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Radial solution of the Logarithmic Laplacian system

applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 114-124页

作者： ZHANG Li-hong NIE Xiao-feng WANG Guo-tao Bashir Ahmad School of Mathematics and Computer Science Shanxi Normal UniversityLinfen 041004China Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia.

The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of th... 详细信息

关键词： the Logarithmic Laplacian system radial symmetry the direct method of moving planes

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Enhanced MADM Strategy with Heptapartitioned Neutrosophic Distance Metrics

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Neutrosophic Sets and Systems 2025年 78卷 74-96页

作者： Eassa, Mohamed Myvizhi, M. Elkholy, Mohamed Abdelhafeez, Ahmed Elbehiery, Hussam Computer Science Department Faculty of Information System and Computer Science October 6 University Giza12585 Egypt Applied Science Research Center Applied Science Private University Amman Jordan Department of Mathematics KPR Institute of Engineering and Technology Tamilnadu Coimbatore India Faculty of Computer Science& Engineering Alamein International University Egypt

In this work, a novel methodological approach to multi-attribute decision-making problems is developed and the notion of Heptapartitioned Neutrosophic Set Distance Measures (HNSDM) is introduced. By averaging the Penta-Partitioned Neutrosophic Distance Measures under particular conditional criteria, the suggested technique ranks the options. Additionally, we explore the fundamental characteristics of HNSDM and provide several illustrative theorems. The Heptapartitioned Neutrosophic Set Distance Measures are formulated based on the Hepta Neutrosophic Set. Lastly, a practical numerical example is provided to illustrate the efficacy of the suggested methodology. © 2025, University of New Mexico. All rights reserved.

关键词： Heptapartitioned Neutrosophic set Heptapartitioned Neutrosophic set and MADM strategy Heptapartitioned set Neutrosophic sine distance measure

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Mathematical modelling of the dynamics of typhoid fever and two modes of treatment in a Health District in Cameroon

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Mathematical Biosciences and Engineering 2025年第2期22卷 477-510页

作者： Tsafack, Thierry Jimy Kum, Cletus Kwa Tassé, Arsène Jaurès Ouemba Tsanou, Berge Department of Mathematics and Computer Science Faculty of Science University of Dschang P.O. Box 67 Dschang Cameroon Department of Mathematics Higher Teacher Training College - Bambili The University of Bamenda P.O. Box 39 Bambili Cameroon School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Department of Mathematics and Applied Mathematics University of Pretoria South Africa IRD Sorbonne University UMMISCO BondyF-93143 France

In this paper, we propose a novel mathematical model for indirectly transmitted typhoid fever disease that incorporates the use of modern and traditional medicines as modes of treatment. Theoretically, we provide two Lyapunov functions to prove the global asymptotic stability of the disease-free equilibrium (DFE) and the endemic equilibrium (EE) when the basic reproduction number (R0) is less than one and greater than one, respectively. The model is calibrated using the number of cumulative cases reported in the Penka-Michel health district in Cameroon. The parameter estimates thus obtained give a value of R0 = 1.2058 > 1,which indicates that the disease is endemic in the region. The forecast of the outbreak up to November 2026 suggests that the number of cases will be 21,270, which calls for urgent attention on this endemic disease. A sensitivity analysis with respect to the basic reproduction number is conducted, and the main parameters that impact the widespread of the disease are determined. The analysis highlights that the environmental transmission rate β and the decay rate µb of the bacteria in the environment are the most influential parameters for R0. This underscores the urgent need for potable water and adequate sanitation within this area to reduce the spread of the disease. Numerically, we illustrate the usefulness of recourse to any mode of treatment to lessen the number of infected cases and the necessity of switching from modern treatment to the traditional treatment, a useful adjuvant therapy. Conversely, we show that the relapse phenomenon increases the burden of the disease. Hence adopting a synergistic therapy approach will significantly mitigate typhoid disease cases and overcome the cycle of poverty within the afflicted communities. © 2025 the Author(s)

关键词： Medicinal chemistry

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Asymmetry and Condition Number of an Elliptic-Parabolic System for Biological Network Formation

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应用数学与计算数学学报 2025年第1期7卷 78-94页

作者： Clarissa Astuto Daniele Boffi Jan Haskovec Peter Markowich Giovanni Russo Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Department of Mathematics"F.Casorati" University of Pavia27100 PaviaItaly Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Department of Mathematics University of Vienna1090 ViennaAustria Department of Mathematics and Computer Science University of Catania95125 CataniaItaly

