403.10992">pdf</a>, <a href="https://arxiv.org/html/2403.10992v2" title="View HTML" id="html-2403.10992" aria-labelledby="html-2403.10992" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.10992" title="Other formats" id="oth-2403.10992" aria-labelledby="oth-2403.10992">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On extended perfect codes </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Vorob'ev,+K">Konstantin Vorob'ev</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span>; Information Theory (cs.IT) </div> <p class='mathjax'> We consider extended $1$-perfect codes in Hamming graphs $H(n,q)$. Such nontrivial codes are known only when $n=2^k$, $k\geq 1$, $q=2$, or $n=q+2$, $q=2^m$, $m\geq 1$. Recently, Bespalov proved nonexistence of extended $1$-perfect codes for $q=3$, $4$, $n>q+2$. In this work, we characterize all positive integers $n$, $r$ and prime $p$, for which there exist such a code in $H(n,p^r)$. We also consider $2$-perfect codes in Hamming $H(n,q)$ and Johnson graphs $J(n,w)$ and find new necessary conditions on there existence. </p> </div> </dd> <dt> <a name='item176'>[176]</a> <a href ="/abs/2403.12859" title="Abstract" id="2403.12859"> arXiv:2403.12859 </a> (replaced) [<a href="/pdf/2403.12859" title="Download PDF" id="pdf-2403.12859" aria-labelledby="pdf-2403.12859">pdf</a>, <a href="https://arxiv.org/html/2403.12859v2" title="View HTML" id="html-2403.12859" aria-labelledby="html-2403.12859" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.12859" title="Other formats" id="oth-2403.12859" aria-labelledby="oth-2403.12859">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Primal Methods for Variational Inequality Problems with Functional Constraints </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+L">Liang Zhang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=He,+N">Niao He</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Muehlebach,+M">Michael Muehlebach</a></div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Math. Program. (2025) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Machine Learning (cs.LG); Machine Learning (stat.ML) </div> <p class='mathjax'> Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due to their simplicity and scalability. However, they typically rely on projection or linear minimization oracles to navigate the feasible set, which becomes computationally expensive in practical scenarios featuring multiple functional constraints. Existing efforts to tackle such functional constrained variational inequality problems have centered on primal-dual algorithms grounded in the Lagrangian function. These algorithms along with their theoretical analysis often require the existence and prior knowledge of the optimal Lagrange multipliers. In this work, we propose a simple primal method, termed Constrained Gradient Method (CGM), for addressing functional constrained variational inequality problems, without requiring any information on the optimal Lagrange multipliers. We establish a non-asymptotic convergence analysis of the algorithm for Minty variational inequality problems with monotone operators under smooth constraints. Remarkably, our algorithms match the complexity of projection-based methods in terms of operator queries for both monotone and strongly monotone settings, while using significantly cheaper oracles based on quadratic programming. Furthermore, we provide several numerical examples to evaluate the efficacy of our algorithms. </p> </div> </dd> <dt> <a name='item177'>[177]</a> <a href ="/abs/2403.16625" title="Abstract" id="2403.16625"> arXiv:2403.16625 </a> (replaced) [<a href="/pdf/2403.16625" title="Download PDF" id="pdf-2403.16625" aria-labelledby="pdf-2403.16625">pdf</a>, <a href="/format/2403.16625" title="Other formats" id="oth-2403.16625" aria-labelledby="oth-2403.16625">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A perfect obstruction theory for SU(2)-Higgs pairs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Schirren,+S">Simon Schirren</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> updated version (March'25) based on recent comments and suggestions </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> We present a new method for constructing virtual cycles for rank-2 Higgs sheaves $(E,\phi)$ on a smooth projective surface $S$. Using this, we redefine the $\mathbf{SU}(2)$-perfect obstruction theory previously constructed by Tanaka-Thomas. The key step in our construction involves modifying the $\mathbf{C}^\times$-localisation formula of Graber-Pandharipande by replacing the torus action with an involution $(E,\phi) \mapsto (E,-\phi^*)$. </p> </div> </dd> <dt> <a name='item178'>[178]</a> <a href ="/abs/2403.16783" title="Abstract" id="2403.16783"> arXiv:2403.16783 </a> (replaced) [<a href="/pdf/2403.16783" title="Download PDF" id="pdf-2403.16783" aria-labelledby="pdf-2403.16783">pdf</a>, <a href="https://arxiv.org/html/2403.16783v2" title="View HTML" id="html-2403.16783" aria-labelledby="html-2403.16783" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.16783" title="Other formats" id="oth-2403.16783" aria-labelledby="oth-2403.16783">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Aryan,+S">Shrey Aryan</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Law,+M+B">Michael B. Law</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 12 pages. v2: extended result to locally symmetric spaces with nonnegative curvature </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Differential Geometry (math.DG) </div> <p class='mathjax'> We establish a concavity principle for solutions to elliptic and parabolic equations on locally symmetric spaces with nonnegative sectional curvature, extending the results of Langford and Scheuer. To the best of our knowledge, this is the first general concavity principle established on spaces with non-constant sectional curvature. </p> </div> </dd> <dt> <a name='item179'>[179]</a> <a href ="/abs/2403.18645" title="Abstract" id="2403.18645"> arXiv:2403.18645 </a> (replaced) [<a href="/pdf/2403.18645" title="Download PDF" id="pdf-2403.18645" aria-labelledby="pdf-2403.18645">pdf</a>, <a href="https://arxiv.org/html/2403.18645v2" title="View HTML" id="html-2403.18645" aria-labelledby="html-2403.18645" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.18645" title="Other formats" id="oth-2403.18645" aria-labelledby="oth-2403.18645">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Some remarks regarding special elements in algebras obtained by the Cayley-Dickson process over Zp </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Flaut,+C">Cristina Flaut</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Baias,+A">Andreea Baias</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Rings and Algebras (math.RA)</span> </div> <p class='mathjax'> In this paper we provide some properties of k-potent elements in algebras obtained by the Cayley-Dickson process over Zp. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over Z3 and we present a method to encrypt plain texts, by using invertible elements in such algebras. </p> </div> </dd> <dt> <a name='item180'>[180]</a> <a href ="/abs/2405.10193" title="Abstract" id="2405.10193"> arXiv:2405.10193 </a> (replaced) [<a href="/pdf/2405.10193" title="Download PDF" id="pdf-2405.10193" aria-labelledby="pdf-2405.10193">pdf</a>, <a href="https://arxiv.org/html/2405.10193v3" title="View HTML" id="html-2405.10193" aria-labelledby="html-2405.10193" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2405.10193" title="Other formats" id="oth-2405.10193" aria-labelledby="oth-2405.10193">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The Lamperti transformation in the infinite-dimensional setting and the genealogies of self-similar Markov processes </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Siri-J%C3%A9gousse,+A">Arno Siri-J茅gousse</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wences,+A+H">Alejandro Hern谩ndez Wences</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We propose a change in focus from the prevalent paradigm based on the branching property as a tool to analyze the structure of population models, to one based on the self-similarity property, which we also introduce for the first time in the setting of measure-valued processes. By extending the well-known Lamperti transformation for self-similar Markov processes to the Banach-valued case we are able to generalize celebrated results in population genetics that describe the frequency-process of measure-valued stable branching processes in terms of the subfamily of Beta-Fleming-Viot processes. In our work we describe the frequency process of populations whose total size evolves as any positive self-similar Markov process in terms of general $\Lambda$-Fleming-Viot processes. Our results demonstrate the potential power of the self-similar perspective for the study of population models in which the reproduction dynamics of the individuals depend on the total population size, allowing for more complex and realistic models. </p> </div> </dd> <dt> <a name='item181'>[181]</a> <a href ="/abs/2405.14167" title="Abstract" id="2405.14167"> arXiv:2405.14167 </a> (replaced) [<a href="/pdf/2405.14167" title="Download PDF" id="pdf-2405.14167" aria-labelledby="pdf-2405.14167">pdf</a>, <a href="https://arxiv.org/html/2405.14167v4" title="View HTML" id="html-2405.14167" aria-labelledby="html-2405.14167" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2405.14167" title="Other formats" id="oth-2405.14167" aria-labelledby="oth-2405.14167">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Sesquilinear pairings on elliptic curves </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Stange,+K+E">Katherine E. Stange</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 19 pages; this version includes corrections and clarifications, in particular concerning the alternate definition of Weil pairing </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span>; Algebraic Geometry (math.AG) </div> <p class='mathjax'> Let $E$ be an elliptic curve with complex multiplication by a ring $R$, where $R$ is an order in an imaginary quadratic field or quaternion algebra. We define sesquilinear pairings ($R$-linear in one variable and $R$-conjugate linear in the other), taking values in an $R$-module, generalizing the Weil and Tate-Lichtenbaum pairings. </p> </div> </dd> <dt> <a name='item182'>[182]</a> <a href ="/abs/2405.17662" title="Abstract" id="2405.17662"> arXiv:2405.17662 </a> (replaced) [<a href="/pdf/2405.17662" title="Download PDF" id="pdf-2405.17662" aria-labelledby="pdf-2405.17662">pdf</a>, <a href="https://arxiv.org/html/2405.17662v4" title="View HTML" id="html-2405.17662" aria-labelledby="html-2405.17662" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2405.17662" title="Other formats" id="oth-2405.17662" aria-labelledby="oth-2405.17662">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Nonlinear steepest descent on a torus: A case study of the Landau-Lifshitz equation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Desiraju,+H">Harini Desiraju</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Its,+A+R">Alexander R. Its</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Prokhorov,+A">Andrei Prokhorov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 49 pages, 9 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI) </div> <p class='mathjax'> We obtain rigorous large time asymptotics for the Landau-Lifshitz equation in the soliton free case by extending the nonlinear steepest descent method to genus 1 surfaces. The methods presented in this paper pave the way to a rigorous analysis of other integrable equations on the torus and enable asymptotic analysis on different regimes of the Landau-Lifshitz equation. </p> </div> </dd> <dt> <a name='item183'>[183]</a> <a href ="/abs/2405.20823" title="Abstract" id="2405.20823"> arXiv:2405.20823 </a> (replaced) [<a href="/pdf/2405.20823" title="Download PDF" id="pdf-2405.20823" aria-labelledby="pdf-2405.20823">pdf</a>, <a href="/format/2405.20823" title="Other formats" id="oth-2405.20823" aria-labelledby="oth-2405.20823">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the cohomology of the Bigolin complex </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Piovani,+R">Riccardo Piovani</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 31 pages; new results have been added in Section 5; the title has been changed; comments are welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span>; Complex Variables (math.CV) </div> <p class='mathjax'> Given a compact complex manifold, we develop Hodge theory for the elliptic complex of differential forms defined by Bigolin in 1969 and recently referred as the Schweitzer complex. We exhibit several $L^2$ orthogonal decompositions of spaces of forms and prove a Hodge decomposition for harmonic forms on compact K盲hler manifolds. Then we compute the cohomology of this Bigolin complex on the small deformations of the complex structure of the Iwasawa manifold, showing that, in this example, this Bigolin cohomology is as powerful as Aeppli and Bott-Chern cohomology, in order to distinguish complex structures. Recall that the double complex of a compact complex manifold decomposes into a direct sum of so-called squares and zigzags, and the zigzags are the only components contributing to cohomology. We prove that, on any compact complex manifold of complex dimension 3, the multiplicities of zigzags in this decomposition are completely characterised by Betti, Hodge, Aeppli numbers plus Bigolin numbers, namely the dimensions of the Bigolin cohomology. This result is sharp, meaning that if we remove Hodge or Bigolin numbers from the previous statement then it becomes false. We then apply this last result to fully describe the double complexes of the small deformations of the Iwasawa manifold. Finally, we partially extend the definition of this complex on almost complex manifolds, providing a cohomological invariant on $1$-forms which is finite dimensional when the manifold is compact. </p> </div> </dd> <dt> <a name='item184'>[184]</a> <a href ="/abs/2406.04877" title="Abstract" id="2406.04877"> arXiv:2406.04877 </a> (replaced) [<a href="/pdf/2406.04877" title="Download PDF" id="pdf-2406.04877" aria-labelledby="pdf-2406.04877">pdf</a>, <a href="/format/2406.04877" title="Other formats" id="oth-2406.04877" aria-labelledby="oth-2406.04877">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A star-comb lemma for infinite digraphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Reich,+F">Florian Reich</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 23 pages, 16 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> The star-comb lemma is a standard tool in infinite graph theory, which states that for every infinite set $U$ of vertices in a connected graph $G$ there exists either a subdivided infinite star in $G$ with all leaves in $U$, or an infinite comb in $G$ with all teeth in $U$. <br>In this paper, we elaborate a counterpart of the star-comb lemma for directed graphs. More precisely, we prove that for every infinite set $U$ of vertices in a strongly connected directed graph $D$, there exists a strongly connected butterfly minor of $D$ with infinitely many teeth in $U$ that is either shaped by a star or shaped by a comb, or is a chain of triangles. </p> </div> </dd> <dt> <a name='item185'>[185]</a> <a href ="/abs/2406.07656" title="Abstract" id="2406.07656"> arXiv:2406.07656 </a> (replaced) [<a href="/pdf/2406.07656" title="Download PDF" id="pdf-2406.07656" aria-labelledby="pdf-2406.07656">pdf</a>, <a href="https://arxiv.org/html/2406.07656v2" title="View HTML" id="html-2406.07656" aria-labelledby="html-2406.07656" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2406.07656" title="Other formats" id="oth-2406.07656" aria-labelledby="oth-2406.07656">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Minimal commutant and double commutant property for analytic Toeplitz operators </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gonz%C3%A1lez,+M+J">Mar铆a Jos茅 Gonz谩lez</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Le%C3%B3n-Saavedra,+F">Fernando Le贸n-Saavedra</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span>; Operator Algebras (math.OA) </div> <p class='mathjax'> In this paper we study the minimality of the commutant of an analytic Toeplitz operator $M_\varphi$, when $M_\varphi$ is defined on the Hardy space $H^2(\mathbb{D})$ and $\varphi\in H^\infty(\mathbb{D})$, denotes a bounded analytic function on $\mathbb{D}$. Specifically we show that the commutant of $M_\varphi$ is minimal if and only if the polynomials on $\varphi$ are weak-star dense in $H^\infty(\mathbb{D})$, that is, $\varphi$ is a weak-star generator of $H^\infty(\mathbb{D})$. We use our result to characterize when the double commutant of an analytic Toeplitz operator $M_\varphi$ is minimal, for a large class of symbols $\varphi$. Namelly, when $\varphi$ is an entire function, or more generally when $\varphi$ belongs to the Thomson-Cowen's class. </p> </div> </dd> <dt> <a name='item186'>[186]</a> <a href ="/abs/2406.10793" title="Abstract" id="2406.10793"> arXiv:2406.10793 </a> (replaced) [<a href="/pdf/2406.10793" title="Download PDF" id="pdf-2406.10793" aria-labelledby="pdf-2406.10793">pdf</a>, <a href="https://arxiv.org/html/2406.10793v2" title="View HTML" id="html-2406.10793" aria-labelledby="html-2406.10793" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2406.10793" title="Other formats" id="oth-2406.10793" aria-labelledby="oth-2406.10793">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Symplectic Extra-gradient Type Method for Solving General Non-monotone Inclusion Problem </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Yuan,+Y">Ya-xiang Yuan</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+Y">Yi Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 37 pages, 7 figures, 1 table. We modify the statement of weak convergence property in V2 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> In recent years, accelerated extra-gradient methods have attracted much attention by researchers, for solving monotone inclusion problems. A limitation of most current accelerated extra-gradient methods lies in their direct utilization of the initial point, which can potentially decelerate numerical convergence rate. In this work, we present a new accelerated extra-gradient method, by utilizing the symplectic acceleration technique. We establish the inverse of quadratic convergence rate by employing the Lyapunov function technique. Also, we demonstrate a faster inverse of quadratic convergence rate alongside its weak convergence property under stronger assumptions. To improve practical efficiency, we introduce a line search technique for our symplectic extra-gradient method. Theoretically, we prove the convergence of the symplectic extra-gradient method with line search. Numerical tests show that this adaptation exhibits faster convergence rates in practice compared to several existing extra-gradient type methods. </p> </div> </dd> <dt> <a name='item187'>[187]</a> <a href ="/abs/2407.03349" title="Abstract" id="2407.03349"> arXiv:2407.03349 </a> (replaced) [<a href="/pdf/2407.03349" title="Download PDF" id="pdf-2407.03349" aria-labelledby="pdf-2407.03349">pdf</a>, <a href="https://arxiv.org/html/2407.03349v2" title="View HTML" id="html-2407.03349" aria-labelledby="html-2407.03349" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.03349" title="Other formats" id="oth-2407.03349" aria-labelledby="oth-2407.03349">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Recursive construction of biorthogonal polynomials for handling polynomial regression </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Rebollo-Neira,+L">Laura Rebollo-Neira</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Laurie,+J">Jason Laurie</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> An adaptive procedure for constructing polynomials which are biorthogonal to the basis of monomials in the same finite-dimensional inner product space is proposed. By taking advantage of available orthogonal polynomials, the proposed methodology reduces the well-known instability problem arising from the matrix inversion involved in classical polynomial regression. The recurrent generation of the biorthogonal basis facilitates the upgrading of all its members to include an additional one. Moreover, it allows for a natural downgrading of the basis. This convenient feature leads to a straightforward approach for reducing the number of terms in the polynomial regression approximation. The merit of this approach is illustrated through a series of examples where the resulting biorthogonal basis is derived from Legendre, Laguerre, and Chebyshev orthogonal polynomials. </p> </div> </dd> <dt> <a name='item188'>[188]</a> <a href ="/abs/2407.04521" title="Abstract" id="2407.04521"> arXiv:2407.04521 </a> (replaced) [<a href="/pdf/2407.04521" title="Download PDF" id="pdf-2407.04521" aria-labelledby="pdf-2407.04521">pdf</a>, <a href="https://arxiv.org/html/2407.04521v2" title="View HTML" id="html-2407.04521" aria-labelledby="html-2407.04521" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.04521" title="Other