检索结果-内蒙古大学图书馆

THE CHARACTERIZATIONS OF HYPERSPACES AND FREE TOPOLOGICAL GROUPS WITH AN ωω-BASE

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Lin, Fucai Liu, Chuan School of mathematics and statistics Minnan Normal University Zhangzhou363000 China Fujian Key Laboratory of Granular Computing and Application Minnan Normal University Zhangzhou363000 China Department of Mathematics Ohio University Zanesville Campus ZanesvilleOH43701 United States

A topological space (X, τ) is said to be have an ωω-base if for each point x ∈ X there exists a neighborhood base {Uα[x]: α ∈ ωω} such that Uβ[x] ⊂ Uα[x] for all α ≤ β in ωω. In this paper, the characterization of a space X is given such that the free Abelian topological group A(X), the hyperspace CL(X) with the Vietoris topology and the hyperspace CL(X) with the Fell topology have ωω-bases respectively. The main results are listed as follows: (1) For a Tychonoff space X, the free Abelian topological group A(X) is a k-space with an ωω-base if and only if X is a topological sum of a discrete space and a submetrizable kω-space. (2) If X is a metrizable space, then (CL(X), τV ) has an ωω-base if and only if X is separable and the boundary of each closed subset of X is σcompact. (3) If X is a metrizable space, then (CL(X), τF ) has an ωω-base consisting of basic neighborhoods if and only if X is a Polish space. (4) If X is a metrizable space, then (CL(X), τF ) is a Fréchet-Urysohn space with an ωω-base, if and only if (CL(X), τF ) is first-countable, if and only if X is a locally compact and second countable *** Codes Primary 54B20, secondary 22A05, 5430, 54D45, 54D70, 54E35 Copyright © 2025, The Authors. All rights reserved.

关键词： Topology

Competence-Based Knowledge Space Theory from the Perspective of Formal Concept Analysis

学校读者我要写书评

暂无评论

SSRN

SSRN 2023年

作者： Huang, Baokun Li, Jinjin Li, Qifang Zhou, Yinfeng Chen, Huiqin School of Mathematics and Statistics Minnan Normal University Fujian Zhangzhou China Fujian Key Laboratory of Granular Computing and Applications Fujian Zhangzhou China School of Mathematics and Statistics Shaanxi Normal University Shaanxi Xi’an China

In this paper, competence-based knowledge space theory (CbKST) is approached from the perspective of formal concept analysis (FCA). The aim is to visualize the relationship between knowledge structure and competence structure. The skill map is transformed into a formal context, and the methodology for constructing the concept lattice is provided. Within a concept lattice, each node, referred to as a concept, embodies a knowledge state and a competence state as its extension and intention, respectively. It is demonstrated that the family of sets formed by the extensions of all concepts is exactly the knowledge structure delineated by the skill map via the corresponding model. Additionally, the difference set of the extensions of the proper sbuconcept-superconcept in a concept lattice reflects the master fringe of the individual knowledge state. A concept lattice is considered favorable if an individual can solve the items of the master fringe only by mastering one skill, and the sufficient and necessary conditions for favorable concept lattices are given. When skills have no inherent surmise relationship, the order in which they are learned can be arbitrary. From the perspective of effective learning, we propose a precedence relation between skills to guide the recommendation of personalized learning schemes. Moreover, it is proved that on a favorable concept lattice, there is a learning path that adheres to the principle of step-by-step and easy-to-difficult. © 2023, The Authors. All rights reserved.

关键词： Formal concept analysis

On sobriety of Scott topology on dcpos

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Xu, Xiaoquan Fujian Key Laboratory of Granular Computing and Applications School of Mathematics and Statistics Minnan Normal University Zhangzhou363000 China

In this paper, we mainly investigate the conditions under which the Scott topology on the product of two posets is equal to the product of the individual Scott topologies and under which the Scott topology on a dcpo is sober. Some such conditions are *** Codes 54D99, 54B20, 06B30, 06B35 Copyright © 2022, The Authors. All rights reserved.

关键词： Topology

Incremental Cognitive Learning Approach Based on Concept Reduction

学校读者我要写书评

暂无评论

SSRN

SSRN 2024年

作者： Liang, Taoju Lin, Yidong Li, Jinjin Wang, Qijun School of Mathematics and Statistics Minnan Normal University Zhangzhou363000 China Institute of Meteorological Big Data-Digital Fujian Minnan Normal University Zhangzhou363000 China Fujian Key Laboratory of Granular Computing and Applications Minnan Normal University Zhangzhou363000 China

Concept-cognitive learning (CCL) offers an innovative approach to classification, and concept reduction serves as a powerful method for compressing data. Nonetheless, most existing CCLs tend to incur information loss during the compression of concept space. On the other hand, current incremental CCLs have limited capacity to effectively utilize newly acquired knowledge. In view of these observations, in this article, we propose a novel incremental CCL method based on concept reduction for dynamic classification. To enhance the efficiency of knowledge acquisition, recover degree is developed to obtain concept reduction from granular concept space. Subsequently, the updating mechanism for concept reduction is explored in dynamic environments. For label recognition, a learning method based on concept reduction is discussed and an incremental learning mechanism for dynamic increased data is further constructed. Empirical studies on twelve datasets from UCI reveal the effectiveness and efficiency of proposed model. © 2024, The Authors. All rights reserved.

关键词： Efficiency

On PM-factorizable topological groups *

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Bao, Meng Xu, Xiaoquan College of Mathematics Sichuan University Chengdu610064 China Fujian Key Laboratory of Granular Computing and Applications Minnan Normal University Zhangzhou363000 China

A topological group G is called PM-factorizable if for every continuous real-valued function f on G, there exists a perfect homomorphism π: G → H onto a metrizable topological group H such that f = g ◦ π, for some continuous real-valued function g on H. It is proved that a topological group is PM-factorizable if and only if it is feathered M-factorizable, and a topological group is PR-factorizable if and only if it is PM-factorizable and ω-narrow. The two results deduce that a topological group G is PR-factorizable if and only if G is feathered R-factorizable. Moreover, some properties about products of PM-factorizable topological groups are investigated. In particular, some interesting properties of M-factorizable topological groups in [8, 10] are strengthened to PM-factorizable topological *** Codes 22A05, 54A25, 54H11. © 2022, CC BY-NC-SA.

关键词： Topology

Coordinate Attention Based 3D-CNN Using Ghost Multi-Scale for Diagnosing Alzheimer’s Disease

学校读者我要写书评

暂无评论

Coordinate Attention Based 3D-CNN Using Ghost Multi-Scale fo...

International Joint Conference on Neural Networks (IJCNN)

作者： Xiaolu Lin Pinya Lu Jie Pan Hongqin Yang Xuemei Ding Fujian Provincial Engineering Research Center for Public Service Big Data Mining and Application Fujian Provincial University Engineering Research Center for Big Data Analysis and Application Fujian Normal University Fuzhou China Xiamen Jingyi Zhikang Technology Co. Ltd Xiamen China Fujian Provincial Key Laboratory for Photonics Technology Key Laboratory of OptoElectronic Science and Technology for Medicine of Ministry of Education Fujian Normal University Fuzhou China School of Computing Engineering and Intelligent Systems Ulster University Derry-Londonderry NI UK

ISBN: (数字)9798350359312

ISBN: (纸本)9798350359329

Alzheimer's disease (AD) is a neurodegenerative disease and mild cognitive impairment (MCI) is the early stage of AD. Previous studies have predominantly focused on binary classification using 3 dimensional - convolutional neural network (3D-CNN) for AD diagnosis, with limited progress in multi-classification. Moreover, the current 3D-CNNs often adopt a single-scale architecture with massive parameters growth. Additionally, obtaining precise location information of brain imaging data is crucial for improving the classification accuracy with 3D-CNN. Hence, we propose a multi-scale 3D-CNN based on coordinate attention mechanism to marvelously capture and integrate 3D features with fewer parameters, improving the accuracy of AD diagnosis. A total of 447 cognitively normal (CN), 512 MCI, and 358 AD sMRI images from the Alzheimer's Disease Neuroimaging Initiative datasets are used for multi-class classification task, yielding a classification accuracy of 92.8%. The model merely involves 2.41 M parameters and achieves the best classification results with the least number of parameters when compared to other representative CNN architectures including ResNet 18, ResNet 34, ConvNeXt tiny, and VGG 11. Through the ablation experiment, the addition of attention mechanism and the multi-scale classification enhances the classification performance by 4.5% and 1.5%, respectively. Furthermore, our model outperforms the other six existing studies in terms of accuracy for classifying AD vs. MCI vs. CN. Overall, this study underscores the efficacy of our approach for AD diagnosis, showcasing its utility in diagnosing AD patients and providing novel insights for diagnosing other neurological disorder diseases.

关键词： Neuroimaging Accuracy Attention mechanisms Three-dimensional displays Resonance Convolutional neural networks Alzheimer's disease

SOME PROPERTIES OF PRE-UNIFORM SPACES

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Lin, Fucai Xie, Yufan Wu, Ting Bao, Meng School of Mathematics and Statistics Minnan Normal University Zhangzhou363000 China Fujian Key Laboratory of Granular Computing and Application Minnan Normal University Zhangzhou363000 China College of Mathematics Sichuan University Chengdu610064 China

In this paper, we introduce the notions of pre-uniform spaces and pre-proximities and investigate some basic properties about them, where the definition of pre-uniformity here is different with the pre-uniformities which are studied in [1], [8] and [12] respectively. First, we prove that each pre-uniform pre-topology is regular, and give an example to show that there exists a pre-uniform structure on a finite set such that the pre-uniform pre-topology is not discrete. Moreover, we give three methods of generating (strongly) pre-uniformities, that is, the definition of a pre-base, a family of strongly pre-uniform covers, or a family of strongly pre-uniform pseudometrics. As an application, we show that each strongly pre-topological group is completely regular. Finally, we pose the concept of the pre-proximity on a set and discuss some properties of the *** Codes 54A05, 54C08, 54E05, 54E15 Copyright © 2022, The Authors. All rights reserved.

关键词： Topology

SOME PROPERTIES OF PRE-TOPOLOGICAL GROUPS

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Lin, Fucai Wu, Ting Xie, Yufan Bao, Meng School of Mathematics and Statistics Minnan Normal University Zhangzhou363000 China Fujian Key Laboratory of Granular Computing and Application Minnan Normal University Zhangzhou363000 China College of Mathematics Sichuan University Chengdu610064 China

In this paper, we pose the concepts of pre-topological groups and some generalizations of pre-topological groups. First, we systematically investigate some basic properties of pre-topological groups;in particular, we prove that each T0 pre-topological group is regular and every almost topological group is completely regular which extends A.A. Markov's theorem to the class of almost topological groups. Moreover, it is shown that an almost topological group is τ-narrow if and only if it can be embedded as a subgroup of a pre-topological product of almost topological groups of weight less than or equal to τ. Finally, the cardinal invariant, the precompactness and the resolvability are investigated in the class of pre-topological *** Codes 22A99, 54A05, 54A25, 54B05, 54C08, 54D05, 54H11, 54H99 Copyright © 2022, The Authors. All rights reserved.

关键词： Topology

An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2023年第1期36卷 433-456页

作者： ELSAWAH A M VISHWAKARMA G K MOHAMED H S FANG Kai-Tai Department of Statistics and Data Science Faculty of Science and TechnologyBeijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519087China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International CollegeZhuhai 519087China Department of Mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt Department of Mathematics&Computing Indian Institute of Technology DhanbadDhanbad 826004India College of Transportation and Civil Engineering Fujian Agriculture and Forestry UniversityFuzhou 350002China The Key Lab of Random Complex Structures and Data Analysis The Chinese Academy of SciencesBeijing 100190China

A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are *** large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not *** paper presents a new effective and easy technique,adjusted Gray map technique(AGMT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation *** justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level *** results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.

关键词： Aberration adjusted Gray map technique Gray map technique Hamming distance moment aberration threshold accepting algorithm uniform design