数学最新文献

{"title":"Optimal rates for functional linear regression with general regularization","authors":"Naveen Gupta, S. Sivananthan, Bharath K. Sriperumbudur","doi":"10.1016/j.acha.2024.101745","DOIUrl":"https://doi.org/10.1016/j.acha.2024.101745","url":null,"abstract":"Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by employing general spectral regularization to approximate the slope function with certain smoothness assumptions. We establish optimal convergence rates for estimation and prediction errors associated with the proposed method under Hölder type source condition, which generalizes and sharpens all the known results in the literature.","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"83 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874073","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":"An integral renewal equation approach to behavioural epidemic models with information index.","authors":"Bruno Buonomo, Eleonora Messina, Claudia Panico, Antonia Vecchio","doi":"10.1007/s00285-024-02172-y","DOIUrl":"https://doi.org/10.1007/s00285-024-02172-y","url":null,"abstract":"<p><p>We propose an integral model describing an epidemic of an infectious disease. The model is behavioural in the sense that the force of infection includes the information index that describes the opinion-driven human behavioural changes. The information index contains a memory kernel to mimic how the individuals maintain memory of the past values of the infection. We obtain sufficient conditions for the endemic equilibrium to be locally stable. In particular, we show that when the infectivity function is represented by an exponential distribution, stability is guaranteed by the weak Erlang memory kernel. However, through numerical simulations, we show that oscillations, possibly self-sustained, may arise when the memory is more focused in the disease's past history, as exemplified by the strong Erlang kernel. We also show the model solutions in cases of different infectivity functions taken from studies where specific diseases like Influenza and SARS are considered.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"8"},"PeriodicalIF":2.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142840130","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":"Variable-Coefficient Evolution Problems via the Fokas Method Part I: Dissipative Case","authors":"Bernard Deconinck,&nbsp;Matthew Farkas","doi":"10.1111/sapm.12800","DOIUrl":"https://doi.org/10.1111/sapm.12800","url":null,"abstract":"<div>\u0000 \u0000 <p>We derive explicit solution representations for linear, dissipative, second-order initial-boundary value problems (IBVPs) with coefficients that are spatially varying, with linear, constant-coefficient, two-point boundary conditions. We accomplish this by considering the variable-coefficient problem as the limit of a constant-coefficient interface problem, previously solved using the unified transform method of Fokas. Our method produces an explicit representation of the solution, allowing us to determine properties of the solution directly. As explicit examples, we demonstrate the solution procedure for different IBVPs of variations of the heat equation, and the linearized complex Ginzburg-Landau (CGL) equation (periodic boundary conditions). We can use this to find the eigenvalues of dissipative second-order linear operators (including non–self-adjoint ones) as roots of a transcendental function, and we can write their eigenfunctions explicitly in terms of the eigenvalues.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861440","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":"Erratum: Multidimensional Sum-Up Rounding for Elliptic Control Systems","authors":"Paul Manns, Christian Kirches","doi":"10.1137/24m1674169","DOIUrl":"https://doi.org/10.1137/24m1674169","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2782-2783, December 2024. <br/> Abstract. We correct a mistake in the paper [P. Manns and C. Kirches, SIAM J. Numer. Anal., 58 (2020), pp. 3427–3447]. The grid refinement strategy in Definition 4.3 needs to ensure that the order of the (sets of) grid cells that are successively refined is preserved over all grid iterations. This was only partially reflected in Definition 4.3, and we correct it here.