DOCSLIB.ORG

A Novel Optimization Algorithm and Other Techniques in Medicinal Chemistry

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Novel Optimization Algorithm and Other Techniques in Medicinal Chemistry A NOVEL OPTIMIZATION ALGORITHM AND OTHER TECHNIQUES IN MEDICINAL CHEMISTRY by Radleigh G. Santos A Dissertation Submitted to the Faculty of The Charles E. Schmidt College of Science in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Florida Atlantic University Boca Raton, Florida May 2012 A NOVEL OPTIMIZATION ALGORITHM AND OTHER TECHNIQUES IN MEDICINAL CHEMISTRY by RadIeigh G. Santos This dissertation was prepared under the direction ofthe candidate's dissertation advisor, Dr. Dragan RaduIovic, Department of Mathematics, and has been approved by the members ofhis supervisory committee. It was submitted to the faculty ofthe Charles E. Schmidt College of Science and was accepted in partial fulfillment of the requirements for the degree ofDoctor ofPhilosophy. SUPERVISORY COMMITIEE: ~'"~-iC-'-Ph-.-O-.------ Di~i~' Richard Houghten, Ph.D. I• Wi ham Kalies, Ph.O. ..., 41~.·~,3._ Hongwei Long,Ph.D. =t- .t.;, ~ Rainer Steinwandt, Ph.D. College of Science ii ACKNOWLEDGEMENTS Since grade school mathematics has always been a joy and inspiration to me, and I am honored to be among the ranks of the highest level of education in the field. I could not have gotten this far were it not for countless people who have been in my life. These are but a notable few who deserve some credit for my achievement: I would like to thank all professors, mathematics or otherwise, from whom I have had the privilege to learn during my time at MIT, Georgia Tech, and FAU. Special thanks to scientists I continue to be privileged to work with at TPIMS: Marc Guilianatti, Jose Medina-Franco, Karina Martinez-Mayorga, Clemencia Pinilla, Valeria Judkowski, Dmitriy Minond, Joanna Davies, and Richard Houghten. I am grateful to my committee members William Kalies, Hongwei Long, and Rainer Steinwandt. Thank you also to Lee Klingler for his support during the final months of the process. Most of all I am thankful for being able to work with my advisor Dragan Radulovic, with whom I have never ceased to enjoy our shared enthusiasm over applied mathematics. Most of all I would like to thank the friends and family who were constant sources of support for me. Thanks to my grandmother Avee. Love, gratitude, and thanks to my wonderful sister Marlisa, who has always been there for me, my brother-in-law Randy, and to my Mother, who always has my back. And finally to my “Mathematical Muse” Denia, my deepest love and thanks, for supporting and believing in me even when I did not. iii ABSTRACT Author: Radleigh G. Santos Title: A Novel Optimization Algorithm and Other Techniques in Medicinal Chemistry Institution: Florida Atlantic University Dissertation Advisor: Dr. Dragan Radulovic Degree: Doctor of Philosophy Year: 2012 In this dissertation we will present a stochastic optimization algorithm and use it and other mathematical techniques to tackle problems arising in medicinal chemistry. In Chapter 1, we present some background about stochastic optimization and the Accelerated Random Search (ARS) algorithm. We then present a novel improvement of the ARS algorithm, Directed Accelerated Random Search (DARS), motivated by some theoretical results, and demonstrate through numerical results that it improves upon ARS. In Chapter 2, we use DARS and other methods to address issues arising from the use of mixture-based combinatorial libraries in drug discovery. In particular, we look at models associated with the biological activity of these mixtures and use them to answer questions about sensitivity and robustness, and also present a novel method for determining the integrity of the synthesis. Finally, in Chapter 3 we present an in-depth analysis of some statistical and mathematical techniques in combinatorial chemistry, including a novel probabilistic approach to using structural similarity to predict the activity landscape. iv A NOVEL OPTIMIZATION ALGORITHM AND OTHER TECHNIQUES IN MEDICINAL CHEMISTRY LIST OF TABLES ......................................................................................................... vii LIST OF FIGURES ........................................................................................................ ix INTRODUCTION ........................................................................................................... 1 CHAPTER 1 A DIRECTED ACCELERATED RANDOM SEARCH ALGORITHM ........... 3 Definitions and Assumptions ............................................................................... 3 Pure Random Search ............................................................................................ 5 Accelerated Random Search ................................................................................ 