数学最新文献

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Neck-pinching of <ns0:math> <ns0:mrow><ns0:mrow><ns0:mi>C</ns0:mi> <ns0:msup><ns0:mi>P</ns0:mi> <ns0:mn>1</ns0:mn></ns0:msup> </ns0:mrow> </ns0:mrow> </ns0:math> -structures in the <ns0:math> <ns0:mrow> <ns0:mrow><ns0:msub><ns0:mi>PSL</ns0:mi> <ns0:mn>2</ns0:mn></ns0:msub> <ns0:mi>C</ns0:mi></ns0:mrow> </ns0:mrow> </ns0:math> -character variety.","authors":"Shinpei Baba","doi":"10.1112/topo.70010","DOIUrl":"https://doi.org/10.1112/topo.70010","url":null,"abstract":"<p><p>We characterize a certain neck-pinching degeneration of (marked) <math> <mrow><mrow><mi>C</mi> <msup><mi>P</mi> <mn>1</mn></msup> </mrow> </mrow> </math> -structures on a closed oriented surface <math><mrow><mi>S</mi></mrow> </math> of genus at least two. In a more general setting, we take a path of <math> <mrow><mrow><mi>C</mi> <msup><mi>P</mi> <mn>1</mn></msup> </mrow> </mrow> </math> -structures <math> <mrow> <mrow><msub><mi>C</mi> <mi>t</mi></msub> <mspace></mspace> <mrow><mo>(</mo> <mi>t</mi> <mo>⩾</mo> <mn>0</mn> <mo>)</mo></mrow> </mrow> </mrow> </math> on <math><mrow><mi>S</mi></mrow> </math> that leaves every compact subset in its deformation space, such that the holonomy of <math> <mrow><msub><mi>C</mi> <mi>t</mi></msub> </mrow> </math> converges in the <math> <mrow> <mrow><msub><mi>PSL</mi> <mn>2</mn></msub> <mi>C</mi></mrow> </mrow> </math> -character variety as <math> <mrow><mrow><mi>t</mi> <mo>→</mo> <mi>∞</mi></mrow> </mrow> </math> . Then, it is well known that the complex structure <math> <mrow><msub><mi>X</mi> <mi>t</mi></msub> </mrow> </math> of <math> <mrow><msub><mi>C</mi> <mi>t</mi></msub> </mrow> </math> also leaves every compact subset in the Teichmüller space of <math><mrow><mi>S</mi></mrow> </math> . In this paper, under an additional assumption that <math> <mrow><msub><mi>X</mi> <mi>t</mi></msub> </mrow> </math> is pinched along a loop <math><mrow><mi>m</mi></mrow> </math> on <math><mrow><mi>S</mi></mrow> </math> , we describe the limit of <math> <mrow><msub><mi>C</mi> <mi>t</mi></msub> </mrow> </math> from different perspectives: namely, in terms of the developing maps, holomorphic quadratic differentials, and pleated surfaces. The holonomy representations of <math> <mrow><mrow><mi>C</mi> <msup><mi>P</mi> <mn>1</mn></msup> </mrow> </mrow> </math> -structures on <math><mrow><mi>S</mi></mrow> </math> are known to be nonelementary (i.e., strongly irreducible and unbounded). We also give a rather exotic example of such a path <math> <mrow><msub><mi>C</mi> <mi>t</mi></msub> </mrow> </math> whose limit holonomy is the trivial representation.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 1","pages":"e70010"},"PeriodicalIF":0.8,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11685183/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142916395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial reduction from syndrome decoding problem to regular decoding problem","authors":"Pavol Zajac","doi":"10.1007/s10623-025-01567-2","DOIUrl":"https://doi.org/10.1007/s10623-025-01567-2","url":null,"abstract":"<p>The regular decoding problem asks for (the existence of) regular solutions to a syndrome decoding problem (SDP). This problem has increased applications in post-quantum cryptography and cryptanalysis. Recently, Esser and Santini explored in depth the connection between the regular (RSD) and classical syndrome decoding problems. They have observed that while RSD to SDP reductions are known (in any parametric regime), a similar generic reduction from SDP to RSD is not known. In our contribution, we examine two different generic polynomial reductions from a syndrome decoding problem to a regular decoding problem instance. The first reduction is based on constructing a special parity check matrix that encodes weight counter progression inside the parity check matrix, which is then the input of the regular decoding oracle. The target regular decoding problem has a significantly longer code length, that depends linearly on the weight parameter of the original SDP. The second reduction is based on translating the SDP to a non-linear system of equations in the Multiple Right-Hand Sides form, and then applying RSD oracle to solve this system. The second reduction has better code length. The ratio between RSD and SDP code length of the second reduction can be bounded by a constant (less than 8).</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"114 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial lower bound on the effective resistance for the one‐dimensional critical long‐range percolation","authors":"Jian Ding, Zherui Fan, Lu‐Jing Huang","doi":"10.1002/cpa.22243","DOIUrl":"https://doi.org/10.1002/cpa.22243","url":null,"abstract":"In this work, we study the critical long‐range percolation (LRP) on , where an edge connects and independently with probability 1 for and with probability for some fixed . Viewing this as a random electric network where each edge has a unit conductance, we show that with high probability the effective resistances from the origin 0 to and from the interval to (conditioned on no edge joining and ) both have a polynomial lower bound in . Our bound holds for all and thus rules out a potential phase transition (around ) which seemed to be a reasonable possibility.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"66 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Approximation of Discontinuous Solutions of the Semilinear Wave Equation","authors":"Jiachuan Cao, Buyang Li, Yanping Lin, Fangyan Yao","doi":"10.1137/24m1635879","DOIUrl":"https://doi.org/10.1137/24m1635879","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 214-238, February 2025. <br/> Abstract. A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can capture the discontinuities of the solutions correctly without spurious oscillations and approximate rough and discontinuous solutions with a higher convergence rate than preexisting methods. Rigorous analysis is presented for the convergence rates of the proposed method in approximating solutions such that [math] for [math]. For discontinuous solutions of bounded variation in one dimension (which allow jump discontinuities), the proposed method is proved to have almost first-order convergence under the step size condition [math], where [math] and [math] denote the time step size and the number of Fourier terms in the space discretization, respectively. Numerical examples are presented in both one and two dimensions to illustrate the advantages of the proposed method in improving the accuracy in approximating rough and discontinuous solutions of the semilinear wave equation. The numerical results are consistent with the theoretical results and show the efficiency of the proposed method.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"20 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143050861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stabilizing Decomposition of Multiparameter Persistence Modules","authors":"Håvard Bakke Bjerkevik","doi":"10.1007/s10208-025-09695-w","DOIUrl":"https://doi.org/10.1007/s10208-025-09695-w","url":null,"abstract":"<p>While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be unstable in a certain precise sense. Until now, it has not been clear that there is any way to get around this and build a meaningful stability theory for multiparameter module decomposition. We introduce new tools, in particular <span>(epsilon )</span>-refinements and <span>(epsilon )</span>-erosion neighborhoods, to start building such a theory. We then define the <span>(epsilon )</span>-pruning of a module, which is a new invariant acting like a “refined barcode” that shows great promise to extract features from a module by approximately decomposing it. Our main theorem can be interpreted as a generalization of the algebraic stability theorem to multiparameter modules up to a factor of 2<i>r</i>, where <i>r</i> is the maximal pointwise dimension of one of the modules. Furthermore, we show that the factor 2<i>r</i> is close to optimal. Finally, we discuss the possibility of strengthening the stability theorem for modules that decompose into pointwise low-dimensional summands, and pose a conjecture phrased purely in terms of basic linear algebra and graph theory that seems to capture the difficulty of doing this. We also show that this conjecture is relevant for other areas of multipersistence, like the computational complexity of approximating the interleaving distance, and recent applications of relative homological algebra to multipersistence.</p>","PeriodicalId":55151,"journal":{"name":"Foundations of Computational Mathematics","volume":"48 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Regularization for a Data Source","authors":"Oscar Leong, Eliza O’ Reilly, Yong Sheng Soh, Venkat Chandrasekaran","doi":"10.1007/s10208-025-09693-y","DOIUrl":"https://doi.org/10.1007/s10208-025-09693-y","url":null,"abstract":"<p>In optimization-based approaches to inverse problems and to statistical estimation, it is common to augment criteria that enforce data fidelity with a regularizer that promotes desired structural properties in the solution. The choice of a suitable regularizer is typically driven by a combination of prior domain information and computational considerations. Convex regularizers are attractive computationally but they are limited in the types of structure they can promote. On the other hand, nonconvex regularizers are more flexible in the forms of structure they can promote and they have showcased strong empirical performance in some applications, but they come with the computational challenge of solving the associated optimization problems. In this paper, we seek a systematic understanding of the power and the limitations of convex regularization by investigating the following questions: Given a distribution, what is the optimal regularizer for data drawn from the distribution? What properties of a data source govern whether the optimal regularizer is convex? We address these questions for the class of regularizers specified by functionals that are continuous, positively homogeneous, and positive away from the origin. We say that a regularizer is optimal for a data distribution if the Gibbs density with energy given by the regularizer maximizes the population likelihood (or equivalently, minimizes cross-entropy loss) over all regularizer-induced Gibbs densities. As the regularizers we consider are in one-to-one correspondence with star bodies, we leverage dual Brunn-Minkowski theory to show that a radial function derived from a data distribution is akin to a “computational sufficient statistic” as it is the key quantity for identifying optimal regularizers and for assessing the amenability of a data source to convex regularization. Using tools such as <span>(Gamma )</span>-convergence from variational analysis, we show that our results are robust in the sense that the optimal regularizers for a sample drawn from a distribution converge to their population counterparts as the sample size grows large. Finally, we give generalization guarantees for various families of star bodies that recover previous results for polyhedral regularizers (i.e., dictionary learning) and lead to new ones for a variety of classes of star bodies. </p>","PeriodicalId":55151,"journal":{"name":"Foundations of Computational Mathematics","volume":"48 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A branching model for intergenerational telomere length dynamics.","authors":"Athanasios Benetos, Olivier Coudray, Anne Gégout-Petit, Lionel Lenôtre, Simon Toupance, Denis Villemonais","doi":"10.1007/s00285-025-02185-1","DOIUrl":"https://doi.org/10.1007/s00285-025-02185-1","url":null,"abstract":"<p><p>We build and study an individual based model of the telomere length's evolution in a population across multiple generations. This model is a continuous time typed branching process, where the type of an individual includes its gamete mean telomere length and its age. We study its Malthusian's behaviour and provide numerical simulations to understand the influence of biologically relevant parameters.