The deterministic-stochastic flow model

确定树和随机树中的生长自旋模型

Growing spin model in deterministic and stochastic trees

我们在确定性和随机（随机）无标度树的拓扑结构中解决了增长的非对称伊辛模型[Phys. Rev. E 89，012105（2014）]，预测其对于小于耦合常数$J$的外部场的非单调行为。在这两种情况下，我们指出，交叉温度对应于最大磁化衰减约为$(\ln \ln N)^{-1}$，其中$N$是在树中的节点数。

Mathematical analysis of a delayed SEIRDS epidemics models: deterministic and stochastic approach

The primary goal of this research is to investigate the impact of delay on the dynamics of the Susceptible-Exposed-Infected-Recovered-Death and Susceptible (SEIRDS) model, to which we add a stochastic term to account for uncertainty in COVID-19 parameter estimations. We run two models, one deterministic and one stochastic, and show that their solutions exist and are unique. We also numerically investigate the impact of immunity loss on the emerging time of a new wave, as well as the necessary condition for the extinction and persistence of the disease.

随机计数数据中的普适确定性模式

Universal deterministic patterns in stochastic count data

本文发现随机计数数据均值与Fano因子图中存在普适确定性模式，并发展理论证明其仅取决于样本大小，适用于多领域数据集。

The deterministic Kermack-McKendrick model bounds the general stochastic epidemic

We prove that, for Poisson transmission and recovery processes, the classic Susceptible $\to$ Infected $\to$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time $t>0$, a strict lower bound on the expected number of suscpetibles and a strict upper bound on the expected number of recoveries in the general stochastic SIR epidemic. The proof is based on the recent message passing representation of SIR epidemics applied to a complete graph.