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This article considers linear processes with values in a separable Hilbert space exhibiting long-range dependence. The scaling limits for the sample autocovariance operators at different time lags are investigated in the topology of their…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…
Suppose that a real valued process X is given as a solution to a stochastic differential equation. Then, for any twice continuously differentiable function f, the backward Kolmogorov equation gives a condition for f(t,X) to be a local…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess…
We introduce a framework for implementing quantum operations as steady states of a subsystem in an extended Hilbert space. Each operation has a spectral criterion for reaching the steady state. This adds a `spectral switch' mechanism to the…
Splitting probabilities quantify the likelihood of particular outcomes out of a set of mutually-exclusive possibilities for stochastic processes and play a central role in first-passage problems. For two-dimensional Markov processes…
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…
Electromagnetic interaction between a sub-wavelength particle (the `probe') and a material surface (the `sample') is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton…
The spectral function of protons in the asymmetric nuclear matter is calculated in the self-consistent T-matrix approach. The spectral function per proton increases with increasing asymmetry. This effect and the density dependence of the…
We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing…
Graph Neural Networks leverage the connectivity structure of graphs as an inductive bias. Latent graph inference focuses on learning an adequate graph structure to diffuse information on and improve the downstream performance of the model.…
Let $L_1,L_2,\dots,L_K$ be a family of closed subspaces of a Hilbert space $H$, $L_1\cap \dots \cap L_K =\{0\}$; let $P_k$ be the orthogonal projection onto $L_k$. We consider two types of consecutive projections of an element $x_0\in H$:…
The correlation functions for models of minimal gravity are discussed. An algorithm is proposed for calculations of invariant ratios from formulas of residues that can be compared with the coefficients of expansion of the partition function…
Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…