Factorizing Historical User Actions for Next-Day Purchase Prediction

It is common practice for many large e-commerce operators to analyze daily logged transaction data to predict customer purchase behavior, which may potentially lead to more effective recommendations and increased sales. Traditional recommendation techniques based on collaborative filtering, although having gained success in video and music recommendation, are not sufficient to fully leverage the diverse information contained in the implicit user behavior on e-commerce platforms. In this article, we analyze user action records in the Alibaba Mobile Recommendation dataset from the Alibaba Tianchi Data Lab, as well as the Retailrocket recommender system dataset from the Retail Rocket website. To estimate the probability that a user will purchase a certain item tomorrow, we propose a new model called Time-decayed Multifaceted Factorizing Personalized Markov Chains (Time-decayed Multifaceted-FPMC), taking into account multiple types of user historical actions not only limited to past purchases but also including various behaviors such as clicks, collects and add-to-carts. Our model also considers the time-decay effect of the influence of past actions. To learn the parameters in the proposed model, we further propose a unified framework named Bayesian Sparse Factorization Machines. It generalizes the theory of traditional Factorization Machines to a more flexible learning structure and trains the Time-decayed Multifaceted-FPMC with the Markov Chain Monte Carlo method. Extensive evaluations based on multiple real-world datasets demonstrate that our proposed approaches significantly outperform various existing purchase recommendation algorithms.

Global strong solutions and large time behavior of 2D tropical climate model with zero thermal diffusion

In this article, we study the global well-posedness and large-time behaviors of solutions to the two-dimensional tropical climate system with zero thermal diffusion for a small initial data in the whole space. The main approaches include high and low frequency decomposition method and exploiting the structure of system (1) to obtain the estimates of thermal dissipation. We utilize the time decay properties of the kernels to a linear differential equation to obtain the decay rates of solutions of the low frequency part and the decay property of exponential operator for the high frequency part. The key ingredient here is the explicit large-time decay rate of solutions.

Time decay for several porous thermoviscoelastic systems of Moore–Gibson–Thompson type

In this paper, we consider several problems arising in the theory of thermoelastic bodies with voids. Four particular cases are considered depending on the choice of the constitutive tensors, assuming different dissipation mechanisms determined by Moore–Gibson–Thompson-type viscosity. For all of them, the existence and uniqueness of solutions are shown by using semigroup arguments. The energy decay of the solutions is also analyzed for each case.

The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien–Tanner system with magnetic field

In this paper, we consider the magnetohydrodynamic (MHD) flow of an incompressible Phan-Thien–Tanner (PTT) fluid in two space dimensions. We focus upon the sharp time decay rates (upper and lower bounds) and global-in-time stability of large strong solutions for the PTT system with magnetic field. Firstly, the convergence of large solutions to the equilibrium have been investigated and these convergence rates are shown to be sharp. We then show that two large solutions converge globally in time as long as two initial data are close to each other. One of the main objectives of this paper is to develop a way to capture L 2 -convergence result via auxiliary logarithmic time decay estimates with the initial data in L p ( R 2 ) ∩ L 2 ( R 2 ). Improving time decay rates for the high-order derivatives of large solutions by using interpolation inequalities. In addition, time-weighted energy estimate, Fourier time-splitting method, semigroup method and iterative scheme have also been utilized.

The M 6.5 Ambon earthquake 26 September 2019: the source mechanism and the aftershock sequence characteristics

The area of Ambon, Maluku is located in the subduction zone in bands where the Australian plate meets the Eurasian plate, thus causing tectonic activities. The Ambon earthquake on 26th September 2019 with 6.5 Magnitude, while the Epicentral coordinates of the earthquake were determined as 3,53° S and 128,39° E and a focal depth of 10 km, according to the Agency for Meteorology Climatology and Geophysics, Indonesia. This earthquake was strongly felt at the biggest shock was felt with intensity VI-VII as unified in Ambon City, while several other areas are reported to have experienced small shaking, such as Intensity V in Masohi, and Intensity IV in Namlea and Namrole. We used a dataset of 24 waveforms of seven sensors, we determine a tabular solution, which have a large moment of 0.4573 x 1019 N-m, the depth is 6 km by minimizing the inversion residual. The method resulting strike and rake fault, with strike: 341.8°; dip; 81.5°; rake: 158.4°, and second nodal plane strike: 75.1°; dip; 68.6°; rake: 9.14°. The mechanisms were compared with those from other agency in agreement. The time decay intervals between mainshocks and significant aftershocks follow Mogi and Utsu’s Law but with a relatively faster rate of decay than that of aftershocks in general.