Sampling From A Manifold

We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to Neyman's smooth test. This article is partially expository, giving an introduction to the tools of geometric measure theory

Multiple symbol differential detection of uncoded and trellis coded MPSK

A differential detection for MPSK, which uses a multiple symbol observation interval, is presented and its performance analyzed and simulated. The technique makes use of maximum-likelihood sequence estimation of the transmitted phases rather than symbol-by-symbol detection as in conventional differential detection. As such the performance of this multiple symbol detection scheme fills the gap between conventional (two-symbol observation) differentially coherent detection of MPSK and ideal coherent of MPSK with differential encoding. The amount of improvement gained over conventional differential detection depends on the number of phases, M, and the number of additional symbol intervals added to the observation. What is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation. The analysis and simulation results presented are for uncoded and trellis coded MPSK

Sampling from a manifold

Abstract: We develop algorithms for sampling from a probability distribution on a submanifold embedded in R n . Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to Neyman's smooth test. This article is partially expository, giving an introduction to the tools of geometric measure theory

Sur la répartition des valeurs des fonctions arithmétiques

La thèse concerne différents aspects de la répartition des fonctions arithmétiques.1. Deshouillers, Iwaniec et Luca se sont récemment intéressés à la répartition modulo 1 de suites qui sont des valeurs moyennes de fonctions multiplicatives, par exemple phi(n)/n où phi est la fonction d'Euler. Nous étendons leur travail à la densité modulo 1 de suites qui sont des valeurs moyennes sur des suites polynômiales, typiquement n^2+1.2. On sait depuis les travaux de Katai, il y a une quarantaine d'années que la fonction de répartition des valeurs de phi(p-1)/(p-1) (où p parcourt les nombres premiers) est continue, purement singulière, strictement croissante entre 0 et 1/2. On précise cette étude en montrant que cette fonction de répartition a une dérivée infinie à gauche de tout point phi(2n)/(2n).AbstractBORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

The spherical mean value operator for compact symmetric spaces

When M is a compact symmetric space, the spherical mean value operator Lr(for a fixed r > 0) acting on L2(M) is considered. The eigenvalues λ for Lrf = λf are explicitly determined in terms of the elementary spherical functions associated with the symmetric space. Alternative proofs are also provided for some results of T. Sunada regarding the special eigenvalues +1 and −1 using a purely harmonic analytic point of view