formats" id="oth-2407.04521" aria-labelledby="oth-2407.04521">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Unified continuous-time q-learning for mean-field game and mean-field control problems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Wei,+X">Xiaoli Wei</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yu,+X">Xiang Yu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yuan,+F">Fengyi Yuan</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Machine Learning (cs.LG); Computational Finance (q-fin.CP) </div> <p class='mathjax'> This paper studies the continuous-time q-learning in mean-field jump-diffusion models when the population distribution is not directly observable. We propose the integrated q-function in decoupled form (decoupled Iq-function) from the representative agent's perspective and establish its martingale characterization, which provides a unified policy evaluation rule for both mean-field game (MFG) and mean-field control (MFC) problems. Moreover, we consider the learning procedure where the representative agent updates the population distribution based on his own state values. Depending on the task to solve the MFG or MFC problem, we can employ the decoupled Iq-function differently to characterize the mean-field equilibrium policy or the mean-field optimal policy respectively. Based on these theoretical findings, we devise a unified q-learning algorithm for both MFG and MFC problems by utilizing test policies and the averaged martingale orthogonality condition. For several financial applications in the jump-diffusion setting, we obtain the exact parameterization of the decoupled Iq-functions and the value functions, and illustrate our q-learning algorithm with satisfactory performance. </p> </div> </dd> <dt> <a name='item189'>[189]</a> <a href ="/abs/2407.05583" title="Abstract" id="2407.05583"> arXiv:2407.05583 </a> (replaced) [<a href="/pdf/2407.05583" title="Download PDF" id="pdf-2407.05583" aria-labelledby="pdf-2407.05583">pdf</a>, <a href="https://arxiv.org/html/2407.05583v2" title="View HTML" id="html-2407.05583" aria-labelledby="html-2407.05583" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.05583" title="Other formats" id="oth-2407.05583" aria-labelledby="oth-2407.05583">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The Ranking-Selberg integral on ${\bf GSp(2)}$ for square free levels </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kuga,+S">Seiji Kuga</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tsuzuki,+M">Masao Tsuzuki</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 46 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span> </div> <p class='mathjax'> We explicitly compute the Rankin-Selberg type integral introduced by Piatetski-Shapiro over adeles for vector-valued Siegel cusp forms of square-free levels $\Gamma_0(N)$. On the way, for particular test functions in the Bessel models of irreducible admissible representations, exact evaluations of the local zeta-integrals are given. </p> </div> </dd> <dt> <a name='item190'>[190]</a> <a href ="/abs/2407.06143" title="Abstract" id="2407.06143"> arXiv:2407.06143 </a> (replaced) [<a href="/pdf/2407.06143" title="Download PDF" id="pdf-2407.06143" aria-labelledby="pdf-2407.06143">pdf</a>, <a href="/format/2407.06143" title="Other formats" id="oth-2407.06143" aria-labelledby="oth-2407.06143">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Parabolic Approximation & Relaxation for MINLP </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=G%C3%B6%C3%9F,+A">Adrian G枚脽</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Burlacu,+R">Robert Burlacu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Martin,+A">Alexander Martin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 41 pages (24 + 17 appendix), 16 figures, currently under review at Journal of Global Optimization </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> We propose an approach based on quadratic approximations for solving general Mixed-Integer Nonlinear Programming (MINLP) problems. Specifically, our approach entails the global approximation of the epigraphs of constraint functions by means of paraboloids, which are polynomials of degree two with univariate quadratic terms, and relies on a Lipschitz property only. These approximations are then integrated into the original problem. To this end, we introduce a novel approach to compute globally valid epigraph approximations by paraboloids via a Mixed-Integer Linear Programming (MIP) model. We emphasize the possibility of performing such approximations a-priori and providing them in form of a lookup table, and then present several ways of leveraging the approximations to tackle the original problem. We provide the necessary theoretical background and conduct computational experiments on instances of the MINLPLib. As a result, this approach significantly accelerates the solution process of MINLP problems, particularly those involving many trigonometric or few exponential functions. In general, we highlight that the proposed technique is able to exploit advances in Mixed-Integer Quadratically-Constrained Programming (MIQCP) to solve MINLP problems. </p> </div> </dd> <dt> <a name='item191'>[191]</a> <a href ="/abs/2407.07682" title="Abstract" id="2407.07682"> arXiv:2407.07682 </a> (replaced) [<a href="/pdf/2407.07682" title="Download PDF" id="pdf-2407.07682" aria-labelledby="pdf-2407.07682">pdf</a>, <a href="https://arxiv.org/html/2407.07682v2" title="View HTML" id="html-2407.07682" aria-labelledby="html-2407.07682" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.07682" title="Other formats" id="oth-2407.07682" aria-labelledby="oth-2407.07682">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Metric mean dimension via subshifts of compact type </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Pessil,+G">Gustavo Pessil</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Published version in Nonlinearity </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> We investigate the metric mean dimension of subshifts of compact type. We prove that the metric mean dimensions of a continuous map and its inverse limit coincide, generalizing Bowen's entropy formula. Building upon this result, we extend the notion of metric mean dimension to discontinuous maps in terms of suitable subshifts. As an application, we show that the metric mean dimension of the Gauss map and that of induced maps of the Manneville-Pomeau family is equal to the box dimension of the corresponding set of discontinuity points, which also coincides with a critical parameter of the pressure operator associated to the geometric potential. </p> </div> </dd> <dt> <a name='item192'>[192]</a> <a href ="/abs/2407.10651" title="Abstract" id="2407.10651"> arXiv:2407.10651 </a> (replaced) [<a href="/pdf/2407.10651" title="Download PDF" id="pdf-2407.10651" aria-labelledby="pdf-2407.10651">pdf</a>, <a href="https://arxiv.org/html/2407.10651v2" title="View HTML" id="html-2407.10651" aria-labelledby="html-2407.10651" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.10651" title="Other formats" id="oth-2407.10651" aria-labelledby="oth-2407.10651">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A recipe based on Lebesgue functions for learning Variably Scaled Kernels via Discontinuous Neural Networks (未NN-VSKs) </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Audone,+G">Gianluca Audone</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Della+Santa,+F">Francesco Della Santa</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Perracchione,+E">Emma Perracchione</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Pieraccini,+S">Sandra Pieraccini</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> The efficacy of interpolating via Variably Scaled Kernels (VSKs) is known to be dependent on the definition of a proper scaling function, but no numerical recipes to construct it are available. Previous works suggest that such a function should mimic the target one, but no theoretical evidence is provided. This paper fills both the gaps: it proves that a scaling function reflecting the target one may lead to enhanced approximation accuracy, and it provides a user-independent tool for learning the scaling function by means of Discontinuous Neural Networks ($\delta$NN), i.e., NNs able to deal with possible discontinuities. Numerical evidence supports our claims, as it shows that the key features of the target function can be clearly recovered in the learned scaling function. </p> </div> </dd> <dt> <a name='item193'>[193]</a> <a href ="/abs/2407.11898" title="Abstract" id="2407.11898"> arXiv:2407.11898 </a> (replaced) [<a href="/pdf/2407.11898" title="Download PDF" id="pdf-2407.11898" aria-labelledby="pdf-2407.11898">pdf</a>, <a href="https://arxiv.org/html/2407.11898v2" title="View HTML" id="html-2407.11898" aria-labelledby="html-2407.11898" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.11898" title="Other formats" id="oth-2407.11898" aria-labelledby="oth-2407.11898">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> When does a Gaussian process have its paths in a reproducing kernel Hilbert space? </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Steinwart,+I">Ingo Steinwart</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 27 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> We investigate for which Gaussian processes there do or do not exist reproducing kernel Hilbert spaces (RKHSs) that contain almost all of their paths. In particular, we establish a new result that makes it possible to exclude the existence of such RKHSs in many cases. Moreover, we combine this negative result with some known techniques to establish positive results. Here it turns out that for many classical families of Gaussian processes we can fully characterize for which members of these families there exist RKHSs containing the paths. Similar characterizations are obtained for Gaussian processes, for which the RKHSs of their covariance functions are Sobolev spaces or Sobolev spaces of mixed smoothness. </p> </div> </dd> <dt> <a name='item194'>[194]</a> <a href ="/abs/2407.14699" title="Abstract" id="2407.14699"> arXiv:2407.14699 </a> (replaced) [<a href="/pdf/2407.14699" title="Download PDF" id="pdf-2407.14699" aria-labelledby="pdf-2407.14699">pdf</a>, <a href="https://arxiv.org/html/2407.14699v3" title="View HTML" id="html-2407.14699" aria-labelledby="html-2407.14699" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.14699" title="Other formats" id="oth-2407.14699" aria-labelledby="oth-2407.14699">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the smoothing theory delooping of disc diffeomorphism and embedding spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Salvatore,+P">Paolo Salvatore</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Turchin,+V">Victor Turchin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 51 pages, slightly improved presentation; A little mistake in Lemma 3.1 corrected: It turned out that the Alexander trick does not work for PD homeomorphisms of a disc. Remark 3.3 added </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Geometric Topology (math.GT)</span>; Algebraic Topology (math.AT) </div> <p class='mathjax'> The celebrated Morlet-Burghelea-Lashof-Kirby-Siebenmann smoothing theory theorem states that the group $\mathrm{Diff}_\partial(D^n)$ of diffeomorphisms of a disc $D^n$ relative to the boundary is equivalent to $\Omega^{n+1}\left(\mathrm{PL}_n/\mathrm{O}_n\right)$ for any $n\geq 1$ and to $\Omega^{n+1}\left(\mathrm{TOP}_n/\mathrm{O}_n\right)$ for $n\neq 4$. We revise smoothing theory results to show that the delooping generalizes to different versions of disc smooth embedding spaces relative to the boundary, namely the usual embeddings, those modulo immersions, and framed embeddings. The latter spaces deloop as $\mathrm{Emb}_\partial^{fr}(D^m,D^n)\simeq\Omega^{m+1}\left(\mathrm{O}_n\backslash\!\!\backslash\mathrm{PL}_n/\mathrm{PL}_{n,m}\right)\simeq \Omega^{m+1}\left(\mathrm{O}_n\backslash\!\!\backslash\mathrm{TOP}_n/\mathrm{TOP}_{n,m}\right)$ for any $n\geq m\geq 1$ ($n\neq 4$ for the second equivalence), where the left-hand side in the case $n-m=2$ or $(n,m)=(4,3)$ should be replaced by the union of the path-components of $\mathrm{PL}$-trivial knots (framing being disregarded). Moreover, we show that for $n\neq 4$, the delooping is compatible with the Budney $E_{m+1}$-action. We use this delooping to combine the Hatcher $\mathrm{O}_{m+1}$-action and the Budney $E_{m+1}$-action into a framed little discs operad $E_{m+1}^{\mathrm{O}_{m+1}}$-action on $\mathrm{Emb}_\partial^{fr}(D^m,D^n)$. </p> </div> </dd> <dt> <a name='item195'>[195]</a> <a href ="/abs/2407.17922" title="Abstract" id="2407.17922"> arXiv:2407.17922 </a> (replaced) [<a href="/pdf/2407.17922" title="Download PDF" id="pdf-2407.17922" aria-labelledby="pdf-2407.17922">pdf</a>, <a href="https://arxiv.org/html/2407.17922v2" title="View HTML" id="html-2407.17922" aria-labelledby="html-2407.17922" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.17922" title="Other formats" id="oth-2407.17922" aria-labelledby="oth-2407.17922">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Yetter-Drinfeld post-Hopf algebras and Yetter-Drinfeld relative Rota-Baxter operators </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Sciandra,+A">Andrea Sciandra</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 24 pages. Additional references. Proposition 3.1.5, Corollary 3.1.12, Proposition 3.1.13 and Example 4.1.3 have been added. Definition 4.0.2 and the proof of Lemma 4.0.5 have been modified. Other minor changes </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Algebra (math.QA)</span>; Category Theory (math.CT); Rings and Algebras (math.RA); Representation Theory (math.RT) </div> <p class='mathjax'> Recently, Li, Sheng and Tang introduced post-Hopf algebras and relative Rota-Baxter operators (on cocommutative Hopf algebras), providing an adjunction between the respective categories under the assumption that the structures involved are cocommutative. We introduce Yetter-Drinfeld post-Hopf algebras, which become usual post-Hopf algebras in the cocommutative setting. In analogy with the correspondence between cocommutative post-Hopf algebras and cocommutative Hopf braces, the category of Yetter-Drinfeld post-Hopf algebras is isomorphic to the category of Yetter-Drinfeld braces introduced by the author in a joint work with D. Ferri. This allows to explore the connection with matched pairs of actions and provide examples of Yetter-Drinfeld post-Hopf algebras. Moreover, we prove that the category of Yetter-Drinfeld post-Hopf algebras is equivalent to a subcategory of Yetter-Drinfeld relative Rota-Baxter operators. The latter structures coincide with the inverse maps of Yetter-Drinfeld 1-cocycles introduced by the author and D. Ferri, and generalise bijective relative Rota-Baxter operators on cocommutative Hopf algebras. Hence the previous equivalence passes to cocommutative post-Hopf algebras and bijective relative Rota-Baxter operators. Once the surjectivity of the Yetter-Drinfeld relative Rota-Baxter operators is removed, the equivalence is replaced by an adjunction and one can recover the result of Li, Sheng and Tang in the cocommutative case. </p> </div> </dd> <dt> <a name='item196'>[196]</a> <a href ="/abs/2408.04954" title="Abstract" id="2408.04954"> arXiv:2408.04954 </a> (replaced) [<a href="/pdf/2408.04954" title="Download PDF" id="pdf-2408.04954" aria-labelledby="pdf-2408.04954">pdf</a>, <a href="https://arxiv.org/html/2408.04954v2" title="View HTML" id="html-2408.04954" aria-labelledby="html-2408.04954" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2408.04954" title="Other formats" id="oth-2408.04954" aria-labelledby="oth-2408.04954">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Some notes concerning preconditioning of linear parabolic optimal control problems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Blank,+L">Luise Blank</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span>; Optimization and Control (math.OC) </div> <p class='mathjax'> In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target function is given over the whole time horizon. When implicit time discretization and conforming finite elements in space are employed we show that the reduced problem formulation has condition numbers which are bounded independently of the discretization level in arbitrary space dimension. In addition we propose for the all-at-once approach, i.e. for the first-order conditions of the unreduced system a preconditioner based on work by Greif and Sch枚tzau, which provides also bounds on the eigenvalue distribution independently of the discretization level. Numerical experiments demonstrate the obtained results and the efficiency of the suggested preconditioners. </p> </div> </dd> <dt> <a name='item197'>[197]</a> <a href ="/abs/2408.13599" title="Abstract" id="2408.13599"> arXiv:2408.13599 </a> (replaced) [<a href="/pdf/2408.13599" title="Download PDF" id="pdf-2408.13599" aria-labelledby="pdf-2408.13599">pdf</a>, <a href="https://arxiv.org/html/2408.13599v2" title="View HTML" id="html-2408.13599" aria-labelledby="html-2408.13599" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2408.13599" title="Other formats" id="oth-2408.13599" aria-labelledby="oth-2408.13599">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Sharp Sobolev and Adams-Trudinger-Moser inequalities for symmetric functions without boundary conditions on hyperbolic spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=%C3%93,+J+M+d">Jo茫o Marcos do 脫</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lu,+G">Guozhen Lu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ponciano,+R">Raon铆 Ponciano</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Differential Geometry (math.DG) </div> <p class='mathjax'> Embedding theorems for symmetric functions without zero boundary condition have been studied on flat Riemannian manifolds, such as the Euclidean space. However, these theorems have only been established on hyperbolic spaces for functions with zero boundary condition. In this work, we focus on sharp Sobolev and Adams-Trudinger-Moser embeddings for radial functions in hyperbolic spaces, considering both bounded and unbounded domains. One of the main features of our approach is that we do not assume boundary zero condition for symmetric functions on geodesic balls or the entire hyperbolic space. Our main results include Theorems 1.2, 1.3, and 1.4, which establish weighted Sobolev embedding theorems, and Theorems 1.5 together with 1.6, which present Adams-Trudinger-Moser type of embedding theorems. In particular, a key result is Theorem 1.1 which is a highly nontrivial comparison result between norms of the higher order covariant derivatives and higher order derivatives of the radial functions. Higher order asymptotic behavior of radial functions on hyperbolic spaces are established to prove our main theorems. This approach includes novel radial lemmata and decay properties of higher order radial Sobolev functions defined in hyperbolic space. </p> </div> </dd> <dt> <a name='item198'>[198]</a> <a href ="/abs/2409.00276" title="Abstract" id="2409.00276"> arXiv:2409.00276 </a> (replaced) [<a href="/pdf/2409.00276" title="Download PDF" id="pdf-2409.00276" aria-labelledby="pdf-2409.00276">pdf</a>, <a href="https://arxiv.org/html/2409.00276v3" title="View HTML" id="html-2409.00276" aria-labelledby="html-2409.00276" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.00276" title="Other formats" id="oth-2409.00276" aria-labelledby="oth-2409.00276">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Exact Recovery Guarantees for Parameterized Nonlinear System Identification Problem under Sparse Disturbances or Semi-Oblivious Attacks </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+H">Haixiang Zhang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yalcin,+B">Baturalp Yalcin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lavaei,+J">Javad Lavaei</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sontag,+E+D">Eduardo D. Sontag</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 43 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Cryptography and Security (cs.CR); Machine Learning (cs.LG); Systems and Control (eess.SY) </div> <p class='mathjax'> In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability $p$, which models the sparsity level of the disturbance vectors over time. These disturbances are drawn from an arbitrary, unknown probability distribution, which may depend on past disturbances, provided that it satisfies a zero-mean assumption. The primary objective of this paper is to learn the system's dynamics within a finite time and analyze the sample complexity as a function of $p$. To achieve this, we examine a LASSO-type non-smooth estimator, and establish necessary and sufficient conditions for its well-specifiedness and the uniqueness of the global solution to the underlying optimization problem. We then provide exact recovery guarantees for the estimator under two distinct conditions: boundedness and Lipschitz continuity of the basis functions. We show that finite-time exact recovery is achieved with high probability, even