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The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
A stochastic model with a continuum of economic agents often involves shocks at both macro and micro levels. This can be formalized by a continuum of random variables that are conditionally independent given the macro level shocks. Based on…
In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a randomly forced particle which collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival…
We present a model of solids made from polygonal cells connected via beams. We calculate the macroscopic elastic moduli from the beam and cell parameters. This modellisation is particularly suited for the simulation of fragmentation…
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…
One of the most important scaling laws of time dependent fracture is Basquin's law of fatigue, namely, that the lifetime of the system increases as a power law with decreasing external load amplitude, $t_f\sim \sigma_0^{-\alpha}$, where the…
Power law potentials dictate interactions across scales and matter, controlling the structure and dynamics of inanimate, and living systems. Though the equilibrium distributions of particles with a power law repulsion were extensively…
We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds.…
We construct the effective theory of electrically charged, spatially extended, infinitely heavy objects at leading power. The theory may be viewed as a generalization of NRQED for particles with a finite charge distribution where the charge…
The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly,…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…
The analogy of classical repulsive interactions emerging from the exchange of mediating particles is revisited with a quantitative approach. Simulations are presented for a particular toy model which are accessible to undergraduate students…
We present a generalized dynamical model describing the sharing of information, and corresponding herd behavior, in a population based on the recent model proposed by Eguiluz and Zimmermann. By introducing a size-dependent probability for…
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average…
Over the last decades, impressive progresses have been made in many experimental domains, e.g. microscopic techniques such as single-particle tracking, leading to plethoric amounts of data. In a large variety of systems, from natural to…
The Foldy-Lax equation is generalized for a medium which consists of particles with both electric and magnetic responses. The result is used to compute fields scattered from ensembles of particles. The computational complexity is reduced by…