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Multiobjective Optimization Using the R2 Utility SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 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
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Book Review:; Stochastic Integral and Differential Equations in Mathematical Modelling SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Chaman Kumar
SIAM Review, Volume 67, Issue 2, Page 411-411, May 2025. A short discussion on stochastic calculus is given under the assumption that the fundamentals of probability theory are known to readers. Some related basic details on probability theory should have been included to make the book more self-contained. Further, analytic solutions of some stochastic differential equations (SDEs), which are used
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Book Review:; Optimal Mass Transport on Euclidean Spaces SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Leon Bungert
SIAM Review, Volume 67, Issue 2, Page 408-411, May 2025. Optimal transport was originally invented by Gaspard Monge [“Mémoire sur la théorie des déblais et des remblais,” Mem. Math. Phys. Acad. Royale Sci., (1781), pp. 666–704] to model the problem of optimally mapping one distribution of mass onto another. This was later reformulated by Leonid Kantorovich as a well-posed linear program using the notion
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Book Review:; Algorithmic Mathematics in Machine Learning SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Hollis Williams, Azza M. Algatheem
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
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Book Review:; Big Data Analytics for Smart Transport and Healthcare Systems SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Esha Datta
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
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Book Review:; Math in Drag SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Laura W. Layton
SIAM Review, Volume 67, Issue 2, Page 404-405, May 2025. “Math is like a drag queen: marvelous, whimsical, at times even controversial, but never boring!” That it how the preface of Math in Drag begins. It is also an excellent description of the book. Math in Drag was authored by Kyne Santos, who often goes by Kyne. Kyne studied mathematics at the University of Waterloo and went viral teaching math
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Featured Review:; How Data Happened: A History from the Age of Reason to the Age of Algorithms SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Rachel Roca
SIAM Review, Volume 67, Issue 2, Page 401-403, May 2025. It’s 7.30 am when my alarm wakes me up and I am greeted by my notifications. While eating breakfast, I watch videos YouTube recommends to me: sometimes news stories, sometimes my guilty pleasure of a new “Say Yes to the Dress” clip. On my way to campus, I play my daylist, a curated playlist from Spotify based on what I normally listen to on a
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Anita T. Layton
SIAM Review, Volume 67, Issue 2, Page 399-399, May 2025.
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Uncertainty Analysis of a Simple River Quality Model Using Differential Inequalities SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Grace D’Agostino, Hermann J. Eberl
SIAM Review, Volume 67, Issue 2, Page 375-398, May 2025. Abstract.We present and discuss the Streeter–Phelps equations, which were the first river quality model. If the parameters are constants, then the model in its linear formulation can be solved explicitly. This reveals, however, that depending on parameters and initial data, the model might predict negative oxygen concentrations, which marks a
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A Nonlocal-to-Local Approach to Aggregation-Diffusion Equations SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 C. Falcó, R. E. Baker, J. A. Carrillo
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
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Computerized Tomography and Reproducing Kernels SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Ho Yun, Victor M. Panaretos
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
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Research Spotlights SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Stefan M. Wild
SIAM Review, Volume 67, Issue 2, Page 319-319, May 2025.
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The Gross–Pitaevskii Equation and Eigenvector Nonlinearities: Numerical Methods and Algorithms SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Patrick Henning, Elias Jarlebring
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
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Survey and Review SIAM Rev. (IF 10.8) Pub Date : 2025-05-08 Marlis Hochbruck
SIAM Review, Volume 67, Issue 2, Page 211-211, May 2025.
