数学最新文献

{"title":"EXPECTATION-MAXIMIZATION FOR STRUCTURE DETERMINATION DIRECTLY FROM CRYO-EM MICROGRAPHS.","authors":"Shay Kreymer, Amit Singer, Tamir Bendory","doi":"10.3934/ipi.2026033","DOIUrl":"10.3934/ipi.2026033","url":null,"abstract":"<p><p>A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional (3-D) molecular structure at unknown locations, taken under unknown viewing directions. All existing cryo-EM algorithmic pipelines first locate and extract the projection images, and then reconstruct the structure from the extracted images. However, if the molecular structure is small, the signal-to-noise ratio (SNR) of the data is very low, making it challenging to accurately detect projection images within the micrograph. Consequently, all standard techniques fail in low-SNR regimes. To recover molecular structures from measurements of low SNR, and in particular small molecular structures, we devise an approximate expectation-maximization algorithm to estimate the 3-D structure directly from the micrograph, bypassing the need to locate the projection images. We corroborate our computational scheme with numerical experiments and present successful structure recoveries from simulated noisy measurements.</p>","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"27 ","pages":"110-133"},"PeriodicalIF":1.6,"publicationDate":"2027-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13384443/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148609636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Threshold dynamics of a reaction-diffusion-advection schistosomiasis model with seasonality","authors":"Yijie Zha ,&nbsp;Xun Cao","doi":"10.1016/j.nonrwa.2026.104617","DOIUrl":"10.1016/j.nonrwa.2026.104617","url":null,"abstract":"<div><div>This paper proposes a reaction-diffusion-advection schistosomiasis model with seasonality based on the life cycle of schistosomiasis (humans, eggs, snails, and cercariae). Using the next generation operator theory, we define the basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> that characterizes the transmission potential of schistosomiasis, and further reveal the threshold dynamics of the system through the monotone dynamical system theory. Specifically, if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, the disease-free periodic solution is globally asymptotically stable, meaning that schistosomiasis will die out; if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, the system admits a unique positive periodic solution that is globally asymptotically stable, indicating that the disease will break out. Numerically, we use data from Ourinhos, Brazil, to analyze the impact of diffusion rates, spatial heterogeneity, advection rates, and seasonality on the transmission of schistosomiasis.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"92 ","pages":"Article 104617"},"PeriodicalIF":1.8,"publicationDate":"2026-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116723","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}

{"title":"Well-posedness results and global attractors for a generalized coupled dynamical system","authors":"Xiuwen Li ,&nbsp;Zhenhai Liu ,&nbsp;Jing Zhao","doi":"10.1016/j.nonrwa.2026.104615","DOIUrl":"10.1016/j.nonrwa.2026.104615","url":null,"abstract":"<div><div>Our present paper investigates theoretical results concerning the well-posedness and global attractor of a novel class of generalized coupling dynamical systems (GCDSs). The system comprises an abstract nonlinear differential inclusion with a history-dependent (h.d.) operator and a generalized variational-hemivariational inequality (GVHVI) with two h.d. operators, formulated within Banach spaces. Our study unfolds in four key aspects. First, we introduce and establish the well-posedness results of the GVHVI by employing the surjectivity theorem for multivalued mappings and techniques from nonlinear functional analysis. Second, we consider and discuss the existence of solutions to the GCDSs by using fixed-point theory under some suitable assumptions. Third, we explore and derive the existence of global attractors for the multivalued semiflow (<em>m</em>-semiflow) described by the GCDSs under some sufficient conditions. Finally, we present an application to a coupled problem, demonstrating the applicability of our theoretical findings.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"92 ","pages":"Article 104615"},"PeriodicalIF":1.8,"publicationDate":"2026-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116724","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}

{"title":"Ill-Posedness of the Euler Equations Linearized around Homogeneous Steady States","authors":"Matei P. Coiculescu","doi":"10.1007/s00021-026-01074-x","DOIUrl":"10.1007/s00021-026-01074-x","url":null,"abstract":"<div><p>Let <span>(L^2_m(mathbb {R}^2))</span> be the space of square-integrable functions on <span>(mathbb {R}^2)</span> with <i>m</i>-fold rotational symmetry. Let <span>(overline{omega }(r,theta ) = r^{-alpha }f(theta ))</span> be a homogeneous steady state of the two-dimensional incompressible Euler equations with <span>((mcdot l))</span>-fold rotational symmetry. If <span>(f(theta ))</span> is a constant function we say that <span>(overline{omega })</span> is a radial power-law vortex. We prove that the incompressible Euler equations in vorticity form, linearized around any homogeneous steady state <span>(overline{omega })</span> that is not a radial power-law vortex, are ill-posed on <span>(L^2_m(mathbb {R}^2))</span> for any <span>(mge 2)</span>, any <span>(lge 1)</span> and <span>(alpha in (0,1))</span>.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"29 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149369250","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}

