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Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm

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Advances in applied mathematics and Mechanics 2024年第1期16卷 237-252页

作者： Alexey Shcheglov Jingzhi Li Chao Wang Alexander Ilin Ye Zhang Faculty of Computational mathematics and Cybernetics Shenzhen MSU-BIT UniversityShenzhenGuangdong 518172China Faculty of Computational mathematics and Cybernetics Lomonosov Moscow State UniversityMoscowRussia department of mathematics&National Center for applied mathematics Shenzhen&SUSTech International Center for mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear ***,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption *** stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.

关键词： Inverse problem quasi-linear dynamic model uniqueness method of successive approximations stability

Performance comparison of machine learning algorithms for maximum displacement prediction in soldier pile wall excavation

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Underground Space 2024年第3期16卷 301-313页

作者： Danial Sheini Dashtgoli Mohammad Hossein Dehnad Seyed Ahmad Mobinipour Michela Giustiniani department of mathematics Informaticsand GeosciencesUniversity of TriesteTrieste 34127Italy National Institute of Oceanography and applied Geophysics-OGS Borgo Grotta Gigante 42/CTriesteSgonico 34010Italy department of Civil Engineering University of QomQom ***Iran

One of the common excavation methods in the construction of urban infrastructures as well as water and wastewater facilities is the excavation through soldier pile *** maximum lateral displacement of pile wall is one of the important variables in controlling the stability of the excavation and its adjacent ***,the application of machine learning methods is widely used in engineering sciences due to its low cost and high speed of *** paper utilized three intelligent machine learning algorithms based on the excavation method through soldier pile walls,namely eXtreme gradient boosting(XGBoost),least square support vector regressor(LS-SVR),and random forest(RF),to predict maximum lateral displacement of pile *** results showed that the implemented XGBoost model performed excellently and could make predictions for maximum lateral displacement of pile walls with the mean absolute error of 0.1669,the highest coefficient of determination 0.9991,and the lowest root mean square error *** the LS-SVR,and RF models were less accurate than the XGBoost model,they provided good prediction results of maximum lateral displacement of pile walls for numerical ***,a sensitivity analysis was performed to determine the most effective parameters in the XGBoost *** analysis showed that soil elastic modulus and excavation height had a strong influence on of maximum lateral displacement of pile wall prediction.

关键词： Soldier pile wall Lateral displacements XGBoost Machine learning Artificial intelligence

Optimization in Machine Learning:a Distribution-Space Approach

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Communications on applied mathematics and Computation 2024年第2期6卷 1217-1240页

作者： Yongqiang Cai Qianxiao Li Zuowei Shen School of Mathematical Sciences Laboratory of Mathematics and Complex SystemsMOEBeijing Normal UniversityBeijing 100875China department of mathematics National University of Singapore21 Lower Kent Ridge RoadSingapore119077Singapore

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space,but with a non-convex constraint set introduced by model *** observation allows us to repose such problems via a suitable relaxation as convex optimization problems in the space of distributions over the training *** derive some simple relationships between the distribution-space problem and the original problem,e.g.,a distribution-space solution is at least as good as a solution in the original ***,we develop a numerical algorithm based on mixture distributions to perform approximate optimization directly in the distribution *** of this approximation is established and the numerical efficacy of the proposed algorithm is illustrated in simple *** both theory and practice,this formulation provides an alternative approach to large-scale optimization in machine learning.

关键词： Machine learning Convex relaxation Optimization Distribution space

Research on Multi-Scale Feature Fusion Network Algorithm Based on Brain Tumor Medical Image Classification

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Computers, Materials & Continua 2024年第6期79卷 5313-5333页

作者： Yuting Zhou Xuemei Yang Junping Yin Shiqi Liu Graduate School China Academy of Engineering PhysicsBeijing100000China department of Computational mathematics Beijing Institute of Applied Physics and Computational MathematicsBeijing100000China National Key Laboratory of Computational Physics Beijing100088China Shanghai Zhangjiang Institute of mathematics Shanghai201203China

Gliomas have the highest mortality rate of all brain *** classifying the glioma risk period can help doctors make reasonable treatment plans and improve patients’survival *** paper proposes a hierarchical multi-scale attention feature fusion medical image classification network(HMAC-Net),which effectively combines global features and local *** network framework consists of three parallel layers:The global feature extraction layer,the local feature extraction layer,and the multi-scale feature fusion layer.A linear sparse attention mechanism is designed in the global feature extraction layer to reduce information *** the local feature extraction layer,a bilateral local attention mechanism is introduced to improve the extraction of relevant information between adjacent *** the multi-scale feature fusion layer,a channel fusion block combining convolutional attention mechanism and residual inverse multi-layer perceptron is proposed to prevent gradient disappearance and network degradation and improve feature representation *** double-branch iterative multi-scale classification block is used to improve the classification *** the brain glioma risk grading dataset,the results of the ablation experiment and comparison experiment show that the proposed HMAC-Net has the best performance in both qualitative analysis of heat maps and quantitative analysis of evaluation *** the dataset of skin cancer classification,the generalization experiment results show that the proposed HMAC-Net has a good generalization effect.

