Search results for "kernel"

Statistics of transitions for Markov chains with periodic forcing

2013

The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular the first Floquet multiplier of the associated generating function can be explicitly computed and related to the equilibrium probability measure of an associated process in higher dimension. An application to the stochastic resonance is presented.

Singular integrals on regular curves in the Heisenberg group

2019

Let $\mathbb{H}$ be the first Heisenberg group, and let $k \in C^{\infty}(\mathbb{H} \, \setminus \, \{0\})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\nabla_{\mathbb{H}}^{n}k(p)| \leq C_{n}\|p\|^{-1 - n}, \qquad p \in \mathbb{H} \, \setminus \, \{0\}, \, n \geq 0.$$ The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the horizontally odd kernel $k(p) = \nabla_{\mathbb{H}} \log \|p\|$. We prove that convolution with $k$, as above, yields an $L^{2}$-bounded operator on regular curves in $\mathbb{H}$. This extends a theorem of G. David to the Heisenberg group. As a corollary of our main result, we infer that all …

Vector-Valued Hardy Spaces

2019

Given a Banach space X, we consider Hardy spaces of X-valued functions on the infinite polytorus, Hardy spaces of X-valued Dirichlet series (defined as the image of the previous ones by the Bohr transform), and Hardy spaces of X-valued holomorphic functions on l_2 ∩ B_{c0}. The chapter is dedicated to study the interplay between these spaces. It is shown that the space of functions on the polytorus always forms a subspace of the one of holomorphic functions, and these two are isometrically isomorphic if and only if X has ARNP. Then the question arises of what do we find in the side of Dirichlet series when we look at the image of the Hardy space of holomorphic functions. This is also answer…

The First Main Theorem

1998

Mixed intersections of non quasi-analytic classes

2008

Given two semi-regular matrices M and M' and two open subsets O and O' [resp. two compact subsets K and K'] of Rr and Rs respectively, we introduce the spaces E(M×M')(O × O') and D(M×M')(O × O') [resp. D(M×M')(K × K')]. In this paper we study their locally convex properties and the structure of their elements. This leads in [10] to tensor product representations of these spaces and to some kernel theorems.

Tuning the Electronic Properties of the Dative N-B Bond with Associated O-B Interaction: Electron Localizability Indicator from X-Ray Wavefunction Re…

2016

Despite the immense growth in interest in difluoroborate dyes, the nature of the interactions of the boron atom within the N-BF2 -O kernel is not yet fully understood. Herein, a set of real-space bonding indicators is used to quantify the electronic characteristics of the dative N-B bond in difluoroborate derivatives. The atoms-in-molecules (AIM) partitioning scheme is complemented by the electron localizability indicator (ELI-D) approach, and both were applied to experimental and theoretical electron-density distributions (X-ray constrained wavefunction fitting vs. DFT calculations). Additionally, Fermi orbital analysis was introduced for small DFT models to support and extend the findings…

Geometry and analysis of Dirichlet forms

2012

Let $ \mathscr E $ be a regular, strongly local Dirichlet form on $L^2(X, m)$ and $d$ the associated intrinsic distance. Assume that the topology induced by $d$ coincides with the original topology on $ X$, and that $X$ is compact, satisfies a doubling property and supports a weak $(1, 2)$-Poincar\'e inequality. We first discuss the (non-)coincidence of the intrinsic length structure and the gradient structure. Under the further assumption that the Ricci curvature of $X$ is bounded from below in the sense of Lott-Sturm-Villani, the following are shown to be equivalent: (i) the heat flow of $\mathscr E$ gives the unique gradient flow of $\mathscr U_\infty$, (ii) $\mathscr E$ satisfies the Ne…

Hybrid chaotic firefly decision making model for Parkinson’s disease diagnosis

2020

Parkinson’s disease is found as a progressive neurodegenerative condition which affects motor circuit by the loss of up to 70% of dopaminergic neurons. Thus, diagnosing the early stages of incidence is of great importance. In this article, a novel chaos-based stochastic model is proposed by combining the characteristics of chaotic firefly algorithm with Kernel-based Naïve Bayes (KNB) algorithm for diagnosis of Parkinson’s disease at an early stage. The efficiency of the model is tested on a voice measurement dataset that is collected from “UC Irvine Machine Learning Repository.” The dynamics of chaos optimization algorithm will enhance the firefly algorithm by introducing six types of chao…

Un modelo no hidrostático global con coordenada vertical basada en altura

2015

Memoria presentada en la Universitat de València para optar grado de de Doctor Esta tesis documenta la investigación que he realizado en modelización atmosférica: se parte de las ecuaciones físicas de la atmósfera y se aplican métodos numéricos eficientes para encontrar una solución a dichas ecuaciones a partir de unas condiciones iniciales dadas. Para este fin, se ha desarrollado un modelo atmosférico cuyas características principales son: espectral en la representación horizontal de los campos, discretización vertical de alto orden de exactitud, y semi-implícito en la integración temporal. Además, el modelo es no hidrostático y tiene una coordenada vertical basada en altura, en vez de la …

A support vector domain method for change detection in multitemporal images

2010

This paper formulates the problem of distinguishing changed from unchanged pixels in multitemporal remote sensing images as a minimum enclosing ball (MEB) problem with changed pixels as target class. The definition of the sphere-shaped decision boundary with minimal volume that embraces changed pixels is approached in the context of the support vector formalism adopting a support vector domain description (SVDD) one-class classifier. SVDD maps the data into a high dimensional feature space where the spherical support of the high dimensional distribution of changed pixels is computed. Unlike the standard SVDD, the proposed formulation of the SVDD uses both target and outlier samples for defi…