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"102 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841374","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":"Corrigendum: A New Lagrange Multiplier Approach for Constructing Structure-Preserving Schemes, II. Bound Preserving","authors":"Qing Cheng, Jie Shen","doi":"10.1137/24m1670895","DOIUrl":"https://doi.org/10.1137/24m1670895","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2784-2787, December 2024. <br/> Abstract. This note is the correction of an error in the proof of Theorem 4.1 in [Q. Cheng and J. Shen, SIAM J. Numer. Anal., 60 (2022), pp. 970–998].","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841425","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":"Swarm-Based Gradient Descent Meets Simulated Annealing","authors":"Zhiyan Ding, Martin Guerra, Qin Li, Eitan Tadmor","doi":"10.1137/24m1657808","DOIUrl":"https://doi.org/10.1137/24m1657808","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2745-2781, December 2024. <br/> Abstract. We introduce a novel method, called swarm-based simulated annealing (SSA), for nonconvex optimization which is at the interface between the swarm-based gradient-descent (SBGD) [J. Lu et al., arXiv:2211.17157; E. Tadmor and A. Zenginoglu, Acta Appl. Math., 190 (2024)] and simulated annealing (SA) [V. Cerny, J. Optim. Theory Appl., 45 (1985), pp. 41–51; S. Kirkpatrick et al., Science, 220 (1983), pp. 671–680; S. Geman and C.-R. Hwang, SIAM J. Control Optim., 24 (1986), pp. 1031–1043]. Similarly to SBGD, we introduce a swarm of agents, each identified with a position, [math] and mass [math], to explore the ambient space. Similarly to SA, the agents proceed in the gradient descent direction, and are subject to Brownian motion. The annealing rate, however, is dictated by a decreasing function of their mass. As a consequence, instead of the SA protocol for time-decreasing temperature, here the swarm decides how to “cool down” agents, depending on their own accumulated mass. The dynamics of masses is coupled with the dynamics of positions: agents at higher ground transfer (part of) their mass to those at lower ground. Consequently, the resulting SSA optimizer is dynamically divided between heavier, cooler agents viewed as “leaders” and lighter, warmer agents viewed as “explorers.” Mean-field convergence analysis and benchmark optimizations demonstrate the effectiveness of the SSA method as a multidimensional global optimizer.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"12 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841384","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":"Concentric-Ring Patterns of Higher-Order Lumps in the Kadomtsev–Petviashvili I Equation","authors":"Bo Yang,&nbsp;Jianke Yang","doi":"10.1111/sapm.70000","DOIUrl":"https://doi.org/10.1111/sapm.70000","url":null,"abstract":"<p>Large-time patterns of general higher-order lump solutions in the Kadomtsev–Petviashvili I (KP-I) equation are investigated. It is shown that when the index vector of the general lump solution is a sequence of consecutive odd integers starting from one, the large-time pattern in the spatial <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(x, y)$</annotation>\u0000 </semantics></math>-plane generically would comprise fundamental lumps uniformly distributed on concentric rings. For other index vectors, the large-time pattern would comprise fundamental lumps in the outer region as described analytically by the nonzero-root structure of the associated Wronskian–Hermite polynomial, together with possible fundamental lumps in the inner region that are uniformly distributed on concentric rings generically. Leading-order predictions of fundamental lumps in these solution patterns are also derived. The predicted patterns at large times are compared to true solutions, and good agreement is observed.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861441","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":"Global Well-Posedness and Asymptotic Behavior of Strong Solutions to an Initial-Boundary Value Problem of 3D Full Compressible MHD Equations","authors":"Hao Xu,&nbsp;Hong Ye,&nbsp;Jianwen Zhang","doi":"10.1007/s00021-024-00915-x","DOIUrl":"10.1007/s00021-024-00915-x","url":null,"abstract":"<div><p>This paper is concerned with an initial-boundary value problem of full compressible magnetohydrodynamics (MHD) equations on 3D bounded domains subject to non-slip boundary condition for velocity, perfectly conducting boundary condition for magnetic field, and homogeneous Dirichlet boundary condition for temperature. The global well-posedness of strong solutions with initial vacuum is established and the exponential decay estimates of the solutions are obtained, provided the initial total energy is suitably small. More interestingly, it is shown that for <span>(pin (3,6))</span>, the <span>(L^p)</span>-norm of the gradient of density remains uniformly bounded for all <span>(tge 0)</span>. This is in sharp contrast to that in (Chen et al. in Global well-posedness of full compressible magnetohydrodynamic system in 3D bounded domains with large oscillations and vacuum. arXiv:2208.04480, Li et al. in Global existence of classical solutions to full compressible Navier–Stokes equations with large oscillations and vacuum in 3D bounded domains. arXiv:2207.00441), where the exponential growth of the gradient of density in <span>(L^p)</span>-norm was explored.