{"title":"Binary normal networks without near reticulations can be reconstructed from their rooted triples.","authors":"Andrew Francis, Charles Semple","doi":"10.1007/s00285-026-02483-2","DOIUrl":"https://doi.org/10.1007/s00285-026-02483-2","url":null,"abstract":"<p><p>Normal networks are an important class of phylogenetic networks that have compelling mathematical properties which align with intuition about inference from genetic data. While tools enabling widespread use of phylogenetic networks in the biological literature are still under mathematical, statistical, and computational development, many such results are being assembled, and in particular for normal phylogenetic networks. For instance, it has been shown that binary normal networks can be reconstructed from the sets of three- and four-leaf rooted phylogenetic trees that they display. It is also known that one can reconstruct particular subclasses of normal networks from just the displayed rooted triples. This applies, for instance, to rooted binary phylogenetic trees and to binary level-1 normal networks. In this paper we address the question of how much of the class of binary normal networks can be reconstructed from just the rooted triples that they display. We find that all except those with substructures that we call \"near-sibling reticulations\" and \"near-stack reticulations\" can be reconstructed just from their rooted triples. This goes some way to answering the natural question of how much information can be extracted from a set of displayed rooted triples, which are arguably the simplest substructure that one may hope for in a phylogenetic object.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149372052","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":"On Zermelo’s Planar Navigation Problem for Convex Bodies, and Implications for Non-convex Optimal Routing","authors":"Matteo Della Rossa,&nbsp;Lorenzo Freddi,&nbsp;Mattia Pinatto","doi":"10.1007/s00245-026-10541-w","DOIUrl":"10.1007/s00245-026-10541-w","url":null,"abstract":"<div><p>We study a generalized version of Zermelo’s navigation problem where the set of admissible velocities is a general compact convex set, replacing the classical Euclidean ball. After establishing existence results under the natural assumption of weak currents, we derive necessary optimality conditions via Pontryagin’s maximum principle and convex analysis. Consequently, in the planar case, the domain of any optimal control is shown to be partitioned into regular and singular regimes. In the former, the optimal control is regular and, under mild additional assumptions, satisfies a Zermelo-like navigation equation while in the latter it is largely undetermined. A necessary condition that can exclude singular regimes is stated and proved, providing a useful tool in applications. In regular regimes our results extend the classical Zermelo navigation equation to general convex control sets within a non-parametric setting. Furthermore, we discuss direct applications to the case of a non-convex control set. As an application, we develop the relevant case of an affine current. The results are illustrated with examples relevant to sailing and ship routing with asymmetric or sail-assisted propulsion, including the presence of waves.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"95 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338638","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":"Relationship between haptotaxis and chemotaxis in cell dynamics.","authors":"Hiroshi Ishii, Hideki Murakawa, Yoshitaro Tanaka","doi":"10.1007/s00285-026-02482-3","DOIUrl":"https://doi.org/10.1007/s00285-026-02482-3","url":null,"abstract":"<p><p>Cell sorting mediated by direct cell-cell contact or cellular protrusions can be described by nonlocal cell-cell adhesion models of haptotaxis type, whereas communication through diffusible chemical signals is described by Keller-Segel type chemotaxis systems. We investigate the mathematical relationship between these two descriptions. We first prove that, in the fast signal diffusion limit, subsequences of weak solutions of a Keller-Segel type parabolic-parabolic chemotaxis system with possibly degenerate nonlinear diffusion and density saturation converge to weak solutions of the corresponding parabolic-elliptic system. Eliminating the elliptic chemical fields rewrites the population equation as a nonlocal adhesion model whose interaction kernel is a finite linear combination of Green functions. We then prove, in arbitrary spatial dimensions, that the periodization of the gradient of a prescribed radially symmetric interaction potential can be approximated by finite linear combinations of gradients of Green functions. Combining these results, we prove that suitable weak solutions of the nonlocal adhesion model and a parabolic-parabolic chemotaxis system can be chosen with an arbitrarily small difference over any fixed finite time interval. Numerical simulations compare the nonlocal, parabolic-elliptic, and parabolic-parabolic models and examine how the number of kernel terms and the relaxation time affect their differences.