This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a...

We consider the probability distribution function (pdf) and the multiscaling properties of the index and the traded volume in the Korean stock market. We observed the power law of the pdf at the fat tail region for the return, volatility, the traded volume, and changes of the traded volume. We...

We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes...

The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy transfer rates, etc., and it is shown that the formula...

The purpose of this paper is to offer a unified discussion of variable-order differential operators in anomalous diffusion modeling. The characteristics of the new models, in contrast to constant-order fractional diffusion models, change with time, space, concentration or other independent...

The solution of reduced Fokker–Planck–Kolmogorov (FPK) equation resulted from the problems in statistical mechanics is formulated as an exponential function of polynomials in state variables. Special measure is taken to satisfy the FPK equation in the weak sense of integration with the...

It has been proved that there are many indicators (petrophysical quantities) for the estimation of petroleum reservoirs. The value of information contained in each indicator is yet to be addressed. In this work, the most famous and applicable petrophysical quantities for a reservoir, which are...

In recent years, many studies have been devoted to complex differential equations (CDE), which appear in very important applications in physics and engineering. This paper aims to investigate one such CDE, containing a random forcing term:...

This paper presents comprehensive analysis of the evolution of the distribution of individual annual incomes across the majority of the population in China from 1992–2009. The cumulative distribution functions (CDFs) and probability density functions (PDFs) are presented. Overall, the CDFs...