R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Exactly Solved Models in Statistical Mechanics

여성사 쓰기의 가능성과 현주소, 한국여성연구소 여성사연구실 지음, 청년사 1999

Owing to the superiority of GNN in learning on graph data and its efficacy in capturing collaborative signals and sequential patterns, utilizing GNN techniques in recommender systems has gain increasing interests in academia and industry. In this survey, we provide a comprehensive review of the most recent works on GNN-based recommender systems. We proposed a classification scheme for organizing existing works. For each category, we briefly clarify the main issues, and detail the corresponding strategies adopted by the representative models. We also discuss the advantages and limitations of the existing strategies. Furthermore, we suggest several promising directions for future researches. We hope this survey can provide readers with a general understanding of the recent progress in this field, and shed some light on future developments.

Graph Neural Networks in Recommender Systems: A Survey

Representation learning on user-item graph for recommendation has evolved from using single ID or interaction history to exploiting higher-order neighbors. This leads to the success of graph convolution networks (GCNs) for recommendation such as PinSage and LightGCN. Despite effectiveness, we argue that they suffer from two limitations: (1) high-degree nodes exert larger impact on the representation learning, deteriorating the recommendations of low-degree (long-tail) items; and (2) representations are vulnerable to noisy interactions, as the neighborhood aggregation scheme further enlarges the impact of observed edges. 
In this work, we explore self-supervised learning on user-item graph, so as to improve the accuracy and robustness of GCNs for recommendation. The idea is to supplement the classical supervised task of recommendation with an auxiliary self-supervised task, which reinforces node representation learning via self-discrimination. Specifically, we generate multiple views of a node, maximizing the agreement between different views of the same node compared to that of other nodes. We devise three operators to generate the views -- node dropout, edge dropout, and random walk -- that change the graph structure in different manners. We term this new learning paradigm as \textit{Self-supervised Graph Learning} (SGL), implementing it on the state-of-the-art model LightGCN. Through theoretical analyses, we find that SGL has the ability of automatically mining hard negatives. Empirical studies on three benchmark datasets demonstrate the effectiveness of SGL, which improves the recommendation accuracy, especially on long-tail items, and the robustness against interaction noises. Our implementations are available at \url{this https URL}.

Self-supervised Graph Learning for Recommendation

Representation learning on user-item graph for recommendation has evolved from using single ID or interaction history to exploiting higher-order neighbors. This leads to the success of graph convolution networks (GCNs) for recommendation such as PinSage and LightGCN. Despite effectiveness, we argue that they suffer from two limitations: (1) high-degree nodes exert larger impact on the representation learning, deteriorating the recommendations of low-degree (long-tail) items; and (2) representations are vulnerable to noisy interactions, as the neighborhood aggregation scheme further enlarges the impact of observed edges. In this work, we explore self-supervised learning on user-item graph, so as to improve the accuracy and robustness of GCNs for recommendation. The idea is to supplement the classical supervised task of recommendation with an auxiliary self-supervised task, which reinforces node representation learning via self-discrimination. Specifically, we generate multiple views of a node, maximizing the agreement between different views of the same node compared to that of other nodes. We devise three operators to generate the views --- node dropout, edge dropout, and random walk --- that change the graph structure in different manners. We term this new learning paradigm asSelf-supervised Graph Learning (SGL), implementing it on the state-of-the-art model LightGCN. Through theoretical analyses, we find that SGL has the ability of automatically mining hard negatives. Empirical studies on three benchmark datasets demonstrate the effectiveness of SGL, which improves the recommendation accuracy, especially on long-tail items, and the robustness against interaction noises. Our implementations are available at \urlhttps://github.com/wujcan/SGL.

Increasing demand for fashion recommendation raises a lot of challenges for online shopping platforms and fashion communities. In particular, there exist two requirements for fashion outfit recommendation: the Compatibility of the generated fashion outfits, and the Personalization in the recommendation process. In this paper, we demonstrate these two requirements can be satisfied via building a bridge between outfit generation and recommendation. Through large data analysis, we observe that people have similar tastes in individual items and outfits. Therefore, we propose a Personalized Outfit Generation (POG) model, which connects user preferences regarding individual items and outfits with Transformer architecture. Extensive offline and online experiments provide strong quantitative evidence that our method outperforms alternative methods regarding both compatibility and personalization metrics. Furthermore, we deploy POG on a platform named Dida in Alibaba to generate personalized outfits for the users of the online application iFashion. This work represents a first step towards an industrial-scale fashion outfit generation and recommendation solution, which goes beyond generating outfits based on explicit queries, or merely recommending from existing outfit pools. As part of this work, we release a large-scale dataset consisting of 1.01 million outfits with rich context information, and 0.28 billion user click actions from 3.57 million users. To the best of our knowledge, this dataset is the largest, publicly available, fashion related dataset, and the first to provide user behaviors relating to both outfits and fashion items.

POG: Personalized Outfit Generation for Fashion Recommendation at Alibaba iFashion

Increasing demand for fashion recommendation raises a lot of challenges for online shopping platforms and fashion communities. In particular, there exist two requirements for fashion outfit recommendation: the Compatibility of the generated fashion outfits, and the Personalization in the recommendation process. In this paper, we demonstrate these two requirements can be satisfied via building a bridge between outfit generation and recommendation. Through large data analysis, we observe that people have similar tastes in individual items and outfits. Therefore, we propose a Personalized Outfit Generation (POG) model, which connects user preferences regarding individual items and outfits with Transformer architecture. Extensive offline and online experiments provide strong quantitative evidence that our method outperforms alternative methods regarding both compatibility and personalization metrics. Furthermore, we deploy POG on a platform named Dida in Alibaba to generate personalized outfits for the users of the online application iFashion. 
This work represents a first step towards an industrial-scale fashion outfit generation and recommendation solution, which goes beyond generating outfits based on explicit queries, or merely recommending from existing outfit pools. As part of this work, we release a large-scale dataset consisting of 1.01 million outfits with rich context information, and 0.28 billion user click actions from 3.57 million users. To the best of our knowledge, this dataset is the largest, publicly available, fashion related dataset, and the first to provide user behaviors relating to both outfits and fashion items.

We give an overview of the integrability of the Hirota-Kimura discretizationmethod applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.

On integrability of hirota-kimura type discretizations

We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.

On integrability of Hirota-Kimura type discretizations

R. Hirota and K. Kimura discovered integrable discretizations of the Euler and the Lagrange tops, given by birational maps. Their method is a specialization to the integrable context of a general d...

/pdf/on-integrability-of-hirota-kimura-type-discretizations-52hdj4lxuk.pdf

Andreas Pfadler

Papers

POG: Personalized Outfit Generation for Fashion Recommendation at Alibaba iFashion

POG: Personalized Outfit Generation for Fashion Recommendation at Alibaba iFashion

On integrability of hirota-kimura type discretizations

On integrability of Hirota-Kimura type discretizations

On integrability of Hirota-Kimura type discretizations. Experimental study of the discrete Clebsch system