Utilization of Real Time Behavior and Geographical Attraction for Location Recommendation

Personalized location recommendation is an increasingly active topic in recent years, which recommends appropriate locations to users based on their temporal and geospatial visiting patterns. Current location recommendation methods usually estimate the users’ visiting preference probabilities from the historical check-ins in batch. However, in practice, when users’ behaviors are updated in real-time, it is often cost-inhibitive to re-estimate and updates users’ visiting preference using the same batch methods due to the number of check-ins. Moreover, an important nature of users’ movement patterns is that users are more attracted to an area where have dense locations with same categories for conducting specific behaviors. In this paper, we propose a location recommendation method called GeoRTGA by utilizing the real time user behaviors and geographical attractions to tackle the problems. GeoRTGA contains two sub-models: real time behavior recommendation model and attraction-based spatial model. The real time behavior recommendation model aims to recommend real-time possible behaviors which users prefer to visit, and the attraction-based spatial model is built to discover the category-based spatial and individualized spatial patterns based on the geographical information of locations and corresponding location categories and check-in numbers. Experiments are conducted on four public real-world check-in datasets, which show that the proposed GeoRTGA outperforms the five existing location recommendation methods.

Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion With Hurst Index Large Than 0.5 I: Self-Repelling Case

Let SH be a sub-fractional Brownian motion with index 12<H<1. In this paper, we consider the linear self-interacting diffusion driven by SH, which is the solution to the equationdXtH=dStH−θ(∫0tXtH−XsHds)dt+νdt,X0H=0,where θ &lt; 0 and ν∈R are two parameters. Such process XH is called self-repelling and it is an analogue of the linear self-attracting diffusion [Cranston and Le Jan, Math. Ann. 303 (1995), 87–93]. Our main aim is to study the large time behaviors. We show the solution XH diverges to infinity, as t tends to infinity, and obtain the speed at which the process XH diverges to infinity as t tends to infinity.

Exploring nonequilibrium phases of photo-doped Mott insulators with generalized Gibbs ensembles

Many experiments show that strong excitations of correlated quantum materials can cause non-thermal phases without equilibrium analogues. Understanding the origin and properties of these nonequilibrium states has been challenging due to the limitations of theoretical methods for nonequilibrium strongly correlated systems. In this work, we introduce a generalized Gibbs ensemble description that enables a systematic analysis of the long-time behavior of photo-doped states in Mott insulators based on equilibrium methods. We demonstrate the power of the method by mapping out the nonequilibrium phase diagram of the one-dimensional extended Hubbard model, which features η-pairing and charge density wave phases in a wide photo-doping range. We furthermore clarify that the peculiar kinematics of photo-doped carriers, and the interaction between them, play an essential role in the formation of these non-thermal phases. Our results establish a new path for the systematic analysis of nonequilibrium strongly correlated systems.