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关键词： CAEN   classification   feature selection   single‐   cell RNA‐   seq  

摘要： Bulk and single-cell RNA-seq (scRNA-seq) data are being used as alternatives to traditional technology in biology and medicine research. These data are used, for example, for the detection of differentially expressed (DE) genes. Several statistical methods have been developed for the classification of bulk and single-cell RNA-seq data. These feature genes are vitally important for the classification of bulk and single-cell RNA-seq data. The majority of genes are not DE and they are thus irrelevant for class distinction. To improve the classification performance and save the computation time, removal of irrelevant genes is necessary. Removal will aid the detection of the important feature genes. Widely used schemes in the literature, such as the BSS/WSS (BW) method, assume that data are normally distributed and may not be suitable for bulk and single-cell RNA-seq data. In this article, a category encoding (CAEN) method is proposed to select feature genes for bulk and single-cell RNA-seq data classification. This novel method encodes categories by employing the rank of sequence samples for each gene in each class. Correlation coefficients are considered for gene and class with the rank of sample and a new rank of category. The highest gene correlation coefficients are considered feature genes, which are the most effective for classifying bulk and single-cell RNA-seq dataset. The sure screening method was also established for rank consistency properties of the proposed CAEN method. Simulation studies show that the classifier using the proposed CAEN method performs better than, or at least as well as, the existing methods in most settings. Existing real datasets were analyzed, with the results demonstrating superior performance of the proposed method over current competitors. The application has been coded into an R package named "CAEN" to facilitate wide use.

关键词： Artin algebra   Cluster tilting subcategory   n-abelian category   Gorenstein projective module  

摘要： Let A be an Artin algebra. In this paper, the notion of nZ-Gorenstein cluster tilting subcategories will be introduced. It is shown that every nZ-cluster tilting subcategory of mod-A is nZ-Gorenstein if and only if A is an Iwanaga-Gorenstein algebra. Moreover, it will be shown that an nZ-Gorenstein cluster tilting subcategory of mod-A is an nZ-cluster tilting subcategory of the exact category Gprj-A, the subcategory of all Gorenstein projective objects of mod-A. Some basic properties of nZ-Gorenstein cluster tilting subcategories will be studied. In particular, we show that they are n-resolving, a higher version of resolving subcategories. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Maximal green sequence   Stability function   Central charge   Brick  

摘要： In this article, we study the relationship among maximal green sequences, complete forward hom-orthogonal sequences and stability functions in abelian length categories. Mainly, we firstly give a one-to-one correspondence between maximal green sequences and complete forward hom-orthogonal sequences via mutual constructions, and then prove that a maximal green sequence can be induced by a central charge if and only if it satisfies crossing inequalities. As applications, we show that crossing inequalities can be computed by c-vectors for finite dimensional algebras;finally, we give the Rotation Lemma for finite dimensional Jacobian algebras. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Category theory   Reaction systems  

摘要： In the literature, one encounters the intensely studied classical set-based reaction systems and the more recently introduced generalization to graph-based reaction systems where the considered graphs are directed, simple, and edge-labeled. In this paper, we propose a categorical approach to reaction systems so that a wider spectrum of data structures becomes available on which reaction systems can be based including various types of graphs and of graph-like structures like unlabeled graphs, vertex-labeled graphs, bipartite graphs, and a variety of types of hypergraphs. But also algebraic structures like monoids fit into the framework. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Amenable category   Degree   3-manifold   Lusternik-Schnirelmann category  

摘要： We discuss the monotonicity problem for the amenable category of closed manifolds under maps of non-zero degree. In dimension three this leads to a variation on a recent theorem of Capovilla, Loh and Moraschini [1]. (c) 2021 Elsevier B.V. All rights reserved.

关键词： 工程管理   管理范畴   工程建设  

摘要： 随着我国工程建设数量和质量的提升,以及现阶段我国对工程建设要求的逐步提高,现阶段我国的工程项目建设,开始更加重视工程管理的重要性。也因此,本文就针对工程建设中,工程管理的范畴和工程管理的重要性进行分析研究,具体的阐述了工程管理的基本概念,并阐述了工程管理的管理范畴,以及工程管理的重要性,希望本文的研究,能够对我国工程管理工作的进行,起到一定的帮助和优化作用。

关键词： 山水画   写意   写意精神  

摘要： 本文以山水画为例浅谈当代中国画缺失的“写意精神”,“写意”并非写意画的一个技法概念,而是贯穿中国传统艺术的一种写意精神。这种精神是中国绘画艺术的重要特征,是当代人需要坚持与弘扬的中国独特的艺术精神。

关键词： Modular functor   Hochschild complex   Mapping class group   Modular category  

摘要： Given any modular category Cover an algebraically closed field k, we extract a sequence (M-g)(g >= 0) of C-bimodules and show that the Hochschild chain complex CH(C;M-g) of C with coefficients in M-g carries a canonical homotopy coherent projective action of the mapping class group of the surface of genus g + 1. The ordinary Hochschild complex of Ccorresponds to CH(C;M-0). This result is obtained as part of the following more comprehensive topological structure: We construct a symmetric monoidal functor F-C: C-Surf(c) -> Ch(k) with values in chain complexes over k defined on a symmetric monoidal category of surfaces whose boundary components are labeled with projective objects in C. The functor F-C satisfies an excision property which is formulated in terms of homotopy coends. In this sense, any modular category gives naturally rise to a modular functor with values in chain complexes. In zeroth homology, it recovers Lyubashenko's mapping class group representations. The chain complexes in our construction are explicitly computable by choosing a marking on the surface, i.e. a cut system and a certain embedded graph. For our proof, we replace the connected and simply connected groupoid of cut systems that appears in the Lego-Teichmuller game by a contractible Kan complex. (C) 2021 Elsevier Inc. All rights reserved.

关键词： 水语   个体量词   认知   范畴  

摘要： 根据语义特征,将水语个体量词分为形状量词、类别量词、专用量词和种类量词。水语个体量词的认知范畴层级较为明晰,本文主要描写类别量词、通用量词和形状量词内部区别特征。首先,量词■ai^(33)、ta■k^(43)把万物区分为人类与非人类两种;其次,在非人类事物中,量词t■^(31)把动物从非人类事物中区分出来,分为动物与非动物两种;在非动物类的事物中,又按外观特征分为形状、规格和存在状态三类;外观特征根据突显与否分为特征突显和特征弱显类;特征突显类又可按维度分为一维、二维与三维;规格可按尺寸分为大、小以及不分规格类;存在状态可以分为液体、气体以及固体。对个体量词的层级鲜明的范畴化区分,体现了水族群体对世界的认知理解。

关键词： 自由时间   劳动时间   “三大形态”理论   人的自由而全面发展  

摘要： 自由时间是伴随社会生产力的飞速发展,从社会必要劳动时间中游离出来的,能为人们在不受外力牵制的情况下参与社会活动而自由支配的时间。马克思、恩格斯在其经典著作中深入阐述了“自由时间”范畴的本真含义,同时,探讨自由时间与闲暇时间、劳动时间等概念的内在逻辑关系,接着描述三种社会形态下的自由时间状况,只有进入共产主义社会,自由时间与劳动时间彼此之间会处于同一的自我和谐状态。