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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=Li%2C+J&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Li%2C+J&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Li%2C+J&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> <li> <a href="/search/?searchtype=author&query=Li%2C+J&start=100" class="pagination-link " aria-label="Page 3" aria-current="page">3 </a> </li> <li> <a href="/search/?searchtype=author&query=Li%2C+J&start=150" class="pagination-link " aria-label="Page 4" aria-current="page">4 </a> </li> <li> <a href="/search/?searchtype=author&query=Li%2C+J&start=200" class="pagination-link " aria-label="Page 5" aria-current="page">5 </a> </li> <li><span class="pagination-ellipsis">…</span></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/2503.21509">arXiv:2503.21509</a> <span> [<a href="https://arxiv.org/pdf/2503.21509">pdf</a>, <a href="https://arxiv.org/format/2503.21509">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Nonlinear Stability of Large-Period Traveling Waves Bifurcating from the Heteroclinic Loop in the FitzHugh-Nagumo Equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Wang%2C+K">Ke Wang</a>, <a href="/search/math?searchtype=author&query=Wu%2C+Q">Qiliang Wu</a>, <a href="/search/math?searchtype=author&query=Yu%2C+Q">Qing Yu</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="2503.21509v1-abstract-short" style="display: inline;"> A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear stability of these periodic waves is established in the setting of the FitzHugh-Nagumo equation, which is a well-known reaction-diffusion model with degenerate dif… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.21509v1-abstract-full').style.display = 'inline'; document.getElementById('2503.21509v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.21509v1-abstract-full" style="display: none;"> A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear stability of these periodic waves is established in the setting of the FitzHugh-Nagumo equation, which is a well-known reaction-diffusion model with degenerate diffusion. First, for general systems, we give the expressions of spectra with small modulus for linearized operators about these periodic waves via the Lyapunov-Schmidt reduction and the Lin-Sandstede method. Second, applying these spectral results to the FitzHugh-Nagumo equation, we establish their diffusive spectral stability. Finally, we consider the nonlinear stability of these periodic waves against localized perturbations. We introduce a spatiotemporal phase modulation $\varphi$, and couple it with the associated modulated perturbation $\mathbf{V}$ along with the unmodulated perturbation $\mathbf{\widetilde{V}}$ to close a nonlinear iteration argument. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.21509v1-abstract-full').style.display = 'none'; document.getElementById('2503.21509v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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">45 pages,4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 34C23; 35B10; 35B35; 35B36 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.19403">arXiv:2503.19403</a> <span> [<a href="https://arxiv.org/pdf/2503.19403">pdf</a>, <a href="https://arxiv.org/ps/2503.19403">ps</a>, <a href="https://arxiv.org/format/2503.19403">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</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"> Extension principles for the Einstein Yang--Mills system </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Junbin Li</a>, <a href="/search/math?searchtype=author&query=Wang%2C+J">Jinhua 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="2503.19403v1-abstract-short" style="display: inline;"> We establish an extension principle for the spherically symmetric Einstein Yang--Mills system (SSEYM) with $H^1$ data. Based on this result, we further prove an extension theorem for developments of weighted $H^1$ data. In particular, the weighted $H^1$ space allows H枚lder continuous data. Therefore, our result is consistence with the conjecture that well-posedness holds for H枚lder continuous data… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.19403v1-abstract-full').style.display = 'inline'; document.getElementById('2503.19403v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.19403v1-abstract-full" style="display: none;"> We establish an extension principle for the spherically symmetric Einstein Yang--Mills system (SSEYM) with $H^1$ data. Based on this result, we further prove an extension theorem for developments of weighted $H^1$ data. In particular, the weighted $H^1$ space allows H枚lder continuous data. Therefore, our result is consistence with the conjecture that well-posedness holds for H枚lder continuous data (with sufficiently many angular derivatives) in vacuum where the axis is included. In contrast to a massless scalar field, the purely magnetic Yang--Mills field in spherical symmetry satisfies a wave-type equation with singular potential. The proof of Christodoulou [10], based on an $L^\infty-L^\infty$ estimate, fails for the Yang--Mills scenario. Instead, we employ the $L^2$ method, which works for the (massless or massive) scalar matter field as well. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.19403v1-abstract-full').style.display = 'none'; document.getElementById('2503.19403v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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">47pages, comments are welcome!</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.17737">arXiv:2503.17737</a> <span> [<a href="https://arxiv.org/pdf/2503.17737">pdf</a>, <a href="https://arxiv.org/format/2503.17737">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Portfolio Management">q-fin.PM</span> <span class="tag is-small is-grey 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="Applications">stat.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computation">stat.CO</span> </div> </div> <p class="title is-5 mathjax"> Bayesian Optimization for CVaR-based portfolio optimization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Millar%2C+R">Robert Millar</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jinglai Li</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="2503.17737v1-abstract-short" style="display: inline;"> Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained minimization problems, seeking to minimize the conditional value-at-risk (a computationally intensive risk measure) under a minimum expected return constraint.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.17737v1-abstract-full').style.display = 'inline'; document.getElementById('2503.17737v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.17737v1-abstract-full" style="display: none;"> Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained minimization problems, seeking to minimize the conditional value-at-risk (a computationally intensive risk measure) under a minimum expected return constraint. The proposed algorithms utilize a new acquisition function, which drives sampling towards the optimal region. Additionally, a new two-stage procedure is developed, which significantly reduces the number of evaluations of the expensive-to-evaluate objective function. The proposed algorithm's competitive performance is demonstrated through practical examples. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.17737v1-abstract-full').style.display = 'none'; document.getElementById('2503.17737v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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 GECCO 2025</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.17092">arXiv:2503.17092</a> <span> [<a href="https://arxiv.org/pdf/2503.17092">pdf</a>, <a href="https://arxiv.org/format/2503.17092">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="Systems and Control">eess.SY</span> </div> </div> <p class="title is-5 mathjax"> Optimal Investment Portfolio of Thyristor- and IGBT-based Electrolysis Rectifiers in Utility-scale Renewable P2H Systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zeng%2C+Y">Yangjun Zeng</a>, <a href="/search/math?searchtype=author&query=Qiu%2C+Y">Yiwei Qiu</a>, <a href="/search/math?searchtype=author&query=Xu%2C+L">Liuchao Xu</a>, <a href="/search/math?searchtype=author&query=Gu%2C+C">Chenjia Gu</a>, <a href="/search/math?searchtype=author&query=Zhou%2C+Y">Yi Zhou</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiarong Li</a>, <a href="/search/math?searchtype=author&query=Chen%2C+S">Shi Chen</a>, <a href="/search/math?searchtype=author&query=Zhou%2C+B">Buxiang 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="2503.17092v1-abstract-short" style="display: inline;"> Renewable power-to-hydrogen (ReP2H) systems require rectifiers to supply power to electrolyzers (ELZs). Two main types of rectifiers, insulated-gate bipolar transistor rectifiers (IGBT-Rs) and thyristor rectifiers (TRs), offer distinct tradeoffs. IGBT-Rs provide flexible reactive power control but are costly, whereas TRs are more affordable with lower power loss but consume a large amount of uncon… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.17092v1-abstract-full').style.display = 'inline'; document.getElementById('2503.17092v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.17092v1-abstract-full" style="display: none;"> Renewable power-to-hydrogen (ReP2H) systems require rectifiers to supply power to electrolyzers (ELZs). Two main types of rectifiers, insulated-gate bipolar transistor rectifiers (IGBT-Rs) and thyristor rectifiers (TRs), offer distinct tradeoffs. IGBT-Rs provide flexible reactive power control but are costly, whereas TRs are more affordable with lower power loss but consume a large amount of uncontrollable reactive power. A mixed configuration of rectifiers in utility-scale ReP2H systems could achieve an decent tradeoff and increase overall profitability. To explore this potential, this paper proposes an optimal investment portfolio model. First, we model and compare the active and reactive power characteristics of ELZs powered by TRs and IGBT-Rs. Second, we consider the investment of ELZs, rectifiers, and var resources and coordinate the operation of renewables, energy storage, var resources, and the on-off switching and load allocation of multiple ELZs. Subsequently, a two-stage stochastic programming (SP) model based on weighted information gap decision theory (W-IGDT) is developed to address the uncertainties of the renewable power and hydrogen price, and we apply the progressive hedging (PH) algorithm to accelerate its solution. Case studies demonstrate that optimal rectifier configurations increase revenue by at most 2.56% compared with using only TRs or IGBT-Rs, as well as those in existing projects. Under the optimal portfolio, reactive power compensation investment is nearly eliminated, with a preferred TR-to-IGBT-R ratio of 3:1. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.17092v1-abstract-full').style.display = 'none'; document.getElementById('2503.17092v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.16786">arXiv:2503.16786</a> <span> [<a href="https://arxiv.org/pdf/2503.16786">pdf</a>, <a href="https://arxiv.org/ps/2503.16786">ps</a>, <a href="https://arxiv.org/format/2503.16786">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Average Nikolskii factors for random trigonometric polynomials </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ling%2C+Y">Yun Ling</a>, <a href="/search/math?searchtype=author&query=Geng%2C+J">Jiaxin Geng</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiansong Li</a>, <a href="/search/math?searchtype=author&query=Wang%2C+H">Heping 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="2503.16786v1-abstract-short" style="display: inline;"> For $1\le p,q\le \infty$, the Nikolskii factor for a trigonometric polynomial $T_{\bf a}$ is defined by $$\mathcal N_{p,q}(T_{\bf a})=\frac{\|T_{\bf a}\|_{q}}{\|T_{\bf a}\|_{p}},\ \ T_{\bf a}(x)=a_{1}+\sum\limits^{n}_{k=1}(a_{2k}\sqrt{2}\cos kx+a_{2k+1}\sqrt{2}\sin kx).$$ We study this average Nikolskii factor for random trigonometric polynomials with independent $N(0,蟽^{2})$ coefficients and obta… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.16786v1-abstract-full').style.display = 'inline'; document.getElementById('2503.16786v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.16786v1-abstract-full" style="display: none;"> For $1\le p,q\le \infty$, the Nikolskii factor for a trigonometric polynomial $T_{\bf a}$ is defined by $$\mathcal N_{p,q}(T_{\bf a})=\frac{\|T_{\bf a}\|_{q}}{\|T_{\bf a}\|_{p}},\ \ T_{\bf a}(x)=a_{1}+\sum\limits^{n}_{k=1}(a_{2k}\sqrt{2}\cos kx+a_{2k+1}\sqrt{2}\sin kx).$$ We study this average Nikolskii factor for random trigonometric polynomials with independent $N(0,蟽^{2})$ coefficients and obtain that the exact order. For $1\leq p<q<\infty$, the average Nikolskii factor is order degree to the 0, as compared to the degree $1/p-1/q$ worst case bound. We also give the generalization to random multivariate trigonometric polynomials. