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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

  •   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

  •   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

  •   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

  •   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

  •   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

  •   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

  •   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

  •   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

  •   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

  •   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

  •   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

  •   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.

  •   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

  •   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

  •   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

  •   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

  •   Research Spotlights
    SIAM Rev. (IF 10.8) Pub Date : 2024-05-09
    Stefan M. Wild

    SIAM Review, Volume 66, Issue 2, Page 285-285, May 2024. The Gauss transform---convolution with a Gaussian in the continuous case and the sum of $N$ Gaussians at $M$ points in the discrete case---is ubiquitous in applied mathematics, from solving ordinary and partial differential equations to probability density estimation to science applications in astrophysics, image processing, quantum mechanics

  •   Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection Methods
    SIAM Rev. (IF 10.8) Pub Date : 2024-05-09
    Julianne Chung, Silvia Gazzola

    SIAM Review, Volume 66, Issue 2, Page 205-284, May 2024. This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the numerical linear algebra community and have proved important in solving inverse problems due to their inherent

  •   Survey and Review
    SIAM Rev. (IF 10.8) Pub Date : 2024-05-09
    Marlis Hochbruck

    SIAM Review, Volume 66, Issue 2, Page 203-203, May 2024. Inverse problems arise in various applications---for instance, in geoscience, biomedical science, or mining engineering, to mention just a few. The purpose is to recover an object or phenomenon from measured data which is typically subject to noise. The article “Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection

  •   Book Reviews
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Anita T. Layton

    SIAM Review, Volume 66, Issue 1, Page 193-201, February 2024. If you are keen to understand the world around us by developing mathematical or data-driven models, or if you are interested in the methodologies that can be used to analyze those models, this collection of reviews may help you identify a useful book or two. Our featured review was written by Tim Hoheisel, on the book Convex Optimization:

  •   NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Zongren Zou, Xuhui Meng, Apostolos F. Psaros, George E. Karniadakis

    SIAM Review, Volume 66, Issue 1, Page 161-190, February 2024. Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision and natural language processing, and by the need for reliable tools in risk-sensitive applications. Recently, various machine learning

  •   Resonantly Forced ODEs and Repeated Roots
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Allan R. Willms

    SIAM Review, Volume 66, Issue 1, Page 149-160, February 2024. In a recent article in this journal, Gouveia and Stone [``Generating Resonant and Repeated Root Solutions to Ordinary Differential Equations Using Perturbation Methods,” SIAM Rev., 64 (2022), pp. 485--499] described a method for finding exact solutions to resonantly forced linear ordinary differential equations, and for finding the general

  •   Education
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Helene Frankowska

    SIAM Review, Volume 66, Issue 1, Page 147-147, February 2024. In this issue the Education section presents two contributions. The first paper, “Resonantly Forced ODEs and Repeated Roots,” is written by Allan R. Willms. The resonant forcing problem is as follows: find $y(\cdot)$ such that $L[y(x)]=u(x)$, where $L[u(x)]=0$ and $L=a_0(x) + \sum_{j=1}^n a_j(x) \frac{d^j}{dx^j}$. The repeated roots problem

  •   A Simple Formula for the Generalized Spectrum of Second Order Self-Adjoint Differential Operators
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Bjørn Fredrik Nielsen, Zdeněk Strakoš

    SIAM Review, Volume 66, Issue 1, Page 125-146, February 2024. We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$ subject to homogeneous Dirichlet or Neumann boundary conditions, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral decomposition $K=Q \Lambda Q^T$, where $Q=Q(x

  •   SIGEST
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    The Editors

    SIAM Review, Volume 66, Issue 1, Page 123-123, February 2024. The SIGEST article in this issue is “A Simple Formula for the Generalized Spectrum of Second Order Self-Adjoint Differential Operators,” by Bjørn Fredrik Nielsen and Zdeněk Strakoš. This paper studies the eigenvalues of second-order self-adjoint differential operators in the continuum and discrete settings. In particular, they investigate

  •   Easy Uncertainty Quantification (EasyUQ): Generating Predictive Distributions from Single-Valued Model Output
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Eva-Maria Walz, Alexander Henzi, Johanna Ziegel, Tilmann Gneiting

    SIAM Review, Volume 66, Issue 1, Page 91-122, February 2024. How can we quantify uncertainty if our favorite computational tool---be it a numerical, statistical, or machine learning approach, or just any computer model---provides single-valued output only? In this article, we introduce the Easy Uncertainty Quantification (EasyUQ) technique, which transforms real-valued model output into calibrated

  •   Research Spotlights
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Stefan M. Wild

    SIAM Review, Volume 66, Issue 1, Page 89-89, February 2024. As modeling, simulation, and data-driven capabilities continue to advance and be adopted for an ever expanding set of applications and downstream tasks, there has been an increased need for quantifying the uncertainty in the resulting predictions. In “Easy Uncertainty Quantification (EasyUQ): Generating Predictive Distributions from Single-Valued

