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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Sun, S"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" 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is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Sun%2C+S&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Sun%2C+S&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Sun%2C+S&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> <li> <a href="/search/?searchtype=author&query=Sun%2C+S&start=100" class="pagination-link " aria-label="Page 3" aria-current="page">3 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.12659">arXiv:2411.12659</a> <span> [<a href="https://arxiv.org/pdf/2411.12659">pdf</a>, <a href="https://arxiv.org/ps/2411.12659">ps</a>, <a href="https://arxiv.org/format/2411.12659">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Induced even cycles in locally sparse graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ding%2C+L">Laihao Ding</a>, <a href="/search/math?searchtype=author&query=Gao%2C+J">Jun Gao</a>, <a href="/search/math?searchtype=author&query=Liu%2C+H">Hong Liu</a>, <a href="/search/math?searchtype=author&query=Luan%2C+B">Bingyu Luan</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shumin Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.12659v1-abstract-short" style="display: inline;"> A graph $G$ is $(c,t)$-sparse if for every pair of vertex subsets $A,B\subset V(G)$ with $|A|,|B|\geq t$, $e(A,B)\leq (1-c)|A||B|$. In this paper we prove that for every $c>0$ and integer $\ell$, there exists $C>1$ such that if an $n$-vertex graph $G$ is $(c,t)$-sparse for some $t$, and has at least $C t^{1-1/\ell}n^{1+1/\ell}$ edges, then $G$ contains an induced copy of $C_{2\ell}$. This resolves… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.12659v1-abstract-full').style.display = 'inline'; document.getElementById('2411.12659v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.12659v1-abstract-full" style="display: none;"> A graph $G$ is $(c,t)$-sparse if for every pair of vertex subsets $A,B\subset V(G)$ with $|A|,|B|\geq t$, $e(A,B)\leq (1-c)|A||B|$. In this paper we prove that for every $c>0$ and integer $\ell$, there exists $C>1$ such that if an $n$-vertex graph $G$ is $(c,t)$-sparse for some $t$, and has at least $C t^{1-1/\ell}n^{1+1/\ell}$ edges, then $G$ contains an induced copy of $C_{2\ell}$. This resolves a conjecture of Fox, Nenadov and Pham. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.12659v1-abstract-full').style.display = 'none'; document.getElementById('2411.12659v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.02665">arXiv:2411.02665</a> <span> [<a href="https://arxiv.org/pdf/2411.02665">pdf</a>, <a href="https://arxiv.org/format/2411.02665">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> A Trust-Region Algorithm for Noisy Equality Constrained Optimization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shigeng Sun</a>, <a href="/search/math?searchtype=author&query=Nocedal%2C+J">Jorge Nocedal</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.02665v1-abstract-short" style="display: inline;"> This paper introduces a modified Byrd-Omojokun (BO) trust region algorithm to address the challenges posed by noisy function and gradient evaluations. The original BO method was designed to solve equality constrained problems and it forms the backbone of some interior point methods for general large-scale constrained optimization. A key strength of the BO method is its robustness in handling probl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.02665v1-abstract-full').style.display = 'inline'; document.getElementById('2411.02665v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.02665v1-abstract-full" style="display: none;"> This paper introduces a modified Byrd-Omojokun (BO) trust region algorithm to address the challenges posed by noisy function and gradient evaluations. The original BO method was designed to solve equality constrained problems and it forms the backbone of some interior point methods for general large-scale constrained optimization. A key strength of the BO method is its robustness in handling problems with rank-deficient constraint Jacobians. The algorithm proposed in this paper introduces a new criterion for accepting a step and for updating the trust region that makes use of an estimate in the noise in the problem. The analysis presented here gives conditions under which the iterates converge to regions of stationary points of the problem, determined by the level of noise. This analysis is more complex than for line search methods because the trust region carries (noisy) information from previous iterates. Numerical tests illustrate the practical performance of the algorithm. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.02665v1-abstract-full').style.display = 'none'; document.getElementById('2411.02665v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.00463">arXiv:2411.00463</a> <span> [<a href="https://arxiv.org/pdf/2411.00463">pdf</a>, <a href="https://arxiv.org/format/2411.00463">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> The learned range test method for the inverse inclusion problem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shiwei Sun</a>, <a href="/search/math?searchtype=author&query=Alberti%2C+G+S">Giovanni S. Alberti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.00463v1-abstract-short" style="display: inline;"> We consider the inverse problem consisting of the reconstruction of an inclusion $B$ contained in a bounded domain $惟\subset\mathbb{R}^d$ from a single pair of Cauchy data $(u|_{\partial惟},\partial_谓u|_{\partial惟})$, where $螖u=0$ in $惟\setminus\overline B$ and $u=0$ on $\partial B$. We show that the reconstruction algorithm based on the range test, a domain sampling method, can be written as a neu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.00463v1-abstract-full').style.display = 'inline'; document.getElementById('2411.00463v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.00463v1-abstract-full" style="display: none;"> We consider the inverse problem consisting of the reconstruction of an inclusion $B$ contained in a bounded domain $惟\subset\mathbb{R}^d$ from a single pair of Cauchy data $(u|_{\partial惟},\partial_谓u|_{\partial惟})$, where $螖u=0$ in $惟\setminus\overline B$ and $u=0$ on $\partial B$. We show that the reconstruction algorithm based on the range test, a domain sampling method, can be written as a neural network with a specific architecture. We propose to learn the weights of this network in the framework of supervised learning, and to combine it with a pre-trained classifier, with the purpose of distinguishing the inclusions based on their distance from the boundary. The numerical simulations show that this learned range test method provides accurate and stable reconstructions of polygonal inclusions. Furthermore, the results are superior to those obtained with the standard range test method (without learning) and with an end-to-end fully connected deep neural network, a purely data-driven method. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.00463v1-abstract-full').style.display = 'none'; document.getElementById('2411.00463v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35R30; 65N21; 68T07 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.13376">arXiv:2410.13376</a> <span> [<a href="https://arxiv.org/pdf/2410.13376">pdf</a>, <a href="https://arxiv.org/format/2410.13376">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuwen Sun</a>, <a href="/search/math?searchtype=author&query=Feng%2C+L">Lihong Feng</a>, <a href="/search/math?searchtype=author&query=Benner%2C+P">Peter Benner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.13376v1-abstract-short" style="display: inline;"> Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided surrogates are being actively researched. However, many methods fail in accurately generalizing in the entire time interval $[0, T]$, when the training data is available only in a training time interval $[0, T_0]$, wit… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.13376v1-abstract-full').style.display = 'inline'; document.getElementById('2410.13376v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.13376v1-abstract-full" style="display: none;"> Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided surrogates are being actively researched. However, many methods fail in accurately generalizing in the entire time interval $[0, T]$, when the training data is available only in a training time interval $[0, T_0]$, with $T_0<T$. To improve the extrapolation capabilities of the surrogate models in the entire time domain, we propose a new deep learning framework, where kernel dynamic mode decomposition (KDMD) is employed to evolve the dynamics of the latent space generated by the encoder part of a convolutional autoencoder (CAE). After adding the KDMD-decoder-extrapolated data into the original data set, we train the CAE along with a feed-forward deep neural network using the augmented data. The trained network can predict future states outside the training time interval at any out-of-training parameter samples. The proposed method is tested on two numerical examples: a FitzHugh-Nagumo model and a model of incompressible flow past a cylinder. Numerical results show accurate and fast prediction performance in both the time and the parameter domain. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.13376v1-abstract-full').style.display = 'none'; document.getElementById('2410.13376v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.11168">arXiv:2410.11168</a> <span> [<a href="https://arxiv.org/pdf/2410.11168">pdf</a>, <a href="https://arxiv.org/format/2410.11168">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> On conical asymptotically flat manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+M">Mingyang Li</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Song Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.11168v1-abstract-short" style="display: inline;"> We prove a conjecture of Petrunin and Tuschmann on the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane. We also survey recent progress and questions concerning gravitational instantons, which serve as our motivation for studying this question. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.11168v1-abstract-full" style="display: none;"> We prove a conjecture of Petrunin and Tuschmann on the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane. We also survey recent progress and questions concerning gravitational instantons, which serve as our motivation for studying this question. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.11168v1-abstract-full').style.display = 'none'; document.getElementById('2410.11168v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Submitted to a special issue in honor of Professor Xiaochun Rong's 70th birthday</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.09661">arXiv:2410.09661</a> <span> [<a href="https://arxiv.org/pdf/2410.09661">pdf</a>, <a href="https://arxiv.org/ps/2410.09661">ps</a>, <a href="https://arxiv.org/format/2410.09661">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> K盲hler-Ricci shrinkers and Fano fibrations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Song Sun</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+J">Junsheng Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.09661v1-abstract-short" style="display: inline;"> In this paper, we build connections between K盲hler-Ricci shrinkers, i.e., complete (possibly non-compact) shrinking gradient K盲hler-Ricci solitons, and algebraic geometry. In particular, we (1). prove that a K盲hler-Ricci shrinker is naturally a quasi-projective variety, using birational algebraic geometry; (2). formulate a conjecture relating the existence of K盲hler-Ricci shrinkers and K-stability… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.09661v1-abstract-full').style.display = 'inline'; document.getElementById('2410.09661v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.09661v1-abstract-full" style="display: none;"> In this paper, we build connections between K盲hler-Ricci shrinkers, i.e., complete (possibly non-compact) shrinking gradient K盲hler-Ricci solitons, and algebraic geometry. In particular, we (1). prove that a K盲hler-Ricci shrinker is naturally a quasi-projective variety, using birational algebraic geometry; (2). formulate a conjecture relating the existence of K盲hler-Ricci shrinkers and K-stability of polarized Fano fibrations, which unifies and extends the YTD type conjectures for K盲hler-Einstein metrics, Ricci-flat K盲hler cone metrics and compact K盲hler-Ricci shrinkers; (3). formulate conjectures connecting tangent flows at singularities of K盲hler-Ricci flows and algebraic geometry, via a 2-step degeneration for the weighted volume of a Fano fibration. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.09661v1-abstract-full').style.display = 'none'; document.getElementById('2410.09661v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.02017">arXiv:2408.02017</a> <span> [<a href="https://arxiv.org/pdf/2408.02017">pdf</a>, <a href="https://arxiv.org/ps/2408.02017">ps</a>, <a href="https://arxiv.org/format/2408.02017">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Existence of generalized solitary waves for a diatomic Fermi-Pasta-Ulam-Tsingou lattice </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Deng%2C+S">Shengfu Deng</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shu-Ming Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.02017v1-abstract-short" style="display: inline;"> This paper concerns the existence of generalized solitary waves (solitary waves with small ripples at infinity) for a diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. It is proved that the FPUT lattice problem has a generalized solitary-wave solution with the amplitude of those ripples algebraically small using dynamical system approach. The problem is first formulated as a dynamical system probl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.02017v1-abstract-full').style.display = 'inline'; document.getElementById('2408.02017v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.02017v1-abstract-full" style="display: none;"> This paper concerns the existence of generalized solitary waves (solitary waves with small ripples at infinity) for a diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. It is proved that the FPUT lattice problem has a generalized solitary-wave solution with the amplitude of those ripples algebraically small using dynamical system approach. The problem is first formulated as a dynamical system problem and then the center manifold reduction theorem with Laurent series expansion is applied to show that this system can be reduced to a system of ordinary differential equations with dimension five. Its dominant system has a homoclinic solution. By applying a perturbation method and adjusting some appropriate constants, it is shown that this homoclinic solution persists for the original dynamical system, which connects to a periodic solution of algebraically small amplitude at infinity (called generalized homoclinic solution), which yields the existence of a generalized solitary wave for the FPUT lattice. The result presented here with the algebraic smallness of those ripples will be needed to show the existence of generalized multi-hump waves for the FPUT lattice later. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.02017v1-abstract-full').style.display = 'none'; document.getElementById('2408.02017v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37L60; 74J35; 34C37; 34D10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.14992">arXiv:2407.14992</a> <span> [<a href="https://arxiv.org/pdf/2407.14992">pdf</a>, <a href="https://arxiv.org/ps/2407.14992">ps</a>, <a href="https://arxiv.org/format/2407.14992">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> On the strength of Burer's lifted convex relaxation to quadratic programming with ball constraints </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=K%C4%B1l%C4%B1n%C3%A7-Karzan%2C+F">Fatma K谋l谋n莽-Karzan</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shengding Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.14992v1-abstract-short" style="display: inline;"> We study quadratic programs with $m$ ball constraints, and the strength of a lifted convex relaxation for it recently proposed by Burer (2024). Burer shows this relaxation is exact when $m=2$. For general $m$, Burer (2024) provides numerical evidence that this lifted relaxation is tighter than the Kronecker product based Reformulation Linearization Technique (RLT) inequalities introduced by Anstre… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.14992v1-abstract-full').style.display = 'inline'; document.getElementById('2407.14992v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.14992v1-abstract-full" style="display: none;"> We study quadratic programs with $m$ ball constraints, and the strength of a lifted convex relaxation for it recently proposed by Burer (2024). Burer shows this relaxation is exact when $m=2$. For general $m$, Burer (2024) provides numerical evidence that this lifted relaxation is tighter than the Kronecker product based Reformulation Linearization Technique (RLT) inequalities introduced by Anstreicher (2017), and conjectures that this must be theoretically true as well. In this note, we provide an affirmative answer to this question and formally prove that this lifted relaxation indeed implies the Kronecker inequalities. Our proof is based on a decomposition of non-rank-one extreme rays of the lifted relaxation for each pair of ball constraints. Burer (2024) also numerically observes that for this lifted relaxation, an RLT-based inequality proposed by Zhen et al. (2021) is redundant, and conjectures this to be theoretically true as well. We also provide a formal proof that Zhen et al. (2021) inequalities are redundant for this lifted relaxation. In addition, we establish that Burer's lifted relaxation is a particular case of the moment-sum-of-squares hierarchy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.14992v1-abstract-full').style.display = 'none'; document.getElementById('2407.14992v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.04150">arXiv:2405.04150</a> <span> [<a href="https://arxiv.org/pdf/2405.04150">pdf</a>, <a href="https://arxiv.org/format/2405.04150">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Subdifferentially polynomially bounded functions and Gaussian smoothing-based zeroth-order optimization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lei%2C+M">Ming Lei</a>, <a href="/search/math?searchtype=author&query=Pong%2C+T+K">Ting Kei Pong</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuqin Sun</a>, <a href="/search/math?searchtype=author&query=Yue%2C+M">Man-Chung Yue</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.04150v1-abstract-short" style="display: inline;"> We introduce the class of subdifferentially polynomially bounded (SPB) functions, which is a rich class of locally Lipschitz functions that encompasses all Lipschitz functions, all gradient- or Hessian-Lipschitz functions, and even some non-smooth locally Lipschitz functions. We show that SPB functions are compatible with Gaussian smoothing (GS), in the sense that the GS of any SPB function is wel… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.04150v1-abstract-full').style.display = 'inline'; document.getElementById('2405.04150v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.04150v1-abstract-full" style="display: none;"> We introduce the class of subdifferentially polynomially bounded (SPB) functions, which is a rich class of locally Lipschitz functions that encompasses all Lipschitz functions, all gradient- or Hessian-Lipschitz functions, and even some non-smooth locally Lipschitz functions. We show that SPB functions are compatible with Gaussian smoothing (GS), in the sense that the GS of any SPB function is well-defined and satisfies a descent lemma akin to gradient-Lipschitz functions, with the Lipschitz constant replaced by a polynomial function. Leveraging this descent lemma, we propose GS-based zeroth-order optimization algorithms with an adaptive stepsize strategy for constrained minimization of SPB functions, and analyze their iteration complexity. An important instrument in our analysis, which could be of independent interest, is the quantification of Goldstein stationarity via the GS gradient. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.04150v1-abstract-full').style.display = 'none'; document.getElementById('2405.04150v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2404.12540">arXiv:2404.12540</a> <span> [<a href="https://arxiv.org/pdf/2404.12540">pdf</a>, <a href="https://arxiv.org/ps/2404.12540">ps</a>, <a href="https://arxiv.org/format/2404.12540">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> </div> </div> <p class="title is-5 mathjax"> State Discretization for Continuous-State MDPs in Infectious Disease Control </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhang%2C+S">Suyanpeng Zhang</a>, <a href="/search/math?searchtype=author&query=Suen%2C+S">Sze-chuan Suen</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2404.12540v3-abstract-short" style="display: inline;"> Repeated decision-making problems under uncertainty may arise in the health policy context, such as infectious disease control for COVID-19 and other epidemics. These problems may sometimes be effectively solved using Markov decision processes (MDPs). However, the continuous or large state space of such problems for capturing infectious disease prevalence renders it difficult to implement tractabl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.12540v3-abstract-full').style.display = 'inline'; document.getElementById('2404.12540v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2404.12540v3-abstract-full" style="display: none;"> Repeated decision-making problems under uncertainty may arise in the health policy context, such as infectious disease control for COVID-19 and other epidemics. These problems may sometimes be effectively solved using Markov decision processes (MDPs). However, the continuous or large state space of such problems for capturing infectious disease prevalence renders it difficult to implement tractable MDPs to identify the optimal disease control policy over time. We therefore develop an algorithm for discretizing continuous states for approximate MDP solutions in this context. We benchmark performance against a uniform discretization using both a synthetic example and an example of COVID-19 in Los Angeles County. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.12540v3-abstract-full').style.display = 'none'; document.getElementById('2404.12540v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2404.03604">arXiv:2404.03604</a> <span> [<a href="https://arxiv.org/pdf/2404.03604">pdf</a>, <a href="https://arxiv.org/format/2404.03604">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> A Unified Algorithmic Framework for Dynamic Assortment Optimization under MNL Choice </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuo Sun</a>, <a href="/search/math?searchtype=author&query=Udwani%2C+R">Rajan Udwani</a>, <a href="/search/math?searchtype=author&query=Shen%2C+Z+M">Zuo-Jun Max Shen</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2404.03604v2-abstract-short" style="display: inline;"> We consider assortment and inventory planning problems with dynamic stockout-based substitution effects, and without replenishment, in two different settings: (1) Customers can see all available products when they arrive, a typical scenario in physical stores. (2) The seller can choose to offer a subset of available products to each customer, which is more common on online platforms. Both settings… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.03604v2-abstract-full').style.display = 'inline'; document.getElementById('2404.03604v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2404.03604v2-abstract-full" style="display: none;"> We consider assortment and inventory planning problems with dynamic stockout-based substitution effects, and without replenishment, in two different settings: (1) Customers can see all available products when they arrive, a typical scenario in physical stores. (2) The seller can choose to offer a subset of available products to each customer, which is more common on online platforms. Both settings are known to be computationally challenging, and the current approximation algorithms for the two settings are quite different. We develop a unified algorithm framework under the MNL choice model for both settings. Our algorithms improve on the state-of-the-art algorithms in terms of approximation guarantee and runtime, and the ability to manage uncertainty in the total number of customers and handle more complex constraints. In the process, we establish various novel properties of dynamic assortment planning (for the MNL choice model) that may be useful more broadly. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.03604v2-abstract-full').style.display = 'none'; document.getElementById('2404.03604v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.17923">arXiv:2403.17923</a> <span> [<a href="https://arxiv.org/pdf/2403.17923">pdf</a>, <a href="https://arxiv.org/format/2403.17923">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Optimizing Vaccine Site Locations While Considering Travel Inconvenience and Public Health Outcomes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhang%2C+S">Suyanpeng Zhang</a>, <a href="/search/math?searchtype=author&query=Suen%2C+S">Sze-chuan Suen</a>, <a href="/search/math?searchtype=author&query=Yu%2C+H">Han Yu</a>, <a href="/search/math?searchtype=author&query=Dessouky%2C+M">Maged Dessouky</a>, <a href="/search/math?searchtype=author&query=Ordonez%2C+F">Fernando Ordonez</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.17923v1-abstract-short" style="display: inline;"> During the COVID-19 pandemic, there were over three million infections in Los Angeles County (LAC). To facilitate distribution when vaccines first became available, LAC set up six mega-sites for dispensing a large number of vaccines to the public. To understand if another choice of mega-site location would have improved accessibility and health outcomes, and to provide insight into future vaccine… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.17923v1-abstract-full').style.display = 'inline'; document.getElementById('2403.17923v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.17923v1-abstract-full" style="display: none;"> During the COVID-19 pandemic, there were over three million infections in Los Angeles County (LAC). To facilitate distribution when vaccines first became available, LAC set up six mega-sites for dispensing a large number of vaccines to the public. To understand if another choice of mega-site location would have improved accessibility and health outcomes, and to provide insight into future vaccine allocation problems, we propose a multi-objective mixed integer linear programming model that balances travel convenience, infection reduction, and equitable distribution. We provide a tractable objective formulation that effectively proxies real-world public health goals of reducing infections while considering travel inconvenience and equitable distribution of resources. Compared with the solution empirically used in LAC in 2020, we recommend more dispersed mega-site locations that result in a 28% reduction in travel inconvenience and avert an additional 1,000 infections. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.17923v1-abstract-full').style.display = 'none'; document.getElementById('2403.17923v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.11178">arXiv:2403.11178</a> <span> [<a href="https://arxiv.org/pdf/2403.11178">pdf</a>, <a href="https://arxiv.org/ps/2403.11178">ps</a>, <a href="https://arxiv.org/format/2403.11178">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> The truncated EM scheme for multiple-delay SDEs with irregular coefficients and application to stochastic volatility model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Liu%2C+Z">Zhuoqi Liu</a>, <a href="/search/math?searchtype=author&query=Wang%2C+Z">Zhaohang Wang</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Siying Sun</a>, <a href="/search/math?searchtype=author&query=Gao%2C+S">Shuaibin Gao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.11178v1-abstract-short" style="display: inline;"> This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H枚lder continuous drifts and locally H枚lder continuous diffusion coefficients. To handle with the superlinear terms in coefficients, the truncated Euler-Maruyama scheme is employed. Under the given conditions, the convergence rates at time $T$ in both $\mathcal{L}^{1}$ and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.11178v1-abstract-full').style.display = 'inline'; document.getElementById('2403.11178v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.11178v1-abstract-full" style="display: none;"> This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H枚lder continuous drifts and locally H枚lder continuous diffusion coefficients. To handle with the superlinear terms in coefficients, the truncated Euler-Maruyama scheme is employed. Under the given conditions, the convergence rates at time $T$ in both $\mathcal{L}^{1}$ and $\mathcal{L}^{2}$ senses are shown by virtue of the Yamada-Watanabe approximation technique. Moreover, the convergence rates over a finite time interval $[0,T]$ are also obtained. Additionally, it should be noted that the convergence rates will not be affected by the number of delay variables. Finally, we perform the numerical experiments on the stochastic volatility model to verify the reliability of the theoretical results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.11178v1-abstract-full').style.display = 'none'; document.getElementById('2403.11178v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.04474">arXiv:2403.04474</a> <span> [<a href="https://arxiv.org/pdf/2403.04474">pdf</a>, <a href="https://arxiv.org/format/2403.04474">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> On the $(k+2,k)$-problem of Brown, Erd艖s and S贸s for $k=5,6,7$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Glock%2C+S">Stefan Glock</a>, <a href="/search/math?searchtype=author&query=Kim%2C+J">Jaehoon Kim</a>, <a href="/search/math?searchtype=author&query=Lichev%2C+L">Lyuben Lichev</a>, <a href="/search/math?searchtype=author&query=Pikhurko%2C+O">Oleg Pikhurko</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shumin Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.04474v1-abstract-short" style="display: inline;"> Let $f^{(r)}(n;s,k)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph containing no subgraph with $k$ edges and at most $s$ vertices. Brown, Erd艖s and S贸s [New directions in the theory of graphs (Proc. Third Ann Arbor Conf., Univ. Michigan 1971), pp. 53--63, Academic Press 1973] conjectured that the limit $\lim_{n\rightarrow \infty}n^{-2}f^{(3)}(n;k+2,k)$ exists for all… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.04474v1-abstract-full').style.display = 'inline'; document.getElementById('2403.04474v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.04474v1-abstract-full" style="display: none;"> Let $f^{(r)}(n;s,k)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph containing no subgraph with $k$ edges and at most $s$ vertices. Brown, Erd艖s and S贸s [New directions in the theory of graphs (Proc. Third Ann Arbor Conf., Univ. Michigan 1971), pp. 53--63, Academic Press 1973] conjectured that the limit $\lim_{n\rightarrow \infty}n^{-2}f^{(3)}(n;k+2,k)$ exists for all $k$. The value of the limit was previously determined for $k=2$ in the original paper of Brown, Erd艖s and S贸s, for $k=3$ by Glock [Bull. Lond. Math. Soc. 51 (2019) 230--236] and for $k=4$ by Glock, Joos, Kim, K眉hn, Lichev and Pikhurko [arXiv:2209.14177, accepted by Proc. Amer. Math. Soc.] while Delcourt and Postle [arXiv:2210.01105, accepted by Proc. Amer. Math. Soc.] proved the conjecture (without determining the limiting value). In this paper, we determine the value of the limit in the Brown-Erd艖s-S贸s Problem for $k\in \{5,6,7\}$. More generally, we obtain the value of $\lim_{n\rightarrow \infty}n^{-2}f^{(r)}(n;rk-2k+2,k)$ for all $r\geq 3$ and $k\in \{5,6,7\}$. In addition, by combining these new values with recent results of Bennett, Cushman and Dudek [arXiv:2309.00182] we obtain new asymptotic values for several generalised Ramsey numbers. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.04474v1-abstract-full').style.display = 'none'; document.getElementById('2403.04474v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">44 pages, 3 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2402.09619">arXiv:2402.09619</a> <span> [<a href="https://arxiv.org/pdf/2402.09619">pdf</a>, <a href="https://arxiv.org/ps/2402.09619">ps</a>, <a href="https://arxiv.org/format/2402.09619">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Signal Processing">eess.SP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Networking and Internet Architecture">cs.NI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistics Theory">math.ST</span> </div> </div> <p class="title is-5 mathjax"> Dynamic Cooperative MAC Optimization in RSU-Enhanced VANETs: A Distributed Approach </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhang%2C+Z">Zhou Zhang</a>, <a href="/search/math?searchtype=author&query=Atapattu%2C+S">Saman Atapattu</a>, <a href="/search/math?searchtype=author&query=Wang%2C+Y">Yizhu Wang</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Sumei Sun</a>, <a href="/search/math?searchtype=author&query=Sithamparanathan%2C+K">Kandeepan Sithamparanathan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2402.09619v1-abstract-short" style="display: inline;"> This paper presents an optimization approach for cooperative Medium Access Control (MAC) techniques in Vehicular Ad Hoc Networks (VANETs) equipped with Roadside Unit (RSU) to enhance network throughput. Our method employs a distributed cooperative MAC scheme based on Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol, featuring selective RSU probing and adaptive transmission… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.09619v1-abstract-full').style.display = 'inline'; document.getElementById('2402.09619v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2402.09619v1-abstract-full" style="display: none;"> This paper presents an optimization approach for cooperative Medium Access Control (MAC) techniques in Vehicular Ad Hoc Networks (VANETs) equipped with Roadside Unit (RSU) to enhance network throughput. Our method employs a distributed cooperative MAC scheme based on Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol, featuring selective RSU probing and adaptive transmission. It utilizes a dual timescale channel access framework, with a ``large-scale'' phase accounting for gradual changes in vehicle locations and a ``small-scale'' phase adapting to rapid channel fluctuations. We propose the RSU Probing and Cooperative Access (RPCA) strategy, a two-stage approach based on dynamic inter-vehicle distances from the RSU. Using optimal sequential planned decision theory, we rigorously prove its optimality in maximizing average system throughput per large-scale phase. For practical implementation in VANETs, we develop a distributed MAC algorithm with periodic location updates. It adjusts thresholds based on inter-vehicle and vehicle-RSU distances during the large-scale phase and accesses channels following the RPCA strategy with updated thresholds during the small-scale phase. Simulation results confirm the effectiveness and efficiency of our algorithm. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.09619v1-abstract-full').style.display = 'none'; document.getElementById('2402.09619v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 5 figures, IEEE ICC 2024</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2402.08909">arXiv:2402.08909</a> <span> [<a href="https://arxiv.org/pdf/2402.08909">pdf</a>, <a href="https://arxiv.org/format/2402.08909">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> A locally mass-conservative enriched Petrov-Galerkin method without penalty for the Darcy flow in porous media </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Chen%2C+H">Huangxin Chen</a>, <a href="/search/math?searchtype=author&query=Dong%2C+P">Piaopiao Dong</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuyu Sun</a>, <a href="/search/math?searchtype=author&query=Wang%2C+Z">Zixuan Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2402.08909v1-abstract-short" style="display: inline;"> In this work we present an enriched Petrov-Galerkin (EPG) method for the simulation of the Darcy flow in porous media. The new method enriches the approximation trial space of the conforming continuous Galerkin (CG) method with bubble functions and enriches the approximation test space of the CG method with piecewise constant functions, and it does not require any penalty term in the weak formulat… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.08909v1-abstract-full').style.display = 'inline'; document.getElementById('2402.08909v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2402.08909v1-abstract-full" style="display: none;"> In this work we present an enriched Petrov-Galerkin (EPG) method for the simulation of the Darcy flow in porous media. The new method enriches the approximation trial space of the conforming continuous Galerkin (CG) method with bubble functions and enriches the approximation test space of the CG method with piecewise constant functions, and it does not require any penalty term in the weak formulation. Moreover, we propose a framework for constructing the bubble functions and consider a decoupled algorithm for the EPG method based on this framework, which enables the process of solving pressure to be decoupled into two steps. The first step is to solve the pressure by the standard CG method, and the second step is a post-processing correction of the first step. Compared with the CG method, the proposed EPG method is locally mass-conservative, while keeping fewer degrees of freedom than the discontinuous Galerkin (DG) method. In addition, this method is more concise in the error analysis than the enriched Galerkin (EG) method. The coupled flow and transport in porous media is considered to illustrate the advantages of locally mass-conservative properties of the EPG method. We establish the optimal convergence of numerical solutions and present several numerical examples to illustrate the performance of the proposed method. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.08909v1-abstract-full').style.display = 'none'; document.getElementById('2402.08909v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 65M60; 65N30; 76S05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.15007">arXiv:2401.15007</a> <span> [<a href="https://arxiv.org/pdf/2401.15007">pdf</a>, <a href="https://arxiv.org/format/2401.15007">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> Design Guidelines for Noise-Tolerant Optimization with Applications in Robust Design </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lou%2C+Y">Yuchen Lou</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shigeng Sun</a>, <a href="/search/math?searchtype=author&query=Nocedal%2C+J">Jorge Nocedal</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.15007v2-abstract-short" style="display: inline;"> The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization algorithms by adapting classical deterministic methods. These adaptations follow certain design guidelines described here, which make use of estimates of the noise… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.15007v2-abstract-full').style.display = 'inline'; document.getElementById('2401.15007v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.15007v2-abstract-full" style="display: none;"> The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization algorithms by adapting classical deterministic methods. These adaptations follow certain design guidelines described here, which make use of estimates of the noise level in the problem. The application of our methodology is illustrated by the development of a line search gradient projection method, which is tested on an engineering design problem. It is shown that a new self-calibrated line search and noise-aware finite-difference techniques are effective even in the high noise regime. Numerical experiments investigate the resiliency of key algorithmic components. A convergence analysis of the line search gradient projection method establishes convergence to a neighborhood of stationarity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.15007v2-abstract-full').style.display = 'none'; document.getElementById('2401.15007v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 90C30; 90C15; 93B51; 65K05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.10308">arXiv:2401.10308</a> <span> [<a href="https://arxiv.org/pdf/2401.10308">pdf</a>, <a href="https://arxiv.org/format/2401.10308">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> </div> </div> <p class="title is-5 mathjax"> Extending Dynamic Origin-Destination Estimation to Understand Traffic Patterns During COVID-19 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Yu%2C+H">Han Yu</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+S">Suyanpeng Zhang</a>, <a href="/search/math?searchtype=author&query=Suen%2C+S">Sze-chuan Suen</a>, <a href="/search/math?searchtype=author&query=Dessouky%2C+M">Maged Dessouky</a>, <a href="/search/math?searchtype=author&query=Ordonez%2C+F">Fernando Ordonez</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.10308v1-abstract-short" style="display: inline;"> Estimating dynamic Origin-Destination (OD) traffic flow is crucial for understanding traffic patterns and the traffic network. While dynamic origin-destination estimation (DODE) has been studied for decades as a useful tool for estimating traffic flow, few existing models have considered its potential in evaluating the influence of policy on travel activity. This paper proposes a data-driven appro… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.10308v1-abstract-full').style.display = 'inline'; document.getElementById('2401.10308v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.10308v1-abstract-full" style="display: none;"> Estimating dynamic Origin-Destination (OD) traffic flow is crucial for understanding traffic patterns and the traffic network. While dynamic origin-destination estimation (DODE) has been studied for decades as a useful tool for estimating traffic flow, few existing models have considered its potential in evaluating the influence of policy on travel activity. This paper proposes a data-driven approach to estimate OD traffic flow using sensor data on highways and local roads. We extend prior DODE models to improve accuracy and realism in order to estimate how policies affect OD traffic flow in large urban networks. We applied our approach to a case study in Los Angeles County, where we developed a traffic network, estimated OD traffic flow between health districts during COVID-19, and analyzed the relationship between OD traffic flow and demographic characteristics such as income. Our findings demonstrate that the proposed approach provides valuable insights into traffic flow patterns and their underlying demographic factors for a large-scale traffic network. Specifically, our approach allows for evaluating the impact of policy changes on travel activity. The approach has practical applications for transportation planning and traffic management, enabling a better understanding of traffic flow patterns and the impact of policy changes on travel activity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.10308v1-abstract-full').style.display = 'none'; document.getElementById('2401.10308v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2310.17608">arXiv:2310.17608</a> <span> [<a href="https://arxiv.org/pdf/2310.17608">pdf</a>, <a href="https://arxiv.org/ps/2310.17608">ps</a>, <a href="https://arxiv.org/format/2310.17608">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> </div> </div> <p class="title is-5 mathjax"> On the generalized numerical criterion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Paul%2C+S+T">Sean Timothy Paul</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Song Sun</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+J">Junsheng Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2310.17608v1-abstract-short" style="display: inline;"> In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2310.17608v1-abstract-full" style="display: none;"> In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.17608v1-abstract-full').style.display = 'none'; document.getElementById('2310.17608v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 53C55 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2310.17449">arXiv:2310.17449</a> <span> [<a href="https://arxiv.org/pdf/2310.17449">pdf</a>, <a href="https://arxiv.org/format/2310.17449">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> </div> </div> <p class="title is-5 mathjax"> On the Hadamard inverse of a resurgent function with only one singularity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+Y">Yong Li</a>, <a href="/search/math?searchtype=author&query=Sauzin%2C+D">David Sauzin</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shanzhong Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2310.17449v1-abstract-short" style="display: inline;"> This note discusses the location of the singularities of the Hadamard inverse of an endlessly continuable function, in the case when the original function has only one singular singularity which is either a single pole or a simple singularity. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2310.17449v1-abstract-full" style="display: none;"> This note discusses the location of the singularities of the Hadamard inverse of an endlessly continuable function, in the case when the original function has only one singular singularity which is either a single pole or a simple singularity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.17449v1-abstract-full').style.display = 'none'; document.getElementById('2310.17449v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2309.10651">arXiv:2309.10651</a> <span> [<a href="https://arxiv.org/pdf/2309.10651">pdf</a>, <a href="https://arxiv.org/ps/2309.10651">ps</a>, <a href="https://arxiv.org/format/2309.10651">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1137/23M1603431">10.1137/23M1603431 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Wave breaking for the generalized Fornberg-Whitham equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Saut%2C+J">Jean-Claude Saut</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shihan Sun</a>, <a href="/search/math?searchtype=author&query=Wang%2C+Y">Yuexun Wang</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+Y">Yi Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2309.10651v1-abstract-short" style="display: inline;"> This paper aims to show that the Cauchy problem of the Burgers equation with a weakly dispersive perturbation involving the Bessel potential (generalization of the Fornberg-Whitham equation) can exhibit wave breaking for initial data with large slope. We also comment on the dispersive properties of the equation. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.10651v1-abstract-full" style="display: none;"> This paper aims to show that the Cauchy problem of the Burgers equation with a weakly dispersive perturbation involving the Bessel potential (generalization of the Fornberg-Whitham equation) can exhibit wave breaking for initial data with large slope. We also comment on the dispersive properties of the equation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.10651v1-abstract-full').style.display = 'none'; document.getElementById('2309.10651v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> SIAM. J. Math. Anal. (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2309.01097">arXiv:2309.01097</a> <span> [<a href="https://arxiv.org/pdf/2309.01097">pdf</a>, <a href="https://arxiv.org/ps/2309.01097">ps</a>, <a href="https://arxiv.org/format/2309.01097">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> </div> </div> <p class="title is-5 mathjax"> An infinite dimensional balanced embedding problem I:existence </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+J">Jingzhou Sun</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Song Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2309.01097v1-abstract-short" style="display: inline;"> We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient flow in a Hilbert space; both the long-time existence and convergence at infinite time are non-trivial. The long time existence is established by choosing a pe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.01097v1-abstract-full').style.display = 'inline'; document.getElementById('2309.01097v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.01097v1-abstract-full" style="display: none;"> We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient flow in a Hilbert space; both the long-time existence and convergence at infinite time are non-trivial. The long time existence is established by choosing a perturbation of the ODE; the convergence depends on a priori bounds that uses techniques in the proof of the Tauber-Hardy-Littlewood theorem. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.01097v1-abstract-full').style.display = 'none'; document.getElementById('2309.01097v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 32Q26; 53C07 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2308.10469">arXiv:2308.10469</a> <span> [<a href="https://arxiv.org/pdf/2308.10469">pdf</a>, <a href="https://arxiv.org/ps/2308.10469">ps</a>, <a href="https://arxiv.org/format/2308.10469">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Upper bounds of dual flagged Weyl characters </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lin%2C+Z">Zhuowei Lin</a>, <a href="/search/math?searchtype=author&query=Peng%2C+S+C+Y">Simon C. Y. Peng</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S+C+C">Sophie C. C. Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2308.10469v1-abstract-short" style="display: inline;"> For a subset $D$ of boxes in an $n\times n$ square grid, let $蠂_{D}(x)$ denote the dual character of the flagged Weyl module associated to $D$. It is known that $蠂_{D}(x)$ specifies to a Schubert polynomial (resp., a key polynomial) in the case when $D$ is the Rothe diagram of a permutation (resp., the skyline diagram of a composition). One can naturally define a lower and an upper bound of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.10469v1-abstract-full').style.display = 'inline'; document.getElementById('2308.10469v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2308.10469v1-abstract-full" style="display: none;"> For a subset $D$ of boxes in an $n\times n$ square grid, let $蠂_{D}(x)$ denote the dual character of the flagged Weyl module associated to $D$. It is known that $蠂_{D}(x)$ specifies to a Schubert polynomial (resp., a key polynomial) in the case when $D$ is the Rothe diagram of a permutation (resp., the skyline diagram of a composition). One can naturally define a lower and an upper bound of $蠂_{D}(x)$. M{茅}sz{谩}ros, St. Dizier and Tanjaya conjectured that $蠂_{D}(x)$ attains the upper bound if and only if $D$ avoids a certain subdiagram. We provide a proof of this conjecture. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.10469v1-abstract-full').style.display = 'none'; document.getElementById('2308.10469v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2307.15782">arXiv:2307.15782</a> <span> [<a href="https://arxiv.org/pdf/2307.15782">pdf</a>, <a href="https://arxiv.org/format/2307.15782">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.jcp.2023.112670">10.1016/j.jcp.2023.112670 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> An Unconditionally Energy-Stable and Orthonormality-Preserving Iterative Scheme for the Kohn-Sham Gradient Flow Based Model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Wang%2C+X">Xiuping Wang</a>, <a href="/search/math?searchtype=author&query=Chen%2C+H">Huangxin Chen</a>, <a href="/search/math?searchtype=author&query=Kou%2C+J">Jisheng Kou</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuyu Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2307.15782v1-abstract-short" style="display: inline;"> We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in time but still continuous in space. The component-wise splitting iterative scheme changes one wave function at a time, similar to the Gauss-Seidel iteration for… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.15782v1-abstract-full').style.display = 'inline'; document.getElementById('2307.15782v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2307.15782v1-abstract-full" style="display: none;"> We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in time but still continuous in space. The component-wise splitting iterative scheme changes one wave function at a time, similar to the Gauss-Seidel iteration for solving a linear equation system. Rigorous mathematical derivations are presented to show our proposed scheme indeed satisfies the desired properties. We then study the fully-discretized scheme, where the space is further approximated by a conforming finite element subspace. For the fully-discretized scheme, not only the preservation of orthogonality and normalization (together we called orthonormalization) can be quickly shown using the same idea as for the semi-discretized scheme, but also the highlight property of the scheme, i.e., the unconditional energy stability can be rigorously proven. The scheme allows us to use large time step sizes and deal with small systems involving only a single wave function during each iteration step. Several numerical experiments are performed to verify the theoretical analysis, where the number of iterations is indeed greatly reduced as compared to similar examples solved by the Kohn-Sham gradient flow based model in the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.15782v1-abstract-full').style.display = 'none'; document.getElementById('2307.15782v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.17335">arXiv:2306.17335</a> <span> [<a href="https://arxiv.org/pdf/2306.17335">pdf</a>, <a href="https://arxiv.org/ps/2306.17335">ps</a>, <a href="https://arxiv.org/format/2306.17335">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Stability of solitary waves for generalized $abcd$-Boussinesq system: The Hamiltonian case </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Filho%2C+R+d+A+C">Roberto de A. Capistrano Filho</a>, <a href="/search/math?searchtype=author&query=Quintero%2C+J+R">Jose Raul Quintero</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shu-Ming Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.17335v3-abstract-short" style="display: inline;"> The $abcd$-Boussinesq system is a model of two equations that can describe the propagation of small-amplitude long waves in both directions in the water of finite depth. Considering the Hamiltonian regimes, where the parameters $b$ and $d$ in the system satisfy $b=d>0$, small solutions in the energy space are globally defined. Then, a variational approach is applied to establish the existence and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.17335v3-abstract-full').style.display = 'inline'; document.getElementById('2306.17335v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.17335v3-abstract-full" style="display: none;"> The $abcd$-Boussinesq system is a model of two equations that can describe the propagation of small-amplitude long waves in both directions in the water of finite depth. Considering the Hamiltonian regimes, where the parameters $b$ and $d$ in the system satisfy $b=d>0$, small solutions in the energy space are globally defined. Then, a variational approach is applied to establish the existence and nonlinear stability of the set of solitary-wave solutions for the generalized $abcb$-Boussinesq system. The main point of the analysis is to show that the traveling-wave solutions of the generalized $abcb$-Boussinesq system converge to nontrivial solitary-wave solutions of the generalized Korteweg-de Vries equation. Moreover, if $p$ is the exponent of the nonlinear terms for the generalized $abcb$-Boussinesq system, then the nonlinear stability of the set of solitary-waves is obtained for any $p$ with $ 0 < p < p_0$ where $p_0 $ is strictly larger than $4$, while it has been known that the critical exponent for the stability of solitary waves of the generalized KdV equations is equal to $ 4$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.17335v3-abstract-full').style.display = 'none'; document.getElementById('2306.17335v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">40 pages. Comments are welcome. We rewrite Lemma 3.1 and add an extra appendix with the concentration-compactness argument</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35B35; 76B25; 35Q35 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.10539">arXiv:2306.10539</a> <span> [<a href="https://arxiv.org/pdf/2306.10539">pdf</a>, <a href="https://arxiv.org/ps/2306.10539">ps</a>, <a href="https://arxiv.org/format/2306.10539">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Tilings in quasi-random $k$-partite hypergraphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shumin Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.10539v1-abstract-short" style="display: inline;"> Given $k\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an $F$-factor in $H$ is a set of vertex disjoint copies of $F$ that together cover the vertex set of $H$. Lenz and Mubayi were first to study the $F$-factor problems in quasi-random $k$-graphs with a minimum degree condition. Recently, Ding, Han, Sun, Wang and Zhou gave the density threshold for having all $3$-partite $3$-gra… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.10539v1-abstract-full').style.display = 'inline'; document.getElementById('2306.10539v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.10539v1-abstract-full" style="display: none;"> Given $k\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an $F$-factor in $H$ is a set of vertex disjoint copies of $F$ that together cover the vertex set of $H$. Lenz and Mubayi were first to study the $F$-factor problems in quasi-random $k$-graphs with a minimum degree condition. Recently, Ding, Han, Sun, Wang and Zhou gave the density threshold for having all $3$-partite $3$-graphs factors in quasi-random $3$-graphs with vanishing minimum codegree condition $惟(n)$. In this paper, we consider embedding factors when the host $k$-graph is $k$-partite and quasi-random with partite minimum codegree condition. We prove that if $p>1/2$ and $F$ is a $k$-partite $k$-graph with each part having $m$ vertices, then for $n$ large enough and $m\mid n$, any $p$-dense $k$-partite $k$-graph with each part having $n$ vertices and partite minimum codegree condition $惟(n)$ contains an $F$-factor. We also present a construction showing that $1/2$ is best possible. Furthermore, for $1\leq \ell \leq k-2$, by constructing a sequence of $p$-dense $k$-partite $k$-graphs with partite minimum $\ell$-degree $惟(n^{k-\ell})$ having no $K_k(m)$-factor, we show that the partite minimum codegree constraint can not be replaced by other partite minimum degree conditions. On the other hand, we prove that $n/2$ is the asymptotic partite minimum codegree threshold for having all fixed $k$-partite $k$-graph factors in sufficiently large host $k$-partite $k$-graphs even without quasi-randomness. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.10539v1-abstract-full').style.display = 'none'; document.getElementById('2306.10539v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: text overlap with arXiv:2108.10731, arXiv:2111.14140</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.09978">arXiv:2305.09978</a> <span> [<a href="https://arxiv.org/pdf/2305.09978">pdf</a>, <a href="https://arxiv.org/format/2305.09978">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Stochastic Ratios Tracking Algorithm for Large Scale Machine Learning Problems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shigeng Sun</a>, <a href="/search/math?searchtype=author&query=Xie%2C+Y">Yuchen Xie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.09978v1-abstract-short" style="display: inline;"> Many machine learning applications and tasks rely on the stochastic gradient descent (SGD) algorithm and its variants. Effective step length selection is crucial for the success of these algorithms, which has motivated the development of algorithms such as ADAM or AdaGrad. In this paper, we propose a novel algorithm for adaptive step length selection in the classical SGD framework, which can be re… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.09978v1-abstract-full').style.display = 'inline'; document.getElementById('2305.09978v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.09978v1-abstract-full" style="display: none;"> Many machine learning applications and tasks rely on the stochastic gradient descent (SGD) algorithm and its variants. Effective step length selection is crucial for the success of these algorithms, which has motivated the development of algorithms such as ADAM or AdaGrad. In this paper, we propose a novel algorithm for adaptive step length selection in the classical SGD framework, which can be readily adapted to other stochastic algorithms. Our proposed algorithm is inspired by traditional nonlinear optimization techniques and is supported by analytical findings. We show that under reasonable conditions, the algorithm produces step lengths in line with well-established theoretical requirements, and generates iterates that converge to a stationary neighborhood of a solution in expectation. We test the proposed algorithm on logistic regressions and deep neural networks and demonstrate that the algorithm can generate step lengths comparable to the best step length obtained from manual tuning. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.09978v1-abstract-full').style.display = 'none'; document.getElementById('2305.09978v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.06879">arXiv:2305.06879</a> <span> [<a href="https://arxiv.org/pdf/2305.06879">pdf</a>, <a href="https://arxiv.org/ps/2305.06879">ps</a>, <a href="https://arxiv.org/format/2305.06879">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Signal Processing">eess.SP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1109/TSP.2023.3328053">10.1109/TSP.2023.3328053 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Convex Quaternion Optimization for Signal Processing: Theory and Applications </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuning Sun</a>, <a href="/search/math?searchtype=author&query=Diao%2C+Q">Qiankun Diao</a>, <a href="/search/math?searchtype=author&query=Xu%2C+D">Dongpo Xu</a>, <a href="/search/math?searchtype=author&query=Bourigault%2C+P">Pauline Bourigault</a>, <a href="/search/math?searchtype=author&query=Mandic%2C+D+P">Danilo P. Mandic</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.06879v1-abstract-short" style="display: inline;"> Convex optimization methods have been extensively used in the fields of communications and signal processing. However, the theory of quaternion optimization is currently not as fully developed and systematic as that of complex and real optimization. To this end, we establish an essential theory of convex quaternion optimization for signal processing based on the generalized Hamilton-real (GHR) cal… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.06879v1-abstract-full').style.display = 'inline'; document.getElementById('2305.06879v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.06879v1-abstract-full" style="display: none;"> Convex optimization methods have been extensively used in the fields of communications and signal processing. However, the theory of quaternion optimization is currently not as fully developed and systematic as that of complex and real optimization. To this end, we establish an essential theory of convex quaternion optimization for signal processing based on the generalized Hamilton-real (GHR) calculus. This is achieved in a way which conforms with traditional complex and real optimization theory. For rigorous, We present five discriminant theorems for convex quaternion functions, and four discriminant criteria for strongly convex quaternion functions. Furthermore, we provide a fundamental theorem for the optimality of convex quaternion optimization problems, and demonstrate its utility through three applications in quaternion signal processing. These results provide a solid theoretical foundation for convex quaternion optimization and open avenues for further developments in signal processing applications. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.06879v1-abstract-full').style.display = 'none'; document.getElementById('2305.06879v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> IEEE Trans. Signal Process., vol. 71, pp. 4106-4115, Oct. 2023 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.06197">arXiv:2305.06197</a> <span> [<a href="https://arxiv.org/pdf/2305.06197">pdf</a>, <a href="https://arxiv.org/format/2305.06197">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> Parametric Dynamic Mode Decomposition for nonlinear parametric dynamical systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuwen Sun</a>, <a href="/search/math?searchtype=author&query=Feng%2C+L">Lihong Feng</a>, <a href="/search/math?searchtype=author&query=Chan%2C+H+S">Hoon Seng Chan</a>, <a href="/search/math?searchtype=author&query=Mili%C4%8Di%C4%87%2C+T">Tamara Mili膷i膰</a>, <a href="/search/math?searchtype=author&query=Vidakovi%C4%87-Koch%2C+T">Tanja Vidakovi膰-Koch</a>, <a href="/search/math?searchtype=author&query=R%C3%B6der%2C+F">Fridolin R枚der</a>, <a href="/search/math?searchtype=author&query=Benner%2C+P">Peter Benner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.06197v2-abstract-short" style="display: inline;"> A non-intrusive model order reduction (MOR) method that combines features of the dynamic mode decomposition (DMD) and the radial basis function (RBF) network is proposed to predict the dynamics of parametric nonlinear systems. In many applications, we have limited access to the information of the whole system, which motivates non-intrusive model reduction. One bottleneck is capturing the dynamics… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.06197v2-abstract-full').style.display = 'inline'; document.getElementById('2305.06197v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.06197v2-abstract-full" style="display: none;"> A non-intrusive model order reduction (MOR) method that combines features of the dynamic mode decomposition (DMD) and the radial basis function (RBF) network is proposed to predict the dynamics of parametric nonlinear systems. In many applications, we have limited access to the information of the whole system, which motivates non-intrusive model reduction. One bottleneck is capturing the dynamics of the solution without knowing the physics inside the "black-box" system. DMD is a powerful tool to mimic the dynamics of the system and give a reliable approximation of the solution in the time domain using only the dominant DMD modes. However, DMD cannot reproduce the parametric behavior of the dynamics. Our contribution focuses on extending DMD to parametric DMD by RBF interpolation. Specifically, a RBF network is first trained using snapshot matrices at limited parameter samples. The snapshot matrix at any new parameter sample can be quickly learned from the RBF network. DMD will use the newly generated snapshot matrix at the online stage to predict the time patterns of the dynamics corresponding to the new parameter sample. The proposed framework and algorithm are tested and validated by numerical examples including models with parametrized and time-varying inputs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.06197v2-abstract-full').style.display = 'none'; document.getElementById('2305.06197v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.11309">arXiv:2303.11309</a> <span> [<a href="https://arxiv.org/pdf/2303.11309">pdf</a>, <a href="https://arxiv.org/ps/2303.11309">ps</a>, <a href="https://arxiv.org/format/2303.11309">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> Bubbling of K盲hler-Einstein metrics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Song Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.11309v2-abstract-short" style="display: inline;"> We prove the finite step termination of bubble trees for singularity formation of polarized K盲hler-Einstein metrics in the non-collapsing situation. We also raise several questions and conjectures in connection with algebraic geometry and Riemannian geometry. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.11309v2-abstract-full" style="display: none;"> We prove the finite step termination of bubble trees for singularity formation of polarized K盲hler-Einstein metrics in the non-collapsing situation. We also raise several questions and conjectures in connection with algebraic geometry and Riemannian geometry. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.11309v2-abstract-full').style.display = 'none'; document.getElementById('2303.11309v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">This is an article written for the memorial volume for Professor Jean-Pierre Demailly. V2: references updated</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.00857">arXiv:2303.00857</a> <span> [<a href="https://arxiv.org/pdf/2303.00857">pdf</a>, <a href="https://arxiv.org/ps/2303.00857">ps</a>, <a href="https://arxiv.org/format/2303.00857">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Cryptography and Security">cs.CR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistics Theory">math.ST</span> </div> </div> <p class="title is-5 mathjax"> An Improved Christofides Mechanism for Local Differential Privacy Framework </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">She Sun</a>, <a href="/search/math?searchtype=author&query=Zhou%2C+L">Li Zhou</a>, <a href="/search/math?searchtype=author&query=Yan%2C+X">Xiaoran Yan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.00857v2-abstract-short" style="display: inline;"> The development of Internet technology enables an analysis on the whole population rather than a certain number of samples, and leads to increasing requirement for privacy protection. Local differential privacy (LDP) is an effective standard of privacy measurement; however, its large variance of mean estimation causes challenges in application. To address this problem, this paper presents a new LD… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.00857v2-abstract-full').style.display = 'inline'; document.getElementById('2303.00857v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.00857v2-abstract-full" style="display: none;"> The development of Internet technology enables an analysis on the whole population rather than a certain number of samples, and leads to increasing requirement for privacy protection. Local differential privacy (LDP) is an effective standard of privacy measurement; however, its large variance of mean estimation causes challenges in application. To address this problem, this paper presents a new LDP approach, an improved Christofides mechanism. It compared four statistical survey methods for conducting surveys on sensitive topics -- modified Warner, Simmons, Christofides, and the improved Christofides mechanism. Specifically, Warner, Simmons and Christofides mechanisms have been modified to draw a sample from the population without replacement, to decrease variance. Furthermore, by drawing cards without replacement based on modified Christofides mechanism, we introduce a new mechanism called the improved Christofides mechanism, which is found to have the smallest variance under certain assumption when using LDP as a measurement of privacy leakage. The assumption is do satisfied usually in the real world. Actually, we decrease the variance to 28.7% of modified Christofides mechanism's variance in our experiment based on the HCOVANY dataset -- a real world dataset of IPUMS USA. This means our method gets a more accurate estimate by using LDP as a measurement of privacy leakage. This is the first time the improved Christofides mechanism is proposed for LDP framework based on comparative analysis of four mechanisms using LDP as the same measurement of privacy leakage. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.00857v2-abstract-full').style.display = 'none'; document.getElementById('2303.00857v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.00201">arXiv:2303.00201</a> <span> [<a href="https://arxiv.org/pdf/2303.00201">pdf</a>, <a href="https://arxiv.org/ps/2303.00201">ps</a>, <a href="https://arxiv.org/format/2303.00201">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> On the Uniqueness of Convex Central Configurations in the Planar $4$-Body Problem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shanzhong Sun</a>, <a href="/search/math?searchtype=author&query=Xie%2C+Z">Zhifu Xie</a>, <a href="/search/math?searchtype=author&query=You%2C+P">Peng You</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.00201v2-abstract-short" style="display: inline;"> In this paper, we provide a rigorous computer-assisted proof (CAP) of the conjecture that there exists a unique convex central configuration for any four fixed positive masses in a given order belonging to a closed domain in the mass space. The proof employs the Krawczyk operator and the implicit function theorem. Notably, we demonstrate that the implicit function theorem can be combined with inte… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.00201v2-abstract-full').style.display = 'inline'; document.getElementById('2303.00201v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.00201v2-abstract-full" style="display: none;"> In this paper, we provide a rigorous computer-assisted proof (CAP) of the conjecture that there exists a unique convex central configuration for any four fixed positive masses in a given order belonging to a closed domain in the mass space. The proof employs the Krawczyk operator and the implicit function theorem. Notably, we demonstrate that the implicit function theorem can be combined with interval analysis, enabling us to estimate the size of the region where the implicit function exists and extend our findings from one mass point to its surrounding neighborhood. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.00201v2-abstract-full').style.display = 'none'; document.getElementById('2303.00201v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages,2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 70F10; 70F15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.07756">arXiv:2302.07756</a> <span> [<a href="https://arxiv.org/pdf/2302.07756">pdf</a>, <a href="https://arxiv.org/format/2302.07756">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Fluid Dynamics">physics.flu-dyn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> Derivation and Efficient Entropy-Production-Rate-Preserving Algorithms for a Thermodynamically Consistent Nonisothermal Model of Incompressible Binary Fluids </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shouwen Sun</a>, <a href="/search/math?searchtype=author&query=Lei%2C+L">Liangliang Lei</a>, <a href="/search/math?searchtype=author&query=Wang%2C+Q">Qi Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2302.07756v2-abstract-short" style="display: inline;"> We present a new hydrodynamic model for incompressible binary fluids that is thermodynamically consistent and non-isothermal. This model follows the generalized Onsager principle and Boussinesq approximation and preserves the volume of each fluid phase and the positive entropy production rate under consistent boundary conditions. To solve the governing partial differential equations in the model n… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.07756v2-abstract-full').style.display = 'inline'; document.getElementById('2302.07756v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.07756v2-abstract-full" style="display: none;"> We present a new hydrodynamic model for incompressible binary fluids that is thermodynamically consistent and non-isothermal. This model follows the generalized Onsager principle and Boussinesq approximation and preserves the volume of each fluid phase and the positive entropy production rate under consistent boundary conditions. To solve the governing partial differential equations in the model numerically, we design a set of second-order, volume and entropy-production-rate preserving numerical algorithms. Using an efficient adaptive time-stepping strategy, we conduct several numerical simulations. These simulations accurately simulate the Rayleigh-B茅nard convection in binary fluids and the interfacial dynamics between two immiscible fluids under the effects of the temperature gradient, gravity, and interfacial forces. Our numerical results show roll cell patterns and thermally induced mixing of binary fluids in a rectangular computational domain with a set of specific boundary conditions: a zero-velocity boundary condition all around, the insulation boundary condition at the lateral boundaries, and an imposed temperature difference vertically. We also perform long-time simulations of interfacial dynamics, demonstrating the robustness of our new structure-preserving schemes and reveal interesting fluid mixing phenomena. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.07756v2-abstract-full').style.display = 'none'; document.getElementById('2302.07756v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.05942">arXiv:2212.05942</a> <span> [<a href="https://arxiv.org/pdf/2212.05942">pdf</a>, <a href="https://arxiv.org/ps/2212.05942">ps</a>, <a href="https://arxiv.org/format/2212.05942">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> Physics-preserving IMPES based multiscale methods for immiscible two-phase flow in highly heterogeneous porous media </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Wang%2C+Y">Yiran Wang</a>, <a href="/search/math?searchtype=author&query=Chung%2C+E">Eric Chung</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuyu Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.05942v1-abstract-short" style="display: inline;"> In this paper, we propose a physics-preserving multiscale method to solve an immiscible two-phase flow problem, which is modeled as a coupling system consisting of Darcy's law and mass conservation equations. We use a new Physics-preserving IMplicit Pressure Explicit Saturation (P-IMPES) scheme in order to maintain the local conservation of mass for both phases. Besides, this scheme is unbiased an… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.05942v1-abstract-full').style.display = 'inline'; document.getElementById('2212.05942v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.05942v1-abstract-full" style="display: none;"> In this paper, we propose a physics-preserving multiscale method to solve an immiscible two-phase flow problem, which is modeled as a coupling system consisting of Darcy's law and mass conservation equations. We use a new Physics-preserving IMplicit Pressure Explicit Saturation (P-IMPES) scheme in order to maintain the local conservation of mass for both phases. Besides, this scheme is unbiased and if the time step is smaller than a certain value, the saturation of both phases are bounds-preserving. When updating velocity, MGMsFEM serves as an efficient solver by computing the unknowns on a coarse grid. We follow the operation splitting techinque to deal with the two-phase flow. In particular, we use an upwind strategy to iterate the saturation explicitly and the MGMsFEM is utilized to compute velocity with a decoupled system on a coarse mesh. To show the efficiency and robustness of the proposed method, we design a set of interesting experiments. A rigorous analysis is also included to serve as a theoretical base of the method, which is well verified by the numerical results. Both simulations and analysis indicate that the method attains a good balance between accuracy and computation cost. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.05942v1-abstract-full').style.display = 'none'; document.getElementById('2212.05942v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">38 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.01722">arXiv:2210.01722</a> <span> [<a href="https://arxiv.org/pdf/2210.01722">pdf</a>, <a href="https://arxiv.org/format/2210.01722">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Aggregations of quadratic inequalities and hidden hyperplane convexity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Blekherman%2C+G">Grigoriy Blekherman</a>, <a href="/search/math?searchtype=author&query=Dey%2C+S+S">Santanu S. Dey</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shengding Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2210.01722v2-abstract-short" style="display: inline;"> We study properties of the convex hull of a set $S$ described by quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take a nonnegative linear combinations of the defining inequalities of $S$. We call such inequalities aggregations. Special aggregations naturally contain the convex hull of $S$, and we give sufficient conditions for such aggregations to define the con… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.01722v2-abstract-full').style.display = 'inline'; document.getElementById('2210.01722v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.01722v2-abstract-full" style="display: none;"> We study properties of the convex hull of a set $S$ described by quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take a nonnegative linear combinations of the defining inequalities of $S$. We call such inequalities aggregations. Special aggregations naturally contain the convex hull of $S$, and we give sufficient conditions for such aggregations to define the convex hull. We introduce the notion of hidden hyperplane convexity (HHC), which is related to the classical notion of hidden convexity of quadratic maps. We show that if the quadratic map associated with $S$ satisfies HHC, then the convex hull of $S$ is defined by special aggregations. To the best of our knowledge, this result generalizes all known results regarding aggregations defining convex hulls. Using this sufficient condition, we are able to recognize previously unknown classes of sets where aggregations lead to convex hull. We show that the condition known as positive definite linear combination together with hidden hyerplane convexity is a sufficient condition for finitely many aggregations to define the convex hull. All the above results are for sets defined using open quadratic inequalities. For closed quadratic inequalities, we prove a new result regarding aggregations giving the convex hull, without topological assumptions on $S$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.01722v2-abstract-full').style.display = 'none'; document.getElementById('2210.01722v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">27 pages, 3 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 90C20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.08981">arXiv:2209.08981</a> <span> [<a href="https://arxiv.org/pdf/2209.08981">pdf</a>, <a href="https://arxiv.org/ps/2209.08981">ps</a>, <a href="https://arxiv.org/format/2209.08981">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s11425-022-2011-6">10.1007/s11425-022-2011-6 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Characterizations of functions in wandering subspaces of the Bergman Shift via the Hardy space of the Bidisc </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shunhua Sun</a>, <a href="/search/math?searchtype=author&query=Xu%2C+A">Anjian Xu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.08981v2-abstract-short" style="display: inline;"> Let $\mathcal{W}$ be the corresponding wandering subspace of an invariant subspace of the Bergman shift. By identifying the Bergman space with $H^2(\mathbb{D}^2)\ominus[z-w]$, a sufficient and necessary conditions of a closed subspace of $H^2(\mathbb{D}^2)\ominus[z-w]$ to be a wandering subspace of an invariant subspace is given also, and a functional charaterization and a coefficient characteriza… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.08981v2-abstract-full').style.display = 'inline'; document.getElementById('2209.08981v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.08981v2-abstract-full" style="display: none;"> Let $\mathcal{W}$ be the corresponding wandering subspace of an invariant subspace of the Bergman shift. By identifying the Bergman space with $H^2(\mathbb{D}^2)\ominus[z-w]$, a sufficient and necessary conditions of a closed subspace of $H^2(\mathbb{D}^2)\ominus[z-w]$ to be a wandering subspace of an invariant subspace is given also, and a functional charaterization and a coefficient characterization for a function in a wandering subspace are given. As a byproduct, we proved that for two invariant subspaces $\mathcal{M}$, $\mathcal{N}$ with $\mathcal{M}\supsetneq\mathcal{N}$ and $dim(\mathcal{N}\ominus B\mathcal{N})<\infty$ $dim(\mathcal{M}\ominus B\mathcal{M})=\infty$, then there is an invariant subspace $\mathcal{L}$ such that $\mathcal{M}\supsetneq\mathcal{L}\supsetneq\mathcal{N}$. Finally, we define an operator from one wandering subspace to another, and get a decomposition theorem for such an operator which is related to the universal property of the Bergman shift. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.08981v2-abstract-full').style.display = 'none'; document.getElementById('2209.08981v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, To appear in Science China Mathematics</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B35 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.00146">arXiv:2209.00146</a> <span> [<a href="https://arxiv.org/pdf/2209.00146">pdf</a>, <a href="https://arxiv.org/format/2209.00146">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symplectic Geometry">math.SG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1360/SCM-2020-0373">10.1360/SCM-2020-0373 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Monodromy of Complexified Planar Kepler Problem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shanzhong Sun</a>, <a href="/search/math?searchtype=author&query=You%2C+P">Peng You</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.00146v1-abstract-short" style="display: inline;"> The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.00146v1-abstract-full" style="display: none;"> The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.00146v1-abstract-full').style.display = 'none'; document.getElementById('2209.00146v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 3 figures. The Chinese version has appeared in SCIENTIA SINICA Mathematica</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 14H15; 37J35; 37J38; 70F05; 70G55; 70H06 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.11959">arXiv:2208.11959</a> <span> [<a href="https://arxiv.org/pdf/2208.11959">pdf</a>, <a href="https://arxiv.org/format/2208.11959">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> </div> </div> <p class="title is-5 mathjax"> A Weak $\infty$-Functor in Morse Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shanzhong Sun</a>, <a href="/search/math?searchtype=author&query=Wang%2C+C">Chenxi Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.11959v1-abstract-short" style="display: inline;"> In the spirit of Morse homology initiated by Witten and Floer, we construct two $\infty$-categories $\mathcal{A}$ and $\mathcal{B}$. The weak one $\mathcal{A}$ comes out of the Morse-Samle pairs and their higher homotopies, and the strict one $\mathcal{B}$ concerns the chain complexes of the Morse functions. Based on the boundary structures of the compactified moduli space of gradient flow lines o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.11959v1-abstract-full').style.display = 'inline'; document.getElementById('2208.11959v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.11959v1-abstract-full" style="display: none;"> In the spirit of Morse homology initiated by Witten and Floer, we construct two $\infty$-categories $\mathcal{A}$ and $\mathcal{B}$. The weak one $\mathcal{A}$ comes out of the Morse-Samle pairs and their higher homotopies, and the strict one $\mathcal{B}$ concerns the chain complexes of the Morse functions. Based on the boundary structures of the compactified moduli space of gradient flow lines of Morse functions with parameters, we build up a weak $\infty$-functor $\mathcal{F}: \mathcal{A}\rightarrow \mathcal{B}$. Higher algebraic structures behind Morse homology are revealed with the perspective of defects in topological quantum field theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.11959v1-abstract-full').style.display = 'none'; document.getElementById('2208.11959v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.05098">arXiv:2208.05098</a> <span> [<a href="https://arxiv.org/pdf/2208.05098">pdf</a>, <a href="https://arxiv.org/ps/2208.05098">ps</a>, <a href="https://arxiv.org/format/2208.05098">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s00222-023-01187-4">10.1007/s00222-023-01187-4 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> No semistability at infinity for Calabi-Yau metrics asymptotic to cones </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Song Sun</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+J">Junsheng Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.05098v3-abstract-short" style="display: inline;"> We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of K盲hler-Einstein metrics. A byproduct of the proof is a polynomial conve… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.05098v3-abstract-full').style.display = 'inline'; document.getElementById('2208.05098v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.05098v3-abstract-full" style="display: none;"> We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of K盲hler-Einstein metrics. A byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds, which bridges the gap between the general theory of Colding-Minicozzi and the classification results of Conlon-Hein. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.05098v3-abstract-full').style.display = 'none'; document.getElementById('2208.05098v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages. v3: various improvements on the presentation; v2: minor improvements on the discussion section</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.10239">arXiv:2207.10239</a> <span> [<a href="https://arxiv.org/pdf/2207.10239">pdf</a>, <a href="https://arxiv.org/format/2207.10239">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistics Theory">math.ST</span> </div> </div> <p class="title is-5 mathjax"> Fixed-domain Posterior Contraction Rates for Spatial Gaussian Process Model with Nugget </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+C">Cheng Li</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Saifei Sun</a>, <a href="/search/math?searchtype=author&query=Zhu%2C+Y">Yichen Zhu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.10239v3-abstract-short" style="display: inline;"> Spatial Gaussian process regression models typically contain finite dimensional covariance parameters that need to be estimated from the data. We study the Bayesian estimation of covariance parameters including the nugget parameter in a general class of stationary covariance functions under fixed-domain asymptotics, which is theoretically challenging due to the increasingly strong dependence among… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.10239v3-abstract-full').style.display = 'inline'; document.getElementById('2207.10239v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.10239v3-abstract-full" style="display: none;"> Spatial Gaussian process regression models typically contain finite dimensional covariance parameters that need to be estimated from the data. We study the Bayesian estimation of covariance parameters including the nugget parameter in a general class of stationary covariance functions under fixed-domain asymptotics, which is theoretically challenging due to the increasingly strong dependence among spatial observations. We propose a novel adaptation of the Schwartz's consistency theorem for showing posterior contraction rates of the covariance parameters including the nugget. We derive a new polynomial evidence lower bound, and propose consistent higher-order quadratic variation estimators that satisfy concentration inequalities with exponentially small tails. Our Bayesian fixed-domain asymptotics theory leads to explicit posterior contraction rates for the microergodic and nugget parameters in the isotropic Matern covariance function under a general stratified sampling design. We verify our theory and the Bayesian predictive performance in simulation studies and an application to sea surface temperature data. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.10239v3-abstract-full').style.display = 'none'; document.getElementById('2207.10239v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.12777">arXiv:2206.12777</a> <span> [<a href="https://arxiv.org/pdf/2206.12777">pdf</a>, <a href="https://arxiv.org/ps/2206.12777">ps</a>, <a href="https://arxiv.org/format/2206.12777">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Hermitian adjacency matrices of mixed multigraphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Yuan%2C+B">Bo-Jun Yuan</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shaowei Sun</a>, <a href="/search/math?searchtype=author&query=Wang%2C+D">Dijian Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.12777v1-abstract-short" style="display: inline;"> A mixed multigraph is obtained from an undirected multigraph by orienting a subset of its edges. In this paper, we study a new Hermitian matrix representation of mixed multigraphs, give an introduction to cospectral operations on mixed multigraphs, and characterize switching equivalent mixed multigraphs in terms of fundamental cycle basis. As an application, an upper bound of cospectral classes of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.12777v1-abstract-full').style.display = 'inline'; document.getElementById('2206.12777v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.12777v1-abstract-full" style="display: none;"> A mixed multigraph is obtained from an undirected multigraph by orienting a subset of its edges. In this paper, we study a new Hermitian matrix representation of mixed multigraphs, give an introduction to cospectral operations on mixed multigraphs, and characterize switching equivalent mixed multigraphs in terms of fundamental cycle basis. As an application, an upper bound of cospectral classes of mixed multigraphs with the same underlying graph is obtained. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.12777v1-abstract-full').style.display = 'none'; document.getElementById('2206.12777v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Mixed multigraph; Hermitian adjacency matrix; Switching equivalence; Cospectral class</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 05C50 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.08205">arXiv:2206.08205</a> <span> [<a href="https://arxiv.org/pdf/2206.08205">pdf</a>, <a href="https://arxiv.org/ps/2206.08205">ps</a>, <a href="https://arxiv.org/format/2206.08205">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Doubly iteratively reweighted algorithm for constrained compressed sensing models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuqin Sun</a>, <a href="/search/math?searchtype=author&query=Pong%2C+T+K">Ting Kei Pong</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.08205v1-abstract-short" style="display: inline;"> We propose a new algorithmic framework for constrained compressed sensing models that admit nonconvex sparsity-inducing regularizers including the log-penalty function as objectives, and nonconvex loss functions such as the Cauchy loss function and the Tukey biweight loss function in the constraint. Our framework employs iteratively reweighted $\ell_1$ and $\ell_2$ schemes to construct subproblems… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.08205v1-abstract-full').style.display = 'inline'; document.getElementById('2206.08205v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.08205v1-abstract-full" style="display: none;"> We propose a new algorithmic framework for constrained compressed sensing models that admit nonconvex sparsity-inducing regularizers including the log-penalty function as objectives, and nonconvex loss functions such as the Cauchy loss function and the Tukey biweight loss function in the constraint. Our framework employs iteratively reweighted $\ell_1$ and $\ell_2$ schemes to construct subproblems that can be efficiently solved by well-developed solvers for basis pursuit denoising such as SPGL1 [6]. We propose a new termination criterion for the subproblem solvers that allows them to return an infeasible solution, with a suitably constructed feasible point satisfying a descent condition. The feasible point construction step is the key for establishing the well-definedness of our proposed algorithm, and we also prove that any accumulation point of this sequence of feasible points is a stationary point of the constrained compressed sensing model, under suitable assumptions. Finally, we compare numerically our algorithm (with subproblems solved by SPGL1 or the alternating direction method of multipliers) against the SCP$_{\rm ls}$ in [41] on solving constrained compressed sensing models with the log-penalty function as the objective and the Cauchy loss function in the constraint, for badly-scaled measurement matrices. Our computational results show that our approaches return solutions with better recovery errors, and are always faster. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.08205v1-abstract-full').style.display = 'none'; document.getElementById('2206.08205v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2201.05932">arXiv:2201.05932</a> <span> [<a href="https://arxiv.org/pdf/2201.05932">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.energy.2022.123226">10.1016/j.energy.2022.123226 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Joint Planning of Distributed Generations and Energy Storage in Active Distribution Networks: A Bi-Level Programming Approach </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+Y">Yang Li</a>, <a href="/search/math?searchtype=author&query=Feng%2C+B">Bo Feng</a>, <a href="/search/math?searchtype=author&query=Wang%2C+B">Bin Wang</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuchao Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2201.05932v1-abstract-short" style="display: inline;"> In order to improve the penetration of renewable energy resources for distribution networks, a joint planning model of distributed generations (DGs) and energy storage is proposed for an active distribution network by using a bi-level programming approach in this paper. In this model, the upper-level aims to seek the optimal location and capacity of DGs and energy storage, while the lower-level op… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.05932v1-abstract-full').style.display = 'inline'; document.getElementById('2201.05932v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.05932v1-abstract-full" style="display: none;"> In order to improve the penetration of renewable energy resources for distribution networks, a joint planning model of distributed generations (DGs) and energy storage is proposed for an active distribution network by using a bi-level programming approach in this paper. In this model, the upper-level aims to seek the optimal location and capacity of DGs and energy storage, while the lower-level optimizes the operation of energy storage devices. To solve this model, an improved binary particle swarm optimization (IBPSO) algorithm based on chaos optimization is developed, and the optimal joint planning is achieved through alternating iterations between the two levels. The simulation results on the PG & E 69-bus distribution system demonstrate that the presented approach manages to reduce the planning deviation caused by the uncertainties of DG outputs and remarkably improve the voltage profile and operational economy of distribution systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.05932v1-abstract-full').style.display = 'none'; document.getElementById('2201.05932v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted by Energy</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Energy 245 (2022) 123226 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2201.00973">arXiv:2201.00973</a> <span> [<a href="https://arxiv.org/pdf/2201.00973">pdf</a>, <a href="https://arxiv.org/format/2201.00973">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> A Trust Region Method for the Optimization of Noisy Functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sun%2C+S">Shigeng Sun</a>, <a href="/search/math?searchtype=author&query=Nocedal%2C+J">Jorge Nocedal</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2201.00973v1-abstract-short" style="display: inline;"> Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple modification of the trust region method to cope with these errors. The new algorithm only requires information about the size of the errors in the function evaluati… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.00973v1-abstract-full').style.display = 'inline'; document.getElementById('2201.00973v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.00973v1-abstract-full" style="display: none;"> Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple modification of the trust region method to cope with these errors. The new algorithm only requires information about the size of the errors in the function evaluations and incurs no additional computational expense. It is shown that, when applied to a smooth (but not necessarily convex) objective function, the iterates of the algorithm visit a neighborhood of stationarity infinitely often, and that the rest of the sequence cannot stray too far away, as measured by function values. Numerical