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id="recent-math.DS" aria-labelledby="recent-math.DS" href="/list/math.DS/recent">recent</a> articles</p> <h3>Showing new listings for Friday, 22 November 2024</h3> <div class='paging'>Total of 24 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math.DS/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> <dl id='articles'> <h3>New submissions (showing 8 of 8 entries)</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2411.13624" title="Abstract" id="2411.13624"> arXiv:2411.13624 </a> [<a href="/pdf/2411.13624" title="Download PDF" id="pdf-2411.13624" aria-labelledby="pdf-2411.13624">pdf</a>, <a href="https://arxiv.org/html/2411.13624v1" title="View HTML" id="html-2411.13624" aria-labelledby="html-2411.13624" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13624" title="Other formats" id="oth-2411.13624" aria-labelledby="oth-2411.13624">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Priori Bounds for H\'enon-like Renormalization </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Crovisier,+S">Sylvain Crovisier</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lyubich,+M">Mikhail Lyubich</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Pujals,+E">Enrique Pujals</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yang,+J">Jonguk Yang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 47 pages, 9 figures. arXiv admin note: substantial text overlap with <a href="https://arxiv.org/abs/2411.08317" data-arxiv-id="2411.08317" class="link-https">arXiv:2411.08317</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> We formulate and prove $\textit{a priori}$ bounds for the renormalization of H茅non-like maps (under certain regularity assumptions). This provides a certain uniform control on the small-scale geometry of the dynamics, and ensures pre-compactness of the renormalization sequence. In a sequel to this paper, a priori bounds are used in the proof of the main results, including renormalization convergence, finite-time checkability of the required regularity conditions and regular unicriticality of the dynamics. </p> </div> </dd> <dt> <a name='item2'>[2]</a> <a href ="/abs/2411.13679" title="Abstract" id="2411.13679"> arXiv:2411.13679 </a> [<a href="/pdf/2411.13679" title="Download PDF" id="pdf-2411.13679" aria-labelledby="pdf-2411.13679">pdf</a>, <a href="https://arxiv.org/html/2411.13679v1" title="View HTML" id="html-2411.13679" aria-labelledby="html-2411.13679" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13679" title="Other formats" id="oth-2411.13679" aria-labelledby="oth-2411.13679">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Characterising exchange of stability in scalar reaction-diffusion equations via geometric blow-up </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Jelbart,+S">Samuel Jelbart</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kuehn,+C">Christian Kuehn</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=S%C3%A1nchez,+A+M">Alejandro Mart铆nez S谩nchez</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Analysis of PDEs (math.AP) </div> <p class='mathjax'> We study the exchange of stability in scalar reaction-diffusion equations which feature a slow passage through transcritical and pitchfork type singularities in the reaction term, using a novel adaptation of the geometric blow-up method. Our results are consistent with known results on bounded spatial domains which were obtained by Butuzov, Nefedov & Schneider using comparison principles like upper and lower solutions in [7], however, from a methodological point of view, the approach is motivated by the analysis of closely related ODE problems using geometric blow-up presented by Krupa & Szmolyan in [34]. After applying the blow-up transformation, we obtain a system of PDEs which can be studied in local coordinate charts. Importantly, the blow-up procedure resolves a spectral degeneracy in which continuous spectrum along the entire negative real axis is 'pushed back' so as to create a spectral gap in the linearisation about particular steady states which arise within the so-called entry and exit charts. This makes it possible to extend slow-type invariant manifolds into and out of a neighbourhood of the singular point using center manifold theory, in a manner which is conceptually analogous to the established approach in the ODE setting. We expect that the approach can be adapted and applied to the study of dynamic bifurcations in PDEs in a wide variety of different contexts. </p> </div> </dd> <dt> <a name='item3'>[3]</a> <a href ="/abs/2411.13858" title="Abstract" id="2411.13858"> arXiv:2411.13858 </a> [<a href="/pdf/2411.13858" title="Download PDF" id="pdf-2411.13858" aria-labelledby="pdf-2411.13858">pdf</a>, <a href="https://arxiv.org/html/2411.13858v1" title="View HTML" id="html-2411.13858" aria-labelledby="html-2411.13858" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13858" title="Other formats" id="oth-2411.13858" aria-labelledby="oth-2411.13858">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Zimmer's conjecture for non-split semisimple Lie groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=An,+J">Jinpeng An</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Brown,+A">Aaron Brown</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhang,+Z">Zhiyuan Zhang</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> We prove many new cases of Zimmer's conjecture for actions by lattices in non-$\mathbb{R}$-split semisimple Lie groups $G$. By prior arguments, Zimmer's conjecture reduces to studying certain probability measures invariant under a minimal parabolic subgroup for the induced $G$-action. <br>Two techniques are introduced to give lower bounds on the dimension of a manifold $M$ admitting a non-isometric action. First, when the Levi component of the stabilizer of the measure has higher-rank simple factors, cocycle superrigidity provides a lower bound on the dimension of $M$. Second, when certain fiberwise coarse Lyapunov distributions are one-dimensional, a measure