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826123","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":"Improved memory and synaptic device performance of HfO2-based multilayer memristor by inserting oxygen gradient TiOx layer","authors":"Jihee Park, Heeseong Jang, Yongjin Byun, Hyesung Na, Hyeonseung Ji, Sungjun Kim","doi":"10.1016/j.chaos.2024.115910","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115910","url":null,"abstract":"Pt/Al/TiO<ce:inf loc=\"post\">x</ce:inf>/HfO<ce:inf loc=\"post\">2</ce:inf>/AlN/Pt devices demonstrate abrupt filamentary resistive switching (RS) that is strongly dependent on the bias polarity due to variations of the defect states in the TiO<ce:inf loc=\"post\">x</ce:inf> layer, which is deposited using pulse direct current (DC) sputtering. In this study, we compare a device with a TiO<ce:inf loc=\"post\">x</ce:inf> layer that serves as an oxygen reservoir layer (which has the same oxygen flow rate) with another device that has three TiO<ce:inf loc=\"post\">x</ce:inf> layers with different oxygen flow rates. Both devices form an AlO<ce:inf loc=\"post\">x</ce:inf> layer that acts as an overshoot suppression layer (OSL) due to a natural oxidation reaction between the TiO<ce:inf loc=\"post\">x</ce:inf> oxygen reservoir layer and the Pt/Al top electrode. Additionally, the ultrathin AlN layer serves as an oxygen barrier layer (OBL) at the interface between the HfO<ce:inf loc=\"post\">2</ce:inf> layer and the Pt/Ti bottom electrode, inhibiting the movement of oxygen ions. The device with three oxygen layers achieves low current characteristics and low-power operation by gradually increasing the breakdown voltage. The optimized device demonstrates excellent linearity in terms of both potentiation and depression based on analog RS characteristics. Moreover, when the change in conductivity is employed as a weight in the neural network, neuromorphic system simulation can achieve a pattern recognition accuracy exceeding 91 %. Essential synaptic functions, including spike-rate-dependent plasticity (SRDP), spike-number-dependent plasticity (SNDP), spike-duration-plasticity (SDDP), and spike amplitude dependent plasticity (SADP), are also demonstrated to mimic biological synapses for neuromorphic computing applications. These results suggest that variations in oxygen flow in the Pt/Al/TiO<ce:inf loc=\"post\">x</ce:inf>/HfO<ce:inf loc=\"post\">2</ce:inf>/AlN/Pt structure could serve as a viable memory device for integration into neuromorphic systems.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"31 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142857627","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":"Exchangeable coalescents beyond the Cannings class.","authors":"Arno Siri-Jégousse, Alejandro H Wences","doi":"10.1007/s00285-024-02173-x","DOIUrl":"https://doi.org/10.1007/s00285-024-02173-x","url":null,"abstract":"<p><p>We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings models, and replace it by a less restrictive condition of non-heritability of reproductive success. We provide a general criterion for the weak convergence of their genealogies to <math><mi>Ξ</mi></math> -coalescents, and apply it to a simple parametrization of our scenario (which, under mild conditions, we also prove to essentially include the general case). We provide examples for such populations, including models with highly-asymmetric offspring distributions and populations undergoing random but recurrent bottlenecks. Finally we study the limit genealogy of a new exponential model which, as previously shown for related models and in spite of its built-in (fitness) inheritance mechanism, can be brought into our setting.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"7"},"PeriodicalIF":2.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142840132","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}