Rigorous confidence intervals for critical probabilities

Rigorous Confidence Intervals on Critical Thresholds in 3 Dimensions

We extend the method of Balister, Bollobás and Walters for determining rigorous confidence intervals for the critical threshold of two dimensional lattices to three (and higher) dimensional lattices. We describe a method for determining a full confidence interval and apply it to show that the critical threshold for bond percolation on the simple cubic lattice is between 0.2485 and 0.2490 with 99.9999% confidence, and the critical threshold for site percolation on the same lattice is between 0.3110 and 0.3118 with 99.9999% confidence.

可教学的二项分布及相关概率或置信区间的正态近似

Teachable normal approximations to binomial and related probabilities or confidence bounds

本文提出了可教学的二项分布及相关概率的正态近似方法，提供误差界和置信区间界，适用于不同层次的学生理解。

Les Probabilités Défaillance comme Indicateurs de Performance des Barrières Techniques de Sécurité - Approche Analytique

French environmental laws require industrialists to include probability criteria in risk assessments, especially to define confidence levels for risk management measures. This paper presents the failure probabilities as efficient indicators for technical safety barrier performances. Generic formulas are proposed to evaluate these probabilities, including failure rate, barrier architecture, full and partial proof tests. In many cases, these results can be directly used to assess safety barrier confidence levels.

二维伯努利渗流模型中临界概率的上界

Upper bounds for critical probabilities in Bernoulli Percolation models

本文研究了有向和无向伯努利渗流模型中临界概率的上界，针对d≥3的所有维度给出了严格的结果。

具有自适应交互概率的有界置信意见动力学模型

A Bounded-Confidence Model of Opinion Dynamics with Adaptive Interaction Probabilities

本文扩展了Deffuant-Weisbuch有界置信模型，引入异质自适应边权重来调节交互概率，并证明了收敛性、边权重长期动力学及有效图的性质，数值模拟显示自适应边权重对不同网络类型的收敛时间有不同影响。

Confidence intervals for nonhomogeneous branching processes and polymerase chain reactions

We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain reactions from uniform samples of the population after the reaction. First, we consider nonhomogeneous processes, which are more adapted to real reactions. Second, recalling that the first moment estimator is analytically known only in the infinite population limit, we provide rigorous confidence intervals for this estimator that are valid for any finite po…