Related papers: Construction of Benford Random Variables: Generato…
It is well known that the output of a Neural Network trained to disentangle between two classes has a probabilistic interpretation in terms of the a-posteriori Bayesian probability, provided that a unary representation is taken for the…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
In random walks, the path representation of the Green's function is an infinite sum over the length of path probability density functions (PDFs). Here we derive and solve, in Laplace space, the recursion relation for the n order path PDF…
We present a rejection method based on recursive covering of the probability density function with equal tiles. The concept works for any probability density function that is pointwise computable or representable by tabular data. By the…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. The proposal…
We describe a density-functional method which aims at computing the ground state electron density and the spectral function at the same time. One basic ingredient of our method is the construction of the spectral function from the first…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
We present a new approach to constructing unconditional pseudorandom generators against classes of functions that involve computing a linear function of the inputs. We give an explicit construction of a pseudorandom generator that fools the…
This paper investigates probability density functions (PDFs) that are continuous everywhere, nearly uniform around the mode of distribution, and adaptable to a variety of distribution shapes ranging from bell-shaped to rectangular. From the…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
The precise analysis of the variance of the profile of a suffix tree has been a longstanding open problem. We analyze three regimes of the asymptotic growth of the variance of the profile of a suffix tree built from a randomly generated…
We present an algorithm for bounding the probability of r-core formation in k-uniform hypergraphs. Understanding the probability of core formation is useful in numerous applications including bounds on the failure rate of Invertible Bloom…
A method for generating random $U(1)$ variables with Boltzmann distribution is presented. It is based on the rejection method with transformation of variables. High efficiency is achieved for all range of temparatures or coupling…
A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos…
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…
We will discuss the key concepts in density functional theory (DFT), how it can be used to model experimental data, and consider how the synergy between DFT and experiment can give significant insights. The discussion will centre on the…
This letter proposes a data-driven method for estimating the probability of wind ramping events without exploiting the exact probability distribution function (PDF) of wind power. Actual wind data validates the proposed method.
It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strings that are random and pairwise independent. If the two…
We present the first prediction of the probability distribution function (PDF) for self-organization of shear flows modeled by a nonlinear diffusion equation with a stochastic forcing. A novel non-perturbative method based on a coherent…