Related papers: Length Distributions in Loop Soups
While the structure of chromatin has been studied in great detail on length scales below 30 nm, amazingly little is known about the higher-order folding motifs of chromatin in interphase. Recent experiments give evidence that the folding…
Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs…
We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to…
The Longest Common Subsequence (LCS) problem is a very important problem in math- ematics, which has a broad application in scheduling problems, physics and bioinformatics. It is known that the given two random sequences of infinite…
The size of drops generated by the capillary-driven disintegration of liquid ligaments plays a fundamental role in several important natural phenomena, ranging from heat and mass transfer at the ocean-atmosphere interface to pathogen…
Let $L$ be subset of $\{3,4,\dots\}$ and let $X_{n,M}^{(L)}$ be the number of cycles belonging to unicyclic components whose length is in $L$ in the random graph $G(n,M)$. We find the limiting distribution of $X_{n,M}^{(L)}$ in the…
Using the maximum-entropy method, we calculate the end-to-end distance distribution of the force stretched chain from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule…
Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with…
Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…
A key task in the study of networked systems is to derive local and global properties that impact connectivity, synchronizability, and robustness; computing shortest paths or geodesics yields measures of network connectivity that can…
We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising…
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical…
This work studies the chord length distribution, in the case where both ends lie on a $N$-dimensional hypersphere ($N \geq 2$). Actually, after connecting this distribution to the recently estimated surface of a hyperspherical cap…
Observed transmission line outage data is grouped into successive generations of events. The empirical distribution of the number of generations in the cascades follows a Zipf distribution that implies the increasing propagation as cascades…
A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non-homogeneous phase-type distribution. It is built by considering one cut-point in the non-negative…
We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means,…
We study the random loop model with crosses and bars on sparse random graphs. Our main objective is to prove the existence of macroscopic loops, in the sense that a loop visits a positive proportion of the vertices. We develop a…
The authors consider the length, $l_N$, of the length of the longest increasing subsequence of a random permutation of $N$ numbers. The main result in this paper is a proof that the distribution function for $l_N$, suitably centered and…
We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for k=1,2,... and for the probability that the record of the…
We study the physics of droplet breakup in a statistically stationary homogeneous and isotropic turbulent flow by means of high resolution numerical investigations based on the multicomponent lattice Boltzmann method. We verified the…