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关键词： L-topology   Tau-convergence space   Extensionality   Connectedness   T-1-separation  

摘要： The extensionality of Tau-convergence spaces is verified for a complete residuated lattice L with the top element Tau. And also the E-connectedness of Tau-convergence spaces for a class E of Tau-convergence spaces is proposed by generalizing Preuss's connectedness of topological spaces. Then we establish a necessary and sufficient condition that for a class K of Tau-convergence spaces, there exists a class E of Tau-convergence spaces such that each space of K is E-connected, where we stress the point that the conclusion benefits from the extensionality of the category of Tau-convergence spaces. We further present a deep relationship between E-connectedness and T-1-separation for Tau-convergence spaces, that is, the E-connectedness of each subset in a Tau-convergence space implies that of its closure if and only if E precisely is a class of Tau-convergence spaces being T-1-separated, and as a natural result, the product theorem for E-connected Tau-convergence spaces is obtained. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Quantale   Stratified L-filter   Stratified L-semiuniform convergence space   Tensor product   Symmetric monoidal category   Monoidal closedness  

摘要： For an integral, commutative unital quantale L, we show that there exists a tensor product between stratified L-semiuniform convergence spaces and, with respect to this tensor product, that the category of stratified L-semiuniform convergence spaces and uniformly continuous maps is a symmetric monoidal category. As a result, we obtain the monoidal closedness of the category of stratified L-semiuniform convergence spaces and uniformly continuous maps. (c) 2020 Elsevier B.V. All rights reserved.

关键词： Fuzzy sets   Fuzzy relations   Category theory  

摘要： An IL-fuzzy relation is a relation valued on a complete lattice IL with a monoidal structure. This paper reviews four categories of IL-fuzzy relations each modelling an area where Fuzzy Set Theory can be applied. We review the notions of these multivalued binary relations and present some basic properties of the corresponding categories aiming at applications in areas such as Computing Science, Linear Logic and Quantum Mechanics. The emphasis is on the monoidal aspects of the categories. Monoidal categories are one of the most applied kinds of categories. A monoidal view of Fuzzy Relations may widen the spectrum of applications of Fuzzy Set Theory. (c) 2021 Elsevier B.V. All rights reserved.

关键词： 古诗英译   意美   "象"范畴   意象   意境  

摘要： 诗歌翻译三美原则中意美的传达最为重要,哲学美学中的"象"范畴为古诗英译的意美再现拓展了研究空间."立象成意"的哲学观念首先向我们证明了诗歌是可译的,诗歌的玄妙抽象之意可以通过实实在在的"象"来表达.古诗英译意美的再现需要在译文中同时实现意象美和意境美.其中意象美的再现要求意象相谐,而意境美的再现强调传递象外之象的内涵.

关键词： Derived categories of coherent   sheaves   Thaddeus pairs  

摘要： We show that the moduli spaces of Thaddeus pairs on smooth projective curves and those of dual pairs are related by d critical flips, which are virtual birational transformations introduced by the second author. We then prove the existence of fully-faithful functors between derived categories of coherent sheaves on these moduli spaces. Our result gives an evidence of a d-critical analogue of Bondal-Orlov, Kawamata's D/K equivalence conjecture, and also a categorification of wall crossing formula of Donaldson-Thomas type invariants on ADHM sheaves introduced by Diaconescu. Crown Copyright (c) 2021 Published by Elsevier Inc. All rights reserved.

关键词： 2-category   (infinity, 2)-category   Complicial set   Nerve  

摘要： We show that the canonical homotopy theory of strict 2-categories embeds in that of (infinity, 2)-categories in the form of 2-(pre)complicial sets. More precisely, we construct a nerve-categorification adjunction that is a Quillen pair between the canonical model structure for 2-categories and the model structure for 2-precomplicial sets. Furthermore, we show that the former model structure is transferred along this nerve and that the nerve is homotopically fully faithful. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Statistical learning   Interpretability   Greedy randomized adaptive search procedure   Proximity between categories  

摘要： We propose a method to reduce the complexity of Generalized Linear Models in the presence of categorical predictors. The traditional one-hot encoding, where each category is represented by a dummy variable, can be wasteful, difficult to interpret, and prone to overfitting, especially when dealing with high-cardinality categorical predictors. This paper addresses these challenges by finding a reduced representation of the categorical predictors by clustering their categories. This is done through a numerical method which aims to preserve (or even, improve) accuracy, while reducing the number of coefficients to be estimated for the categorical predictors. Thanks to its design, we are able to derive a proximity measure between categories of a categorical predictor that can be easily visualized. We illustrate the performance of our approach in real-world classification and count-data datasets where we see that clustering the categorical predictors reduces complexity substantially without harming accuracy.

关键词： Super quantum groups   Modified traces   Witten-Reshetikhin-Turaev invariants  

摘要： We examine two different m-traces in the category of representations over the quantum Lie superalgebra associated to sl(m vertical bar n) at root of unity. The first m-trace is on the ideal of projective modules and leads to new Extended Topological Quantum Field Theories. The second m-trace is on the ideal of perturbative typical modules. We consider the quotient with respect to negligible morphisms coming from this m-trace and show that in the case of sl(2 vertical bar 1) this quotient leads to 3-manifolds invariants. We conjecture that the quotient category of perturbatives over quantum sl(m vertical bar n) leads to 3-manifold invariants and more generally ETQFTs. (C) 2021 Elsevier Inc. All rights reserved.

关键词： aspect-category sentiment analysis   graph convolutional network   public opinion analysis   topic model   weak supervision learning  

摘要： Aspect-category sentiment classification of microblog comments aims to identify the sentiment polarity of different opinion aspects in microblog comments, which is meaningful for the analysis of public opinion. At present, most of aspect-category sentiment classification methods need much annotation data, and regard comments as independent samples, without using of the relationship between comments. This article proposes an aspect-category sentiment classification method based on tensor graph convolutional networks. First, the combination of a comment and its aspect category is regarded as a hybrid node, and the original representation of a hybrid node is encoded by the Bert model. Second, sentiment graph and semantic graph are constructed according to the semantic similarity and sentimental relevance between hybrid nodes, and they are stacked into a tensor. Then two convolution operations, including intra-graph convolution and inter-graph convolution, are performed for each layer of graph tensor. In this way, hybrid nodes can learn and merge the heterogeneous information of different graphs. Finally, under the supervision of few labeled comments, the sentiment classification can be completed based on the features of the hybrid nodes. Experimental results on two microblog datasets show that the proposed model can significantly improve the performance of sentiment classification compared with other baseline models.