rigidity argument provides additional invariance of the measure if the associated root spaces are higher-dimensional. </p> </div> </dd> <dt> <a name='item4'>[4]</a> <a href ="/abs/2411.14132" title="Abstract" id="2411.14132"> arXiv:2411.14132 </a> [<a href="/pdf/2411.14132" title="Download PDF" id="pdf-2411.14132" aria-labelledby="pdf-2411.14132">pdf</a>, <a href="https://arxiv.org/html/2411.14132v1" title="View HTML" id="html-2411.14132" aria-labelledby="html-2411.14132" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14132" title="Other formats" id="oth-2411.14132" aria-labelledby="oth-2411.14132">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Transients versus network interactions give rise to multistability through trapping mechanism </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Rossi,+K+L">Kalel L. Rossi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Medeiros,+E+S">Everton S. Medeiros</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ashwin,+P">Peter Ashwin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Feudel,+U">Ulrike Feudel</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Submitted to Chaos </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Chaotic Dynamics (nlin.CD) </div> <p class='mathjax'> In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients that give rise to multistability from such interplay remain poorly understood. In a network of coupled excitable units, we show that this interplay generating multistability occurs through a competition between the units' transient dynamics and their coupling. Specifically, the diffusive coupling between the units manages to reinject them in the excitability region of their individual state space and effectively trap them there. We show that this trapping mechanism leads to the coexistence of multiple types of oscillations: periodic, quasiperiodic, and even chaotic, although the units separately do not oscillate. Interestingly, we show that the attractors emerge through different types of bifurcations - in particular, the periodic attractors emerge through either saddle-node of limit cycles bifurcations or homoclinic bifurcations - but in all cases the reinjection mechanism is present. </p> </div> </dd> <dt> <a name='item5'>[5]</a> <a href ="/abs/2411.14203" title="Abstract" id="2411.14203"> arXiv:2411.14203 </a> [<a href="/pdf/2411.14203" title="Download PDF" id="pdf-2411.14203" aria-labelledby="pdf-2411.14203">pdf</a>, <a href="https://arxiv.org/html/2411.14203v1" title="View HTML" id="html-2411.14203" aria-labelledby="html-2411.14203" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14203" title="Other formats" id="oth-2411.14203" aria-labelledby="oth-2411.14203">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Piecewise quasiconformal dynamical systems of the unit circle </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Luo,+Y">Yusheng Luo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ntalampekos,+D">Dimitrios Ntalampekos</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 38 pages, 9 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Complex Variables (math.CV) </div> <p class='mathjax'> We study piecewise quasiconformal covering maps of the unit circle. We provide sufficient conditions so that a conjugacy between two such dynamical systems has a quasiconformal or David extension to the unit disk. Our main result generalizes the main result of <a href="https://arxiv.org/abs/2010.11256" data-arxiv-id="2010.11256" class="link-https">arXiv:2010.11256</a>, which deals with piecewise analytic maps. As applications, we provide a classification of piecewise quasiconformal maps of the circle up to quasisymmetric conjugacy, we prove a general conformal mating theorem for Blaschke products, and we study the quasiconformal geometry of parabolic basins. </p> </div> </dd> <dt> <a name='item6'>[6]</a> <a href ="/abs/2411.14240" title="Abstract" id="2411.14240"> arXiv:2411.14240 </a> [<a href="/pdf/2411.14240" title="Download PDF" id="pdf-2411.14240" aria-labelledby="pdf-2411.14240">pdf</a>, <a href="https://arxiv.org/html/2411.14240v1" title="View HTML" id="html-2411.14240" aria-labelledby="html-2411.14240" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14240" title="Other formats" id="oth-2411.14240" aria-labelledby="oth-2411.14240">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Modeling and dynamics near irregular elongated asteroids </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Mart%C3%ADnez,+E">E. Mart铆nez</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=J.Vidarte">J.Vidarte</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=J.L.Zapata">J.L.Zapata</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we formulate the Hamiltonian equations of motion for this system. Our analysis reveals a family of periodic circular orbits parameterized by angular momentum. Additionally, we utilize the axial symmetry resulting from rotations around the segment's axis to consider the corresponding reduced system. This approach identifies several reduced-periodic orbits by analyzing appropriate Poincar茅 sections. These periodic orbits are then reconstructed into quasi-periodic orbits within the full dynamical system. </p> </div> </dd> <dt> <a name='item7'>[7]</a> <a href ="/abs/2411.14297" title="Abstract" id="2411.14297"> arXiv:2411.14297 </a> [<a href="/pdf/2411.14297" title="Download PDF" id="pdf-2411.14297" aria-labelledby="pdf-2411.14297">pdf</a>, <a href="https://arxiv.org/html/2411.14297v1" title="View HTML" id="html-2411.14297" aria-labelledby="html-2411.14297" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14297" title="Other formats" id="oth-2411.14297" aria-labelledby="oth-2411.14297">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Limitations of the Generalized Pareto Distribution-based estimators for the local dimension </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=del+Amo,+I">Ignacio del Amo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Datseris,+G">George Datseris</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Holland,+M">Mark