when $p$ approaches 1. Unlike prior works, which primarily focus on independent and identically distributed (i.i.d.) disturbances and provide only asymptotic guarantees for system learning, this study presents the first finite-time analysis of nonlinear dynamical systems under a highly general disturbance model. Our framework allows for possible temporal correlations in the disturbances and accommodates semi-oblivious adversarial attacks, significantly broadening the scope of existing theoretical results. </p> </div> </dd> <dt> <a name='item199'>[199]</a> <a href ="/abs/2409.02924" title="Abstract" id="2409.02924"> arXiv:2409.02924 </a> (replaced) [<a href="/pdf/2409.02924" title="Download PDF" id="pdf-2409.02924" aria-labelledby="pdf-2409.02924">pdf</a>, <a href="https://arxiv.org/html/2409.02924v2" title="View HTML" id="html-2409.02924" aria-labelledby="html-2409.02924" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.02924" title="Other formats" id="oth-2409.02924" aria-labelledby="oth-2409.02924">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Note on the Lalescu Sequence </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Mantegazza,+C">Carlo Mantegazza</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Melillo,+N+P">Nicola Pio Melillo</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Mathematics (math.GM)</span> </div> <p class='mathjax'> We prove that the Lalescu sequence is monotonically decreasing. </p> </div> </dd> <dt> <a name='item200'>[200]</a> <a href ="/abs/2409.04765" title="Abstract" id="2409.04765"> arXiv:2409.04765 </a> (replaced) [<a href="/pdf/2409.04765" title="Download PDF" id="pdf-2409.04765" aria-labelledby="pdf-2409.04765">pdf</a>, <a href="https://arxiv.org/html/2409.04765v2" title="View HTML" id="html-2409.04765" aria-labelledby="html-2409.04765" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.04765" title="Other formats" id="oth-2409.04765" aria-labelledby="oth-2409.04765">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Continuous-Time Online Distributed Seeking for Generalized Nash Equilibrium of Nonmonotone Online Game </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Chen,+J">Jianing Chen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Qian,+S">Sichen Qian</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Dang,+C">Chuangyin Dang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Qin,+S">Sitian Qin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> This work has been submitted to the lEEE for possible publication </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Systems and Control (eess.SY) </div> <p class='mathjax'> This paper mainly investigates a class of distributed generalized Nash equilibrium (GNE) seeking problems for online nonmonotone game with time-varying coupling inequality constraints. Based on a time-varying control gain, a novel continuous-time distributed GNE seeking algorithm is proposed, which realizes the constant regret bound and sublinear fit bound, matching those of the criteria for online optimization problems. Furthermore, to reduce unnecessary communication among players, a dynamic event-triggered mechanism involving internal variables is introduced into the distributed GNE seeking algorithm, while the constant regret bound and sublinear fit bound are still achieved. Also, the Zeno behavior is strictly prohibited. Finally, a numerical example is given to demonstrate the validity of the theoretical results. </p> </div> </dd> <dt> <a name='item201'>[201]</a> <a href ="/abs/2409.14222" title="Abstract" id="2409.14222"> arXiv:2409.14222 </a> (replaced) [<a href="/pdf/2409.14222" title="Download PDF" id="pdf-2409.14222" aria-labelledby="pdf-2409.14222">pdf</a>, <a href="/format/2409.14222" title="Other formats" id="oth-2409.14222" aria-labelledby="oth-2409.14222">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Achieving $h$- and $p$-robust monolithic multigrid solvers for the Stokes equations </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Rafiei,+A">Amin Rafiei</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=MacLachlan,+S">Scott MacLachlan</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> The numerical analysis of higher-order mixed finite-element discretizations for saddle-point problems, such as the Stokes equations, has been well-studied in recent years. While the theory and practice of such discretizations is now well-understood, the same cannot be said for efficient preconditioners for solving the resulting linear (or linearized) systems of equations. In this work, we propose and study variants of the well-known Vanka relaxation scheme that lead to effective geometric multigrid preconditioners for both the conforming Taylor-Hood discretizations and non-conforming ${\bf H}(\text{div})$-$L^2$ discretizations of the Stokes equations. Numerical results demonstrate robust performance with respect to FGMRES iteration counts for increasing polynomial order for some of the considered discretizations, and expose open questions about stopping tolerances for effectively preconditioned iterations at high polynomial order. </p> </div> </dd> <dt> <a name='item202'>[202]</a> <a href ="/abs/2409.14480" title="Abstract" id="2409.14480"> arXiv:2409.14480 </a> (replaced) [<a href="/pdf/2409.14480" title="Download PDF" id="pdf-2409.14480" aria-labelledby="pdf-2409.14480">pdf</a>, <a href="https://arxiv.org/html/2409.14480v2" title="View HTML" id="html-2409.14480" aria-labelledby="html-2409.14480" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.14480" title="Other formats" id="oth-2409.14480" aria-labelledby="oth-2409.14480">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Large-Time Asymptotics for the Kadomtsev-Petviashvili I Equation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Donmazov,+S">Samir Donmazov</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+J">Jiaqi Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Perry,+P">Peter Perry</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 60 pages, 2 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> We prove large time asymptotics for solutions of the KP I equation with small initial data. Our assumptions on the initial data rule out lump solutions but give a precise description of the radiation field at large times. Our analysis uses the inverse scattering method and involves large-time asymptotics for solutions to a non-local Riemann-Hilbert problem. </p> </div> </dd> <dt> <a name='item203'>[203]</a> <a href ="/abs/2410.21248" title="Abstract" id="2410.21248"> arXiv:2410.21248 </a> (replaced) [<a href="/pdf/2410.21248" title="Download PDF" id="pdf-2410.21248" aria-labelledby="pdf-2410.21248">pdf</a>, <a href="https://arxiv.org/html/2410.21248v2" title="View HTML" id="html-2410.21248" aria-labelledby="html-2410.21248" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.21248" title="Other formats" id="oth-2410.21248" aria-labelledby="oth-2410.21248">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Filtered instanton homology and cosmetic surgery </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Daemi,+A">Aliakbar Daemi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Eismeier,+M+M">Mike Miller Eismeier</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lidman,+T">Tye Lidman</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 33 pages, 3 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Geometric Topology (math.GT)</span> </div> <p class='mathjax'> The cosmetic surgery conjecture predicts that for a non-trivial knot in the three-sphere, performing two different Dehn surgeries results in distinct oriented three-manifolds. Hanselman reduced the problem to $\pm 2$ or $\pm 1/n$ surgeries being the only possible cosmetic surgeries. We remove the case of $\pm 1/n$-surgeries using the Chern-Simons filtration on Floer's original irreducible-only instanton homology, reducing the conjecture to the case of $\pm 2$ surgery on genus $2$ knots with trivial Alexander polynomial. We also prove some similar results for surgeries on knots in $S^2 \times S^1$. As key steps in establishing these results, we define invariants of the oriented homeomorphism type of three-manifolds derived from filtered instanton Floer homology and introduce a new surgery relationship for Floer's instanton homology. </p> </div> </dd> <dt> <a name='item204'>[204]</a> <a href ="/abs/2410.23457" title="Abstract" id="2410.23457"> arXiv:2410.23457 </a> (replaced) [<a href="/pdf/2410.23457" title="Download PDF" id="pdf-2410.23457" aria-labelledby="pdf-2410.23457">pdf</a>, <a href="https://arxiv.org/html/2410.23457v2" title="View HTML" id="html-2410.23457" aria-labelledby="html-2410.23457" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.23457" title="Other formats" id="oth-2410.23457" aria-labelledby="oth-2410.23457">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Approximation of maps from algebraic polyhedra to real algebraic varieties </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bilski,+M">Marcin Bilski</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kucharz,+W">Wojciech Kucharz</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 20 pages, paper slightly reorganized, minor corrections made </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> Given a finite simplicial complex $\mathcal{K}$ in $\mathbb{R}^n$ and a real algebraic variety $Y,$ by a $\mathcal{K}$-regular map $|\mathcal{K}|\rightarrow Y$ we mean a continuous map whose restriction to every simplex in $\mathcal{K}$ is a regular map. A simplified version of our main result says that if $Y$ is a uniformly retract rational variety and if $k, l$ are integers satisfying $0\leq l\leq k,$ then every $\mathcal{C}^l$ map $|\mathcal{K}|\rightarrow Y$ can be approximated in the $\mathcal{C}^l$ topology by $\mathcal{K}$-regular maps of class $\mathcal{C}^k.$ By definition, $Y$ is uniformly retract rational if for every point $y\in Y$ there is a Zariski open neighborhood $V\subset Y$ of $y$ such that the identity map of $V$ is the composite of regular maps $V\rightarrow W\rightarrow V,$ where $W\subset\mathbb{R}^p$ is a Zariski open set for some $p$ depending on $y.$ </p> </div> </dd> <dt> <a name='item205'>[205]</a> <a href ="/abs/2411.19891" title="Abstract" id="2411.19891"> arXiv:2411.19891 </a> (replaced) [<a href="/pdf/2411.19891" title="Download PDF" id="pdf-2411.19891" aria-labelledby="pdf-2411.19891">pdf</a>, <a href="https://arxiv.org/html/2411.19891v2" title="View HTML" id="html-2411.19891" aria-labelledby="html-2411.19891" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.19891" title="Other formats" id="oth-2411.19891" aria-labelledby="oth-2411.19891">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Identities for the product of Two Dirichlet Series Satisfying Hecke's Functional Equation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Berndt,+B+C">Bruce C. Berndt</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Xie,+L">Likun Xie</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages. Final version, to appear in Journal of Mathematical Analysis and Applications </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span> </div> <p class='mathjax'> We derive a general formula for the product of two Dirichlet series that satisfy Hecke's functional equation. Several examples are provided to demonstrate the applicability of the formula. In addition, we discuss prior work on similar products and clarify certain issues arising in the existing literature. </p> </div> </dd> <dt> <a name='item206'>[206]</a> <a href ="/abs/2412.06514" title="Abstract" id="2412.06514"> arXiv:2412.06514 </a> (replaced) [<a href="/pdf/2412.06514" title="Download PDF" id="pdf-2412.06514" aria-labelledby="pdf-2412.06514">pdf</a>, <a href="/format/2412.06514" title="Other formats" id="oth-2412.06514" aria-labelledby="oth-2412.06514">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Finite Volume Method for Elastic Waves in Heterogeneous, Anisotropic and Fractured Media </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Jacobsen,+I+K">Ingrid Kristine Jacobsen</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Berre,+I">Inga Berre</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Nordbotten,+J+M">Jan Martin Nordbotten</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Stefansson,+I">Ivar Stefansson</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> Numerical modeling of elastic wave propagation in the subsurface requires applicability to heterogeneous, anisotropic and discontinuous media, as well as support of free surface boundary conditions. Here we study the cell-centered finite volume method Multi-Point Stress Approximation with weak symmetry (MPSA-W) for solving the elastic wave equation. Finite volume methods are geometrically flexible, locally conserving and they are suitable for handling material discontinuities and anisotropies. For discretization in time we have utilized the Newmark method, thereby developing an MPSA-Newmark discretization for the elastic wave equation. An important aspect of this work is the integration of absorbing boundary conditions into the MPSA-Newmark method to limit possible boundary reflections. <br>We verify the MPSA-Newmark discretization numerically for model problems. Convergence analysis of MPSA-Newmark is performed using a known solution in a medium with homogeneous Dirichlet boundary conditions. The analysis demonstrates the expected convergence rates of second order for primary variables (displacements) and between first and second order for secondary variables (tractions). Further verification is conducted through convergence analysis with the inclusion of absorbing boundary conditions. The stability of the scheme is shown through numerical energy decay analyses for waves travelling with various incidence angles onto the absorbing boundaries. Lastly, we present simulation examples of wave propagation in fractured, heterogeneous and transversely isotropic media to demonstrate the versatility of the MPSA-Newmark discretization. </p> </div> </dd> <dt> <a name='item207'>[207]</a> <a href ="/abs/2412.13929" title="Abstract" id="2412.13929"> arXiv:2412.13929 </a> (replaced) [<a href="/pdf/2412.13929" title="Download PDF" id="pdf-2412.13929" aria-labelledby="pdf-2412.13929">pdf</a>, <a href="https://arxiv.org/html/2412.13929v2" title="View HTML" id="html-2412.13929" aria-labelledby="html-2412.13929" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2412.13929" title="Other formats" id="oth-2412.13929" aria-labelledby="oth-2412.13929">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A novel necessary and sufficient condition for the stability of $2\times 2$ first-order linear hyperbolic systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Balogoun,+I">Isma茂la Balogoun</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Auriol,+J">Jean Auriol</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Boussaada,+I">Islam Boussaada</a> (1 and 3), <a href="https://arxiv.org/search/math?searchtype=author&query=Mazanti,+G">Guilherme Mazanti</a> (1 and 2) ((1) Universit茅 Paris-Saclay, CNRS, CentraleSup茅lec, Inria, Laboratoire des Signaux et Syst猫mes, Gif-sur-Yvette, France, (2) F茅d茅ration de Math茅matiques de CentraleSup茅lec, Gif-sur-Yvette, France, (3) IPSA Paris, Ivry-sur-Seine, France)</div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Systems Control Lett., 199:Paper No. 106066, 9 pp., 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Analysis of PDEs (math.AP) </div> <p class='mathjax'> In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability problem for an integral difference equation, that is, a difference equation with distributed delay. Building upon a St茅p谩n--Hassard argument variation theorem originally designed for time-delay systems of retarded type, we then introduce a theorem that counts the number of unstable roots of our integral difference equation. This leads to the expected necessary and sufficient stability criterion for the system of first-order linear hyperbolic partial differential equations. Finally, we validate our theoretical findings through simulations. </p> </div> </dd> <dt> <a name='item208'>[208]</a> <a href ="/abs/2412.16071" title="Abstract" id="2412.16071"> arXiv:2412.16071 </a> (replaced) [<a href="/pdf/2412.16071" title="Download PDF" id="pdf-2412.16071" aria-labelledby="pdf-2412.16071">pdf</a>, <a href="https://arxiv.org/html/2412.16071v2" title="View HTML" id="html-2412.16071" aria-labelledby="html-2412.16071" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2412.16071" title="Other formats" id="oth-2412.16071" aria-labelledby="oth-2412.16071">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Good Scales and Non-Compactness of Squares </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Levine,+M">Maxwell Levine</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mildenberger,+H">Heike Mildenberger</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Removed a problematic subsection towards the end, corrected a number of typos and minor misstatements </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic (math.LO)</span> </div> <p class='mathjax'> Cummings, Foreman, and Magidor investigated the extent to which square principles are compact at singular cardinals. The first author proved that if $\kappa$ is a singular strong limit of uncountable cofinality, all scales on $\kappa$ are good, and $\square^*_\delta$ holds for all $\delta<\kappa$, then $\square_\kappa^*$ holds. In this paper we will present a strongly contrasting result for $\aleph_\omega$. We construct a model in which $\square_{\aleph_n}$ holds for all $n<\omega$, all scales on $\aleph_\omega$ are good, but in which $\square_{\aleph_\omega}^*$ fails and some weak forms of internal approachability for $[H(\aleph_{\omega+1})]^{\aleph_1}$ fail. This requires an extensive analysis of the dominating and approximation properties of a version of Namba forcing. We also prove some supporting results. </p> </div> </dd> <dt> <a name='item209'>[209]</a> <a href ="/abs/2412.17873" title="Abstract" id="2412.17873"> arXiv:2412.17873 </a> (replaced) [<a href="/pdf/2412.17873" title="Download PDF" id="pdf-2412.17873" aria-labelledby="pdf-2412.17873">pdf</a>, <a href="https://arxiv.org/html/2412.17873v2" title="View HTML" id="html-2412.17873" aria-labelledby="html-2412.17873" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2412.17873" title="Other formats" id="oth-2412.17873" aria-labelledby="oth-2412.17873">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Revisit Hamiltonian $S^1$-manifolds of dimension 6 with 4 fixed points </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Li,+H">Hui Li</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Symplectic Geometry (math.SG)</span>; Differential Geometry (math.DG) </div> <p class='mathjax'> If the circle acts in a Hamiltonian way on a compact symplectic manifold of dimension $2n$, then there are at least $n+1$ fixed points. The case that there are exactly $n+1$ isolated fixed points has its importance due to various reasons. Besides dimension 2 with 2 fixed points, and dimension 4 with 3 fixed points, which are known, the next interesting case is dimension 6 with 4 fixed points, for which the integral cohomology ring and the total Chern class of the manifold, and the sets of weights of the circle action at the fixed points are classified by Tolman. In this note, we use a new different argument to prove Tolman's results for the dimension 6 with 4 fixed points case. We observe that the integral cohomology ring of the manifold has a nice basis in terms of the moment map values of the fixed points, and the largest weight between two fixed points is nicely related to the first Chern class of the manifold. We will use these ingredients to determine the sets of weights of the circle action at the fixed points, and moreover to determine the global invariants the integral cohomology ring and total Chern class of the manifold. The idea allows a direct approach of the problem, and the argument is short and easy to follow. </p> </div> </dd> <dt> <a name='item210'>[210]</a> <a href ="/abs/2501.02752" title="Abstract" id="2501.02752"> arXiv:2501.02752 </a> (replaced) [<a href="/pdf/2501.02752" title="Download PDF" id="pdf-2501.02752" aria-labelledby="pdf-2501.02752">pdf</a>, <a href="https://arxiv.org/html/2501.02752v2" title="View HTML" id="html-2501.02752" aria-labelledby="html-2501.02752" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2501.02752" title="Other formats" id="oth-2501.02752" aria-labelledby="oth-2501.02752">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Douglas-Rachford algorithm for nonmonotone multioperator inclusion problems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Alcantara,+J+H">Jan Harold Alcantara</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Takeda,+A">Akiko Takeda</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 31 pages; Added Prop 4.6; Fixed typos </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> The Douglas-Rachford algorithm is a classic splitting method for finding a zero of the sum of two maximal monotone operators. It has also been applied to settings that involve one weakly and one strongly monotone operator. In this work, we extend