7 The Finite Descent ARS Algorithm ............................................................... 8 Limitations of Accelerated Random Search ................................................ 11 Directed Accelerated Random Search ............................................................... 15 Directional Information Present in the ARS Visit Record........................... 15 The DARS Heuristic .................................................................................... 19 Numerical Results .............................................................................................. 23 Demonstrative Function ............................................................................... 24 Benchmark Functions .................................................................................. 26 Systems of Equations ................................................................................... 31 The Domains of Linear and Nonlinear Programming Problems ................. 36 Conclusion ......................................................................................................... 41 2 OPTIMIZATION AND NUMERICAL MODELING IN MEDICINAL CHEMISTRY .................................................................................................... 44 Introduction ........................................................................................................ 44 Biological Activity ....................................................................................... 44 Mixture-Based Combinatorial Libraries ...................................................... 45 The Modeling of Chemical Mixtures ................................................................. 47 The Harmonic Mean Model ......................................................................... 48 Implications of the Harmonic Mean Model ................................................. 55 Extension of the Harmonic Mean Model ..................................................... 62 Determining the Integrity of Novel Mixture-Based Combinatorial Libraries ... 66 Experimental Synthesis Procedure .............................................................. 67 v Determining the Proper Reagent Ratio ........................................................ 68 Differences in Reaction Rate Caused by Multiple Simultaneous Reactions ...................................................................................................... 71 Differences in Reaction Rate Caused by Different On-Resin Amino Acids ............................................................................................................ 73 Conclusion ......................................................................................................... 79 3 STATISTICAL AND PROBABILISTIC METHOD IN COMPUTATIONAL CHEMISTRY ................................................................. 80 Introduction ........................................................................................................ 80 The Structural-Activity Relationship ........................................................... 80 The Biological Target for Study .................................................................. 82 Standard Methodology ....................................................................................... 84 Description of Data Set ................................................................................ 84 2D and 3D Structural Similarity .................................................................. 85 Property Similarities .................................................................................... 85 Activity Similarity ....................................................................................... 87 Activity Landscape with SAS Maps ............................................................ 87 Consensus SAS Map .................................................................................... 90 Results and Discussion of Standard Methods .................................................... 91 Distribution of Fingerprint Similarity Measures.......................................... 91 Correlation Between Molecular Similarities ............................................... 91 The Activity Landscape ............................................................................... 93 Consensus Models of the Activity Landscape: Consensus SAS Maps...... 107 Dual-Parasite SAR and Consensus Selectivity Cliffs ................................ 108 Conclusions and Perspectives .................................................................... 109 Predictivity Analysis of Structural and Property Similarities .......................... 111 Threshold Determination Heuristic............................................................ 111 Testing Methodology ................................................................................