Holland</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Chaotic Dynamics (nlin.CD) </div> <p class='mathjax'> Two dynamical indicators, the local dimension and the extremal index, used to quantify persistence in phase space have been developed and applied to different data across various disciplines. These are computed using the asymptotic limit of exceedances over a threshold, which turns to be a Generalized Pareto Distribution in many cases. However the derivation of the asymptotic distribution requires mathematical properties which are not present even in highly idealized dynamical systems, and unlikely to be present in real data. Here we examine in detail issues that arise when estimating these quantities for some known dynamical systems with a particular focus on how the geometry of an invariant set can affect the regularly varying properties of the invariant measure. We demonstrate that singular measures supported on sets of non-integer dimension are typically not regularly varying and that the absence of regular variation makes the estimates resolution dependent. We show as well that the most common extremal index estimation method is ambiguous for continuous time processes sampled at fixed time steps, which is an underlying assumption in its application to data. </p> </div> </dd> <dt> <a name='item8'>[8]</a> <a href ="/abs/2411.14312" title="Abstract" id="2411.14312"> arXiv:2411.14312 </a> [<a href="/pdf/2411.14312" title="Download PDF" id="pdf-2411.14312" aria-labelledby="pdf-2411.14312">pdf</a>, <a href="https://arxiv.org/html/2411.14312v1" title="View HTML" id="html-2411.14312" aria-labelledby="html-2411.14312" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14312" title="Other formats" id="oth-2411.14312" aria-labelledby="oth-2411.14312">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Density of Stable Interval Translation Maps </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Drach,+K">Kostiantyn Drach</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Staresinic,+L">Leon Staresinic</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=van+Strien,+S">Sebastian van Strien</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> Assume that the interval $I=[0,1)$ is partitioned into finitely many intervals $I_1,\dots,I_r$ and consider a map $T\colon I\to I$ so that $T_{\vert I_s}$ is a translation for each $1 \le s \le r$. We do not assume that the images of these intervals are disjoint. Such maps are called Interval Translation Maps. Let $ITM(r)$ be the space of all such transformations, where we fix $r$ but not the intervals $I_1,\dots,I_r$, nor the translations. The set $X(T):=\bigcap_{n\ge 0} T^n[0,1)$ can be a finite union of intervals (in which case the map is called of finite type), or is a disjoint union of finitely many intervals and a Cantor set (in which case the map is called of infinite type). In this paper we show that there exists an open and dense subset $\mathcal{S}(r)$ of $ITM(r)$ consisting of stable maps, i.e. each $T\in \mathcal{S}(r)$ is of finite type, the first return map to any component of $X(T)$ corresponds to a circle rotation and $\mathcal{S}(r) \ni T \mapsto X(T)$ is continuous in the Hausdorff topology. </p> </div> </dd> </dl> <dl id='articles'> <h3>Cross submissions (showing 6 of 6 entries)</h3> <dt> <a name='item9'>[9]</a> <a href ="/abs/2411.13561" title="Abstract" id="2411.13561"> arXiv:2411.13561 </a> (cross-list from math.NA) [<a href="/pdf/2411.13561" title="Download PDF" id="pdf-2411.13561" aria-labelledby="pdf-2411.13561">pdf</a>, <a href="https://arxiv.org/html/2411.13561v1" title="View HTML" id="html-2411.13561" aria-labelledby="html-2411.13561" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13561" title="Other formats" id="oth-2411.13561" aria-labelledby="oth-2411.13561">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Model discovery on the fly using continuous data assimilation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Newey,+J">Joshua Newey</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Whitehead,+J+P">Jared P Whitehead</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Carlson,+E">Elizabeth Carlson</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span>; Dynamical Systems (math.DS); Data Analysis, Statistics and Probability (physics.data-an) </div> <p class='mathjax'> We review an algorithm developed for parameter estimation within the Continuous Data Assimilation (CDA) approach. We present an alternative derivation for the algorithm presented in a paper by Carlson, Hudson, and Larios (CHL, 2021). This derivation relies on the same assumptions as the previous derivation but frames the problem as a finite dimensional root-finding problem. Within the approach we develop, the algorithm developed in (CHL, 2021) is simply a realization of Newton's method. We then consider implementing other derivative based optimization algorithms; we show that the Levenberg Maqrquardt algorithm has similar performance to the CHL algorithm in the single parameter estimation case and generalizes much better to fitting multiple parameters. We then implement these methods in three example systems: the Lorenz '63 model, the two-layer Lorenz '96 model, and the Kuramoto-Sivashinsky equation. </p> </div> </dd> <dt> <a name='item10'>[10]</a> <a href ="/abs/2411.13569" title="Abstract" id="2411.13569"> arXiv:2411.13569 </a> (cross-list from math.NA) [<a href="/pdf/2411.13569" title="Download PDF" id="pdf-2411.13569" aria-labelledby="pdf-2411.13569">pdf</a>, <a href="https://arxiv.org/html/2411.13569v1" title="View HTML" id="html-2411.13569" aria-labelledby="html-2411.13569" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13569" title="Other formats" id="oth-2411.13569" aria-labelledby="oth-2411.13569">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Unconditionally stable symplectic integrators for the Navier-Stokes equations and other dissipative systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Sungkeetanon,+S">Sutthikiat