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Book Review:; Mathematical Pictures at a Data Science Exhibition SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Bamdad Hosseini
SIAM Review, Volume 67, Issue 1, Page 208-209, March 2025. The book Mathematical Pictures at a Data Science Exhibition aims to introduce the reader to the many mathematical ideas that congregate under the ever-expanding umbrella of data science. Given the meteoric rise of this field and the immense speed at which it often moves, this book acts as a welcome road map for graduate students and researchers
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Book Review:; Elegant Simulations. From Simple Oscillators to Many-Body Systems SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Omar Morandi
SIAM Review, Volume 67, Issue 1, Page 207-208, March 2025. Elegant Simulations covers various aspects of modeling and simulating mechanical systems described at the elementary level by many-interacting particles. The book presents the topics from an original and fresh point of view. The complex many-body dynamics is reproduced at the elementary level in terms of simple models that are easy to understand
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Book Review:; Essential Statistics for Data Science: A Concise Crash Course SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 David Banks
SIAM Review, Volume 67, Issue 1, Page 206-207, March 2025. This is a bold book! Professor Zhu wants to provide the basic statistical knowledge needed by data scientists in a super-short volume. It reminds me a bit of Larry Wasserman’s All of Statistics (Springer, 2014), but is aimed at Masters students (often from fields other than statistics) or advanced undergraduates (also often from other fields)
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Book Review:; Probability Adventures SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Nevena Marić
SIAM Review, Volume 67, Issue 1, Page 205-206, March 2025. The first look at Probability Adventures brought back memories of a conference in Ubatuba, Brazil, in 2001, where as a young Master’s student I worried that true science had to be deadly serious. Fortunately, several inspiring teachers came to the rescue. Andrei Toom’s words resonated deeply with me when he began his lecture by saying, “Every
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Book Review:; Numerical Methods in Physics with Python. Second Edition SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Gabriele Ciaramella
SIAM Review, Volume 67, Issue 1, Page 204-205, March 2025. Numerical Methods in Physics with Python by Alex Gezerlis is an excellent example of a textbook built on long and established teaching experience. The goals are clearly defined in the preface: Gezerlis aims to gently introduce undergraduate physics students to the branch of numerical methods and their concrete implementation in Python. To this
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Featured Review:; Numerical Integration of Differential Equations SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 John C. Butcher, Robert M. Corless
SIAM Review, Volume 67, Issue 1, Page 197-204, March 2025. The book under review was originally published under the auspices of the National Research Council in 1933 (the year John was born), and it was republished as a Dover edition in 1956 (three years before Rob was born). At 108 pages—including title page, preface, table of contents, and index—it’s very short. Even so, it contains a significant
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Anita T. Layton
SIAM Review, Volume 67, Issue 1, Page 195-196, March 2025.
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Neighborhood Watch in Mechanics: Nonlocal Models and Convolution SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Thomas Nagel, Tymofiy Gerasimov, Jere Remes, Dominik Kern
SIAM Review, Volume 67, Issue 1, Page 176-193, March 2025. Abstract.This paper is intended to serve as a low-hurdle introduction to nonlocality for graduate students and researchers with an engineering mechanics or physics background who did not have a formal introduction to the underlying mathematical basis. We depart from simple examples motivated by structural mechanics to form a physical intuition
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Graph Neural Networks and Applied Linear Algebra SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Nicholas S. Moore, Eric C. Cyr, Peter Ohm, Christopher M. Siefert, Raymond S. Tuminaro
SIAM Review, Volume 67, Issue 1, Page 141-175, March 2025. Abstract.Sparse matrix computations are ubiquitous in scientific computing. Given the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NNs). Unfortunately, multilayer perceptron (MLP) NNs are typically not natural for either graph or sparse matrix computations
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Limits of Learning Dynamical Systems SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Tyrus Berry, Suddhasattwa Das
SIAM Review, Volume 67, Issue 1, Page 107-137, March 2025. Abstract.A dynamical system is a transformation of a phase space, and the transformation law is the primary means of defining as well as identifying the dynamical system and is the object of focus of many learning techniques. However, there are many secondary aspects of dynamical systems—invariant sets, the Koopman operator, and Markov approximations—that
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The Troublesome Kernel: On Hallucinations, No Free Lunches, and the Accuracy-Stability Tradeoff in Inverse Problems SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Nina M. Gottschling, Vegard Antun, Anders C. Hansen, Ben Adcock
SIAM Review, Volume 67, Issue 1, Page 73-104, March 2025. Abstract.Methods inspired by artificial intelligence (AI) are starting to fundamentally change computational science and engineering through breakthrough performance on challenging problems. However, the reliability and trustworthiness of such techniques is a major concern. In inverse problems in imaging, the focus of this paper, there is increasing
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Research Spotlights SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Stefan M. Wild
SIAM Review, Volume 67, Issue 1, Page 71-71, March 2025.
