Related papers: Combinatorial and approximative analyses in a spat…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine…
Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting systems described in terms of continuous-time Markov chains, their embedded discrete-time Markov chains and…
This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…
Two main features of the observable distribution of visible matter are the space correlations of galaxy positions and the mass function of galaxies. As discussed in Pietronero and Sylos Labini on this issue ([1], see also [2],[3]), the…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…
For a given pcf self-similar fractal, a certain network (weighted graph) is constructed whose ideal boundary is (homeomorphic to) the fractal. This construction is the first representation of a connected self-similar fractal as the boundary…
In this paper, we propose an efficient pseudo-marginal Markov chain Monte Carlo (MCMC) sampling approach to draw samples from posterior shape distributions for image segmentation. The computation time of the proposed approach is independent…
The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…
We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…
Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…
Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
The main focus of this work is the asymptotic behavior of mass-conservative homogeneous fragmentations. Considering the logarithm of masses makes the situation reminiscent of branching random walks. The standard approach is to study {\bf…
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a…