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arXiv 2025年

作者： Asgari, Kiana Montanari, Andrea Saeed, Basil Department of Management Science and Engineering Stanford University United States Department of Statistics Department of Mathematics Stanford University United States Department of Electrical Engineering Stanford University United States

We consider a general model for high-dimensional empirical risk minimization whereby the data xi are d-dimensional isotropic Gaussian vectors, the model is parametrized by Θ ∈ Rd×k, and the loss depends on the data via the projection ΘTxi. This setting covers as special cases classical statistics methods (e.g. multinomial regression and other generalized linear models), but also two-layer fully connected neural networks with k hidden neurons. We use the Kac-Rice formula from Gaussian process theory to derive a bound on the expected number of local minima of this empirical risk, under the proportional asymptotics in which n, d → ∞, with n d. Via Markov’s inequality, this bound allows to determine the positions of these minimizers (with exponential deviation bounds) and hence derive sharp asymptotics on the estimation and prediction error. In this paper, we apply our characterization to convex losses, where high-dimensional asymptotics were not (in general) rigorously established for k ≥ 2. We show that our approach is tight and allows to prove previously conjectured results. In addition, we characterize the spectrum of the Hessian at the minimizer. A companion paper applies our general result to non-convex examples. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

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Rician Channel Modelling for Super Wideband MIMO Communications

Rician Channel Modelling for Super Wideband MIMO Communicati...

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IEEE Conference on Wireless Communications and Networking

作者： Peter J. Smith Sachitha C. Bandara Erfan Khordad Robin Evans Rajitha Senanayake Department of Electrical and Electronic Engineering University of Melbourne Melbourne Australia School of Mathematics and Statistics Victoria University of Wellington Wellington New Zealand

ISBN: (数字)9798350368369

ISBN: (纸本)9798350368376

Recent developments in Multiple-Input-Multiple-Output (MIMO) technology include packing a large number of antenna elements in a compact array to access the bandwidth benefits provided by higher mutual coupling (MC). The resulting super-wideband (SW) systems require a circuit-theoretic framework to handle the MC and channel models which span extremely large bands. Hence, in this paper, we make two key contributions. First, we develop a physically-consistent Rician channel model for use with SW systems. Secondly, we express the circuit-theoretic models in terms of a standard MIMO model, so that insights into the effects of antenna layouts, MC, and bandwidth can be made using standard communication theory. For example, we show the bandwidth widening resulting from the new channel model. In addition, we show that MC distorts line-of-sight paths which has beamforming implications. We also highlight the interaction between spatial correlation and MC and show that tight coupling reduces spatial correlations at low frequencies.

关键词： Mutual coupling Correlation Computational modeling Frequency-domain analysis Rician channels Channel models Integrated circuit modeling Wideband Standards Antenna arrays

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Artificial intelligent approach for flow stability in Eyring Powell hybrid nanofluids via porous shrinking sheets

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Journal of Molecular Liquids 2025年 422卷

作者： Fatima, Nahid Kouki, Marouan Khan, Muhammad Imran Amjad, Arslan Bin Asghar, Zaheer Zeeshan, Ahmad Ijaz, Nouman Department of Mathematics and Sciences Prince Sultan University Riyadh11586 Saudi Arabia Department of Information System Faculty of Computing and Information Technology Northern Border University Rafha Saudi Arabia Department of Mathematics and Statistics International Islamic University Islamabad 44000 Pakistan Centre for Mathematical Sciences Pakistan Institute of Engineering and Applied Sciences Nilore Islamabad45650 Pakistan Department of Physics and Applied Mathematics Pakistan Institute of Engineering and Applied Sciences Nilore Islamabad45650 Pakistan Department of Mathematics College of Science Korea University 145 Anam-ro Seongbuk-gu Seoul02841 Korea Republic of Department of Mathematics and Statistics Punjab Group of Colleges G.T. Road Jada Jhelum49600 Pakistan

