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ELLIPTIC EQUATION WITH CRITICAL EXPONENT AND DIPOLE POTENTIAL: EXISTENCE AND DECAY ESTIMATES

Acta Mathematica Scientia 2025年第2期45卷 636-658页

作者： Yu SU Zhisu LIU Senli LIU School of Mathematics and Big Data Anhui University of Science and TechnologyHuainan 232001China School of Mathematics and Physics China University of GeosciencesWuhan 430074China Institute for Advanced Marine Research China University of GeosciencesGuangzhou 511462China College of Mathematics and Computing Science Hunan University of Science and TechnologyXiangtan 411201China

The paper is concerned with a class of elliptic equation with critical exponent and Dipole *** precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of n... 详细信息

关键词： Dipole potential decay estimation Hardy Sobolev critical exponent Henon Sobolev critical exponent

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Attention-Enhanced and Knowledge-Fused Dual Item Representations Network for Recommendation

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Tsinghua science and Technology 2025年第2期30卷 585-599页

作者： Qiang Hua Jiachao Zhou Feng Zhang Chunru Dong Dachuan Xu College of Mathematics and Information Science Hebei UniversityBaoding 071002China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China

Integrating Knowledge Graphs(KGs)into recommendation systems as supplementary information has become a prevalent *** leveraging the semantic relationships between entities in KGs,recommendation systems can better comprehend user *** to the unique structure of KGs,methods based on Graph Neural Networks(GNNs)have emerged as the current technical ***,existing GNN-based methods struggle to(1)filter out noisy information in real-world KGs,and(2)differentiate the item representations obtained from the knowledge graph and bipartite *** this paper,we introduce a novel model called Attention-enhanced and Knowledge-fused Dual item representations Network for recommendation(namely AKDN)that employs attention and gated mechanisms to guide aggregation on both knowledge graphs and bipartite *** particular,we firstly design an attention mechanism to determine the weight of each edge in the information aggregation on KGs,which reduces the influence of noisy information on the items and enables us to obtain more accurate and robust representations of the ***,we exploit a gated aggregation mechanism to differentiate collaborative signals and knowledge information,and leverage dual item representations to fuse them together for better capturing user behavior *** conduct extensive experiments on two public datasets which demonstrate the superior performance of our AKDN over state-of-the-art methods,like Knowledge Graph Attention Network(KGAT)and Knowledge Graph-based Intent Network(KGIN).

关键词： Recommender System(RS) Knowledge Graph(KG) Graph Neural Networks(GNN) attention mechanism

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Paired Transmission in Networks

Paired Transmission in Networks

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International Conference on Computational Engineering, ICCE 2023

作者： Sujana G, Jessy Sharon, Jane Olive Anitha, J. Department of Computer Science SRM Institute of Science and Technology Vadapalani Chennai India Department of Computing Technologies SRM Institute of Science and Technology Chennai India Department of Mathematics Rajalakshmi Institute of Technology Chennai India

ISBN: (纸本)9783031777639

The transmission of a vertex is defined as the sum of the lengths of all shortest paths between the chosen vertex and all other vertices in G. The transmission of a graph G is the sum of the transmissions of all its vertices which is nothing but twice its Wiener index. In location theory, sets of vertices, with the minimum (or maximum) distance in a graph, play a special role because they form target sets for locations of facilities. The framework is made more general by considering the sum of distances to a specified multiset of vertices referred to as profiles. In this paper, we have defined paired transmission of vertices for a network as a special case of profiles, referred to as a paired facility location. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Network theory (graphs)

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Construction Of Almost Unbiased Estimator For Population Mean Using Neutrosophic Information

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Neutrosophic Sets and Systems 2025年 76卷 449-463页

作者： Singh, Rajesh Kumari, Anamika Smarandache, Florentin Tiwari, Shobh Nath Department of Statistics Institute of Science Banaras Hindu University Uttar Pradesh Varanasi221005 India Department of Data Science and Computing Manipal Academy of Higher Education India Department of Mathematics University of New Mexico 705 Gurley Ave Gallup United States

In classical statistics, the population mean is estimated using determinate, crisp data value when auxiliary information is known. These estimates can often be biased. The main objective of this study is to introduce the neutrosophic estimator with the minimum mean squared error (MSE) for the unknown value of the population mean as well as overcome the limitations of classical statistics when dealing with ambiguous or indeterminate data. Neutrosophic statistics was introduced by Florentin Smarandache. It is a generalisation of classical statistics that addresses ambiguous, unclear, vague, and indeterminate data. In this study, we have proposed neutrosophic almost unbiased estimator that use known neutrosophic auxiliary parameters to estimate the neutrosophic population mean of the primary variable. Equations for bias and mean squared error are calculated for the suggested estimators up to the first order of approximation. The proposed estimator performs better than the other existing estimators with respect to the MSE and percent relative efficiency (PRE) criteria. The estimator with the highest PRE or lowest MSE is advised for practical utility in various kinds of application areas. The theoretical conclusions are validated by the empirical analysis, which made use of the real data sets. © 2025, University of New Mexico. All rights reserved.

