Birth and Death in a Continuous Opinion Dynamics Model. The consensus case

基于生灭过程微分-差分方程解析解的计数统计

Counting statistics based on the analytic solutions of the differential-difference equation for birth-death processes

该研究针对生灭过程速率随系统规模波动、其微分-差分方程难获非渐近解的问题，推导了无近似的解析解，得到计数统计表达式，揭示了系统规模统计性质的决定因素，为生灭过程定量研究开辟新方向。

Decay of Scale-Free Property in Birth-and-Death Network

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Birth, survival and death of languages by Monte Carlo simulation

Simulations of physicists for the competition between adult languages since 2003 are reviewed. How many languages are spoken by how many people? How many languages are contained in various language families? How do language similarities decay with geographical distance, and what effects do natural boundaries have? New simulations of bilinguality are given in an appendix.

Approximation of the first passage time distribution for the birth-death processes

We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain closed-form expressions. We apply the method to the three selected birth-death processes and the sophisticated order-book model exhibiting long-range memory. We discuss how our approach contributes to the competition between spurious and true long-range memory models.

Bessel-like birth-death process

We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDEs is of high importance for the alternatives of modeling. We propose and generalize the Bessel-like birth-death process having clear representation by the SDEs. The new process helps to integrate the alternatives of description and to derive the equations for the probability dens…

Coupling between death spikes and birth troughs. Part 2: Comparative analysis of salient features

In part 1 we identified a new coupling between death spikes and birth dips that occurs following catastrophic events such as influenza pandemics and earthquakes. Here we seek to characterize some of the key features. We introduce a transfer function defined as the amplitude of the birth trough (the output) divided by the amplitude of the death spike (the input). This has two features: it is always smaller than one so is an attenuation factor and as a function of the amplitude of the death spike, it may be characterized by a power law with exponent close to unity. Since many countries do not pu…