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The inverse nullity pair problem and the strong nullity interlacing property

Linear Algebra and Its Applications 2024年 699卷 539-568页

作者： Abiad, Aida Curtis, Bryan A. Flagg, Mary Hall, H. Tracy Lin, Jephian C.-H. Shader, Bryan Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands Department of Mathematics: Analysis Logic and Discrete Mathematics Ghent University Ghent Belgium Department of Mathematics Iowa State University AmesIA50011 United States Department of Mathematics Statistics and Computer Science University of St. Thomas HoustonTX United States Hall Labs LLC ProvoUT United States Department of Applied Mathematics National Sun Yat-sen University Kaohsiung80424 Taiwan University of Wyoming Colorado United States

The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph G. In this paper, we refer to the i-nullity pair of a matrix A as (null(A),null(A(i)), where A(i) is the matrix obtained from A by removing the i-th row and column. The inverse i-nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair. © 2024 Elsevier Inc.

关键词： Matrix algebra

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Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

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computer Systems science & Engineering 2023年第8期46卷 1631-1651页

作者： Pramote Charongrattanasakul Wimonmas Bamrungsetthapong Poom Kumam Division of Mathematics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology KrungthepBangkok10120Thailand Division of Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiPathum Thani12110Thailand Center of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research Laboratory Room SCL 802 Fixed Point LaboratoryScience Laboratory BuildingDepartments of MathematicsFaculty of ScienceKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand

A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)*** accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is *** economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s *** results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are *** indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated *** AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling *** real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

关键词： Accelerated life test acceleration factor adaptive of multiple dependent state sampling plan average sample number total cost of inspection weibull distribution

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Intelligent Machine-Failure Prediction System (IMPS) 3

Intelligent Machine-Failure Prediction System (IMPS)

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3rd International Conference on Innovative Practices in Technology and Management, ICIPTM 2023

作者： Bennet, Preethi Samantha Bennet, Deepthi Tabitha Anitha, D. Thiagarajar College of Engineering Department of Applied Mathematics and Computational Science Madurai India

ISBN: (纸本)9798350336238

In mission critical systems, system failure is a major hazard and may cause huge losses including loss or threat to lives. Organisations, industries, hospitals and companies can benefit hugely if an accurate prediction of the impending failure can be made, with enough time to initiate appropriate maintenance routines. Here, we propose and demonstrate that machine failure prediction can be done using suitable machine learning models with high accuracy. We apply the principles of Logistic Regression, Bootstrap Aggregation and Multinomial Logistic Regression to a predictive maintenance dataset of 10,000 data points to predict machine failure under five independent failure modes. Applying ensemble methods like bootstrap aggregation push the accuracy to greater than 99% The machine fails even if one failure mode is true. We are able to predict the possible cause of failure too, with a high accuracy of up to 99%. © 2023 IEEE.

关键词： Forecasting

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A Survey - Soil Feature Analysis Using Clustering Techniques and Predict Various Crops in Madurai District 1

A Survey - Soil Feature Analysis Using Clustering Techniques...

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1st International Conference in Advanced Innovation on Smart City, ICAISC 2023

作者： Sakthipriya, Dhinakaran Chandrakumar, Thangavel Johnson, B. Prem, Kumar J.B. Thiagarajar College of Engineering Department of Applied Mathematics and Computational Science Madurai India

ISBN: (纸本)9781665472753

In Tamil Nadu, seasonal soil fertility, rainfall, and temperature account for more than 65% of agricultural output. Soils are one of the most valuable natural resources on the planet. The study's goal was to analyze and survey the historical changes in soil parameter Index of Madurai District and Taluks, South India, using Clustering techniques of unsupervised learning to perform well for this proposed work. In this proposed work to involved, the survey should focus on the Soil parameters (N-Nitrogen, P-Phosphorus, K-potassium), rainfall, and temperature data retrieved from the agriculture government portal for the last five years. The study compares two machine learning clustering techniques, Hierarchical Clustering and K-Means Clustering in estimating soil features at Madurai Taluks. With the use of new agricultural technology, this proposed initiative intends to offer a better suggestion for obtaining an acceptable level of crop output to the Madurai surrounding blocks to get more benefits. © 2023 IEEE.

关键词： Soils

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A New Generative Mathematical Model for Coverless Steganography System Based on Image Generation

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computers, Materials & Continua 2023年第3期74卷 5087-5103页

作者： Al-Hussien Seddik Mohammed Salah Gamal Behery Ahmed El-harby Ahmed Ismail Ebada Sokea Teng Yunyoung Nam Mohamed Abouhawwash Department of Computer Science Faculty of ScienceMinia UniversityMiniaEgypt Department of Computer Science Faculty of Computers and Artificial IntelligenceDamietta UniversityNew DamiettaEgypt Department of ICT Convergence Soonchunhyang UniversityAsan31538Korea Department of Mathematics Faculty of ScienceMansoura UniversityMansoura35516Egypt Department of Computational Mathematics Scienceand Engineering(CMSE)Michigan State UniversityEast Lansing48824MIUSA

The ability of any steganography system to correctly retrieve the secret message is the primary criterion for measuring its ***,researchers have tried to generate a new natural image driven from only the secret message bits rather than using a cover to embed the secret message within it;this is called the stego *** paper proposes a new secured coverless steganography system using a generative mathematical model based on semi Quick Response(QR)code and maze game image *** system consists of two *** first component contains two processes,encryption process,and hiding *** encryption process encrypts secret message bits in the form of a semi-QR code image whereas the hiding process conceals the pregenerated semi-QR code in the generated maze game *** the other hand,the second component contains two processes,extraction and decryption,which are responsible for extracting the semi-QR code from the maze game image and then retrieving the original secret message from the extracted semi-QR code image,*** results were obtained using the bit error rate(BER)*** results confirmed that the system achieved high hiding capacity,good performance,and a high level of robustness against attackers compared with other coverless steganography methods.