Load more

Recommended publications
  • A Time-Stepping Method for Stiff Multibody Dynamics with Contact
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2002; 55:753–784 (DOI: 10.1002/nme.512) A time-stepping method for sti multibody dynamics with contact and friction‡ Mihai Anitescu1;∗;† and Florian A. Potra2 1Department of Mathematics; University of Pittsburgh; Thackeray 301; Pittsburgh; PA 15213; U.S.A. 2Department of Mathematics; University of Maryland; Baltimore County; Baltimore; MD 21250; U.S.A. SUMMARY We dene a time-stepping procedure to integrate the equations of motion of sti multibody dynamics with contact and friction. The friction and non-interpenetration constraints are modelled by complemen- tarity equations. Stiness is accommodated by a technique motivated by a linearly implicit Euler method. We show that the main subproblem, a linear complementarity problem, is consistent for a suciently small time step h. In addition, we prove that for the most common type of sti forces encountered in rigid body dynamics, where a damping or elastic force is applied between two points of the system, the method is well dened for any time step h. We show that the method is stable in the sti limit, unconditionally with respect to the damping parameters, near the equilibrium points of the springs. The integration step approaches, in the sti limit, the integration step for a system where the sti forces have been replaced by corresponding joint constraints. Simulations for one- and two-dimensional examples demonstrate the stable behaviour of the method. Published in 2002 by John Wiley & Sons, Ltd. KEY WORDS: multibody dynamics; rigid bodies; Coulomb friction; sti methods; linear complemen- tarity problems; linearly implicitly integration 1.
    [Show full text]
  • General Index
    General Index Accelerated convergence of series 172ff. Annealing, method of simulated 398f., 448ff. Accuracy 31f. assessment 459 achievable in minimization 402, 408, 415 for continuous variables 448, 455f. achievable in root finding 357 schedule 449 contrasted with fidelity 843, 851 thermodynamic analogy 448f. CPU different from memory 192 traveling salesman problem 449ff. vs. stability 715, 740, 841, 855 ANSI/ISO C++ standard 3 Accuracy parameters 17, 956f. Antonov-Saleev variant of Sobol’ sequence Acknowledgments xiii 314ff. Adams-Bashford-Moulton method 752 Apple xx Adams’ stopping criterion 377 Macintosh 896 Adaptive integration 133, 146, 714, 719ff., Approximate inverse of matrix 60 729ff., 737f., 742, 748, 753f., 799 Approximation of functions 108f. Adaptive Monte Carlo integration 320ff., by Chebyshev polynomials 197f., 524 323ff. Pade´ approximant 206ff. Addition, multiple precision 917 by rational functions 209ff. Addition theorem, elliptic integrals 266 by wavelets 605f., 793 ADI (alternating direction implicit) method see also Fitting 858, 872f., 917 Arithmetic Adjoint operator 878 arbitrary precision 891, 916ff. Adobe Illustrator xiv, xx floating point 891 Advective equation 837 IEEE standard 289, 893 AGM (arithmetic geometric mean) 917 rounding 892 Airy function 216, 245, 255 Arithmetic coding 891, 912ff. routine for 255f. Arithmetic-geometric mean (AGM) method Aitken’s delta squared process 172 917 Aitken’s interpolation algorithm 111 Array AIX (IBM) 4 C style 20, 941 Algorithms, non-numerical 891ff. centered subarray of 122 Aliasing 506, 581 classes 20ff., 25ff., 941, 950, 953 see also Fourier transform constructors 26, 29 All-poles model 578 index range xi, 21 see also Maximum entropy method (MEM) one-dimensional 20 All-zeros model 578 resize function not assumed 23 see also Periodogram size function 26, 30 Allocation of storage 941 three-dimensional 27 Alternating-direction implicit method (ADI) two-dimensional 20 858, 872f., 917 unit-offset xi, 21 Alternating series 172f.