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Risk-Adaptive Approaches to Stochastic Optimization: A Survey SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Johannes O. Royset
SIAM Review, Volume 67, Issue 1, Page 3-70, March 2025. Abstract.Uncertainty is prevalent in engineering design and data-driven problems and, more broadly, in decision making. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey
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Survey and Review SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Marlis Hochbruck
SIAM Review, Volume 67, Issue 1, Page 1-1, March 2025.
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Anita T. Layton
SIAM Review, Volume 66, Issue 4, Page 795-805, November 2024. If you are teaching a course (or otherwise looking for a text) in the techniques and applications of mathematical modeling, or mathematical approaches that analyze or solve those equations, you may find one of the reviews in this issue's collection interesting. Our featured review was written by Shawn Ryan, on the book Mathematical Modeling
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Developing Workforce with Mathematical Modeling Skills SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Ariel Cintrón-Arias, Ryan Andrew Nivens, Anant Godbole, Calvin B. Purvis
SIAM Review, Volume 66, Issue 4, Page 778-792, November 2024. Mathematicians have traditionally been a select group of academics who produce high-impact ideas enabling substantial results in several fields of science. Throughout the past 35 years, undergraduates enrolling in mathematics or statistics have represented a nearly constant proportion of approximately 1% of bachelor degrees awarded in the
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Sandpiles and Dunes: Mathematical Models for Granular Matter SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Piermarco Cannarsa, Stefano Finzi Vita
SIAM Review, Volume 66, Issue 4, Page 751-777, November 2024. Granular materials are everywhere, in the environment but also in our pantry. Their properties are different from those of any solid material, due to the possibility of sudden phenomena such as avalanches or landslides. Here we present a brief survey on their characteristics and on what can be found (from the past thirty years) in the recent
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Education SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Hélène Frankowska
SIAM Review, Volume 66, Issue 4, Page 749-749, November 2024. In this issue the Education section presents two contributions. The first paper, “Sandpiles and Dunes: Mathematical Models for Granular Matter,” by Piermarco Cannarsa and Stefano Finzi Vita, presents a review of mathematical models for formation of sand piles and dunes. In nature and everyday life various materials appear as conglomerates
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A Bridge between Invariant Theory and Maximum Likelihood Estimation SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal
SIAM Review, Volume 66, Issue 4, Page 721-747, November 2024. We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We present a dictionary that relates notions of stability from geometric invariant theory to the existence and uniqueness of a maximum likelihood estimate. Our dictionary holds for both discrete and continuous
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SIGEST SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 The Editors
SIAM Review, Volume 66, Issue 4, Page 719-719, November 2024. The SIGEST article in this issue, “A Bridge between Invariant Theory and Maximum Likelihood Estimation,” by Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, and Anna Seigal, uncovers the deep connections between geometric invariant theory and statistical methods, specifically maximum likelihood estimation (MLE) by connecting it to norm
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Feynman's Inverse Problem SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Adrian Kirkeby
SIAM Review, Volume 66, Issue 4, Page 694-718, November 2024. We analyze an inverse problem for water waves posed by Richard Feynman in the BBC documentary Fun to Imagine. We show that the problem can be modeled as an inverse Cauchy problem for gravity-capillary waves, conduct a detailed analysis of the Cauchy problem, and give a uniqueness proof for the inverse problem. Somewhat surprisingly, this
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Sigmoid Functions, Multiscale Resolution of Singularities, and $hp$-Mesh Refinement SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Daan Huybrechs, Lloyd N. Trefethen
SIAM Review, Volume 66, Issue 4, Page 683-693, November 2024. In this short, conceptual paper we observe that closely related mathematics applies in four contexts with disparate literatures: (1) sigmoidal and RBF approximation of smooth functions, (2) rational approximation of analytic functions with singularities, (3) $hp\kern .7pt$-mesh refinement for solution of \pdes, and (4) double exponential
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Research Spotlights SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Stefan M. Wild
