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SSRN 2025年

作者： Li, Meng Xu, Haoyuan Yang, Meihua Zhen, Maoding Basic Department Information Engineering University Zhengzhou450001 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China School of Mathematics Hefei University of Technology Hefei230009 China

In this paper, we develop an exhaustive analysis on standing waves with prescribed mass for the coupled Hartree-Fock system, which is introduced by Hartree in the 1920's and developed by Fock for describing large systems of identical fermions. This seems to be the first contribution regarding the multiplicity as well as the synchronized mass collapse behaviors of the normalized solutions to Hartree-Fock systemwith Hardy-Littlewood-Sobolev critical exponent. These results are a continuation of the works \cite{CJL21} and \cite{JL23} concerning normalized solutions for Hartree equations to Hartree-Fock system with Hardy-Littlewood-Sobolev critical exponent. © 2025, The Authors. All rights reserved.

关键词： Sensitivity analysis

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A mathematical study of a tuberculosis model with fractional derivatives

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第4期12卷 215-240页

作者： Hamadjam Abboubakar Pushpendra Kumar Vedat Suat Erturk Anoop Kumar Department of Computer Engineering University Institute of Technology University of Ngaoundere P.O.Box 455NgaoundereCameroon Department of Mathematics and Statistics School of Basic and Applied Sciences Central University of Punjab Bathinda Punjab-151001India Department of Mathematics Ondokuz Mayis University Atakum-55200SamsunTurkey Department of Mathematics and Statistics School of Basic and Applied Sciences Central University of Punjab Bathinda Punjab-151001India 2

In this work,we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis(TB)model with two fractional derivatives,namely,Caputo–Fabrizio fractional derivative and the new generalized Caputo fractional deriva*** begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the ***,we study the global asymptotic stability of disease-free equilibrium of the fractional *** also prove,for each fractional model,the existence and uniqueness of *** iterative solution of the two models is computed using the Predictor–Corrector *** realistic parameter values,we perform numerical simulations for different values of the fractional *** results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo–Fabrizio fractional derivative and the classical integer-order TB model.

关键词： TB model Caputo–Fabrizio(CF)fractional derivative asymptotic stability Predictor–Corrector Method(PCM) generalized Caputo derivative

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Multi-Track Music Generation Network Based on a Hybrid Learning Module

Multi-Track Music Generation Network Based on a Hybrid Learn...

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2023 IEEE International Conference on Multimedia and Expo Workshops, ICMEW 2023

作者： Zhang, Donghui Hu, Ziqing Li, Xiaobing Tie, Yun Qi, Lin School of Electrical and Information Engineering Zhengzhou University Zhengzhou China University of Notre Dame Department of Applied and Computational Mathematics and Statistics South Bend on Lake MI United States Central Conservatory of Music Department of Music Artificial Intelligence Beijing China

ISBN: (纸本)9798350313154

Generative models has been widely used for symbolic music generation. However, the quality of the music produced is hindered by the inadequate modeling of the harmonic and rhythmic relationships among various instruments, as well as the neglect of musical principles. To address the aforementioned challenges, we propose an attention-based hybrid learning multitrack music generation(HL-MTMG) model that incorporates regularization of musical rules and simultaneous exploitation between intra-track and inter-track information, resulting in the generation of high-quality symbolic music that conforms to established musical principles. Through extensive examinations of musical structures, specifically rhythm, and assessments by domain experts, our study demonstrates that HL-MTMG exhibits significant improvements in musical integrity and fluency in comparison to symbolic music generation models, such as, MuseGAN and HRNN. © 2023 IEEE.

关键词： Music

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Decision Predicate Graphs: Enhancing Interpretability in Tree Ensembles

arXiv

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arXiv 2024年

作者： Arrighi, Leonardo Pennella, Luca Tavares, Gabriel Marques Junior, Sylvio Barbon Department of Mathematics and Geosciences University of Trieste Trieste Italy Department of Economics Business Mathematics and Statistics University of Trieste Italy LMU Munich Munich Germany Munich Germany Department of Engineering and Architecture University of Trieste Trieste Italy

Understanding the decisions of tree-based ensembles and their relationships is pivotal for machine learning model interpretation. Recent attempts to mitigate the human-in-the-loop interpretation challenge have explored the extraction of the decision structure underlying the model taking advantage of graph simplification and path emphasis. However, while these efforts enhance the visualisation experience, they may either result in a visually complex representation or compromise the interpretability of the original ensemble model. In addressing this challenge, especially in complex scenarios, we introduce the Decision Predicate Graph (DPG) as a model-agnostic tool to provide a global interpretation of the model. DPG is a graph structure that captures the tree-based ensemble model and learned dataset details, preserving the relations among features, logical decisions, and predictions towards emphasising insightful points. Leveraging well-known graph theory concepts, such as the notions of centrality and community, DPG offers additional quantitative insights into the model, complementing visualisation techniques, expanding the problem space descriptions, and offering diverse possibilities for extensions. Empirical experiments demonstrate the potential of DPG in addressing traditional benchmarks and complex classification scenarios. © 2024, CC BY-SA.