We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network *** numerical method is based on a nonlinear finite difference scheme on a uniform Cartesian grid in a two-dimensional(2D)*** focus is on the impact of different discretization methods and choices of regularization parameters on the symmetry of the numerical *** particular,we show that using the symmetric alternating direction implicit(ADI)method for time discretization helps preserve the symmetry of the solution,compared to the(non-symmetric)ADI ***,we study the effect of the regularization by the isotropic background perme-ability r＞0,showing that the increased condition number of the elliptic problem due to decreasing value of r leads to loss of *** show that in this case,neither the use of the symmetric ADI method preserves the symmetry of the ***,we perform the numerical error analysis of our method making use of the Wasserstein distance.

关键词： Bionetwork formation Cai-Hu model Leaf venation Asymmetry Conditioning number Finite-difference scheme Semi-implicit Symmetric alternating direction implicit(ADI) Wasserstein distance

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Throughput Prediction Using LS-SVM For 4g-LTE Network and Beyond

Throughput Prediction Using LS-SVM For 4g-LTE Network and Be...

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2024 International Conference on Telecommunications and Intelligent Systems, ICTIS 2024

作者： Hamdani, Mostefa Sahnoune, Ahmed Merzougui, Mokhtar Douara, Abdelmalek Khatemi, Fouad University El Wancharissi Laboratory of Electronics Computer Science and Applied Mathematics Faculty of Science and Technology Department of Mathematics and Computer Science Algeria University El Wancharissi Laboratory of Electronics Computer Science and Applied Mathematics Faculty of Science and Technology Department of Science and Technology Algeria

ISBN: (纸本)9798331527396

The integration of Artificial Intelligence(AI) with Long-Term Evolution (LTE) networks offers substantial potential for improving communication infrastructure. By harnessing AI algorithms, it is possible to dynamically optimize network parameters, proactively predict and mitigate equipment failures, and enhance Quality of Service (QoS) by prioritizing critical services through real-time analysis of key performance indicators. This study focuses on predicting network throughput using Least Square Support Vector Machine (LS-SVM). The predictive models developed can trigger adaptive network reconfigurations, ensuring that the network responds promptly to changing conditions. Simulation results reveal that the integration of LS-SVM significantly improves prediction accuracy, enabling more effective implementation of self-organizing network strategies in real-time. © 2024 IEEE.

关键词： Long Term Evolution (LTE)

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Faithful geometric measures for genuine tripartite entanglement

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Physical Review A 2024年第1期110卷 L010402-L010402页

作者： Xiaozhen Ge Lijun Liu Yong Wang Yu Xiang Guofeng Zhang Li Li Shuming Cheng Department of Control Science and Engineering Department of Applied Mathematics The Department of Mathematics and Computer Science State Key Laboratory for Mesoscopic Physics School of Physics Frontiers Science Center for Nano-optoelectronics and Collaborative Innovation Center of Quantum Matter Shanghai Institute of Intelligent Science and Technology Institute for Advanced Study

We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation Ei|jkα≤Ej|ikα+Ek|ijα holds for all subadditive bipartite entanglement measure E, all permutations under parties i,j,k, all α∈[0,1], and all pure tripartite states. Then, we rigorously prove that the nonobtuse triangle area, enclosed by side Eα with 0<α≤1/2, is a measure for genuine tripartite entanglement. Finally, it is significantly strengthened for qubits that given a set of subadditive and nonsubadditive measures, some state is always found to violate the triangle relation for any α>1, and the triangle area is not a measure for any α>1/2. Our results pave the way to study discrete and continuous multipartite entanglement within a unified framework.

关键词： Entanglement measures Quantum correlations in quantum information Quantum correlations, foundations & formalism Resource theories

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New logarithmic step size for stochastic gradient descent

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Frontiers of computer science 2025年第1期19卷 109-118页

作者： Mahsa Soheil SHAMAEE Sajad Fathi HAFSHEJANI Zeinab SAEIDIAN Department of Computer Science Faculty of Mathematical ScienceUniversity of KashanKashan 87317-53153Iran Department of Applied Mathematics Shiraz University of TechnologyShiraz 13876-71557Iran Department of Mathematical Sciences University of KashanKashan 87317-53153Iran

In this paper, we propose a novel warm restart technique using a new logarithmic step size for the stochastic gradient descent (SGD) approach. For smooth and non-convex functions, we establish an O(1/√T) convergence rate for the SGD. We conduct a comprehensive implementation to demonstrate the efficiency of the newly proposed step size on the FashionMinst, CIFAR10, and CIFAR100 datasets. Moreover, we compare our results with nine other existing approaches and demonstrate that the new logarithmic step size improves test accuracy by 0.9% for the CIFAR100 dataset when we utilize a convolutional neural network (CNN) model.

