SIAM ReviewPub Date : 2026-05-13DOI: 10.1137/25m1800111
Anita T. Layton
{"title":"Book Review:; Biological Rhythms","authors":"Anita T. Layton","doi":"10.1137/25m1800111","DOIUrl":"https://doi.org/10.1137/25m1800111","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 465-466, June 2026. <br/> Daniel B. Forger’s Biological Rhythms is an engaging, compact, and intellectually generous exploration of the clocks that govern life. Written for the MIT Press “Essential Knowledge” series, the book aims to offer a rigorous but accessible introduction to the science of circadian and other biological rhythms. Forger succeeds admirably, distilling a wide swath of chronobiology—spanning physiology, neuroscience, endocrinology, and applied mathematics—into a volume that is approachable, fascinating, and often surprisingly personal.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"32 1","pages":"464-466"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2026-05-13DOI: 10.1137/24m166944x
Sarah Cannon, Moon Duchin, Dana Randall, Parker Rule
{"title":"Spanning Trees and Redistricting: New Methods for Sampling and Validation","authors":"Sarah Cannon, Moon Duchin, Dana Randall, Parker Rule","doi":"10.1137/24m166944x","DOIUrl":"https://doi.org/10.1137/24m166944x","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 349-381, June 2026. <br/> Abstract.Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now signed on to decisions finding that computational methods can provide key evidence. Today, the leading approaches to the benchmarking of districting plans are based on the use of spanning trees for sampling graph partitions. We present a new reversible recombination algorithm and rigorously prove its fundamental properties. Furthermore, we argue for a canonical sampling distribution called the spanning tree distribution that is well adapted to redistricting and provides a principled foundation for comparing and validating methods. Together with a highly efficient (and open-source) implementation that can generate and handle large datasets, this work provides the most powerful null model to date for the gerrymandering problem, meeting an urgent democratic challenge with sound scientific methodology.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"20 1","pages":"349-381"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2026-05-13DOI: 10.1137/25m1809501
J. M. Almira
{"title":"Book Review:; A Brief History of Mathematics for Curious Minds","authors":"J. M. Almira","doi":"10.1137/25m1809501","DOIUrl":"https://doi.org/10.1137/25m1809501","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 466-467, June 2026. <br/> Reading a book about the history of mathematics is never a waste of time, especially if you are a working mathematician, whether applied or pure. Obviously, there are many excellent monographs devoted to specific periods such as nineteenth-century mathematics, or to specific subjects such as mathematical analysis, and these serve specialists very well. The book under review is more ambitious and attempts to cover the whole history of mathematics under the additional assumption that the intended reader is a layperson, not necessarily a professional mathematician. Remarkably, this ambitious task is carried out in just over 200 pages organized into ten chapters, complemented by a bibliography, a name index, and 32 short appendices containing mathematical gems.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"149 1","pages":"466-467"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2026-05-13DOI: 10.1137/24m1640987
Hyukjun (Jay) Gweon
{"title":"Book Review:; Applied Statistical Learning: With Case Studies in Stata","authors":"Hyukjun (Jay) Gweon","doi":"10.1137/24m1640987","DOIUrl":"https://doi.org/10.1137/24m1640987","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 462-463, June 2026. <br/> Statistical learning has become an essential component across a wide range of research fields. Among the many textbooks that lay the foundations of theory and practice, Matthias Schonlau’s Applied Statistical Learning: With Case Studies in Stata is a valuable addition—not only for undergraduate and graduate students and course instructors, but also for applied researchers, particularly those who use Stata for data analysis.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"1 1","pages":"462-463"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2026-05-13DOI: 10.1137/24m1687650
Jane Shaw MacDonald, Rafael Odoñez Cardales, John M. Stockie
