Showing papers in "Siam Review in 2020"
TL;DR: In this article, simplicial complexes extend this dyadic model of graphs to polyadic re-consistencies, which is a ubiquitous framework for studying complex systems and data, using graphs to model pairwise relationships between entities.
Abstract: Using graphs to model pairwise relationships between entities is a ubiquitous framework for studying complex systems and data. Simplicial complexes extend this dyadic model of graphs to polyadic re...
179 citations
TL;DR: In this paper, the main results on input-to-state stability for infinite-dimensional systems are reviewed in a pedagogical but exhaustive manner, and a survey is presented.
Abstract: In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems. This property allows for the estimation of the impac...
124 citations
TL;DR: This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph LaPLacian, requiring only knowledge of linear algebra and graph theory.
Abstract: This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian. We will discuss basic properties including cohomology and Hodge theory. T...
120 citations
TL;DR: This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations is coupled with a static or time-varying set-valued operator in the feed system.
Abstract: This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations is coupled with a static or time-varying set-valued operator in the feed...
75 citations
TL;DR: The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, and particle physics as discussed by the authors.
Abstract: The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, spe...
64 citations
TL;DR: In this paper, a generalized tensor decomposition is proposed for network analysis and sensor data processing, with applications including network analysis, sensor data analysis, and network data processing in unsupervised machine learning.
Abstract: Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized...
51 citations
TL;DR: In this paper, first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general square matrix, not assumed to be Hermitian or normal, is presented.
Abstract: We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general square matrix, not assumed to be Hermitian or normal. The eigenval...
47 citations
TL;DR: A generalization of the MSF formalism is established that can characterize the stability of any cluster synchronization pattern, even when the oscillators and/or their interactions are nonidentical, and leads to an algorithm that is error-tolerant and orders of magnitude faster than existing symmetry-based algorithms.
Abstract: The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchr...
43 citations
TL;DR: One of the simplest ways to generate data for least-squares problems is to use polynomial approximations, a ubiquitous technique in numerical computation, to estimate the squares of the ellipsoidal inequality.
Abstract: Polynomial approximations constructed using a least-squares approach form a ubiquitous technique in numerical computation. One of the simplest ways to generate data for least-squares problems is wi...
42 citations
TL;DR: Many problems in nature, being characterized by a parameter, are of interest both with a fixed parameter value and with the parameter approaching an asymptotic limit.
Abstract: Many problems in nature, being characterized by a parameter, are of interest both with a fixed parameter value and with the parameter approaching an asymptotic limit. Numerical schemes that are con...
30 citations
TL;DR: Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary as discussed by the authors, and it arises in various applications in fields su...
Abstract: Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications in fields su...
TL;DR: A method for forecasting elections from the perspective of dynamical systems is developed, which borrows ideas from epidemiology, and it performs as well as popular forecasters for the 2012 and 2016 U.S. races for president, senators, and governors.
Abstract: Forecasting elections---a challenging, high-stakes problem---is the subject of much uncertainty, subjectivity, and media scrutiny. To shed light on this process, we develop a method for forecasting...
TL;DR: When the authors use Krylov subspace solutions to approximate the cubic-regularized Newton step, the results recover the strongest known convergence guarantees to approximate second-order stationary points of general smooth nonconvex functions.
Abstract: We consider minimization of indefinite quadratics with either trust-region (norm) constraints or cubic regularization. Despite the nonconvexity of these problems we prove that, under mild assumptio...
TL;DR: In mechanics, one often describes microscopic processes such as those leading to friction between relative interfaces using macroscopic variables (relative velocity, temperature, etc.) in order to solve the inequality between relative velocity and temperature.
Abstract: In mechanics, one often describes microscopic processes such as those leading to friction between relative interfaces using macroscopic variables (relative velocity, temperature, etc.) in order to ...
TL;DR: A simulation of the Lagrangian particle trajectories of fluids shows how uncertainty in velocity data contributes to uncertainty in the model of these trajectories.
Abstract: Uncertainties in velocity data are often ignored when computing Lagrangian particle trajectories of fluids. Modeling these as noise in the velocity field leads to a random deviation from each traje...
TL;DR: Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques as discussed by the authors.
Abstract: Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR w...
TL;DR: In this paper, the authors studied the time correlation functions of coupled linear Langevin dynamics with and without inertial effects, both analytically and numerically, and showed that the model equation represents the physical behavior.
Abstract: We study the time correlation functions of coupled linear Langevin dynamics with and without inertial effects, both analytically and numerically. The model equation represents the physical behavior...
TL;DR: A gentle but rigorous introduction to quantum computing intended for discrete mathematicians, starting from a small set of assumptions on the behavior of quantum computing devices, and describing two well-known algorithms using the formalism developed in previous sections.
Abstract: This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we...
TL;DR: A large number of undergraduates have limited experience with mathematical modeling, and in an effort to respond to various initiatives, such as the recommendations outlined in [S.
Abstract: Most undergraduates have limited experience with mathematical modeling. In an effort to respond to various initiatives, such as the recommendations outlined in [S. Garfunkel and M. Montgomery, eds....
TL;DR: These algorithms can be used for convolution problems with multidimensional inputs or for filters larger than size of four, extending the state-of-the-art in Winograd-based convolution algorithms.
Abstract: The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of...
TL;DR: In this paper, the interplay between the internal structure of its entities and their interconnection may play a fundamental role in the global functioning of the system, and the authors define the...
Abstract: In a complex system, the interplay between the internal structure of its entities and their interconnection may play a fundamental role in the global functioning of the system. Here, we define the ...
TL;DR: An elementary proof of a generalization of Kirchoff's matrix tree theorem to directed, weighted graphs is presented based on a specific factorization of the Laplacian matrices associated to the graphs, which only involves the two incidence matrices that capture the graph's topology.
Abstract: We present an elementary proof of a generalization of Kirchhoff's matrix tree theorem to directed, weighted graphs. The proof is based on a specific factorization of the Laplacian matrices associat...
TL;DR: In this paper, the Runge example for interpolation and the Wilkinson's example for rootfinding are compared. But they are based on two classical examples in the theory of numerical analysis, namely, Runge and Wilkinson's examples.
Abstract: We look at two classical examples in the theory of numerical analysis, namely, the Runge example for interpolation and Wilkinson's example (actually two examples) for rootfinding. We use the modern...
TL;DR: For example, since the 1960s, Democrats and Republicans in the U.S. Congress have taken increasingly polarized positions, while the public's policy positions have remained centrist and moderate as mentioned in this paper.
Abstract: Since the 1960s, Democrats and Republicans in the U.S. Congress have taken increasingly polarized positions, while the public's policy positions have remained centrist and moderate. We explain this...
TL;DR: A new operator based approach to matrix analysis is introduced that is an extension of a tool introduced long ago by MacMahon to analyze the partitions of partitions in matrix analysis.
Abstract: In this work we introduce a new operator based approach to matrix analysis. Our main technical tool comprises an extension of a tool introduced long ago by MacMahon to analyze the partitions of nat...
TL;DR: Boundary-value problems involving the linear differential equation y'' - x y' + y = 0 have surprising properties as $\varepsilon\to 0$, and this equation from eight points of v...
Abstract: Boundary-value problems involving the linear differential equation $\varepsilon y'' - x y' + y = 0$ have surprising properties as $\varepsilon\to 0$. We examine this equation from eight points of v...