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arXiv 2025年

作者： Cai, HanQin Huang, Longxiu Department of Statistics and Data Science Department of Computer Science University of Central Florida Orlando32816 United States Department of Computational Mathematics Science and Engineering Department of Mathematics Michigan State University East Lansing48824 United States

Tensor dimensionality reduction is one of the fundamental tools for modern data science. To address the high computational overhead, fiber-wise sampled subtensors that preserve the original tensor rank are often used in designing efficient and scalable tensor dimensionality reduction. However, the theory of property inheritance for subtensors is still underdevelopment, that is, how the essential properties of the original tensor will be passed to its subtensors. This paper theoretically studies the property inheritance of the two key tensor properties, namely incoherence and condition number, under the tensor train setting. We also show how tensor train rank is preserved through fiber-wise sampling. The key parameters introduced in theorems are numerically evaluated under various settings. The results show that the properties of interest can be well preserved to the subtensors formed via fiber-wise sampling. Overall, this paper provides several handy analytic tools for developing efficient tensor analysis methods. Copyright © 2025, The Authors. All rights reserved.

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Robust Multilinear Principal Component Analysis

arXiv

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arXiv 2025年

作者： Hirari, Mehdi Centofanti, Fabio Hubert, Mia Van Aelst, Stefan Section of Statistics and Data Science Department of Mathematics KU Leuven Belgium Department of Industrial Engineering University of Naples Federico II Naples Italy

Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data. It performs dimension reduction similar to PCA for multivariate data. However, standard MPCA is sensitive to outliers. It is highly influenced by observations deviating from the bulk of the data, called casewise outliers, as well as by individual outlying cells in the tensors, so-called cellwise outliers. This latter type of outlier is highly likely to occur in tensor data, as tensors typically consist of many cells. This paper introduces a novel robust MPCA method that can handle both types of outliers simultaneously, and can cope with missing values as well. This method uses a single loss function to reduce the influence of both casewise and cellwise outliers. The solution that minimizes this loss function is computed using an iteratively reweighted least squares algorithm with a robust initialization. Graphical diagnostic tools are also proposed to identify the different types of outliers that have been found by the new robust MPCA method. The performance of the method and associated graphical displays is assessed through simulations and illustrated on two real datasets. Copyright © 2025, The Authors. All rights reserved.

关键词： Principal component analysis

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Contractive Difference-of-Convex Algorithms

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Journal of Optimization Theory and Applications 2025年第1期206卷 1-21页

作者： He, Songnian Dong, Qiao-Li Rassias, Michael Th. Tianjin Key Laboratory for Advanced Signal Processing and College of Science Civil Aviation University of China Tianjin300300 China Department of Mathematics and Engineering Sciences Hellenic Military Academy Vari Attikis16673 Greece Institute for Advanced Study Program in Interdisciplinary Studies 1 Einstein Dr Princeton08540 United States

The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be solved by iterative methods such as proximal gradient algorithm. However, these algorithms essentially belong to some iterative methods of fixed point problems of averaged mappings, and their convergence speed is generally slow. Furthermore, there is seldom research on the termination rule of these iterative algorithms solving the subproblem of DCA. To overcome these defects, we firstly show that the subproblem of the linearized proximal method (LPM) in each iteration is equal to the fixed point problem of a contraction. Secondly, by using Picard iteration to approximately solve the subproblem of LPM in each iteration, we propose a contractive difference-of-convex algorithm (cDCA) where an adaptive termination rule is presented. Both global subsequential convergence and global convergence of the whole sequence of cDCA are established. Finally, preliminary results from numerical experiments are promising. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Conjugate gradient method

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Lung Cancer Diagnosis Based on Object Detection Technology 14th

Lung Cancer Diagnosis Based on Object Detection Technology

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14th International Conference on Frontier Computing, FC 2024

作者： Xu, Jia-Lang Wang, Pei-Yun Huang, Tzu-Hsuan Hsu, Ying-Lin Huang, Kuo-Yang Chen, Mu-Yen Artificial Intelligence Development Center Changhua Christian Hospital Changhua Taiwan Doctoral Program in Data Science and Industrial Analytics National Chung Hsing University Taichung Taiwan Department of Applied Mathematics and Institute of Statistics National Chung Hsing University Taichung Taiwan Division of Chest Medicine Department of Internal Medicine Changhua Christian Hospital Changhua Taiwan Department of Engineering Science National Cheng Kung University Tainan Taiwan

