Related papers: Normal forms of random braids
Let a simple random walk run inside a torus of dimension three or higher for a number of steps which is a constant proportion of the volume. We examine geometric properties of the range, the random subgraph induced by the set of vertices…
According to a general probabilistic principle, the natural divisors of friable integers (i.e.~free of large prime factors) should normally present a Gaussian distribution. We show that this indeed is the case with conditional density…
Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability.…
For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present…
The change in the normal between any two nearby points on a closed, smooth surface is bounded with respect to the local feature size (distance to the medial axis). An incorrect proof of this lemma appeared as part of the analysis of the…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
We report a statistical analysis over more than eight thousand songs. Specifically, we investigate the probability distribution of the normalized sound amplitudes. Our findings seems to suggest a universal form of distribution which…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…
This article discusses random hypergraphs with varying hyperedge sizes, admitting large hyperedges with size tending to infinity, and heavy-tailed limiting hyperedge size distributions. The main result describes a threshold for the random…
Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population averaged…
We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but…
This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density $\lambda$ of the sets grows to infinity and the mean volume $\rho$ of the sets tends to zero. Assuming that the volume…
A symbolic-computational algorithm, fully implemented in Maple, is described, that computes explicit expressions for generating functions that enable the efficient computations of the expectation, variance, and higher moments, of the random…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven…
We prove that the Garside length a braid is equal to a winding-number type invariant of the curve diagram of the braid.
We prove new probabilistic upper bounds on generalization error of complex classifiers that are combinations of simple classifiers. Such combinations could be implemented by neural networks or by voting methods of combining the classifiers,…