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.16786v1-abstract-full').style.display = 'none'; document.getElementById('2503.16786v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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">17 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 26D05; 42A05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.16030">arXiv:2503.16030</a> <span> [<a href="https://arxiv.org/pdf/2503.16030">pdf</a>, <a href="https://arxiv.org/format/2503.16030">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"> Quantitative twisted recurrence properties for piecewise expanding maps on $[0,1]^d$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jiachang Li</a>, <a href="/search/math?searchtype=author&query=Ma%2C+C">Chao Ma</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="2503.16030v1-abstract-short" style="display: inline;"> Let $T:[0,1]^d \rightarrow[0,1]^d$ be a piecewise expanding map with an absolutely continuous (with respect to the $d$-dimensional Lebesgue measure $m_d$) $T$-invariant probability measure $渭$. Let $\left\{\mathbf{r}_n\right\}$ be a sequence of vectors satisfying the conditons that $\mathbf{r}_n=\left(r_{n, 1}, \ldots, r_{n, d}\right) \in\left(\mathbb{R}_{\geq 0}\right)^d$, the sequence… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.16030v1-abstract-full').style.display = 'inline'; document.getElementById('2503.16030v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.16030v1-abstract-full" style="display: none;"> Let $T:[0,1]^d \rightarrow[0,1]^d$ be a piecewise expanding map with an absolutely continuous (with respect to the $d$-dimensional Lebesgue measure $m_d$) $T$-invariant probability measure $渭$. Let $\left\{\mathbf{r}_n\right\}$ be a sequence of vectors satisfying the conditons that $\mathbf{r}_n=\left(r_{n, 1}, \ldots, r_{n, d}\right) \in\left(\mathbb{R}_{\geq 0}\right)^d$, the sequence $\left\{\frac{\max _{1 \leq i \leq d}\hspace{1ex}r_{n, i}}{\min _{1 \leq i \leq d}\hspace{1ex}r_{n, i}}\right\}$ is bounded and $\lim _{n \rightarrow \infty} \max _{1 \leq i \leq d}r_{n, i}=0$. Let $\left\{未_n\right\}$ be a sequence of non-negative real numbers with $\lim _{n \rightarrow \infty} 未_n=0$. Under the assumptions that $渭$ is exponentially mixing and its density is sufficiently regular, we prove that the $渭$-measure of the following sets $$\mathcal{R}^f\left(\left\{\mathbf{r}_n\right\}\right)=\left\{\mathbf{x} \in[0,1]^d: T^n \mathbf{x} \in R\left(f(\mathbf{x}), \mathbf{r}_n\right) \text { for infinitely many } n \in \mathbb{N} \right\} $$ and $$\mathcal{R}^{f \times}\left(\left\{未_n\right\}\right)=\left\{\mathbf{x} \in[0,1]^d: T^n \mathbf{x} \in H\left(f(\mathbf{x}), 未_n\right) \text { for infinitely many } n \in \mathbb{N} \right\}$$ obeys zero-full laws determined by the convergence or divergence of natural volume sums. Here, $R(f(\mathbf{x}), \mathbf{r}_n)$ and $H(f(\mathbf{x}), 未_n)$ represent targets as, respectively, coordinate-parallel hyperrectangles with bounded aspect ratio, and hyperboloids, both centered at $f(\mathbf{x})$. $f: [0,1]^d \rightarrow [0,1]^d$ is a piecewise Lipschitz vector function. Our results not only unify quantitative recurrence properties and the shrinking target problem for piecewise expanding maps on $[0,1]^d$, but also reveal that the two problems and cross-component recurrence can coexist in distinct directions on $[0,1]^d$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.16030v1-abstract-full').style.display = 'none'; document.getElementById('2503.16030v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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">37pages, 1 figure. arXiv admin note: text overlap with arXiv:2302.05149, arXiv:2208.06112 by other authors</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.15826">arXiv:2503.15826</a> <span> [<a href="https://arxiv.org/pdf/2503.15826">pdf</a>, <a href="https://arxiv.org/ps/2503.15826">ps</a>, <a href="https://arxiv.org/format/2503.15826">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"> Fourth-order uniformly accurate integrators with long time near conservations for the nonlinear Dirac equation in the nonrelativistic regime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Wang%2C+L">Lina Wang</a>, <a href="/search/math?searchtype=author&query=Wang%2C+B">Bin Wang</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiyong Li</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="2503.15826v1-abstract-short" style="display: inline;"> In this paper, we propose two novel fourth-order integrators that exhibit uniformly high accuracy and long-term near conservations for solving the nonlinear Dirac equation (NLDE) in the nonrelativistic regime. In this regime, the solution of the NLDE exhibits highly oscillatory behavior in time, characterized by a wavelength of O($\varepsilon^{2}$) with a small parameter $\varepsilon>0$. To ensure… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.15826v1-abstract-full').style.display = 'inline'; document.getElementById('2503.15826v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.15826v1-abstract-full" style="display: none;"> In this paper, we propose two novel fourth-order integrators that exhibit uniformly high accuracy and long-term near conservations for solving the nonlinear Dirac equation (NLDE) in the nonrelativistic regime. In this regime, the solution of the NLDE exhibits highly oscillatory behavior in time, characterized by a wavelength of O($\varepsilon^{2}$) with a small parameter $\varepsilon>0$. To ensure uniform temporal accuracy, we employ a two-scale approach in conjunction with exponential integrators, utilizing operator decomposition techniques for the NLDE. The proposed methods are rigorously proved to achieve fourth-order uniform accuracy in time for all $\varepsilon\in (0,1]$. Furthermore, we successfully incorporate symmetry into the integrator, and the long-term near conservation properties are analyzed through the modulated Fourier expansion. The proposed schemes are readily extendable to linear Dirac equations incorporating magnetic potentials, the dynamics of traveling wave solutions and the two/three-dimensional Dirac equations. The validity of all theoretical ndings and extensions is numerically substantiated through a series of numerical experiments. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.15826v1-abstract-full').style.display = 'none'; document.getElementById('2503.15826v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35Q41; 65M70; 65N35; 81Q05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.14278">arXiv:2503.14278</a> <span> [<a href="https://arxiv.org/pdf/2503.14278">pdf</a>, <a href="https://arxiv.org/ps/2503.14278">ps</a>, <a href="https://arxiv.org/format/2503.14278">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="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Controllability concepts for mean-field dynamics with reduced-rank coefficients </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Goreac%2C+D">Dan Goreac</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Juan Li</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+X">Xinru 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="2503.14278v1-abstract-short" style="display: inline;"> In this paper we explore several novel notions of exact controllability for mean-field linear controlled stochastic differential equations (SDEs). A key feature of our study is that the noise coefficient is not required to be of full rank. We begin by demonstrating that classical exact controllability with $\mathbb{L}^2$-controls necessarily requires both rank conditions on the noise introduced in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.14278v1-abstract-full').style.display = 'inline'; document.getElementById('2503.14278v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.14278v1-abstract-full" style="display: none;"> In this paper we explore several novel notions of exact controllability for mean-field linear controlled stochastic differential equations (SDEs). A key feature of our study is that the noise coefficient is not required to be of full rank. We begin by demonstrating that classical exact controllability with $\mathbb{L}^2$-controls necessarily requires both rank conditions on the noise introduced in [8] and subsequent works. When these rank conditions are not satisfied, we introduce alternative rank requirements on the drift, which enable exact controllability by relaxing the regularity of the controls. In cases where both the aforementioned rank conditions fail, we propose and characterize a new notion of exact terminal controllability to normal laws (ETCNL). Additionally, we investigate a new class of Wasserstein-set-valued backward SDEs that arise naturally associated to ETCNL. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.14278v1-abstract-full').style.display = 'none'; document.getElementById('2503.14278v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.14187">arXiv:2503.14187</a> <span> [<a href="https://arxiv.org/pdf/2503.14187">pdf</a>, <a href="https://arxiv.org/ps/2503.14187">ps</a>, <a href="https://arxiv.org/format/2503.14187">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"> Non-convergence of the Navier-Stokes equations toward the Euler equations in weak Besov spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Yu%2C+Y">Yanghai Yu</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jinlu Li</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="2503.14187v1-abstract-short" style="display: inline;"> In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier-Stokes equations in the whole space. It was proved in \cite[J. Funct. Anal., 276 (2019)]{GZ} that given initial data $u_0\in B^{s}_{p,r}$ with $1\leq r<\infty$, the solutions of the Navier-Stokes equations converge strongly in $B^{s}_{p,r}$ to the Euler equations as the viscosity parameter tends t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.14187v1-abstract-full').style.display = 'inline'; document.getElementById('2503.14187v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.14187v1-abstract-full" style="display: none;"> In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier-Stokes equations in the whole space. It was proved in \cite[J. Funct. Anal., 276 (2019)]{GZ} that given initial data $u_0\in B^{s}_{p,r}$ with $1\leq r<\infty$, the solutions of the Navier-Stokes equations converge strongly in $B^{s}_{p,r}$ to the Euler equations as the viscosity parameter tends to zero. In the case when $r=\infty$, we prove the failure of the $B^{s}_{p,\infty}$-convergence of the Navier-Stokes equations toward the Euler equations in the inviscid limit. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.14187v1-abstract-full').style.display = 'none'; document.getElementById('2503.14187v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.14108">arXiv:2503.14108</a> <span> [<a href="https://arxiv.org/pdf/2503.14108">pdf</a>, <a href="https://arxiv.org/ps/2503.14108">ps</a>, <a href="https://arxiv.org/format/2503.14108">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Metric Geometry">math.MG</span> </div> </div> <p class="title is-5 mathjax"> On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Liang%2C+C">Chong-Wei Liang</a>, <a href="/search/math?searchtype=author&query=Shen%2C+C">Chun-Yen 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="2503.14108v1-abstract-short" style="display: inline;"> The Falconer distance problem for Cartesian product sets was introduced and studied by Iosevich and Liu (\cite{MR3525385}). In this paper, by implementing a new observation on Cartesian product sets associated with a particular parabolic structure, we study the pinned version of Falconer distance problem for Cartesian product sets, and improve the threshold for the Falconer distance set in \cite{M… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.14108v1-abstract-full').style.display = 'inline'; document.getElementById('2503.14108v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.14108v1-abstract-full" style="display: none;"> The Falconer distance problem for Cartesian product sets was introduced and studied by Iosevich and Liu (\cite{MR3525385}). In this paper, by implementing a new observation on Cartesian product sets associated with a particular parabolic structure, we study the pinned version of Falconer distance problem for Cartesian product sets, and improve the threshold for the Falconer distance set in \cite{MR3525385} in certain case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.14108v1-abstract-full').style.display = 'none'; document.getElementById('2503.14108v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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. Any comment is welcome!!</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.12158">arXiv:2503.12158</a> <span> [<a href="https://arxiv.org/pdf/2503.12158">pdf</a>, <a href="https://arxiv.org/ps/2503.12158">ps</a>, <a href="https://arxiv.org/format/2503.12158">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="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> A stochastic maximum principle of mean-field type with monotonicity conditions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=He%2C+B">Bowen He</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Juan Li</a>, <a href="/search/math?searchtype=author&query=Li%2C+Z">Zhanxin Li</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="2503.12158v1-abstract-short" style="display: inline;"> The objective of this paper is to weaken the Lipschitz condition to a monotonicity condition and to study the corresponding Pontryagin stochastic maximum principle (SMP) for a mean-field optimal control problem under monotonicity conditions.The dynamics of the controlled state process is governed by a mean-field stochastic differential equation (SDE) whose coefficients depend not only on the contr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.12158v1-abstract-full').style.display = 'inline'; document.getElementById('2503.12158v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.12158v1-abstract-full" style="display: none;"> The objective of this paper is to weaken the Lipschitz condition to a monotonicity condition and to study the corresponding Pontryagin stochastic maximum principle (SMP) for a mean-field optimal control problem under monotonicity conditions.The dynamics of the controlled state process is governed by a mean-field stochastic differential equation (SDE) whose coefficients depend not only on the control, the controlled state process itself but also on its law, and in particular, these coefficients satisfy the monotonicity condition with respect to both the controlled state process and its distribution. The associated cost functional is also of mean-field type. Under the assumption of a convex control domain we derive the SMP, which provides a necessary optimality condition for control processes. Under additional convexity assumptions on the Hamiltonian, we further prove that this necessary condition is also a sufficient one. To achieve this, we first address the challenges related to the existence and the uniqueness of solutions for mean-field backward stochastic differential equations and mean-field SDEs whose coefficients satisfy monotonicity conditions with respect to both the solution as well as its distribution. On the other hand we also construct several illustrative examples demonstrating the generality of our results compared to existing literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.12158v1-abstract-full').style.display = 'none'; document.getElementById('2503.12158v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.11986">arXiv:2503.11986</a> <span> [<a href="https://arxiv.org/pdf/2503.11986">pdf</a>, <a href="https://arxiv.org/format/2503.11986">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="Fluid Dynamics">physics.flu-dyn</span> </div> </div> <p class="title is-5 mathjax"> An Acoustic Inversion-Based Flow Measurement Model in 3D Hydrodynamic Systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jiwei Li</a>, <a href="/search/math?searchtype=author&query=Qiu%2C+L">Lingyun Qiu</a>, <a href="/search/math?searchtype=author&query=Wang%2C+Z">Zhongjing Wang</a>, <a href="/search/math?searchtype=author&query=Yu%2C+H">Hui Yu</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="2503.11986v1-abstract-short" style="display: inline;"> This study extends the flow measurement method initially proposed in [22] to three-dimensional scenarios, addressing the growing need for accurate and efficient non-contact flow measurement techniques in complex hydrodynamic environments. Compared to conventional Acoustic Doppler Current Profilers (ADCPs) and remote sensing-based flow monitoring, the proposed method enables high-resolution, contin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.11986v1-abstract-full').style.display = 'inline'; document.getElementById('2503.11986v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.11986v1-abstract-full" style="display: none;"> This study extends the flow measurement method initially proposed in [22] to three-dimensional scenarios, addressing the growing need for accurate and efficient non-contact flow measurement techniques in complex hydrodynamic environments. Compared to conventional Acoustic Doppler Current Profilers (ADCPs) and remote sensing-based flow monitoring, the proposed method enables high-resolution, continuous water velocity measurement, making it well-suited for hazardous environments such as floods, strong currents, and sediment-laden rivers. Building upon the original approach, we develop an enhanced model that incorporates multiple emission directions and flexible configurations of receivers. These advancements improve the adaptability and accuracy of the method when applied to three-dimensional flow fields. To evaluate its feasibility, we conducted extensive numerical simulations designed to mimic real-world hydrodynamic conditions. The results demonstrate that the proposed method effectively handles diverse and complex flow field configurations, highlighting its potential for practical applications in water resource management and hydraulic engineering. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.11986v1-abstract-full').style.display = 'none'; document.getElementById('2503.11986v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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, 11 figures, submitted to Journal of Hydrology</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35R30; 65M32; 00A71 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.10487">arXiv:2503.10487</a> <span> [<a href="https://arxiv.org/pdf/2503.10487">pdf</a>, <a href="https://arxiv.org/format/2503.10487">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="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Sediment Concentration Estimation via Multiscale Inverse Problem and Stochastic Homogenization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jiwei Li</a>, <a href="/search/math?searchtype=author&query=Qiu%2C+L">Lingyun Qiu</a>, <a href="/search/math?searchtype=author&query=Wang%2C+Z">Zhongjing Wang</a>, <a href="/search/math?searchtype=author&query=Yu%2C+H">Hui Yu</a>, <a href="/search/math?searchtype=author&query=Zheng%2C+S">Siqin Zheng</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="2503.10487v1-abstract-short" style="display: inline;"> In this work, we contribute to the broader understanding of inverse problems by introducing a versatile multiscale modeling framework tailored to the challenges of sediment concentration estimation. Specifically, we propose a novel approach for sediment concentration measurement in water flow, modeled as a multiscale inverse medium problem. To address the multiscale nature of the sediment distribu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.10487v1-abstract-full').style.display = 'inline'; document.getElementById('2503.10487v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.10487v1-abstract-full" style="display: none;"> In this work, we contribute to the broader understanding of inverse problems by introducing a versatile multiscale modeling framework tailored to the challenges of sediment concentration estimation. Specifically, we propose a novel approach for sediment concentration measurement in water flow, modeled as a multiscale inverse medium problem. To address the multiscale nature of the sediment distribution, we treat it as an inhomogeneous random field and use the homogenization theory in deriving the effective medium model. The inverse problem is formulated as the reconstruction of the effective medium model, specifically, the sediment concentration, from partial boundary measurements. Additionally, we develop numerical algorithms to improve the efficiency and accuracy of solving this inverse problem. Our numerical experiments demonstrate the effectiveness of the proposed model and methods in producing accurate sediment concentration estimates, offering new insights into sediment concentration measurement in complex environments. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.10487v1-abstract-full').style.display = 'none'; document.getElementById('2503.10487v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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">20 pages, 7 figures, submitted to Archive for Rational Mechanics and Analysis</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35B27; 35R30; 76M50 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.10237">arXiv:2503.10237</a> <span> [<a href="https://arxiv.org/pdf/2503.10237">pdf</a>, <a href="https://arxiv.org/format/2503.10237">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"> Efficient Diffusion Posterior Sampling for Noisy Inverse Problems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Wang%2C+C">Chao 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="2503.10237v1-abstract-short" style="display: inline;"> The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires estimating the expectation of clean image given the current image and the measurement. With the theoretical expectation expression, the crucial task of solving… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.10237v1-abstract-full').style.display = 'inline'; document.getElementById('2503.10237v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.10237v1-abstract-full" style="display: none;"> The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires estimating the expectation of clean image given the current image and the measurement. With the theoretical expectation expression, the crucial task of solving inverse problems is to estimate the noisy likelihood function at the intermediate image sample. Using the Tweedie's formula and the known noise model, the existing diffusion posterior sampling methods perform gradient descent step with backpropagation through the pretrained diffusion model. To alleviate the costly computation and intensive memory consumption of the backpropagation, we propose an alternative maximum-a-posteriori (MAP)-based surrogate estimator to the expectation. With this approach and further density approximation, the MAP estimator for linear inverse problem is the solution to a traditional regularized optimization, of which the loss comprises of data fidelity term and the diffusion model related prior term. Integrating the MAP estimator into a general denoising diffusion implicit model (DDIM)-like sampler, we achieve the general solving framework for inverse problems. Our approach highly resembles the existing $螤$GDM without the manifold projection operation of the gradient descent direction. The developed method is also extended to nonlinear JPEG decompression. The performance of the proposed posterior sampling is validated across a series of inverse problems, where both VP and VE SDE-based pretrained diffusion models are taken into consideration. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.10237v1-abstract-full').style.display = 'none'; document.getElementById('2503.10237v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.07916">arXiv:2503.07916</a> <span> [<a href="https://arxiv.org/pdf/2503.07916">pdf</a>, <a href="https://arxiv.org/format/2503.07916">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"> Convexification With the Viscocity Term for Electrical Impedance Tomography </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Klibanov%2C+M+V">Michael V. Klibanov</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jingzhi Li</a>, <a href="/search/math?searchtype=author&query=Yang%2C+Z">Zhipeng Yang</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="2503.07916v1-abstract-short" style="display: inline;"> A version of the globally convergent convexification numerical method is constructed for the problem of Electrical Impedance Tomography in the 2D case. An important element of this version is the presence of the viscosity term. Global convergence analysis is carried out. Results of numerical experiments are presented. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.07916v1-abstract-full" style="display: none;"> A version of the globally convergent convexification numerical method is constructed for the problem of Electrical Impedance Tomography in the 2D case. An important element of this version is the presence of the viscosity term. Global convergence analysis is carried out. Results of numerical experiments are presented. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.07916v1-abstract-full').style.display = 'none'; document.getElementById('2503.07916v1-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.05440">arXiv:2503.05440</a> <span> [<a href="https://arxiv.org/pdf/2503.05440">pdf</a>, <a href="https://arxiv.org/ps/2503.05440">ps</a>, <a href="https://arxiv.org/format/2503.05440">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> A path description for $\varepsilon$-characters of representations of type $A$ restricted quantum loop algebras at roots of unity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=An%2C+X">Xiao-Juan An</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jian-Rong Li</a>, <a href="/search/math?searchtype=author&query=Luo%2C+Y">Yan-Feng Luo</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+W">Wen-Ting 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="2503.05440v1-abstract-short" style="display: inline;"> Fix $\varepsilon^{2\ell}=1$ with $\ell \geq 2$. In this paper, we show that all finite-dimensional simple modules of any restricted quantum loop algebra $U_{\varepsilon}^{\rm res}({L\mathfrak{sl}_{n+1}})$ in a certain category can be transformed into snake modules. We obtain an effective and concrete path description for $\varepsilon$-characters of any simple module with highest $l$-weight of degr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.05440v1-abstract-full').style.display = 'inline'; document.getElementById('2503.05440v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.05440v1-abstract-full" style="display: none;"> Fix $\varepsilon^{2\ell}=1$ with $\ell \geq 2$. In this paper, we show that all finite-dimensional simple modules of any restricted quantum loop algebra $U_{\varepsilon}^{\rm res}({L\mathfrak{sl}_{n+1}})$ in a certain category can be transformed into snake modules. We obtain an effective and concrete path description for $\varepsilon$-characters of any simple module with highest $l$-weight of degree two and any Kirillov-Reshetikhin module of $U_{\varepsilon}^{\rm res}({L\mathfrak{sl}_{n+1}})$. As an application of our path description, we obtain a necessary and sufficient condition for the tensor product of two fundamental representations of $U_{\varepsilon}^{\rm res}({L\mathfrak{sl}_{n+1}})$ to be irreducible. Additionally, we obtain a necessary condition for the tensor product of two or more fundamental representations of $U_{\varepsilon}^{\rm res}({L\mathfrak{sl}_{n+1}})$ to be irreducible. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.05440v1-abstract-full').style.display = 'none'; document.getElementById('2503.05440v1-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, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 17B37 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.05140">arXiv:2503.05140</a> <span> [<a href="https://arxiv.org/pdf/2503.05140">pdf</a>, <a href="https://arxiv.org/format/2503.05140">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Mixed norm estimates for dilated averages over planar curves </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Junfeng Li</a>, <a href="/search/math?searchtype=author&query=Lou%2C+Z">Zengjian Lou</a>, <a href="/search/math?searchtype=author&query=Yu%2C+H">Haixia Yu</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="2503.05140v1-abstract-short" style="display: inline;"> In this paper, we investigate the mixed norm estimates for the operator $ T $associated with a dilated plane curve $(ut, u纬(t))$, defined by \[ Tf(x, u) := \int_{0}^{1} f(x_1 - ut, x_2 - u纬(t)) \, dt, \] where $ x := (x_1, x_2) $ and $纬$ is a general plane curve satisfying appropriate smoothness and curvature conditions. Our results partially address a problem posed by Hickman [J. Funct. Anal. 201… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.05140v1-abstract-full').style.display = 'inline'; document.getElementById('2503.05140v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.05140v1-abstract-full" style="display: none;"> In this paper, we investigate the mixed norm estimates for the operator $ T $associated with a dilated plane curve $(ut, u纬(t))$, defined by \[ Tf(x, u) := \int_{0}^{1} f(x_1 - ut, x_2 - u纬(t)) \, dt, \] where $ x := (x_1, x_2) $ and $纬$ is a general plane curve satisfying appropriate smoothness and curvature conditions. Our results partially address a problem posed by Hickman [J. Funct. Anal. 2016] in the two-dimensional setting. More precisely, we establish the $ L_x^p(\mathbb{R}^2) \rightarrow L_x^q L_u^r(\mathbb{R}^2 \times [1, 2]) $ (space-time) estimates for $ T $, whenever $(\frac{1}{p},\frac{1}{q})$ satisfy \[ \max\left\{0, \frac{1}{2p} - \frac{1}{2r}, \frac{3}{p} - \frac{r+2}{r}\right\} < \frac{1}{q} \leq \frac{1}{p} < \frac{r+1}{2r} \] and $$1 + (1 + 蠅)\left(\frac{1}{q} - \frac{1}{p}\right) > 0,$$ where $ r \in [1, \infty] $ and $ 蠅:= \limsup_{t \rightarrow 0^+} \frac{\ln|纬(t)|}{\ln t} $. These results are sharp, except for certain borderline cases. Additionally, we examine the $ L_x^p(\mathbb{R}^2) \rightarrow L_u^r L_x^q(\mathbb{R}^2 \times [1, 2]) $ (time-space) estimates for $T $, which are especially almost sharp when $p=2$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.05140v1-abstract-full').style.display = 'none'; document.getElementById('2503.05140v1-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> 6 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.05069">arXiv:2503.05069</a> <span> [<a href="https://arxiv.org/pdf/2503.05069">pdf</a>, <a href="https://arxiv.org/ps/2503.05069">ps</a>, <a href="https://arxiv.org/format/2503.05069">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"> On the continuous properties for the 3D incompressible rotating Euler equations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jinlu Li</a>, <a href="/search/math?searchtype=author&query=Yu%2C+Y">Yanghai Yu</a>, <a href="/search/math?searchtype=author&query=Zhu%2C+N">Neng 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="2503.05069v1-abstract-short" style="display: inline;"> In this paper, we consider the Cauchy problem for the 3D Euler equations with the Coriolis force in the whole space. We first establish the local-in-time existence and uniqueness of solution to this system in $B^s_{p,r}(\R^3)$. Then we prove that the Cauchy problem is ill-posed in two different sense: (1) the solution of this system is not uniformly continuous dependence on the initial data in the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.05069v1-abstract-full').style.display = 'inline'; document.getElementById('2503.05069v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.05069v1-abstract-full" style="display: none;"> In this paper, we consider the Cauchy problem for the 3D Euler equations with the Coriolis force in the whole space. We first establish the local-in-time existence and uniqueness of solution to this system in $B^s_{p,r}(\R^3)$. Then we prove that the Cauchy problem is ill-posed in two different sense: (1) the solution of this system is not uniformly continuous dependence on the initial data in the same Besov spaces, which extends the recent work of Himonas-Misio艂ek \cite[Comm. Math. Phys., 296, 2010]{HM1} to the general Besov spaces framework; (2) the solution of this system cannot be H枚lder continuous in time variable in the same Besov spaces. In particular, the solution of the system is discontinuous in the weaker Besov spaces at time zero. To the best of our knowledge, our work is the first one addressing the issue on the failure of H枚lder continuous in time of solution to the classical Euler equations with(out) the Coriolis force. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.05069v1-abstract-full').style.display = 'none'; document.getElementById('2503.05069v1-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> 6 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.03482">arXiv:2503.03482</a> <span> [<a href="https://arxiv.org/pdf/2503.03482">pdf</a>, <a href="https://arxiv.org/ps/2503.03482">ps</a>, <a href="https://arxiv.org/format/2503.03482">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"> A note on Spectral Volume comparison for manifolds with weakly convex boundary </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jia Li</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="2503.03482v1-abstract-short" style="display: inline;"> We establish a new boundary version of spectral volume comparison theorem in this paper. Let $(M^n,g)(n\geq 3)$ be a connected, smooth compact n-dimensional manifold with weakly convex boundary. If there exist a positive function $w\in C^{\infty}(M)$ that satisfies: \begin{equation*} \begin{cases} -\frac{n-1}{n-2}螖w+\Ric w\geq (n-1)w, \frac{\partial w}{\partial 畏}=0. \end{cases} \end{equat… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.03482v1-abstract-full').style.display = 'inline'; document.getElementById('2503.03482v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.03482v1-abstract-full" style="display: none;"> We establish a new boundary version of spectral volume comparison theorem in this paper. Let $(M^n,g)(n\geq 3)$ be a connected, smooth compact n-dimensional manifold with weakly convex boundary. If there exist a positive function $w\in C^{\infty}(M)$ that satisfies: \begin{equation*} \begin{cases} -\frac{n-1}{n-2}螖w+\Ric w\geq (n-1)w, \frac{\partial w}{\partial 畏}=0. \end{cases} \end{equation*} then $\Vol(M)\leq \Vol(\bS^n_{+})$, and equality holds if and only if $M^n$ is isometric to the unit round hemisphere $\bS^{n}_{+}=\{x\in\bR^{n+1}: |x|=1, x_{n+1}\geq 0\}\subset\bR^{n+1}$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.03482v1-abstract-full').style.display = 'none'; document.getElementById('2503.03482v1-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> 5 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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">16pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.00891">arXiv:2503.00891</a> <span> [<a href="https://arxiv.org/pdf/2503.00891">pdf</a>, <a href="https://arxiv.org/ps/2503.00891">ps</a>, <a href="https://arxiv.org/format/2503.00891">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="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Distributionally chaotic $C_0$-semigroups on complex sectors </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Jiang%2C+Z">Zhen Jiang</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jian Li</a>, <a href="/search/math?searchtype=author&query=Yang%2C+Y">Yini Yang</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="2503.00891v1-abstract-short" style="display: inline;"> We explore distributional chaos for $C_0$-semigroups of linear operators on Banach spaces whose index set is a sector in the complex plane. We establish the relationship between distributional sensitivity and distributional chaos by characterizing them in terms of distributionally (semi-)irregular vectors. Additionally, we provide conditions under which a $C_0$-semigroup admits a linear manifold o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.00891v1-abstract-full').style.display = 'inline'; document.getElementById('2503.00891v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.00891v1-abstract-full" style="display: none;"> We explore distributional chaos for $C_0$-semigroups of linear operators on Banach spaces whose index set is a sector in the complex plane. We establish the relationship between distributional sensitivity and distributional chaos by characterizing them in terms of distributionally (semi-)irregular vectors. Additionally, we provide conditions under which a $C_0$-semigroup admits a linear manifold of distributionally irregular vectors. Furthermore, we delve into the study of distributional chaos for the translation $C_0$-semigroup on weighted $L_p$-spaces with a complex sector as the index set. We obtain a sufficient condition for dense distributional chaos, expressed in terms of the weight. In particular, we construct an example of a translation $C_0$-semigroup with a complex sector index set that is Devaney chaotic but not distributionally chaotic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.00891v1-abstract-full').style.display = 'none'; document.getElementById('2503.00891v1-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, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </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">17 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/2502.20768">arXiv:2502.20768</a> <span> [<a href="https://arxiv.org/pdf/2502.20768">pdf</a>, <a href="https://arxiv.org/ps/2502.20768">ps</a>, <a href="https://arxiv.org/format/2502.20768">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> </div> </div> <p class="title is-5 mathjax"> Convex inequalities in Hilbert $C^*$-modules </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Wu%2C+K">Kangjian Wu</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jia Li</a>, <a href="/search/math?searchtype=author&query=Xu%2C+Q">Qingxiang 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="2502.20768v1-abstract-short" style="display: inline;"> The H$\ddot{\rm o}$lder-McCarty inequalities are originally derived in the Hilbert space case and have been generalized via a convex inequality. The main purpose of this paper is to extend this convex inequality to the Hilbert $C^*$-module case, and meanwhile to make some investigations on the H$\ddot{\rm o}$lder-McCarty inequalities in the Hilbert $C^*$-module case. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.20768v1-abstract-full" style="display: none;"> The H$\ddot{\rm o}$lder-McCarty inequalities are originally derived in the Hilbert space case and have been generalized via a convex inequality. The main purpose of this paper is to extend this convex inequality to the Hilbert $C^*$-module case, and meanwhile to make some investigations on the H$\ddot{\rm o}$lder-McCarty inequalities in the Hilbert $C^*$-module case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.20768v1-abstract-full').style.display = 'none'; document.getElementById('2502.20768v1-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.20259">arXiv:2502.20259</a> <span> [<a href="https://arxiv.org/pdf/2502.20259">pdf</a>, <a href="https://arxiv.org/ps/2502.20259">ps</a>, <a href="https://arxiv.org/format/2502.20259">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> </div> </div> <p class="title is-5 mathjax"> Notes on the numerical radius for adjointable operators on Hilbert $C^*$-modules </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">J. Li</a>, <a href="/search/math?searchtype=author&query=Wu%2C+K">K. Wu</a>, <a href="/search/math?searchtype=author&query=Xu%2C+Q">Q. 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="2502.20259v1-abstract-short" style="display: inline;"> Given a Hilbert module $H$ over a $C^*$-algebra, let $\mathcal{L}(H)$ be the set of all adjointable operators on $H$. For each $T\in\mathcal{L}(H)$, its numerical radius is defined by $w(T)=\sup\big\{\|\langle Tx, x \rangle\|: x\in H, \|x\|=1\big\}$. It is proved that $w(T)=\|T\|$ whenever $T$ is normal. Examples are constructed to show that there exist Hilbert module $H$ over certain $C^*$-algebr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.20259v1-abstract-full').style.display = 'inline'; document.getElementById('2502.20259v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.20259v1-abstract-full" style="display: none;"> Given a Hilbert module $H$ over a $C^*$-algebra, let $\mathcal{L}(H)$ be the set of all adjointable operators on $H$. For each $T\in\mathcal{L}(H)$, its numerical radius is defined by $w(T)=\sup\big\{\|\langle Tx, x \rangle\|: x\in H, \|x\|=1\big\}$. It is proved that $w(T)=\|T\|$ whenever $T$ is normal. Examples are constructed to show that there exist Hilbert module $H$ over certain $C^*$-algebra and $T_1,T_2\in \mathcal{L}(H)$ with $T_1^2=0$ such that $w(T_1)\ne \frac12 \|T_1\|$ and $\sup\limits_{胃\in [0,2蟺]}\|\mbox{Re}(e^{i胃}T_2)\|<w(T_2)$. In addition, a new characterization of the spatial numerical radius is given, and it is proved that $w\big(蟺(T)\big)\le w(T)$ for every faithful representation $(蟺, X)$ of $\mathcal{L}(H)$ and every $T\in\mathcal{L}(H)$. Some inequalities are derived based on the newly obtained results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.20259v1-abstract-full').style.display = 'none'; document.getElementById('2502.20259v1-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, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.18100">arXiv:2502.18100</a> <span> [<a href="https://arxiv.org/pdf/2502.18100">pdf</a>, <a href="https://arxiv.org/ps/2502.18100">ps</a>, <a href="https://arxiv.org/format/2502.18100">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"> Realizing degree sequences with $\mathcal S_3$-connected graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Guan%2C+R">Rui Guan</a>, <a href="/search/math?searchtype=author&query=Jiang%2C+C">Chenglin Jiang</a>, <a href="/search/math?searchtype=author&query=Lai%2C+H">Hong-Jian Lai</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiaao Li</a>, <a href="/search/math?searchtype=author&query=Li%2C+X">Xinyuan Li</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="2502.18100v1-abstract-short" style="display: inline;"> A graph $G$ is $\mathcal S_3$-connected if, for any mapping $尾: V (G) \mapsto {\mathbb Z}_3$ with $\sum_{v\in V(G)} 尾(v)\equiv 0\pmod3$, there exists a strongly connected orientation $D$ satisfying $d^{+}_D(v)-d^{-}_D(v)\equiv 尾(v)\pmod{3}$ for any $v \in V(G)$. It is known that $\mathcal S_3$-connected graphs are contractible configurations for the property of flow index strictly less than three.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.18100v1-abstract-full').style.display = 'inline'; document.getElementById('2502.18100v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.18100v1-abstract-full" style="display: none;"> A graph $G$ is $\mathcal S_3$-connected if, for any mapping $尾: V (G) \mapsto {\mathbb Z}_3$ with $\sum_{v\in V(G)} 尾(v)\equiv 0\pmod3$, there exists a strongly connected orientation $D$ satisfying $d^{+}_D(v)-d^{-}_D(v)\equiv 尾(v)\pmod{3}$ for any $v \in V(G)$. It is known that $\mathcal S_3$-connected graphs are contractible configurations for the property of flow index strictly less than three. In this paper, we provide a complete characterization of graphic sequences that have an $\mathcal{S}_{3}$-connected realization: A graphic sequence $蟺=(d_1,\, \ldots,\, d_n )$ has an $\mathcal S_3$-connected realization if and only if $\min \{d_1,\, \ldots,\, d_n\} \ge 4$ and $\sum^n_{i=1}d_i \ge 6n - 4$. Consequently, every graphic sequence $蟺=(d_1,\, \ldots,\, d_n )$ with $\min \{d_1,\, \ldots,\, d_n\} \ge 6$ has a realization $G$ with flow index strictly less than three. This supports a conjecture of Li, Thomassen, Wu and Zhang [European J. Combin., 70 (2018) 164-177] that every $6$-edge-connected graph has flow index strictly less than three. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.18100v1-abstract-full').style.display = 'none'; document.getElementById('2502.18100v1-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </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, 6 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/2502.16501">arXiv:2502.16501</a> <span> [<a href="https://arxiv.org/pdf/2502.16501">pdf</a>, <a href="https://arxiv.org/ps/2502.16501">ps</a>, <a href="https://arxiv.org/format/2502.16501">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"> Pressure-robustness in Stokes-Darcy Optimal Control Problem with reconstruction operator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jingshi Li</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+J">Jiachuan Zhang</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+R">Ran 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="2502.16501v1-abstract-short" style="display: inline;"> This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement of normal continuity at interfaces, within the framework of the mixed finite element method (FEM). The methodology involves the strategic deployment of a recon… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.16501v1-abstract-full').style.display = 'inline'; document.getElementById('2502.16501v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.16501v1-abstract-full" style="display: none;"> This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement of normal continuity at interfaces, within the framework of the mixed finite element method (FEM). The methodology involves the strategic deployment of a reconstruction operator, which is adeptly applied to both the constraint equations and the cost functional. This is complemented by a judicious selection of finite element spaces that are tailored for approximation and reconstruction purposes. The synergy of these methodological choices leads to the realization of a discretization scheme that is pressure-robust, thereby enhancing the robustness and reliability of numerical simulations in computational mathematics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.16501v1-abstract-full').style.display = 'none'; document.getElementById('2502.16501v1-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> 23 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.16482">arXiv:2502.16482</a> <span> [<a href="https://arxiv.org/pdf/2502.16482">pdf</a>, <a href="https://arxiv.org/ps/2502.16482">ps</a>, <a href="https://arxiv.org/format/2502.16482">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 Posteriori Error Estimation for Pressure-Robust Finite Element Methods Applied to the Stokes Optimal Control Problem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jingshi Li</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+J">Jiachuan 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="2502.16482v1-abstract-short" style="display: inline;"> This paper study a posteriori error estimates for the pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the Stokes equations. We develop an enhanced residual-based a posteriori error estimator that is independent of pressure and establish its global reliability and effici… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.16482v1-abstract-full').style.display = 'inline'; document.getElementById('2502.16482v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.16482v1-abstract-full" style="display: none;"> This paper study a posteriori error estimates for the pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the Stokes equations. We develop an enhanced residual-based a posteriori error estimator that is independent of pressure and establish its global reliability