SIAM Review最新文献_第3页

Book Review:; Big Data Analytics for Smart Transport and Healthcare Systems 书评:;智能交通和医疗系统的大数据分析

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/24m1637581

Esha Datta

引用次数: 0

A Nonlocal-to-Local Approach to Aggregation-Diffusion Equations 聚集扩散方程的非局部到局部方法

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/25m1726248

C. Falcó, R. E. Baker, J. A. Carrillo

{"title":"A Nonlocal-to-Local Approach to Aggregation-Diffusion Equations","authors":"C. Falcó, R. E. Baker, J. A. Carrillo","doi":"10.1137/25m1726248","DOIUrl":"https://doi.org/10.1137/25m1726248","url":null,"abstract":"SIAM Review, Volume 67, Issue 2, Page 353-372, May 2025. <br/> Abstract.Over the past few decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based models and consist of systems of nonlocal partial differential equations. Using differential adhesion between cells as a biological case study, we introduce a novel local model of aggregation-diffusion phenomena. This system of local aggregation-diffusion equations is fourth-order, resembling thin-film or Cahn–Hilliard type equations. In this framework, cell sorting phenomena are explained through relative surface tensions between distinct cell types. The local model emerges as a limiting case of short-range interactions, providing a significant simplification of earlier nonlocal models while preserving the same phenomenology. This simplification makes the model easier to implement numerically and more amenable to calibration to quantitative data. In addition, we discuss recent analytical results based on the gradient flow structure of the model, along with open problems and future research directions.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"17 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143920681","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

Research Spotlights 研究聚光灯

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/24m1717907

Stefan M. Wild

引用次数: 0

The Gross–Pitaevskii Equation and Eigenvector Nonlinearities: Numerical Methods and Algorithms Gross-Pitaevskii方程和特征向量非线性：数值方法和算法

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/22m1516324

Patrick Henning, Elias Jarlebring

引用次数: 0

SIGEST 团体

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/24m1717932

The Editors

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Book Review:; Algorithmic Mathematics in Machine Learning 书评:;机器学习中的算法数学

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/24m1702611

Hollis Williams, Azza M. Algatheem

引用次数: 0

Survey and Review 调查及检讨

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/24m1717890

Marlis Hochbruck

引用次数: 0

Education 教育

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/24m1717919

Hélène Frankowska

引用次数: 0

Computerized Tomography and Reproducing Kernels 计算机断层扫描和核复现

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/23m1616716

Ho Yun, Victor M. Panaretos

{"title":"Computerized Tomography and Reproducing Kernels","authors":"Ho Yun, Victor M. Panaretos","doi":"10.1137/23m1616716","DOIUrl":"https://doi.org/10.1137/23m1616716","url":null,"abstract":"SIAM Review, Volume 67, Issue 2, Page 321-350, May 2025. <br/> Abstract.The X-ray transform is one of the most fundamental integral operators in image processing and reconstruction. In this paper, we revisit the formalism of the X-ray transform by considering it as an operator between reproducing kernel Hilbert spaces (RKHSs). Within this framework, the X-ray transform can be viewed as a natural analogue of Euclidean projection. The RKHS framework considerably simplifies projection image interpolation, and it leads to an analogue of the celebrated representer theorem for the problem of tomographic reconstruction. It leads to methodology that is dimension-free and stands apart from conventional filtered backprojection techniques, as it does not hinge on the Fourier transform. It also allows us to establish sharp stability results at a genuinely functional level (i.e., without recourse to discretization), but in the realistic setting where the data are discrete and noisy. The RKHS framework is versatile, accommodating any reproducing kernel on a unit ball, affording a high level of generality. When the kernel is chosen to be rotation-invariant, explicit spectral representations can be obtained, elucidating the regularity structure of the associated Hilbert spaces. Moreover, the reconstruction problem can be solved at the same computational cost as filtered backprojection.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"37 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143920690","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

Multiobjective Optimization Using the R2 Utility 使用R2实用工具的多目标优化

IF 10.2 1区数学

SIAM Review Pub Date : 2025-05-08 DOI: 10.1137/23m1578371

Ben Tu, Nikolas Kantas, Robert M. Lee, Behrang Shafei

{"title":"Multiobjective Optimization Using the R2 Utility","authors":"Ben Tu, Nikolas Kantas, Robert M. Lee, Behrang Shafei","doi":"10.1137/23m1578371","DOIUrl":"https://doi.org/10.1137/23m1578371","url":null,"abstract":"SIAM Review, Volume 67, Issue 2, Page 213-255, May 2025. <br/> Abstract.The goal of multiobjective optimization is to identify a collection of points which describe the best possible trade-offs among the multiple objectives. In order to solve this vector-valued optimization problem, practitioners often appeal to the use of scalarization functions in order to transform the multiobjective problem into a collection of single-objective problems. This set of scalarized problems can then be solved using traditional single-objective optimization techniques. In this paper, we formalize this convention into a general mathematical framework. We show how this strategy effectively recasts the original multiobjective optimization problem into a single-objective optimization problem defined over sets. An appropriate class of objective functions for this new problem is that of the R2 utilities, which are utility functions that are defined as a weighted integral over the scalarized optimization problem. As part of our work, we show that these utilities are monotone and submodular set functions that can be optimized effectively using greedy optimization algorithms. We then analyze the performance of these greedy algorithms both theoretically and empirically. Our analysis largely focuses on Bayesian optimization, which is a popular probabilistic framework for black-box optimization.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"72 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143927310","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