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We develop a model for the cohomology of the complement of a hypersurface arrangement inside a smooth projective complex variety. This generalizes the case of normal crossing divisors, discovered by P. Deligne in the context of the mixed…
In a companion article we have introduced a notion of multiscale functional inequalities for functions $X(A)$ of an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. These inequalities are multiscale weighted versions…
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking…
Margot (1994) in his doctoral dissertation studied extended formulations of combinatorial polytopes that arise from "smaller" polytopes via some composition rule. He introduced the "projected faces property" of a polytope and showed that…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…
New sequences of orthogonal polynomials with ultra-exponential weight functions are discovered. In particular, it gives an explicit solution to the Ditkin-Prudnikov problem (1966). The 3-term recurrence relations, explicit representations,…
Pairwise Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. Variables correspond to nodes of a graph, with edges between nodes corresponding to conditional…
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for…
Within the applications of spatial point processes, it is increasingly becoming common that events are labeled by marks, prompting an exploration beyond the spatial distribution of events by incorporating the marks in the undertaken…
Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of…
The main purpose of this paper is to provide a structure theorem for codimension one singular transversely projective foliationson projective manifolds. To reach our goal, we firstly extend Corlette-Simpson's classification of rank two…
An interesting class of orthogonal representations consists of the so-called turn-regular ones, i.e., those that do not contain any pair of reflex corners that "point to each other" inside a face. For such a representation H it is possible…
This is the second part of the paper 0709.3806v2. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as four-point correlation function with one completely degenerate and one…
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…
Undirected graphical models have been successfully used to jointly model the spatial and the spectral dependencies in earth observing hyperspectral images. They produce less noisy, smooth, and spatially coherent land cover maps and give top…
We determine the image of the monodromy map for meromorphic projective structures with poles of orders greater than two. This proves the analogue of a theorem of Gallo-Kapovich-Marden, and answers a question of Allegretti and Bridgeland.…