关键词： Decision trees

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Estimation of Life Table Values Using Mortality Models: A Case Study of the Indian Population 4

Estimation of Life Table Values Using Mortality Models: A Ca...

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4th International Conference on Technological Advancements in Computational Sciences, ICTACS 2024

作者： Rakhra, Manik Kumar, Rakesh Suri, Sonia Chahal, Avneet Kaur Cheema, Gagandeep Singh School of Computer Science and Engineering Lovely Professional University Punjab Phagwara India Lovely Professional University Department of Mathematics and Statistics Phagwara India Lovely Professional University Department of Interior and Furniture Design Punjab Phagwara India Mittal School of Business Lovely Professional University Punjab Phagwara India

ISBN: (纸本)9798350387490

The purpose of our research is to determine the mortality rates of the Indian population by employing a number of different mortality models. statistics on mortality were gathered from the life tables for India that were published by the World Health Organization (WHO), and these statistics were used in this research. The statistics on mortality were meticulously reviewed to determine whether or not they conformed to the Pareto distribution, Markham's rule, and Gompertz law. The relevant parameters that are essential for computing the l(x) values were able to be determined as a result of this. Within the scope of this study, a comprehensive analysis is carried out with the purpose of shedding light on the efficiency and practicability of a number of mortality models in accurately determining life table values for India. © 2024 IEEE.

关键词： Comprehensive Analysis Efficiency Gompertz Law Indian Population l(x) Values Life Tables Makeham's Rule Mortality Models Mortality Rates Pareto Distribution Practicability World Health Organization (WHO)

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Optical soliton propagation in the Benjamin–Bona–Mahoney–Peregrine equation using two analytical schemes

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Optik 2023年第1期287卷

作者： Mahmood, Irfan Hussain, Ejaz Mahmood, Asif Anjum, Arfan Shah, Syed Asif Ali College of Science Department of Mathematics Shanghai University China Department of Mathematics University of the Punjab Quaid-e-Azam Campus Lahore54590 Pakistan College of Engineering Chemical Engineering Department King Saud University Riyadh Saudi Arabia Department of Mathematics and Statistics The University of Lahore 1-km Defence Road Lahore54000 Pakistan

The purpose of this research is to investigate the nonlinear partial differential equation known as Benjamin–Bona–Mahoney–Peregrine equation. Two versatile techniques, namely the extended [Formula presented]-expansion method and modified auxiliary equation method is used to extract the exact solutions of the nonlinear Benjamin–Bona–Mahoney–Peregrine equation. Consequently, a diverse range of novel collections of exact traveling wave solutions are identified such as kink, bright, singular kink and periodic soliton solution. To provide a physical understanding, several of the discovered solutions are shown in figures. The resulting solutions are of the trigonometric, hyperbolic, and rational varieties and the stability analysis are also discussed. In addition to this, the graphical aspects of the produced solutions are investigated. Due to the vital necessity of this aspect, we make use of the suitable parameter values to place a priority on the physical aspects of the provided findings by utilizing 3D and contour charts. The suggested procedures are of great use and can be extended to additional nonlinear evolutionary equations that reflect nonlinear physical frameworks in the nonlinear sciences. © 2023 Elsevier GmbH

关键词： Solitons

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On weight and variance uncertainty in neural networks for regression tasks

arXiv

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arXiv 2025年

作者： Monemi, Moein Amini, Morteza Taheri, S. Mahmoud Arashi, Mohammad School of Engineering Science College of Engineering University of Tehran Tehran Iran Department of Statistics School of Mathematics Statistics and Computer Science College of Science University of Tehran Tehran Iran Department of Statistics Faculty of Mathematical Sciences Ferdowsi University of Mashhad Mashhad*** Iran

We consider the problem of weight uncertainty proposed by [Blundell et al. (2015). Weight uncertainty in neural network. In International conference on machine learning, 1613-1622, PMLR.] in neural networks (NNs) specialized for regression tasks. We further investigate the effect of variance uncertainty in their model. We show that including the variance uncertainty can improve the prediction performance of the Bayesian NN. Variance uncertainty enhances the generalization of the model by considering the posterior distribution over the variance parameter. We examine the generalization ability of the proposed model using a function approximation example and further illustrate it with the riboflavin genetic data set. We explore fully connected dense networks and dropout NNs with Gaussian and spike-and-slab priors, respectively, for the network weights. © 2025, CC BY.