关键词： Mean square error

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Domination Number in Sierpiński Networks

Domination Number in Sierpiński Networks

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International Conference on Computational Engineering, ICCE 2023

作者： Anitha, J. Rajasingh, Indra Sharon, Jane Olive Department of Mathematics Rajalakshmi Institute of Technology Chennai India Department of Mathematics for Excellence Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Chennai India Department of Computing Technologies SRM Institute of Science and Technology Chennai India

ISBN: (纸本)9783031777639

If there is at least one neighbour in K for each vertex in V that is not in K, then a set K⊆V(G) is a dominating set (DS) in G(V,E). The minimal cardinality of a DS of G is the domination number(DN) of G, represented by γ(G). In this paper, we determine the γ(G) for Sierpiński networks, Str and the divide-and-swap cubic networks, DSCr. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： 68R10 81Q30 82B20 82C20 Divide-and-swap cubic networks Dominating set Sierpiński Networks

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Insights from Univalent Foundations: A Case Study Using Double Categories 33

Insights from Univalent Foundations: A Case Study Using Doub...

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33rd EACSL Annual Conference on Computer science Logic, CSL 2025

作者： Rasekh, Nima van der Weide, Niels Ahrens, Benedikt North, Paige Randall Institute of Mathematics and Computer Science University of Greifswald Germany Institute for Computing and Information Sciences Radboud University Nijmegen Netherlands Delft University of Technology Netherlands University of Birmingham United Kingdom Department of Information and Computing Sciences Mathematical Institute Utrecht University Netherlands

ISBN: (纸本)9783959773621

Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating not just objects, but also morphisms capturing interactions between objects. Of particular importance in some applications are double categories, which are categories with two classes of morphisms, axiomatizing two different kinds of interactions between objects. These have found applications in many areas of mathematics and theoretical computer science, for instance, the study of lenses, open systems, and rewriting. However, double categories come with a wide variety of equivalences, which makes it challenging to transport structure along equivalences. To deal with this challenge, we propose the univalence maxim: each notion of equivalence of categorical structures has a corresponding notion of univalent categorical structure which induces that notion of equivalence. We also prove corresponding univalence principles, which allow us to transport structure and properties along equivalences. In this way, the usually informal practice of reasoning modulo equivalence becomes grounded in an entirely formal logical principle. We apply this perspective to various double categorical structures, such as (pseudo) double categories and double bicategories. Concretely, we characterize and formalize their definitions in Coq UniMath up to chosen equivalences, which we achieve by establishing their univalence principles. © Nima Rasekh, Niels van der Weide, Benedikt Ahrens, and Paige Randall North.

关键词： Choquet integral

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LayerCFL:an efcient federated learning with layer-wised clustering

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Cybersecurity 2025年第1期8卷 72-85页

作者： Jie Yuan Rui Qian Tingting Yuan Mingliang Sun Jirui Li Xiaoyong Li School of Cyberspace Security Beijing University of Posts and TelecommunicationsBeijingChina Key Laboratory of Trustworthy Distributed Computing and Service(BUPT) Ministry of EducationBeijingChina Institute of Computer Science Faculty of Mathematics and Computer ScienceUniversity of GoettingenGöettingenGermany School of Information Technology Henan University of Chinese MedicineZhengzhouHenanChina

Federated Learning(FL)sufers from the Non-IID problem in practice,which poses a challenge for efcient and accurate model *** address this challenge,prior research has introduced clustered FL(CFL),which involves clustering clients and training them *** its potential benefts,CFL can be computationally and communicationally expensive when the data distribution is unknown *** is because CFL involves the entire neural networks of involved clients in computing the clusters during training,which can become increasingly timeconsuming with large-sized *** tackle this issue,this paper proposes an efcient CFL approach called LayerCFL that employs a Layer-wised clustering *** LayerCFL,clients are clustered based on a limited number of layers of neural networks that are pre-selected using statistical and experimental *** experimental results demonstrate the efectiveness of LayerCFL in mitigating the impact of Non-IID data,improving the accuracy of clustering,and enhancing computational efciency.

关键词： Federated learning Clustered federated learning Non-IID Layer-wised clustering

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Robotic Cognitive Behavioural Therapy: rCBT 16th

Robotic Cognitive Behavioural Therapy: rCBT

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16th International Conference on Social Robotics, ICSR + BioMed 2024

作者： Samani, Hooman Zaraki, Abolfazl Davies, Daisy-Rose Fernando, Owen Noel Newton Creative Computing Institute University of the Arts London London United Kingdom and Robotics Research Group University of Hertfordshire Hatfield United Kingdom School of Engineering Computing and Mathematics University of Plymouth Plymouth United Kingdom College of Computing and Data Science Nanyang Technological University Singapore Singapore

ISBN: (纸本)9789819789627

This paper introduces Robotic Cognitive Behavioural Therapy (rCBT) as a novel approach to overcoming the limitations of traditional Cognitive Behavioural Therapy (CBT) in treating emotional and psychological issues. After a brief overview of CBT and its inherent challenges, this paper explores the innovative application of physical robots in therapy, building on the success of technology-based CBT methods that have effectively treated various mental health conditions. The proposed rCBT solution is a compact, portable, and cost-effective 3D-printed robot designed to aid individuals with anxiety or depression. This robot includes interactive features such as a diary, health questionnaires, daily mood monitoring, to-do lists, mindfulness exercises, and a crisis helpline, enabling users to track their emotional states and activities. These functions support healthcare professionals and users in identifying emotional patterns and triggers. The robot can monitor physiological signals like heart rate. This research aims to enhance the accessibility and effectiveness of CBT, suggesting that rCBT could significantly broaden the therapy’s reach and improve mental health outcomes for a larger population. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Social robots

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A General Framework for Clustering and Distribution Matching with Bandit Feedback

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IEEE Transactions on Information Theory 2025年第3期71卷 2116-2139页

作者： Yavas, Recep Can Huang, Yuqi Tan, Vincent Y. F. Scarlett, Jonathan CNRS@CREATE DesCartes Program CREATE Tower 138602 Singapore National University of Singapore Department of Computer Science Queenstown119077 Singapore National University of Singapore School of Computing Department of Information Systems and Analytics Queenstown119077 Singapore National University of Singapore Department of Mathematics Department of Electrical and Computer Engineering Queenstown119077 Singapore Institute of Data Science National University of Singapore Department of Computer Science The Department of Mathematics Queenstown119077 Singapore

We develop a general framework for clustering and distribution matching problems with bandit feedback. We consider a K-armed bandit model where some subset of K arms is partitioned into M groups. Within each group, the random variable associated to each arm follows the same distribution on a finite alphabet. At each time step, the decision maker pulls an arm and observes its outcome from the random variable associated to that arm. Subsequent arm pulls depend on the history of arm pulls and their outcomes. The decision maker has no knowledge of the distributions of the arms or the underlying partitions. The task is to devise an online algorithm to learn the underlying partition of arms with the least number of arm pulls on average and with an error probability not exceeding a pre-determined value δ. Several existing problems fall under our general framework, including finding M pairs of arms, odd arm identification, and N-ary clustering of K arms belong to our general framework. We derive a non-asymptotic lower bound on the average number of arm pulls for any online algorithm with an error probability not exceeding δ. Furthermore, we develop a computationally-efficient online algorithm based on the Track-and-Stop method and Frank-Wolfe algorithm, and show that the average number of arm pulls of our algorithm asymptotically matches that of the lower bound. Our refined analysis also uncovers a novel bound on the speed at which the average number of arm pulls of our algorithm converges to the fundamental limit as δ vanishes. © 1963-2012 IEEE.

关键词： Random variables

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Mixed finite element methods for biharmonic obstacle problems

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SeMA Journal 2025年 1-10页

作者： Piersanti, Paolo Sun, Tianyu School of Science and Engineering The Chinese University of Hong Kong (Shenzhen) 2001 Longxiang Blvd. Longgang District Shenzhen China Department of Mathematics and Institute for Scientific Computing and Applied Mathematics Indiana University Bloomington 729 East Third Street Bloomington IN United States

This paper is devoted to the study of an alternative Finite Element Method to the one originally proposed by Ciarlet & Raviart, and then complemented by Ciarlet & Glowinski, for studying the numerical approximation of the solution of the biharmonic problem. In addition to providing an alternative way of approximating the solution of the biharmonic problem, the method here presented is valid also in the context where the solution to the biharmonic problem is subjected to a constraint. The theoretical results we derived are complemented by a series of numerical experiments. © The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada 2025.

关键词： Elasticity theory Finite element method Obstacle problems Penalty method Variational inequalities

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