{"title":"A Mathematical Model for Nordic Skiing","authors":"Jane Shaw MacDonald, Rafael Odoñez Cardales, John M. Stockie","doi":"10.1137/24m1687650","DOIUrl":"https://doi.org/10.1137/24m1687650","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 423-455, June 2026. <br/> Abstract.Nordic skiing provides fascinating opportunities for mathematical modeling studies that exploit methods and insights from physics, applied mathematics, data analysis, scientific computing, and sports science. A typical ski course winds over varied terrain with frequent changes in elevation and direction, and so its geometry is naturally described by a three-dimensional space curve. The skier travels along a course under the influence of various forces, and their dynamics can be described using a nonlinear system of ordinary differential equations (ODEs) that are derived from Newton’s laws of motion. We develop an algorithm for solving the governing equations that combines Hermite spline interpolation, numerical quadrature, and a high-order ODE solver. Numerical simulations are compared with measurements of skiers on actual courses to demonstrate the effectiveness of the model. Throughout, we aim to illustrate how elementary concepts from undergraduate courses in calculus and scientific computing can be applied to the study of real problems in sport, which we hope will provide stimulating examples for both instructors and students. At the same time, we demonstrate how these concepts are capable of providing novel insights into skiing that should also be of interest to sport scientists.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"18 1","pages":"423-455"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2026-05-13DOI: 10.1137/24m1715519
Joel Wendin, Claudio Altafini
{"title":"Gradient Flow Equations for Deep Linear Neural Networks: A Survey from a Network Perspective","authors":"Joel Wendin, Claudio Altafini","doi":"10.1137/24m1715519","DOIUrl":"https://doi.org/10.1137/24m1715519","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 293-345, June 2026. <br/> Abstract.This paper surveys recent progress in understanding the dynamics and loss landscape of the gradient flow equations associated with deep linear neural networks, i.e., the gradient descent training dynamics (in the limit when the step size goes to 0) of deep neural networks missing the activation functions and subject to quadratic loss functions. When formulated in terms of the adjacency matrix of the neural network, as is done in this paper, these gradient flow equations form a class of converging matrix ODEs which is nilpotent, polynomial, isospectral, and with conservation laws. A detailed description of the loss landscape shows that it is described in detail and is characterized by infinitely-many global minima and saddle points, both strict and nonstrict, but that it lacks local minima and maxima. The loss function itself is a positive semidefinite Lyapunov function for the gradient flow, and its level sets are unbounded invariant sets of critical points with critical values that correspond to the amount of singular values of the input-output data learnt by the gradient along a certain trajectory. The adjacency matrix representation we use in the paper allows us to highlight the existence of a quotient space structure in which each critical value of the loss function is represented only once, while all other critical points with the same critical value belong to the fiber associated to the quotient space. It also allows us to easily determine stable and unstable submanifolds at the saddle points, even when the Hessian fails to obtain them.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"257 1","pages":"293-345"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2026-02-09DOI: 10.1137/24m1628591
Gabriele Ciaramella, Martin J. Gander, Tommaso Vanzan
{"title":"A Gentle Introduction to Interpolation on the Grassmann Manifold","authors":"Gabriele Ciaramella, Martin J. Gander, Tommaso Vanzan","doi":"10.1137/24m1628591","DOIUrl":"https://doi.org/10.1137/24m1628591","url":null,"abstract":"SIAM Review, Volume 68, Issue 1, Page 172-203, February 2026. <br/> Abstract. This paper offers a self-contained exposition of the fundamental mathematical and computational tools for interpolation on the Grassmann manifold, including detailed derivations of geodesics and explicit formulations of the exponential and logarithmic maps. The presentation emphasizes intuition and draws continuous parallels with the Euclidean setting. This pedagogical approach facilitates the understanding of linear, piecewise linear, and high-order interpolation algorithms, as well as their extension to more general manifolds. Two numerical examples are finally used to illustrate the potential of these algorithms: one in the context of parametric model order reduction, and another drawn from stationary iterative methods for linear systems.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"385 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146138552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}