The hardcore model is a fundamental probabilistic model extensively studied in statistical physics, probability theory, and computer science. It defines a Gibbs distribution over independent sets of a given graph, parameterized by a vertex activity λ > 0. For graphs of maximum degree ∆, a well-known computational phase transition occurs at the tree-uniqueness threshold ${\lambda _c}(\Delta ) = \frac{{{{(\Delta - 1)}^{\Delta - 1}}}}{{{{(\Delta - 2)}^\Delta }}}$, where the mixing behavior of the Glauber dynamics (a simple Markov chain) undergoes a sharp transition: it mixes in nearly linear time for λc(∆), in polynomial but super-linear time at λ = λc(∆), and experiences exponential slowdown for λ > λc(∆).It is conjectured that random regular graphs exhibit different mixing behavior, with the slowdown occurring far beyond the uniqueness threshold. We confirm this conjecture by showing that, for the hardcore model on random ∆-regular graphs, the Glauber dynamics mixes rapidly with high probability when $\lambda = O\left( {1/\sqrt \Delta } \right)$, which is significantly beyond the uniqueness threshold λc(∆) ≈ e/∆. Our result establishes a sharp distinction between the hardcore model on worst-case and beyond-worst-case instances, showing that the worst-case and average-case complexities of sampling and counting are fundamentally different.This result of rapid mixing on random instances follows from a new criterion we establish for rapid mixing of Glauber dynamics for any distribution supported on a downward closed set family. Our criterion is simple, general, and easy to check. In addition to proving new mixing conditions for the hardcore model, we also establish improved mixing time bounds for sampling uniform matchings or b-matchings on graphs, the random cluster model on matroids with q ∈ [0,1), and the determinantal point process. Our proof of this new criterion for rapid mixing combines and generalizes several recent tools in a novel way, including a trickle-down theorem for field dynamics, spectral/entropic stability, and a new comparison result between field dynamics and Glauber dynamics.

We examine various perspectives on the decay of correlation for the uniform distribution over proper $q$-edge colorings of graphs with maximum degree $Δ$. First, we establish the coupling independence property when $q\ge 3Δ$ for general graphs. Together with the work of Chen et al. (2024), this result implies a fully polynomial-time approximation scheme (FPTAS) for counting the number of proper $q$-edge colorings. Next, we prove the strong spatial mixing property on trees, provided that $q> (3+o(1))Δ$. The strong spatial mixing property is derived from the spectral independence property of a version of the weighted edge coloring distribution, which is established using the matrix trickle-down method developed in Abdolazimi, Liu and Oveis Gharan (FOCS, 2021) and Wang, Zhang and Zhang (STOC, 2024). Finally, we show that the weak spatial mixing property holds on trees with maximum degree $Δ$ if and only if $q\ge 2Δ-1$.

Recently, three-dimensional (3D) point clouds have become more and more popular as they can represent 3D scenes and objects conveniently for applications like immersive communication and autonomous driving, etc. However, the huge data volume of 3D point clouds and the variable channel band width prevent its efficient and reliable transmission. We propose a deep joint source-channel coding method for point cloud geometry, namely DeepJSCC-PCG, by leveraging DeepJSCC and the octree-based adaptive voxelization to overcome the “cliff effect” caused by traditional separate source and channel coding (SSCC). Specifically, DeepJSCC-PCG first partitions the point cloud into non-overlapping voxel blocks via octree decomposition and prunes empty regions for efficient computation. Second, a 3D convolution-based neural network is specially designed to extract compact semantic features from the sparse data structure of the voxel blocks efficiently. Finally, the extracted features are transmitted through fading channels corrupted by Gaussian or Rayleigh noise, and subsequently decoded for reconstruction. The neural network is trained in an end-to-end fashion, allowing for the rebuilding of a high-quality point cloud. Experiments on the ModelNet40 and 8i datasets demonstrated that DeepJSCC CPCGsignificantly outperforms existing DeepJSCC methods and traditional SSCC methods.

Social networks, with tremendous popularity all over the world, have become the most important platform for many services in the past years. Location, as part of users' basic information, is always the key to many recommendation services in social networks. Most of the previous research works focus on inferring on the users' home locations. However, it is not enough as many people in social networks have multiple location tags, including home location, work location and on. In this paper, we propose a multiple location tags inference algorithm, i.e. MuLTI to build complete location profiles for users in social networks. We formulate the correlations between the users' location tags and their friendships, tweets, and then infer the users' locations in each of their friendships and tweets. It reflects the activity level of users to be in different locations. Apart from the activity level, we also consider the time span of users to be in different locations, so as to infer the users' long-term location tags better, as we find that users may also be active in their temporal locations. Experiments show that MuLTI improves the precision by about 15%, and the recall by about 25% compared with the state-of-the-art algorithms.

With tremendous popularity, OSNs have become the most important platform for marketing and advertising during the past years. Meanwhile, spamming has already become a very serious problem in OSNs, drawing the attention of both academic and industry communities. In this paper, we investigate the problem of spammer detection from the perspective of user behaviors, including relation creation, user activeness, user interaction and tweet content. We quantitatively explore their correlations with spammer detection and find that tweet content is the most important factor for spammer detection, followed by relation creation. Based on these behavior factors, we propose a novel cascading framework CWB-SPAM for spammer detection in OSNs. Experiments on dataset crawled from Sina Microblog show that the proposed algorithm outperforms over all classical algorithms we investigated in terms of F-score1• Experiments also demonstrate that as a probabilistic classification model, the proposed CWB-SPAM has a good ranking quality. It enables the OSN operators to make tradeoff between precision and recall easily so that the proposed algorithm can be used in different scenarios. Besides, we also note that the proposed framework can be used in other probabilistic binary classification models and thus applied in more scenarios.

In this paper, many aspects related to characteristics and development of IPv6 network are investigated. Additionally, in order to gain a deep view of IPv6 network, we correlate our system with a user authentication system, so we explore some meaningful user behaviors. According to the analysis, we obtain a comprehensive knowledge of current operating situation of IPv6 network which, we believe, can provide an experimental basis for IPv6 network operators and researchers.

This paper focuses on the problem of searching for diversified landmarks with photos. More particularly, we propose a system called DLMSearch which handles image query, searches for diversified landmarks and provides representative visual summaries. DLMSearch allows a user to upload a query photo and searches for landmarks with high relevance and diversity in real time. Then DLMSearch presents a delicate photo summary for each returned landmark, considering both visual representativeness and diversity. Quantative evaluations on a web-scale landmark photo collection demonstrate the effectiveness of the DLMSearch system. Experimental results verify the merits of the proposed system.

This demo focuses on the problem of searching for diversified landmarks with photos as input. More particularly, we propose a system called DLMSearch that allows a user to upload a photo as a query and searches for a diverse set of relevant landmarks in real time. It also presents a photo summary for each retrieved landmark, considering both visual representativeness and diversity. Our online demo is available at http://lm.apexlab.org/landmark/demo.