the Douglas-Rachford algorithm to address multioperator inclusion problems involving $m$ ($m\geq 2$) weakly and strongly monotone operators, reformulated as a two-operator inclusion in a product space. By selecting appropriate parameters, we establish the convergence of the algorithm to a fixed point, from which solutions can be extracted. Furthermore, we illustrate its applicability to sum-of-$m$-functions minimization problems characterized by weakly convex and strongly convex functions. For general nonconvex problems in finite-dimensional spaces, comprising Lipschitz continuously differentiable functions and a proper closed function, we provide global subsequential convergence guarantees. </p> </div> </dd> <dt> <a name='item211'>[211]</a> <a href ="/abs/2501.03719" title="Abstract" id="2501.03719"> arXiv:2501.03719 </a> (replaced) [<a href="/pdf/2501.03719" title="Download PDF" id="pdf-2501.03719" aria-labelledby="pdf-2501.03719">pdf</a>, <a href="https://arxiv.org/html/2501.03719v2" title="View HTML" id="html-2501.03719" aria-labelledby="html-2501.03719" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2501.03719" title="Other formats" id="oth-2501.03719" aria-labelledby="oth-2501.03719">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Shape Taylor expansion for wave scattering problems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bao,+G">Gang Bao</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ma,+H">Haoran Ma</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lai,+J">Jun Lai</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Li,+J">Jingzhi Li</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span>; Analysis of PDEs (math.AP); Differential Geometry (math.DG) </div> <p class='mathjax'> The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high order shape derivatives required for this expansion poses significant challenges with conventional methods. This paper addresses these difficulties by introducing elegant recurrence formulas for computing high order shape derivatives. The derivation employs tools from exterior differential forms, Lie derivatives, and material derivatives. The work establishes a unified framework for computing the high order shape perturbations in scattering problems. In particular, the recurrence formulas are applicable to both acoustic and electromagnetic scattering models under a variety of boundary conditions, including Dirichlet, Neumann, impedance, and transmission types. </p> </div> </dd> <dt> <a name='item212'>[212]</a> <a href ="/abs/2501.04229" title="Abstract" id="2501.04229"> arXiv:2501.04229 </a> (replaced) [<a href="/pdf/2501.04229" title="Download PDF" id="pdf-2501.04229" aria-labelledby="pdf-2501.04229">pdf</a>, <a href="https://arxiv.org/html/2501.04229v5" title="View HTML" id="html-2501.04229" aria-labelledby="html-2501.04229" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2501.04229" title="Other formats" id="oth-2501.04229" aria-labelledby="oth-2501.04229">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Three-precision iterative refinement with parameter regularization and prediction for solving large sparse linear systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ge,+J">Jifeng Ge</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+J">Juan Zhang</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing low-precision arithmetic, particularly half-precision (FP16), for computationally intensive inner iterations, the method achieves substantial acceleration while maintaining high numerical accuracy. Key challenges such as overflow in FP16 and convergence issues for low precision are addressed through careful backward error analysis and the application of a regularization parameter $\alpha$. Furthermore, the integration of low-precision arithmetic into the parameter prediction process, using Gaussian process regression (GPR), significantly reduces computational time without degrading performance. The method is particularly effective for large-scale linear systems arising from discretized partial differential equations and other high-dimensional problems, where both accuracy and efficiency are critical. Numerical experiments demonstrate that the use of FP16 and mixed-precision strategies not only accelerates computation but also ensures robust convergence, making the approach advantageous for various applications. The results highlight the potential of leveraging lower-precision arithmetic to achieve superior computational efficiency in high-performance computing. </p> </div> </dd> <dt> <a name='item213'>[213]</a> <a href ="/abs/2501.16096" title="Abstract" id="2501.16096"> arXiv:2501.16096 </a> (replaced) [<a href="/pdf/2501.16096" title="Download PDF" id="pdf-2501.16096" aria-labelledby="pdf-2501.16096">pdf</a>, <a href="https://arxiv.org/html/2501.16096v3" title="View HTML" id="html-2501.16096" aria-labelledby="html-2501.16096" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2501.16096" title="Other formats" id="oth-2501.16096" aria-labelledby="oth-2501.16096">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A New Approach for Fourier Extension Based on Weighted Generalized Inverse </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Zhao,+Z">Zhenyu Zhao</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+Y">Yanfei Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yagola,+A+G">Anatoly G. Yagola</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Li,+X">Xusheng Li</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> This paper examines the Fourier extension from a new perspective of solving the compact operator equation with perturbed data. By converting the approximation target from the best approximate solution to the weighted best approximate solution, the oscillation in the extended region has been overcome. The error estimation of the solution is theoretically established. Furthermore, we point out the difficulties faced by the original weighted operator in calculation due to the limitation of machine precision and propose an effective correction operator. The relevant parameters involved in the method are further tested, and finally the effectiveness of the method is verified through numerical experiments. </p> </div> </dd> <dt> <a name='item214'>[214]</a> <a href ="/abs/2501.19263" title="Abstract" id="2501.19263"> arXiv:2501.19263 </a> (replaced) [<a href="/pdf/2501.19263" title="Download PDF" id="pdf-2501.19263" aria-labelledby="pdf-2501.19263">pdf</a>, <a href="https://arxiv.org/html/2501.19263v3" title="View HTML" id="html-2501.19263" aria-labelledby="html-2501.19263" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2501.19263" title="Other formats" id="oth-2501.19263" aria-labelledby="oth-2501.19263">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Pseudo-cones and measure transport </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Schneider,+R">Rolf Schneider</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 7 pages; changes in the proof of Theorem 2 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Metric Geometry (math.MG)</span> </div> <p class='mathjax'> A recent result on the Gauss image problem for pseudo-cones can be interpreted as a measure transport, performed by the reverse radial Gauss map of a pseudo-cone. We find a cost function that is minimized by this transport map, and we prove an analogue of Rockafellar's characterization of the subdifferentials of convex functions. </p> </div> </dd> <dt> <a name='item215'>[215]</a> <a href ="/abs/2502.06154" title="Abstract" id="2502.06154"> arXiv:2502.06154 </a> (replaced) [<a href="/pdf/2502.06154" title="Download PDF" id="pdf-2502.06154" aria-labelledby="pdf-2502.06154">pdf</a>, <a href="https://arxiv.org/html/2502.06154v2" title="View HTML" id="html-2502.06154" aria-labelledby="html-2502.06154" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.06154" title="Other formats" id="oth-2502.06154" aria-labelledby="oth-2502.06154">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The formality of the Goldman-Turaev Lie bialgebra on a closed surface </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Taniguchi,+T">Toyo Taniguchi</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 31 pages, 3 figures. Minor improvements </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Algebra (math.QA)</span>; Algebraic Topology (math.AT); Geometric Topology (math.GT); Rings and Algebras (math.RA) </div> <p class='mathjax'> We reformulate the Kashiwara-Vergne groups and associators in higher genera, introduced in Alekseev-Kawazumi-Kuno-Naef, in terms of non-commutative connections using the tools developed in a previous paper. As the main result, the case of closed surfaces is dealt with to determine the pro-unipotent automorphism group of the associated graded of the Goldman-Turaev Lie bialgebra. </p> </div> </dd> <dt> <a name='item216'>[216]</a> <a href ="/abs/2502.09098" title="Abstract" id="2502.09098"> arXiv:2502.09098 </a> (replaced) [<a href="/pdf/2502.09098" title="Download PDF" id="pdf-2502.09098" aria-labelledby="pdf-2502.09098">pdf</a>, <a href="https://arxiv.org/html/2502.09098v2" title="View HTML" id="html-2502.09098" aria-labelledby="html-2502.09098" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.09098" title="Other formats" id="oth-2502.09098" aria-labelledby="oth-2502.09098">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Multi-agent systems with multiple-wise interaction: Propagation of chaos and macroscopic limit </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Paul,+T">Thierry Paul</a> (LYSM), <a href="https://arxiv.org/search/math?searchtype=author&query=Rossi,+S">Stefano Rossi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tr%C3%A9lat,+E">Emmanuel Tr茅lat</a> (LJLL (UMR\_7598), CaGE)</div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> We consider interacting multi-agent systems where the interaction is not only pairwise but involves simultaneous interactions among multiple agents (multiple-wise interaction). By passing through the mesoscopic and macroscopic limits with a fixed multiple-wise interaction of order $m$, we derive a macroscopic equation in the limit $m \rightarrow \infty$, capturing the dominant effects in large-size multiple-wise order. </p> </div> </dd> <dt> <a name='item217'>[217]</a> <a href ="/abs/2502.09485" title="Abstract" id="2502.09485"> arXiv:2502.09485 </a> (replaced) [<a href="/pdf/2502.09485" title="Download PDF" id="pdf-2502.09485" aria-labelledby="pdf-2502.09485">pdf</a>, <a href="https://arxiv.org/html/2502.09485v3" title="View HTML" id="html-2502.09485" aria-labelledby="html-2502.09485" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.09485" title="Other formats" id="oth-2502.09485" aria-labelledby="oth-2502.09485">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Flow approach on the monotonicity of shape functionals </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Huang,+Y">Yong Huang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Li,+Q">Qinfeng Li</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Xie,+S">Shuangquan Xie</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yang,+H">Hang Yang</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span> </div> <p class='mathjax'> We develop a geometric flow framework to investigate the following two classical shape functionals: the torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. First, by constructing novel deformation paths governed by stretching flows, we prove several new monotonicity properties of the torsional rigidity and the first eigenvalue along the evolutions restricted to triangles and rhombuses. These results also lead to new and simpler proofs of some known results, unifying and extending prior symmetrization-based proofs. Second, utilizing the mean curvature flow, we give a new proof of the Saint-Venant inequality for smooth convex bodies. This might represent the first flow-based proof to establish geometric functional inequalities that couple both the domain and the state function associated with it. Third, by discovering a gradient norm inequality for the sides of rectangles, we prove monotonicity and stronger rigidity results of the torsional rigidity on rectangles. </p> </div> </dd> <dt> <a name='item218'>[218]</a> <a href ="/abs/2502.13118" title="Abstract" id="2502.13118"> arXiv:2502.13118 </a> (replaced) [<a href="/pdf/2502.13118" title="Download PDF" id="pdf-2502.13118" aria-labelledby="pdf-2502.13118">pdf</a>, <a href="https://arxiv.org/html/2502.13118v2" title="View HTML" id="html-2502.13118" aria-labelledby="html-2502.13118" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.13118" title="Other formats" id="oth-2502.13118" aria-labelledby="oth-2502.13118">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The Normal Play of the Domination Game </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Brito,+J+M">Jo茫o Marcos Brito</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Martins,+N">Nicolas Martins</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sampaio,+R">Rudini Sampaio</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span>; Discrete Mathematics (cs.DM) </div> <p class='mathjax'> In 2010, Bre拧ar, Klav啪ar and Rall introduced the optimization variant of the graph domination game and the game domination number. In 2024, Leo Versteegen obtained the celebrated proof of the Conjecture $\frac{3}{5}$ on this variant of the domination game, proposed by Kinnersley, West and Zamani in 2013. In this paper, we investigate for the first time the normal play of the domination game, which we call \textsc{Normal Domination Game}, that is an impartial game where the last to play wins. We use the Sprague-Grundy theory to prove that Alice (the first player) wins in the path $P_n$ if and only if $n$ is not a multiple of $4$, and wins in the cycle $C_n$ if and only if $n=4k+3$ for some integer $k$. Finally, we obtain a polynomial time algorithm to decide the winner for any disjoint union of paths and cycles in the \textsc{Normal Domination Game} and its natural partizan variant. </p> </div> </dd> <dt> <a name='item219'>[219]</a> <a href ="/abs/2502.16465" title="Abstract" id="2502.16465"> arXiv:2502.16465 </a> (replaced) [<a href="/pdf/2502.16465" title="Download PDF" id="pdf-2502.16465" aria-labelledby="pdf-2502.16465">pdf</a>, <a href="https://arxiv.org/html/2502.16465v3" title="View HTML" id="html-2502.16465" aria-labelledby="html-2502.16465" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.16465" title="Other formats" id="oth-2502.16465" aria-labelledby="oth-2502.16465">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Integral Ricci Curvature for Graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Oliv%C3%A9,+X+R">Xavier Ramos Oliv茅</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span>; Differential Geometry (math.DG) </div> <p class='mathjax'> We introduce the notion of integral Ricci curvature $I_{\kappa_0}$ for graphs, which measures the amount of Ricci curvature below a given threshold $\kappa_0$. We focus our attention on the Lin-Lu-Yau Ricci curvature. As applications, we prove a Bonnet-Myers-type diameter estimate, a Moore-type estimate on the number of vertices of a graph in terms of the maximum degree $d_M$ and diameter $D$, and a Lichnerowicz-type estimate for the first eigenvalue $\lambda_1$ of the Graph Laplacian, generalizing the results obtained by Lin, Lu, and Yau. All estimates are uniform, depending only on geometric parameters like $\kappa_0$, $I_{\kappa_0}$, $d_M$, or $D$, and do not require the graphs to be positively curved. </p> </div> </dd> <dt> <a name='item220'>[220]</a> <a href ="/abs/2502.16768" title="Abstract" id="2502.16768"> arXiv:2502.16768 </a> (replaced) [<a href="/pdf/2502.16768" title="Download PDF" id="pdf-2502.16768" aria-labelledby="pdf-2502.16768">pdf</a>, <a href="https://arxiv.org/html/2502.16768v2" title="View HTML" id="html-2502.16768" aria-labelledby="html-2502.16768" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.16768" title="Other formats" id="oth-2502.16768" aria-labelledby="oth-2502.16768">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Friedman vs P贸lya </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Alves,+R">Raphael Alves</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rosales,+R+A">Rafael A. Rosales</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 4 pages, 1 figure, corrected minor typos </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> Suppose an urn contains initially any number of balls of two colours. One ball is drawn randomly and then put back with $\alpha$ balls of the same colour and $\beta$ balls of the opposite colour. Both cases, $\beta=0$ and $\beta>0$ are well known and correspond respectively to P贸lya's and Friedman's replacement schemes. We consider a mixture of both of these: with probability $p\in(0,1]$ balls are replaced according to Friedman's recipe and with probability $1-p$ according to the one by P贸lya. Independently of the initial urn composition and independently of $\alpha$, $\beta$, and the value of $p>0$, we show that the proportion of balls of one colour converges almost surely to $\frac12$. The latter is the limit behaviour obtained by using Friedman's scheme alone, i.e. when $p=1$. Our result follows by adapting an argument due to D. S. Ornstein. </p> </div> </dd> <dt> <a name='item221'>[221]</a> <a href ="/abs/2503.00926" title="Abstract" id="2503.00926"> arXiv:2503.00926 </a> (replaced) [<a href="/pdf/2503.00926" title="Download PDF" id="pdf-2503.00926" aria-labelledby="pdf-2503.00926">pdf</a>, <a href="https://arxiv.org/html/2503.00926v2" title="View HTML" id="html-2503.00926" aria-labelledby="html-2503.00926" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.00926" title="Other formats" id="oth-2503.00926" aria-labelledby="oth-2503.00926">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Principalization on logarithmically foliated orbifolds </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Abramovich,+D">Dan Abramovich</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=da+Silva,+A+B">Andr茅 Belotto da Silva</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Temkin,+M">Michael Temkin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=W%C5%82odarczyk,+J">Jaros艂aw W艂odarczyk</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> We have introduced the notion of a thick class of foliations. We have also established a criterion for reducing the singularities of the pullback of a foliation in a thick class C to another foliation within the same class </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span> </div> <p class='mathjax'> In characteristic zero, we construct principalization of ideals on smooth orbifolds endowed with a normal crossings divisor and a foliation. We then illustrate how the method can be used in the general study of foliations via two applications. First, we provide a resolution of singularities of Darboux totally integrable foliations in arbitrary dimensions -- including rational and meromorphic Darboux foliations. Second, we show how to transform a generically transverse section into a transverse section. </p> </div> </dd> <dt> <a name='item222'>[222]</a> <a href ="/abs/2503.01624" title="Abstract" id="2503.01624"> arXiv:2503.01624 </a> (replaced) [<a href="/pdf/2503.01624" title="Download PDF" id="pdf-2503.01624" aria-labelledby="pdf-2503.01624">pdf</a>, <a href="https://arxiv.org/html/2503.01624v4" title="View HTML" id="html-2503.01624" aria-labelledby="html-2503.01624" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.01624" title="Other formats" id="oth-2503.01624" aria-labelledby="oth-2503.01624">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the module of derivations of a line arrangement </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Dimca,+A">Alexandru Dimca</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> v4: Theorem 1.6 is new and its proof is given in the new Section 4 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span>; Combinatorics (math.CO) </div> <p class='mathjax'> To each multiple point $p$ in a line arrangement $\mathcal A$ in the complex projective plane we associate a derivation $\tilde D_p \in D_0( \mathcal A)$. We show first that these derivations span a large subspace of $D_0(\mathcal A)$. To each such derivation $\tilde D_p \in D_0(\mathcal A)$ we associate a polynomial $g_p$ which seems to play a key role in the characterization of the freeness of $\mathcal A$, as well as in the study of the position of the multiple points of $\mathcal A$ with respect to unions of lines. </p> </div> </dd> <dt> <a name='item223'>[223]</a> <a href ="/abs/2503.05572" title="Abstract" id="2503.05572"> arXiv:2503.05572 </a> (replaced) [<a href="/pdf/2503.05572" title="Download PDF" id="pdf-2503.05572" aria-labelledby="pdf-2503.05572">pdf</a>, <a href="https://arxiv.org/html/2503.05572v2" title="View HTML" id="html-2503.05572" aria-labelledby="html-2503.05572" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.05572" title="Other formats" id="oth-2503.05572" aria-labelledby="oth-2503.05572">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Word problems and embedding-obstructions in cellular automata groups on groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Salo,+V">Ville