Related papers: The Path to Recent Progress on Small Gaps Between …
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…
We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial ingredient in our work are recent…
We derive heuristically formula for the $k$--moments $M_k(x)$ of the gaps between consecutive primes$<x $ represented directly by $x$$\pi(x)$ --- the number of primes up to: $M_k(x)= \Gamma(k+1)x^k/\pi^{k-1}(x)+\mathcal{O}(x)$, We…
It is shown how simple assumptions lead to piecewise linear behavior, which is observed in certain phase transitions.
We analyze the inequality $\sqrt{P_{k+1}}-\sqrt{P_{k}}<1,\ k\in\mathbb{N}$, discuss the existence of primes on arbitrary intervals $(r,s),\ r<s,\ r,s\in\mathbb{R}$, and finally address the issue of primes between squares of naturals.
This paper introduces new subdifferential concepts together with their main properties and place with respect to other subdifferential notions.
This talk will review selected topics in rapidity gap physics. In particular I will discuss diffractive jet production and the possibility of searching for the higgs boson using diffraction at the LHC; the dipole picture of diffraction and…
Ideally, the time that an incremental algorithm uses to process a change should be a function of the size of the change rather than, say, the size of the entire current input. Based on a formalization of ``the set of things changed'' by an…
This article gives an overview, aimed at theoretical particle physicists, of some recent developments in cosmology.
This paper gives a short survey of recent trends in the emerging field of big data. It explains the definitions and useful methods. In addition, application fields of smart buildings and smart grids are discussed.
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
Prime numbers appeared in contexts spanning statistical mechanics, quantum mechanics and dynamical systems. However, the mechanisms governing the irregularities observed in their sequence and linking them to physical systems remained…
In this expository article, we describe the recent approach, motivated by ergodic theory, towards detecting arithmetic patterns in the primes, and in particular establishing that the primes contain arbitrarily long arithmetic progressions.…
This is the preface to the special issue of the Journal of Physics A: Mathematical and Theoretical, entitled "New trends in first-passage methods and applications in the life sciences and engineering"
We study the first occurrences of gaps between primes in the arithmetic progression (P): $r$, $r+q$, $r+2q$, $r+3q,\ldots,$ where $q$ and $r$ are coprime integers, $q>r\ge1$. The growth trend and distribution of the first-occurrence gap…
We study arithmetic functions $\Phi(x;d,a)$, called prime running functions, whose value at $x$ sums the gaps between primes $p_k \equiv a\ (\text{mod}\ d)$ below $x$ and the next following prime $p_{k+1}$, up to $x$. (The following prime…
I present an overview of some current topics in the measurement of Parton Distribution Functions.
We propose a method to describe the short-distance behavior of an interface fluctuating in the presence of the wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average height of the…
We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a specific bound. From a rigorous analysis of this model, we…