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The Fleming-Viot process with parent-independent mutation process is one particular neutral population genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high,…
The experimental search for the QCD critical point by means of relativistic heavy-ion collisions necessitates the development of dynamical models of fluctuations. In this work we study the fluctuations of the net-baryon density near the…
In a highly influential paper twenty years ago, Barab\'asi and Albert [Science 286, 509 (1999)] showed that networks undergoing generic growth processes with preferential attachment evolve towards scale-free structures. In any finite…
In this Letter, we investigate how changes in the system entropy influence the characteristic time scale of the system molecular dynamics near the glass transition. Independently of any model of thermodynamic evolution of the time scale,…
The paper studies the problem of detecting and locating change points in multivariate time-evolving data. The problem has a long history in statistics and signal processing and various algorithms have been developed primarily for simple…
We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…
We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…
Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges…
Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…
We study the Tangled Nature model of macro evolution and demonstrate that the co-evolutionary dynamics produces an increasingly correlated core of well occupied types. At the same time the entire configuration of types becomes increasing…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a…
Although the cooperative dynamics emerging from a network of interacting players has been exhaustively investigated, it is not yet fully understood when and how network reciprocity drives cooperation transitions. In this work, we…
We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance…
Results are presented for the time evolution of fermions initially in a non-zero temperature normal phase, following the switch on of an attractive interaction. The dynamics are studied in the disordered phase close to the critical point,…
Static and dynamical properties of elastic phase transitions under the influence of short--range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg--Landau theory for…
In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$…