Recommender systems filter contents/items valuable to users by inferring preferences from user features and historical behaviors. Mainstream approaches follow the learning-to-rank paradigm, which focus on discovering and modeling item topics (e.g., categories), and capturing user preferences on these topics based on historical interactions. However, this paradigm often neglects the modeling of user characteristics and their social roles, which are logical confounders influencing the correlated interest and user preference transition. To bridge this gap, we introduce the user role identification task and the behavioral logic modeling task that aim to explicitly model user roles and learn the logical relations between item topics and user social roles. We show that it is possible to explicitly solve these tasks through an efficient integration framework of Large Language Model (LLM) and recommendation systems, for which we propose TagCF. On the one hand, TagCF exploits the (Multi-modal) LLM's world knowledge and logic inference ability to extract realistic tag-based virtual logic graphs that reveal dynamic and expressive knowledge of users, refining our understanding of user behaviors. On the other hand, TagCF presents empirically effective integration modules that take advantage of the extracted tag-logic information, augmenting the recommendation performance. We conduct both online experiments and offline experiments with industrial and public datasets as verification of TagCF's effectiveness, and we empirically show that the user role modeling strategy is potentially a better choice than the modeling of item topics. Additionally, we provide evidence that the extracted logic graphs are empirically a general and transferable knowledge that can benefit a wide range of recommendation tasks. Our code is available in https://github.com/Code2Q/TagCF.

For an edge-colored graph, its minimum color degree is the minimum number of distinct colors appearing on the edges incident with a vertex, and its maximum monochromatic degree is the maximum number of edges with the same color incident with a vertex. A cycle in an edge-colored graph is called properly colored if any two consecutive edges of the cycle have distinct colors. We investigate sufficient conditions in terms of the minimum color degree and maximum monochromatic degree for the existence of short properly colored cycles in edge-colored complete graphs. In particular, we obtain sharp results for the existence of properly colored C4’s, and we characterize the extremal graphs for several known results on the existence of properly colored triangles. Moreover, we obtain sharp sufficient conditions guaranteeing that every vertex is contained in a properly colored triangle or C4, respectively.

Let $k$ be a positive integer. Bermond and Thomassen conjectured in 1981 that every digraph with minimum outdegree at least $2k-1$ contains $k$ vertex-disjoint cycles. This conjecture is famous as one of a hundred unsolved problems selected in [A. Bondy and M. R. Murty, Graph Theory, Springer-Verlag, London, 2008]. Lichiardopol, Pór, and Sereni proved in [ SIAM J. Discrete Math., 23 (2009), pp. 979--992] that the above conjecture holds for $k=3$. Let $g$ be the girth, i.e., the length of the shortest cycle, of a given digraph. Bang-Jensen, Bessy, and Thomassé conjectured in [ J. Graph Theory, 75 (2014), pp. 284--302] that every digraph with girth $g$ and minimum outdegree at least $\frac{g}{g-1}k$ contains $k$ vertex-disjoint cycles. Thomassé conjectured around 2006 that every oriented graph (a digraph without 2-cycles) with girth $g$ and minimum outdegree at least $h$ contains a path of length $h(g-1)$, where $h$ is a positive integer. In this paper, we first present a new shorter proof of the Bermond--Thomassen conjecture for the case of $k=3$, and then we disprove the conjecture proposed by Bang-Jensen, Bessy, and Thomassé. Finally, we disprove the even girth case of the conjecture proposed by Thomassé.

With the wide deployment of various kinds of sensors in fixed infrastructures and in mobile devices, technologies and applications of crowd-sensing has drawn attentions in the fields of mobile computing. This paper studies the design of frameworks for crowd-sensing process in a distributed environment. We discuss the realization of the compatibilities of devices and services, as well as the algorithms of dealing with transmitting and accessing large amount of sensing data. We present a new distributed crowd-sensing framework called DASF, which is based on context data servers. The framework consists of three layers: hardware device layer, context data layer, and smart service layer. The key innovations and features of the framework are illustrated in detail. Through experiments and results analyses, DASF is shown to have good compatibility in heterogeneous device platforms, and it is capable of dealing with heavy load of accessing with practical significance.