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3-d Shock-Free Compressible Euler Flows with Amplitude Blowup and Pile-Up of Characteristics 具有振幅放大和堆积特性的三维无激波可压缩欧拉流
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-10-16 DOI: 10.1007/s00205-026-02260-x
Helge Kristian Jenssen
{"title":"3-d Shock-Free Compressible Euler Flows with Amplitude Blowup and Pile-Up of Characteristics","authors":"Helge Kristian Jenssen","doi":"10.1007/s00205-026-02260-x","DOIUrl":"10.1007/s00205-026-02260-x","url":null,"abstract":"<div><p>Recent works have demonstrated that self-similar radial Euler flows of an ideal polytropic gas in 2 and 3 dimensions can drive primary (non-differentiated) flow variables to infinity at the center of motion. Unsurprisingly, this type of behavior can generate an outgoing shock wave from the point of collapse. In this work we prove that there is an alternative scenario possible in 3-d flow: an incoming, radial <span>(C^1)</span> flow suffers blowup at a single point, including in density and pressure, and yet remains <span>(C^1)</span> beyond collapse. No shock is generated despite the fact that the density gradient <span>(nabla _{{textbf{x}}}rho )</span>, as well as the density of characteristics, becomes unbounded at the center of motion at time of blowup. Furthermore, we verify that this behavior is possible even in cases where the fluid is everywhere moving toward the center of motion at time of collapse, in which case also <span>({{,textrm{div},}}_{{textbf{x}}}{textbf{u}}rightarrow -infty )</span>. These phenomena underscore the subtlety of shock formation in multi-d flow.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189733","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}
引用次数: 0
Symbolic dynamics for nonuniformly hyperbolic flows in high dimension 高维非均匀双曲流的符号动力学
IF 1.4 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2026-10-16 DOI: 10.1112/jlms.70731
Yuri Lima, Juan Carlos Mongez, João Paulo Nascimento
{"title":"Symbolic dynamics for nonuniformly hyperbolic flows in high dimension","authors":"Yuri Lima,&nbsp;Juan Carlos Mongez,&nbsp;João Paulo Nascimento","doi":"10.1112/jlms.70731","DOIUrl":"https://doi.org/10.1112/jlms.70731","url":null,"abstract":"<p>We construct symbolic dynamics for flows with positive speed in any dimension: for each <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$chi &gt;0$</annotation>\u0000 </semantics></math>, we code a set that has full measure for every invariant probability measure that is <span></span><math>\u0000 <semantics>\u0000 <mi>χ</mi>\u0000 <annotation>$chi$</annotation>\u0000 </semantics></math>-hyperbolic. In particular, the coded set contains all hyperbolic periodic orbits with Lyapunov exponents outside of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mo>−</mo>\u0000 <mi>χ</mi>\u0000 <mo>,</mo>\u0000 <mi>χ</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$[-chi,chi]$</annotation>\u0000 </semantics></math>. This extends the recent work of Buzzi, Crovisier, and Lima for three-dimensional flows with positive speed [Buzzi et al., Adv. Math. <b>479</b> (2025), 110410]. As an application, we code homoclinic classes of measures by suspensions of irreducible countable Markov shifts, and prove that each such class has at most one probability measure that maximizes the entropy.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149206079","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}
引用次数: 0
Monitoring the convergence speed of PDHG to find better primal and dual step sizes 监测PDHG的收敛速度，寻找较好的原步长和双步长
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2026-10-16 DOI: 10.1093/imanum/drag084
Olivier Fercoq
{"title":"Monitoring the convergence speed of PDHG to find better primal and dual step sizes","authors":"Olivier Fercoq","doi":"10.1093/imanum/drag084","DOIUrl":"https://doi.org/10.1093/imanum/drag084","url":null,"abstract":"Abstract Primal–dual algorithms for the resolution of convex–concave saddle point problems usually come with one or several step size parameters. Within the range where convergence is guaranteed choosing well the step size can make the difference between a slow or a fast algorithm. A usual way to adaptively set step sizes is to ensure that there is a fair balance between primal and dual variable’s amount of change. In this work we show how to find empirically better step sizes for the primal–dual hybrid gradient (PDHG), that is, step sizes that decrease faster than the objective value in practice. Getting inspiration from quadratic problems we base our method on a spectral radius estimation procedure and try to minimize this spectral radius, which is directly related to the rate of convergence. Building on power iterations we could produce spectral radius estimates that are always smaller than 1 and work also in the case of conjugate principal eigenvalues. Moreover, since our spectral radius estimates only rely on residual norms our method can be readily adapted to more general convex–concave saddle point problems. In a second part we extend these results to a randomized version of PDHG called PURE-CD. We design a statistical test to compare observed convergence rates and decide whether a step size is better than another. Numerical experiments on least squares, sparse SVM, TV-L1 denoising, TV-L2 denoising, square-root lasso and logistic regression problems support our findings.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"12 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208860","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}
引用次数: 0
Multiscale Spatio-Temporal Data Monitoring Using Forward Elimination and Scale Information Criterion 基于前向消去和尺度信息准则的多尺度时空数据监测
IF 3.7 1区 数学
Journal of the American Statistical Association Pub Date : 2026-10-16 DOI: 10.1080/01621459.2026.2742473
Kai Yang,Peihua Qiu
{"title":"Multiscale Spatio-Temporal Data Monitoring Using Forward Elimination and Scale Information Criterion","authors":"Kai Yang,Peihua Qiu","doi":"10.1080/01621459.2026.2742473","DOIUrl":"https://doi.org/10.1080/01621459.2026.2742473","url":null,"abstract":"","PeriodicalId":17227,"journal":{"name":"Journal of the American Statistical Association","volume":"20 1","pages":"1-86"},"PeriodicalIF":3.7,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208607","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}
引用次数: 0
Error bounds for full space-time splitting discretizations of semilinear SPDEs—with a focus on dG domain decompositions 半线性spdes全时空分裂离散化的误差界，重点研究了dG域分解
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2026-10-16 DOI: 10.1093/imanum/drag087
Monika Eisenmann,Eskil Hansen,Marvin Jans
{"title":"Error bounds for full space-time splitting discretizations of semilinear SPDEs—with a focus on dG domain decompositions","authors":"Monika Eisenmann,Eskil Hansen,Marvin Jans","doi":"10.1093/imanum/drag087","DOIUrl":"https://doi.org/10.1093/imanum/drag087","url":null,"abstract":"Abstract We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a noniterative domain decomposition approach. Such methods can help to parallelize the code and utilize distributed hardware. The domain decomposition is integrated via the Douglas–Rachford splitting scheme, in which each split operator acts on a single part of the domain. For an efficient space discretization of the underlying equation we chose the discontinuous Galerkin method as it suits the parallelization strategy well. For this fully discretized scheme we provide a strong space-time convergence result under easily verifiable stability assumptions. We conclude the manuscript with numerical experiments validating our theoretical findings.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"53 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149210372","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}
引用次数: 0
Low-rank approximation of analytic kernels 解析核的低秩逼近
IF 2.1 2区 数学
IMA Journal of Numerical Analysis Pub Date : 2026-10-16 DOI: 10.1093/imanum/drag083
Marcus Webb
{"title":"Low-rank approximation of analytic kernels","authors":"Marcus Webb","doi":"10.1093/imanum/drag083","DOIUrl":"https://doi.org/10.1093/imanum/drag083","url":null,"abstract":"Abstract Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly low-rank structure occurs is essential for their analysis and further development. This paper provides a framework for bounding the best low-rank approximation error of matrices arising from samples of a kernel that is analytically continuable in one of its variables to an open region of the complex plane. Elegantly, the low-rank approximations used in the proof are computable by rational interpolation using the roots and poles of Zolotarev rational functions, leading to a fast algorithm for their construction.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"51 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208861","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}
引用次数: 0
Inverse Transmutation Operator for (alpha )-Hyperholomorphic Functions in Clifford Analysis Clifford分析中(alpha ) -超全纯函数的逆变换算子
IF 1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-10-16 DOI: 10.1007/s00006-026-01462-6
Doan Cong Dinh, Luong Thi Tuyet
{"title":"Inverse Transmutation Operator for (alpha )-Hyperholomorphic Functions in Clifford Analysis","authors":"Doan Cong Dinh,&nbsp;Luong Thi Tuyet","doi":"10.1007/s00006-026-01462-6","DOIUrl":"10.1007/s00006-026-01462-6","url":null,"abstract":"<div><p>This paper revisits <span>(alpha )</span>-hyperholomorphic functions in Clifford analysis, that is, functions satisfying the equation <span>( Du - ualpha = 0, )</span> where <i>D</i> denotes the Dirac operator in <span>(mathbb {R}^n)</span> and <span>(alpha in mathbb {C}_{0,n})</span>. A transmutation operator for <span>(alpha )</span>-hyperholomorphic functions has previously been constructed, mapping each monogenic function in a star-like domain to an <span>(alpha )</span>-hyperholomorphic one. In the present work, we derive explicit integral kernels for the inverse of this operator.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189663","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}
引用次数: 0
Degenerations of the Fourth Order q-Garnier System Arising from Confluences in Quivers 颤振中汇聚引起的四阶q-Garnier系统的退化
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-10-16 DOI: 10.1007/s11040-026-09595-7