关键词： stochastic gradient descent logarithmic step size warm restart technique

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Detection of Mobile LoRa Jammers

Detection of Mobile LoRa Jammers

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2023 IEEE Virtual Conference on Communications, VCC 2023

作者： Bleszynski, Bartlomiej Jozef Orfanidis, Charalampos Fafoutis, Xenofon Department of Applied Mathematics and Computer Science Denmark

ISBN: (纸本)9798350318807

Low Power Wide Area Networks (LPWANs) plat-forms (LoRa, NB-IoT, Sigfox) came to add a missing piece to the Internet of Things (IoT) ecosystem, namely long range communication in low power. LPWAN platforms are characterized by low data rate and long transmission time. LoRa specifically, has a data rate from 27 to 0.3 kbps and the transmission time of a single packet might be more than 1.5 seconds for some cases. These characteristics render LPWANs vulnerable to jamming attacks as a malicious user can perform a jamming attack from long range and the long transmission time is allowing a large time window to perform the attack. Moreover, if the jamming node is mobile (i.e., attached on a vehicle or an Unmanned Aerial Vehicle (UAV)), the current countermeasures proposed by the literature will not be relevant anymore. In this paper we investigate if it is possible to detect a mobile LoRa jammer based on the impact of the Doppler effect and based on a combination of signal strength and the entropy of the transmitted data. The results, obtained by utilizing commercial hardware, reveal that we could detect a potential mobile jammer that follows a deceptive jamming strategy with random payload, but further investigation is required for more sophisticated jamming attacks. © 2023 IEEE.

关键词： Internet of things

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Continuous-Time Graph Representation with Sequential Survival Process 38

Continuous-Time Graph Representation with Sequential Surviva...

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38th AAAI Conference on Artificial Intelligence, AAAI 2024

作者： Çelikkanat, Abdulkadir Nakis, Nikolaos Mørup, Morten Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark

ISBN: (纸本)1577358872

Over the past two decades, there has been a tremendous increase in the growth of representation learning methods for graphs, with numerous applications across various fields, including bioinformatics, chemistry, and the social sciences. However, current dynamic network approaches focus on discrete-time networks or treat links in continuous-time networks as instantaneous events. Therefore, these approaches have limitations in capturing the persistence or absence of links that continuously emerge and disappear over time for particular durations. To address this, we propose a novel stochastic process relying on survival functions to model the durations of links and their absences over time. This forms a generic new likelihood specification explicitly accounting for intermittent edge-persistent networks, namely GRAS2P: Graph Representation with Sequential Survival Process. We apply the developed framework to a recent continuous time dynamic latent distance model characterizing network dynamics in terms of a sequence of piecewise linear movements of nodes in latent space. We quantitatively assess the developed framework in various downstream tasks, such as link prediction and network completion, demonstrating that the developed modeling framework accounting for link persistence and absence well tracks the intrinsic trajectories of nodes in a latent space and captures the underlying characteristics of evolving network structure. Copyright © 2024, Association for the Advancement of Artificial Intelligence (***). All rights reserved.

关键词： Random processes

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Decoder ensembling for learned latent geometries 1

Decoder ensembling for learned latent geometries

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1st Geometry-Grounded Representation Learning and Generative Modeling Workshop, GRaM 2024 at the 41st International Conference on Machine Learning, ICML 2024

作者： Syrota, Stas Moreno-Muñoz, Pablo Hauberg, Søren Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric, allowing for a standard differential geometric analysis of the latent space. Unfortunately, data manifolds are generally compact and easily disconnected or filled with holes, suggesting a topological mismatch to the Euclidean latent space. The most established solution to this mismatch is to let uncertainty be a proxy for topology, but in neural network models, this is often realized through crude heuristics that lack principle and generally do not scale to high-dimensional representations. We propose using ensembles of decoders to capture model uncertainty and show how to easily compute geodesics on the associated expected manifold. Empirically, we find this simple and reliable, thereby coming one step closer to easy-to-use latent geometries. Copyright 2024 by the author(s).

关键词： Topology

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