Sungkeetanon</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Gaglione,+J+S">Joseph S. Gaglione</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Chapman,+R+L">Robert L. Chapman</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kelly,+T+M">Tyler M. Kelly</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Cushman,+H+A">Howard A. Cushman</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Odom,+B+H">Blakeley H. Odom</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=MacGavin,+B">Bryan MacGavin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Elamin,+G+A">Gafar A. Elamin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Washuta,+N+J">Nathan J. Washuta</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Crosmer,+J+E">Jonathan E. Crosmer</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=DeVoria,+A+C">Adam C. DeVoria</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sanders,+J+W">John W. Sanders</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18 pages, 7 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span>; Dynamical Systems (math.DS); Fluid Dynamics (physics.flu-dyn) </div> <p class='mathjax'> Symplectic integrators offer vastly superior performance over traditional numerical techniques for conservative dynamical systems, but their application to \emph{dissipative} systems is inherently difficult due to dissipative systems' lack of symplectic structure. Leveraging the intrinsic variational structure of higher-order dynamics, this paper presents a general technique for applying existing symplectic integration schemes to dissipative systems, with particular emphasis on viscous fluids modeled by the Navier-Stokes equations. Two very simple such schemes are developed here. Not only are these schemes unconditionally stable for dissipative systems, they also outperform traditional methods with a similar degree of complexity in terms of accuracy for a given time step. For example, in the case of viscous flow between two infinite, flat plates, one of the schemes developed here is found to outperform both the implicit Euler method and the explicit fourth-order Runge-Kutta method in predicting the velocity profile. To the authors' knowledge, this is the very first time that a symplectic integration scheme has been applied successfully to the Navier-Stokes equations. We interpret the present success as direct empirical validation of the canonical Hamiltonian formulation of the Navier-Stokes problem recently published by Sanders~\emph{et al.} More sophisticated symplectic integration schemes are expected to exhibit even greater performance. It is hoped that these results will lead to improved numerical methods in computational fluid dynamics. </p> </div> </dd> <dt> <a name='item11'>[11]</a> <a href ="/abs/2411.13680" title="Abstract" id="2411.13680"> arXiv:2411.13680 </a> (cross-list from q-bio.QM) [<a href="/pdf/2411.13680" title="Download PDF" id="pdf-2411.13680" aria-labelledby="pdf-2411.13680">pdf</a>, <a href="https://arxiv.org/html/2411.13680v1" title="View HTML" id="html-2411.13680" aria-labelledby="html-2411.13680" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13680" title="Other formats" id="oth-2411.13680" aria-labelledby="oth-2411.13680">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Long-term predictive models for mosquito borne diseases: a narrative review </div> <div class='list-authors'><a href="https://arxiv.org/search/q-bio?searchtype=author&query=Bastos,+M+M">Marcio Maciel Bastos</a>, <a href="https://arxiv.org/search/q-bio?searchtype=author&query=Carvalho,+L+M">Luiz Max Carvalho</a>, <a href="https://arxiv.org/search/q-bio?searchtype=author&query=Araujo,+E+C">Eduardo Correa Araujo</a>, <a href="https://arxiv.org/search/q-bio?searchtype=author&query=Coelho,+F+C">Fl谩vio Code莽o Coelho</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantitative Methods (q-bio.QM)</span>; Dynamical Systems (math.DS); Biological Physics (physics.bio-ph) </div> <p class='mathjax'> In face of climate change and increasing urbanization, the predictive mosquito-borne diseases (MBD) transmission models require constant updates. Thus, is urgent to comprehend the driving forces of this non stationary behavior, observed through spatial and incidence expansion. We observed that temperature is a critical driver in predictive models for MBD transmission, also being consistently used in multiple reviewed papers with considerable incidence predictive capacity. Rainfall, however, have more subtle importance as moderate precipitation creates breeding sites for mosquitoes, but excessive rainfall can reduce larvae populations. We highlight the frequent use of mechanistic models, particularly those that integrate temperature-dependent biological parameters of disease transmission in incidence proxies as the Vectorial Capacity (VC) and temperature-based basic reproduction number $R_0(t)$, for example. These models show the importance of climate variables, but the socio-demographic factors are often not considered. This gap is a significant opportunity for future research to incorporate socio-demographic data into long-term predictive models for more comprehensive and reliable forecasts. With this survey, we outline the most promising paths to be followed by long-term MBD transmission research and highlighting the potential facing challenges. Thus, we offer a valuable foundation for enhancing disease forecasting models and supporting more effective public health interventions, specially in the long term. </p> </div> </dd> <dt> <a name='item12'>[12]</a> <a href ="/abs/2411.13923" title="Abstract" id="2411.13923"> arXiv:2411.13923 </a> (cross-list from math.PR) [<a href="/pdf/2411.13923" title="Download PDF" id="pdf-2411.13923" aria-labelledby="pdf-2411.13923">pdf</a>, <a href="https://arxiv.org/html/2411.13923v1" title="View HTML" id="html-2411.13923" aria-labelledby="html-2411.13923" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13923" title="Other formats" id="oth-2411.13923" aria-labelledby="oth-2411.13923">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Fourier dimension of Gaussian multiplicative chaos </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Lin,+Z">Zhaofeng Lin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Qiu,+Y">Yanqi Qiu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tan,+M">Mingjie Tan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> This is the first version of our work on Fourier dimension of GMC. New version with more comprehensive and simpler proof, together with illustrative pictures and applications, generalizations of the main result will be updated soon </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Mathematical Physics (math-ph); Dynamical Systems (math.DS); Functional Analysis (math.FA) </div> <p class='mathjax'> We obtain the precise Fourier dimension of the Gaussian multiplicative chaos on the unit interval. Our main result confirms a conjecture of Garban-Vargas. </p> </div> </dd> <dt> <a name='item13'>[13]</a> <a href ="/abs/2411.13939" title="Abstract" id="2411.13939"> arXiv:2411.13939 </a> (cross-list from math.ST) [<a href="/pdf/2411.13939" title="Download PDF" id="pdf-2411.13939" aria-labelledby="pdf-2411.13939">pdf</a>, <a href="https://arxiv.org/html/2411.13939v1" title="View HTML" id="html-2411.13939" aria-labelledby="html-2411.13939" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13939" title="Other formats" id="oth-2411.13939" aria-labelledby="oth-2411.13939">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Filtering and Statistical Properties of Unimodal Maps Perturbed by Heteroscedastic Noises </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Lillo,+F">Fabrizio Lillo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Marmi,+S">Stefano Marmi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tanzi,+M">Matteo Tanzi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Vaienti,+S">Sandro Vaienti</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Statistics Theory (math.ST)</span>; Dynamical Systems (math.DS); Probability (math.PR) </div> <p class='mathjax'> We propose a theory of unimodal maps perturbed by an heteroscedastic Markov chain noise and experiencing another heteroscedastic noise due to uncertain observation. We address and treat the filtering problem showing that by collecting more and more observations, one would predict the same distribution for the state of the underlying Markov chain no matter one's initial guess. Moreover we give other limit theorems, emphasizing in particular concentration inequalities and extreme value and Poisson distributions. Our results apply to a family of maps arising from a model of systemic risk in finance. </p> </div> </dd> <dt> <a name='item14'>[14]</a> <a href ="/abs/2411.14350" title="Abstract" id="2411.14350"> arXiv:2411.14350 </a> (cross-list from math.PR) [<a href="/pdf/2411.14350" title="Download PDF" id="pdf-2411.14350" aria-labelledby="pdf-2411.14350">pdf</a>, <a href="https://arxiv.org/html/2411.14350v1" title="View HTML" id="html-2411.14350" aria-labelledby="html-2411.14350" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14350" title="Other formats" id="oth-2411.14350" aria-labelledby="oth-2411.14350">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Randomized Geodesic Flow on Hyperbolic Groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kupffer,+L">Luzie Kupffer</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mj,+M">Mahan Mj</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mukherjee,+C">Chiranjib Mukherjee</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Dynamical Systems (math.DS); Group Theory (math.GR); Geometric Topology (math.GT) </div> <p class='mathjax'> Motivated by Gromov's geodesic flow problem on hyperbolic groups $G$, we develop in this paper an analog using random walks. This leads to a notion of a harmonic analog $\Theta$ of the Bowen-Margulis-Sullivan measure on $\partial^2 G$. We provide three different but related constructions of $\Theta$: 1) by moving the base-point along a quasigeodesic ray 2) by moving the base-point along random walk trajectories 3) directly as a push-forward under the boundary map to $\partial^2 G$ of a measure inherited from studying all bi-infinite random walk trajectories (with no restriction on base-point) on $G^{\mathbb{Z}}$. <br>Of these, the third construction is the most involved and needs new techniques. It relies on developing a framework where we can treat bi-infinite random walk trajectories as analogs of bi-infinite geodesics on complete simply connected negatively curved manifolds. Geodesic flow on a hyperbolic group is typically not well-defined due to non-uniqueness of geodesics. We circumvent this problem in the random walk setup by considering \emph{all} trajectories. We thus get a well-defined \emph{discrete flow} given by the $\mathbb{Z}-$shift on bi-infinite random walk trajectories. The $\mathbb{Z}-$shift is the random analog of the time one map of the geodesic flow. As an analog of ergodicity of the geodesic flow on a closed negatively curved manifold, we establish ergodicity of the $G$-action on $(\partial^2G, \Theta)$. </p> </div> </dd> </dl> <dl id='articles'> <h3>Replacement submissions (showing 10 of 10 entries)</h3> <dt> <a name='item15'>[15]</a> <a href ="/abs/2211.11234" title="Abstract" id="2211.11234"> arXiv:2211.11234 </a> (replaced) [<a href="/pdf/2211.11234" title="Download PDF" id="pdf-2211.11234" aria-labelledby="pdf-2211.11234">pdf</a>, <a href="https://arxiv.org/html/2211.11234v4" title="View HTML" id="html-2211.11234" aria-labelledby="html-2211.11234" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2211.11234" title="Other formats" id="oth-2211.11234" aria-labelledby="oth-2211.11234">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The measure transfer for subshifts induced by a morphism of free monoids </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=B%C3%A9daride,+N">Nicolas B茅daride</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Hilion,+A">Arnaud Hilion</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lustig,+M">Martin Lustig</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> Every