Related papers: Analysis of systematic scan Metropolis algorithms …
Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often…
We describe algorithms to represent and compute groups of Hecke characters. We make use of an id{\`e}lic point of view and obtain the whole family of such characters, including transcendental ones. We also show how to isolate the algebraic…
The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the…
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
We study the computational complexity of a Metropolis-Hastings algorithm for Bayesian community detection. We first establish a posterior strong consistency result for a natural prior distribution on stochastic block models under the…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
We develop several applications of the fact that the Yokonuma--Hecke algebra of the general linear group GL is isomorphic to a direct sum of matrix algebras associated to Iwahori--Hecke algebras of type A. This includes a description of the…
A general method for computing irreducible representations of Weyl groups and Iwahori-Hecke algebras was introduced earlier by the first author. The representations of the algebras of types $A_n$, $B_n$, $D_n$ and $G_2$ were computed and it…
We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov…
This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…
Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large…
Metropolis algorithms are classical tools for sampling from target distributions, with broad applications in statistics and scientific computing. Their convergence speed is governed by the spectral gap of the associated Markov operator.…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…
Meta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with…
In this paper, and a second part to follow, we complete the programme (initiated more than 15 years ago) of determining the decomposition numbers and verifying James' Conjecture for Iwahori--Hecke algebras of exceptional type. The new…
Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report about the generalization of these elementary rotations towards canonical transformations acting in…
Consider the problem of approximating a given probability distribution on the cube $[0,1]^n$ via the use of a square lattice discretization with mesh-size $1/N$ and the Metropolis algorithm. Here the dimension $n$ is fixed and we focus for…
In this paper we study the Hecke algebra associated with a complex reflection group W. We discuss some properties of the Galois group of the splitting field of this algebra, and study its action on the so-called fake degrees of W. The…
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…