ISBN: (纸本)9789819623945

With the rise of artificial intelligence, many people nowadays use artificial intelligence to help solve some problems in life, and the medical field is also with the rise of artificial intelligence, many people are slowly applying artificial intelligence to medical images to assist in decision-making, this study proposes a Yolov8 algorithm for object tracking of CT images of lung cancer, which can quickly tell the doctor where the cancer is and what the type of cancer is. The results of this study show that the Box_Loss, Cls_Loss, and Dfl_loss of the Yolov8 algorithm in detecting the location of lung cancer are 1.3689, 0.4552, and 1.5569 in the validation data, respectively, and thus this study suggests that this method can help physicians know the location of the tumor and what kind of tumor it belongs to. Therefore, this study suggests that this method can help physicians know the location of the tumor and the type of tumor. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Lung cancer

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Determinant Estimation under Memory Constraints and Neural Scaling Laws

arXiv

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arXiv 2025年

作者： Ameli, Siavash van der Heide, Chris Hodgkinson, Liam Roosta, Fred Mahoney, Michael W. ICSI Department of Statistics University of California Berkeley United States Dept. of Electrical and Electronic Engineering University of Melbourne Australia School of Mathematics and Statistics University of Melbourne Australia CIRES School of Mathematics and Physics University of Queensland Australia ICSI LBNL Department of Statistics University of California Berkeley United States

Calculating or accurately estimating log-determinants of large positive semi-definite matrices is of fundamental importance in many machine learning tasks. While its cubic computational complexity can already be prohibitive, in modern applications, even storing the matrices themselves can pose a memory bottleneck. To address this, we derive a novel hierarchical algorithm based on block-wise computation of the LDL decomposition for large-scale log-determinant calculation in memory-constrained settings. In extreme cases where matrices are highly ill-conditioned, accurately computing the full matrix itself may be infeasible. This is particularly relevant when considering kernel matrices at scale, including the empirical Neural Tangent Kernel (NTK) of neural networks trained on large datasets. Under the assumption of neural scaling laws in the test error, we show that the ratio of pseudo-determinants satisfies a power-law relationship, allowing us to derive corresponding scaling laws. This enables accurate estimation of NTK log-determinants from a tiny fraction of the full dataset;in our experiments, this results in a ∼100,000× speedup with improved accuracy over competing approximations. Using these techniques, we successfully estimate log-determinants for dense matrices of extreme sizes, which were previously deemed intractable and inaccessible due to their enormous scale and computational demands. Copyright © 2025, The Authors. All rights reserved.

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FEA of entropy generation due to free convection of hybrid-nanofluid in a partially heated tilted porous enclosure with wavy wall

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International Journal of Numerical Methods for Heat and Fluid Flow 2025年

作者： Barman, Prabir Kumar, B.V. Rathish Department of Mathematics and Statistics Indian Institute of Technology Kanpur Kanpur India Department of Engineering Sciences Atal Bihari Vajpayee Indian Institute of Information Technology and Management Gwalior India

Purpose: This study aims to analyze entropy generation in free convection within a partially heated wavy non-Darcy porous cavity, considering the presence of hybrid nanofluid and the impact of the cavity's inclination angle. Design/methodology/approach: The coupled nonlinear equations modeling of the convection process in a hybrid nanofluid saturated non-Darcy porous cavity are solved by the Galerkin finite element method. The cavity is at low ambient temperature along the wavy wall and exposed to a partial heat flux on the left wall, keeping the remaining walls thermally insulated. Findings: The results obtained for entropy generation are analyzed using a wide number of governing parameters. The results show that the Bejan number is increased due to the hybrid nanofluid and the non-Darcian inertial forces. Originality/value: The study of entropy generation is crucial for designing industrial equipment and other systems involving porous cavities. This research significantly contributes to the engineering design of heat transfer devices that use a wavy porous cavity, particularly under partial heating conditions. Unlike traditional approaches based on Darcy’s law, this investigation uses the Darcy–Forchheimer relations to provide a more accurate analysis. © 2025, Emerald Publishing Limited.

关键词： Natural convection

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Analytical dynamics to the interactions of a diffusive mussel–algae model

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Partial Differential Equations in Applied mathematics 2025年 14卷

作者： Jawaz, Muhammad Shahzad, Muhammad Ahmed, Nauman Baber, Muhammad Zafarullah Iqbal, Muhammad Akgül, Ali Department of Mathematics and Statistics The University of Lahore Lahore Pakistan Department of Electronics and Communication Engineering Saveetha School of Engineering SIMATS Chennai Tamilnadu India Siirt University Art and Science Faculty Department of Mathematics Siirt 56100 Turkey Department of Computer Engineering Biruni University 34010 Topkapı Istanbul Turkey Near East University Mathematics Research Center Department of Mathematics Near East Boulevard PC: 99138 Nicosia/Mersin 10 – Turkey Department of Mathematics and Statistics The University of Lahore Sargodha Campus Sargodha Pakistan

This paper examines the diffusive mussel–algae model and explores soliton solutions and wave structures using advanced analytical techniques, particularly the new auxiliary equation method. The proposed method reveals a variety of solution types, including hyperbolic, parabolic, and mixed forms. These closed-form results provide the nature of the current problem. These solutions are validated against known results and numerical simulations. Additionally, we describe two-dimensional and three-dimensional graphical representations of the solutions, illustrating their spatial and temporal dynamics. This study enhances the theoretical understanding of mussel algae interactions and offers practical insights for eco-logical management, showcasing the contributions of the approach to resolving complex ecological dynamics © 2025 The Authors

关键词： Algebraic Dynamics Phenomena Physical System Transformations Velocity Wave structures

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Modelling and control of a multi-product pipeline transportation process

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International Journal of Information Technology (Singapore) 2025年 1-11页

作者： Jiménez-Cabas, Javier Piñeres-Espitia, Gabriel Rodelo-Serrano, Esteban Pamucar, Dragan Ramirez-Leon, Hermes Butt, Shariq Aziz Naz, Sumera Simic, Vladimir Computer Science and Electronic Department Universidad de La Costa Barranquilla Colombia Departamento de Ingeniería Mecánica Universidad Simón Bolívar Barranquilla Venezuela Department of Operations Research and Statistics Faculty of Organizational Sciences University of Belgrade Belgrade Serbia Department of Industrial Engineering & Management Yuan Ze University Taoyuan Taiwan Department of Mechanics and Mathematics Western Caspian University Baku Azerbaijan Faculty of Transport and Traffic Engineering University of Belgrade Vojvode Stepe 305 Belgrade 11010 Serbia Department of Computer Science and Engineering College of Informatics Korea University Seoul 02841 South Korea School of Systems and Technology Department of Computer Science University of Management and Technology Lahore Pakistan Department of Mathematics Division of Science and Technology University of Education Lahore Pakistan

One of the most critical processes in the petroleum industry is transporting crude oil and its derivatives. Usually, it is done, due to easiness and economic aspects, through pipelines;several products, such as gasoline, kerosene, naphtha, and liquefied petroleum gas, among others, are moved in batch processes to both distribution and storage centers or transport ships. Since these transport systems transport different products, many works have focused on developing optimization strategies for scheduling these pipelines. That is, strategies that seek to optimize the use of the pipeline by establishing at what time points certain products must be transported. These strategies would be located at the planning level in the automation pyramid. In this work, on the other hand, different control strategies are proposed for a pipeline, but at the operation level. These strategies would be located at the control level, below the planning strategies in the automation pyramid. A pipeline of three pipe sections is modeled to develop the proposed control strategies, and the mathematical model is validated with actual data. The results show that, first, the proposed model approximates the actual behavior of the pipeline quite well and, second, that the combination of PID and feedforward control is an excellent alternative to implement control strategies for the operation of liquid transportation systems through pipelines. © Bharati Vidyapeeth's Institute of Computer Applications and Management 2025.