non-erasing monoid morphism $\sigma: \mathcal{A}^* \to \mathcal{B}^*$ induces a {\em measure transfer map} $\sigma_X^{\mathcal{M}}: \mathcal{M}(X) \to \mathcal{M}(\sigma(X))$ between the measure cones $\mathcal{M}(X)$ and $\mathcal{M}(\sigma(X))$, associated to any subshift $X \subset \mathcal{A}^{\mathbb{Z}}$ and its image subshift $\sigma(X) \subset \mathcal{B}^{\mathbb{Z}}$ respectively. We define and study this map in detail and show that it is continuous, linear and functorial. It also turns out to be surjective \cite{BHL2.8-II}. Furthermore, an efficient technique to compute the value of the transferred measure $\sigma_X^{\mathcal{M}(\mu)}$ on any cylinder $[w]$ (for $w \in \mathcal{B}^*$) is presented. <br>\smallskip \noindent {\bf Theorem:} If a non-erasing morphism $\sigma: \mathcal{A}^* \to \mathcal{B}^*$ is injective on the shift-orbits of some subshift $X \subset \mathcal{A}^\mathbb{Z}$, then $\sigma^{\mathcal{M}_X}$ is injective. <br>\smallskip <br>The assumption on $\sigma$ that it is ``injective on the shift-orbits of $X$'' is strictly weaker than ``recognizable in $X$'', and strictly stronger than ``recognizable for aperiodic points in $X$''. The last assumption does in general not suffice to obtain the injectivity of the measure transfer map $\sigma_X^{\mathcal{M}}$. </p> </div> </dd> <dt> <a name='item16'>[16]</a> <a href ="/abs/2403.08884" title="Abstract" id="2403.08884"> arXiv:2403.08884 </a> (replaced) [<a href="/pdf/2403.08884" title="Download PDF" id="pdf-2403.08884" aria-labelledby="pdf-2403.08884">pdf</a>, <a href="https://arxiv.org/html/2403.08884v3" title="View HTML" id="html-2403.08884" aria-labelledby="html-2403.08884" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.08884" title="Other formats" id="oth-2403.08884" aria-labelledby="oth-2403.08884">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A note on spectral properties of random $S$-adic systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Solomyak,+B">Boris Solomyak</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Revision after the referee report. To appear in the volume of Pure and Applied Functional Analysis dedicated to the memory of <a href="http://A.M.Vershik" rel="external noopener nofollow" class="link-external link-http">this http URL</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> The paper is concerned with random $S$-adic systems arising from an i.i.d. sequence of unimodular substitutions. Using equidistribution results of Benoist and Quint, we show in Theorem 3.3 that, under some natural assumptions, if the Lyapunov exponent of the spectral cocycle is strictly less that 1/2 of the Lyapunov exponent of the random walk on $SL(2,\mathbb{R})$ driven by the sequence of substitution matrices, then almost surely the spectrum of the $S$-adic $\mathbb{Z}$-action is singular with respect to any (fixed in advance) continuous measure. Finally, the appendix discusses the weak-mixing property for random $S$-adic systems associated to the family of substitutions introduced in Example 4.2. </p> </div> </dd> <dt> <a name='item17'>[17]</a> <a href ="/abs/2405.05661" title="Abstract" id="2405.05661"> arXiv:2405.05661 </a> (replaced) [<a href="/pdf/2405.05661" title="Download PDF" id="pdf-2405.05661" aria-labelledby="pdf-2405.05661">pdf</a>, <a href="https://arxiv.org/html/2405.05661v3" title="View HTML" id="html-2405.05661" aria-labelledby="html-2405.05661" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2405.05661" title="Other formats" id="oth-2405.05661" aria-labelledby="oth-2405.05661">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Dynamics of a multilink wheeled vehicle: partial solutions and unbounded speedup </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Artemova,+E">Elizaveta Artemova</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Bizyaev,+I">Ivan Bizyaev</a></div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> International Journal of Non-Linear Mechanics, 2024, vol. 165, 104774, 10 pp </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> A mathematical model featuring the motion of a multilink wheeled vehicle is developed using a nonholonomic model. A detailed analysis of the inertial motion is made. Fixed points of the reduced system are identified, their stability is analyzed, and invariant manifolds are found. For the case of three platforms (links), a phase portrait for motion on an invariant manifold is shown and trajectories of the attachment points of the wheel pairs of the three-link vehicle are presented. In addition, an analysis is made of motion in the case where the leading platform has a rotor whose angular velocity is a periodic function of time. The existence of trajectories for which one of the velocity components increases without bound is established, and the asymptotics for it is found. </p> </div> </dd> <dt> <a name='item18'>[18]</a> <a href ="/abs/2409.16624" title="Abstract" id="2409.16624"> arXiv:2409.16624 </a> (replaced) [<a href="/pdf/2409.16624" title="Download PDF" id="pdf-2409.16624" aria-labelledby="pdf-2409.16624">pdf</a>, <a href="https://arxiv.org/html/2409.16624v2" title="View HTML" id="html-2409.16624" aria-labelledby="html-2409.16624" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.16624" title="Other formats" id="oth-2409.16624" aria-labelledby="oth-2409.16624">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Removable dynamics in the Nose-Hoover and Moore-Spiegel Oscillators </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Igra,+E">Eran Igra</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA) </div> <p class='mathjax'> We study the dynamics of the Nose-Hoover and Moore-Spiegel Oscillators, and in particular, their topological dynamics. We prove the dynamics of both these systems can be reduced to a flow on a solid torus, with at most a finite number of attracting periodic trajectories. As a consequence, we obtain that every periodic trajectory for the Nose-Hoover and the Moore-Spiegel Oscillators is a Torus knot. </p> </div> </dd> <dt> <a name='item19'>[19]</a> <a