关键词： Neural network models

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NEW C0 INTERIOR PENALTY METHOD FOR MONGE-AMPÈRE EQUATIONS

arXiv

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arXiv 2024年

作者： Chu, Tianyang Guo, Hailong Zhang, Zhimin LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematics and Statistics The University of Melbourne ParkvilleVIC3010 Australia Department of Mathematics Wayne State University DetroitMI48202 United States

Monge-Ampère equation is a prototype second-order fully nonlinear partial differential equation. In this paper, we propose a new idea to design and analyze the C0 interior penalty method to approximation the viscosity solution of the Monge-Ampère equation. The new methods is inspired from the discrete Miranda-Talenti estimate. Based on the vanishing moment representation, we approximate the Monge-Ampère equation by the fourth order semi-linear equation with some additional boundary conditions. We will use the discrete Miranda-Talenti estimates to ensure the well-posedness of the numerical scheme and derive the error estimates. © 2024, CC BY.

关键词： Partial differential equations

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Joint IoT Device Selection and Health-Aware Beamforming Design for MIMO-WPT

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IEEE Transactions on Mobile Computing 2024年第9期23卷 8822-8838页

作者： Wang, Chih-Hang Shi, Yishuo Yang, De-Nian Chen, Wei-Yu Chen, Wen-Tsuen Academia Sinica Institute of Information Science Taipei115201 Taiwan Wenzhou University Department of Statistics and Information Science College of Mathematics and Physics Wenzhou325035 China Academia Sinica Institute of Information Science The Research Center for Information Technology Innovation Taipei115201 Taiwan University of Southern California Department of Electrical and Computer Engineering Los AngelesCA90007 United States National Tsing Hua University Department of Computer Science Hsinchu300044 Taiwan

Wireless power transfer (WPT) has emerged to enhance the robustness of the energy harvesting Internet of Things (EH-IoT), whereas beamforming has been leveraged to significantly boost the efficiency of far-field WPT. Nevertheless, potential negative impacts due to high electromagnetic fields (EMF) exposure for radiation-susceptible users have not been thoroughly considered in the design of WPT for EH-IoT with IoT application-level requirements (e.g., coverage). In this article, we explore the health-aware beamforming and IoT selection problem under the EH and human safety constraints. First, we formulate a new optimization problem Health-Aware Beamforming and IoT Selection (HABIS) and prove the NP-hardness. Second, we design an approximation algorithm, named Minimum Radiation Exposure and Maximum IoT Coverage (MREMIC), to exploit the EH-health dependency (EHHD) graph for properly addressing the trade-off between EH efficiency and potential EMF radiation exposure to human bodies. We also discover the optimal health-aware beamforming to minimize the total radiation energy absorption of humans. Simulation results show that MREMIC can effectively charge IoT devices and significantly outperforms existing EH approaches by more than 200% regarding human safety. © 2002-2012 IEEE.

关键词： Energy harvesting

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Design and fabrication of photovoltaics based on MFS (Ag/BaTiO3/silicon p-type) structure

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Materials Science for Energy Technologies 2024年第1期7卷 29-34页

作者： Irzaman Dahrul, M. Rahmani, M. Rukyati, A.M. Samsidar Nurhidayah Deswardani, F. Peslinof, M. Jenie, R.P. Iskandar, J. Wahyuni, Y. Priandana, K. Siskandar, R. Department of Physics Faculty of Mathematics and Natural Sciences IPB University Bogor16680 Indonesia Department of Physics Faculty of Sciences and Technology Jambi University Jambi36361 Indonesia Department of Nutrition Faculty of Health Science and Technology Binawan University East Jakarta13630 Indonesia Department of Computer Engineering Pakuan University Bogor16142 Indonesia Department of Computer Science IPB University Bogor16680 Indonesia Computer Engineering Technology Study Program College of Vocational Studies IPB University West Java Bogor16151 Indonesia

The experiment was carried out by growing BaTiO3 (Undoped or Li-doped) on p-type Si(1 0 0) substrates using the Chemical Solution Deposition (CSD) method and spin coating at a rotational speed of 3000 rpm for 60 s, followed by heating at 850 °C. The characterization results show that the bandgap energy value of the thin film due to lithium doping reduces the bandgap energy value. This is presumably because the donor atom added to a semiconductor causes the allowable energy level to be slightly below the conduction band. The presence of this new band causes the thin film bandgap energy to decrease with a five-valent tantalum dip. The morphological properties showed that the BaTiO3/Si(1 0 0) thin film particles in the deposited lithium had a fairly homogeneous grain. With the addition of lithium acetate as a binder into barium titanate, the grain size is getting smaller because it is suspected that the lithium-ion radius is smaller than the barium-ion radius. Measurement of I-V on the thin film shows that the output voltage value increases with more light intensity hitting the surface of the thin film. The greater the light intensity, the greater the energy of the photons, so the electrons are easier to jump. The three things above (both electrical and morphological properties) conclude that the thin films grown have the potential for photovoltaics. © 2023

关键词： Thin films

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