  •   Finite Element Methods Respecting the Discrete Maximum Principle for Convection-Diffusion Equations
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Gabriel R. Barrenechea, Volker John, Petr Knobloch

    SIAM Review, Volume 66, Issue 1, Page 3-88, February 2024. Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solutions of these equations satisfy, under certain conditions, maximum principles, which represent physical bounds of the solution. That the same bounds are respected by numerical approximations of the solution is often of

  •   Survey and Review
    SIAM Rev. (IF 10.8) Pub Date : 2024-02-08
    Marlis Hochbruck

    SIAM Review, Volume 66, Issue 1, Page 1-1, February 2024. Numerical methods for partial differential equations can only be successful if their numerical solutions reflect fundamental properties of the physical solution of the respective PDE. For convection-diffusion equations, the conservation of some specific scalar quantities is crucial. When physical solutions satisfy maximum principles representing

  •   Book Reviews
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Volker H. Schulz

    SIAM Review, Volume 65, Issue 4, Page 1187-1197, November 2023. Our section starts with the featured review of Glenn Ledder's book Mathematical Modeling for Epidemiology and Ecology. This review is a joint work of 10 authors from Anita Layton's group. This shows that one can efficiently combine a reading course with an introduction to scientific work and the writing of a review. All reviewers are enthusiastic

  •   Hysteresis and Stability
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Amenda N. Chow, Kirsten A. Morris, Gina F. Rabbah

    SIAM Review, Volume 65, Issue 4, Page 1171-1184, November 2023. A common definition of hysteresis is that the graph of the state of the system displays looping behavior as the input of the system varies. Alternatively, a dynamical systems perspective can be used to define hysteresis as a phenomenon arising from multiple equilibrium points. Consequently, hysteresis is a topic that can be used to illustrate

  •   Incorporating Computational Challenges into a Multidisciplinary Course on Stochastic Processes
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Mark Jayson Cortez, Alan Eric Akil, Krešimir Josić, Alexander J. Stewart

    SIAM Review, Volume 65, Issue 4, Page 1152-1170, November 2023. Quantitative methods and mathematical modeling are playing an increasingly important role across disciplines. As a result, interdisciplinary mathematics courses are increasing in popularity. However, teaching such courses at an advanced level can be challenging. Students often arrive with different mathematical backgrounds, different interests

  •   The Reflection Method for the Numerical Solution of Linear Systems
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Margherita Guida, Carlo Sbordone

    SIAM Review, Volume 65, Issue 4, Page 1137-1151, November 2023. We present Cimmino's reflection algorithm for the numerical solution of linear systems, which starts with an arbitrary point in $\mathbb{R}^n$ that gets reflected with respect to the system's hyperplanes. The centroid of the ensuing collection of points becomes the starting point of the next iteration. We provide error estimates for the

  •   Education
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Hèléne Frankowska

    SIAM Review, Volume 65, Issue 4, Page 1135-1135, November 2023. In this issue the Education section presents three contributions. The first paper “The Reflection Method for the Numerical Solution of Linear Systems,” by Margherita Guida and Carlo Sbordone, discusses the celebrated Gianfranco Cimmino reflection algorithm for the numerical solution of linear systems $Ax=b$, where $A$ is a nonsingular

  •   Are Adaptive Galerkin Schemes Dissipative?
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Rodrigo M. Pereira, Natacha Nguyen van yen, Kai Schneider, Marie Farge

    SIAM Review, Volume 65, Issue 4, Page 1109-1134, November 2023. Adaptive Galerkin numerical schemes integrate time-dependent partial differential equations with a finite number of basis functions, and a subset of them is selected at each time step. This subset changes over time discontinuously according to the evolution of the solution; therefore the corresponding projection operator is time-dependent

  •   SIGEST
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    The Editors

    SIAM Review, Volume 65, Issue 4, Page 1107-1107, November 2023. The SIGEST article in this issue is “Are Adaptive Galerkin Schemes Dissipative?” by Rodrigo M. Pereira, Natacha Nguyen van yen, Kai Schneider, and Marie Farge. “Although this may seem a paradox, all exact science is dominated by the idea of approximation.” With this quote from Bertrand Russell from 1931 commences this issue's SIGEST article

  •   A Benchmark for the Bayesian Inversion of Coefficients in Partial Differential Equations
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    David Aristoff, Wolfgang Bangerth

    SIAM Review, Volume 65, Issue 4, Page 1074-1105, November 2023. Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases the number of variables used to parameterize these coefficients is large, and oobtaining meaningful

  •   Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Kailiang Wu, Chi-Wang Shu