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149372053","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":"Age-structured HPV dynamics under randomly switching epidemiological regimes.","authors":"Serigne Diagne, Maryam Diarra, Ousmane Seydi","doi":"10.1007/s00285-026-02480-5","DOIUrl":"https://doi.org/10.1007/s00285-026-02480-5","url":null,"abstract":"<p><p>Human papillomavirus (HPV) is a common sexually transmitted infection whose transmission and disease progression depend strongly on age and are shaped by prevention strategies such as vaccination and screening. Temporal changes in transmission conditions, contact patterns, and healthcare conditions may induce epidemiological regimes that switch over time, making it difficult to characterize long-term transmission and invasion thresholds. We study an age-structured model for HPV transmission in a randomly fluctuating epidemiological environment, where temporal variability in epidemiological conditions is represented by a finite-state continuous-time Markov chain, while vaccination is assumed to remain fixed across regimes. Each regime is governed by a deterministic age-structured system. Using semigroup methods, we characterize the invasion threshold of the randomly switching system, relate it to the reproduction numbers of the regime-specific models, and derive fast- and slow-switching limits. We further establish exponential extinction of the infected population in mean and almost surely when the random reproduction number is below one, while above the threshold we obtain instability of the linearized first-moment dynamics. Our results provide a rigorous mathematical framework for understanding HPV dynamics under temporally varying epidemiological conditions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149372051","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":"Seifert cobordisms and the Chen–Yang volume conjecture","authors":"Renaud Detcherry,&nbsp;Efstratia Kalfagianni,&nbsp;Shashini Marasinghe","doi":"10.1112/jlms.70760","DOIUrl":"https://doi.org/10.1112/jlms.70760","url":null,"abstract":"<p>We study the large-<span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math> asymptotic behavior of the Turaev–Viro invariants <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>;</mo>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mfrac>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>π</mi>\u0000 <mi>i</mi>\u0000 </mrow>\u0000 <mi>r</mi>\u0000 </mfrac>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$TV_r(M; e^{frac{2pi i}{r}})$</annotation>\u0000 </semantics></math> of 3-manifolds with toroidal boundary, under the operation of gluing a Seifert-fibered 3-manifold along a component of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>M</mi>\u0000 </mrow>\u0000 <annotation>$partial M$</annotation>\u0000 </semantics></math>. We show that the Turaev–Viro invariants volume conjecture is closed under this operation. As an application, we prove the volume conjecture for all Seifert fibered 3-manifolds with boundary and for large classes of graph 3-manifolds.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 5","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70760","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149356423","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":"Restricted mean time lost ratio regression: percentage of restricted mean time lost due to specific cause.","authors":"Thomas Scheike, Shiro Tanaka","doi":"10.1007/s10985-026-09726-w","DOIUrl":"https://doi.org/10.1007/s10985-026-09726-w","url":null,"abstract":"<p><p>The restricted mean time (RMST) up to a given time horizon has increased in popularity due to its more direct interpretation in terms of average time alive. In the competing risks setting, Andersen (2013) showed how the RMST can be decomposed into different causes of death via the restricted mean time lost (RMTL), still up to the given time horizon, and how one can perform regression for such an outcome. In practical work, when interpreting the effects of covariates in the competing risks setting, one should consider how covariates affect the RMTL for the different causes of death. We suggest that a useful way to do this is to consider regression models for the relationship between the total RMTL and the RMTL due to different causes. This leads to RMTL ratio regression models where the percentage of the RMTL is modeled via some regression model, such as logistic regression leading to an odds-ratio interpretation of covariate effects, or by log-odds product models that have the advantage of giving the percentage for a key prognostic factor. The methodology can be extended to the full decomposition of RMTL into all considered causes of death by using multinomial regression models or the similar extension of the log-odds product models. We show how to achieve the locally semiparametrically efficient estimator for ratio-regression models. Finally, we address how the ratio can be estimated in a causal setting.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149358156","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}