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The constant rate birth--death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces `reconstructed trees' which describe the relationship between extant…
We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed…
Some models of clustering processes are formulated and analytically solved employing generating functions methods. Those models include events which result from combined action of the coagulation and fragmentation processes. Fragmentation…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size…
We present derivations of the contagion condition for a range of spreading mechanisms on families of generalized random networks and bipartite random networks. We show how the contagion condition can be broken into three elements, two…
This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a…
We introduce a new microscopic model of the outages in transmission power grids. This model accounts for the automatic response of the grid to load fluctuations that take place on the scale of minutes, when the optimum power flow…
We introduce a general approach to characterize composite fading models based on inverse gamma (IG) shadowing. We first determine to what extent the IG distribution is an adequate choice for modeling shadow fading, by means of a…
For taxonomic levels higher than species, the abundance distributions of number of subtaxa per taxon tend to approximate power laws, but often show strong deviationns from such a law. Previously, these deviations were attributed to…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…
We propose a means to relate properties of an interconnected system to its separate component systems in the presence of cascade-like phenomena. Building on a theory of interconnection reminiscent of the behavioral approach to systems…
We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $\gamma$. We use the branching process approach to obtain scaling…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…
This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…
We investigate a class of stochastic aggregation processes involving two types of clusters: active and passive. The mass distribution is obtained analytically for several aggregation rates. When the aggregation rate is constant, we find…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…