Most previous investigations on spatial Public Goods Game assume that individuals treat neighbors equivalently, which is in sharp contrast with realistic situations, where bias is ubiquitous. We construct a model to study how a selective investment mechanism affects the evolution of cooperation....

Time delay, accounting for constant incubation period or sojourn times in an infective state, widely exists in most biological systems like epidemiological models. However, the effect of time delay on spatial epidemic models is not well understood. In this paper, spatial pattern of an epidemic...

One of the central issues in epidemiology is the study of the distribution of disease. And time delay widely exists in the process of disease spread. Thus, in this paper, we presented an epidemic model with spatial diffusion and time delay. By mathematical analysis, we find two different types...

Large-scale data are analysed using the Wigner function. It is shown that the ‘frequency variable’ provides important information, which is lost with other techniques. The method is applied to ‘sentiment analysis’ in data from social networks and also to financial data.

A method, based on symmetry considerations, is presented by which the size of the shift operator matrix appropriate to an M x ∞ lattice with periodic boundary conditions (in the M-direction) can be reduced by a factor of M-1. Since the computation time required to obtain the eigenvalues of...

We argue that the statistical character of wave propagation in random media can be described in terms of two universal parameters which are average properties of eigenmodes of the field. We show that the width and spacing of electromagnetic modes can be determined from the measurement of the...