
Theory and applications of DoE (design of experiments) in pharmaceutical technology
Maruška, Julie ; Duintjer Tebbens, Erik Jurjen (advisor) ; Svozil, Daniel (referee) ; Muselík, Jan (referee)
Charles University, Faculty of pharmacy in Hradec Králové Department: Department of Pharmaceutical Technology Department of Biophysics and Physical Chemistry Candidate: Mgr. Julie Maruška Supervisor: Assoc. Prof. Dipl.Math. Erik Jurjen Duintjer Tebbens, Ph.D. Consultant: Assoc. Prof. PharmDr. Zdeňka Šklubalová, Ph.D. Title of dissertation: Theory and applications of DoE (design of experiments) in pharmaceutical technology The conventional process for developing new medicines involves selecting combinations of various types of factors that impact numerous properties of the final dosage form. This scenario is wellsuited for using methods from the statistical field of design of experiments (DoE). Currently, the latest publications on pharmaceutical technology related to the development of new dosage forms are increasingly beginning to incorporate experimental design techniques, which are the subject of study in this work. This interdisciplinary dissertation thesis is an annotated summary of the publication and research activities of the author and aims to explore the DoE approaches focusing on their practical applications within the realm of pharmaceutical technology; to apply the selected techniques in actual processes of pharmaceutical technology; and to present a review of the most useful...


Approximation by the TLS method: linear data fitting for problems with unprecise models
Pokorná, Kateřina ; Hnětynková, Iveta (advisor) ; Duintjer Tebbens, Erik Jurjen (referee)
In this thesis, we concern ourselves with the linear approximation problem, where errors in both the observation and the data are considered. We focus on the total least squares problem (TLS), which may be used in solving such tasks. We summarise ba sic theory of the existence and uniqueness of the TLS solution, present the classic TLS algorithm and examine some possible complications, which may appear during its imple mentation. Furthermore, we shall study the singular value decomposition (SVD), which is used in constructing the TLS solution. As the SVD is rather difficult to compute, we discuss one of the possible methods of approximating only its part necessary for the construction of the TLS solution, the so called singular triplets. This method is based on GolubKahan iterative bidiagonalization. Finally, we shall test how the quality of the approximation of the smallest singular triplets influences the computed TLS solution. 1


BohlMarek decomposition applied to a class of biochemical networks with conservation properties
Papáček, Štěpán ; Matonoha, Ctirad ; Duintjer Tebbens, Jurjen
This study presents an application of one special technique, further called as BohlMarek decomposition, related to the mathematical modeling of biochemical networks with mass conservation properties. We continue in direction of papers devoted to inverse problems of parameter estimation for mathematical models describing the druginduced enzyme production networks [3]. However, being aware of the complexity of general physiologically based pharmacokinetic (PBPK) models, here we focus on the case of enzymecatalyzed reactions with a substrate transport chain [5]. Although our ultimate goal is to develop a reliable method for fitting the model parameters to given experimental data, here we study certain numerical issues within the framework of optimal experimental design [6]. Before starting an experiment on a real biochemical network, we formulate an optimization problem aiming to maximize the information content of the corresponding experiment. For the abovesketched optimization problem, the computational costs related to the two formulations of the same biochemical network, being (i) the classical formulation x˙(t) = Ax(t) + b(t) and (ii) the 'quasilinear' BohlMarek formulation x˙M(t) = M(x(t)) xM(t), can be determined and compared.


The small sample size problem in gene expression tasks
Athanasiadis, Savvas ; Duintjer Tebbens, Erik Jurjen (advisor) ; Kalina, Jan (referee)
Charles University in Prague Faculty of Pharmacy in Hradec Králové Department of Biophysics and Physical Chemistry Candidate: Savvas Athanasiadis Supervisor: Jurjen Duintjer Tebbens Title of diploma thesis: The small sample size problem in gene expression tasks The thesis addresses classification of genes to tumor types based on their gene expression signatures. The number of variables (aminoacids) to be inves tigated is typically very high (in the thousands) while it is expensive and time consuming to analyze a high number of genes; usually at most tens of them are available. The combination of a small sample size with a large number of variables makes standard statistical classification methods inappropriate. The thesis focuses on a modification of a standard classification method, Fisher's linear discriminant analysis, for the case where the number of samples is smaller than the number of variables. It proposes an improved strategy to test this modified method with leaveoneout cross validation. Using so called low rank updates of the involved covariance matrices, the computational costs of the cross validation process can be reduced by an order of magnitude. Memory demands are reduced as well.

 

Matrixfree preconditioning
Trojek, Lukáš ; Duintjer Tebbens, Erik Jurjen (advisor) ; Tůma, Miroslav (referee)
The diploma theses is focused on matrixfree preconditioning of a linear system. It gives a very brief introduction into the area of iterative methods, preconditioning and matrixfree environment. The emphasis is put on a detailed description of a variant of LU factorization which can be computed in a matrixfree manner and on a new technique connected with this factorization for preconditioning by incomplete LU factors in matrixfree environment. Its main features are storage of only one of the two incomplete factors and low memory costs during the computation of the stored factor. The thesis closes with numerical experiments demonstrating the efficiency of the proposed technique.

 

Efficient implementation of dimension reduction methods for highdimensional statistics
Pekař, Vojtěch ; Duintjer Tebbens, Erik Jurjen (advisor) ; Hnětynková, Iveta (referee)
The main goal of our thesis is to make the implementation of a classification method called linear discriminant analysis more efficient. It is a model of multivariate statistics which, given samples and their membership to given groups, attempts to determine the group of a new sample. We focus especially on the highdimensional case, meaning that the number of variables is higher than number of samples and the problem leads to a singular covariance matrix. If the number of variables is too high, it can be practically impossible to use the common methods because of the high computational cost. Therefore, we look at the topic from the perspective of numerical linear algebra and we rearrange the obtained tasks to their equivalent formulation with much lower dimension. We offer new ways of solution, provide examples of particular algorithms and discuss their efficiency. Powered by TCPDF (www.tcpdf.org)


Matrix computations for mixtures and solutions
Voborníková, Iveta ; Duintjer Tebbens, Erik Jurjen (advisor) ; Bernhauerová, Veronika (referee)
Charles University in Prague, Faculty of Pharmacy in Hradec Králové Department of Biophysics and Physical Chemistry Candidate: Iveta Voborníková Thesis supervisor: doc. Dipl.Math. Erik Jurjen Duintjer Tebbens, Ph.D. Title of diploma thesis: Matrix computations for mixtures and solutions In this work, we determined drug concentrations from mixtures using multicompo nent analysis without separating them. The condition was the knowledge of the molar absorption coefficients of individual drugs for certain wavelenghts. To do this, we used tools from matrix calculations, especially the MoorePenrose inverse, and we were in terested in whether we would achieve more accurate results using standard, square systems or overdetermined systems of linear equations. Based on the results, we came to the conclusion that there is no dependence between the accuracy of the results and the number of wavelengths used. Only in some cases did the results appear to be more accurate when using overdetermined systems with a higher number of wavelengths. Keywords: mixtures, solutions, linear systems, least squares problems, MoorePenrose pseudoinverses 1

 