Related papers: A polynomial eigenvalue approach for multiplex net…
Using methods from algebraic graph theory and convex optimization, we study the relationship between local structural features of a network and spectral properties of its Laplacian matrix. In particular, we derive expressions for the…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…
We provide a first systematic treatment of so-called rectangular multispectral perturbation theory. With their paper from 2003, Hochstenbach and Plestenjak ["Backward Error, Condition Numbers, and Pseudospectra for the Multiparameter…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…
It is known that a $2\times 2$ quaternionic matrix has one, two or an infinite number of left eigenvalues, but the available algebraic proofs are difficult to generalize to higher orders. In this paper a different point of view is adopted…
Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…
Our aim is to study matrix polynomials over max-algebras and their growth in terms of a max-induced semi-norm. We investigate the relationship between the asymptotic growth of polynomial products and the joint spectral radius of the…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…
We develop new theoretical results on matrix perturbation to shed light on the impact of architecture on the performance of a deep network. In particular, we explain analytically what deep learning practitioners have long observed…
In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown…
From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different networks (layers).…
The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from…
The constant increase in the complexity of data networks motivates the search for strategies that make it possible to reduce current monitoring times. This paper shows the way in which multilayer network representation and the application…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…