This study aims to analyze flow stability using a computational intelligence technique that integrates a Levenberg-Marquardt approach utilizing artificial intelligence implemented through a backpropagation neural network. AI-based LMS-BPNN approach is utilized to examine the flow behavior of Eyring Powell hybrid nanofluid over a porous shrinking sheet. By applying skillful transformations, a set of ordinary differential equations is obtained from the partial differential equations that describe the hybrid nanofluid. Scenarios 1–5 illustrate how the built-in MATLAB function, bvp4c, solves ordinary differential equations systems by carefully modifying input parameters to get the initial or reference solution. The numerical data was split into three groups: 10 % for testing, 10 % for validation, and 80 % for training. The LMS-BPNN was used to find approximate solutions for these scenarios. To verify the effectiveness and reliability of LMS-BPNN, we employed regression analysis, error metrics, and correlation index (R)-based fitness curves. In each scenario, the temperature and velocity profiles gradually approached the boundary conditions as expected. The flow performance outcomes for the dual solution (Cfx and Nux) are also analyzed using the LMS-BPNN method. The perturbation scheme is applied to the boundary layer problem to obtain the eigenvalues problem. The unsteady solution f(η,τ) converges to steady solution fo(η) for τ→∞ when γ≥0. However, an unsteady solution f(η,τ) diverges to a steady solution fo(η) for τ→∞ when γ © 2025 Elsevier B.V.

关键词： Eigenvalues and eigenfunctions

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RETRACTED ARTICLE: Nature analysis of Cross fluid flow with inclined magnetic dipole (Microsystem Technologies, (2023), 29, 5, (697-714), 10.1007/s00542-023-05438-5)

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Microsystem Technologies 2025年

作者： Ayub, Assad Sabir, Zulqurnain Said, Salem Ben Baskonus, Haci Mehmet Sadat, R. Ali, Mohamed R. Department of Mathematics and Statistics Hazara University Manshera21300 Pakistan Department of Mathematical Science College of Science United Arab Emirates University Abu Dhabi Al Ain United Arab Emirates Department of Mathematics and Science Education Harran University Sanliurfa Turkey Department of Mathematics Faculty of Engineering Zagazig University Zagazig Egypt Faculty of Engineering and Technology Future University in Egypt New Cairo11835 Egypt Basic Engineering Mathematics Department Benha Faculty of Engineering Benha University Benha Egypt Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon

The Editors in Chief have retracted this article after serious concerns have been raised regarding the correctness and consistency of the mathematical formulation. Specifically, it appears that multiple equations include undefined parameters and other terms with wrong units/dimensions. In the nomenclature a few parameters indicated by the same symbol are attributed different definitions and meanings. Again, in the nomenclature, other parameters are defined, despite they are never used in the equations describing the physical problem. Given the extent of the inaccuracies, the Editors have lost confidence in the contents of this article. Authors Assad Ayub and Haci Mehmet Baskonus disagree with this retraction. The other authors have not responded to correspondence regarding this retraction. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

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Clustering-based Low Rank Approximation Method

arXiv

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arXiv 2025年

作者： Zhu, Yujun Zhu, Jie Arshad, Hizba Wang, Zhongming Ming, Ju School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan China Department of Mathematics and Statistics Florida International University MiamiFL United States

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form of clustering generators and similarity metrics so that it is more suitable for matrix-structured data relative to conventional partitioning methods. In our approach, we first pre-classify the initial matrix collection into several small subset clusters and then sequentially compress the matrices within the clusters. This strategy enhances the numerical precision of the low-rank approximation. In essence, we combine the ideas of GLRAM and clustering into a hybrid algorithm for dimensionality reduction. The proposed algorithm can be viewed as the generalization of both techniques. Theoretical analysis and numerical experiments are established to validate the feasibility and effectiveness of the proposed algorithm. © 2025, CC BY-NC-ND.

关键词： Matrix algebra

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Review of UAVs for efficient agrochemical spray application

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International Journal of Agricultural and Biological engineering 2025年第1期18卷 1-9页

作者： Narayan Raosaheb Gatkal Sachin Madhukar Nalawade Girishkumar Balasaheb Bhanage Ramesh Kumar Sahni Avdhoot Ashok Walunj Pravin Bhaskar Kadam Musrrat Ali Department of Farm Machinery and Power Engineering Dr.Annasaheb Shinde College of Agricultural Engineering and TechnologyMahatma Phule Krishi VidyapeethRahuri 413722MaharashtraIndia Centre for Advanced Agricultural Science and Technology for Climate Smart Agriculture and Water Management(CAAST-CSAWM) Dr.Annasaheb Shinde College of Agricultural Engineering and TechnologyMahatma Phule Krishi VidyapeethRahuri 413722AhmednagarMaharashtraIndia Central Institute of Agricultural Engineering Bhopal 462038Madya PradeshIndia Department of Mathematics and Statistics College of ScienceKing Faisal UniversityAl-Ahsa 31982Saudi Arabia