SIAM Review, Volume 66, Issue 4, Page 681-681, November 2024. Logarithmic transformations are used broadly in data science, mathematics, and engineering, and yet they can still reveal surprising connections between seemingly unrelated disciplines. This issue's first research spotlight, “Sigmoid Functions, Multiscale Resolution of Singularities, and $hp$-Mesh Refinement,” illuminates how the change
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Oscillatory Networks: Insights from Piecewise-Linear Modeling SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Stephen Coombes, Mustafa Şayli, Rüdiger Thul, Rachel Nicks, Mason A. Porter, Yi Ming Lai
SIAM Review, Volume 66, Issue 4, Page 619-679, November 2024. There is enormous interest---both mathematically and in diverse applications---in understanding the dynamics of coupled-oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology, and more. It is common to describe the rich emergent behavior in these systems in terms of complex patterns
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Survey and Review SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Marlis Hochbruck
SIAM Review, Volume 66, Issue 4, Page 617-617, November 2024. Neural oscillations are periodic activities of neurons in the central nervous system of eumetazoa. In an oscillatory neural network, neurons are modeled by coupled oscillators. Oscillatory networks are employed for describing the behavior of complex systems in biology or ecology with respect to the connectivity of the network components
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Education SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Hélène Frankowska
SIAM Review, Volume 66, Issue 3, Page 573-573, May 2024. In this issue the Education section presents “Combinatorial and Hodge Laplacians: Similarities and Differences,” by Emily Ribando-Gros, Rui Wang, Jiahui Chen, Yiying Tong, and Guo-Wei Wei. Combinatorial Laplacians and their spectra are important tools in the study of molecular stability, electrical networks, neuroscience, deep learning, signal
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Operator Learning Using Random Features: A Tool for Scientific Computing SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Nicholas H. Nelsen, Andrew M. Stuart
SIAM Review, Volume 66, Issue 3, Page 535-571, May 2024. Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing, which may often be framed in terms of operators mapping between spaces of functions. Building on the classical
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Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Abigail Hickok, Benjamin Jarman, Michael Johnson, Jiajie Luo, Mason A. Porter
SIAM Review, Volume 66, Issue 3, Page 481-500, May 2024. It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites, availability of transportation, and ease of travel. We use persistent homology, which is a tool from topological
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Research Spotlights SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Stefan M. Wild
SIAM Review, Volume 66, Issue 3, Page 479-479, May 2024. Equitable distribution of geographically dispersed resources presents a significant challenge, particularly in defining quantifiable measures of equity. How can we optimally allocate polling sites or hospitals to serve their constituencies? This issue's first Research Spotlight, “Persistent Homology for Resource Coverage: A Case Study of Access
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Combinatorial and Hodge Laplacians: Similarities and Differences SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Emily Ribando-Gros, Rui Wang, Jiahui Chen, Yiying Tong, Guo-Wei Wei
SIAM Review, Volume 66, Issue 3, Page 575-601, May 2024. As key subjects in spectral geometry and combinatorial graph theory, respectively, the (continuous) Hodge Laplacian and the combinatorial Laplacian share similarities in revealing the topological dimension and geometric shape of data and in their realization of diffusion and minimization of harmonic measures. It is believed that they also both
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Cardinality Minimization, Constraints, and Regularization: A Survey SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Andreas M. Tillmann, Daniel Bienstock, Andrea Lodi, Alexandra Schwartz
SIAM Review, Volume 66, Issue 3, Page 403-477, May 2024. We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and we give concrete examples from diverse application fields such as signal and image processing, portfolio selection, and machine learning. The paper
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When Data Driven Reduced Order Modeling Meets Full Waveform Inversion SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Liliana Borcea, Josselin Garnier, Alexander V. Mamonov, Jörn Zimmerling
SIAM Review, Volume 66, Issue 3, Page 501-532, May 2024. Waveform inversion is concerned with estimating a heterogeneous medium, modeled by variable coefficients of wave equations, using sources that emit probing signals and receivers that record the generated waves. It is an old and intensively studied inverse problem with a wide range of applications, but the existing inversion methodologies are
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Anita T. Layton
SIAM Review, Volume 66, Issue 3, Page 605-615, May 2024. The theme of this collection of book reviews is arguably about the “usefulness” of mathematics, or how we can try to understand aspects of our world by developing mathematical or data-driven models. Thus, it is fitting that our featured review is written by John Stillwell, on the book Why Does Math Work . . . If It's Not Real?, written by Dragan
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Survey and Review SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Marlis Hochbruck
SIAM Review, Volume 66, Issue 3, Page 401-401, May 2024. In “Cardinality Minimization, Constraints, and Regularization: A Survey," Andreas M. Tillmann, Daniel Bienstock, Andrea Lodi, and Alexandra Schwartz consider a class of optimization problems that involve the cardinality of variable vectors in constraints or in the objective function. Such problems have many important applications, e.g., medical
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SIGEST SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 The Editors
SIAM Review, Volume 66, Issue 3, Page 533-533, May 2024. The SIGEST article in this issue is “Operator Learning Using Random Features: A Tool for Scientific Computing,” by Nicholas H. Nelsen and Andrew M. Stuart. This work considers the problem of operator learning in infinite-dimensional Banach spaces through the use of random features. The driving application is the approximation of solution operators
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Anita T. Layton
SIAM Review, Volume 66, Issue 2, Page 391-399, May 2024. As I sat down to write this introduction, I became curious how the books chosen for review have changed over the past decades. So I scanned through a few SIREV Book Review section introductions written 10, 20 or more years ago by former section editors. That act of procrastination allows me to put the current collection of reviews in “historical
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Dynamics of Signaling Games SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Hannelore De Silva, Karl Sigmund
SIAM Review, Volume 66, Issue 2, Page 368-387, May 2024. This tutorial describes several basic and much-studied types of interactions with incomplete information, analyzing them by means of evolutionary game dynamics. The games include sender-receiver games, owner-challenger contests, costly advertising, and calls for help. We model the evolution of populations of players reacting to each other and
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The Poincaré Metric and the Bergman Theory SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Steven G. Krantz
SIAM Review, Volume 66, Issue 2, Page 355-367, May 2024. We treat the Poincaré metric on the disc. In particular we emphasize the fact that it is the canonical holomorphically invariant metric on the unit disc. Then we generalize these ideas to the Bergman metric on a domain in complex space. Along the way we treat the Bergman kernel and study its invariance and uniqueness properties.
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Education SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Hélène Frankowska
SIAM Review, Volume 66, Issue 2, Page 353-353, May 2024. In this issue the Education section presents two contributions. The first paper, “The Poincaré Metric and the Bergman Theory,” by Steven G. Krantz, discusses the Poincaré metric on the unit disc in the complex space and the Bergman metric on an arbitrary domain in any dimensional complex space. To define the Bergman metric the notion of Bergman
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Nonsmooth Optimization over the Stiefel Manifold and Beyond: Proximal Gradient Method and Recent Variants SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Shixiang Chen, Shiqian Ma, Anthony Man-Cho So, Tong Zhang
SIAM Review, Volume 66, Issue 2, Page 319-352, May 2024. We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this class of problems converge slowly in practice, involve subproblems that can be as difficult as the original problem, or lack rigorous convergence guarantees. In
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SIGEST SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 The Editors
SIAM Review, Volume 66, Issue 2, Page 317-317, May 2024. The SIGEST article in this issue is “Nonsmooth Optimization over the Stiefel Manifold and Beyond: Proximal Gradient Method and Recent Variants,” by Shixiang Chen, Shiqian Ma, Anthony Man-Cho So, and Tong Zhang. This work considers nonsmooth optimization on the Stiefel manifold, the manifold of orthonormal $k$-frames in $\mathbb{R}^n$. The authors
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A New Version of the Adaptive Fast Gauss Transform for Discrete and Continuous Sources SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Leslie F. Greengard, Shidong Jiang, Manas Rachh, Jun Wang
SIAM Review, Volume 66, Issue 2, Page 287-315, May 2024. We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave representation of the Gaussian kernel and a new hierarchical merging scheme. For continuous source distributions sampled on adaptive tensor product grids, we exploit