and efficiency. The proposed a posteriori error estimator enables the separation of velocity and pressure errors in a posteriori error estimation, ensuring velocity-related estimates are free of pressure influence. Numerical experiments confirm our conclusions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.16482v1-abstract-full').style.display = 'none'; document.getElementById('2502.16482v1-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> 23 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.13445">arXiv:2502.13445</a> <span> [<a href="https://arxiv.org/pdf/2502.13445">pdf</a>, <a href="https://arxiv.org/ps/2502.13445">ps</a>, <a href="https://arxiv.org/format/2502.13445">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"> Efficient Iterative Decoupling Methods for Thermo-Poroelasticity Based on a Four-Field Formulation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Cai%2C+M">Mingchao Cai</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jingzhi Li</a>, <a href="/search/math?searchtype=author&query=Li%2C+Z">Ziliang Li</a>, <a href="/search/math?searchtype=author&query=Liu%2C+Q">Qiang Liu</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="2502.13445v1-abstract-short" style="display: inline;"> This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this four-field model, we present both a coupled finite element method and a decoupled iterative finite element method. We prove the stability and optimal convergence of the coupled finite element method. Furthermore, we est… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.13445v1-abstract-full').style.display = 'inline'; document.getElementById('2502.13445v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.13445v1-abstract-full" style="display: none;"> This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this four-field model, we present both a coupled finite element method and a decoupled iterative finite element method. We prove the stability and optimal convergence of the coupled finite element method. Furthermore, we establish the convergence of the decoupled iterative method. This paper focuses primarily on analyzing the iterative decoupled algorithm. It demonstrates that the algorithm's convergence does not require any additional assumptions about physical parameters or stabilization parameters. Numerical results are provided to demonstrate the effectiveness and theoretical validity of these new methods. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.13445v1-abstract-full').style.display = 'none'; document.getElementById('2502.13445v1-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </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 journal</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.13115">arXiv:2502.13115</a> <span> [<a href="https://arxiv.org/pdf/2502.13115">pdf</a>, <a href="https://arxiv.org/ps/2502.13115">ps</a>, <a href="https://arxiv.org/format/2502.13115">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="Cryptography and Security">cs.CR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistics Theory">math.ST</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">stat.ML</span> </div> </div> <p class="title is-5 mathjax"> Near-Optimal Private Learning in Linear Contextual Bandits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Chen%2C+F">Fan Chen</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiachun Li</a>, <a href="/search/math?searchtype=author&query=Rakhlin%2C+A">Alexander Rakhlin</a>, <a href="/search/math?searchtype=author&query=Simchi-Levi%2C+D">David Simchi-Levi</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="2502.13115v1-abstract-short" style="display: inline;"> We analyze the problem of private learning in generalized linear contextual bandits. Our approach is based on a novel method of re-weighted regression, yielding an efficient algorithm with regret of order $\sqrt{T}+\frac{1}伪$ and $\sqrt{T}/伪$ in the joint and local model of $伪$-privacy, respectively. Further, we provide near-optimal private procedures that achieve dimension-independent rates in pr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.13115v1-abstract-full').style.display = 'inline'; document.getElementById('2502.13115v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.13115v1-abstract-full" style="display: none;"> We analyze the problem of private learning in generalized linear contextual bandits. Our approach is based on a novel method of re-weighted regression, yielding an efficient algorithm with regret of order $\sqrt{T}+\frac{1}伪$ and $\sqrt{T}/伪$ in the joint and local model of $伪$-privacy, respectively. Further, we provide near-optimal private procedures that achieve dimension-independent rates in private linear models and linear contextual bandits. In particular, our results imply that joint privacy is almost "for free" in all the settings we consider, partially addressing the open problem posed by Azize and Basu (2024). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.13115v1-abstract-full').style.display = 'none'; document.getElementById('2502.13115v1-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.12754">arXiv:2502.12754</a> <span> [<a href="https://arxiv.org/pdf/2502.12754">pdf</a>, <a href="https://arxiv.org/format/2502.12754">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="Number Theory">math.NT</span> </div> </div> <p class="title is-5 mathjax"> Density of shapes of periodic tori in the cubic case </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Dang%2C+N">Nguyen-Thi Dang</a>, <a href="/search/math?searchtype=author&query=Gargava%2C+N">Nihar Gargava</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jialun Li</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="2502.12754v1-abstract-short" style="display: inline;"> Consider the compact orbits of the $\mathbb{R}^2$ action of the diagonal group on $\operatorname{SL}(3,\mathbb{R})/\operatorname{SL}(3,\mathbb{Z})$, the so-called periodic tori. For any periodic torus, the set of periods of the orbit forms a lattice in $\mathbb{R}^2$. Such a lattice, re-scaled to covolume one, gives a shape point in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.12754v1-abstract-full').style.display = 'inline'; document.getElementById('2502.12754v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.12754v1-abstract-full" style="display: none;"> Consider the compact orbits of the $\mathbb{R}^2$ action of the diagonal group on $\operatorname{SL}(3,\mathbb{R})/\operatorname{SL}(3,\mathbb{Z})$, the so-called periodic tori. For any periodic torus, the set of periods of the orbit forms a lattice in $\mathbb{R}^2$. Such a lattice, re-scaled to covolume one, gives a shape point in $\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$. We prove that the shapes of all periodic tori are dense in $\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$. This implies the density of shapes of the unit groups of totally real cubic orders. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.12754v1-abstract-full').style.display = 'none'; document.getElementById('2502.12754v1-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37PXX; 37A44 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.11739">arXiv:2502.11739</a> <span> [<a href="https://arxiv.org/pdf/2502.11739">pdf</a>, <a href="https://arxiv.org/ps/2502.11739">ps</a>, <a href="https://arxiv.org/format/2502.11739">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"> The structure of weakly stable CMC hypersurfaces with free boundary </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jia Li</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="2502.11739v2-abstract-short" style="display: inline;"> In this paper, we prove that a complete noncompact weakly stable free boundary CMC $H$-hypersurface $(M^{n},\partial M)$ properly immersed in $(N^ {n+1},\partial N)$ must have one end, provided that $N$ has bounded geometry and weakly convex boundary, satisfies $\inf\Ric_{N}>-\frac{1}{n}H^2$ and $\biRic_{N}\geq \frac{(n-5)}{4}H^2$. Secondly, we establish a non-existence result for noncompact free… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.11739v2-abstract-full').style.display = 'inline'; document.getElementById('2502.11739v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.11739v2-abstract-full" style="display: none;"> In this paper, we prove that a complete noncompact weakly stable free boundary CMC $H$-hypersurface $(M^{n},\partial M)$ properly immersed in $(N^ {n+1},\partial N)$ must have one end, provided that $N$ has bounded geometry and weakly convex boundary, satisfies $\inf\Ric_{N}>-\frac{1}{n}H^2$ and $\biRic_{N}\geq \frac{(n-5)}{4}H^2$. Secondly, we establish a non-existence result for noncompact free boundary CMC hypersurfaces under certain conditions, as detailed in Theorem \ref{thm 4}. Finally, we give a rigidity theorem for free boundary minimal hypersurfaces in $5$-manifolds. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.11739v2-abstract-full').style.display = 'none'; document.getElementById('2502.11739v2-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </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</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.04872">arXiv:2502.04872</a> <span> [<a href="https://arxiv.org/pdf/2502.04872">pdf</a>, <a href="https://arxiv.org/format/2502.04872">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Commutative Algebra">math.AC</span> </div> </div> <p class="title is-5 mathjax"> Cohen-Macaulayness of powers of edge ideals of edge-weighted graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jiaxin Li</a>, <a href="/search/math?searchtype=author&query=Trung%2C+T+N">Tran Nam Trung</a>, <a href="/search/math?searchtype=author&query=Zhu%2C+G">Guangjun 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="2502.04872v1-abstract-short" style="display: inline;"> In this paper, we characterize the Cohen-Macaulayness of the second power $I(G_蠅)^2$ of the weighted edge ideal $I(G_蠅)$ when the underlying graph $G$ is a very well-covered graph. We also characterize the Cohen-Macaulayness of all ordinary powers of $I(G_蠅)^n$ when $G$ is a tree with a perfect matching consisting of pendant edges and the induced subgraph $G[V(G)\setminus S]$ of $G$ on… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.04872v1-abstract-full').style.display = 'inline'; document.getElementById('2502.04872v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.04872v1-abstract-full" style="display: none;"> In this paper, we characterize the Cohen-Macaulayness of the second power $I(G_蠅)^2$ of the weighted edge ideal $I(G_蠅)$ when the underlying graph $G$ is a very well-covered graph. We also characterize the Cohen-Macaulayness of all ordinary powers of $I(G_蠅)^n$ when $G$ is a tree with a perfect matching consisting of pendant edges and the induced subgraph $G[V(G)\setminus S]$ of $G$ on $V(G)\setminus S$ is a star, where $S$ is the set of all leaf vertices, or if $G$ is a connected graph with a perfect matching consisting of pendant edges and the induced subgraph $G[V(G)\setminus S]$ of $G$ on $V(G)\setminus S$ is a complete graph and the weight function $蠅$ satisfies $蠅(e)=1$ for all $e\in E(G[V(G)\setminus S])$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.04872v1-abstract-full').style.display = 'none'; document.getElementById('2502.04872v1-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 13C15; 13C14; Secondary 05E40; 13F20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.04618">arXiv:2502.04618</a> <span> [<a href="https://arxiv.org/pdf/2502.04618">pdf</a>, <a href="https://arxiv.org/format/2502.04618">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</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"> Robust Quantum Control for Bragg Pulse Design in Atom Interferometry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Baker%2C+L+S">Luke S. Baker</a>, <a href="/search/math?searchtype=author&query=de+Lima%2C+A+L+P">Andre Luiz P. de Lima</a>, <a href="/search/math?searchtype=author&query=Harter%2C+A">Andrew Harter</a>, <a href="/search/math?searchtype=author&query=Uzun%2C+C">Ceren Uzun</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jr-Shin Li</a>, <a href="/search/math?searchtype=author&query=Zlotnik%2C+A">Anatoly Zlotnik</a>, <a href="/search/math?searchtype=author&query=Martin%2C+M+J">Michael J. Martin</a>, <a href="/search/math?searchtype=author&query=Boshier%2C+M+G">Malcolm G. Boshier</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="2502.04618v2-abstract-short" style="display: inline;"> We formulate a robust optimal control algorithm to synthesize minimum energy pulses that can transfer a cold atom system into various momentum states. The algorithm uses adaptive linearization of the evolution operator and sequential quadratic programming to iterate the control towards a minimum energy signal that achieves optimal target state fidelity. Robustness to parameter variation is achieve… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.04618v2-abstract-full').style.display = 'inline'; document.getElementById('2502.04618v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.04618v2-abstract-full" style="display: none;"> We formulate a robust optimal control algorithm to synthesize minimum energy pulses that can transfer a cold atom system into various momentum states. The algorithm uses adaptive linearization of the evolution operator and sequential quadratic programming to iterate the control towards a minimum energy signal that achieves optimal target state fidelity. Robustness to parameter variation is achieved using Legendre polynomial approximation over the domain of variation. The method is applied to optimize the Bragg beamsplitting operation in ultra-cold atom interferometry. Even in the presence of 10-40% variability in the initial momentum dispersion of the atomic cloud and the intensity of the optical pulse, the algorithm reliably converges to a control protocol that robustly achieves unprecedented momentum levels with high fidelity for a single-frequency multi-photon Bragg diffraction scheme (e.g. $|\pm 40\hbar k\rangle$). Advantages of the proposed method are demonstrated by comparison to stochastic optimization using sampled parameter values. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.04618v2-abstract-full').style.display = 'none'; document.getElementById('2502.04618v2-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LA-UR-25-20049 <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 49M37; 78A37; 81V80 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.04610">arXiv:2502.04610</a> <span> [<a href="https://arxiv.org/pdf/2502.04610">pdf</a>, <a href="https://arxiv.org/format/2502.04610">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"> A note on logarithmic mean equicontinuity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Kwietniak%2C+D">Dominik Kwietniak</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jian Li</a>, <a href="/search/math?searchtype=author&query=Pourmand%2C+H">Habibeh Pourmand</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="2502.04610v1-abstract-short" style="display: inline;"> We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based of logarithmic (harmonic) mean convergence in place of Ces脿ro convergence. We introduce logarithmic mean equicontinuity and show that a topological dynamical system is logarithmically mean equicontinuous if and only if it is mean equicontinuous. