Related papers: Percolation theory of self-exciting temporal proce…
A method is presented that, when used in conjunction with single molecule experimental techniques, allows for the extraction of rates and mechanical properties of a biomolecule undergoing transitions between mechanically distinct states.…
Many complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by sudden energy releases called avalanches. Recently, it has been pointed out that several basic features of avalanche…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process.…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
The hypersphere model is a simple one-parameter model of the potential energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in $\mathbb{R}^{3N}$ in which $N$ is the…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
The Hawkes process is a self-exciting sample point process. It has wide applications in finance, social networks, criminology, seismology, and many other fields. With the development of storage technology, data-driven models are attracting…
The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently-connected network of linear Hawkes processes. It extends previous studies that have explored the case of a (linear)…
A phase diagram for a one-dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding the dynamics of the model: strength of disorder and range of stress relaxation. When the range of stress…
A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase…
Although the time profiles of gamma ray bursts (GRBs) show extremely diverse behavior, their average statistical properties such as the average peak-aligned profile and the auto-correlation function show simple stretched-exponential…
Bootstrap percolation transition may be first order or second order, or it may have a mixed character where a first order drop in the order parameter is preceded by critical fluctuations. Recent studies have indicated that the mixed…
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…
Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of terms which correspond to individual 'processes' or 'fluxes'. Frequently, these…