Related papers: Quantifying Local Randomness in Human DNA and RNA …
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
We analyze some local properties of sparse Erdos-Renyi graphs, where $d(n)/n$ is the edge probability. In particular we study the behavior of very short paths. For $d(n)=n^{o(1)}$ we show that $G(n,d(n)/n)$ has asymptotically almost surely…
DNA and other biopolymers differ from classical polymers due to their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the `torsional…
In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as…
The nature of the quantitative distribution of the 64 DNA codons in the human genome has been an issue of debate for over a decade. Some groups have proposed that the quantitative distribution of the DNA codons ordered as a rank-frequency…
Cultural traits such as words, names, decorative styles, and technical standards often assume arbitrary values and are thought to evolve neutrally. But neutral evolution cannot explain why some traits come and go in cycles of popularity…
Any reliable biomarker has to be specific, generalizable, and reproducible across individuals and contexts. The exact values of such a biomarker must represent similar health states in different individuals and at different times within the…
The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a…
Researchers have demonstrated that humans are unable to generate a sequence of random numbers that corresponds in a statistical sense to a simple distribution such as the uniform distribution. The purpose of this article is to present the…
We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…
The main topic of this present thesis is the study of the asymptotic behaviour of sequences modulo 1. In particular, by using ergodic and dynamical methods, a new insight to problems concerning the asymptotic behaviour of multidimensional…
We consider the problem of performing a random walk in a distributed network. Given bandwidth constraints, the goal of the problem is to minimize the number of rounds required to obtain a random walk sample. Das Sarma et al. [PODC'10] show…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
We provide an ergodic theory framework to study statistical properties of smooth sequences over the odd alphabet {1, 3}. The arithmetic nature of this alphabet yields a partition of the subshift of smooth sequences based on their local…
Consider an algorithm performing a computation on a huge random object. Is it necessary to generate the entire object up front, or is it possible to provide query access to the object and sample it incrementally "on-the-fly"? Such an…
A great variety of complex systems ranging from user interactions in communication networks to transactions in financial markets can be modeled as temporal graphs, which consist of a set of vertices and a series of timestamped and directed…
Using the discrepancy metric, we analyze the rate of convergence of a random walk on the circle generated by d rotations, and establish sharp rates that show that badly approximable d-tuples in R^d give rise to walks with the fastest…
Topological and metric entropies of the DNA sequences from different organisms were calculated. Obtained results were compared each other and with ones of corresponding artificial sequences. For all envisaged DNA sequences there is a…