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"21"},"PeriodicalIF":2.2,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143043216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Total population for a resource-limited single consumer model.","authors":"Xiaoqing He, Wei-Ming Ni, Zihan Ye, Bo Zhang","doi":"10.1007/s00285-025-02186-0","DOIUrl":"https://doi.org/10.1007/s00285-025-02186-0","url":null,"abstract":"<p><p>In the past several decades, much attention has been focused on the effects of dispersal on total populations of species. In Zhang (EL 20:1118-1128, 2017), a rigorous biological experiment was performed to confirm the mathematical conclusion: Dispersal tends to enhance populations under a suitable hypothesis. In addition, mathematical models keeping track of resource dynamics in population growth were also proposed in Zhang (EL 20:1118-1128, 2017) to understand this remarkable phenomenon. In these models, the self-regulated quantity \"loss rate\" of the population seems, in general, difficult to measure experimentally. Our main goal in this paper is to study the effects of relations between the loss rate and the resources, the role of dispersal, and the impact of their interactions on total populations. We compare the total population for small and large diffusion under various correlations between loss rate and the resources. Biological evidence seems to support some specific correlations between the loss rate and the resources.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"20"},"PeriodicalIF":2.2,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143043222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"OP-HHO based feature selection improves the performance of depression classification framework: A gender biased multiband research","authors":"Kun Li, PeiYun Zhong, Li Dong, LingMin Wang, Luo-Luo Jiang","doi":"10.1016/j.amc.2025.129317","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129317","url":null,"abstract":"Depression, as a common yet severe mood disorder, can cause irreversible damage to the brain if not detected and treated in a timely manner. Unfortunately, due to the current limitations of medical and technological conditions, only a small number of patients have been able to receive appropriate treatment. Although the traditional Harris Hawk's Optimization (HHO) algorithm has a strong searching ability for global optima which is helpful of early diagnosis of depression, it is highly prone to getting stuck in local optima during the early iterations. In view of this, the Optimized-Parameter Harris Hawk's Optimization (OP-HHO) algorithm proposed in this study is devised by integrating an exponential decay function. This incorporation endows the algorithm with the capacity to dynamically modulate the search step size, progressively diminish the escape energy, thereby bolstering the local search capabilities and efficaciously circumventing the problem of premature convergence that may stem from overzealous global exploration. The performance of the OP-HHO was tested using 23 benchmark functions. Based on the features selected by the OP-HHO algorithm, depression classification was carried out using the K-Nearest Neighbor (KNN) algorithm in combination with the MODMA database. The accuracy rate reached 96.36% - 97.30% across different brain wave frequencies under happy stimuli, and 100% under sad stimuli. Moreover, the classification results in the overall electroencephalogram (EEG) signals also showed excellent performance. This indicates that the OP-HHO algorithm is highly effective in accurately identifying the key features of depression. Our comparative study conducted reveals the existence of gender differences, which are expected to serve as effective features to further improve the accuracy of depression classification, opening up new avenues for the development of depression diagnosis techniques.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"3 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A difference finite element method based on nonconforming finite element methods for 3D elliptic problems","authors":"Jianjian Song, Dongwoo Sheen, Xinlong Feng, Yinnian He","doi":"10.1007/s10444-025-10219-x","DOIUrl":"https://doi.org/10.1007/s10444-025-10219-x","url":null,"abstract":"<p>In this paper, a class of 3D elliptic equations is solved by using the combination of the finite difference method in one direction and nonconforming finite element methods in the other two directions. A finite-difference (FD) discretization based on <span>(P_1)</span>-element in the <i>z</i>-direction and a finite-element (FE) discretization based on <span>(P_1^{NC})</span>-nonconforming element in the (<i>x</i>, <i>y</i>)-plane are used to convert the 3D equation into a series of 2D ones. This paper analyzes the convergence of <span>(P_1^{NC})</span>-nonconforming finite element methods in the 2D elliptic equation and the error estimation of the <span>({H^1})</span>-norm of the DFE method. Finally, in this paper, the DFE method is tested on the 3D elliptic equation with the FD method based on the <span>(P_1)</span> element in the <i>z</i>-direction and the FE method based on the Crouzeix-Raviart element, the <span>(P_1)</span> linear element, the Park-Sheen element, and the <span>(Q_1)</span> bilinear element, respectively, in the (<i>x</i>, <i>y</i>)-plane.</p>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"44 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}