Related papers: Google matrix analysis of DNA sequences
The formal verification of large probabilistic models is important and challenging. Exploiting the concurrency that is often present is one way to address this problem. Here we study a restricted class of asynchronous distributed…
Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables…
Metabolic networks are known to be scale free but the evolutionary origin of this structural property is not clearly understood. One way of studying the dynamical process is to compare the metabolic networks of species that have arisen at…
In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In…
Random walks on discrete lattices are fundamental models that form the basis for our understanding of transport and diffusion processes. For a single random walker on complex networks, many properties such as the mean first passage time and…
We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which…
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of…
Evolution consists of distinct stages: cosmological, biological, linguistic. Since biology verges on natural sciences and linguistics, we expect that it shares structures and features from both forms of knowledge. Indeed, in DNA we…
Generative statistical models of chord sequences play crucial roles in music processing. To capture syntactic similarities among certain chords (e.g. in C major key, between G and G7 and between F and Dm), we study hidden Markov models and…
Social networking websites face a constant barrage of spam, unwanted messages that distract, annoy, and even defraud honest users. These messages tend to be very short, making them difficult to identify in isolation. Furthermore, spammers…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
Mays celebrated theoretical work of the 70s contradicted the established paradigm by demonstrating that complexity leads to instability in biological systems. Here Mays random-matrix modelling approach is generalized to realistic…
We introduce a formalism based on a continuous time approximation, to study the characteristics of Page Rank random walks. We find that the diffusion of the occupancy probability has a dynamics that exponentially "forgets" the initial…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
The spread of a real symmetric matrix is defined as the difference between its largest and smallest eigenvalue. The study of graph-related matrices has attracted considerable attention, leading to a substantial body of findings. In this…
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…
There are several ideas being used today for Web information retrieval, and specifically in Web search engines. The PageRank algorithm is one of those that introduce a content-neutral ranking function over Web pages. This ranking is applied…
We investigate the fundamental statistical features of tagged (or annotated) networks having a rich variety of attributes associated with their nodes. Tags (attributes, annotations, properties, features, etc.) provide essential information…
More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…