Salo</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 39 pages + 9 page appendix; v2 has a new nonembeddability result (nonembeddability mod centers) and makes many small corrections </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Group Theory (math.GR)</span>; Computational Complexity (cs.CC); Formal Languages and Automata Theory (cs.FL); Dynamical Systems (math.DS) </div> <p class='mathjax'> We study groups of reversible cellular automata, or CA groups, on groups. More generally, we consider automorphism groups of subshifts of finite type on groups. It is known that word problems of CA groups on virtually nilpotent groups are in co-NP, and can be co-NP-hard. We show that under the Gap Conjecture of Grigorchuk, their word problems are PSPACE-hard on all other groups. On free and surface groups, we show that they are indeed always in PSPACE. On a group with co-NEXPTIME word problem, CA groups themselves have co-NEXPTIME word problem, and on the lamplighter group (which itself has polynomial-time word problem) we show they can be co-NEXPTIME-hard. We show also two nonembeddability results: the group of cellular automata on a non-cyclic free group does not embed in the group of cellular automata on the integers (this solves a question of Barbieri, Carrasco-Vargas and Rivera-Burgos); and the group of cellular automata in dimension $D$ does not embed in a group of cellular automata in dimension $d$ if $D \geq 3d+2$ (this solves a question of Hochman). </p> </div> </dd> <dt> <a name='item224'>[224]</a> <a href ="/abs/2503.06711" title="Abstract" id="2503.06711"> arXiv:2503.06711 </a> (replaced) [<a href="/pdf/2503.06711" title="Download PDF" id="pdf-2503.06711" aria-labelledby="pdf-2503.06711">pdf</a>, <a href="https://arxiv.org/html/2503.06711v2" title="View HTML" id="html-2503.06711" aria-labelledby="html-2503.06711" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.06711" title="Other formats" id="oth-2503.06711" aria-labelledby="oth-2503.06711">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Categories meet semigroups in various ways </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=P%C3%A9csi,+B">Bertalan P茅csi</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Category Theory (math.CT)</span> </div> <p class='mathjax'> This paper touches on several interaction points of semigroups and constructions from category theory: An adjunction is established between categories with selected arrows and semigroups. Regular semigroups are characterized by split epi - split mono factorization of the Karoubi envelope. We investigate how semigroupads (monads without requirement of unit transformation) map semigroups to semigroups and ensure certain properties provided they hold on meta level. </p> </div> </dd> <dt> <a name='item225'>[225]</a> <a href ="/abs/2503.07804" title="Abstract" id="2503.07804"> arXiv:2503.07804 </a> (replaced) [<a href="/pdf/2503.07804" title="Download PDF" id="pdf-2503.07804" aria-labelledby="pdf-2503.07804">pdf</a>, <a href="https://arxiv.org/html/2503.07804v4" title="View HTML" id="html-2503.07804" aria-labelledby="html-2503.07804" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.07804" title="Other formats" id="oth-2503.07804" aria-labelledby="oth-2503.07804">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Achievable Rate Regions for Multi-terminal Quantum Channels via Coset Codes </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Gouiaa,+F">Fatma Gouiaa</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Padakandla,+A">Arun Padakandla</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> This update contains all the inner bounds proven in the previous version. A few typographical and notation errors have been corrected. To provide a unified treatment of both broadcast and interference, we have included our inner bounds derived for the $3-$user QBC proven in <a href="https://arxiv.org/abs/2503.08755" data-arxiv-id="2503.08755" class="link-https">arXiv:2503.08755</a> as Section III of this manuscript. arXiv admin note: substantial text overlap with <a href="https://arxiv.org/abs/2203.00110" data-arxiv-id="2203.00110" class="link-https">arXiv:2203.00110</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Information Theory (cs.IT)</span>; Quantum Physics (quant-ph) </div> <p class='mathjax'> We undertake a Shannon theoretic study of the problem of communicating classical information over (i) a $3-$user quantum interference channel (QIC) and (ii) a $3-$user quantum broadcast channel (QBC). Our focus is on characterizing inner bounds. In our previous work, we had demonstrated that coding strategies based on coset codes can yield strictly larger inner bounds. Adopting the powerful technique of \textit{tilting}, \textit{smoothing} and \textit{augmentation} discovered by Sen recently, and combining with our coset code strategy we derive a new inner bound to the classical-quantum capacity region of both the $3-$user QIC and $3-$user QBC. The derived inner bound subsumes all current known bounds. </p> </div> </dd> <dt> <a name='item226'>[226]</a> <a href ="/abs/2503.07918" title="Abstract" id="2503.07918"> arXiv:2503.07918 </a> (replaced) [<a href="/pdf/2503.07918" title="Download PDF" id="pdf-2503.07918" aria-labelledby="pdf-2503.07918">pdf</a>, <a href="/format/2503.07918" title="Other formats" id="oth-2503.07918" aria-labelledby="oth-2503.07918">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The Hidden Toll of COVID-19 on Opioid Mortality in Georgia: A Bayesian Excess Opioid Mortality Analysis </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Peterkin,+C+J">Cyen J. Peterkin</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Waller,+L+A">Lance A. Waller</a> (1), <a href="https://arxiv.org/search/math?searchtype=author&query=Peterson,+E+N">Emily N. Peterson</a> (1) ((1) Department of Biostatistics and Bioinformatics, Emory Rollins School of Public Health)</div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Statistics Theory (math.ST)</span> </div> <p class='mathjax'> COVID-19 has had a large scale negative impact on the health of opioid users exacerbating the health of an already vulnerable population. Critical information on the total impact of COVID-19 on opioid users is unknown due to a lack of comprehensive data on COVID-19 cases, inaccurate diagnostic coding, and lack of data coverage. To assess the impact of COVID-19 on small-area opioid mortality, we developed a Bayesian hierarchical excess opioid mortality modeling approach. We incorporate spatio-temporal autocorrelation structures to allow for sharing of information across small areas and time to reduce uncertainty in small area estimates. Excess mortality is defined as the difference between observed trends after a crisis and expected trends based on observed historical trends, which captures the total increase in observed mortality rates compared to what was expected prior to the crisis. We illustrate the application of our approach to assess excess opioid mortality risk estimates for 159 counties in GA. Using our proposed approach will help inform interventions in opioid-related public health responses, policies, and resource allocation. The application of this work also provides a general framework for improving the estimation and mapping of health indicators during crisis periods for the opioid user population. </p> </div> </dd> <dt> <a name='item227'>[227]</a> <a href ="/abs/2503.09458" title="Abstract" id="2503.09458"> arXiv:2503.09458 </a> (replaced) [<a href="/pdf/2503.09458" title="Download PDF" id="pdf-2503.09458" aria-labelledby="pdf-2503.09458">pdf</a>, <a href="https://arxiv.org/html/2503.09458v2" title="View HTML" id="html-2503.09458" aria-labelledby="html-2503.09458" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.09458" title="Other formats" id="oth-2503.09458" aria-labelledby="oth-2503.09458">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Star decompositions and independent sets in random regular graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Harangi,+V">Viktor Harangi</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span>; Probability (math.PR) </div> <p class='mathjax'> A $k$-star decomposition of a graph is a partition of its edges into $k$-stars (i.e., $k$ edges with a common vertex). The paper studies the following problem: for what values of $k>d/2$ does the random $d$-regular graph have a $k$-star decomposition (asymptotically almost surely, provided that the number of edges is divisible by $k$)? <br>Delcourt, Greenhill, Isaev, Lidick媒, and Postle proposed the following conjecture. It is easy to see that a $k$-star decomposition necessitates the existence of an independent set of density $1-d/(2k)$. So let $k^{\mathrm{ind}}_d$ be the largest $k$ for which the random $d$-regular graph a.a.s. contains an independent set of this density. Clearly, $k$-star decompositions cannot exist for $k>k^{\mathrm{ind}}_d$. The conjecture suggests that this is essentially the only restriction: there is a threshold $k^\star_d$ such that $k$-star decompositions exist if and only if $k \leq k^\star_d$, and it (basically) coincides with the other threshold, i.e., $k^\star_d \approx k^{\mathrm{ind}}_d$. <br>We confirm this conjecture for sufficiently large $d$ by showing that a $k$-star decomposition exists if $d/2< k < k^{\mathrm{ind}}_d$. In fact, we prove the existence even if $k=k^{\mathrm{ind}}_d$ for degrees $d$ with asymptotic density $1$. </p> </div> </dd> <dt> <a name='item228'>[228]</a> <a href ="/abs/2503.10828" title="Abstract" id="2503.10828"> arXiv:2503.10828 </a> (replaced) [<a href="/pdf/2503.10828" title="Download PDF" id="pdf-2503.10828" aria-labelledby="pdf-2503.10828">pdf</a>, <a href="https://arxiv.org/html/2503.10828v2" title="View HTML" id="html-2503.10828" aria-labelledby="html-2503.10828" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.10828" title="Other formats" id="oth-2503.10828" aria-labelledby="oth-2503.10828">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Differential topology of the spaces of asymptotically stable vector fields and Lyapunov functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kvalheim,+M+D">Matthew D. Kvalheim</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 35 pages; version 2 improves exposition and former section 9, now an appendix </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Algebraic Topology (math.AT); Geometric Topology (math.GT); Optimization and Control (math.OC) </div> <p class='mathjax'> We study the topology of the space of all smooth asymptotically stable vector fields on $\mathbb{R}^n$, as well as the space of all proper smooth Lyapunov functions for such vector fields. We prove that both spaces are path-connected and simply connected when $n\neq 4,5$ and weakly contractible when $n\leq 3$. Moreover, both spaces have the weak homotopy type of the nonlinear Grassmannian of submanifolds of $\mathbb{R}^n$ diffeomorphic to the $n$-disc. <br>The proofs rely on Lyapunov theory and differential topology, such as the work of Smale and Perelman on the generalized Poincar茅 conjecture and results of Smale, Cerf, and Hatcher on the topology of diffeomorphism groups of discs. Applications include a partial answer to a question of Conley, a parametric Hartman-Grobman theorem for nonyperbolic but asymptotically stable equilibria, and a parametric Morse lemma for degenerate minima. We also study the related topics of hyperbolic equilibria, Morse minima, and relative homotopy groups of the space of asymptotically stable vector fields inside the space of those vanishing at a single point. </p> </div> </dd> <dt> <a name='item229'>[229]</a> <a href ="/abs/2503.11569" title="Abstract" id="2503.11569"> arXiv:2503.11569 </a> (replaced) [<a href="/pdf/2503.11569" title="Download PDF" id="pdf-2503.11569" aria-labelledby="pdf-2503.11569">pdf</a>, <a href="https://arxiv.org/html/2503.11569v2" title="View HTML" id="html-2503.11569" aria-labelledby="html-2503.11569" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.11569" title="Other formats" id="oth-2503.11569" aria-labelledby="oth-2503.11569">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Improvement of Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind and their theoretical analysis </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Okayama,+T">Tomoaki Okayama</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Keywords: Volterra integral equations, Fredholm integral equations, collocation method, Sinc approximation, SE transformation, DE transformation </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span> </div> <p class='mathjax'> Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind were proposed in 2012 and 2013 by multiple authors independently. Their theoretical analyses and numerical experiments suggest that the presented methods can attain root-exponential convergence. However, the convergence of these methods has not been strictly proved. This study first improves their methods to make them easier to implement, and provides a convergence theorem of the improved method. For the same equations, another Sinc-collocation method was proposed in 2016. This method is regarded as an improvement in the variable transformation employed in the method proposed in 2012. The method in 2016 may attain a higher rate than the previous methods, but its convergence has not yet been proved. For the method in 2016 as well, this study improves it to be easy to implement, and provides a convergence theorem. </p> </div> </dd> <dt> <a name='item230'>[230]</a> <a href ="/abs/2503.11931" title="Abstract" id="2503.11931"> arXiv:2503.11931 </a> (replaced) [<a href="/pdf/2503.11931" title="Download PDF" id="pdf-2503.11931" aria-labelledby="pdf-2503.11931">pdf</a>, <a href="https://arxiv.org/html/2503.11931v2" title="View HTML" id="html-2503.11931" aria-labelledby="html-2503.11931" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.11931" title="Other formats" id="oth-2503.11931" aria-labelledby="oth-2503.11931">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Positive Scalar Curvature and crystallographic fundamental groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Barcenas,+N">Noe Barcenas</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Velasquez,+M">Mario Velasquez</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Topology (math.AT)</span>; Differential Geometry (math.DG); Group Theory (math.GR) </div> <p class='mathjax'> We examine positive and negative results for the Gromov-Lawson-Rosenberg Conjecture within the class of crystallographic groups. We give necessary conditions within the class of split extensions of free abelian by cyclic groups to satisfy the unstable Gromov-Lawson-Rosenberg Conjecture. We also give necessary conditions within the same class of groups, producing an infinite number of counterexamples for the conjecture. </p> </div> </dd> <dt> <a name='item231'>[231]</a> <a href ="/abs/2503.12277" title="Abstract" id="2503.12277"> arXiv:2503.12277 </a> (replaced) [<a href="/pdf/2503.12277" title="Download PDF" id="pdf-2503.12277" aria-labelledby="pdf-2503.12277">pdf</a>, <a href="https://arxiv.org/html/2503.12277v4" title="View HTML" id="html-2503.12277" aria-labelledby="html-2503.12277" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.12277" title="Other formats" id="oth-2503.12277" aria-labelledby="oth-2503.12277">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On a conjecture of Erd艖s and Graham about the Sylvester's sequence </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Li,+Z">Zheng Li</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tang,+Q">Quanyu Tang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 23 pages; v2 generalizes the previous results; v3 fixes some typographical errors and adds several remarks; v4 corrects the definition of underapproximation and adds a final section proposing several open problems </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span>; Classical Analysis and ODEs (math.CA) </div> <p class='mathjax'> Let $\{u_n\}_{n=1}^{\infty}$ be the Sylvester's sequence (sequence A000058 in the OEIS), and let $ a_1 < a_2 < \cdots $ be any other positive integer sequence satisfying $ \sum_{i=1}^\infty \frac{1}{a_i} = 1 $. In this paper, we solve a conjecture of Erd艖s and Graham, which asks whether $$ \liminf_{n\to\infty} a_n^{\frac{1}{2^n}} < \lim_{n\to\infty} u_n^{\frac{1}{2^n}} = c_0 = 1.264085\ldots. $$ We prove this conjecture using a constructive approach. Furthermore, assuming that the unproven claim of Erd艖s and Graham that "all rationals have eventually greedy best Egyptian underapproximations" holds, we establish a generalization of this conjecture using a non-constructive approach. [This paper solves Problem 315 on Bloom's website "Erd艖s problems".] </p> </div> </dd> <dt> <a name='item232'>[232]</a> <a href ="/abs/2503.13337" title="Abstract" id="2503.13337"> arXiv:2503.13337 </a> (replaced) [<a href="/pdf/2503.13337" title="Download PDF" id="pdf-2503.13337" aria-labelledby="pdf-2503.13337">pdf</a>, <a href="https://arxiv.org/html/2503.13337v2" title="View HTML" id="html-2503.13337" aria-labelledby="html-2503.13337" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.13337" title="Other formats" id="oth-2503.13337" aria-labelledby="oth-2503.13337">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Chau,+T">Trung Chau</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Erey,+N">Nursel Erey</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Maithani,+A">Aryaman Maithani</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 20 pages. Minor revisions. Comments welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Commutative Algebra (math.AC)</span>; Combinatorics (math.CO) </div> <p class='mathjax'> Every monomial ideal $I$ has a Scarf complex, which is a subcomplex of its minimal free resolution. We say that $I$ is Scarf if its Scarf complex is also its minimal free resolution. In this paper, we fully characterize all pairs $(G,n)$ of a graph $G$ and an integer $n$ such that the squarefree power $I(G)^{[n]}$ or the symbolic power $I(G)^{(n)}$ of the edge ideal $I(G)$ is Scarf. We also determine all graphs $G$ such that its cover ideal $J(G)$ is Scarf, with an explicit description when $G$ is either chordal or bipartite. </p> </div> </dd> <dt> <a name='item233'>[233]</a> <a href ="/abs/2503.13810" title="Abstract" id="2503.13810"> arXiv:2503.13810 </a> (replaced) [<a href="/pdf/2503.13810" title="Download PDF" id="pdf-2503.13810" aria-labelledby="pdf-2503.13810">pdf</a>, <a href="https://arxiv.org/html/2503.13810v2" title="View HTML" id="html-2503.13810" aria-labelledby="html-2503.13810" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.13810" title="Other formats" id="oth-2503.13810" aria-labelledby="oth-2503.13810">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Limit theorems for the fluctuation of the mixed elephant random walk in the superdiffusive case </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Tokumitsu,+G">Go Tokumitsu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yano,+K">Kouji Yano</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> Motivated by the previous results by Coletti--de Lima--Gava--Luiz (2020) and Shiozawa (2022), we study the fluctuation of the mixed elephant random walk in the superdiffusive case, and prove the Central Limit Theorem and the Law of Iterated Logarithm with subtracting a random drift. </p> </div> </dd> <dt> <a name='item234'>[234]</a> <a href ="/abs/2503.14107" title="Abstract" id="2503.14107"> arXiv:2503.14107 </a> (replaced) [<a href="/pdf/2503.14107" title="Download PDF" id="pdf-2503.14107" aria-labelledby="pdf-2503.14107">pdf</a>, <a href="https://arxiv.org/html/2503.14107v2" title="View HTML" id="html-2503.14107" aria-labelledby="html-2503.14107" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.14107" title="Other formats" id="oth-2503.14107" aria-labelledby="oth-2503.14107">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A von Neumann algebraic approach to Quantum Theory on curved spacetime </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Labuschagne,+L+E">Louis E Labuschagne</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Majewski,+W+A">W Adam Majewski</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 28 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span> </div> <p class='mathjax'> By extending the method developed in our recent paper \cite{LM} we present the AQFT framework in terms of von Neumann algebras. In particular, this approach allows for a categorical description of AQFT as well as providing a natural and intrinsic framework for a description of entanglement. Turning to dynamical aspects of QFT we show that Killing local flows may be lifted to the algebraic setting in curved space-time. Furthermore, conditions under which quantum Lie derivatives of such local flows exist are provided. The central question that then emerges is how such quantum local flows might be described in interesting representations. We show that quasi-free representations of Weyl algebra fit the presented framework perfectly. Finally, the problem of enlarging the set of observables is discussed. We point out the usefulness of Orlicz space techniques to encompass