    [Show full text]
  • AN16-LS16 Abstracts
    AN16-LS16 Abstracts Abstracts are printed as submitted by the authors. Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference web: www.siam.org/meetings/ Membership and Customer Service: 800-447-7426 (US & Canada) or +1-215-382-9800 (worldwide) 2 2016 SIAM Annual Meeting Table of Contents AN16 Annual Meeting Abstracts ................................................4 LS16 Life Sciences Abstracts ...................................................157 SIAM Presents Since 2008, SIAM has recorded many Invited Lectures, Prize Lectures, and selected Minisymposia from various conferences. These are available by visiting SIAM Presents (http://www.siam.org/meetings/presents.php). 2016 SIAM Annual Meeting 3 AN16 Abstracts 4 AN16 Abstracts SP1 University of Cambridge AWM-SIAM Sonia Kovalevsky Lecture - Bioflu- [email protected] ids of Reproduction: Oscillators, Viscoelastic Net- works and Sticky Situations JP1 From fertilization to birth, successful mammalian repro- Spatio-temporal Dynamics of Childhood Infectious duction relies on interactions of elastic structures with a Disease: Predictability and the Impact of Vaccina- fluid environment. Sperm flagella must move through cer- tion vical mucus to the uterus and into the oviduct, where fertil- ization occurs. In fact, some sperm may adhere to oviduc- Violent epidemics of childhood infections such as measles tal epithelia, and must change their pattern
    [Show full text]
  • General Index to Volumes 1 and 2
    General Index to Volumes 1 and 2 In this index, page numbers 1 through 934 refer to Volume 1, Numerical Recipes in Fortran 77, while page numbers 935 through 1446 refer to Volume 2, Numerical Recipes in Fortran 90. Front matter in Volume 1 is indicated by page numbers in the range 1/i through 1/xxxi, while front matter in Volume 2 is indicated 2/i through 2/xx. Abstract data types 2/xiii, 1030 Alpha AXP 2/xix Accelerated convergence of series 160ff., Alternating-direction implicit method (ADI) 1070 847, 861f., 906 Accuracy 19f. Alternating series 160f., 1070 achievable in minimization 392, 397, 404 Alternative extended Simpson's rule 128 achievable in root ®nding 346f. American National Standards Institute (ANSI) contrasted with ®delity 832, 840 2/x, 2/xiii CPU different from memory 181 Amoeba 403 vs. stability 704, 729, 830, 844 see also Simplex, method of Nelder and Accuracy parameters 1362f. Mead Acknowledgments 1/xvi, 2/ix Ampli®cation factor 828, 830, 832, 840, 845f. Ada 2/x Amplitude error 831 Adams-Bashford-Moulton method 741 Analog-to-digital converter 812, 886 Adams' stopping criterion 366 Analyticity 195 Adaptive integration 123, 135, 703, 708ff., Analyze/factorize/operate package 64, 824 720, 726, 731f., 737, 742ff., 788, 1298ff., Anderson-Darling statistic 621 1303, 1308f. Andrew's sine 697 Monte Carlo 306ff., 1161ff. Annealing, method of simulated 387f., 436ff., Addition, multiple precision 907, 1353 1219ff. Addition theorem, elliptic integrals 255 assessment 447 ADI (alternating direction implicit) method for continuous variables 437, 443ff., 1222 847, 861f., 906 schedule 438 Adjoint operator 867 thermodynamic analogy 437 Adobe Illustrator 1/xvi, 2/xx traveling salesman problem 438ff., 1219ff.
    [Show full text]
  • Advanced Numerical Analysis
    Advanced Numerical Analysis Lecture Notes Prof. Daniel Kressner EPFL / SB / MATHICSE / ANCHP Spring 2015 May 21, 2015 Remarks • Although not necessary, you may find it helpful to complement these lecture notes with additional literature. These lecture notes are based on material from [DB] P. Deuflhard and F. Bornemann. Scientific computing with ordinary differential equations. Texts in Applied Mathematics, 42. Springer, 2002. [E] F. Eisenbrand. Lecture notes on Discrete Optimization, 2013. Available from http://disopt.epfl.ch/Opt2013. [HLW] E. Hairer, Ch. Lubich, and G. Wanner. Geometric numerical integra- tion. Structure-preserving algorithms for ordinary differential equations. Springer Series in Computational Mathematics, 31. Springer, 2010. [HNW] E. Hairer, S. P. Nørsett, and G. Wanner. Solving ordinary differen- tial equations. I. Nonstiff problems. Second edition. Springer Series in Computational Mathematics, 8. Springer, 1993. [HW] E. Hairer and G. Wanner. Solving ordinary differential equations. II. Stiff and differential-algebraic problems. Second revised edition. Springer Series in Computational Mathematics, 14. Springer-Verlag, Berlin, 2010. [K] C. T. Kelley. Iterative Methods for Optimization. SIAM, 1999. [Kr] J. Krieger. Equations Diff´erentielles Ordinaires, 2014. Lecture notes available from http://pde.epfl.ch/page-44573-en.html. [N] Yu. Nesterov. Introductory Lectures on Convex Optimization. A Basic Course, 2004. [NW] J. Nocedal and S. J. Wright. Numerical optimization. Second edi- tion. Springer Series in Operations Research and Financial Engineering. Springer, 2006. [UU] M. Ulbrich and S. Ulbrich. Nichtlineare Optimierung, Birkh¨auserVer- lag, 2012. Please note: None of these books is needed to prepare for the exam. These lecture notes are entirely sufficient. • Sections or paragraphs marked by a ? contain complementary material that is not part of the exam.
