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Effects of porous-wall acceleration on laminar flows in semi-porous channels with a rectangular cross section

CHINESE JOURNAL OF PHYSICS 2024年 89卷 834-858页

作者： Kalibe, Bernard Lamara, Maurice Nyobe, Elisabeth Ngo Pemha, Elkana Univ Yaounde I Fac Sci Appl Mech Lab POB 812 Yaounde Cameroon Univ Yaounde I Natl Adv Sch Engn Yaounde Dept Math & Phys Sci POB 8390 Yaounde Cameroon

This paper aims to examine the effects of wall acceleration on the steady laminar flow of an incompressible newtonian fluid along a semi -porous channel with a rectangular cross section. The lower wall of the channel is impermeable and at rest, while the upper wall is porous, and experiences longitudinal acceleration so that the flow is steady despite the accelerated movement of the wall. The fluid is injected or suctioned through the porous wall at uniform and constant velocity, orthogonally to the wall. The positive acceleration ratio defined as the ratio of longitudinal and transverse velocities, and the Reynolds number constructed by adding these velocities are the governing parameters. The similarity -solutions method, which is applied for the vorticity stream -function equation, gives numerical solutions using the shooting technique. Results indicate that the flow under study exists in the case of injection if the acceleration ratio does not exceed the value of 1, but in the case of suction, the flow remains unchanged if the acceleration ratio varies above the value of 9.5. For increasing acceleration ratios, the absolute value of transverse velocity decreases, the transverse pressure gradient remains unchanged at a specific fluid layer, the absolute value of longitudinal velocity increases near the porous wall and decreases near the impermeable wall, and in the case of injection, the algebraic wall shear stress decreases for the impermeable wall and increases for the porous wall. In the case of suction, there is a specific fluid layer at which the longitudinal velocity cancels by changing sign.

关键词： Laminar flows along semi-porous channels with rectangular cross section and accelerated walls Navier-Stokes equations Vorticity equation Similarity-solutions approach Shooting method newton-raphson algorithm

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Minorize-maximize algorithm for the generalized odds rate model for clustered current status data

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2023年第4期51卷 1150-1170页

作者： Wang, Tong He, Kejun Ma, Wei Bandyopadhyay, Dipankar Sinha, Samiran Nankai Univ Sch Stat & Data Sci Tianjin Peoples R China Texas A&M Univ Dept Stat College Stn TX 77843 USA Renmin Univ China Ctr Appl Stat Inst Stat & Big Data Beijing Peoples R China Virginia Commonwealth Univ Dept Biostat Richmond VA USA

Current status data are widely used in epidemiology and public health, where the only observable information is the random inspection time and the event status at inspection. This article presents a unified methodology to analyze such complex data subject to clustering. Given the random clustering effect, the time to event is assumed to follow a semiparametric generalized odds rate (GOR) model. The nonparametric component of the GOR model is approximated via penalized splines, with a set of knot points that increase with the sample size. The within-subject correlation is accounted for by a random (frailty) effect. For estimation, a novel MM algorithm is developed that allows the separation of the parametric and nonparametric components of the model. This separation makes the problem conducive to applying the newton-raphson algorithm that quickly returns the roots. The work is accompanied by a complexity analysis of the algorithm, a rigorous asymptotic proof, and the related semiparametric efficiency of the proposed methodology. The finite sample performance of the proposed method is assessed via simulation studies. Furthermore, the proposed methodology is illustrated via real data analysis on periodontal disease studies accompanied by diagnostic checks to identify influential observations.

关键词： Current status data efficient estimation frailty generalized odds rate minorization function newton-raphson algorithm

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Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data

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COMPUTATIONAL ECONOMICS 2023年第2期61卷 529-557页

作者： Bartolucci, Francesco Valentini, Francesco Pigini, Claudia Univ Perugia Dept Econ Via A Pascoli 20 I-06123 Perugia Italy Marche Polytech Univ Dept Econ & Social Sci Ple Martelli 8 I-60121 Ancona Italy

We propose a general recursive algorithm for the computation of the conditional probability function of the quadratic exponential model for binary panel data given the total of the responses, which is a sufficient statistic for the individual intercept parameter. This recursion permits to implement conditional and pseudo-conditional maximum likelihood estimators of the parameters of this model, and related models such as the dynamic logit model, even when one or more statistical units are observed at many occasions. In this way we solve a typical problem in dealing with distributions with a complex normalizing constant. The advantage in terms of computational load with respect to standard techniques is assessed by simulation and illustrated by an application based on a popular dataset about brand loyalty.

