Related papers: Control of Volterra systems with scalar kernels
An observability problem for linear autonomous distributed systems in the class of linear operations is considered. A criterion of observability with respect to terminal state has been proved. A connection with observability with respect to…
Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly,…
Many estimation problems in astrophysics are highly complex, with high-dimensional, non-standard data objects (e.g., images, spectra, entire distributions, etc.) that are not amenable to formal statistical analysis. To utilize such data and…
We develop the analytical method of field momenta for analyzing the dynamics of optical vector solitons in photorefractive nonlinear media. First, we derive the effective evolution equations for the parameters of multi-component solitons…
We prove some vector-valued inequalities for fractional integrals defined in the context of two different orthonormal systems of Laguerre functions. Our results are based on estimates of the corresponding kernels with precise control of the…
With the explosion of distributed energy resources (DERs), voltage regulation in distribution networks has been facing a great challenge. This paper derives an asynchronous distributed voltage control strategy based on the partial…
In this paper we deal with some open problems concerned with gamma subordinators. In particular, we provide a representation for the moments of the inverse gamma subordinator. Then, we focus on $\lambda$-potentials and we study the…
We define a class of functions which have a known decay rate coupled with a periodic fluctuation. We identify conditions on the kernel of a linear summation convolution Volterra equation which give the equivalence of the kernel lying in…
Interferometric observations of stars in late stages of stellar evolution and the impact of VLTI observations are discussed. Special attention is paid to the spectral information that can be derived from these observations and on the…
In the paper, we propose an analytical and numerical approach to identify scalar parameters (coefficients, orders of fractional derivatives) in the multi-term fractional differential operator in time, $\mathbf{D}_t$. To this end, we analyze…
Support vector machines and kernel methods have recently gained considerable attention in chemoinformatics. They offer generally good performance for problems of supervised classification or regression, and provide a flexible and…
We derive unique Banach-valued solutions to stochastic Volterra equations with random coefficients that may depend on pure chance and involve singular kernels. In particular, for controlled and distribution-dependent coefficients these…
We prove that under H\"ormander's type conditions on the coefficients of the unobservable component of a partially observable diffusion process the filtering density is infinitely differentiable and can be represented as the integral of an…
Recent data from the Auger Observatory on low energy secondary cosmic ray particles are analyzed to study temporal correlations together with data on the daily sunspot numbers and neutron monitor data. Standard spectral analysis…
We present a number of cases of optimal control of Volterra and Fredholm integral equations that are solvable in the sense that the problem can be reduced to a solvable integral equation. This is conceptually analogous to the role of the…
We study a class of backtests for forecast distributions in which the test statistic depends on a spectral transformation that weights exceedance events by a function of the modeled probability level. The weighting scheme is specified by a…
Since the early 1970s, stellar population modelling has been one of the basic tools for understanding the physics of unresolved systems from observation of their integrated light. Models allow us to relate the integrated spectra (or…
Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall…
True Volterra equations are inherently non stationary and therefore do not admit $\textit{genuine stationary regimes}$ over finite horizons. This motivates the study of the finite-time behavior of the solutions to scaled inhomogeneous…
Several models for the Monte Carlo simulation of Compton scattering on electrons are quantitatively evaluated with respect to a large collection of experimental data retrieved from the literature. Some of these models are currently…