Related papers: Analytic aspects of the bi-free partial R-transfor…
Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…
Bipartite incidence graph sampling provides a unified representation of many sampling situations for the purpose of estimation, including the existing unconventional sampling methods, such as indirect, network or adaptive cluster sampling,…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
Extending ideas of A.N. Parshin and D.V. Osipov, Harmonic Analysis is developed for filtered infinite dimensional modules over a ring. We establish Pontryagin duality, the Fourier inversion formula, Plancherel formula and Poisson summation…
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
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…
The algebra Mul[[B]] of formal multilinear function series over an algebra B and its quotient SymMul[[B]] are introduced, as well as corresponding operations of formal composition. In the setting of Mul[[B]], the unsymmetrized R- and…
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically…
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
In this article, we introduce a new variable selection technique through trimming for finite mixture of regression models. Compared to the traditional variable selection techniques, the new method is robust and not sensitive to outliers.…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge $c\leqslant 1$, scaling exponents of harmonic measure…
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…
This paper is on further development of discrete complex analysis introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is…
We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on $\R$. The formula is given in terms of the $R$-transform of the first measure, and…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using harmonic means and completely partitioned weighted geometric means. Our result…
In this paper we present a theoretical analysis of a recently proposed two-dimensional Cellular Automata model for traffic flow in cities with the novel ingredient of turning capability. Numerical simulations of this model show that there…
The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical…