学科服务 更多>>

关键词： 18D10 (primary)   16T05   20E45   20N20   81R50 (secondary)  

摘要： In this paper, we study conjugacy classes for pivotal fusion categories. In particular, we prove a Burnside type formula for the structure constants concerning the product of two conjugacy class sums of such a fusion category. For a braided weakly integral fusion category C, we show that these structure constants multiplied by dim(C) are non-negative integers, extending some results obtained by Zhou and Zhu (see Preprint, 2019, arXiv:1912.07831v1) in the settings of semisimple quasitriangular Hopf algebras.

关键词： extriangulated category   abelian category   cluster tilting subcategory   Gorenstein dimension  

摘要： Let C be a triangulated category and X be a cluster tilting subcategory of C. Koenig and Zhu showed that the quotient category C/X is Gorenstein of Gorenstein dimension at most one. But this is not always true when C becomes an exact category. The notion of an extriangulated category was introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. Now let C be an extriangulated category with enough projectives and enough injectives, and X a cluster tilting subcategory of C. We show that under certain conditions, the quotient category C/X is Gorenstein of Gorenstein dimension at most one. As an application, this result generalizes the work by Koenig and Zhu.

关键词： Optimization  

摘要： In geographic data analysis, one is often given point data of different categories (such as facilities of a university categorized by department). Drawing upon recent research on set visualization, we want to visualize category membership by connecting points of the same category with visual links. Existing approaches that follow this path usually insist on connecting all members of a category, which may lead to many crossings and visual clutter. We propose an approach that avoids crossings between connections of different categories completely. Instead of connecting all data points of the same category, we subdivide categories into smaller, local clusters where needed. We do a case study comparing the legibility of drawings produced by our approach and those by existing approaches. In our problem formulation, we are additionally given a graph G on the data points whose edges express some sort of proximity. Our aim is to find a subgraph G ' of G with the following properties: (i) edges connect only data points of the same category, (ii) no two edges cross, and (iii) the number of connected components (clusters) is minimized. We then visualize the clusters in G '. For arbitrary graphs, the resulting optimization problem, Cluster Minimization, is NP-hard (even to approximate). Therefore, we introduce two heuristics. We do an extensive benchmark test on real-world data. Comparisons with exact solutions indicate that our heuristics do astonishing well for certain relative-neighborhood graphs.

关键词： Economic policy uncertainty   Spillovers   Network connectedness   US-China trade war  

摘要： This study investigates the interconnection of policy uncertainties between the world's two largest countries, the US and China, and sheds light on whether and how the US-China trade war affects each party. Given the deep-seated economic integration and trade linkage between the two countries, these characterizations are essential for understanding how policy shocks propagate spatially. Using fiscal, monetary, and trade policy data from January 2000 to December 2019, I provide ample evidence of bilateral, multilateral, and system-wide measures of policy uncertainty connectedness. Monetary policy is most likely to be the leader of policy uncertainty in China, while fiscal policy is more likely to be the leader in the US. The cross-category connectedness is not constant over time. Overall, the direction of spillover is from the US to China, although this changes in different periods owing to different environments. These findings are useful for policymakers to monitor the effectiveness of policies and to help investors avoid economic policy uncertainty shocks induced by return fluctuations. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Leibniz cohomology   Chevalley-Eilenberg cohomology   Change of rings spectral sequence   Cohomology vanishing   Semi-simple Leibniz algebra   Ext category of Leibniz bimodules  

摘要： In this article, we generalize Loday and Pirashvili's [11] computation of the Ext-category of Leibniz bimodules for a simple Lie algebra to the case of a simple (non Lie) Leibniz algebra. Most of the arguments generalize easily, while the main new ingredient is the Feldvoss-Wagemann's cohomology vanishing theorem for semi-simple Leibniz algebras. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Session feature embedding   Few-shot   Unknown attack detection   Intra categories generation   Generative adversarial cooperative network (GACN)  

摘要： In the network traffic intrusion detection, deep learning based schemes have attracted lots of achievements. However, in real-world scenarios, data is often insufficient (few-shot), which leads to various deviations between the models prediction and the ground truth. Consequently, downstream tasks such as unknown attack detection based on few-shot will be limited by insufficient data. In this paper, we propose a novel unknown attack detection method based on Intra Categories Generation in Embedding Space, namely SFE-GACN, which might be the solution of few-shot problem. Concretely, we first propose Session Feature Embedding (SFE) to summarize the context of basic granularity of network traffic: sessions, bring the insufficient data to the pre-trained embedding space. In this way, we achieve the goal of preliminary information extension in the few-shot case. Second, we further propose the Generative Adversarial Cooperative Network (GACN), which improves the conventional Generative Adversarial Network by supervising the generated sample to avoid falling into similar categories, and thus enables samples to generate intra categories. Our proposed SFE-GACN achieved that it can accurately generate session samples in the case of few-shot, and ensure the difference between categories during data augmentation. The detection results show that compared to the state-of-the-art method, the average TPR is 8.38% higher, and the average FPR is 12.77% lower. In addition, we evaluated the graphics generation capabilities of GACN on the graphics dataset, the result shows our proposed GACN can be popularized for generating easy-confused multi-categories graphics. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Object-oriented metrics   Fault prediction   Ensemble   Machine learning   Nimenyi test   Statistical tests  

摘要： The quality of the software being developed varies with the size and complexity of the software. It is a matter of concern in software development as it impairs the faith of customers on the software companies. The quality of software can be improved if the prediction of faults and flaws in it are done in the early phases of the software development and thus reducing the resources to be used in the testing phase. The rise in the use of Object-Oriented technology for developing software has paved the way for considering the Object-Oriented metrics for software fault prediction. Numerous machine learning and statistical techniques have been used to predict the defects in software using these software metrics as independent variables and bug proneness as dependent variable. Our work aims at finding the best category and hence the best classifier for classification of faults. This work uses twenty-one classifiers belonging to five categories of classification on five open source software having Object-Oriented metrics. The classification LearnerApp of MATLAB has been used to evaluate various classification models. The work proposes the use of Ensemble and SVM techniques over KNN, Regression, and Tree. The bagged trees (ensemble) and cubic (SVM) are found to be the best predictors amongst the twenty-one classifiers.

关键词： Mal'tsev categories   Internal groupoids   Simplicial objects   Galois theory   Central extensions   Monotone-light factorization  

摘要： We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and, moreover, a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois structure, and show that regular epimorphisms admit a relative monotone-light factorization system in the sense of Chikhladze. We also draw some comparison with Kan complexes. By comparing the reflections of simplicial objects and reflexive graphs into groupoids, we exhibit a connection with weighted commutators (as defined by Gran, Janelidze and Ursini). (C) 2020 Elsevier B.V. All rights reserved.

关键词： Graph homomorphism   Homotopy   2-category   Homotopy category   Skeleton of a category  

摘要： We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of what we call 'spider moves.' We then create a category by modding out by the 2-cells of our 2-category and use the spider moves to show that for finite graphs, this category is a homotopy category in the sense that it satisfies the universal property for localizing homotopy equivalences. We then show that finite stiff graphs form a skeleton of this homotopy category.