href ="/abs/2411.12411" title="Abstract" id="2411.12411"> arXiv:2411.12411 </a> (replaced) [<a href="/pdf/2411.12411" title="Download PDF" id="pdf-2411.12411" aria-labelledby="pdf-2411.12411">pdf</a>, <a href="https://arxiv.org/html/2411.12411v2" title="View HTML" id="html-2411.12411" aria-labelledby="html-2411.12411" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.12411" title="Other formats" id="oth-2411.12411" aria-labelledby="oth-2411.12411">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Classification of the trajectories of uncharged particles in the Schwarzschild-Melvin metric </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bizyaev,+I">Ivan Bizyaev</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Corrected typo in title </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Physical Review D, 2024, vol. 110, 104031 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; General Relativity and Quantum Cosmology (gr-qc) </div> <p class='mathjax'> This paper investigates the trajectories of neutral particles in the Schwarzschild-Melvin spacetime. After reduction by cyclic coordinates this problem reduces to investigating a two-degree-of-freedom Hamiltonian system that has no additional integral. A classification of regions of possible motion of a particle is performed according to the values of the momentum and energy integrals. Bifurcations of periodic solutions of the reduced system are analyzed using a Poincare map. </p> </div> </dd> <dt> <a name='item20'>[20]</a> <a href ="/abs/2104.14678" title="Abstract" id="2104.14678"> arXiv:2104.14678 </a> (replaced) [<a href="/pdf/2104.14678" title="Download PDF" id="pdf-2104.14678" aria-labelledby="pdf-2104.14678">pdf</a>, <a href="https://arxiv.org/html/2104.14678v3" title="View HTML" id="html-2104.14678" aria-labelledby="html-2104.14678" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2104.14678" title="Other formats" id="oth-2104.14678" aria-labelledby="oth-2104.14678">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Locally moving groups and laminar actions on the line </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Brum,+J">Joaqu铆n Brum</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Bon,+N+M">Nicol谩s Matte Bon</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rivas,+C">Crist贸bal Rivas</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Triestino,+M">Michele Triestino</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 205 pages, 11 figures; v2 is a major revision after report: title changed (previously 'Locally moving groups acting on the line and $\mathbb{R}$-focal actions'), structure reworked (chapters organized into 3 parts, each devoted to a single main theorem), many results strengthend to nearly optimal statements (requiring different approaches), digressions removed. To appear as an Ast茅risque volume </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Group Theory (math.GR)</span>; Dynamical Systems (math.DS) </div> <p class='mathjax'> We prove various results that, given a sufficiently rich subgroup $G$ of the group of homeomorphisms on the real line, describe the structure of the other possible actions of $G$ on the line, and address under which conditions such actions must be semi-conjugate to the natural defining action of $G$. The main assumption is that $G$ should be locally moving, meaning that for every open interval the subgroup of elements fixing pointwise its complement, acts on it without fixed points. We show that when $G$ is a locally moving group, every $C^1$ action of $G$ on the real line is semi-conjugate to its standard action or to a non-faithful action. The situation is much wilder when considering actions by homeomorphisms: for a large class of groups, we describe uncountably many conjugacy classes of faithful minimal actions. Next, we prove structure theorems for $C^0$ actions, based on the study of laminar actions, which are actions on the line preserving a lamination. When $G$ is a group of homeomorphisms of the line acting minimally, and with a non-trivial compactly supported element, then any faithful minimal action of $G$ on the line is either laminar or conjugate to its standard action. Moreover, when $G$ is a locally moving group with a suitable finite generation condition, for any faithful minimal laminar action there is a map from the lamination to the line, called a horograding, which is equivariant with respect to the action on the lamination and the standard one, and with some extra suitable conditions. This establishes a tight relation between all minimal actions on the line of such groups, and their standard actions. Finally, based on an analysis of the space of harmonic actions, we show that for a large class of locally moving groups, the standard action is locally rigid, in the sense that sufficiently small perturbations in the compact-open topology give semi-conjugate actions. </p> </div> </dd> <dt> <a name='item21'>[21]</a> <a href ="/abs/2403.14931" title="Abstract" id="2403.14931"> arXiv:2403.14931 </a> (replaced) [<a href="/pdf/2403.14931" title="Download PDF" id="pdf-2403.14931" aria-labelledby="pdf-2403.14931">pdf</a>, <a href="https://arxiv.org/html/2403.14931v2" title="View HTML" id="html-2403.14931" aria-labelledby="html-2403.14931" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.14931" title="Other formats" id="oth-2403.14931" aria-labelledby="oth-2403.14931">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Structured stability analysis of networked systems with uncertain links </div> <div class='list-authors'><a href="https://arxiv.org/search/eess?searchtype=author&query=Mariano,+S">Simone Mariano</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Cantoni,+M">Michael Cantoni</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Systems and Control (eess.SY)</span>; Dynamical Systems (math.DS) </div> <p class='mathjax'> An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the uncertain networked system, under the assumption that stability is achieved with ideal links. The conditions are decentralized