Related papers: Quantifying Local Randomness in Human DNA and RNA …
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…
Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random…
Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels…
We consider the problem of detecting a random walk on a graph, based on observations of the graph nodes. When visited by the walk, each node of the graph observes a signal of elevated mean, which we assume can be different across different…
An RNA sequence is a word over an alphabet on four elements $\{A,C,G,U\}$ called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can…
Excited random walks (ERWs) are a self-interacting non-Markovian random walk in which the future behavior of the walk is influenced by the number of times the walk has previously visited its current site. We study the speed of the walk,…
We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ)^d, d >= 3, until u N^d time steps, u > 0, and the model of random interlacements recently introduced by Sznitman. In…
We consider the hypothesis that Evolution promotes population-wide genome patterns that, under randomization, ensures the External Validity of adaptations across population members. An adaptation is Externally Valid (EV) if its effect holds…
The so called long range correlation properties of DNA sequences are studied using the variance analyses of the density distribution of a single or a group of nucleotides in a model independent way. This new method which was suggested…
The weights of a neural network are typically initialized at random, and one can think of the functions produced by such a network as having been generated by a prior over some function space. Studying random networks, then, is useful for a…
We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our…
We study variable-speed random walks on $\mathbb Z$ driven by a family of nearest-neighbor time-dependent random conductances $\{a_t(x,x+1)\colon x\in\mathbb Z, t\ge0\}$ whose law is assumed invariant and ergodic under space-time shifts. We…
Inspired by the study of edge statistics of random band matrices, we investigate random walks on large $d$-dimensional periodic lattices, whose transition matrices are determined by discretized density functions. Under certain moment…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
Gene duplication is a fundamental evolutionary mechanism that contributes to biological complexity and diversity (Fortna et al., 2004). Traditionally, research has focused on the duplication of gene sequences (Zhang, 1914). However,…
Thousands of candidate human-specific regulatory sequences (HSRS) have been identified, supporting the hypothesis that unique to human phenotypes result from human-specific alterations of genomic regulatory networks. Here, conservation…
In this paper we study two natural models of \textit{random temporal} graphs. In the first, the \textit{continuous} model, each edge $e$ is assigned $l_e$ labels, each drawn uniformly at random from $(0,1]$, where the numbers $l_e$ are…
Our paper gives bounds for the rate of convergence for a class of random walks on the d-dimensional torus generated by a set of n vectors in R^d/Z^d. We give bounds on the discrepancy distance from Haar measure; our lower bound holds for…
A quantitative theory on the construction and the evolution of the genetic code is proposed. Through introducing the concept of mutational deterioration (MD) and developing a theoretical formalism on MD minimization we have proved: 1, the…