    SIAM Review, Volume 65, Issue 4, Page 1031-1073, November 2023. Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in the relativistic case the fluid velocity is upper bounded by the speed of light, etc. As widely realized, it is crucial to develop bound-preserving numerical

  •   Research Spotlights
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Stefan M. Wild

    SIAM Review, Volume 65, Issue 4, Page 1029-1029, November 2023. This issue's two Research Spotlights highlight techniques for obtaining ever more realistic solutions to challenging systems of partial differential equations (PDEs). Although borne from different fields of applied mathematics, both papers aim to leverage prior information to improve the fidelity and practical solution of PDEs. How predictive

  •   An Introductory Review on A Posteriori Error Estimation in Finite Element Computations
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Ludovic Chamoin, Frédéric Legoll

    SIAM Review, Volume 65, Issue 4, Page 963-1028, November 2023. This article is a review of basic concepts and tools devoted to a posteriori error estimation for problems solved with the finite element method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems, approximated by a conforming numerical discretization. The main goal of this review is to present

  •   Getting the Lay of the Land in Discrete Space: A Survey of Metric Dimension and Its Applications
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Richard C. Tillquist, Rafael M. Frongillo, Manuel E. Lladser

    SIAM Review, Volume 65, Issue 4, Page 919-962, November 2023. The metric dimension of a graph is the smallest number of nodes required to identify all other nodes uniquely based on shortest path distances. Applications of metric dimension include discovering the source of a spread in a network, canonically labeling graphs, and embedding symbolic data in low-dimensional Euclidean spaces. This survey

  •   Survey and Review
    SIAM Rev. (IF 10.8) Pub Date : 2023-11-07
    Marlis Hochbruck

    SIAM Review, Volume 65, Issue 4, Page 917-917, November 2023. The metric dimension $\beta(G)$ of a graph $G = (V,E)$ is the smallest cardinality of a subset $S$ of vertices such that all other vertices are uniquely determined by their distances to the vertices in the resolving set $S$. Finding the metric dimension of a graph is an NP-hard problem. Determining whether the metric dimension is less than

  •   Book Reviews
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Volker H. Schulz

    SIAM Review, Volume 65, Issue 3, Page 905-915, August 2023. This collection of reviews encompasses a wide range of topics. We kick off with an insightful featured review by Chris Oats on the book Probabilistic Numerics, written by Philipp Hennig, Michael A. Osborne, and Hans P. Kersting. Oats expresses his own fascination with the topic and highly recommends delving into the substantial tome. Continuing

  •   Piecewise Smooth Models of Pumping a Child's Swing
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Brigid Murphy, Paul Glendinning

    SIAM Review, Volume 65, Issue 3, Page 887-902, August 2023. Some simple models of a child swinging on a playground swing are presented. These are analyzed using techniques from Lagrangian mechanics with a twist: the child changes the configuration of the system by sudden movements of their body at key moments in the oscillation. This can lead to jumps in the generalized coordinates describing the system

  •   The One-Dimensional Version of Peixoto's Structural Stability Theorem: A Calculus-Based Proof
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Aminur Rahman, D. Blackmore

    SIAM Review, Volume 65, Issue 3, Page 869-886, August 2023. Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems, they are often treated rather superficially, if at all, in upper level undergraduate courses on dynamical systems or differential equations. This is mainly because

  •   Education
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Hélène Frankowska

    SIAM Review, Volume 65, Issue 3, Page 867-867, August 2023. In this issue, the Education section presents two contributions. “The One-Dimensional Version of Peixoto's Structural Stability Theorem: A Calculus-Based Proof,” by Aminur Rahman and D. Blackmore, proposes, in the one-dimensional setting, a novel proof of Peixoto's structural stability and density theorem, which is fundamental in dynamical

  •   Bayesian Inverse Problems Are Usually Well-Posed
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Jonas Latz

    SIAM Review, Volume 65, Issue 3, Page 831-865, August 2023. Inverse problems describe the task of blending a mathematical model with observational data---a fundamental task in many scientific and engineering disciplines. The solvability of such a task is usually classified through its well-posedness. A problem is well-posed if it has a unique solution that depends continuously on input or data. Inverse

  •   SIGEST
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    The Editors

    SIAM Review, Volume 65, Issue 3, Page 829-829, August 2023. The SIGEST article in this issue, which comes from the SIAM/ASA Journal on Uncertainty Quantification, is “Bayesian Inverse Problems Are Usually Well-Posed,” by Jonas Latz. The author investigates the well-posedness of Bayesian approaches to inverse problems, generalizing the framework of well-posedness introduced by Andrew Stuart to a set

  •   Does the Helmholtz Boundary Element Method Suffer from the Pollution Effect?
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    J. Galkowski, E. A. Spence

