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The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization with space-time grid for a parabolic diffusion problem and from the approximation of…

Numerical Analysis · Mathematics 2023-02-17 Matthias Bolten , Sven-Erik Ekström , Isabella Furci , Stefano Serra-Capizzano

Given a sequence of complex square matrices, $a_n$, consider the sequence of their partial products, defined by $p_n=p_{n-1}a_{n}$. What can be said about the asymptotics as $n\to\infty$ of the sequence $f(p_n)$, where $f$ is a continuous…

Complex Variables · Mathematics 2009-01-12 Douglas Bowman , James Mc Laughlin

Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…

Number Theory · Mathematics 2021-08-12 Michael Coons , James Evans , Neil Manibo

We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained…

Machine Learning · Computer Science 2025-08-27 Levi Rauchwerger , Stefanie Jegelka , Ron Levie

In this paper, we derive a unified method for establishing the distributional convergence of linear eigenvalue statistics (LES) for generalized patterned random matrices. We prove that for an $N \times N$ generalized patterned random matrix…

Probability · Mathematics 2025-03-14 Kiran Kumar A. S. , Shambhu Nath Maurya , Koushik Saha

We are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain $\Omega\subset {\mathbb R}^d$, $d\ge 1$. We assume $\Omega$ to be Lebesgue measurable with regular boundary and contained,…

Numerical Analysis · Mathematics 2020-09-14 Andrea Adriani , Davide Bianchi , Stefano Serra-Capizzano

In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved.…

Logic · Mathematics 2020-09-09 Artur Piȩkosz

In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain $\Omega\subset {\mathbb R}^d$, $d\ge 1$. When $\Omega=[0,1]$, such graphs include the standard Toeplitz…

Numerical Analysis · Mathematics 2021-11-30 Andrea Adriani , Davide Bianchi , Paola Ferrari , Stefano Serra-Capizzano

In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose $G_1, G_2, G_3, \ldots$ is a sequence of finite and connected graphs that share a common universal cover $T$ and such that…

Combinatorics · Mathematics 2019-08-30 Brice Huang , Mustazee Rahman

It is known that the generating function $f$ of a sequence of Toeplitz matrices $\{T_n(f)\}_n$ may not describe the asymptotic distribution of the eigenvalues of $T_n(f)$ if $f$ is not real. In a recent paper, we assume as a working…

Numerical Analysis · Mathematics 2019-11-26 Sven-Erik Ekström , Paris Vassalos

Recently proposed Gated Linear Networks present a tractable nonlinear network architecture, and exhibit interesting capabilities such as learning with local error signals and reduced forgetting in sequential learning. In this work, we…

Machine Learning · Computer Science 2022-12-13 Qianyi Li , Haim Sompolinsky

We study incompatibility of measurements and its relation to steering and nonlocality in a class of finite dimensional general probabilistic theories (GPT).The basic idea is to represent finite collections of measurements as affine maps of…

Quantum Physics · Physics 2018-08-01 Anna Jenčová

It is known that the generating function $f$ of a sequence of Toeplitz matrices $\{T_n(f)\}_n$ may not describe the asymptotic distribution of the eigenvalues of $T_n(f)$ if $f$ is not real. In this paper, we assume as a working hypothesis…

Numerical Analysis · Mathematics 2021-08-17 Sven-Erik Ekström

When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for…

Numerical Analysis · Mathematics 2023-03-23 Armando Coco , Sven-Erik Ekström , Giovanni Russo , Stefano Serra-Capizzano , Santina Chiara Stissi

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…

Optimization and Control · Mathematics 2021-12-08 Helmut Gfrerer , Jiri V. Outrata

In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…

Functional Analysis · Mathematics 2014-07-25 Stevan Pilipovic , Dimitris Scarpalezos , Jasson Vindas

This paper investigates the generalized beta-logarithmic matrix function (GBLMF),which combines the extended beta matrix function and the logarithmic mean. The study establishes essential properties of this function, including functional…

Functional Analysis · Mathematics 2025-02-24 Nabiullah Khan , Rakibul Sk , Mehbub Hassan

In this article, we define a very important sequence of functions, all the functions of this sequence present behaviors very close to that of the Collatz function. The study of such functions allows us to obtain very interesting results…

General Mathematics · Mathematics 2021-07-13 Raouf Rajab

There are several Teichm\"uller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal…

Geometric Topology · Mathematics 2018-09-25 Daniele Alessandrini , Lixin Liu , Athanase Papadopoulos , Weixu Su

Consider the ensembles of real symmetric Toeplitz matrices and real symmetric Hankel matrices whose entries are i.i.d. random variables chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments.…

Probability · Mathematics 2014-11-14 Kirk Swanson , Steven J. Miller , Kimsy Tor , Karl Winsor