A phase-field model of relaxor ferroelectrics based on random field theory

A mechanically coupled phase-field model is proposed for the first time to simulate the peculiar behavior of relaxor ferroelectrics. Based on the random field theory for relaxors, local random fields are introduced to characterize the effect of chemical disorder. This generic model is developed from a thermodynamic framework and the microforce theory and is implemented by a nonlinear finite element method. Simulation results show that the model can reproduce relaxor features, such as domain miniaturization, small remnant polarization and large piezoelectric response. In particular, the influence of random field strength on these features are revealed. Simulation results on domain structure and hysteresis behavior are discussed and compared with related experimental results.Comment: 8 figure

New Planar P-time Computable Six-Vertex Models and a Complete Complexity Classification

We discover new P-time computable six-vertex models on planar graphs beyond Kasteleyn's algorithm for counting planar perfect matchings. We further prove that there are no more: Together, they exhaust all P-time computable six-vertex models on planar graphs, assuming #P is not P. This leads to the following exact complexity classification: For every parameter setting in ${\mathbb C}$ for the six-vertex model, the partition function is either (1) computable in P-time for every graph, or (2) #P-hard for general graphs but computable in P-time for planar graphs, or (3) #P-hard even for planar graphs. The classification has an explicit criterion. The new P-time cases in (2) provably cannot be subsumed by Kasteleyn's algorithm. They are obtained by a non-local connection to #CSP, defined in terms of a "loop space". This is the first substantive advance toward a planar Holant classification with not necessarily symmetric constraints. We introduce M\"obius transformation on ${\mathbb C}$ as a powerful new tool in hardness proofs for counting problems.Comment: 61 pages, 16 figures. An extended abstract appears in SODA 202

Deep Learning based Recommender System: A Survey and New Perspectives

With the ever-growing volume of online information, recommender systems have been an effective strategy to overcome such information overload. The utility of recommender systems cannot be overstated, given its widespread adoption in many web applications, along with its potential impact to ameliorate many problems related to over-choice. In recent years, deep learning has garnered considerable interest in many research fields such as computer vision and natural language processing, owing not only to stellar performance but also the attractive property of learning feature representations from scratch. The influence of deep learning is also pervasive, recently demonstrating its effectiveness when applied to information retrieval and recommender systems research. Evidently, the field of deep learning in recommender system is flourishing. This article aims to provide a comprehensive review of recent research efforts on deep learning based recommender systems. More concretely, we provide and devise a taxonomy of deep learning based recommendation models, along with providing a comprehensive summary of the state-of-the-art. Finally, we expand on current trends and provide new perspectives pertaining to this new exciting development of the field.Comment: The paper has been accepted by ACM Computing Surveys. https://doi.acm.org/10.1145/328502

On the convergence analysis of DCA

In this paper, we propose a clean and general proof framework to establish the convergence analysis of the Difference-of-Convex (DC) programming algorithm (DCA) for both standard DC program and convex constrained DC program. We first discuss suitable assumptions for the well-definiteness of DCA. Then, we focus on the convergence analysis of DCA, in particular, the global convergence of the sequence $\{x^k\}$ generated by DCA under the Lojasiewicz subgradient inequality and the Kurdyka-Lojasiewicz property respectively. Moreover, the convergence rate for the sequences $\{f(x^k)\}$ and $\{\|x^k-x^*\|\}$ are also investigated. We hope that the proof framework presented in this article will be a useful tool to conveniently establish the convergence analysis for many variants of DCA and new DCA-type algorithms