    [Show full text]
  • General Index
    General Index Accelerated convergence of series 166ff. schedule 445 Accuracy 28f. thermodynamic analogy 444f. achievable in minimization 398, 404, 410 traveling salesman problem 445ff. achievable in root ®nding 353 ANSI C standard 2f., 14, 25, 930, 941 contrasted with ®delity 841, 849 ANSI macro 17, 930 CPU different from memory 186 Antonov-Saleev variant of Sobol' sequence vs. stability 710, 736, 839, 853 310ff. Acknowledgments xii Apple xvii Adams-Bashford-Moulton method 749 Macintosh 894 Adams' stopping criterion 373 Approximate inverse of matrix 57 Adaptive integration 129, 141, 709, 714ff., Approximation of functions 105f. 725ff., 733f., 737, 744, 749f., 797 by Chebyshev polynomials 191f., 519 Adaptive Monte Carlo integration 316ff., PadÂe approximant 200ff. 319ff. by rational functions 204ff. Addition, multiple precision 916 by wavelets 601f., 791 Addition theorem, elliptic integrals 262 see also Fitting ADI (alternating direction implicit) method Arguments, conversion of data types 24f., 856, 870f., 915 930 Adjoint operator 876 Arithmetic Adobe Illustrator xiii, xvii arbitrary precision 889, 915ff. Advective equation 835 complex 23f., 948ff. AGM (arithmetic geometric mean) 915 ¯oating point 889 Airy function 210, 240, 250 IEEE standard 285, 890f. routine for 250f. rounding 890 Aitken's delta squared process 166 Arithmetic coding 889, 910ff. Aitken's interpolation algorithm 108 Arithmetic-geometric mean (AGM) method Algorithms, non-numerical 889ff. 915 Aliasing 501, 576 Array see also Fourier transform centered subarray of 119 All-poles model 573 how to allocate 19 see also Maximum entropy method (MEM) All-zeros model 573 index range 18 see also Periodogram one-dimensional 18 Allocation of storage 19, 21f., 940ff. relation to C pointer 18 Alternating-direction implicit method (ADI) three-dimensional 23 856, 870f., 915 two-dimensional 20f.
    [Show full text]
  • Numerical Analysis in Nonlinear Least Squares Methods and Applications
    Department of Electrical and Computer Engineering Numerical Analysis in Nonlinear Least Squares Methods and Applications Christina Nguk Ling Eu This thesis is presented for the Degree of Master of Philosophy (Electrical and Computer Engineering) of Curtin University December 2017 DECLARATION To the best of my knowledge and belief this thesis contains no material previously published by any other person except where due acknowledgment has been made. This thesis contains no material which has been accepted for the award of any other degree or diploma in any university. i ACKNOWLEDGEMENTS I would like to express my special thanks to my main supervisor, Professor Bean San Goh, for his quality guidance, continual encouragement and endless support through- out my MPhil study. During my research, he has provided mewith invaluable academic advice and insightful suggestions and steered me into the right direction whenever I am heading towards the wrong path in my research. The door to his office was always open whenever I ran into a trouble spot or had a problem on my research or writing. He is not only a good supervisor but as a good friend as well. I would also like to thank my co-supervisor, Dr. Hendra Gunawan Harno, for his continual patience, guidance and support throughout my research. He has always been helpful and supportive whenever I faced any academic and administrative issues. He always tried his best to help me by providing any possible assistance. My sincere thanks also goes to my second co-supervisor, Dr. Garenth King Hann Lim, for his support and cooperation throughout my years of study.
    [Show full text]
  • Evaluating and Generalization of Methods of Cyclic Coordinate, Hooke – Jeeves, and Rosenbrock
    Computational Research 2(3): 31-43, 2014 http://www.hrpub.org DOI: 10.13189/cr.2014.020301 Evaluating and Generalization of Methods of Cyclic Coordinate, Hooke – Jeeves, and Rosenbrock Mohammad Ali Khandan, Mehdi Delkhosh* Department of Mathematics and Computer, Damghan University, Damghan, Iran *Corresponding Author: [email protected] Copyright © 2014 Horizon Research Publishing All rights reserved. Abstract In optimization problems, we are looking for simultaneously). The method of Rosenbrock tests m (m is the best point for our problem. Problems always classify to number of optimized decision variables) orthogonal search unary or n-ary with bound or unbound. In this paper, we directions which are equal to coordinate axes only at the first evaluate three methods, Cyclic Coordinate, Hooke – Jeeves, iteration. Rosenbrock search is a numerical optimization and Rosenbrock on n dimensional space for unbounded algorithm applicable to optimization problems in which the problem and we speak about the advantages and objective function is inexpensive to compute and the disadvantages of these three methods. We offer solutions for derivative either does not exist or cannot be computed some disadvantages and we give generalized algorithms to efficiently. improve the methods. Another type of method, namely dynamic programming, has been used extensively in stand management optimization Keywords Golden Section Method, Cyclic Coordinate [8]. It differs from direct search methods so that, instead of Method, Hooke – Jeeves Method, Rosenbrock Method seeking optimal values for continuous decision variables, it finds the optimal sequence of stand states defined by classified values of several growing stock characteristics (for instance, basal area, mean diameter, and stand age).
    [Show full text]
  • Chapter 1 Introduction
    Chapter Intro duction There is scarcely a mo dern journal whether of engineering economics management mathematics physics or the so cial sciences in which the concept optimization is missing from the sub ject index If one abstracts from all sp ecialist p oints of view the recurring problem is to select a b etter or b est Leibniz eventuallyheintro duced the term optimal alternativefromamonganumb er of p ossible states of aairs However if one were to followthehyp othesis of Leibniz as presented in his Theodicee that our world is the b est of all p ossible worlds one could justiably sink into passive fatalism There would b e nothing to improve or to optimize Biology esp ecially since Darwin has replaced the static world picture of Leibniz time by a dynamic one that of the more or less gradual development of the sp ecies culminat ing in the app earance of man Paleontology is providing an increasingly complete picture of organic evolution Socalled missing links rep eatedly turn out to b e not missing but rather hitherto undiscovered stages of this pro cess Very much older than the recogni tion that man is the result or b etter intermediate state of a meliorization pro cess is the seldomquestioned assumption that he is a p erfect end pro duct the pinnacle of cre ation Furthermore long b efore man conceived of himself as an active participantin the development of things he had unconsciously inuenced this evolution There can b e no doubt that his ability and eorts to make the environment meet his needs raised him ab ove other forms of life
    [Show full text]
  • Peer Methods in Optimal Control
