Related papers: Walking through the Gaussian Primes
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
The problem of which Gauss diagram can be realized by plane curves is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. We show that needed conditions for realizability of a Gauss…
In our previous work, we defined a prime walk (PW) on a square grid and presented several intriguing numerical results. Here, we demonstrate the main conjecture presented there, namely, that the area covered by the prime walk is unbounded.…
This paper presents a new multi-query motion planning algorithm for linear Gaussian systems with the goal of reaching a Euclidean ball with high probability. We develop a new formulation for ball-shaped ambiguity sets of Gaussian…
We provide improved complexity results for symmetric primal--dual interior-point algorithms in conic optimization. The results follow from new uniform bounds on a key complexity measure for primal--dual metrics at pairs of primal and dual…
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
This work proposes a proof of the simplest cubic primes counting problem. It shows that the subset of primes {p = n^3 + 2 is prime : n => 1} is an infinite subset of primes. Further, the expected order of magnitude of the cubic primes…
We give a polynomial time approximation scheme (PTAS) for computing the supremum of a Gaussian process. That is, given a finite set of vectors $V\subseteq\mathbb{R}^d$, we compute a $(1+\varepsilon)$-factor approximation to $\mathop…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…
Given a set of moment restrictions (MRs) that overidentify a parameter $\theta$, we investigate a semiparametric Bayesian approach for inference on $\theta$ that does not restrict the data distribution $F$ apart from the MRs. As main…
In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under…
We consider the Gaussian limit law for the distribution of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an optimal bound for the speed of convergence, thereby improving on previous estimates…
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the…
We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of integration is…
In this article, we propose and develop a novel Bayesian algorithm for optimization of functions whose first and second partial derivatives are known. The basic premise is the Gaussian process representation of the function which induces a…
We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest possible gap between consecutive primes assuming the Riemann…
One aspect of Chebyshev's bias is the phenomenon that a prime number, $ q $, modulo another prime number, $ p$, experimentally seems to be slightly more likely to be a nonquadratic residue than a quadratic residue. We thought it would be…