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  •   Book Reviews
    SIAM Rev. (IF 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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 10.2) 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

  •   Education
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    Hélène Frankowska

    SIAM Review, Volume 65, Issue 2, Page 537-537, May 2023. The Education section in this issue presents two contributions. In `"Nesterov's Method for Convex Optimization," Noel J. Walkington proposes a teaching guide for a first course in optimization of this well-known algorithm for computing the minimum of a convex function. This algorithm, first proposed in 1983 by Yuri Nesterov, though well recognized

  •   Nonlinear Perron--Frobenius Theorems for Nonnegative Tensors
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    Antoine Gautier, Francesco Tudisco, Matthias Hein

    SIAM Review, Volume 65, Issue 2, Page 495-536, May 2023. We present a unifying Perron--Frobenius theory for nonlinear spectral problems defined in terms of nonnegative tensors. By using the concept of tensor shape partition, our results include, as a special case, a wide variety of particular tensor spectral problems considered in the literature and can be applied to a broad set of problems involving

  •   SIGEST
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    The Editors

    SIAM Review, Volume 65, Issue 2, Page 493-493, May 2023. The SIGEST article in this issue is “Nonlinear Perron--Frobenius Theorems for Nonnegative Tensors,” by Antoine Gautier, Francesco Tudisco, and Matthias Hein. Most computational and applied mathematicians will be aware of the results that Perron published in 1907 about the eigensystems of positive matrices, which were then extended by Frobenius

  •   The Role of Directionality, Heterogeneity, and Correlations in Epidemic Risk and Spread
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    Antoine Allard, Cristopher Moore, Samuel V. Scarpino, Benjamin M. Althouse, Laurent Hébert-Dufresne

    SIAM Review, Volume 65, Issue 2, Page 471-492, May 2023. Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume mass-action contact patterns and undirected contact networks, meaning that the individuals most likely to spread the disease are also the most at risk of contracting it from others. Here, we review results from the theory of random directed graphs

  •   Contour Integral Methods for Nonlinear Eigenvalue Problems: A Systems Theoretic Approach
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    Michael C. Brennan, Mark Embree, Serkan Gugercin

    SIAM Review, Volume 65, Issue 2, Page 439-470, May 2023. Contour integral methods for eigenvalue problems seek to compute a subset of the spectrum in a bounded region of the complex plane. We briefly survey this class of algorithms, establishing a relationship to system realization and rational interpolation techniques in control theory. This connection casts contour integral methods for linear and

  •   Research Spotlights
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    Stefan M. Wild

    SIAM Review, Volume 65, Issue 2, Page 437-437, May 2023. As highlighted by Tisseur and Meerbergen in SIAM Review, 43 (2001), pp. 235--286, nonlinear eigenvalue problems arise in diverse applications such as acoustics of high-speed trains, the study of elastic materials, fluid mechanical control, and pedestrian-induced structural vibrations. In this issue's first Research Spotlights article, “Contour

  •   Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    Laurent Condat, Daichi Kitahara, Andrés Contreras, Akira Hirabayashi

    SIAM Review, Volume 65, Issue 2, Page 375-435, May 2023. Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they consist of simple operations, handling the terms in the objective function separately. In this overview,

  •   Hawkes Processes Modeling, Inference, and Control: An Overview
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    Rafael Lima

    SIAM Review, Volume 65, Issue 2, Page 331-374, May 2023. Hawkes processes are a type of point process that models self-excitement among time events. They have been used in a myriad of applications, ranging from finance and earthquakes to crime rates and social network activity analysis. Recently, a variety of different tools and algorithms have been presented at top-tier machine learning conferences

  •   Survey and Review
    SIAM Rev. (IF 10.2) Pub Date : 2023-05-09
    Marlis Hochbruck

    SIAM Review, Volume 65, Issue 2, Page 329-329, May 2023. A point process is called self-exciting if the arrival of an event increases the probability of similar events for some period of time. Typical examples include earthquakes, which frequently cause aftershocks due to increased geological tension in their region; raised intrusion rates in the vicinity of a burglary; retweets in social media incited

  •   Book Reviews
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    Volker H. Schulz

    SIAM Review, Volume 65, Issue 1, Page 319-328, February 2023. Our section starts with Rob Kirby's featured review on the book Numerical Methods for Elliptic and Parabolic Partial Differential Equations, written by Peter Knabner and Lutz Angermann. Our reviewer finds several aspects in this book not similarly covered in other books and recommends that the reader of the review fill a bit of open bookshelf

