Probabilistic inference problems have very broad practical applications. To solve this kind of problems under conditions of certainty, an effective mathematical apparatus has been developed. In real situations, obtaining deterministic estimates of relevant probabilities is often difficult; therefore, problems with handling uncertain estimates of probabilities appear. This paper examines the problem of probabilistic inference with probability trees provided that the initial probabilities are given in the form of intervals of their possible values.

Bitcoin has been launched for over a decade and made an increasing impact on the world’s financial order, which attracted extensive attention of researchers. Bitcoin system runs on a dynamic P2P network, containing tens of thousands of nodes including reachable nodes and unreachable nodes. In this article, a detection system BNS (Bitcoin Network Sniffer) was prososed, which could collect as many Bitcoin nodes as possible. For reachable nodes, the authors designed an algorithm BRF (Bitcoin Reachable-nodes Finding) based on node activity evaluation, which reduced the nodes to be detected and greatly shortened the detection time. For unreachable nodes, the authors trained a dicision tree model BUF(Bitcoin Unreachable-nodes Finding) to identify unreachable nodes based on attribute features from massive node addresses. Experiments showed that BNS performed better than the website "Bitnodes" in total number and efficiency. Based on the experimental results, the authors analyzed the real network size, node "churn" and geographical distribution.

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control system with bounded disturbances. First, by constructing an appropriate Lyapunov-Krasovskii functional, we obtained a delay-dependent condition, which determed the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in form of liner matrix inequalities is given to solve the problem of controller design with reachable set estimation. Finally, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to verify the usefulness of our result.

Most of the existing influence maximization algorithms are not suitable for large-scale social networks due to their high time complexity or limited influence propagation range. Therefore, a D-RIS influence maximization algorithm is proposed based on the independent cascade model and combined with the reverse reachable set sampling. Under the premise that the influence propagation function satisfies monotonicity and submodularity, the D-RIS algorithm uses automatic debugging method to determine the critical value of the number of reverse reachable sets, which not only obtains a better influence propagation range, and greatly reduce the time complexity. The experimental results on the two real data sets of Slashdot and Epinions show that D-RIS algorithm is close to the CELF algorithm and higher than RIS algorithm, HighDegree algorithm, LIR algorithm and pBmH algorithm in influence propagation range. At the same time, it is significantly better than the CELF algorithm and RIS algorithm in running time, which indicates that D-RIS algorithm is more suitable for large scale social network.