Insect infestation attacks in agricultural ecosystems are becoming more common because of global warming as well as farmland environmental circumstances,necessitating the development of new crop production *** application is one of the most common strategies for protecting the entire growing period of plants or shrubs against pests and pathogens in *** rapid,effective,and profitable application of plant control substances via unmanned aerial vehicle(UAV)crop spraying is anticipated to be a key new *** compared to ground spraying,UAV spraying saves chemicals,water,time,does not damage crop plants or balls of crop,and does not create soil *** using UAV,pesticide drift and deposition must be managed in order to use pesticides safely,effectively,and *** paper focuses on agrochemical spraying by unmanned aerial vehicles and the key parameters that influence spray effectiveness,such as the operating parameters of nozzle type,flying speed,flight height,type of nozzle,and type of UAV model,for reducing drift and increasing application *** multirotor UAV is most suitable for spraying due to its fast operation,safety,not requiring a runway for takeoff and landing,and lower cost as compared to fixed-wing and *** can also be used for crop disease identification,soil health monitoring,livestock monitoring,field mapping,*** paper aims to review the development of various UAV models,optimization of operating parameters,effect of nozzle on UAV spraying,characterization of droplet deposition,drift reduction technology,UAV-based remote sensing for plant protection,and cost comparison of UAV to conventional ground sprayer.

关键词： deposition drift flight height flying speed nozzle unmanned aerial vehicle(UAV)

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An Additive Shared Frailty Model for Recurrent Gap Time Data in the Presence of Zero-Recurrence Subjects 26th

An Additive Shared Frailty Model for Recurrent Gap Time Data...

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26th Congress of the Portuguese Statistical Society, SPE 2023

作者： Sousa-Ferreira, Ivo Abreu, Ana Maria Rocha, Cristina Department of Mathematics Faculty of Exact Sciences and Engineering University of Madeira Funchal Portugal CEAUL – Faculty of Sciences University of Lisbon Lisbon Portugal CIMA University of Madeira Funchal Portugal Department of Statistics and Operational Research Faculty of Sciences University of Lisbon Lisbon Portugal CEAUL – Faculty of Sciences University of Lisbon Lisbon Portugal

ISBN: (纸本)9783031689482

A new shared frailty model for recurrent gap time data is introduced, assuming that frailty acts additively on a Weibull rate function derived from a non-homogeneous Poisson process. The frailty is included with two purposes: to handle within-subject correlation and to accommodate zero-recurrence subjects. With this intention, we assume that the frailty has a non-central chi-squared distribution with zero degrees of freedom. The proposed model has two special cases without frailty, namely the Weibull rate model and the classical homogeneous Poisson process. Furthermore, since the model is fully specified, the maximum likelihood method is applied for parameters estimation based on a marginal likelihood function. Particular attention is devoted to the likelihood construction for bivariate recurrent event data. An application to a well-known data set is provided to elucidate the practical contribution of the new survival model. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Degrees of freedom (mechanics)

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Enhancing Utility in Differential Privacy Models Through Feature Extraction and Knowledge Distillation 2nd

Enhancing Utility in Differential Privacy Models Through Fe...

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2nd International Conference on Data Security and Privacy Protection, DSPP 2024

作者： He, Shuyao Xu, Ting Shen, Fangzhou He, Weijie Yang, Haowei College of Engineering Northeastern University Boston United States Department of Computer Science University of Massachusetts Boston Boston United States Department of Mathematics and Statistics San Jose State University San Jose United States Fielding School of Public Health UCLA Los Angeles United States Cullen College of Engineering University of Houston Houston United States

ISBN: (纸本)9789819785452

In recent years, the privacy security of deep learning models has received widespread attention, and many articles have pointed out that deep learning models are vulnerable to various privacy attacks. As a typical application of data privacy protection technology differential privacy in deep learning models, the Differentially Private Stochastic Gradient Descent (DPSGD) algorithm has gradually become one of the main technologies for privacy security protection of deep learning models and has been widely used in academic and industrial research. However, DPSGD also has some unavoidable shortcomings, that is, when DPSGD provides privacy protection for deep learning models, it will damage the classification accuracy of the model. In this paper, we are inspired by model compression technology and propose a method of using pre-trained models as feature extractor, combined with knowledge distillation technology. Our method can reduce the input dimension of the model, achieve the effect of reducing the model gradient norm. In this way, we can achieve a significant improvement in model classification accuracy under the same privacy budget, especially in complex data sets (such as the ImageNet data set). Extensive experiments demonstrate that our method achieves State-of-the-Art on multiple datasets. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Differential privacy

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Qualitative Analysis for Hartree-Fock System with Hardy-Littlewood-Sobolev Critical Exponent

SSRN

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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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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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