相关论文: Analytical approximation for Landau's constants by…
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…
We present two different approaches towards the Landau-Zener problem: (i) The Markov approximation in the integro-differential equation for one of the two probability amplitudes, and (ii) an amplitude-and-phase analysis of the linear second…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
A new approach is presented for the calculation of p_n and pi_n which uses the Lambert W function. An approximation is first found and using a calculation technique it makes it possible to have an estimate of these two quantities more…
We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient…
In the paper, we introduce a matrix method to constructively determine spaces of polynomial solutions (in general, multiplied by exponentials) to a system of constant coefficient linear PDE's with polynomial (multiplied by exponentials)…
Applicability of the previously introduced method of modified diagonal Baker-Gammel approximants is extended to truncated perturbative series (TPS) of any order in gauge theories. The approximants reproduce the TPS when expanded in power…
Explicit formulae for the B\'ezier coefficients of the constrained dual Bernstein basis polynomials are derived in terms of the Hahn orthogonal polynomials. Using difference properties of the latter polynomials, efficient recursive scheme…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B…
We calculate the least upper bounds for approximations in the metric of the space $L_2$ by linear methods of summation of Fourier series on classes of periodic functions $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers…
In this didactic note, we describe a procedure to derive successive approximations of $\pi$ using Euler Beta functions. It is an interesting exercise for undergraduate students, since it involves polynomial roots, integral calculations,…
Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in [arXiv:2007.08591], we develop a novel implicit particle method for the Landau equation in the framework of the…
The main aim of this paper is to further develop the multiple-correction method that formulated in our previous works~\cite{CXY, Cao}. As its applications, we establish a kind of hybrid-type finite continued fraction approximations related…
We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…
We propose a novel score-based particle method for solving the Landau equation in plasmas, that seamlessly integrates learning with structure-preserving particle methods [arXiv:1910.03080]. Building upon the Lagrangian viewpoint of the…
This paper deals with Poisson approximation to weighted sums of locally dependent random variables using Stein's method. The derived result represents a significant improvement of existing results. To illustrate the effectiveness of our…
Motivation: Modeling biological signaling networks using ordinary differential equations (ODEs) has proven to be a powerful technique for generating insight into cellular dynamics, but it typically requires estimating rate parameters based…