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We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by…
The homogeneous reconstructed evolutionary process is a birth-death process without observed extinct lineages. Each species evolves independently with the same diversification rates (speciation rate $\lambda(t)$ and extinction rate…
Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…
A fully threaded tree (FTT) for adaptive refinement of regular meshes is described. By using a tree threaded at all levels, tree traversals for finding nearest neighbors are avoided. All operations on a tree including tree modifications are…
In this paper we are concerned with the learnability of energies from data obtained by observing time evolutions of their critical points starting at random initial equilibria. As a byproduct of our theoretical framework we introduce the…
This paper considers the dynamics of edges in a network. The Dynamic Bond Percolation (DBP) process models, through stochastic local rules, the dependence of an edge $(a,b)$ in a network on the states of its neighboring edges. Unlike…
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…
In a critically self--organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes,…
In many complex systems, the dynamical evolution of the different components can result in adaptation of the connections between them. We consider the problem of how a fully connected network of discrete-state dynamical elements which can…
We study the extinction time $\uptau$ of the contact process on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on $\Z$, then, uniformly over all trees of degree…
We introduce the exit time finite state projection (ETFSP) scheme, a truncation-based method that yields approximations to the exit distribution and occupation measure associated with the time of exit from a domain (i.e., the time of first…
We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all…
We present analytical results for the effect of preferential node deletion on the structure of networks that evolve via node addition and preferential attachment. To this end, we consider a preferential-attachment-preferential-deletion…
We study the Boolean dynamics of the "quenched" Kauffman models with a directed scale-free network, comparing with that of the original directed random Kauffman networks and that of the directed exponential-fluctuation networks. We have…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…