Accurately identifying influential nodes in complex networks is crucial for understanding their structure and dynamics. Traditional methods for measuring node centrality often struggle to capture the inherent uncertainties in node relationships and to model specific higher-order interaction patterns, limiting their reliable evaluations in hypergraph contexts. To address this challenge, we propose a novel approach called Fuzzy Multi-Hierarchical Centrality (FMHC), which integrates fuzzy theory with multi-hierarchical topological analysis for centrality assessment in hypergraphs. By synthesizing inter-node fuzzy distances, node-to-edge fuzzy membership degrees, and mutual information associations among nodes and edges, FMHC constructs a multi-hierarchical evaluation architecture to generate comprehensive and discriminative importance scores for each node. Extensive experiments on nine real-world datasets demonstrate that FMHC consistently outperforms eight classical and state-of-the-art benchmarks across three key evaluation criteria: the capacity to identify nodes with high spreading influence, alignment with the Susceptible-Infected-Recovered (SIR) epidemic model, and monotonicity in ranking discrimination. These findings validate the effectiveness, robustness, and superiority of FMHC in hypergraph environments.

Motivated by the statistical analysis of the discrete optimal transport problem, we prove distributional limits for the solutions of linear programs with random constraints.Such limits were first obtained by Klatt, Munk, & Zemel (2022), but their expressions for the limits involve a computationally intractable decomposition of $\mathbb{R}^m$ into a possibly exponential number of convex cones.We give a new expression for the limit in terms of auxiliary linear programs, which can be solved in polynomial time.We also leverage tools from random convex geometry to give distributional limits for the entire set of random optimal solutions, when the optimum is not unique.Finally, we describe a simple, data-driven method to construct asymptotically valid confidence sets in polynomial time.

The paper presents a framework for automatically natural image sketching, motivated by imitating the human line drawing process. The algorithm consists of two steps: sketch extraction and sketch rendering, using the recent computer vision and graphics techniques. In the first step, we design a bottom-up filter bank (low-level features) to propose sketch strength, position and orientation, and then trace and complete sketch following Gestalt laws (middle-level cues). In the second step, each sketch is rendered using a sketch-stroke model, accounting for the length, smoothness, width, and profile strength. Experimental results demonstrate the proposed approach is able to generate expressive sketch paintings from natural images.

Bee zone is a large-scale live video streaming system, which adopts dual-protocol-stack technology and gossip-like protocol to build an unstructured P2P application layer overlay, which can be used in IPv4/v6 hybrid network environment. We run the system during the 2010 FIFA World Cup South Africa. By collecting the logs from the system when it works, we study the workload, performance, and dynamics of the system. Based on these logs, we show that (1) the system can be used in hybrid network environment, which makes the playback smooth and reduces latency at end users. (2) it can make good use of IPv6 bandwidth, and (3) the dynamics of the system is slow. Our results fully verified the performance of Bee zone, and indicate the use of IPv6 channel can improves the performance of the P2P video streaming system.