The last decade has witnessed the apparition of applied problems typified by very high-dimensional variables, in marketing database or gene expression studies for instance. Graphical models (Lauritzen (1996)) enable concise representations of associational relations between variables. If the graph is known, the parameters of the model are easily estimated. However, a quite challenging issue is ...

We study a class of linear first and second order partial differential equations driven by weak geometric p-rough paths, and prove the existence of a unique solution for these equations. This solution depends continuously on the driving rough path. This allows a robust approach to stochastic partial differential equations. In particular, we may replace Brownian motion by more general Gaussian a...

Algorithm 1 Seidel(A, b, c) 1: if there is only one variable then 2: Treat all inequalities in Ax ≤ b as equalities and solve for x in each. 3: Return the point out of these that maximizes c. 4: end if 5: if there are as many constraints as variables then 6: Solve the linear system Ax = b using Gaussian elimination and return the resulting point. 7: end if 8: Pick a constraint h : aix ≤ bi unif...

Sparse Gaussian Elimination on High Performance Computers

The problem of computing the lower tail of a Gaussian norm is considered in this paper. Based on large deviations arguments, a bound on these tails is derived which is tighter than those obtained by other methods. Conditional exponential moment bounds are also derived and as an application, L 2 type Onsager-Machlup functionals for diiusions are computed.

We present new complexity results on the class of 0/1/All constraints. The central idea involves functional elimination, a general method of elimination whose focus is on the subclass of functional constraints. One result is that for the subclass of "All" constraints, strong n-consistency and minimality is achievable in O(en) time, where e, n are the number of constraints and variables. The mai...

We study monoids generated by Zariski-van Kampen generators in the 17 fundamental groups of the complement of logarithmic free divisors in C listed by Sekiguchi (Theorem 1). Five of them are Artin monoids and eight of them are free abelian monoids. The remaining four monoids are not Gaußian and, hence, are neither Garside nor Artin (Theorem 2). However, we introduce, similarly to Artin monoids,...

We examine the extent to which Gaussian relay networks can be approximated by deterministic networks, and present two results, one negative and one positive. The gap between the capacities of a Gaussian relay network and a corresponding linear deterministic network can be unbounded. The key reasons are that the linear deterministic model fails to capture the phase of received signals, and there...

In general, the noise that is present in real-world 3D surface scan data prevents accurate curvature calculation. In this paper we show how curvature can be extracted from noisy data by applying filtering after a noisy curvature calculation. To this end, we extend the standard Gaussian filter (as used in 2D image processing) by taking adjacent point distances along the scanned surface into acco...

Contents Preface vii Chapter 1. Introduction 1 1.1. Random polynomials and their zeros 1 1.2. Basic notions and definitions 6 1.3. Hints and solutions 11 Chapter 2. Gaussian Analytic Functions 13 2.