unbounded field operators. In particular, a well-defined framework within which one can manipulate such operators is necessary for the correct presentation of (semiclassical) Einstein's equation. </p> </div> </dd> <dt> <a name='item235'>[235]</a> <a href ="/abs/2503.14511" title="Abstract" id="2503.14511"> arXiv:2503.14511 </a> (replaced) [<a href="/pdf/2503.14511" title="Download PDF" id="pdf-2503.14511" aria-labelledby="pdf-2503.14511">pdf</a>, <a href="https://arxiv.org/html/2503.14511v2" title="View HTML" id="html-2503.14511" aria-labelledby="html-2503.14511" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.14511" title="Other formats" id="oth-2503.14511" aria-labelledby="oth-2503.14511">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Green relations over finite monoids of $G$-equivariant functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ruiz-Medina,+R+H">Ramon H- Ruiz-Medina</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lara-G%C3%B3mez,+V+M">Victor M. Lara-G贸mez</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Group Theory (math.GR)</span> </div> <p class='mathjax'> For a group $G$ acting over a set $X$, the set of all the $G$-equivariant functions, i.e., the set of functions which conmute with the action, ($g\cdot f(x)=g\cdot f(x), \forall g\in G, \forall x\in X$), is a monoid with the composition. The Green Relations are powerful tools to comprehend the structure of a semigroup. We study the case where $X$ is a finite set and compute the green relations for its monoid of $G$-equivariant functions, attempting to describe them based on some particular elements in the monoid called elementary collapsings. </p> </div> </dd> <dt> <a name='item236'>[236]</a> <a href ="/abs/2503.14968" title="Abstract" id="2503.14968"> arXiv:2503.14968 </a> (replaced) [<a href="/pdf/2503.14968" title="Download PDF" id="pdf-2503.14968" aria-labelledby="pdf-2503.14968">pdf</a>, <a href="https://arxiv.org/html/2503.14968v2" title="View HTML" id="html-2503.14968" aria-labelledby="html-2503.14968" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.14968" title="Other formats" id="oth-2503.14968" aria-labelledby="oth-2503.14968">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Vertex degree sums for rainbow matchings in 3-uniform hypergraphs </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Liu,+H">Haorui Liu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lu,+M">Mei Lu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+Y">Yan Wang</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+Y">Yi Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> page 11 1 figure. arXiv admin note: text overlap with <a href="https://arxiv.org/abs/2004.12558" data-arxiv-id="2004.12558" class="link-https">arXiv:2004.12558</a> by other authors </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Combinatorics (math.CO)</span> </div> <p class='mathjax'> Let $n \in 3\mathbb{Z}$ be sufficiently large. Zhang, Zhao and Lu proved that if $H$ is a 3-uniform hypergraph with $n$ vertices and no isolated vertices, and if $deg(u)+deg(v) > \frac{2}{3}n^2 - \frac{8}{3}n + 2$ for any two vertices $u$ and $v$ that are contained in some edge of $H$, then $ H $ admits a perfect matching. In this paper, we prove that the rainbow version of Zhang, Zhao and Lu's result is asymptotically true. More specifically, let $\delta > 0$ and $ F_1, F_2, \dots, F_{n/3} $ be 3-uniform hypergraphs on a common set of $n$ vertices. For each $ i \in [n/3] $, suppose that $F_i$ has no isolated vertices and $deg_{F_i}(u)+deg_{F_i}(v) > \left( \frac{2}{3} + \delta \right)n^2$ holds for any two vertices $u$ and $v$ that are contained in some edge of $F_i$. Then $ \{ F_1, F_2, \dots, F_{n/3} \} $ admits a rainbow matching. Note that this result is asymptotically tight. </p> </div> </dd> <dt> <a name='item237'>[237]</a> <a href ="/abs/2503.15736" title="Abstract" id="2503.15736"> arXiv:2503.15736 </a> (replaced) [<a href="/pdf/2503.15736" title="Download PDF" id="pdf-2503.15736" aria-labelledby="pdf-2503.15736">pdf</a>, <a href="https://arxiv.org/html/2503.15736v2" title="View HTML" id="html-2503.15736" aria-labelledby="html-2503.15736" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.15736" title="Other formats" id="oth-2503.15736" aria-labelledby="oth-2503.15736">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Convergence Rate Analysis of the Join-the-Shortest-Queue System </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ma,+Y">Yuanzhe Ma</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Maguluri,+S+T">Siva Theja Maguluri</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span> </div> <p class='mathjax'> The Join-the-Shortest-Queue (JSQ) policy is among the most widely used routing algorithms for load balancing systems and has been extensively studied. Despite its simplicity and optimality, exact characterization of the system remains challenging. Most prior research has focused on analyzing its performance in steady-state in certain asymptotic regimes such as the heavy-traffic regime. However, the convergence rate to the steady-state in these regimes is often slow, calling into question the reliability of analyses based solely on the steady-state and heavy-traffic approximations. To address this limitation, we provide a finite-time convergence rate analysis of a JSQ system with two symmetric servers. In sharp contrast to the existing literature, we directly study the original system as opposed to an approximate limiting system such as a diffusion approximation. Our results demonstrate that for such a system, the convergence rate to its steady-state, measured in the total variation distance, is $O \left(\frac{1}{(1-\rho)^3} \frac{1}{t} \right)$, where $\rho \in (0,1)$ is the traffic intensity. </p> </div> </dd> <dt> <a name='item238'>[238]</a> <a href ="/abs/2503.15813" title="Abstract" id="2503.15813"> arXiv:2503.15813 </a> (replaced) [<a href="/pdf/2503.15813" title="Download PDF" id="pdf-2503.15813" aria-labelledby="pdf-2503.15813">pdf</a>, <a href="https://arxiv.org/html/2503.15813v2" title="View HTML" id="html-2503.15813" aria-labelledby="html-2503.15813" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.15813" title="Other formats" id="oth-2503.15813" aria-labelledby="oth-2503.15813">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> An isopermetric inequality for lower order Neumann eigenvalues in Gauss space </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gao,+Y">Yi Gao</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+K">Kui Wang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Comments are welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Spectral Theory (math.SP)</span>; Analysis of PDEs (math.AP) </div> <p class='mathjax'> We prove a sharp isoperimetric inequality for the harmonic mean of the first $m-1$ nonzero Neumann eigenvalues for bounded Lipschitz domains symmetric about the origin in Gauss space. Our result generalizes the Szeg枚-Weinberger type inequality in Gauss space, as proved in [8, Theorem 4.1]. </p> </div> </dd> <dt> <a name='item239'>[239]</a> <a href ="/abs/2503.15894" title="Abstract" id="2503.15894"> arXiv:2503.15894 </a> (replaced) [<a href="/pdf/2503.15894" title="Download PDF" id="pdf-2503.15894" aria-labelledby="pdf-2503.15894">pdf</a>, <a href="https://arxiv.org/html/2503.15894v2" title="View HTML" id="html-2503.15894" aria-labelledby="html-2503.15894" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.15894" title="Other formats" id="oth-2503.15894" aria-labelledby="oth-2503.15894">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The Gaussian central limit theorem for a stationary time series with infinite variance </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Matsui,+M">Muneya Matsui</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mikosch,+T">Thomas Mikosch</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 22 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Statistics Theory (math.ST) </div> <p class='mathjax'> We consider a borderline case: the central limit theorem for a strictly stationary time series with infinite variance but a Gaussian limit. In the iid case a well-known sufficient condition for this central limit theorem is regular variation of the marginal distribution with tail index $\alpha=2$. In the dependent case we assume the stronger condition of sequential regular variation of the time series with tail index $\alpha=2$. We assume that a sample of size $n$ from this time series can be split into $k_n$ blocks of size $r_n\to\infty$ such that $r_n/n\to 0$ as $n\to\infty$ and that the block sums are asymptotically independent. Then we apply classical central limit theory for row-wise iid triangular arrays. The necessary and sufficient conditions for such independent block sums will be verified by using large deviation results for the time series. We derive the central limit theorem for $m$-dependent sequences, linear processes, stochastic volatility processes and solutions to affine stochastic recurrence equations whose marginal distributions have infinite variance and are regularly varying with tail index $\alpha=2$. </p> </div> </dd> <dt> <a name='item240'>[240]</a> <a href ="/abs/2503.16039" title="Abstract" id="2503.16039"> arXiv:2503.16039 </a> (replaced) [<a href="/pdf/2503.16039" title="Download PDF" id="pdf-2503.16039" aria-labelledby="pdf-2503.16039">pdf</a>, <a href="https://arxiv.org/html/2503.16039v2" title="View HTML" id="html-2503.16039" aria-labelledby="html-2503.16039" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.16039" title="Other formats" id="oth-2503.16039" aria-labelledby="oth-2503.16039">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> How much should we care about what others know? Jump signals in optimal investment under relative performance concerns </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bank,+P">Peter Bank</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sedrakjan,+G">Gemma Sedrakjan</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span> </div> <p class='mathjax'> We present a multi-agent and mean-field formulation of a game between investors who receive private signals informing their investment decisions and who interact through relative performance concerns. A key tool in our model is a Poisson random measure which drives jumps in both market prices and signal processes and thus captures common and idiosyncratic noise. Upon receiving a jump signal, an investor evaluates not only the signal's implications for stock price movements but also its implications for the signals received by her peers and for their subsequent investment decisions. A crucial aspect of this assessment is the distribution of investor types in the economy. These types determine their risk aversion, performance concerns, and the quality and quantity of their signals. We demonstrate how these factors are reflected in the corresponding HJB equations, characterizing an agent's optimal response to her peers' signal-based strategies. The existence of equilibria in both the multi-agent and mean-field game is established using Schauder's Fixed Point Theorem under suitable conditions on investor characteristics, particularly their signal processes. Finally, we present numerical case studies that illustrate these equilibria from a financial-economic perspective. This allows us to address questions such as how much investors should care about the information known by their peers. </p> </div> </dd> <dt> <a name='item241'>[241]</a> <a href ="/abs/2008.05569" title="Abstract" id="2008.05569"> arXiv:2008.05569 </a> (replaced) [<a href="/pdf/2008.05569" title="Download PDF" id="pdf-2008.05569" aria-labelledby="pdf-2008.05569">pdf</a>, <a href="https://arxiv.org/html/2008.05569v5" title="View HTML" id="html-2008.05569" aria-labelledby="html-2008.05569" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2008.05569" title="Other formats" id="oth-2008.05569" aria-labelledby="oth-2008.05569">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A new notion of commutativity for the algorithmic Lov谩sz Local Lemma </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Harris,+D+G">David G. Harris</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Iliopoulos,+F">Fotis Iliopoulos</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Kolmogorov,+V">Vladimir Kolmogorov</a></div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> RANDOM 2021 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Data Structures and Algorithms (cs.DS)</span>; Probability (math.PR) </div> <p class='mathjax'> The Lov谩sz Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works revealed that the LLL has intimate connections with a class of stochastic local search algorithms for finding such desirable objects. In particular, it can be seen as a sufficient condition for this type of algorithms to converge fast. <br>Besides conditions for existence of and fast convergence to desirable objects, one may naturally ask further questions regarding properties of these algorithms. For instance, "are they parallelizable?", "how many solutions can they output?", "what is the expected "weight" of a solution?", etc. These questions and more have been answered for a class of LLL-inspired algorithms called commutative. In this paper we introduce a new, very natural and more general notion of commutativity (essentially matrix commutativity) which allows us to show a number of new refined properties of LLL-inspired local search algorithms with significantly simpler proofs. </p> </div> </dd> <dt> <a name='item242'>[242]</a> <a href ="/abs/2009.13678" title="Abstract" id="2009.13678"> arXiv:2009.13678 </a> (replaced) [<a href="/pdf/2009.13678" title="Download PDF" id="pdf-2009.13678" aria-labelledby="pdf-2009.13678">pdf</a>, <a href="https://arxiv.org/html/2009.13678v3" title="View HTML" id="html-2009.13678" aria-labelledby="html-2009.13678" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2009.13678" title="Other formats" id="oth-2009.13678" aria-labelledby="oth-2009.13678">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Noise Variance Estimation Using Asymptotic Residual in Compressed Sensing </div> <div class='list-authors'><a href="https://arxiv.org/search/eess?searchtype=author&query=Hayakawa,+R">Ryo Hayakawa</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> accepted to APSIPA Transactions on Signal and Information Processing </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> APSIPA Transactions on Signal and Information Processing, vol. 12, no. 1, e46, Nov. 2023 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Signal Processing (eess.SP)</span>; Information Theory (cs.IT) </div> <p class='mathjax'> In compressed sensing, measurements are typically contaminated by additive noise, and therefore, information about the noise variance is often needed to design algorithms. In this paper, we propose a method for estimating the unknown noise variance in compressed sensing problems. The proposed method, called asymptotic residual matching (ARM), estimates the noise variance from a single measurement vector on the basis of the asymptotic result for the $\ell_{1}$ optimization problem. Specifically, we derive the asymptotic residual corresponding to the $\ell_{1}$ optimization and show that it depends on the noise variance. The proposed ARM approach obtains the estimate by comparing the asymptotic residual with the actual one, which can be obtained by empirical reconstruction without the information on the noise variance. For the proposed ARM, we also propose a method to choose a reasonable parameter based on the asymptotic residual. Simulation results show that the proposed noise variance estimation outperforms several conventional methods, especially when the problem size is small. We also show that, by using the proposed method, we can tune the regularization parameter of the $\ell_{1}$ optimization to achieve good reconstruction performance, even when the noise variance is unknown. </p> </div> </dd> <dt> <a name='item243'>[243]</a> <a href ="/abs/2109.13479" title="Abstract" id="2109.13479"> arXiv:2109.13479 </a> (replaced) [<a href="/pdf/2109.13479" title="Download PDF" id="pdf-2109.13479" aria-labelledby="pdf-2109.13479">pdf</a>, <a href="https://arxiv.org/html/2109.13479v5" title="View HTML" id="html-2109.13479" aria-labelledby="html-2109.13479" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2109.13479" title="Other formats" id="oth-2109.13479" aria-labelledby="oth-2109.13479">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Knowledge Transfer based Evolutionary Deep Neural Network for Intelligent Fault Diagnosis </div> <div class='list-authors'><a href="https://arxiv.org/search/eess?searchtype=author&query=Sharma,+A+K">Arun K. Sharma</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Verma,+N+K">Nishchal K. Verma</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Submitted to IEEE Transactions on Sustainable Computing </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Signal Processing (eess.SP)</span>; Artificial Intelligence (cs.AI); Systems and Control (eess.SY); Optimization and Control (math.OC) </div> <p class='mathjax'> A faster response with commendable accuracy in intelligent systems is essential for the reliability and smooth operations of industrial machines. Two main challenges affect the design of such intelligent systems: (i) the selection of a suitable model and (ii) domain adaptation if there is a continuous change in operating conditions. Therefore, we propose an evolutionary Net2Net transformation (EvoN2N) that finds the best suitable DNN architecture with limited availability of labeled data samples. Net2Net transformation-based quick learning algorithm has been used in the evolutionary framework of Non-dominated sorting genetic algorithm II to obtain the best DNN architecture. Net2Net transformation-based quick learning algorithm uses the concept of knowledge transfer from one generation to the next for faster fitness evaluation. The proposed framework can obtain the best model for intelligent fault diagnosis without a long and time-consuming search process. The proposed framework has been validated on the Case Western Reserve University dataset, the Paderborn University dataset, and the gearbox fault detection dataset under different operating conditions. The best models obtained are capable of demonstrating an excellent diagnostic performance and classification accuracy of almost up to 100% for most of the operating conditions. </p> </div> </dd> <dt> <a name='item244'>[244]</a> <a href ="/abs/2110.00675" title="Abstract" id="2110.00675"> arXiv:2110.00675 </a> (replaced) [<a href="/pdf/2110.00675" title="Download PDF" id="pdf-2110.00675" aria-labelledby="pdf-2110.00675">pdf</a>, <a href="https://arxiv.org/html/2110.00675v5" title="View HTML" id="html-2110.00675" aria-labelledby="html-2110.00675" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2110.00675" title="Other formats" id="oth-2110.00675" aria-labelledby="oth-2110.00675">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Tsukamoto,+H">Hiroyasu Tsukamoto</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Chung,+S">Soon-Jo Chung</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Slotine,+J+E">Jean-Jacques E. Slotine</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Annual Reviews in Control, Preprint Version, Accepted, Oct. 1st </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Annual Reviews in Control; Volume 52; 2021; Pages 135-169; ISSN 1367-5788 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Robotics (cs.RO); Systems and Control (eess.SY); Optimization and Control (math.OC) </div> <p class='mathjax'> Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. By using a squared differential length as a Lyapunov-like function, its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, indicating that many parallels can be drawn between well-known linear systems theory and contraction theory for nonlinear systems. Furthermore, contraction theory takes advantage of a superior robustness property of exponential stability used in conjunction with the comparison lemma. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit the systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The objective of this paper is, therefore, to present a tutorial overview of contraction theory and its advantages in nonlinear stability analysis of deterministic and stochastic systems, with an emphasis on deriving formal robustness and stability guarantees for various learning-based and data-driven automatic control methods. