Related papers: Correlation time in extremal self-organized critic…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
A wide variety of complex systems exhibit large fluctuations both in space and time that often can be attributed to the presence of some kind of critical phenomena. Under such critical scenario it is well known that the properties of the…
A punctuated equilibrium model of biological evolution with relative fitness between different species being the fundamental driving force of evolution is introduced. Mutation is modeled as a fitness updating cellular automaton process…
Collective behaviour in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological…
Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
We give rigorous analytical results on the temporal behavior of two-point correlation functions --also known as dynamical response functions or Green's functions-- in closed many-body quantum systems. We show that in a large class of…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
The short-time and long-time dynamics of the Bak-Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibits an initial…
The existence of power-law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
Although atomistic simulations of proteins and other biological systems are approaching microsecond timescales, the quality of trajectories has remained difficult to assess. Such assessment is critical not only for establishing the…
We propose a hidden variable analysis of collapse dynamics in which the state's reduction process may take a finite time $\delta t$. A full characterization of the model is given for the case of black boxes. By introducing nonlocal perfect…
We develop a theory of finite-time scaling for dynamic quantum criticality by considering the competition among an external time scale, an intrinsic reaction time scale and an imaginary time scale arising respectively from an external…
Here we provide a detailed analysis, along with some extensions and additonal investigations, of a recently proposed self-organised model for the evolution of complex networks. Vertices of the network are characterised by a fitness variable…
Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations…