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d-optimal designs for Hierarchical Linear Models with Heteroscedastic Errors

Communications in Mathematics and Statistics 2022年第4期10卷 669-679页

作者： Xin Liu Rong-Xian Yue Kashinath Chatterjee College of Science Donghua UniversityShanghai 201620People’s Republic of China department of Mathematics Shanghai Normal UniversityShanghai 200234People’s Republic of China department of Statistics Visva-Bharati UniversitySantiniketanIndia

This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic *** equivalence theorem is established to characterize d-optimality of designs for the prediction based on the mean squared error *** admissibility of designs is also considered and a sufficient condition to simplify the design problem is *** results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.

关键词： d-optimal design Heteroscedasticity Mean squared error matrix Mixed-effect model Equivalence theorem Admissibility

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Formulation of self-nanoemulsifying drug delivery systems containing monoacyl phosphatidylcholine and Kolliphor^(■) RH40 using experimental design

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Asian Journal of Pharmaceutical Sciences 2018年第6期13卷 536-545页

作者： Thuy Tran Thomas Rades Anette Müllertz department of Pharmacy Faculty of Health and Medical Sciences University of Copenhagen Bioneer: FARMA Faculty of Health and Medical Sciences University of Copenhagen

The development of self-nanoemulsifying drug delivery systems(SNEddS) to enhance the oral bioavailability of lipophilic drugs is usually based on traditional one-factor-at-a-time approaches. These approaches may be inadequate to analyse the effect of each excipient and their potential interactions on the emulsion droplet size formed when dispersing the SNEddS in an aqueous environment. The current study investigates the emulsion droplet sizes formed from SNEddS containing different levels of the natural surfactant monoacyl phosphatidylcholine to reduce the concentration of the synthetic surfactant polyoxyl 40 hydrogenated castor oil(Kolliphor ~? RH40). Monoacyl phosphatidylcholine was used in the form of Lipoid S LPC 80(LPC, containing approximately 80% monoacyl phosphatidylcholine, 13% phosphatidylcholine and 4% concomitant components). The investigated SNEddS comprised of long-chain or medium-chain glycerides(40% to 75%), Kolliphor ~? RH40(5% to 55%), LPC(0 to 40%) and ethanol(0 to 10%). d-optimal design, multiple linear regression, and partial least square regression were used to screen different SNEddS within the investigated excipient ranges and to analyse the effect of each excipient on the resulting droplet size of the dispersed SNEddS measured by dynamic light scattering. All investigated formulations formed nano-emulsions with droplet sizes from about 20 to 200 nm. The use of mediumchain glycerides was more likely to result in smaller and more monodisperse droplet sizes compared to the use of long-chain glycerides. Kolliphor~? RH40 exhibited the most significant effect on reducing the emulsion droplet sizes. Increasing LPC concentration increased the emulsion droplet sizes, possibly because of the reduction of Kolliphor~? RH40 concentration. A higher concentration of ethanol resulted in an insignificant reduction of the emulsion droplet size. The study provides different ternary diagrams of SNEddS containing LPC and Kolliphor ~? RH40 as a reference for form

关键词： Monoacyl phosphatidylcholine Self-nanoemulsifying drug delivery systems d-optimal design Polyoxyl 40 hydrogenated castor oil Kolliphor^(■)(RH40) droplet size Cryogenic transmission electron microscopy

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An Efficient Sampling Method for Regression-Based Polynomial Chaos Expansion

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Communications in Computational Physics 2013年第4期13卷 1173-1188页

作者： Samih Zein Benoit Colson Francois Glineur Samtech H.Q. LMS International8 rue des chasseurs ardennais AngleurBelgium Center for Operations Research and Econometrics&Information and Communication Technologies Electronics and Applied Mathematics InstituteUniversite catholique de LouvainB-1348 Louvain-la-NeuveBelgium

The polynomial chaos expansion(PCE)is an efficient numerical method for performing a reliability *** relates the output of a nonlinear system with the uncertainty in its input parameters using a multidimensional polynomial approximation(the so-called PCE).Numerically,such an approximation can be obtained by using a regression method with a suitable design of *** cost of this approximation depends on the size of the design of *** the design of experiments is large and the system is modeled with a computationally expensive FEA(Finite Element Analysis)model,the PCE approximation becomes *** aim of this work is to propose an algorithm that generates efficiently a design of experiments of a size defined by the user,in order to make the PCE approximation computationally *** is an optimization algorithm that seeks to find the best design of experiments in the d-optimal sense for the *** algorithm is a coupling between genetic algorithms and the Fedorov exchange *** efficiency of our approach in terms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.

关键词： Polynomial chaos expansion regression d-optimal design Fedorov Algorithm genetic algorithms

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