  •   Surprises in a Classic Boundary-Layer Problem
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    William A. Clark, Mario W. Gomes, Arnaldo Rodriguez-Gonzalez, Leo C. Stein, Steven H. Strogatz

    SIAM Review, Volume 65, Issue 1, Page 291-315, February 2023. We revisit a textbook example of a singularly perturbed nonlinear boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem to have been overlooked previously, including a pitchfork bifurcation in the number of solutions as one varies the small parameter, and transcendentally small terms in the initial conditions that

  •   Chaos Game Representation
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    Eunice Y. S. Chan, Robert M. Corless

    SIAM Review, Volume 65, Issue 1, Page 261-290, February 2023. The chaos game representation (CGR) is an interesting method to visualize one-dimensional sequences. In this paper, we show how to construct a chaos game representation. The applications mentioned here are biological, and CGR was able to uncover patterns in DNA or proteins in them that were previously unknown. We also show how CGR might

  •   Education
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    Hélène Frankowska

    SIAM Review, Volume 65, Issue 1, Page 259-260, February 2023. In this issue the Education section presents two contributions. The first paper is “Chaos Game Representation” (CGR), written by Eunice Y. S. Chan and Robert M. Corless. The chaos game is an algorithm which allows us to produce pictures like fractal structures associated with one-dimensional sequences of integers and, in this way, to “visualize”

  •   Improbability of Collisions of Point-Vortices in Bounded Planar Domains
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    Martin Donati

    SIAM Review, Volume 65, Issue 1, Page 227-257, February 2023. In this paper, we prove that in bounded planar domains with $C^{2,\alpha}$ boundary, for almost every initial condition in the sense of the Lebesgue measure, the point-vortex system has a global solution, meaning that there is no collision between two point-vortices or with the boundary. This extends the work previously done in [C. Marchioro

  •   SIGEST
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    The Editors

    SIAM Review, Volume 65, Issue 1, Page 225-225, February 2023. The SIGEST article in this issue, “Improbability of Collisions of Point-Vortices in Bounded Planar Domains,” by Martin Donati, is based on the 2022 SIAM Journal on Mathematics Analysis article “Two-Dimensional Point Vortex Dynamics in Bounded Domains: Global Existence for Almost Every Initial Data.” This work concerns point-vortex dynamics

  •   Learning Dynamical Systems with Side Information
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    Amir Ali Ahmadi, Bachir El Khadir

    SIAM Review, Volume 65, Issue 1, Page 183-223, February 2023. We present a mathematical and computational framework for learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the dynamical system we would like to learn, besides trajectory data, and is typically inferred from domain-specific knowledge

  •   Bump Attractors and Waves in Networks of Leaky Integrate-and-Fire Neurons
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    Daniele Avitabile, Joshua L. Davis, Kyle Wedgwood

    SIAM Review, Volume 65, Issue 1, Page 147-182, February 2023. Bump attractors are wandering localized patterns observed in in vivo experiments of spatially extended neurobiological networks. They are important for the brain's navigational system and specific memory tasks. A bump attractor is characterized by a core in which neurons fire frequently, while those away from the core do not fire. These

  •   Research Spotlights
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    Stefan M. Wild

    SIAM Review, Volume 65, Issue 1, Page 145-145, February 2023. What surprising patterns do fluid dynamics and neurobiological networks have in common? In this issue's first Research Spotlights article, “Bump Attractors and Waves in Networks of Leaky Integrate-and-Fire Neurons,” a connection is made between the waves at the onset of pipe turbulence and the localized traveling waves in spiking neural

  •   Flow-Based Algorithms for Improving Clusters: A Unifying Framework, Software, and Performance
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    Kimon Fountoulakis, Meng Liu, David F. Gleich, Michael W. Mahoney

    SIAM Review, Volume 65, Issue 1, Page 59-143, February 2023. Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to “refine” or “improve” a given cluster that has been obtained by some other method. In this survey, we focus on principled algorithms

  •   Marginal Likelihood Computation for Model Selection and Hypothesis Testing: An Extensive Review
    SIAM Rev. (IF 10.2) Pub Date : 2023-02-09
    F. Llorente, L. Martino, D. Delgado, J. López-Santiago

    SIAM Review, Volume 65, Issue 1, Page 3-58, February 2023. This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratios of constants) is a fundamental issue in many applications in statistics, applied mathematics, signal processing, and machine learning. This article

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