Doubly stochastic Yule cascades (Part I): The explosion problem in the time-reversible case

Motivated by the probabilistic methods for nonlinear differential equations introduced by McKean (1975) for the Kolmogorov-Petrovski-Piskunov (KPP) equation, and by Le Jan and Sznitman (1997) for the incompressible Navier-Stokes equations (NSE), we identify a new class of stochastic cascade models, referred to as doubly stochastic Yule cascades. We establish non-explosion criteria under the assumption that the randomization of Yule intensities from generation to generation is by an ergodic time-reversible Markov process. In addition to the cascade models that arise in the analysis of certain deterministic nonlinear differential equations, this model includes the multiplicative branching random walks, the branching Markov processes, and the stochastic generalizations of the percolation and/or cell ageing models introduced by Aldous and Shields (1988) and independently by Athreya (1985).     

A real-time monitoring approach for bivariate event data

Early detection of changes in the frequency of events is an important task in many fields, such as disease surveillance, monitoring of high-quality processes, reliability monitoring, and public health. This article focuses on detecting changes in multivariate event data by monitoring the time-between-events (TBE). Existing multivariate TBE charts are limited because they only signal after an event occurred for each of the individual processes. This results in delays (i.e., long time-to-signal), especially when we are interested in detecting a change in one or a few processes with different rates. We propose a bivariate TBE chart, which can signal in real-time. We derive analytical expressions for the control limits and average time-to-signal performance, conduct a performance evaluation and compare our chart to an existing method. Our findings showed that our method is an effective approach for monitoring bivariate TBE data and has better detection ability than the existing method under transient shifts and is more generally applicable. A significant benefit of our method is that it signals in real-time and that the control limits are based on analytical expressions. The proposed method is implemented on two real-life datasets from reliability and health surveillance.     

Recent Results on Recurrent Solutions and Limit Distributions of SDEs

The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial) differential equations (SDE in short). Under some suitable conditions, we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.     

带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质

本文考虑了带有某种相依重尾冲击的Poisson噪音过程尾的一致渐近性质.当冲击是二元上尾渐近独立的非负随机变量具有长尾和控制变化尾分布且噪音函数具有正的上下界时,得到了过程尾概率的一致渐近公式.进而,当冲击具有连续的一致变化尾分布时,去除了噪音函数具有正的下界的限制.对于噪音函数不一定具有正的上界的情形,当冲击具有两两负象限相依结构时,也得到了一致渐近性结果.     

Ultrasound-assisted polysaccharide extraction from Cercis chinensis and properites,antioxidant activity of polysaccharide

The purpose of the study was to improve the extraction of polysaccharide from the leaves of Cercis chinensis Bunge using ultrasound, and compare the difference between boiling and ultrasound extraction in terms of polysaccharide content, monosaccharide compounds, and evaluate how the factors affected the bioactivity. The best conditions, according to the single factor experiments and the Box-Bohnken design (BBD), were an intensity of ultrasound of 180 W, duration of extraction of 40 min, proportion of water to material of 15:1 (g/g), and a higher polysaccharide yield of 20.02 ± 0.55 (mg/g) than in boiling extraction (16.09 ± 0.82 mg/g). The antioxidative experiment suggested the polysaccharide by ultrasound exhibited higher DPPH, hydroxyl radical scavenging capacities, and reducing power at 1.2–1.4 mg/mL, which was superior to the boiling polysaccharide. Further analysis showed that the ultrasonic purified polysaccharides like Gla, N-Glu, and GluA contained more total sugar and uronic acids than the boiling method did. This may indicate that the ultrasonic isolation of the polysaccharides increase the antioxidant activity of the polysaccharides.     

Search for charm-quark production via dimuons in neutrino telescopes

Dimuon events induced by charm-quark productions from neutrino deep inelastic scattering (DIS) processes have been studied in traditional DIS experiments for decades. The recent progress in neutrino telescopes makes it possible to search for such dimuon events at energies far beyond the laboratory scale. In this study, we construct a simulation framework to calculate yields and distributions of dimuon signals in an IceCube-like km³ scale neutrino telescope. Owing to the experimental limitation in the resolution of double-track lateral distance, only dimuons produced outside the detector volume are considered. Detailed information about simulation results for a 10-year exposure is presented. As an earlier paper[Physical Review D 105, 093005 (2022)] and ours report on a similar situation, we use that paper as a baseline to conduct comparisons. We then estimate the impacts of different calculation methods of muon energy losses. Finally, we study the experimental potential of dimuon searches under the hypothesis of single-muon background only. Our results based on a simplified double-track reconstruction indicate a moderate sensitivity, especially with the ORCA configuration. Further developments on both the reconstruction algorithm and possible detector designs are thus required and are under investigation.     

地圈动力学的THMCB多元关联过程及其分析

地圈中广泛发育的动力学过程属于多元关联过程,它们是在岩土圈与水圈、大气圈、生物圈相互作用中进行的。它们的活动可以概括为热力学、流体力学、固体力学、化学和生物学等基本物质运动的作用及系统的演化。由于它们之间有着互动影响和制约,以及由此引发的能量的转换和参数的变异,因而密切相关。本文建议确立THMCB多元关联过程的概念,开展多元关联过程的研究和分析,以期对地圈动力学过程进行系统有效的综合评价和预测。     

Herbart and “Psychological Research on the Strength of a Given Impression”

Herbart in 1812 published an analysis of sensory process formation, using differential equations, and attempted to relate within the same model considerations of upper and lower limits of sensory intensity, and the time course of process evolution within those limits. The analysis he proposed anticipates later psychophysics by at least half a century. It is perhaps the earliest example of a formal nonlinear dynamical treatment in theoretical psychology.     

三峡工程对下游及河口环境的影响分析

本文概括了三峡建库后引起下游水沙动力因子的基本变化，论述了三峡水库对下游及河口生态和环境的主要影响，并通过对目前仍难以确定的一些问题的仔细分析，为长江中下游及河口地区的综合开发和环境保护提供准确的科学依据     

Defect assessment procedure based on ductile tearing process

Strain hardening, crack growth resistance and nonuniform load distribution have significant effects on the ductile tearing process. A defect assessment procedure incorporating with the above features is proposed in the present paper, with the final appearance of “design curves” to facilitate engineering applications.