基于概率主题模型的京津冀协同发展研究主题演化分析

京津冀协同发展是当前各学科领域共同关注的热点话题。为深入了解京津冀协同发展话题的研究趋势,以2009～2019年中国知网收录的14 235篇与京津冀协同发展相关的期刊论文为研究对象,采用概率主题模型方法,提出以困惑度、主题平均相似度为指标确定最优主题数,结合文献发表时间挖掘期刊论文潜在主题,从主题强度和主题相似度等多个角度分析主题演化趋势。通过数据分析,挖掘10个潜在主题,生成主题强度年度变化趋势,构建主题内容演化路径,分析主题演化规律。以期为深刻认识京津冀协同发展和科学决策提供理论依据。     

Modeling Skill Dependence in Probabilistic Competence Structures

In knowledge space theory (KST) a competence structure is a set theoretical representation of the dependencies among a given set of skills. A probabilistic model for skill dependence is proposed which respects a precise correspondence requirement between set theoretical and probabilistic representations of skill dependence. An empirical application on integer subtraction problems at the primary school shows that the proposed model fits the data pretty well. Moreover, in a comparison with an unrestricted skill based version of the basic local independence model (BLIM), the proposed model fits better than this last, indicating that the restrictions implied by the correspondence requirement are not too strong.     

基于GPR与概率神经网络的城市道路路基病害预警模型研究

近年来由道路路基病害所导致的城市道路塌陷事故频繁发生,造成人员伤亡和巨大的经济损失。针对城市道路路基病害所带来的诸多问题与安全隐患,提出了一种基于探地雷达与概率神经网络的城市道路路基病害预警模型。首先在分析路基病害成因的基础上建立了城市道路路基病害评价指标体系;然后依托城市道路路基病害动态演化物理模型,使用探地雷达采集并积累样本数据;最后基于样本数据建立概率神经网络预警模型并进行仿真分析,结果表明预警准确率达到88.9%。该预警模型在郑州市中牟县的滨河路和荟萃路进行了应用试验,预警结果与实际情况基本吻合,表明该预警模型可对城市道路路基病害做出有效预警,为道路养护和工程整治设计提供技术支撑。     

The size Ramsey number of short subdivisions of bounded degree graphs

For graphs G and F, write if any coloring of the edges of G with colors yields a monochromatic copy of the graph F. Suppose is obtained from a graph S with s vertices and maximum degree d by subdividing its edges h times (that is, by replacing the edges of S by paths of length h + 1). We prove that there exists a graph G with no more than edges for which holds, provided that . We also extend this result to the case in which Q is a graph with maximum degree d on q vertices with the property that every pair of vertices of degree greater than 2 are distance at least h + 1 apart. This complements work of Pak regarding the size Ramsey number of “long subdivisions” of bounded degree graphs.     

概率有限自动机的交换性

提出了一类概率有限自动机并给出其交换的概念,得到了此类自动机交换的一些刻画,定义了两个概率有限自动机的和与积,并且得到了和自动机、积自动机交换的充要条件。     

半序概率度量空间中增算子的不动点定理

不动点理论是非线性泛函分析的重要组成部分,对非线性微分积分方程的研究有重要意义.半序方法是研究非线性算子方程问题的主要方法之一,在概率度量空间中通过泛函引入半序,并利用此半序研究概率度量空间中增算子的不动点的存在性问题,得到一些不动点存在性定理.     

Discovery Through Gossip

We study randomized gossip‐based processes in dynamic networks that are motivated by information discovery in large‐scale distributed networks such as peer‐to‐peer and social networks. A well‐studied problem in peer‐to‐peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self‐stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying network — new edges are added to the network — and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications. This paper studies and analyzes two natural gossip‐based discovery processes. In the push discovery or triangulation process, each node repeatedly chooses two random neighbors and connects them (i.e., “pushes” their mutual information to each other). In the pull discovery process or the two‐hop walk, each node repeatedly requests or “pulls” a random contact from a random neighbor and connects itself to this two‐hop neighbor. Both processes are lightweight in the sense that the amortized work done per node is constant per round, local, and naturally robust due to the inherent randomized nature of gossip. Our main result is an almost‐tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n‐node graph both processes take rounds to connect every node to all other nodes with high probability, whereas is a lower bound. We also study the two‐hop walk in directed graphs, and show that it takes time with high probability, and that the worst‐case bound is tight for arbitrary directed graphs, whereas Ω(n²) is a lower bound for strongly connected directed graphs. A key technical challenge that we overcome in our work is the analysis of a randomized process that itself results in a constantly changing network leading to complicated dependencies in every round. We discuss implications of our results and their analysis to discovery problems in P2P networks as well as to evolution in social networks. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 565–587, 2016     

Robust stability analysis of stochastic neural networks with Markovian jumping parameters and probabilistic time‐varying delays

This article discusses the issue of robust stability analysis for a class of Markovian jumping stochastic neural networks (NNs) with probabilistic time‐varying delays. The jumping parameters are represented as a continuous‐time discrete‐state Markov chain. Using the stochastic stability theory, properties of Brownian motion, the information of probabilistic time‐varying delay, the generalized Ito's formula, and linear matrix inequality (LMI) technique, some novel sufficient conditions are obtained to guarantee the stochastical stability of the given NNs. In particular, the activation functions considered in this article are reasonably general in view of the fact that they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. The main features of this article are described in the following: first one is that, based on generalized Finsler lemma, some improved delay‐dependent stability criteria are established and the second one is that the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions. By resorting to the Lyapunov–Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established using an efficient LMI approach. Finally, two numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–72, 2016     

Some properties for probabilistic and multinomial (probabilistic) values on cooperative games

We investigate the conditions for the coefficients of probabilistic and multinomial values of cooperative games necessary and/or sufficient in order to satisfy some properties, including marginal contributions, balanced contributions, desirability relation and null player exclusion property. Moreover, a similar analysis is conducted for transfer property of probabilistic power indices on the domain of simple games.