inasmuch as each involves only agent and uncertainty model parameters that are local to a corresponding link. This makes the main result, which imposes no restriction on network structure, suitable for the study of large-scale systems. </p> </div> </dd> <dt> <a name='item22'>[22]</a> <a href ="/abs/2406.16787" title="Abstract" id="2406.16787"> arXiv:2406.16787 </a> (replaced) [<a href="/pdf/2406.16787" title="Download PDF" id="pdf-2406.16787" aria-labelledby="pdf-2406.16787">pdf</a>, <a href="https://arxiv.org/html/2406.16787v3" title="View HTML" id="html-2406.16787" aria-labelledby="html-2406.16787" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2406.16787" title="Other formats" id="oth-2406.16787" aria-labelledby="oth-2406.16787">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Parrondo paradox in susceptible-infectious-susceptible dynamics over periodic temporal networks </div> <div class='list-authors'><a href="https://arxiv.org/search/physics?searchtype=author&query=Sejunti,+M+I">Maisha Islam Sejunti</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Taylor,+D">Dane Taylor</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Masuda,+N">Naoki Masuda</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 10 figures </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Mathematical Biosciences, Volume 378, December 2024, 109336 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Physics and Society (physics.soc-ph)</span>; Dynamical Systems (math.DS) </div> <p class='mathjax'> Many social and biological networks periodically change over time with daily, weekly, and other cycles. Thus motivated, we formulate and analyze susceptible-infectious-susceptible (SIS) epidemic models over temporal networks with periodic schedules. More specifically, we assume that the temporal network consists of a cycle of alternately used static networks, each with a given duration. We observe a phenomenon in which two static networks are individually above the epidemic threshold but the alternating network composed of them renders the dynamics below the epidemic threshold, which we refer to as a Parrondo paradox for epidemics. We find that network structure plays an important role in shaping this phenomenon, and we study its dependence on the connectivity between and number of subpopulations in the network. We associate such paradoxical behavior with anti-phase oscillatory dynamics of the number of infectious individuals in different subpopulations. </p> </div> </dd> <dt> <a name='item23'>[23]</a> <a href ="/abs/2409.04322" title="Abstract" id="2409.04322"> arXiv:2409.04322 </a> (replaced) [<a href="/pdf/2409.04322" title="Download PDF" id="pdf-2409.04322" aria-labelledby="pdf-2409.04322">pdf</a>, <a href="https://arxiv.org/html/2409.04322v2" title="View HTML" id="html-2409.04322" aria-labelledby="html-2409.04322" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.04322" title="Other formats" id="oth-2409.04322" aria-labelledby="oth-2409.04322">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Integrability of polynomial vector fields and a dual problem </div> <div class='list-authors'><a href="https://arxiv.org/search/nlin?searchtype=author&query=Petek,+T">Tatjana Petek</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Romanovski,+V">Valery Romanovski</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Exactly Solvable and Integrable Systems (nlin.SI)</span>; Classical Analysis and ODEs (math.CA); Dynamical Systems (math.DS) </div> <p class='mathjax'> We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality the case of quadratic vector fields is considered in detail. </p> </div> </dd> <dt> <a name='item24'>[24]</a> <a href ="/abs/2410.11754" title="Abstract" id="2410.11754"> arXiv:2410.11754 </a> (replaced) [<a href="/pdf/2410.11754" title="Download PDF" id="pdf-2410.11754" aria-labelledby="pdf-2410.11754">pdf</a>, <a href="https://arxiv.org/html/2410.11754v3" title="View HTML" id="html-2410.11754" aria-labelledby="html-2410.11754" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.11754" title="Other formats" id="oth-2410.11754" aria-labelledby="oth-2410.11754">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Measurable splittings and the measured group theoretic structure of wreath products </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Tucker-Drob,+R">Robin Tucker-Drob</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wr%C3%B3bel,+K">Konrad Wr贸bel</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 37 pages, 1 figure, minor revisions and corrections </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Group Theory (math.GR)</span>; Dynamical Systems (math.DS); Logic (math.LO); Operator Algebras (math.OA) </div> <p class='mathjax'> Let $\Gamma$ be a countable group that admits an essential measurable splitting (for instance, any group measure equivalent to a free product of nontrivial groups). <br>We show: (1) for any two nontrivial countable groups $B$ and $C$ that are measure equivalent, the wreath product groups $B\wr\Gamma$ and $C\wr\Gamma$ are measure equivalent (in fact, orbit equivalent) -- this is interesting even in the case when the groups $B$ and $C$ are finite; and (2) the groups $B\wr \Gamma$ and $(B\times\mathbf{Z})\wr\Gamma$ are measure equivalent (in fact, orbit equivalent) for every nontrivial countable group $B$. <br>On the other hand, we show that certain wreath product actions are not even stably orbit equivalent if $\Gamma$ is instead assumed to be a sofic icc group that is Bernoulli superrigid, and $B$ and $C$ have different cardinalities. </p> </div> </dd> </dl> <div class='paging'>Total of 24 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math.DS/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> </div> </div> </div> </main> <footer style="clear: both;"> <div class="columns is-desktop" role="navigation" aria-label="Secondary" style="margin: -0.75em -0.75em 0.75em -0.75em"> <!-- Macro-Column 1 --> <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; 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