关键词： Clustered data Conditional maximum likelihood estimation Longitudinal data newton-raphson algorithm

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Left-truncated and right-censored field failure data: Review of parametric analysis for reliability

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2022年第7期38卷 3919-3934页

作者： Emura, Takeshi Michimae, Hirofumi Kurume Univ Biostat Ctr Kurume Fukuoka Japan Inst Stat Math Res Ctr Med & Hlth Data Sci Tokyo Japan Kitasato Univ Sch Pharm Dept Clin Med Biostat Tokyo Japan

In field reliability analyses, a data collection period is given to monitor the failure events from the field. Left-truncation arises due to early failures occurring before the data collection period, and right-censoring arises for late failures occurring beyond the monitoring period. Naive analyses of left-truncated and right-censored data lead to biased estimation of the population lifetime of interest. A variety of models and methods have been developed to analyze the left-truncated and right-censored data for field reliability analyses. The goal of the paper is to review the existing models and methods for fitting left-truncated and right-censored data. Our review includes the existing statistical models, such as the exponential, Weibull, lognormal, gamma, Gompertz, Lomax, and spline models. We comprehensively review the statistical issues of maximum likelihood estimation, model selection, residual lifetime prediction, and Bayesian methods. Some of these methods are illustrated through the field reliability analysis of the electric power transformer dataset.

关键词： Akaike's information criterion EM algorithm lognormal distribution newton-raphson algorithm Reliability Weibull distribution

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Item Response Models to investigate Maltese Attitudes towards Xenophobia 36

Item Response Models to investigate Maltese Attitudes toward...

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36th Annual European Simulation and Modelling Conference (ESM)

作者： Camilleri, Liberato Apap, Denise Univ Malta Dept Stat & Operat Res Msida 06 Msd Malta

ISBN: (纸本)9789492859242

Item Response Theory (IRT) models are used to evaluate the relationships between the latent trait of interest and the items measuring the trait and accommodate both binary and ordinal response data. For dichotomous responses the one-parameter (1-PL) and two-parameter (2-PL) Rasch models are used, while 1-PL and the 2-PL Rating Scale Model (RSM) are applicable in instances when the test items contain more than two ordinal response categories. A description of the marginal maximum likelihood estimation technique and the numerical optimization algorithm are provided since these techniques used in this paper. The main causes of irregular immigration include injustice, unemployment, political instability, lack of opportunities to live a decent life, poverty, and war. One of the biggest concerns of our time is the xenophobic behavior of an increasing number of individuals towards irregular immigrants. This fear of strangers is often manifested in prejudicial and hostile attitudes that may lead to methodical oppression and systematic denial of human rights. Using the responses of a sample of 300 individuals, this paper investigates the xenophobic attitudes of Maltese adults towards irregular immigrants, using IRT models.

关键词： Item response theory Rasch model Rating scale model Adaptive quadrature newton-raphson algorithm

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Multilevel Survival Models to investigate Survival Durations of Patients requiring Aortic Valve Replacement 36

Multilevel Survival Models to investigate Survival Durations...

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36th Annual European Simulation and Modelling Conference (ESM)

作者： Camilleri, Liberato Grech, Aiden Manche, Alex Univ Malta Dept Stat & Operat Res Msida 06 Msd Malta

ISBN: (纸本)9789492859242

Traditional survival models are based on the assumption that the population under investigation is fairly homogenous and that a few observed covariates can explain the data very well. However, in real survival data sets there is often considerably unobserved heterogeneity which cannot be simply explained by a few covariates. Survival data having a multilevel structure is often encountered across a range of disciplines, including epidemiology, public health, education, electronics, sociology and engineering. Such data can be used to estimate the survival duration of electronic devices in several environmental conditions, assess the safety of medical devices and therapies on patients with different frailties, estimate the life expectancy of humans in different regions, and evaluate the profitability of financial schemes in different economic conditions, amongst other applications. This paper presents the theoretical framework of multilevel mixed effects survival models to address the frailty (unobserved heterogeneity) that may exist in the data. It is common to assume a proportional hazards structure that is conditional on frailty, which is basically a proportional hazards model with mixed effects. These models will be used to analyze the survival durations of patients following aortic valve replacement surgery and will incorporate both fixed and random group-level effects. To accommodate the nesting structure of the model, the patients (level-1 units) will be nested by their diabetes condition (level-2 units). Using the facilities of STATA, these models will be fitted using both the frequentist and Bayesian approaches by assuming an Exponential or a Weibull survival distribution. For the Bayesian approach, normal priors and inverse-gamma hyperpriors will be assumed

关键词： Multilevel Survival models Weibull distribution Aortic valve replacement surgery Adaptive quadrature newton-raphson algorithm

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Estimation under copula-based Markov normal mixture models for serially correlated data

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2021年第12期50卷 4483-4515页

作者： Lin, Wei-Cheng Emura, Takeshi Sun, Li-Hsien Natl Cent Univ Grad Inst Stat Chungli 32001 Taiwan

We propose an estimation method under a copula-based Markov model for serially correlated data. Motivated by the fat-tailed distribution of financial assets, we select a normal mixture distribution for the marginal distribution. Based on the normal mixture distribution for the marginal distribution and the Clayton copula for serial dependence, we obtain the corresponding likelihood function. In order to obtain the maximum likelihood estimators, we apply the newton-raphson algorithm with appropriate transformations and initial values. We conduct simulation studies to evaluate the performance of the proposed method. In the empirical analysis, the stock price of Dow Jones Industrial Average is analyzed for illustration.