results illustrate how the classical trust region algorithm may fail in the presence of noise, and how the proposed algorithm ensures steady progress towards stationarity in these cases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.00973v1-abstract-full').style.display = 'none'; document.getElementById('2201.00973v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 65K05; 68Q25; 65G99; 90C30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2112.15223">arXiv:2112.15223</a> <span> [<a href="https://arxiv.org/pdf/2112.15223">pdf</a>, <a href="https://arxiv.org/format/2112.15223">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> </div> </div> <p class="title is-5 mathjax"> Resurgence and Partial Theta Series </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Han%2C+L">Li Han</a>, <a href="/search/math?searchtype=author&query=Li%2C+Y">Yong Li</a>, <a href="/search/math?searchtype=author&query=Sauzin%2C+D">David Sauzin</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shanzhong Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2112.15223v3-abstract-short" style="display: inline;"> We consider partial theta series associated with periodic sequences of coefficients, of the form $螛(蟿) := \sum_{n>0} n^谓f(n) e^{i蟺n^2蟿/M}$, with $谓$ non-negative integer and an $M$-periodic function $f : \mathbb{Z} \rightarrow \mathbb{C}$. Such a function is analytic in the half-plane $\{Im(蟿)>0\}$ and as $蟿$ tends non-tangentially to any $伪\in\mathbb{Q}$, a formal power series appears in the asym… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.15223v3-abstract-full').style.display = 'inline'; document.getElementById('2112.15223v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2112.15223v3-abstract-full" style="display: none;"> We consider partial theta series associated with periodic sequences of coefficients, of the form $螛(蟿) := \sum_{n>0} n^谓f(n) e^{i蟺n^2蟿/M}$, with $谓$ non-negative integer and an $M$-periodic function $f : \mathbb{Z} \rightarrow \mathbb{C}$. Such a function is analytic in the half-plane $\{Im(蟿)>0\}$ and as $蟿$ tends non-tangentially to any $伪\in\mathbb{Q}$, a formal power series appears in the asymptotic behaviour of $螛(蟿)$, depending on the parity of $谓$ and $f$. We discuss the summability and resurgence properties of these series by means of explicit formulas for their formal Borel transforms, and the consequences for the modularity properties of $螛$, or its ``quantum modularity'' properties in the sense of Zagier's recent theory. The Discrete Fourier Transform of $f$ plays an unexpected role and leads to a number-theoretic analogue of 脡calle's ``Bridge Equations''. The motto is: (quantum) modularity = Stokes phenomenon + Discrete Fourier Transform. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.15223v3-abstract-full').style.display = 'none'; document.getElementById('2112.15223v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages. More details given w.r.t. initial announcements</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2112.13321">arXiv:2112.13321</a> <span> [<a href="https://arxiv.org/pdf/2112.13321">pdf</a>, <a href="https://arxiv.org/ps/2112.13321">ps</a>, <a href="https://arxiv.org/format/2112.13321">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1093/imrn/rnac291">10.1093/imrn/rnac291 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Linear Principal Minor Polynomials: Hyperbolic Determinantal Inequalities and Spectral Containment </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Blekherman%2C+G">Grigoriy Blekherman</a>, <a href="/search/math?searchtype=author&query=Kummer%2C+M">Mario Kummer</a>, <a href="/search/math?searchtype=author&query=Sanyal%2C+R">Raman Sanyal</a>, <a href="/search/math?searchtype=author&query=Shu%2C+K">Kevin Shu</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shengding Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2112.13321v1-abstract-short" style="display: inline;"> A linear principal minor polynomial or lpm polynomial is a linear combination of principal minors of a symmetric matrix. By restricting to the diagonal, lpm polynomials are in bijection to multiaffine polynomials. We show that this establishes a one-to-one correspondence between homogeneous multiaffine stable polynomials and PSD-stable lpm polynomials. This yields new construction techniques for h… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.13321v1-abstract-full').style.display = 'inline'; document.getElementById('2112.13321v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2112.13321v1-abstract-full" style="display: none;"> A linear principal minor polynomial or lpm polynomial is a linear combination of principal minors of a symmetric matrix. By restricting to the diagonal, lpm polynomials are in bijection to multiaffine polynomials. We show that this establishes a one-to-one correspondence between homogeneous multiaffine stable polynomials and PSD-stable lpm polynomials. This yields new construction techniques for hyperbolic polynomials and allows us to generalize the well-known Fisher--Hadamard and Koteljanskii inequalities from determinants to PSD-stable lpm polynomials. We investigate the relationship between the associated hyperbolicity cones and conjecture a relationship between the eigenvalues of a symmetric matrix and the values of certain lpm polynomials evaluated at that matrix. We refer to this relationship as spectral containment. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.13321v1-abstract-full').style.display = 'none'; document.getElementById('2112.13321v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2112.05943">arXiv:2112.05943</a> <span> [<a href="https://arxiv.org/pdf/2112.05943">pdf</a>, <a href="https://arxiv.org/ps/2112.05943">ps</a>, <a href="https://arxiv.org/format/2112.05943">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> A strongly mass conservative method for the coupled Brinkman-Darcy flow and transport </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhao%2C+L">Lina Zhao</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shuyu Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2112.05943v2-abstract-short" style="display: inline;"> In this paper, a strongly mass conservative and stabilizer free scheme is designed and analyzed for the coupled Brinkman-Darcy flow and transport. The flow equations are discretized by using a strongly mass conservative scheme in mixed formulation with a suitable incorporation of the interface conditions. In particular, the interface conditions can be incorporated into the discrete formulation nat… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.05943v2-abstract-full').style.display = 'inline'; document.getElementById('2112.05943v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2112.05943v2-abstract-full" style="display: none;"> In this paper, a strongly mass conservative and stabilizer free scheme is designed and analyzed for the coupled Brinkman-Darcy flow and transport. The flow equations are discretized by using a strongly mass conservative scheme in mixed formulation with a suitable incorporation of the interface conditions. In particular, the interface conditions can be incorporated into the discrete formulation naturally without introducing additional variables. Moreover, the proposed scheme behaves uniformly robust for various values of viscosity. A novel upwinding staggered DG scheme in mixed form is exploited to solve the transport equation, where the boundary correction terms are added to improve the stability. A rigorous convergence analysis is carried out for the approximation of the flow equations. The velocity error is shown to be independent of the pressure and thus confirms the pressure-robustness. Stability and a priori error estimates are also obtained for the approximation of the transport equation; moreover, we are able to achieve a sharp stability and convergence error estimates thanks to the strong mass conservation preserved by our scheme. In particular, the stability estimate depends only on the true velocity on the inflow boundary rather than on the approximated velocity. Several numerical experiments are presented to verify the theoretical findings and demonstrate the performances of the method. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.05943v2-abstract-full').style.display = 'none'; document.getElementById('2112.05943v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.14140">arXiv:2111.14140</a> <span> [<a href="https://arxiv.org/pdf/2111.14140">pdf</a>, <a href="https://arxiv.org/ps/2111.14140">ps</a>, <a href="https://arxiv.org/format/2111.14140">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Tiling multipartite hypergraphs in Quasi-random Hypergraphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ding%2C+L">Laihao Ding</a>, <a href="/search/math?searchtype=author&query=Han%2C+J">Jie Han</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shumin Sun</a>, <a href="/search/math?searchtype=author&query=Wang%2C+G">Guanghui Wang</a>, <a href="/search/math?searchtype=author&query=Zhou%2C+W">Wenling Zhou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.14140v2-abstract-short" style="display: inline;"> Given $k\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an \emph{$F$-factor} in $H$ is a set of vertex disjoint copies of $F$ that together covers the vertex set of $H$. Lenz and Mubayi studied the $F$-factor problems in quasi-random $k$-graphs with minimum degree $惟(n^{k-1})$. In particular, they constructed a sequence of $1/8$-dense quasi-random $3$-graphs $H(n)$ with minimum de… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.14140v2-abstract-full').style.display = 'inline'; document.getElementById('2111.14140v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.14140v2-abstract-full" style="display: none;"> Given $k\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an \emph{$F$-factor} in $H$ is a set of vertex disjoint copies of $F$ that together covers the vertex set of $H$. Lenz and Mubayi studied the $F$-factor problems in quasi-random $k$-graphs with minimum degree $惟(n^{k-1})$. In particular, they constructed a sequence of $1/8$-dense quasi-random $3$-graphs $H(n)$ with minimum degree $惟(n^2)$ and minimum codegree $惟(n)$ but with no $K_{2,2,2}$-factor. We prove that if $p>1/8$ and $F$ is a $3$-partite $3$-graph with $f$ vertices, then for sufficiently large $n$, all $p$-dense quasi-random $3$-graphs of order $n$ with minimum codegree $惟(n)$ and $f\mid n$ have $F$-factors. That is, $1/8$ is the density threshold for ensuring all $3$-partite $3$-graphs $F$-factors in quasi-random $3$-graphs given a minimum codegree condition $惟(n)$. Moreover, we show that one can not replace the minimum codegree condition by a minimum vertex degree condition. In fact, we find that for any $p\in(0,1)$ and $n\ge n_0$, there exist $p$-dense quasi-random $3$-graphs of order $n$ with minimum degree $惟(n^2)$ having no $K_{2,2,2}$-factor. In particular, we study the optimal density threshold of $F$-factors for each $3$-partite $3$-graph $F$ in quasi-random $3$-graphs given a minimum codegree condition $惟(n)$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.14140v2-abstract-full').style.display = 'none'; document.getElementById('2111.14140v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages. Accepted by Journal of Combinatorial Theory, Series B</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.09287">arXiv:2111.09287</a> <span> [<a href="https://arxiv.org/pdf/2111.09287">pdf</a>, <a href="https://arxiv.org/ps/2111.09287">ps</a>, <a href="https://arxiv.org/format/2111.09287">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> </div> </div> <p class="title is-5 mathjax"> Asymptotically Calabi metrics and weak Fano manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hein%2C+H">Hans-Joachim Hein</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Song Sun</a>, <a href="/search/math?searchtype=author&query=Viaclovsky%2C+J">Jeff Viaclovsky</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+R">Ruobing Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.09287v2-abstract-short" style="display: inline;"> We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises from a generalized Tian-Yau construction on the compactification, and we prove a strong uniqueness theorem. We also give an application of this result to the surface case. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.09287v2-abstract-full" style="display: none;"> We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises from a generalized Tian-Yau construction on the compactification, and we prove a strong uniqueness theorem. We also give an application of this result to the surface case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.09287v2-abstract-full').style.display = 'none'; document.getElementById('2111.09287v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.07714">arXiv:2111.07714</a> <span> [<a href="https://arxiv.org/pdf/2111.07714">pdf</a>, <a href="https://arxiv.org/format/2111.07714">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1134/S1560354722010063">10.1134/S1560354722010063 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Elliptic fixed points with an invariant foliation: Some facts and more questions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Chenciner%2C+A">Alain Chenciner</a>, <a href="/search/math?searchtype=author&query=Sauzin%2C+D">David Sauzin</a>, <a href="/search/math?searchtype=author&query=Sun%2C+S">Shanzhong Sun</a>, <a href="/search/math?searchtype=author&query=Wei%2C+Q">Qiaoling Wei</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.07714v1-abstract-short" style="display: inline;"> We address the following question: let F:(R^2,0)->(R^2,0) be an analytic local diffeomorphism defined in the neighborhood of the non resonant elliptic fixed point 0 and let 桅be a formal conjugacy to a normal form N. Supposing F leaves invariant the foliation by circles centered at 0, what is the analytic nature of 桅and N? </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.07714v1-abstract-full" style="display: none;"> We address the following question: let F:(R^2,0)->(R^2,0) be an analytic local diffeomorphism defined in the neighborhood of the non resonant elliptic fixed point 0 and let 桅be a formal conjugacy to a normal form N. Supposing F leaves invariant the foliation by circles centered at 0, what is the analytic nature of 桅and N? <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.07714v1-abstract-full').style.display = 'none'; document.getElementById('2111.07714v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37E30 (Primary) 37G05 (Secondary) </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" 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