Related papers: Euclidean algorithms are Gaussian over imaginary q…

Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…

In a recent paper the author proved a theorem to the effect that the matrix of normalized Euclidean distances on the set of specially distributed random points in the $n$-dimensional Euclidean space $\mathbb R^{n}$ with independent…

This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…

The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler--Poisson) integral over a finite boundary, as it is necessary for instance for the error function…

We consider a search algorithm for the output distribution that achieves the channel capacity of a discrete memoryless channel. We will propose an algorithm by iterated projections of an output distribution onto affine subspaces in the set…

We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions. This structure arises in several optimization problems in statistics and machine learning, e.g., for matrix scaling,…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

It is shown that if the Euclidean path integral measure of a minimally coupled free quantum scalar field on a classical metric background is interpreted as probability of observing the field configuration given the background metric then…

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…

The proof of the theorem, which states that the Euclidean metric on the set of random points in an $n$-dimensional Euclidean space with the distribution of a special class, converges in probability in the limit $n\rightarrow\infty$ to the…

This paper provides a general and abstract approach to approximate ergodic regimes of Markov and Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton & Pages (2002) and based on simulation algorithms…

This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…

We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this…

We present a new quantum algorithm for estimating the mean of a real-valued random variable obtained as the output of a quantum computation. Our estimator achieves a nearly-optimal quadratic speedup over the number of classical i.i.d.…

We prove that all imaginary biquadratic fields and cyclic quartic fields of class number $1$ are Euclidean.

In this article, we consider the Euclidean dispersion problems. Let $P=\{p_{1}, p_{2}, \ldots, p_{n}\}$ be a set of $n$ points in $\mathbb{R}^2$. For each point $p \in P$ and $S \subseteq P$, we define $cost_{\gamma}(p,S)$ as the sum of…

When partitioning workflows in realistic scenarios, the knowledge of the processing units is often vague or unknown. A naive approach to addressing this issue is to perform many controlled experiments for different workloads, each…

We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…

The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…

We study the angular process related to random walks in the Euclidean and in the non-Euclidean space where steps are Cauchy distributed. This leads to different types of non-linear transformations of Cauchy random variables which preserve…