关键词： Medical image classification feature fusion transformer

SIRS epidemic modeling using fractional-ordered differential equations:Role of fear effect

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International Journal of Biomathematics 2024年第5期17卷 79-100页

作者： Shiv Mangal O.P.Misra Joydip Dhar School of mathematics and Allied Sciences Jiwaji University GwaliorMadhya PradeshIndia department of mathematics Post Graduate College BinaMadhya PradeshIndia department of applied Sciences Atal Bihari Vajpayee-Indian Institute of Information Technology and Management GwaliorMadhya PradeshIndia

In this paper,an SIRS epidemic model using Grunwald-Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious *** criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction *** condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation ***,using the Grunwald-Letnikov approximation,the simulation is carried out to confirm the validity of analytic results *** the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021,we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical *** the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases.

关键词： SIRS epidemic model fear effect Mittag-Leffler function Hopf bifurcation parameter estimation

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

Non-thermal atmospheric-pressure positive pulsating corona discharge in degradation of textile dye Reactive Blue 19 enhanced by Bi_(2)O_(3) catalyst

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Plasma Science and Technology 2024年第2期26卷 104-113页

作者： Milica PETROVIC Dragan RADIVOJEVIC Sasa RANCEV Nena VELINOV Milos KOSTIC Danijela BOJIC Aleksandar BOJIC department of Chemistry Faculty of Sciences and MathematicsUniversity of NisNis 18000Serbia department of Physics Faculty of Sciences and MathematicsUniversity of NisNis 18000Serbia

In this work,monoclinic Bi_(2)O_(3) was applied for the first time,to the best of our knowledge,as a catalyst in the process of dye degradation by a non-thermal atmospheric-pressure positive pulsating corona *** research focused on the interaction of the plasma-generated species and the catalyst,as well as the role of the catalyst in the degradation *** decomposition of the anthraquinone reactive dye Reactive Blue 19(RB 19) was performed in a selfmade reactor ***_(2)O_(3) was prepared by electrodeposition followed by thermal treatment,and characterized by x-ray diffraction,scanning electron microscopy and energy-dispersive xray *** was observed that the catalyst promoted decomposition of plasma-generated H_(2)O_(2) into ·OH radicals,the principal dye-degrading reagent,which further attacked the dye *** catalyst improved the decolorization rate by 2.5 times,the energy yield by 93.4%and total organic carbon removal by 7.1%.Excitation of the catalyst mostly occurred through strikes by plasma-generated reactive ions and radical species from the air,accelerated by the electric field,as well as by fast electrons with an energy of up to 15 eV generated by the streamers reaching the liquid *** strikes transferred the energy to the catalyst and created the electrons and holes,which further reacted with H_(2)O_(2) and water,producing ·OH *** was indentified as the primary role of the catalyst in this *** reactions followed pseudo first-order *** of H_(2)O_(2) and the dye degradation rate increased with increase in the input *** optimal catalyst dose was 500 mg·dm^(-3).The decolorization rate was a little lower in river water compared with that in deionized water due to the side reactions of ·OH radicals with organic matter and inorganic ions dissolved in the river water.

关键词： corona RB 19 Bi_(2)O_(3) catalyst degradation

On power series statistical convergence and new uniform integrability of double sequences

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applied mathematics(A Journal of Chinese Universities) 2024年第3期39卷 519-532页

作者： Sevda Y■ld■z Kamil Demirci Sinop University Department of MathematicsSinopTurkey

In the present paper,we mostly focus on P_(p)^(2)-statistical *** will look into the uniform integrability via the power series method and its characterizations for double ***,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

关键词： power series methods statistical convergence uniform integrability double sequences

Fuzzy Difference Equations in Diagnoses of Glaucoma from Retinal Images Using Deep Learning

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Computer Modeling in Engineering & Sciences 2024年第4期139卷 801-816页

作者： D.Dorathy Prema Kavitha L.Francis Raj Sandeep Kautish Abdulaziz S.Almazyad Karam M.Sallam Ali Wagdy Mohamed department of mathematics Voorhees CollegeVelloreTamil NaduIndia Chandigarh Group of Colleges JhanjeriMohaliPunjabIndia department of Computer Engineering College of Computer and Information SciencesKing Saud UniversityP.O.Box 51178Riyadh11543Saudi Arabia Faculty of Science and Technology School of IT and SystemsUniversity of CanberraCanberraAustralia Operations Research department Faculty of Graduate Studies for Statistical ResearchCairo UniversityGiza12613Egypt applied Science Research Center Applied Science Private UniversityAmman11937Jordan

The intuitive fuzzy set has found important application in decision-making and machine *** enrich and utilize the intuitive fuzzy set,this study designed and developed a deep neural network-based glaucoma eye detection using fuzzy difference equations in the domain where the retinal images *** image detections are categorized as normal eye recognition,suspected glaucomatous eye recognition,and glaucomatous eye *** degrees associated with weighted values are calculated to determine the level of concentration between the fuzzy partition and the retinal *** proposed model was used to diagnose glaucoma using retinal images and involved utilizing the Convolutional Neural Network(CNN)and deep learning to identify the fuzzy weighted regularization between *** methodology was used to clarify the input images and make them adequate for the process of glaucoma *** objective of this study was to propose a novel approach to the early diagnosis of glaucoma using the Fuzzy Expert System(FES)and Fuzzy differential equation(FDE).The intensities of the different regions in the images and their respective peak levels were *** the peak regions were identified,the recurrence relationships among those peaks were then *** partitioning was done due to varying degrees of similar and dissimilar concentrations in the *** and dissimilar concentration levels and spatial frequency generated a threshold image from the combined fuzzy matrix and *** distinguished between a normal and abnormal eye condition,thus detecting patients with glaucomatous eyes.

关键词： Convolutional Neural Network(CNN) glaucomatous eyes fuzzy difference equation intuitive fuzzy sets image segmentation retinal images