关键词： Coverless steganography data hiding information security QR code maze game

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The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws:An Alternative Technique

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Advances in applied mathematics and Mechanics 2023年第4期15卷 1023-1055页

作者： Rooholah Abedian Mehdi Dehghan School of Engineering Science College of EngineeringUniversity of TehranIran Department of Applied Mathematics Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyNo.424Hafez Ave.TehranIran

To solve conservation laws,efficient schemes such as essentially nonoscillatory(ENO)and weighted ENO(WENO)have been introduced to control the Gibbs *** on radial basis functions(RBFs)with the classical WENO-JS weights,a new type of WENO schemes has been proposed to solve conservation laws[*** et al.,***.,70(2017),pp.551–575].The purpose of this paper is to introduce a new formulation of conservative finite difference RBFWENO schemes to solve conservation *** the usual method for reconstructing the flux functions,the flux function is generated directly with the conservative *** with Guo and Jung(2017),the main advantage of this framework is that arbitrary monotone fluxes can be employed,while in Guo and Jung(2017)only smooth flux splitting can be used to reconstruct flux *** 1D and 2D benchmark problems are prepared to demonstrate the good performance of the new scheme.

关键词： Weighted essentially non-oscillatory scheme radial basis functions interpolation ﬁnite difference method hyperbolic conservation laws

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From Donkeys to Kings in Tournaments 32

From Donkeys to Kings in Tournaments

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32nd Annual European Symposium on Algorithms, ESA 2024

作者： Abboud, Amir Grossman, Tomer Naor, Moni Solomon, Tomer Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Tel Aviv University Israel

ISBN: (纸本)9783959773386

A tournament is an orientation of a complete graph. A vertex that can reach every other vertex within two steps is called a king. We study the complexity of finding k kings in a tournament graph. We show that the randomized query complexity of finding k ≤ 3 kings is O(n), and for the deterministic case it takes the same amount of queries (up to a constant) as finding a single king (the best known deterministic algorithm makes O(n3/2) queries). On the other hand, we show that finding k ≥ 4 kings requires Ω(n2) queries, even in the randomized case. We consider the RAM model for k ≥ 4. We show an algorithm that finds k kings in time O(kn2), which is optimal for constant values of k. Alternatively, one can also find k ≥ 4 kings in time nω (the time for matrix multiplication). We provide evidence that this is optimal for large k by suggesting a fine-grained reduction from a variant of the triangle detection problem. © Amir Abboud, Tomer Grossman, Moni Naor, and Tomer Solomon;licensed under Creative Commons License CC-BY 4.0.

关键词： Graph theory

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Analysis of Student Behaviour on Large Learning Management Systems 31

Analysis of Student Behaviour on Large Learning Management S...

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31st International Conference on Software, Telecommunications and computer Networks, SoftCOM 2023

作者： Mehnen, Lars Mandl, Thomas Pohn, Birgit Blaickner, Matthias Dregely, Isabel University of Applied Sciences Technikum Wien Faculty Computer Science and Applied Mathematics Department of Computer Science Austria

ISBN: (纸本)9798350301076

This paper presents a comprehensive analysis of student behaviour on Moodle, a widely used Learning Management System (LMS), in a large university setting with over 2000 students. The study investigates the distribution of student access to the LMS relative to the deadlines of quizzes (self-checked). Further, it explores the correlation between student engagement with course materials and their academic performance, finding that students with higher grades tend to access course materials earlier and more frequently before quiz deadlines. The paper also examines the distribution of two different student engagement with quizzes across different weekdays, highlighting distinct patterns between weekdays and weekends, and a unique trend on Saturdays due to lecture schedules for two study types-full-Time and part-Time. These findings provide valuable insights into student learning behaviours on large LMS, with potential implications for enhancing teaching strategies and improving student outcomes. The paper contributes to the growing body of research on learning analytics and offers a foundation for future studies in this area. © 2023 University of Split, FESB.

关键词： Students

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A dive into spectral inference networks: improved algorithms for self-supervised learning of continuous spectral representations

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applied mathematics and Mechanics(English Edition) 2023年第7期44卷 1199-1224页

作者： J.WU S.F.WANG P.PERDIKARIS Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA 19104U.S.A. Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA 19104U.S.A.

We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint *** represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency *** formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the ***,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of *** effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video *** results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.

关键词： spectral learning partial differential equation(PDE) neural network slow features analysis

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Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through computational Methods

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computer Modeling in Engineering & sciences 2024年第10期141卷 311-329页

作者： Umar Shafique Mohamed Mahyoub Al-Shamiri Ali Raza Emad Fadhal Muhammad Rafiq Nauman Ahmed Department of Mathematics National College of Business Administration and EconomicsLahore54660Pakistan Department of Mathematics Applied CollegeMahayl AssirKing Khalid UniversityAbha62529Saudi Arabia Department of Physical Sciences The University of ChenabGujrat50700Pakistan Department of Mathematics&Statistics College of ScienceKing Faisal UniversityP.O.Box 400Al-Ahsa31982Saudi Arabia Department of Computer Science and Mathematics Lebanese American UniversityBeirut1102-2801Lebanon Department of Mathematics Faculty of Science and TechnologyUniversity of Central PunjabLahore54000Pakistan Department of Mathematics and Statistics University of LahoreLahore54000Pakistan

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal *** is a devastating disease and remains a significant public health *** study investigates a bacterial meningitis model through deterministic and stochastic ***-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and *** model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric ***,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known *** and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic ***,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step *** addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is *** simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

关键词： Bacterial Meningitis disease stochastic delayed model stability analysis extinction and persistence computational methods

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