SIAM Review, Volume 67, Issue 2, Page 405-406, May 2025. Big Data Analytics for Smart Transport and Healthcare Systems explores the praxis of data analysis for urban, human-focused datasets. Through a series of timely case studies, the authors demonstrate the need for interdisciplinary approaches to studying big data. This text, which covers topics ranging from flight status to the COVID-19 pandemic, introduces crucial tools for effective and responsible data science and will prove useful for data scientists across a variety of fields.
{"title":"Book Review:; Big Data Analytics for Smart Transport and Healthcare Systems","authors":"Esha Datta","doi":"10.1137/24m1637581","DOIUrl":"https://doi.org/10.1137/24m1637581","url":null,"abstract":"SIAM Review, Volume 67, Issue 2, Page 405-406, May 2025. <br/> Big Data Analytics for Smart Transport and Healthcare Systems explores the praxis of data analysis for urban, human-focused datasets. Through a series of timely case studies, the authors demonstrate the need for interdisciplinary approaches to studying big data. This text, which covers topics ranging from flight status to the COVID-19 pandemic, introduces crucial tools for effective and responsible data science and will prove useful for data scientists across a variety of fields.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"1 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143920678","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}
SIAM Review, Volume 67, Issue 2, Page 353-372, May 2025. 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.
{"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}
SIAM Review, Volume 67, Issue 2, Page 256-317, May 2025. Abstract.In this review paper, we provide an overview of numerical methods used in the study of the Gross–Pitaevskii eigenvalue problem (GPEVP). The GPEVP is an important nonlinear Schrödinger equation that is used in quantum physics to describe the ground states of ultracold bosonic gases. The discretization of the GPEVP leads to a nonlinear eigenvalue problem with eigenvector nonlinearities. The rich variety of numerical techniques in the literature for tackling the GPEVP has ingredients from linear algebra, partial differential equations, and numerical optimization as well as gradient flows on Riemannian manifolds. We review this heterogeneous body of literature with a focus on a unified treatment of seemingly different approaches, algorithms, and method properties, and we point to open problems and future challenges in the field.
{"title":"The Gross–Pitaevskii Equation and Eigenvector Nonlinearities: Numerical Methods and Algorithms","authors":"Patrick Henning, Elias Jarlebring","doi":"10.1137/22m1516324","DOIUrl":"https://doi.org/10.1137/22m1516324","url":null,"abstract":"SIAM Review, Volume 67, Issue 2, Page 256-317, May 2025. <br/> Abstract.In this review paper, we provide an overview of numerical methods used in the study of the Gross–Pitaevskii eigenvalue problem (GPEVP). The GPEVP is an important nonlinear Schrödinger equation that is used in quantum physics to describe the ground states of ultracold bosonic gases. The discretization of the GPEVP leads to a nonlinear eigenvalue problem with eigenvector nonlinearities. The rich variety of numerical techniques in the literature for tackling the GPEVP has ingredients from linear algebra, partial differential equations, and numerical optimization as well as gradient flows on Riemannian manifolds. We review this heterogeneous body of literature with a focus on a unified treatment of seemingly different approaches, algorithms, and method properties, and we point to open problems and future challenges in the field.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"25 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143920691","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}
SIAM Review, Volume 67, Issue 2, Page 406-408, May 2025. The 2024 Nobel Prize in Physics was awarded to John Hopfield and Geoffrey Hinton for their work on artificial intelligence and machine learning. The award has been somewhat controversial in the physics community and prompted some heated debates, since the only apparent use of physics is the Boltzmann distribution in the sampling function of the Boltzmann machine [D. H. Ackley, G. E. Hinton, and T. J. Sejnowski, Cog. Sci., 9 (1985), pp. 147–169]. If we leave aside this debate for the time being, it is undeniable that artificial intelligence and machine learning have had a transformative effect on various areas of science and technology.
SIAM评论，第67卷，第2期，第406-408页，2025年5月。2024年诺贝尔物理学奖授予约翰·霍普菲尔德和杰弗里·辛顿，以表彰他们在人工智能和机器学习方面的贡献。该奖项在物理界引起了一些争议，并引发了一些激烈的争论，因为物理学的唯一明显用途是玻尔兹曼机抽样函数中的玻尔兹曼分布[D]。H. Ackley， G. E. Hinton， T. J. Sejnowski, Cog。科学。， 9(1985)，第147-169页]。如果我们暂时抛开这个争论，不可否认的是，人工智能和机器学习已经对各个科学技术领域产生了变革性的影响。
{"title":"Book Review:; Algorithmic Mathematics in Machine Learning","authors":"Hollis Williams, Azza M. Algatheem","doi":"10.1137/24m1702611","DOIUrl":"https://doi.org/10.1137/24m1702611","url":null,"abstract":"SIAM Review, Volume 67, Issue 2, Page 406-408, May 2025. <br/> The 2024 Nobel Prize in Physics was awarded to John Hopfield and Geoffrey Hinton for their work on artificial intelligence and machine learning. The award has been somewhat controversial in the physics community and prompted some heated debates, since the only apparent use of physics is the Boltzmann distribution in the sampling function of the Boltzmann machine [D. H. Ackley, G. E. Hinton, and T. J. Sejnowski, Cog. Sci., 9 (1985), pp. 147–169]. If we leave aside this debate for the time being, it is undeniable that artificial intelligence and machine learning have had a transformative effect on various areas of science and technology.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"25 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143920677","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}
SIAM Review, Volume 67, Issue 2, Page 321-350, May 2025. 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.
{"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}
Ben Tu, Nikolas Kantas, Robert M. Lee, Behrang Shafei
SIAM Review, Volume 67, Issue 2, Page 213-255, May 2025. 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.
{"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}
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