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.04610v1-abstract-full" style="display: none;"> We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based of logarithmic (harmonic) mean convergence in place of Ces脿ro convergence. We introduce logarithmic mean equicontinuity and show that a topological dynamical system is logarithmically mean equicontinuous if and only if it is mean equicontinuous. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.04610v1-abstract-full').style.display = 'none'; document.getElementById('2502.04610v1-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> 6 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </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">16 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37B05; 37B25; 37A05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.03495">arXiv:2502.03495</a> <span> [<a href="https://arxiv.org/pdf/2502.03495">pdf</a>, <a href="https://arxiv.org/ps/2502.03495">ps</a>, <a href="https://arxiv.org/format/2502.03495">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Methodology">stat.ME</span> </div> </div> <p class="title is-5 mathjax"> Capacity Constraints in Ball and Urn Distribution Problems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jingwei Li</a>, <a href="/search/math?searchtype=author&query=Robertazzi%2C+T+G">Thomas G. Robertazzi</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="2502.03495v1-abstract-short" style="display: inline;"> This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive theoretical framework that addresses both upper and lower capacity constraints under different distribution conditions, elaborating on the combinatorial implic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.03495v1-abstract-full').style.display = 'inline'; document.getElementById('2502.03495v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.03495v1-abstract-full" style="display: none;"> This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive theoretical framework that addresses both upper and lower capacity constraints under different distribution conditions, elaborating on the combinatorial implications of such variations. Through rigorous analysis, we derive analytical solutions that cater to different constrained environments, providing a robust theoretical basis for future empirical and theoretical investigations. These solutions are pivotal for advancing research in fields that rely on precise distribution strategies, such as physics and parallel processing. The paper not only generalizes classical distribution problems but also introduces novel methodologies for tackling capacity variations, thereby broadening the utility and applicability of distribution theory in practical and theoretical contexts. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.03495v1-abstract-full').style.display = 'none'; document.getElementById('2502.03495v1-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </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 a preprint version of the manuscript</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 05A15(Primary); 60C05(Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.03090">arXiv:2502.03090</a> <span> [<a href="https://arxiv.org/pdf/2502.03090">pdf</a>, <a href="https://arxiv.org/ps/2502.03090">ps</a>, <a href="https://arxiv.org/format/2502.03090">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computation">stat.CO</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"> Gaussian Processes Regression for Uncertainty Quantification: An Introductory Tutorial </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jinglai Li</a>, <a href="/search/math?searchtype=author&query=Wang%2C+H">Hongqiao 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="2502.03090v2-abstract-short" style="display: inline;"> Gaussian Process Regression (GPR) is a powerful nonparametric regression method that is widely used in Uncertainty Quantification (UQ) for constructing surrogate models. This tutorial serves as an introductory guide for beginners, aiming to offer a structured and accessible overview of GPR's applications in UQ. We begin with an introduction to UQ and outline its key tasks, including uncertainty pr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.03090v2-abstract-full').style.display = 'inline'; document.getElementById('2502.03090v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.03090v2-abstract-full" style="display: none;"> Gaussian Process Regression (GPR) is a powerful nonparametric regression method that is widely used in Uncertainty Quantification (UQ) for constructing surrogate models. This tutorial serves as an introductory guide for beginners, aiming to offer a structured and accessible overview of GPR's applications in UQ. We begin with an introduction to UQ and outline its key tasks, including uncertainty propagation, risk estimation, optimization under uncertainty, parameter estimation, and sensitivity analysis. We then introduce Gaussian Processes (GPs) as a surrogate modeling technique, detailing their formulation, choice of covariance kernels, hyperparameter estimation, and active learning strategies for efficient data acquisition. The tutorial further explores how GPR can be applied to different UQ tasks, including Bayesian quadrature for uncertainty propagation, active learning-based risk estimation, Bayesian optimization for optimization under uncertainty, and surrogate-based sensitivity analysis. Throughout, we emphasize how to leverage the unique formulation of GP for these UQ tasks, rather than simply using it as a standard surrogate model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.03090v2-abstract-full').style.display = 'none'; document.getElementById('2502.03090v2-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, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.02900">arXiv:2502.02900</a> <span> [<a href="https://arxiv.org/pdf/2502.02900">pdf</a>, <a href="https://arxiv.org/ps/2502.02900">ps</a>, <a href="https://arxiv.org/format/2502.02900">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 Note on the Convergence of Muon and Further </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jiaxiang Li</a>, <a href="/search/math?searchtype=author&query=Hong%2C+M">Mingyi Hong</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="2502.02900v1-abstract-short" style="display: inline;"> In this note, we inspect the convergence of a new optimizer for pretraining LLMs, namely the Muon optimizer. Such an optimizer is closely related to a specialized steepest descent method where the update direction is the minimizer of the quadratic approximation of the objective function under spectral norm. We provide the convergence analysis on both versions of the optimizer and discuss its impli… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.02900v1-abstract-full').style.display = 'inline'; document.getElementById('2502.02900v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.02900v1-abstract-full" style="display: none;"> In this note, we inspect the convergence of a new optimizer for pretraining LLMs, namely the Muon optimizer. Such an optimizer is closely related to a specialized steepest descent method where the update direction is the minimizer of the quadratic approximation of the objective function under spectral norm. We provide the convergence analysis on both versions of the optimizer and discuss its implications. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.02900v1-abstract-full').style.display = 'none'; document.getElementById('2502.02900v1-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> 5 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.00424">arXiv:2502.00424</a> <span> [<a href="https://arxiv.org/pdf/2502.00424">pdf</a>, <a href="https://arxiv.org/ps/2502.00424">ps</a>, <a href="https://arxiv.org/format/2502.00424">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/10.1142/S0218127425500154">10.1142/S0218127425500154 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dense uniform Li-Yorke chaos for linear operators on a Banach space </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jian Li</a>, <a href="/search/math?searchtype=author&query=Wang%2C+X">Xinsheng 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="2502.00424v2-abstract-short" style="display: inline;"> This paper focuses on the dense uniform Li-Yorke chaos for linear operators on a Banach space. Some sufficient conditions and equivalent conditions are established under which the dynamical system is densely uniformly Li-Yorke chaotic. It is shown that there are plenty of densely uniformly Li-Yorke chaotic operators. For unilateral backward weighted shifts and bilateral backward weighted shifts on… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.00424v2-abstract-full').style.display = 'inline'; document.getElementById('2502.00424v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.00424v2-abstract-full" style="display: none;"> This paper focuses on the dense uniform Li-Yorke chaos for linear operators on a Banach space. Some sufficient conditions and equivalent conditions are established under which the dynamical system is densely uniformly Li-Yorke chaotic. It is shown that there are plenty of densely uniformly Li-Yorke chaotic operators. For unilateral backward weighted shifts and bilateral backward weighted shifts on $\ell^p$, it is shown that Li-Yorke chaos is equivalent to dense uniform Li-Yorke chaos. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.00424v2-abstract-full').style.display = 'none'; document.getElementById('2502.00424v2-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </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">16 pages, Accepted by International Journal of Bifurcation and Chaos</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.00318">arXiv:2502.00318</a> <span> [<a href="https://arxiv.org/pdf/2502.00318">pdf</a>, <a href="https://arxiv.org/format/2502.00318">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"> Sub-Sequential Physics-Informed Learning with State Space Model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Xu%2C+C">Chenhui Xu</a>, <a href="/search/math?searchtype=author&query=Liu%2C+D">Dancheng Liu</a>, <a href="/search/math?searchtype=author&query=Hu%2C+Y">Yuting Hu</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiajie Li</a>, <a href="/search/math?searchtype=author&query=Qin%2C+R">Ruiyang Qin</a>, <a href="/search/math?searchtype=author&query=Zheng%2C+Q">Qingxiao Zheng</a>, <a href="/search/math?searchtype=author&query=Xiong%2C+J">Jinjun Xiong</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="2502.00318v1-abstract-short" style="display: inline;"> Physics-Informed Neural Networks (PINNs) are a kind of deep-learning-based numerical solvers for partial differential equations (PDEs). Existing PINNs often suffer from failure modes of being unable to propagate patterns of initial conditions. We discover that these failure modes are caused by the simplicity bias of neural networks and the mismatch between PDE's continuity and PINN's discrete samp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.00318v1-abstract-full').style.display = 'inline'; document.getElementById('2502.00318v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.00318v1-abstract-full" style="display: none;"> Physics-Informed Neural Networks (PINNs) are a kind of deep-learning-based numerical solvers for partial differential equations (PDEs). Existing PINNs often suffer from failure modes of being unable to propagate patterns of initial conditions. We discover that these failure modes are caused by the simplicity bias of neural networks and the mismatch between PDE's continuity and PINN's discrete sampling. We reveal that the State Space Model (SSM) can be a continuous-discrete articulation allowing initial condition propagation, and that simplicity bias can be eliminated by aligning a sequence of moderate granularity. Accordingly, we propose PINNMamba, a novel framework that introduces sub-sequence modeling with SSM. Experimental results show that PINNMamba can reduce errors by up to 86.3\% compared with state-of-the-art architecture. Our code is available at https://github.com/miniHuiHui/PINNMamba. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.00318v1-abstract-full').style.display = 'none'; document.getElementById('2502.00318v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2502.00284">arXiv:2502.00284</a> <span> [<a href="https://arxiv.org/pdf/2502.00284">pdf</a>, <a href="https://arxiv.org/format/2502.00284">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Bounded-Confidence Models of Multi-Dimensional Opinions with Topic-Weighted Discordance </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+G+J">Grace Jingying Li</a>, <a href="/search/math?searchtype=author&query=Luo%2C+J">Jiajie Luo</a>, <a href="/search/math?searchtype=author&query=Chu%2C+W">Weiqi Chu</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="2502.00284v1-abstract-short" style="display: inline;"> People's opinions on a wide range of topics often evolve over time through their interactions with others. Models of opinion dynamics primarily focus on one-dimensional opinions which represent opinions on one topic. However, opinions on various topics are rarely isolated; instead, they can be interdependent and exhibit correlations. In a bounded-confidence model (BCM) of opinion dynamics, agents… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.00284v1-abstract-full').style.display = 'inline'; document.getElementById('2502.00284v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.00284v1-abstract-full" style="display: none;"> People's opinions on a wide range of topics often evolve over time through their interactions with others. Models of opinion dynamics primarily focus on one-dimensional opinions which represent opinions on one topic. However, opinions on various topics are rarely isolated; instead, they can be interdependent and exhibit correlations. In a bounded-confidence model (BCM) of opinion dynamics, agents influence each other's opinions only if their opinions are sufficiently similar. We extend classical agent-based BCMs -- namely, the Hegeselmann--Krause BCM, which has synchronous interactions, and the Deffuant--Weisbuch BCM, which has asynchronous interactions -- to a multidimensional setting, in which the opinions are multidimensional vectors representing opinions of different topics and opinions on different topics are interdependent. To measure opinion differences between agents, we introduce topic-weighted discordance functions that account for opinion differences in all topics. We use the regions of receptiveness to characterize the steady-state opinion clusters and provide an analytical approach to compute these regions. In addition, we numerically simulate our models on various networks with initial opinions drawn from a variety of distributions. When initial opinions are correlated across different topics, our topic-weighted BCMs yield significantly different results in both transient and steady states compared to baseline models, where the dynamics of each opinion topic are independent. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.00284v1-abstract-full').style.display = 'none'; document.getElementById('2502.00284v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </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, 17 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 91D30; 05C82; 37H05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.17495">arXiv:2501.17495</a> <span> [<a href="https://arxiv.org/pdf/2501.17495">pdf</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"> Feasible Path SQP Algorithm for Simulation-based Optimization Surrogated with Differentiable Machine Learning Models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhang%2C+Z">Zixuan Zhang</a>, <a href="/search/math?searchtype=author&query=Song%2C+X">Xiaowei Song</a>, <a href="/search/math?searchtype=author&query=Zeng%2C+Y">Yujiao Zeng</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jie Li</a>, <a href="/search/math?searchtype=author&query=Nie%2C+Y">Yaling Nie</a>, <a href="/search/math?searchtype=author&query=Zhu%2C+M">Min Zhu</a>, <a href="/search/math?searchtype=author&query=Chen%2C+J">Jianhua Chen</a>, <a href="/search/math?searchtype=author&query=Wang%2C+L">Linmin Wang</a>, <a href="/search/math?searchtype=author&query=Xiao%2C+X">Xin Xiao</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="2501.17495v1-abstract-short" style="display: inline;"> With the development of artificial intelligence, simulation-based optimization problems, which present a significant challenge in the process systems engineering community, are increasingly being addressed with the surrogate-based framework. In this work, we propose a deterministic algorithm framework based on feasible path sequential quadratic programming for optimizing differentiable machine lea… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.17495v1-abstract-full').style.display = 'inline'; document.getElementById('2501.17495v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.17495v1-abstract-full" style="display: none;"> With the development of artificial intelligence, simulation-based optimization problems, which present a significant challenge in the process systems engineering community, are increasingly being addressed with the surrogate-based framework. In this work, we propose a deterministic algorithm framework based on feasible path sequential quadratic programming for optimizing differentiable machine learning models embedded problems. The proposed framework effectively addresses two key challenges: (i) achieving the computation of first- and second-order derivatives of machine learning models' outputs with respect to inputs; and (ii) by introducing the feasible path method, the massive intermediate variables resulting from the algebraic formulation of machine learning models eliminated. Surrogate models for six test functions and two process simulations were established and optimized. All six test functions were successfully optimized to the global optima, demonstrating the framework's effectiveness. The optimization time for all cases did not exceed 2s, highlighting the efficiency of the algorithm. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.17495v1-abstract-full').style.display = 'none'; document.getElementById('2501.17495v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.17146">arXiv:2501.17146</a> <span> [<a href="https://arxiv.org/pdf/2501.17146">pdf</a>, <a href="https://arxiv.org/format/2501.17146">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"> A total curvature estimate of closed hypersurfaces in non-positively curved symmetric spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jiangtao Li</a>, <a href="/search/math?searchtype=author&query=Lin%2C+Z">Zuo Lin</a>, <a href="/search/math?searchtype=author&query=Xu%2C+L">Liang 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="2501.17146v1-abstract-short" style="display: inline;"> In this paper, we prove a total curvature estimate of closed hypersurfaces in simply-connected non-positively curved symmetric spaces, and as a corollary, we obtain an isoperimetric inequality for such manifolds. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.17146v1-abstract-full" style="display: none;"> In this paper, we prove a total curvature estimate of closed hypersurfaces in simply-connected non-positively curved symmetric spaces, and as a corollary, we obtain an isoperimetric inequality for such manifolds. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.17146v1-abstract-full').style.display = 'none'; document.getElementById('2501.17146v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </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> 53C35; 52A38; 51M16 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.15367">arXiv:2501.15367</a> <span> [<a href="https://arxiv.org/pdf/2501.15367">pdf</a>, <a href="https://arxiv.org/ps/2501.15367">ps</a>, <a href="https://arxiv.org/format/2501.15367">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Commutative Algebra">math.AC</span> </div> </div> <p class="title is-5 mathjax"> Depth of powers of edge ideals of edge-weighted integrally closed cycles </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhu%2C+G">Guangjun Zhu</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiaxin Li</a>, <a href="/search/math?searchtype=author&query=Cui%2C+Y">Yijun Cui</a>, <a href="/search/math?searchtype=author&query=Yang%2C+Y">Yi Yang</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="2501.15367v1-abstract-short" style="display: inline;"> This paper gives some exact formulas for the depth of powers of the edge ideal of an edge-weighted integrally closed cycle. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.15367v1-abstract-full" style="display: none;"> This paper gives some exact formulas for the depth of powers of the edge ideal of an edge-weighted integrally closed cycle. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.15367v1-abstract-full').style.display = 'none'; document.getElementById('2501.15367v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.15292">arXiv:2501.15292</a> <span> [<a href="https://arxiv.org/pdf/2501.15292">pdf</a>, <a href="https://arxiv.org/format/2501.15292">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"> Parameter-Robust Preconditioners for A Four-Field Thermo-Poroelasticity Model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Cai%2C+M">Mingchao Cai</a>, <a href="/search/math?searchtype=author&query=Kuchta%2C+M">Miroslav Kuchta</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jingzhi Li</a>, <a href="/search/math?searchtype=author&query=Li%2C+Z">Ziliang Li</a>, <a href="/search/math?searchtype=author&query=Mardal%2C+K">Kent-Andre Mardal</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="2501.15292v1-abstract-short" style="display: inline;"> We study a thermo-poroelasticity model which describes the interaction between the deformation of an elastic porous material and fluid flow under non-isothermal conditions. The model involves several parameters that can vary significantly in practical applications, posing a challenge for developing discretization techniques and solution algorithms that handle such variations effectively. We propos… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.15292v1-abstract-full').style.display = 'inline'; document.getElementById('2501.15292v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.15292v1-abstract-full" style="display: none;"> We study a thermo-poroelasticity model which describes the interaction between the deformation of an elastic porous material and fluid flow under non-isothermal conditions. The model involves several parameters that can vary significantly in practical applications, posing a challenge for developing discretization techniques and solution algorithms that handle such variations effectively. We propose a four-field formulation and apply a conforming finite element discretization. The primary focus is on constructing and analyzing preconditioners for the resulting linear system. Two preconditioners are proposed: one involves regrouping variables and treating the 4-by-4 system as a 2-by-2 block form, while the other is directly constructed from the 4-by-4 coupled operator. Both preconditioners are demonstrated to be robust with respect to variations in parameters and mesh refinement. Numerical experiments are presented to demonstrate the effectiveness of the proposed preconditioners and validate their theoretical performance under varying parameter settings. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.15292v1-abstract-full').style.display = 'none'; document.getElementById('2501.15292v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </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</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 65M60; 65F08; 65F10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.15033">arXiv:2501.15033</a> <span> [<a href="https://arxiv.org/pdf/2501.15033">pdf</a>, <a href="https://arxiv.org/ps/2501.15033">ps</a>, <a href="https://arxiv.org/format/2501.15033">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Number Theory">math.NT</span> </div> </div> <p class="title is-5 mathjax"> Anisotropic quadratic equations in three variables </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jiamin Li</a>, <a href="/search/math?searchtype=author&query=Liu%2C+J">Jianya Liu</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="2501.15033v1-abstract-short" style="display: inline;"> Let $f(x_1, x_2, x_3)$ be an indefinite anisotropic integral quadratic form with determinant $d(f)$, and $t$ a non-zero integer such that $d(f)t$ is square-free. It is proved in this paper that, as long as there is one integral solution to $f(x_1, x_2, x_3) = t$, there are infinitely many such solutions for which (i) $x_1$ has at most $6$ prime factors, and (ii) the product $x_1 x_2$ has at most… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.15033v1-abstract-full').style.display = 'inline'; document.getElementById('2501.15033v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.15033v1-abstract-full" style="display: none;"> Let $f(x_1, x_2, x_3)$ be an indefinite anisotropic integral quadratic form with determinant $d(f)$, and $t$ a non-zero integer such that $d(f)t$ is square-free. It is proved in this paper that, as long as there is one integral solution to $f(x_1, x_2, x_3) = t$, there are infinitely many such solutions for which (i) $x_1$ has at most $6$ prime factors, and (ii) the product $x_1 x_2$ has at most $16$ prime factors. Various methods, such as algebraic theory of quadratic forms, harmonic analysis, Jacquet-Langlands theory, as well as combinatorics, interact here, and the above results come from applying the sharpest known bounds towards Selberg's eigenvalue conjecture. Assuming the latter the number $6$ or $16$ may be reduced to $5$ or $14$, respectively. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.15033v1-abstract-full').style.display = 'none'; document.getElementById('2501.15033v1-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> 24 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 11P32; 11D09; 11N36 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.14576">arXiv:2501.14576</a> <span> [<a href="https://arxiv.org/pdf/2501.14576">pdf</a>, <a href="https://arxiv.org/format/2501.14576">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="Systems and Control">eess.SY</span> </div> </div> <p class="title is-5 mathjax"> Dynamic Operation and Control of a Multi-Stack Alkaline Water Electrolysis System with Shared Gas Separators and Lye Circulation: A Model-Based Study </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Qiu%2C+Y">Yiwei Qiu</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiatong Li</a>, <a href="/search/math?searchtype=author&query=Zeng%2C+Y">Yangjun Zeng</a>, <a href="/search/math?searchtype=author&query=Zhou%2C+Y">Yi Zhou</a>, <a href="/search/math?searchtype=author&query=Chen%2C+S">Shi Chen</a>, <a href="/search/math?searchtype=author&query=Qiu%2C+X">Xiaoyan Qiu</a>, <a href="/search/math?searchtype=author&query=Zhou%2C+B">Buxiang Zhou</a>, <a href="/search/math?searchtype=author&query=He%2C+G">Ge He</a>, <a href="/search/math?searchtype=author&query=Ji%2C+X">Xu Ji</a>, <a href="/search/math?searchtype=author&query=Li%2C+W">Wenying Li</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="2501.14576v1-abstract-short" style="display: inline;"> An emerging approach for large-scale hydrogen production using renewable energy is to integrate multiple alkaline water electrolysis (AWE) stacks into a single balance of plant (BoP) system, sharing components such as gas-lye separation and lye circulation. This configuration, termed the $N$-in-1 AWE system, packs $N$ stacks into a modular system, reducing land requirements, the complexity of plan… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.14576v1-abstract-full').style.display = 'inline'; document.getElementById('2501.14576v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.14576v1-abstract-full" style="display: none;"> An emerging approach for large-scale hydrogen production using renewable energy is to integrate multiple alkaline water electrolysis (AWE) stacks into a single balance of plant (BoP) system, sharing components such as gas-lye separation and lye circulation. This configuration, termed the $N$-in-1 AWE system, packs $N$ stacks into a modular system, reducing land requirements, the complexity of plant topology, and overall capital costs. However, the coupling of these stacks through the shared BoP introduces challenges in dynamic operation under varying energy inputs, making their performance unclear compared to traditional 1-in-1 systems. To address this, we develop a state-space model of the $N$-in-1 AWE system, capturing the dynamic behaviors of lye circulation, temperature, and HTO impurity, and their impact on energy conversion efficiency. We then propose a nonlinear model predictive controller (NMPC) to coordinately optimize inter-stack electrolytic current distribution, lye flow, and cooling, enabling the system to dynamically track varying load commands while maximizing efficiency, stabilizing temperature, and limiting HTO impurity accumulation. Simulation studies on a 4,000 Nm$^3$/h-rated 4-in-1 system verify the proposed controller under dynamic operation. Comparison with 4 independent 1-in-1 systems reveals that, with proper control, the $N$-in-1 configuration offers comparable flexibility in accommodating real-world wind power inputs. The average differences in the root-mean-square errors (RMSEs) for load-tracking and stack temperature stabilization, and specific energy consumption are below 0.014 MW, 2.356 K, and 0.003 kWh/Nm$^3$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.14576v1-abstract-full').style.display = 'none'; document.getElementById('2501.14576v1-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> 24 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.08485">arXiv:2501.08485</a> <span> [<a href="https://arxiv.org/pdf/2501.08485">pdf</a>, <a href="https://arxiv.org/format/2501.08485">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="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Formulation a new SIR model with non-local mobility </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Applegate%2C+C">Ciana Applegate</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jiaxu Li</a>, <a href="/search/math?searchtype=author&query=Han%2C+D">Dan Han</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="2501.08485v1-abstract-short" style="display: inline;"> In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions among susceptible, infected, and recovered states, they typically neglect the inherent spatial mobility of particles. To address this limitation, we introduce a no… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.08485v1-abstract-full').style.display = 'inline'; document.getElementById('2501.08485v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.08485v1-abstract-full" style="display: none;"> In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions among susceptible, infected, and recovered states, they typically neglect the inherent spatial mobility of particles. To address this limitation, we introduce a novel dynamical SIR model that incorporates nonlocal spatial motion for three distinct particle types, thereby bridging the gap between epidemiological theory and real-world mobility patterns. This paper primarily focuses on analyzing the long-term behavior of this dynamic system, with specific emphasis on the computation of first and second moments. We propose a new reproduction number $R_0^m$ and compare it with the classical reproduction number $R_0$ in the traditional SIR model. Furthermore, we rigorously examine the phenomenon of intermittency within the context of this enhanced SIR model. The results contribute to a more comprehensive understanding of pandemic spread dynamics, considering both the interplay between disease transmission and population mobility and the impact of spatial motion on the system's behavior over time. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.08485v1-abstract-full').style.display = 'none'; document.getElementById('2501.08485v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.06240">arXiv:2501.06240</a> <span> [<a href="https://arxiv.org/pdf/2501.06240">pdf</a>, <a href="https://arxiv.org/format/2501.06240">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="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> The Convergence of Dynamic Routing between Capsules </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ye%2C+D">Daoyuan Ye</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Juntao Li</a>, <a href="/search/math?searchtype=author&query=Shen%2C+Y">Yiting 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="2501.06240v1-abstract-short" style="display: inline;"> Capsule networks(CapsNet) are recently proposed neural network models with new processing layers, specifically for entity representation and discovery of images. It is well known that CapsNet have some advantages over traditional neural networks, especially in generalization capability. At the same time, some studies report negative experimental results. The causes of this contradiction have not b… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.06240v1-abstract-full').style.display = 'inline'; document.getElementById('2501.06240v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.06240v1-abstract-full" style="display: none;"> Capsule networks(CapsNet) are recently proposed neural network models with new processing layers, specifically for entity representation and discovery of images. It is well known that CapsNet have some advantages over traditional neural networks, especially in generalization capability. At the same time, some studies report negative experimental results. The causes of this contradiction have not been thoroughly analyzed. The preliminary experimental results show that the behavior of routing algorithms does not always produce good results as expected, and in most cases, different routing algorithms do not change the classification results, but simply polarize the link strength, especially when they continue to repeat without stopping. To realize the true potential of the CapsNet, deep mathematical analysis of the routing algorithms is crucial. In this paper, we will give the objective function that is minimized by the dynamic routing algorithm, which is a concave function. The dynamic routing algorithm can be regarded as nonlinear gradient method to solving an optimization algorithm under linear constraints, and its convergence can be strictly proved mathematically. Furthermore, the mathematically rigorous proof of the convergence is given for this class of iterative routing procedures. We analyze the relation between the objective function and the constraints solved by the dynamic routing algorithm in detail, and perform the corresponding routing experiment to analyze the effect of our convergence proof. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.06240v1-abstract-full').style.display = 'none'; document.getElementById('2501.06240v1-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> 8 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.03719">arXiv:2501.03719</a> <span> [<a href="https://arxiv.org/pdf/2501.03719">pdf</a>, <a href="https://arxiv.org/ps/2501.03719">ps</a>, <a href="https://arxiv.org/format/2501.03719">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="Analysis of PDEs">math.AP</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"> Shape Taylor expansion for wave scattering problems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bao%2C+G">Gang Bao</a>, <a href="/search/math?searchtype=author&query=Ma%2C+H">Haoran Ma</a>, <a href="/search/math?searchtype=author&query=Lai%2C+J">Jun Lai</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Jingzhi Li</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="2501.03719v2-abstract-short" style="display: inline;"> The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high order shape derivatives required for this expansion poses significant challenges with conventional methods. This paper addresses these difficulties by introducing e… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.03719v2-abstract-full').style.display = 'inline'; document.getElementById('2501.03719v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.03719v2-abstract-full" style="display: none;"> The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high order shape derivatives required for this expansion poses significant challenges with conventional methods. This paper addresses these difficulties by introducing elegant recurrence formulas for computing high order shape derivatives. The derivation employs tools from exterior differential forms, Lie derivatives, and material derivatives. The work establishes a unified framework for computing the high order shape perturbations in scattering problems. In particular, the recurrence formulas are applicable to both acoustic and electromagnetic scattering models under a variety of boundary conditions, including Dirichlet, Neumann, impedance, and transmission types. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.03719v2-abstract-full').style.display = 'none'; document.getElementById('2501.03719v2-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 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35Q61; 35J05; 35R30; 49J50; 78M50 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.03255">arXiv:2501.03255</a> <span> [<a href="https://arxiv.org/pdf/2501.03255">pdf</a>, <a href="https://arxiv.org/format/2501.03255">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Mathematics">math.GM</span> </div> </div> <p class="title is-5 mathjax"> A novel STAP algorithm via volume cross-correlation function on the Grassmann manifold </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jia-Mian Li</a>, <a href="/search/math?searchtype=author&query=Chen%2C+J">Jian-Yi Chen</a>, <a href="/search/math?searchtype=author&query=Li%2C+B">Bing-Zhao Li</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="2501.03255v1-abstract-short" style="display: inline;"> The performance of space-time adaptive processing (STAP) is often degraded by factors such as limited sample size and moving targets. Traditional clutter covariance matrix (CCM) estimation relies on Euclidean metrics, which fail to capture the intrinsic geometric and structural properties of the covariance matrix, thus limiting the utilization of structural information in the data. To address thes… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.03255v1-abstract-full').style.display = 'inline'; document.getElementById('2501.03255v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.03255v1-abstract-full" style="display: none;"> The performance of space-time adaptive processing (STAP) is often degraded by factors such as limited sample size and moving targets. Traditional clutter covariance matrix (CCM) estimation relies on Euclidean metrics, which fail to capture the intrinsic geometric and structural properties of the covariance matrix, thus limiting the utilization of structural information in the data. To address these issues, the proposed algorithm begins by constructing Toeplitz Hermitian positive definite (THPD) matrices from the training samples. The Brauer disc (BD) theorem is then employed to filter out THPD matrices containing target signals, retaining only clutter-related matrices. These clutter matrices undergo eigendecomposition to construct the Grassmann manifold, enabling CCM estimation through the volume cross-correlation function (VCF) and gradient descent method. Finally, the filter weight vector is computed for filtering. By fully leveraging the structural information in radar data, this approach significantly enhances both accuracy and robustness of clutter suppression. Experimental results on simulated and measured data demonstrate superior performance of the proposed algorithm in heterogeneous environments. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.03255v1-abstract-full').style.display = 'none'; document.getElementById('2501.03255v1-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> 30 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </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">26 pages, 10 figs</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.00780">arXiv:2501.00780</a> <span> [<a href="https://arxiv.org/pdf/2501.00780">pdf</a>, <a href="https://arxiv.org/format/2501.00780">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="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Solving McKean-Vlasov Equation by deep learning particle method </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jingyuan Li</a>, <a href="/search/math?searchtype=author&query=Liu%2C+W">Wei Liu</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="2501.00780v1-abstract-short" style="display: inline;"> We introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for this equation rely on the interacting particle method combined with techniques based on the It么-Taylor expansion. The convergence rate of this approach is determin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.00780v1-abstract-full').style.display = 'inline'; document.getElementById('2501.00780v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.00780v1-abstract-full" style="display: none;"> We introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for this equation rely on the interacting particle method combined with techniques based on the It么-Taylor expansion. The convergence rate of this approach is determined by two parameters: the number of particles $N$ and the time step size $h$ for each Euler iteration. However, for extended time horizons or equations with larger Lipschitz coefficients, this method is often limited, as it requires a significant increase in Euler iterations to achieve the desired precision $蔚$. To overcome the challenges posed by the difficulty of parallelizing the simulation of continuous interacting particle systems, which involve solving high-dimensional coupled SDEs, we propose a meshless MV-SDE solver grounded in Physics-Informed Neural Networks (PINNs) that does not rely on the propagation of chaos result. Our method constructs a pseudo MV-SDE using It么 calculus, then quantifies the discrepancy between this equation and the original MV-SDE, with the error minimized through a loss function. This loss is controlled via an optimization algorithm, independent of the time step size, and we provide an error estimate for the loss function. The advantages of our approach are demonstrated through corresponding simulations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.00780v1-abstract-full').style.display = 'none'; document.getElementById('2501.00780v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.20754">arXiv:2412.20754</a> <span> [<a href="https://arxiv.org/pdf/2412.20754">pdf</a>, <a href="https://arxiv.org/format/2412.20754">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"> Selberg, Ihara and Berkovich </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Jialun Li</a>, <a href="/search/math?searchtype=author&query=Matheus%2C+C">Carlos Matheus</a>, <a href="/search/math?searchtype=author&query=Pan%2C+W">Wenyu Pan</a>, <a href="/search/math?searchtype=author&query=Tao%2C+Z">Zhongkai Tao</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="2412.20754v1-abstract-short" style="display: inline;"> We use the Selberg zeta function to study the limit behavior of resonances in a degenerating family of Kleinian Schottky groups. We prove that, after a suitable rescaling, the Selberg zeta functions converge to the Ihara zeta function of a limiting finite graph associated to the relevant non-Archimedean Schottky group acting on the Berkovich projective line. Moreover, we show that these techniqu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.20754v1-abstract-full').style.display = 'inline'; document.getElementById('2412.20754v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.20754v1-abstract-full" style="display: none;"> We use the Selberg zeta function to study the limit behavior of resonances in a degenerating family of Kleinian Schottky groups. We prove that, after a suitable rescaling, the Selberg zeta functions converge to the Ihara zeta function of a limiting finite graph associated to the relevant non-Archimedean Schottky group acting on the Berkovich projective line. Moreover, we show that these techniques can be used to get an exponential error term in a result of McMullen (recently extended by Dang and Mehmeti) about the asymptotics for the vanishing rate of the Hausdorff dimension of limit sets of certain degenerating Schottky groups generating symmetric three-funnel surfaces. Here, one key idea is to introduce an intermediate zeta function capturing \emph{both} non-Archimedean and Archimedean information (while the traditional Selberg, resp. Ihara zeta functions concern only Archimedean, resp. non-Archimedean properties). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.20754v1-abstract-full').style.display = 'none'; document.getElementById('2412.20754v1-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> 30 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">54 pages, 4 figures</span> </p> </li> </ol> <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=Li%2C+J&start=50" class="pagination-next" >Next 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