The magnetization ripple is a microstructure formed in thin ferromagnetic films. It can be described by minimizers of a nonconvex energy functional leading to a nonlocal and nonlinear elliptic SPDE in two dimensions driven by white noise, which is singular. We address the universal character of the magnetization ripple using variational methods based on Γ-convergence. Due to the infinite energy of

Abstract not available

Low-rank tensor representations can provide highly compressed approximations of functions. These concepts, which essentially amount to generalizations of classical techniques of separation of variables, have proved to be particularly fruitful for functions of many variables. We focus here on problems where the target function is given only implicitly as the solution of a partial differential equation

The present review paper has several objectives. Its primary aim is to give an idea of the general features of virtual element methods (VEMs), which were introduced about a decade ago in the field of numerical methods for partial differential equations, in order to allow decompositions of the computational domain into polygons or polyhedra of a very general shape.Nonetheless, the paper is also addressed

Floating-point numbers have an intuitive meaning when it comes to physics-based numerical computations, and they have thus become the most common way of approximating real numbers in computers. The IEEE-754 Standard has played a large part in making floating-point arithmetic ubiquitous today, by specifying its semantics in a strict yet useful way as early as 1985. In particular, floating-point operations

This article surveys research on the application of compatible finite element methods to large-scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa’s C-grid finite difference scheme to the finite element world. They are constructed from a discrete de Rham complex, which is a sequence of finite element spaces linked by the operators of differential calculus. The use

We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control. The structure is ideal for automated network-based modelling since it is invariant under power-conserving interconnection, congruence transformations and Galerkin projection. Moreover, stability and passivity properties are easily shown. Condensed forms under orthogonal transformations

One of the main challenges in molecular dynamics is overcoming the ‘timescale barrier’: in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based

A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone. Cones that are homogeneous and self-dual are called symmetric. Conic optimization problems over symmetric cones have been extensively studied, particularly in the literature on interior-point algorithms, and as the foundation of modelling tools for convex optimization. In this paper we consider the

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

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

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

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

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

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

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

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

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

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,

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

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

Abstract A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring biological systems raises the need for addressing more complex data, e.g., graphs, strings, and probability distributions. To fill this gap, this paper proposes

Abstract not available

Published in The American Statistician (Vol. 77, No. 2, 2023)

We recognize the careful reading of and thought-provoking commentary on our work by Rice and Lumley. Further, we appreciate the opportunity to respond and clarify our position regarding the three presented concerns. We address these points in three sections below and conclude with final remarks in Section 4.

Published in The American Statistician (Vol. 77, No. 2, 2023)

Published in The American Statistician (Vol. 77, No. 2, 2023)

We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2. A big novelty is that this critical space is due to an instability mechanism which is

Published in The American Statistician (Just accepted, 2023)

Abstract We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modelling for arbitrary outcomes. We replace the strict parametric distribution formulating such a model by a transformation function, which in turn is estimated from data. Doing so not only makes the model distribution-free but also allows to