关键词： control strategies liquid transportation modeling of system

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Gasoline and Crude Oil Price Prediction using Multi-headed Variational Neighbour Search-tuned Recurrent Neural Networks

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Computational Economics 2025年 1-36页

作者： Kljajic, Maja Mizdrakovic, Vule Jovanovic, Luka Bacanin, Nebojsa Simic, Vladimir Pamucar, Dragan Zivkovic, Miodrag Business Economics Singidunum University Danijelova 32 Belgrade 11000 Serbia Department of Mathematics Saveetha School of Engineering SIMATS Thandalam Tamilnadu Chennai 602105 India Informatics and Computing Singidunum University Danijelova 32 Belgrade 11000 Serbia Sinergija University Raje Banjičića Bijeljina 76300 Bosnia and Herzegovina University of Belgrade Faculty of Transport and Traffic Engineering Vojvode Stepe 305 Belgrade 11010 Serbia Yuan Ze University College of Engineering Department of Industrial Engineering and Management Taoyuan City 320315 Taiwan Department of Computer Science and Engineering College of Informatics Korea University Seoul 02841 South Korea Department of Operations Research and Statistics Faculty of Organizational Sciences University of Belgrade Belgrade Serbia Department of Mechanics and Mathematics Western Caspian University Baku Azerbaijan İstinye University Faculty of Engineering and Natural Sciences Industrial Engineering Department İstanbul Turkey

The rapidly growing worldwide demand for energy and finite reservoirs of fossil fuels have intensified interest in energy projection research. Artificial intelligence, particularly in time series forecasting, holds significant promise for enhancing predictions of both cost and demand, offering numerous prospective applications over various domains. Numerous variables, ranging from socio-economic conditions to distribution, supply, and international policies, exert influence on global price fluctuations. Thus, crafting precise forecasts necessitates consideration of these multifaceted factors. Through an examination of existing literature, a discernible gap emerges in the quest for advancement in this domain. Consequently, this study proposes to delve into the perspective of employing multi-headed long short-term memory (LSTM) models for gasoline and crude oil price prediction, an area largely untouched by multi-headed approaches. Moreover, recognizing the computational demands of such models, this research emphasizes the development of lightweight methodologies, characterized by a modest neuron within each layer and trained over a limited epoch count. Given the pivotal role of hyper-parameter selection in algorithm performance, an adapted version of the variable neighbour search algorithm is introduced to aid in tuning the model’s architecture and training parameters. A comprehensive side-by-side comparison is undertaken utilizing gasoline and oil data sourced from diverse public repositories, employing a variety of contemporary optimizers. The resultant outcomes are subjected to strict statistical scrutiny to ascertain the robustness and significance of the findings. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Crude oil prices Gasoline prices Modified VNS Multi-headed long short-term memory models Time series prediction

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Fuzzy multi-objective optimization model to design a sustainable closed-loop manufacturing system

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PeerJ Computer Science 2025年 11卷 e2591-e2591页

作者： Kousar, Sajida Alvi, Asma Kausar, Nasreen Garg, Harish Kadry, Seifedine Kim, Jungeun Department of Mathematics and Statistics International Islamic University Islamabad Pakistan Department of Mathematics Faculty of Arts and Sciences Yildiz Technical University Istanbul Turkey Punjab Patiala India Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon MEU Research Unit Middle East University Amman Jordan Department of Computer Engineering Inha University Incheon Korea Republic of

Republicans and Democrats practically everywhere have been demonstrating concerns about environmental conservation to achieve sustainable development goals (SDGs) since the turn of the century. To promote fuel (energy) savings and a reduction in the amount of carbon dioxide CO2 emissions in several enterprises, actions have been taken based on the concepts described. This study proposes an environmentally friendly manufacturing system designed to minimize environmental impacts. Specifically, it aims to develop a sustainable manufacturing process that accounts for energy consumption and CO2 emissions from direct and indirect energy sources. A multi-objective mathematical model has been formulated, incorporating financial and environmental constraints, to minimize overall costs, energy consumption, and CO2 emissions within the manufacturing framework. The input model parameters for real-world situations are generally unpredictable, so a fuzzy multi-objective model will be developed as a way to handle it. The validity of the proposed ecological industrial design will be tested using a scenario-based approach. Results demonstrate the high reliability, applicability, and effectiveness of the proposed network when analyzed using the developed techniques. Copyright 2025 Kousar et al. Distributed under Creative Commons CC-BY 4.0

关键词： Smart manufacturing

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