Kazuya Matsugashita, Takao Suzuki, Satoshi Tsuchimi
{"title":"Degenerations of the Fourth Order q-Garnier System Arising from Confluences in Quivers","authors":"Kazuya Matsugashita,&nbsp;Takao Suzuki,&nbsp;Satoshi Tsuchimi","doi":"10.1007/s11040-026-09595-7","DOIUrl":"10.1007/s11040-026-09595-7","url":null,"abstract":"<div><p>The <i>q</i>-Garnier system was first proposed by Sakai, and alternative directions for its discrete time evolutions were provided by Nagao and Yamada. Recently, it was shown that all of those evolution directions are derived from a birational representation of an extended affine Weyl group which arises from the cluster algebraic construction established by Masuda, Okubo and Tsuda. In this article, we investigate a degeneration structure of the fourth order <i>q</i>-Garnier system by using confluences in quivers.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189739","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}
引用次数: 0
A research on machine learning based gene selection algorithms for RNA-seq data. 基于机器学习的RNA-seq数据基因选择算法研究。
IF 0.4 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2026-10-16 eCollection Date: 2026-01-01 DOI: 10.1515/sagmb-2025-0074
Merve Kasikci, Osman Dag
{"title":"A research on machine learning based gene selection algorithms for RNA-seq data.","authors":"Merve Kasikci, Osman Dag","doi":"10.1515/sagmb-2025-0074","DOIUrl":"https://doi.org/10.1515/sagmb-2025-0074","url":null,"abstract":"<p><p>Discovering differentially expressed genes (DEGs) is an essential process for diagnosis and treatment. In this study, we evaluate the capacity of machine learning algorithms to identify genes that are simulated as truly differentially expressed. We first obtain nine real datasets from The Cancer Genome Atlas Program. We conduct Monte Carlo simulation by exploring the characteristics of the real datasets (i.e. the number of genes). Since these datasets have highly imbalanced class distributions, datasets with the same characteristics are also generated with balanced class ratios. In this way, 18 scenarios are obtained with a total number of 19,947 genes of which 10 genes are simulated significantly different between the two groups. After the pre-processing steps including filtering, normalization, transformation and univariate analysis, gene selection is conducted with five machine learning algorithms. These are biosigner algorithm, GMDH-type neural network algorithm, Determan's optimal gene selection algorithm with random forest, support vector machines and elastic net generalized linear models. Five-fold cross validation is used for improving gene selection performances. Recall, precision and F-measure are taken into account for the evaluation of gene selection performances. All algorithms show higher average performance in balanced scenarios than in unbalanced scenarios. Elastic net generally achieves favorable average performance in both balanced and unbalanced scenarios.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"25 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197238","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}
引用次数: 0
Deciphering dengue fever transmission on higher-order networks. 破译登革热在高阶网络上的传播。
IF 2.7 4区 数学
Journal of Mathematical Biology Pub Date : 2026-10-15 DOI: 10.1007/s00285-026-02433-y
Linhe Zhu, Bingxin Li, Shuling Shen
{"title":"Deciphering dengue fever transmission on higher-order networks.","authors":"Linhe Zhu, Bingxin Li, Shuling Shen","doi":"10.1007/s00285-026-02433-y","DOIUrl":"https://doi.org/10.1007/s00285-026-02433-y","url":null,"abstract":"<p><p>Dengue fever is a viral infection transmitted to humans through the bites of infected mosquitoes. Modeling dengue transmission is crucial for control, given its risk to half the world's population. This paper develops a host-to-host transmission model within hypergraphs constructed from simplicial complexes. Necessary conditions for the emergence of Turing instability in dengue dynamical systems naturally coupled on hypergraphs are derived. Furthermore, a multiplex network framework is constructed on hypergraphs by incorporating the influence of information on dengue transmission, and expressions for dengue outbreak thresholds are derived. Theoretical results are verified through numerical simulations. The Turing instability phenomenon in higher-order networks is investigated, while periodic diffusion effects are analyzed. Higher-order networks elevate the thresholds for dengue outbreaks within the multiplex network framework. Finally, to link theory with practice, we employ Physics-Informed Neural Networks (PINNs) to fit and predict dengue case data. By embedding the transmission model as physical constraints and constructing hypergraphs informed by geographical adjacency and tourism mobility, the PINNs achieves interpretable predictions and accurate parameter estimation. This study offers a feasible framework for understanding and predicting dengue transmission in complex real-world environments.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197343","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}
引用次数: 0
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