关键词： Log return Copula Normal mixture distribution newton-raphson algorithm Markov model

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Electrical Characterization and Efficiency Enhancement of Dye Sensitized Solar Cell Using Natural Sensitizer and TiO2 Nanoparticles Deposited by Electrophoretic Technique

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IEEE JOURNAL OF PHOTOVOLTAICS 2021年第4期11卷 1004-1013页

作者： Azizi, Tarek Kaddachi, Zouhour Ben Karoui, Moufida Touihri, Ala Eddinne Gharbi, Rached Ecole Natl Supurieure Ingenieurs Tunis Dept Elect Engn Tunis 1008 Tunisia Ctr Rech Technol Energie Lab Photovolta Tunis 1008 Tunisia

This article concerns the use of anthocyanin, mallow and their mixture as a low-cost natural dyes to sensitize the photo-anodes of dye sensitized solar cells (DSSCs) based on titanium dioxide (TiO2) layers, and investing their effect on the electrical performance of the realized cells. In fact, different layers of porous titanium dioxide (TiO2) were deposited on fluorine-doped tin oxide glass (FTO) via the electrophoretic deposition (EPD) technique, and then sensitized with natural dyes to form the photo-anode electrode for the DSSC. Four DSSCs are manufactured: three cells, each one is formed by a TiO2 single layer and a cell formed by two TiO2 layers. An electric model, with five parameters based on of the newton-raphson algorithm (NR), was used to extract the electrical parameters of the cell and establish a comparative study between simulated and experimental current-voltage characteristic (J-V). An improvement of short-circuit current and efficiency was obtained for the DSSC with two layers of TiO2 and sensitized with the mixture of mallow and anthocyanin. Indeed, an increase of short circuit current from 0.34 to 1.98 mA/cm(2) was observed and the efficiency reached 0.58%. This increase was more confirmed by external quantum efficiency (EQE). Nevertheless, after 96 hours under standard lighting at room temperature of 25 degrees C, a degradation of the efficiency of the cell with a rate value of 24% was noted.

关键词： Dye sensitized solar cell electrical model electrophoretic deposition J-V characteristics mixture of natural dyes natural dyes newton-raphson algorithm photovoltaic technology

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An Improved Monte Carlo EM Acceleration algorithm

International Core Journal of Engineering

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International Core Journal of Engineering 2024年第5期10卷 493-499页

作者： Yugui Lu Qunlan Li

In this paper, an improved Monte Carlo EM (MCEM) acceleration algorithm is proposed, aiming at solving the problems of slow convergence and difficult integral calculation of the traditional MCEM algorithm when dealing with complex models. The article first reviews the basic concepts and application background of EM algorithms and MCEM algorithms, and then points out the limitations of MCEM algorithms with high-dimensional data and complex models. To overcome these challenges, the authors introduce a new algorithm that approximates the solution of N-R step integrals by means of a Monte Carlo simulation method, which improves the convergence speed of the algorithm and maintains the quadratic convergence property. Specifically, the improved MCEM acceleration algorithm consists of the following key steps: random sampling in the E1 step, computation of the expectation in the E2 step, maximization of the objective function in the M step, and approximation of the integral using the Monte Carlo method in the improved N-R step. Through numerical examples, the authors demonstrate the advantages of the improved algorithm over the original MCEM algorithm and the MCEM accelerated algorithm in terms of accuracy of parameter estimation and speed of convergence. In addition, the article discusses the effect of random number selection on the performance of the algorithm and provides a method for choosing the appropriate number of random numbers. In conclusion, the improved MCEM acceleration algorithm effectively improves the computational efficiency and accuracy of the results when dealing with complex data models, which has important practical application value for statistical analysis in the era of big data.

关键词： MCEM algorithm newton-raphson algorithm Monte Carlo Simulation

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Shrinking the Covariance Matrix Using Convex Penalties on the Matrix-Log Transformation

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2021年第2期30卷 442-451页

作者： Yi, Mengxi Tyler, David E. Univ Int Business & Econ Sch Stat Beijing Peoples R China Rutgers State Univ Dept Stat Piscataway NJ 08854 USA

Forq-dimensional data, penalized versions of the sample covariance matrix are important when the sample size is small or modest relative toq. Since the negative log-likelihood under multivariate normal sampling is convex in Sigma(-1), the inverse of the covariance matrix, it is common to consider additive penalties which are also convex in Sigma(-1). More recently, Deng and Tsui and Yu et al. have proposed penalties which are strictly functions of the roots of Sigma and are convex in log Sigma, but not in Sigma(-1). The resulting penalized optimization problems, though, are neither convex in log Sigma nor in Sigma(-1). In this article, however, we show these penalized optimization problems to be geodesically convex in Sigma. This allows us to establish the existence and uniqueness of the corresponding penalized covariance matrices. More generally, we show that geodesic convexity in Sigma is equivalent to convexity in log Sigma for penalties which are functions of the roots of Sigma. In addition, when using such penalties, the resulting penalized optimization problem reduces to a q-dimensional convex optimization problem on the logs of the roots of Sigma, which can then be readily solved via newton's algorithm. Supplementary materials for this article are available online.

关键词： Geodesic convexity newton-raphson algorithm Penalized likelihood

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