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Global Piecewise Analysis of HIV Model with Bi-Infectious Categories under Ordinary Derivative and Non-Singular Operator with Neural Network Approach

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Computer Modeling in Engineering & sciences 2025年第1期142卷 609-633页

作者： Ghaliah Alhamzi Badr Saad TAlkahtani Ravi Shanker Dubey Mati ur Rahman Department of Mathematics and Statistics College of ScienceImam Mohammad Ibn Saud Islamic University(IMSIU)Riyadh13318Saudi Arabia Department of Mathematics College of ScienceKing Saud UniversityRiyadh11989Saudi Arabia Department of Mathematics Amity School of Applied SciencesAmity University RajasthanJaipur302002India school of mathematical sciences Jiangsu UniversityZhenjiang212013China Department of Computer Science and Mathematics Lebanese American UniversityBeirut13-5053Lebanon

This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary *** HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered *** total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,*** proposed model is tested separately for unique solutions and existence on bi *** numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons *** proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler *** cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said *** study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered *** obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.

关键词： HIV infection model qualitative scheme approximate solution piecewise global operator neural network

Robust Estimation of Parameters in Nonlinear Ordinary Differential Equation Models

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Journal of Systems Science & Complexity 2016年第1期29卷 41-60页

作者： QIU Yanping HU Tao LIANG Baosheng CUI Hengjian school of mathematical sciences Beijing Normal UniversityBeijing 100875China school of mathematical sciences and bcmiis Capital Normal UniversityBeijing 100048China

Ordinary differential equation(ODE) models are widely used to model dynamic processes in many scientific *** estimation is usually a challenging problem,especially in nonlinear ODE *** most popular method,nonlinear least square estimation,is shown to be strongly sensitive to *** this paper,robust estimation of parameters using M-estimators is proposed,and their asymptotic properties are obtained under some regular *** authors also provide a method to adjust Huber parameter automatically according to the ***,a method is presented to estimate the initial values of parameters and state *** efficiency and robustness are well balanced in Huber estimators,which is demonstrated via numerical simulations and chlorides data analysis.

关键词： Asymptotic properties Huber parameter ordinary differential equation robust estimation

Constructions of derived equivalences for algebras and rings

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Frontiers of Mathematics in China 2017年第1期12卷 1-18页

作者： Changchang XI school of mathematical sciences bcmiis Capital Normal University Beijing 100048 China

In this article, we shall survey some aspects of our recent （or related） constructions of derived equivalences for algebras and rings.

关键词： Derived equivalence Frobenius-finite algebra recollement stable equivalence tilting complex Yoneda algebra

Partial Penalized Empirical Likelihood Ratio Test Under Sparse Case

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 327-344页

作者： Shan-shan WANG Heng-jian CUI school of Economics and Management Beihang University school of mathematical sciences & bcmiis Capital Normal University

A consistent test via the partial penalized empirical likelihood approach for the parametric hy- pothesis testing under the sparse case, called the partial penalized empirical likelihood ratio （PPELR） test, is proposed in this paper. Our results are demonstrated for the mean vector in multivariate analysis and regression coefficients in linear models, respectively. And we establish its asymptotic distributions under the null hypoth- esis and the local alternatives of order n-1/2 under regularity conditions. Meanwhile, the oracle property of the partial penalized empirical likelihood estimator also holds. The proposed PPELR test statistic performs as well as the ordinary empirical likelihood ratio test statistic and outperforms the full penalized empirical like- lihood ratio test statistic in term of size and power when the null parameter is zero. Moreover, the proposed method obtains the variable selection as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed method in hypothesis testing and variable selection.

关键词： Chi-squared distribution empirical likelihood partial penalized empirical likelihood SCAD sparse

Numerical Discretization-Based Kernel Type Estimation Methods for Ordinary Differential Equation Models

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Acta Mathematica Sinica,English Series 2015年第8期31卷 1233-1254页

作者： Tao HU Yan Ping QIU Heng Jian CUI Li Hong CHEN school of mathematical sciences & bcmiis Capital Normal University school of mathematical sciences Beijing Normal University Fujian College of Water Conservancy and Eletric Power

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation（ODE） models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method（kernel smoothing or local polynomial fitting） in the first stage, and a numerical discretization method（Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method） in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational *** properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.

关键词： Nonparametric regression kernel smoothing local polynomial fitting parametric identification ordinary differential equation nume

Miyaoka-type inequalities for terminal threefolds with nef anti-canonical divisors

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Science China Mathematics 2025年第01期 1-18页

作者： Masataka Iwai Chen Jiang Haidong Liu Department of Mathematics Graduate School of ScienceOsaka University Shanghai Center for mathematical sciences & school of mathematical sciences Fudan University Department of mathematics Sun Yat-sen University

In this paper,we study Miyaoka-type inequalities on Chern classes of terminal projective 3-folds with nef anti-canonical *** X be a terminal projective 3-fold such that-KXis *** show that if c1（X） · c2（X）≠0,then c1（X） · c2（X） ≥ 1/252;if further X is not rationally connected,then c1（X） · c2（X） ≥ 4/5 and this inequality is *** order to prove this,we give a partial classification of such varieties along with many *** also study the nonvanishing of c1（X）dim X-2· c2（X） for terminal weak Fano varieties and prove a Miyaoka-Kawamata-type inequality.

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In vivo direct neuronal conversion as a therapeutic strategy for ischemic stroke

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Neural Regeneration Research 2025年第8期20卷 2309-2310页

作者： Takashi Irie Taito Matsuda Department of Stem Cell Biology and Medicine Graduate School of Medical SciencesKyushu UniversityFukuokaJapan Department of Neurology Neurological InstituteGraduate School of Medical SciencesKyushu UniversityFukuokaJapan

Stroke causes neuronal loss,which ultimately results in persistent neurological ***,stroke was the third-leading cause of death and disability combined in all ages in 2019,after neonatal disorders and ischemic heart *** that year,there were 12.2 million incident strokes,101 million prevalent strokes,and 143 million disability-adjusted life-years due to stroke.

关键词： neonatal death therapeutic

Lipid droplets in the nervous system:involvement in cell metabolic homeostasis

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Neural Regeneration Research 2025年第3期20卷 740-750页

作者： Yuchen Zhang Yiqing Chen Cheng Zhuang Jingxuan Qi Robert Chunhua Zhao Jiao Wang school of Life sciences Shanghai UniversityShanghaiChina school of Medicine Shanghai UniversityShanghaiChina Institute of Basic Medical sciences Chinese Academy of Medical sciences School of Basic MedicinePeking Union Medical CollegeBeijingChina Center of Excellence in Tissue Engineering Chinese Academy of Medical SciencesBeijingChina Beijing Key Laboratory of New Drug Development and Clinical Trial of Stem Cell Therapy BeijingChina

Lipid droplets serve as primary storage organelles for neutral lipids in neurons,glial cells,and other cells in the nervous *** droplet formation begins with the synthesis of neutral lipids in the endoplasmic ***,lipid droplets were recognized for their role in maintaining lipid metabolism and energy homeostasis;however,recent research has shown that lipid droplets are highly adaptive organelles with diverse functions in the nervous *** addition to their role in regulating cell metabolism,lipid droplets play a protective role in various cellular stress ***,lipid droplets exhibit specific functions in neurons and glial *** of lipid droplet formation leads to cellular dysfunction,metabolic abnormalities,and nervous system *** review aims to provide an overview of the role of lipid droplets in the nervous system,covering topics such as biogenesis,cellular specificity,and ***,it will explore the association between lipid droplets and neurodegenerative *** the involvement of lipid droplets in cell metabolic homeostasis related to the nervous system is crucial to determine the underlying causes and in exploring potential therapeutic approaches for these diseases.

关键词： Alzheimer's disease lipid droplet biogenesis lipid droplets lipid metabolism nervous system neurodegenerative disorders oxidative stress Parkinson's disease

Harnessing therapeutic potential of induced pluripotent stem cell–derived endothelial cells for remyelination in the central nervous system

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Neural Regeneration Research 2025年第6期20卷 1715-1716页

作者： Dan Ma Nona Pop Aston Medical school College of Health and Life SciencesAston UniversityBirminghamUK

Myelin is the protective sheath surrounding nerve fibers, and its damage(demyelination) occurs in many central nervous system(CNS) diseases, including multiple sclerosis(MS), traumatic injury, neurodegenerative diseases such as Alzheimer's disease, and mental disorders such as schizophrenia(Barateiro et al., 2016). Repair of damaged myelin sheaths(remyelination) often fails in MS, leading to neuronal loss and irreversible functional deficits.

关键词： myelin protective diseases