    SIAM Review, Volume 65, Issue 3, Page 806-828, August 2023. In $d$ dimensions, accurately approximating an arbitrary function oscillating with frequency $\lesssim k$ requires $\sim$$k^d$ degrees of freedom. A numerical method for solving the Helmholtz equation (with wavenumber $k$ and in $d$ dimensions) suffers from the pollution effect if, as $k→∞$, the total number of degrees of freedom needed to

  •   Compartment Models with Memory
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Timothy Ginn, Lynn Schreyer

    SIAM Review, Volume 65, Issue 3, Page 774-805, August 2023. The beauty and simplicity of compartment modeling makes it a useful approach for simulating dynamics in an amazingly wide range of applications, which are growing rapidly especially in global carbon cycling, hydrological network flows, and epidemiology and population dynamics. These contexts, however, often involve compartment-to-compartment

  •   Neural ODE Control for Classification, Approximation, and Transport
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Domènec Ruiz-Balet, Enrique Zuazua

    SIAM Review, Volume 65, Issue 3, Page 735-773, August 2023. We analyze neural ordinary differential equations (NODEs) from a control theoretical perspective to address some of the main properties and paradigms of deep learning (DL), in particular, data classification and universal approximation. These objectives are tackled and achieved from the perspective of the simultaneous control of systems of

  •   Research Spotlights
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Stefan M. Wild

    SIAM Review, Volume 65, Issue 3, Page 733-733, August 2023. The three articles in this issue's Research Spotlight section highlight the breadth of problems and approaches that have differential equations as a central component. In the first article, “Neural ODE Control for Classification, Approximation, and Transport,” authors Domènec Ruiz-Balet and Enrique Zuazua seek to expand understanding of some

  •   Erratum: On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Hongyu Miao, Alan S. Perelson, Hulin Wu

    SIAM Review, Volume 65, Issue 3, Page 732-732, August 2023. This erratum corrects an error in the coefficients of equation (6.23) in the original paper [H. Miao, X. Xia, A. S. Perelson, and H. Wu, SIAM Rev., 53 (2011), pp. 3--39].

  •   What Are Higher-Order Networks?
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Christian Bick, Elizabeth Gross, Heather A. Harrington, Michael T. Schaub

    SIAM Review, Volume 65, Issue 3, Page 686-731, August 2023. Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity of graphs: A graph consists of nothing more than a set of vertices and a set of edges, describing relationships

  •   On and Beyond Total Variation Regularization in Imaging: The Role of Space Variance
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Monica Pragliola, Luca Calatroni, Alessandro Lanza, Fiorella Sgallari

    SIAM Review, Volume 65, Issue 3, Page 601-685, August 2023. Over the last 30 years a plethora of variational regularization models for image reconstruction have been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned in basic courses in mathematical image processing is the celebrated Rudin--Osher--Fatemi (ROF) model

  •   Survey and Review
    SIAM Rev. (IF 10.8) Pub Date : 2023-08-08
    Marlis Hochbruck

    SIAM Review, Volume 65, Issue 3, Page 599-599, August 2023. Apart from a short erratum, which concerns the correction of some coefficients in a differential equation in the original paper, this issue contains two Survey and Review articles. “On and Beyond Total Variation Regularization in Imaging: The Role of Space Variance,” authored by Monica Pragliola, Luca Calatroni, Alessandro Lanza, and Fiorella

  •   Book Reviews
    SIAM Rev. (IF 10.8) Pub Date : 2023-05-09
    Volker H. Schulz

    SIAM Review, Volume 65, Issue 2, Page 591-598, May 2023. We begin the section with Alexander Mamonov's review on the book An Introduction to the Mathematical Theory of Inverse Problems, written by Andreas Kirsch. Our reviewer describes it as a classic in the field of inverse problems and recommends it to all readers inclined to the theory and solution of inverse problems. The next review discusses

  •   A Comprehensive Proof of Bertrand's Theorem
    SIAM Rev. (IF 10.8) Pub Date : 2023-05-09
    Patrick De Leenheer, John Musgrove, Tyler Schimleck

    SIAM Review, Volume 65, Issue 2, Page 563-588, May 2023. A cornerstone result in Newtonian mechanics is Bertrand's Theorem concerning the behavior of the solutions of the classical two-body problem. It states that among all possible gravitational laws there are only two exhibiting the property that all bounded orbits are closed. One of these is Newtonian gravitation, the other being Hookean gravitation

  •   Nesterov's Method for Convex Optimization
    SIAM Rev. (IF 10.8) Pub Date : 2023-05-09
    Noel J. Walkington

    SIAM Review, Volume 65, Issue 2, Page 539-562, May 2023. While Nesterov's algorithm for computing the minimum of a convex function is now over forty years old, it is rarely presented in texts for a first course in optimization. This is unfortunate since for many problems this algorithm is superior to the ubiquitous steepest descent algorithm, and it is equally simple to implement. This article presents

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