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks. </p> </div> </dd> <dt> <a name='item245'>[245]</a> <a href ="/abs/2208.03123" title="Abstract" id="2208.03123"> arXiv:2208.03123 </a> (replaced) [<a href="/pdf/2208.03123" title="Download PDF" id="pdf-2208.03123" aria-labelledby="pdf-2208.03123">pdf</a>, <a href="https://arxiv.org/html/2208.03123v3" title="View HTML" id="html-2208.03123" aria-labelledby="html-2208.03123" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2208.03123" title="Other formats" id="oth-2208.03123" aria-labelledby="oth-2208.03123">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Watson-Crick conjugates of words and languages </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Mahalingam,+K">Kalpana Mahalingam</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Maity,+A">Anuran Maity</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Formal Languages and Automata Theory (cs.FL)</span>; Combinatorics (math.CO) </div> <p class='mathjax'> In this work, we explore the concept of Watson-Crick conjugates, also known as $\theta$-conjugates (where $\theta$ is an antimorphic involution), of words and languages. This concept extends the classical idea of conjugates by incorporating the Watson-Crick complementarity of DNA sequences. Our investigation initially focuses on the properties of $\theta$-conjugates of words. We then define $\theta$-conjugates of a language and study closure properties of certain families of languages under the $\theta$-conjugate operation. Furthermore, we analyze the iterated $\theta$-conjugate of both words and languages. Finally, we discuss the idea of $\theta$-conjugate-free languages and examine some decidability problems related to it. </p> </div> </dd> <dt> <a name='item246'>[246]</a> <a href ="/abs/2307.09216" title="Abstract" id="2307.09216"> arXiv:2307.09216 </a> (replaced) [<a href="/pdf/2307.09216" title="Download PDF" id="pdf-2307.09216" aria-labelledby="pdf-2307.09216">pdf</a>, <a href="https://arxiv.org/html/2307.09216v2" title="View HTML" id="html-2307.09216" aria-labelledby="html-2307.09216" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2307.09216" title="Other formats" id="oth-2307.09216" aria-labelledby="oth-2307.09216">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Rough PDEs for local stochastic volatility models </div> <div class='list-authors'><a href="https://arxiv.org/search/q-fin?searchtype=author&query=Bank,+P">Peter Bank</a>, <a href="https://arxiv.org/search/q-fin?searchtype=author&query=Bayer,+C">Christian Bayer</a>, <a href="https://arxiv.org/search/q-fin?searchtype=author&query=Friz,+P+K">Peter K. Friz</a>, <a href="https://arxiv.org/search/q-fin?searchtype=author&query=Pelizzari,+L">Luca Pelizzari</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 36 pages, 2 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Finance (q-fin.MF)</span>; Probability (math.PR) </div> <p class='mathjax'> In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time-inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely understand the conditional LSV dynamics and reveal their Markovian nature. The latter allows us to connect the conditional dynamics to so-called rough partial differential equations (RPDEs), through a Feynman-Kac type of formula. In terms of European pricing, conditional on realizations of one Brownian motion, we can compute conditional option prices by solving the corresponding linear RPDEs, and then average over all samples to find unconditional prices. Our approach depends only minimally on the specification of the volatility, making it applicable for a wide range of classical and rough LSV models, and it establishes a PDE pricing method for non-Markovian models. Finally, we present a first glimpse at numerical methods for RPDEs and apply them to price European options in several rough LSV models. </p> </div> </dd> <dt> <a name='item247'>[247]</a> <a href ="/abs/2401.14086" title="Abstract" id="2401.14086"> arXiv:2401.14086 </a> (replaced) [<a href="/pdf/2401.14086" title="Download PDF" id="pdf-2401.14086" aria-labelledby="pdf-2401.14086">pdf</a>, <a href="https://arxiv.org/html/2401.14086v4" title="View HTML" id="html-2401.14086" aria-labelledby="html-2401.14086" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2401.14086" title="Other formats" id="oth-2401.14086" aria-labelledby="oth-2401.14086">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Generating Likely Counterfactuals Using Sum-Product Networks </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Nemecek,+J">Jiri Nemecek</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Pevny,+T">Tomas Pevny</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Marecek,+J">Jakub Marecek</a></div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> The Thirteenth International Conference on Learning Representations (ICLR 2025) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Artificial Intelligence (cs.AI)</span>; Machine Learning (cs.LG); Optimization and Control (math.OC) </div> <p class='mathjax'> The need to explain decisions made by AI systems is driven by both recent regulation and user demand. The decisions are often explainable only post hoc. In counterfactual explanations, one may ask what constitutes the best counterfactual explanation. Clearly, multiple criteria must be taken into account, although "distance from the sample" is a key criterion. Recent methods that consider the plausibility of a counterfactual seem to sacrifice this original objective. Here, we present a system that provides high-likelihood explanations that are, at the same time, close and sparse. We show that the search for the most likely explanations satisfying many common desiderata for counterfactual explanations can be modeled using Mixed-Integer Optimization (MIO). We use a Sum-Product Network (SPN) to estimate the likelihood of a counterfactual. To achieve that, we propose an MIO formulation of an SPN, which can be of independent interest. The source code with examples is available at <a href="https://github.com/Epanemu/LiCE" rel="external noopener nofollow" class="link-external link-https">this https URL</a>. </p> </div> </dd> <dt> <a name='item248'>[248]</a> <a href ="/abs/2404.17429" title="Abstract" id="2404.17429"> arXiv:2404.17429 </a> (replaced) [<a href="/pdf/2404.17429" title="Download PDF" id="pdf-2404.17429" aria-labelledby="pdf-2404.17429">pdf</a>, <a href="https://arxiv.org/html/2404.17429v3" title="View HTML" id="html-2404.17429" aria-labelledby="html-2404.17429" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2404.17429" title="Other formats" id="oth-2404.17429" aria-labelledby="oth-2404.17429">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Separation capacity of linear reservoirs with random connectivity matrix </div> <div class='list-authors'><a href="https://arxiv.org/search/stat?searchtype=author&query=Boutaib,+Y">Youness Boutaib</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (stat.ML)</span>; Machine Learning (cs.LG); Probability (math.PR) </div> <p class='mathjax'> A natural hypothesis for the success of reservoir computing in generic tasks is the ability of the untrained reservoir to map different input time series to separable reservoir states - a property we term separation capacity. We provide a rigorous mathematical framework to quantify this capacity for random linear reservoirs, showing that it is fully characterised by the spectral properties of the generalised matrix of moments of the random reservoir connectivity matrix. Our analysis focuses on reservoirs with Gaussian connectivity matrices, both symmetric and i.i.d., although the techniques extend naturally to broader classes of random matrices. In the symmetric case, the generalised matrix of moments is a Hankel matrix. Using classical estimates from random matrix theory, we establish that separation capacity deteriorates over time and that, for short inputs, optimal separation in large reservoirs is achieved when the matrix entries are scaled with a factor $\rho_T/\sqrt{N}$, where $N$ is the reservoir dimension and $\rho_T$ depends on the maximum input length. In the i.i.d.\ case, we establish that optimal separation with large reservoirs is consistently achieved when the entries of the reservoir matrix are scaled with the exact factor $1/\sqrt{N}$, which aligns with common implementations of reservoir computing. We further give upper bounds on the quality of separation as a function of the length of the time series. We complement this analysis with an investigation of the likelihood of this separation and its consistency under different architectural choices. </p> </div> </dd> <dt> <a name='item249'>[249]</a> <a href ="/abs/2407.13867" title="Abstract" id="2407.13867"> arXiv:2407.13867 </a> (replaced) [<a href="/pdf/2407.13867" title="Download PDF" id="pdf-2407.13867" aria-labelledby="pdf-2407.13867">pdf</a>, <a href="https://arxiv.org/html/2407.13867v3" title="View HTML" id="html-2407.13867" aria-labelledby="html-2407.13867" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.13867" title="Other formats" id="oth-2407.13867" aria-labelledby="oth-2407.13867">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Poincare gauge gravity from nonmetric gravity </div> <div class='list-authors'><a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Wheeler,+J+T">James T. Wheeler</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Clarified details of Section 4 </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Nuclear Physics B, Volume 1014, 2025, 116860, ISSN 0550-3213 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Relativity and Quantum Cosmology (gr-qc)</span>; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) </div> <p class='mathjax'> We consider general linear gauge theory, with independent solder form and connection. These spaces have both torsion and nonmetricity. We show that the Cartan structure equations together with the defining equation for nonmetricity allow the mixed symmetry components of nonmetricity to be absorbed into an altered torsion tensor. Field redefinitions reduce the structure equations to those of Poincare gauge theory, with local Lorentz symmetry and metric compatibility. In order to allow recovery the original torsion and nonmetric fields, we replace the definition of nonmetricity by an additional structure equation and demand integrability of the extended system. We show that the maximal Lie algebra compatible with the enlarged set is isomorphic to the conformal Lie algebra. From this Lorentzian conformal geometry, we establish that the difference between the field strength of special conformal transformations and the torsion and is given by the mixed symmetry nonmetricity of an equivalent asymmetric system. </p> </div> </dd> <dt> <a name='item250'>[250]</a> <a href ="/abs/2409.08774" title="Abstract" id="2409.08774"> arXiv:2409.08774 </a> (replaced) [<a href="/pdf/2409.08774" title="Download PDF" id="pdf-2409.08774" aria-labelledby="pdf-2409.08774">pdf</a>, <a href="https://arxiv.org/html/2409.08774v2" title="View HTML" id="html-2409.08774" aria-labelledby="html-2409.08774" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.08774" title="Other formats" id="oth-2409.08774" aria-labelledby="oth-2409.08774">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> An Attack on $p$-adic Lattice Public-key Cryptosystems and Signature Schemes </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Zhang,+C">Chi Zhang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 26 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Cryptography and Security (cs.CR)</span>; Number Theory (math.NT) </div> <p class='mathjax'> Lattices have many significant applications in cryptography. In 2021, the $p$-adic signature scheme and public-key encryption cryptosystem were introduced. They are based on the Longest Vector Problem (LVP) and the Closest Vector Problem (CVP) in $p$-adic lattices. These problems are considered to be challenging and there are no known deterministic polynomial time algorithms to solve them. In this paper, we improve the LVP algorithm in local fields. The modified LVP algorithm is a deterministic polynomial time algorithm when the field is totally ramified and $p$ is a polynomial in the rank of the input lattice. We utilize this algorithm to attack the above schemes so that we are able to forge a valid signature of any message and decrypt any ciphertext. Although these schemes are broken, this work does not mean that $p$-adic lattices are not suitable in constructing cryptographic primitives. We propose some possible modifications to avoid our attack at the end of this paper. </p> </div> </dd> <dt> <a name='item251'>[251]</a> <a href ="/abs/2409.13815" title="Abstract" id="2409.13815"> arXiv:2409.13815 </a> (replaced) [<a href="/pdf/2409.13815" title="Download PDF" id="pdf-2409.13815" aria-labelledby="pdf-2409.13815">pdf</a>, <a href="https://arxiv.org/html/2409.13815v3" title="View HTML" id="html-2409.13815" aria-labelledby="html-2409.13815" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.13815" title="Other formats" id="oth-2409.13815" aria-labelledby="oth-2409.13815">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Reductions of GKZ Systems and Applications to Cosmological Correlators </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Grimm,+T+W">Thomas W. Grimm</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Hoefnagels,+A">Arno Hoefnagels</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 45 pages plus appendices (16 pages), 4 figures, v2: Fixed typos, including an important one in the abstract, added references, v3: added discussion on boundary conditions </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; General Relativity and Quantum Cosmology (gr-qc); Algebraic Geometry (math.AG) </div> <p class='mathjax'> A powerful approach to computing Feynman integrals or cosmological correlators is to consider them as solution to systems of differential equations. Often these can be chosen to be Gelfand-Kapranov-Zelevinsky (GKZ) systems. However, their naive construction introduces a significant amount of unnecessary complexity. In this paper we present an algorithm which allows for reducing these GKZ systems to smaller subsystems if a parameter associated to the GKZ systems is resonant. These simpler subsystems can then be solved separately resulting in solutions for the full system. The algorithm makes it possible to check when reductions happen and allows for finding the associated simpler solutions. While originating in the mathematical theory of D-modules analyzed via exact sequences of Euler-Koszul homologies, the algorithm can be used without knowledge of this framework. We motivate the need for such reduction techniques by considering cosmological correlators on an FRW space-time and solve the tree-level single-exchange correlator in this way. It turns out that this integral exemplifies an interesting relation between locality and the reduction of the differential equations. </p> </div> </dd> <dt> <a name='item252'>[252]</a> <a href ="/abs/2409.19931" title="Abstract" id="2409.19931"> arXiv:2409.19931 </a> (replaced) [<a href="/pdf/2409.19931" title="Download PDF" id="pdf-2409.19931" aria-labelledby="pdf-2409.19931">pdf</a>, <a href="https://arxiv.org/html/2409.19931v4" title="View HTML" id="html-2409.19931" aria-labelledby="html-2409.19931" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.19931" title="Other formats" id="oth-2409.19931" aria-labelledby="oth-2409.19931">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> T-duality on Almost Hermitian Spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Kimura,+T">Tetsuji Kimura</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Sasaki,+S">Shin Sasaki</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Shiozawa,+K">Kenta Shiozawa</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 34 pages, references added </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Nucl.Phys.B 1014 (2025) 116870 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph) </div> <p class='mathjax'> We investigate T-duality transformation on an almost bi-hermitian space with torsion. By virtue of the Buscher rule, we completely describe not only the covariant derivative of geometrical objects but also the Nijenhuis tensor. We apply this description to an almost bi-hermitian space with isometry and investigate integrability on its T-dualized one. We find that hermiticity is not a sufficient condition to preserve integrability under T-duality transformations. However, in the presence of the K盲hler condition, the T-dualized space still admits integrability of the almost complex structures. We also observe that the form of H-flux is suitable for string compactification scenarios. </p> </div> </dd> <dt> <a name='item253'>[253]</a> <a href ="/abs/2410.01118" title="Abstract" id="2410.01118"> arXiv:2410.01118 </a> (replaced) [<a href="/pdf/2410.01118" title="Download PDF" id="pdf-2410.01118" aria-labelledby="pdf-2410.01118">pdf</a>, <a href="https://arxiv.org/html/2410.01118v2" title="View HTML" id="html-2410.01118" aria-labelledby="html-2410.01118" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.01118" title="Other formats" id="oth-2410.01118" aria-labelledby="oth-2410.01118">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Sparse Actuation for LPV Systems with Full-State Feedback in $\mathcal{H}_2/\mathcal{H}_\infty$ Framework </div> <div class='list-authors'><a href="https://arxiv.org/search/eess?searchtype=author&query=Kumar,+T">Tanay Kumar</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Bhattacharya,+R">Raktim Bhattacharya</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Submitted to American Control Conference 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Systems and Control (eess.SY)</span>; Optimization and Control (math.OC) </div> <p class='mathjax'> This paper addresses the sparse actuation problem for nonlinear systems represented in the Linear Parameter-Varying (LPV) form. We propose a convex optimization framework that concurrently determines actuator magnitude limits and the state-feedback law that guarantees a user-specified closed-loop performance in the $\mathcal{H}_2/\mathcal{H}_\infty$ sense. We also demonstrate that sparse actuation is achieved when the actuator magnitude-limits are minimized in the $l_1$ sense. This is the first paper that addresses this problem for LPV systems. The formulation is demonstrated in a vibration control problem for a flexible wing. </p> </div> </dd> <dt> <a name='item254'>[254]</a> <a href ="/abs/2410.08796" title="Abstract" id="2410.08796"> arXiv:2410.08796 </a> (replaced) [<a href="/pdf/2410.08796" title="Download PDF" id="pdf-2410.08796" aria-labelledby="pdf-2410.08796">pdf</a>, <a href="https://arxiv.org/html/2410.08796v2" title="View HTML" id="html-2410.08796" aria-labelledby="html-2410.08796" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.08796" title="Other formats" id="oth-2410.08796" aria-labelledby="oth-2410.08796">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Calibrated Computation-Aware Gaussian Processes </div> <div class='list-authors'><a href="https://arxiv.org/search/stat?searchtype=author&query=Hegde,+D">Disha Hegde</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Adil,+M">Mohamed Adil</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Cockayne,+J">Jon Cockayne</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Accepted at the 28th International Conference on Artificial Intelligence and Statistics (AISTATS), 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (stat.ML)</span>; Machine Learning (cs.LG); Numerical Analysis (math.NA) </div> <p class='mathjax'> Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting probabilistic linear solvers to reduce complexity, widening the posterior with additional computational uncertainty due to reduced computation. However, the most commonly used CAGP framework results in (sometimes dramatically) conservative uncertainty quantification, making the posterior unrealistic in practice. In this work, we prove that if the utilised probabilistic linear solver is calibrated, in a rigorous statistical sense, then so too is the induced CAGP. We thus propose a new CAGP framework, CAGP-GS, based on using Gauss-Seidel iterations for the underlying probabilistic linear solver. CAGP-GS performs favourably compared to existing approaches when the test set is low-dimensional and few iterations are performed. We test the calibratedness on a synthetic problem, and compare the performance to existing approaches on a large-scale global temperature regression problem. </p> </div> </dd> <dt> <a name='item255'>[255]</a> <a href ="/abs/2410.12969" title="Abstract" id="2410.12969"> arXiv:2410.12969 </a> (replaced) [<a href="/pdf/2410.12969" title="Download PDF" id="pdf-2410.12969" aria-labelledby="pdf-2410.12969">pdf</a>, <a href="https://arxiv.org/html/2410.12969v2" title="View HTML" id="html-2410.12969" aria-labelledby="html-2410.12969" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.12969" title="Other formats" id="oth-2410.12969" aria-labelledby="oth-2410.12969">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Poincare field theory for massless particles </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Sazdovi%C4%87,+B">B. Sazdovi膰</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 25 pages We added three sections which considers cases with highest helicity </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> Our main proposition is that field equations for all spins can be obtained from Casimir eigenvalue equations for Poincare group. We have already confirm that statement for massive scalar, spinor and vector fields in Ref.[1]. In the present article we are going to confirm this statement for massless vector, second and fourth rang tensor fields. In particular we will obtain Maxwell equations and Einstein equation in weak field approximation. <br>As is well known, Wigner define a particles as irreducible representation of Poincare group [2,3]. But, as Weinberg noted in [4] irreducible representations for massless vector field with helicities $\pm 1$ do not exist. In the present article we will conform this statement for a wide class of massless fields. They are not Lorentz invariant since their Lorentz transformations have additional term in the form of gauge transformations. Such fields can appear in the theory only in the form which do not depend on corresponding gauge parameters. These forms are our equations of motion and they are by definition gauge invariant. So, the massless case is significantly different from massive one. In the end we will show that our approach can reproduce main contributions from well known articles with highest helicity. </p> </div> </dd> <dt> <a name='item256'>[256]</a> <a href ="/abs/2410.13954" title="Abstract" id="2410.13954"> arXiv:2410.13954 </a> (replaced) [<a href="/pdf/2410.13954" title="Download PDF" id="pdf-2410.13954" aria-labelledby="pdf-2410.13954">pdf</a>, <a href="https://arxiv.org/html/2410.13954v2" title="View HTML" id="html-2410.13954" aria-labelledby="html-2410.13954" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.13954" title="Other formats" id="oth-2410.13954" aria-labelledby="oth-2410.13954">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Nonlinear Stochastic Gradient Descent and Heavy-tailed Noise: A Unified Framework and High-probability Guarantees </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Armacki,+A">Aleksandar Armacki</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Yu,+S">Shuhua Yu</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Sharma,+P">Pranay Sharma</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Joshi,+G">Gauri Joshi</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Bajovic,+D">Dragana Bajovic</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Jakovetic,+D">Dusan Jakovetic</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Kar,+S">Soummya Kar</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 40 pages, 6 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Optimization and Control (math.OC) </div> <p class='mathjax'> We study high-probability convergence in online learning, in the presence of heavy-tailed noise. To combat the heavy tails, a general framework of nonlinear SGD methods is considered, subsuming several popular nonlinearities like sign, quantization, component-wise and joint clipping. In our work the nonlinearity is treated in a black-box manner, allowing us to establish unified guarantees for a broad range of nonlinear methods. For symmetric noise and non-convex costs we establish convergence of gradient norm-squared, at a rate $\widetilde{\mathcal{O}}(t^{-1/4})$, while for the last iterate of strongly convex costs we establish convergence to the population optima, at a rate $\mathcal{O}(t^{-\zeta})$, where $\zeta \in (0,1)$ depends on noise and problem parameters. Further, if the noise is a (biased) mixture of symmetric and non-symmetric components, we show convergence to a neighbourhood of stationarity, whose size depends on the mixture coefficient, nonlinearity and noise. Compared to state-of-the-art, who only consider clipping and require unbiased noise with bounded $p$-th moments, $p \in (1,2]$, we provide guarantees for a broad class of nonlinearities, without any assumptions on noise moments. While the rate exponents in state-of-the-art depend on noise moments and vanish as $p \rightarrow 1$, our exponents are constant and strictly better whenever $p < 6/5$ for non-convex and $p < 8/7$ for strongly convex costs. Experiments validate our theory, showing that clipping is not always the optimal nonlinearity, further underlining the value of a general framework. </p> </div> </dd> <dt> <a name='item257'>[257]</a> <a href ="/abs/2411.04352" title="Abstract" id="2411.04352"> arXiv:2411.04352 </a> (replaced) [<a href="/pdf/2411.04352" title="Download PDF" id="pdf-2411.04352" aria-labelledby="pdf-2411.04352">pdf</a>, <a href="https://arxiv.org/html/2411.04352v2" title="View HTML" id="html-2411.04352" aria-labelledby="html-2411.04352" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.04352" title="Other formats" id="oth-2411.04352" aria-labelledby="oth-2411.04352">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The High-Order Magnetic Near-Axis Expansion: Ill-Posedness and Regularization </div> <div class='list-authors'><a href="https://arxiv.org/search/physics?searchtype=author&query=Ruth,+M">Maximilian Ruth</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Jorge,+R">Rogerio Jorge</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Bindel,+D">David Bindel</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 43 pages, 8 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Plasma Physics (physics.plasm-ph)</span>; Numerical Analysis (math.NA) </div> <p class='mathjax'> When analyzing stellarator configurations, it is common to perform an asymptotic expansion about the magnetic axis. This so-called near-axis expansion is convenient for the same reason asymptotic expansions often are, namely, it reduces the dimension of the problem. This leads to convenient and quickly computed expressions of physical quantities, such as quasisymmetry and stability criteria, which can be used to gain further insight. However, it has been repeatedly found that the expansion diverges at high orders in the distance from axis, limiting the physics the expansion can describe. In this paper, we show that the near-axis expansion diverges in vacuum due to ill-posedness and that it can be regularized to improve its convergence. Then, using realistic stellarator coil sets, we demonstrate numerical convergence of the vacuum magnetic field and flux surfaces to the true values as the order increases. We numerically find that the regularization improves the solutions of the near-axis expansion under perturbation, and we demonstrate that the radius of convergence of the vacuum near-axis expansion is correlated with the distance from the axis to the coils. </p> </div> </dd> <dt> <a name='item258'>[258]</a> <a href ="/abs/2411.08905" title="Abstract" id="2411.08905"> arXiv:2411.08905 </a> (replaced) [<a href="/pdf/2411.08905" title="Download PDF" id="pdf-2411.08905" aria-labelledby="pdf-2411.08905">pdf</a>, <a href="https://arxiv.org/html/2411.08905v2" title="View HTML" id="html-2411.08905" aria-labelledby="html-2411.08905" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.08905" title="Other formats" id="oth-2411.08905" aria-labelledby="oth-2411.08905">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Synthesis Method for Obtaining Characteristic Modes of Multi-Structure Systems via independent Structure T-Matrix </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Shi,+C">Chenbo Shi</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Gu,+X">Xin Gu</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Liang,+S">Shichen Liang</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Pan,+J">Jin Pan</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Zuo,+L">Le Zuo</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Computational Engineering, Finance, and Science (cs.CE)</span>; Numerical Analysis (math.NA) </div> <p class='mathjax'> This paper presents a novel and efficient method for characteristic mode decomposition in multi-structure systems. By leveraging the translation and rotation matrices of vector spherical wavefunctions, our approach enables the synthesis of a composite system's characteristic modes using independently computed simulations of its constituent structures. The computationally intensive translation process is simplified by decomposing it into three streamlined sub-tasks: rotation, z-axis translation, and inverse rotation, collectively achieving significant improvements in computational efficiency. Furthermore, this method facilitates the exploration of structural orientation effects without incurring additional computational overhead. A series of illustrative numerical examples is provided to validate the accuracy of the proposed method and underscore its substantial advantages in both computational efficiency and practical applicability. </p> </div> </dd> <dt> <a name='item259'>[259]</a> <a href ="/abs/2411.09447" title="Abstract" id="2411.09447"> arXiv:2411.09447 </a> (replaced) [<a href="/pdf/2411.09447" title="Download PDF" id="pdf-2411.09447" aria-labelledby="pdf-2411.09447">pdf</a>, <a href="https://arxiv.org/html/2411.09447v2" title="View HTML" id="html-2411.09447" aria-labelledby="html-2411.09447" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.09447" title="Other formats" id="oth-2411.09447" aria-labelledby="oth-2411.09447">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Instability of nonlinear scalar field on strongly charged asymptotically AdS black hole background </div> <div class='list-authors'><a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Ficek,+F">Filip Ficek</a>, <a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Maliborski,+M">Maciej Maliborski</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 13 pages, 8 figures </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Phys. Rev. D 111, 064017 (2025) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Relativity and Quantum Cosmology (gr-qc)</span>; High Energy Physics - Theory (hep-th); Analysis of PDEs (math.AP) </div> <p class='mathjax'> The conformally invariant scalar equation permits the Robin boundary condition at infinity of asymptotically-AdS spacetimes. We show how the dynamics of conformal cubic scalar field on the Reissner-Nordstr枚m-anti-de Sitter background depend on the black hole size, charge, and choice of the boundary condition. We study the whole range of admissible charges, including the extremal case. In particular, we observe the transition in stability of the field for large black holes at the specific critical value of the charge. Similarities between Reissner-Nordstr枚m and Kerr black hole let us suspect that a similar effect may also occur in rotating black holes. </p> </div> </dd> <dt> <a name='item260'>[260]</a> <a href ="/abs/2501.05315" title="Abstract" id="2501.05315"> arXiv:2501.05315 </a> (replaced) [<a href="/pdf/2501.05315" title="Download PDF" id="pdf-2501.05315" aria-labelledby="pdf-2501.05315">pdf</a>, <a href="https://arxiv.org/html/2501.05315v2" title="View HTML" id="html-2501.05315" aria-labelledby="html-2501.05315" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2501.05315" title="Other formats" id="oth-2501.05315" aria-labelledby="oth-2501.05315">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Counting Equilibria of the Electrostatic Potential </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Edelsbrunner,+H">Herbert Edelsbrunner</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Fillmore,+C">Christopher Fillmore</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Oliveira,+G">Gon莽alo Oliveira</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> This new version contains a further major development, a new improved upper bound on the number of equilibria to the electrostatic potential </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Computational Geometry (cs.CG)</span>; Mathematical Physics (math-ph); Combinatorics (math.CO) </div> <p class='mathjax'> In 1873, James C. Maxwell conjectured that the electric field generated by $n$ point charges in generic position has at most $(n-1)^2$ isolated zeroes. The first (non-optimal) upper bound was only obtained in 2007 by Gabrielov, Novikov and Shapiro, who also posed two additional interesting conjectures. <br>In this article, we give the best upper bound known to date on the number of zeroes of the electric field, and construct a counterexample to a conjecture of Gabrielov, Novikov and Shapiro that the number of equilibria cannot exceed those of the distance function defined by the unit point charges. <br>Finally, we note that it is quite possible that Maxwell's quadratic upper bound is not tight, so it is prudent to find smaller bounds. Hence, we also explore examples and construct configurations of charges achieving the highest ratios of the number of electric field zeroes by point charges found to this day. </p> </div> </dd> <dt> <a name='item261'>[261]</a> <a href ="/abs/2501.18326" title="Abstract" id="2501.18326"> arXiv:2501.18326 </a> (replaced) [<a href="/pdf/2501.18326" title="Download PDF" id="pdf-2501.18326" aria-labelledby="pdf-2501.18326">pdf</a>, <a href="https://arxiv.org/html/2501.18326v2" title="View HTML" id="html-2501.18326" aria-labelledby="html-2501.18326" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2501.18326" title="Other formats" id="oth-2501.18326" aria-labelledby="oth-2501.18326">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Transductions of Graph Classes Admitting Product Structure </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Hlin%C4%9Bn%C3%BD,+P">Petr Hlin臎n媒</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Jedelsk%C3%BD,+J">Jan Jedelsk媒</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Logic in Computer Science (cs.LO)</span>; Combinatorics (math.CO) </div> <p class='mathjax'> In a quest to thoroughly understand the first-order transduction hierarchy of hereditary graph classes, some questions in particular stand out; such as, what properties hold for graph classes that are first-order transductions of planar graphs (and of similar classes)? When addressing this (so-far wide open) question, we turn to the concept of a product structure - being a subgraph of the strong product of a path and a graph of bounded tree-width, introduced by Dujmovic et al. [JACM 2020]. Namely, we prove that any graph class which is a first-order transduction of a class admitting such product structure, up to perturbations also meets a structural description generalizing the concept of a product structure in a dense hereditary way - the latter concept being introduced just recently by Hlineny and Jedelsky under the name of H-clique-width [MFCS 2024]. Using this characterization, we show that the class of the 3D grids, as well as a class of certain modifications of 2D grids, are not first-order transducible from classes admitting a product structure, and in particular not from the class of planar graphs. </p> </div> </dd> <dt> <a name='item262'>[262]</a> <a href ="/abs/2502.04210" title="Abstract" id="2502.04210"> arXiv:2502.04210 </a> (replaced) [<a href="/pdf/2502.04210" title="Download PDF" id="pdf-2502.04210" aria-labelledby="pdf-2502.04210">pdf</a>, <a href="/format/2502.04210" title="Other formats" id="oth-2502.04210" aria-labelledby="oth-2502.04210">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Algorithmic causal structure emerging through compression </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Wendong,+L">Liang Wendong</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Buchholz,+S">Simon Buchholz</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Sch%C3%B6lkopf,+B">Bernhard Sch枚lkopf</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Extended version of the camera-ready paper accepted at CLeaR 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Artificial Intelligence (cs.AI); Computational Complexity (cs.CC); Information Theory (cs.IT) </div> <p class='mathjax'> We explore the relationship between causality, symmetry, and compression. We build on and generalize the known connection between learning and compression to a setting where causal models are not identifiable. We propose a framework where causality emerges as a consequence of compressing data across multiple environments. We define algorithmic causality as an alternative definition of causality when traditional assumptions for causal identifiability do not hold. We demonstrate how algorithmic causal and symmetric structures can emerge from minimizing upper bounds on Kolmogorov complexity, without knowledge of intervention targets. We hypothesize that these insights may also provide a novel perspective on the emergence of causality in machine learning models, such as large language models, where causal relationships may not be explicitly identifiable. </p> </div> </dd> <dt> <a name='item263'>[263]</a> <a href ="/abs/2502.11825" title="Abstract" id="2502.11825"> arXiv:2502.11825 </a> (replaced) [<a href="/pdf/2502.11825" title="Download PDF" id="pdf-2502.11825" aria-labelledby="pdf-2502.11825">pdf</a>, <a href="https://arxiv.org/html/2502.11825v2" title="View HTML" id="html-2502.11825" aria-labelledby="html-2502.11825" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.11825" title="Other formats" id="oth-2502.11825" aria-labelledby="oth-2502.11825">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Quasi-Local Black Hole Horizons: Recent Advances </div> <div class='list-authors'><a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Ashtekar,+A">Abhay Ashtekar</a>, <a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Krishnan,+B">Badri Krishnan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 83 Pages, 11 figures. Minor edits. References added </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Relativity and Quantum Cosmology (gr-qc)</span>; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) </div> <p class='mathjax'> While the early literature on black holes focused on event horizons, subsequently it was realized that their teleological nature makes them unsuitable for many physical applications both in classical and quantum gravity. Therefore, over the past two decades, event horizons have been steadily replaced by quasi-local horizons which do not suffer from teleology. In numerical simulations event horizons can be located as an `after thought' only after the entire space-time has been constructed. By contrast, quasi-local horizons naturally emerge in the course of these simulations, providing powerful gauge-invariant tools to extract physics from the numerical outputs. They also lead to interesting results in mathematical GR, providing unforeseen insights. For example, for event horizons we only have a qualitative result that their area cannot decrease, while for quasi-local horizons the increase in the area during a dynamical phase is quantitatively related to local physical processes at the horizon. In binary black hole mergers, there are interesting correlations between observables associated with quasi-local horizons and those defined at future null infinity. Finally, the quantum Hawking process is naturally described as formation and evaporation of a quasi-local horizon. This review focuses on the dynamical aspects of quasi-local horizons in classical general relativity, emphasizing recent results and ongoing research. </p> </div> </dd> <dt> <a name='item264'>[264]</a> <a href ="/abs/2502.12063" title="Abstract" id="2502.12063"> arXiv:2502.12063 </a> (replaced) [<a href="/pdf/2502.12063" title="Download PDF" id="pdf-2502.12063" aria-labelledby="pdf-2502.12063">pdf</a>, <a href="https://arxiv.org/html/2502.12063v2" title="View HTML" id="html-2502.12063" aria-labelledby="html-2502.12063" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.12063" title="Other formats" id="oth-2502.12063" aria-labelledby="oth-2502.12063">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Low-Rank Thinning </div> <div class='list-authors'><a href="https://arxiv.org/search/stat?searchtype=author&query=Carrell,+A+M">Annabelle Michael Carrell</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Gong,+A">Albert Gong</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Shetty,+A">Abhishek Shetty</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Dwivedi,+R">Raaz Dwivedi</a>, <a href="https://arxiv.org/search/stat?searchtype=author&query=Mackey,+L">Lester Mackey</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (stat.ML)</span>; Machine Learning (cs.LG); Optimization and Control (math.OC); Statistics Theory (math.ST); Methodology (stat.ME) </div> <p class='mathjax'> The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially reducing the number of summary points. However, existing guarantees cover only a restricted range of distributions and kernel-based quality measures and suffer from pessimistic dimension dependence. To address these deficiencies, we introduce a new low-rank analysis of sub-Gaussian thinning that applies to any distribution and any kernel, guaranteeing high-quality compression whenever the kernel or data matrix is approximately low-rank. To demonstrate the broad applicability of the techniques, we design practical sub-Gaussian thinning approaches that improve upon the best known guarantees for approximating attention in transformers, accelerating stochastic gradient training through reordering, and distinguishing distributions in near-linear time. </p> </div> </dd> </dl> <div class='paging'>Total of 264 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> </div> </div> </div> </main> <footer style="clear: both;"> <div class="columns is-desktop" role="navigation" aria-label="Secondary" style="margin: -0.75em -0.75em 0.75em -0.75em">  <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul style="list-style: none; 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