Related papers: On Pair Correlation of Sequences
This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…
The article determines the asymptotic shape of the extremal clusters in stationary regularly varying random fields. To deduce this result, we present a general framework for the Poisson approximation of point processes on Polish spaces…
Cooperation in cellular networks is a promising scheme to improve system performance. Existing works consider that a user dynamically chooses the stations that cooperate for his/her service, but such assumption often has practical…
For $N\in\mathbb{N}$, let $\pi_N$ be the law of the number of fixed points of a random permutation of $\{1, 2, ..., N\}$. Let $\mathcal{P}$ be a Poisson law of parameter 1.A classical result shows that $\pi_N$ converges to $\mathcal{P}$ for…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
The paper deals with real valued sequences and its distribution on real line.
We extend the classical associative PI-theory to Associative Pairs, and in doing so, we introduce related notions already present for algebras (and Jordan systems) as the ones of PI-element and PI-ideal, extended centroid and central…
Optical orthogonal codes (OOCs) are sets of $(0,1)$-sequences with good auto- and cross-correlation properties. They were originally introduced for use in multi-access communication, particularly in the setting of optical CDMA…
It is an open question whether the fractional parts of nonlinear polynomials at integers have the same fine-scale statistics as a Poisson point process. Most results towards an affirmative answer have so far been restricted to almost sure…
Given a dataset $S$ of points in $\mathbb{R}^2$, the range closest-pair (RCP) problem aims to preprocess $S$ into a data structure such that when a query range $X$ is specified, the closest-pair in $S \cap X$ can be reported efficiently.…
We present a new approach to derive the connectivity properties of pairwise interacting n-body systems in thermal equilibrium. We formulate an integral equation that relates the pair connectedness to the distribution of nearest neighbors.…
Let $p$ be a large prime, and let $C$ be a hyperelliptic curve over $\mathbb{F}_p$. We study the distribution of the $x$-coordinates in short intervals when the $y$-coordinates lie in a prescribed interval, and the distribution of the…
Pearson's correlation coefficient is a popular statistical measure to summarize the strength of association between two continuous variables. It is usually interpreted via its square as percentage of variance of one variable predicted by…
This paper proposes a new paradigm and computational framework for identification of correspondences between sub-structures of distinct composite systems. For this, we define and investigate a variant of traditional data clustering, termed…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
Several results about the union-closed sets conjecture are presented.
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
Let $\{ a(x) \}_{x=1}^{\infty}$ be a positive, real-valued, lacunary sequence. This note shows that the pair correlation function of the fractional parts of the dilations $\alpha a(x)$ is Poissonian for Lebesgue almost every $\alpha\in…
The possibilities of unlike particle correlations for a study of the space-time asymmetries in particle production, including the sequence of particle emission, are demonstrated.