Related papers: On Buffon Machines and Numbers

The exponential and Gaussian functions are among the most fundamental and important operations, appearing ubiquitously throughout all areas of science, engineering, and mathematics. Whereas formally, it is well-known that any function may…

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…

Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…

Bayesian statistics is a cornerstone of imaging sciences, underpinning many and varied approaches from Markov random fields to score-based denoising diffusion models. In addition to powerful image estimation methods, the Bayesian paradigm…

An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…

The Favard length of a subset of the plane is defined as the average of its orthogonal projections. This quantity is related to the probabilistic Buffon needle problem; that is, the Favard length of a set is proportional to the probability…

In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…

In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…

Calculations and mechanistic explanations for the probabilistic movement of objects at the highly relevant cm length scales has been lacking and overlooked due to the complexity of current techniques. Predicting the final-configuration…

Boson sampling is a problem for which quantum devices could prove to go beyond classical computing using only linear optics and photon preparation and counting. While theoretically important, there is a lack of practical applications for…

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…

Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…

We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak…

One of the big challenges in astrophysics is the comparison of complex simulations to observations. As many codes do not directly generate observables (e.g. hydrodynamic simulations), the last step in the modelling process is often a…

We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation $\pi \in \mathbb{S}_n$ is proportional to $q^{\textrm{inv}(\pi)}$ where $0<q\le 1$ and…

We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and…

We analysed the distribution of the number of goals scored in each of the 51 football matches played in the UEFA EURO 2020 final phase as well as the waiting times between scores (also considering censored times). We found that the Poisson…

In this paper we get an estimate of Favard length of an arbitrary neighbourhood of an arbitrary self-similar Cantor set. Consider $L$ closed disjoint discs of radius $1/L$ inside the unit disc. By using linear maps of smaller disc onto the…

We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…

Physical Unclonable Functions (PUFs) are widely used to generate random Numbers. In this paper we propose a new architecture in which an Arbiter Based PUF has been employed as a nonlinear function in Nonlinear Feedback Shift Register (NFSR)…