    Peer Methods in Optimal Control Vom Fachbereich Mathematik der Technischen Universität Darmstadt zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Dipl.-Math. Dirk Schröder aus Dieburg Tag der Einreichung: 05.02.2016, Tag der Prüfung: 28.04.2016 Darmstadt 2016 — D 17 1. Gutachten: Prof. Dr. Jens Lang 2. Gutachten: Prof. Dr. Stefan Ulbrich Fachbereich Mathematik AG Numerik und Wissenschaftliches Rechnen Peer Methods in Optimal Control Genehmigte Dissertation von Dipl.-Math. Dirk Schröder aus Dieburg 1. Gutachten: Prof. Dr. Jens Lang 2. Gutachten: Prof. Dr. Stefan Ulbrich Tag der Einreichung: 05.02.2016 Tag der Prüfung: 28.04.2016 Darmstadt 2016 — D 17 Für Helene Zusammenfassung In dieser Arbeit werden implizite und linear implizite Peer-Methoden im Kontext der Optimierung mit gewöhnlichen oder partiellen Differentialgleichungen als Nebenbedin- gungen untersucht. In vielen Anwendungsproblemen, wie dem Kühlen von Glas, einer wandernden Flam- menfront in einem gekühlten Kanal, oder dem Härten von Stahl, können die zugrunde liegenden physikalischen Prozesse durch gewöhnliche oder partielle Differentialglei- chungen modelliert werden. Der Wunsch diese Vorgänge zu optimieren, führt zum Feld der optimalen Steuerung mit Differentialgleichungen. In einem Optimierungsalgorithmus müssen die Nebenbedingungen, also in unserem Fall ein System von gewöhnlichen oder partiellen Differentialgleichungen, mehrmals ausgewertet werden. Daher ist eine effiziente Diskretisierung der Differentialgleichun- gen sehr wichtig. Für gewöhnliche Differentialgleichungen und zur Zeitdiskretisie- rung parabolischer partieller Differentialgleichungen werden gerne Runge-Kutta- und Rosenbrock-Methoden benutzt. Allerdings zeigen diese Methoden bei sehr steifen Pro- blemen und bei der Diskretisierung parabolischer Probleme oft nicht die zu erwartende, klassische Konvergenzordnung. Dieses Phänomen wird Ordnungsreduktion genannt. Eine vielversprechende Alternative sind Peer-Methoden.
    [Show full text]
  • Computational Parameter Selection and Simulation of Complex Sphingolipid Pathway Metabolism
    Computational Parameter Selection and Simulation of Complex Sphingolipid Pathway Metabolism A Thesis Presented to The Academic Faculty by Peter A. Henning In Partial Fulfillment of the Requirements for the Degree Master of Science in Biomedical Engineering Department of Biomedical Engineering Georgia Institute of Technology August 2006 Copyright c 2006 by Peter A. Henning To my family, Dale, Christine, and Sara, I couldn’t have made it through these trying times without you. iii ACKNOWLEDGEMENTS I would like to acknowledge Gautam Goel and Eberhard Voit for their useful insights into past, present, and future of Systems Biology. I would like to thank Dr. Al Merrill and his group for not only providing the sphingolipid experimental data but also for providing expertise in both sphingolipids and mass spectometry. I’d like to thank my fellow researchers Jin Young Hong, John Phan, Pushkar Mukewar, David Stiles, and Paul Tan for answering my at times ridiculous questions on software and various other topics. I would like to also thank my fellow BME classmates for making the semesters fulfilling requirements not only tolerable but at times fun. I’d like to extend my gratitude to Bob Lee and Maggie Cam for their insight into what changes were necessary to make myself a successful researcher and inspiring me to take possession of my graduate degree. I would like to extend my thanks to the BME Department, Georgia Tech, Emory, and NIDDK for this opportunity to be part of cutting edge research. Last but certainly not least, I am grateful for the support from all of my friends.
    [Show full text]
  • Economathematics (M.Sc.) Winter Term 2011/2012 Long Version Date: 09.09.2011
    Economathematics (M.Sc.) Winter Term 2011/2012 Long version Date: 09.09.2011 Department of Economics and Business Engineering Department of Mathematics KIT - University of the State of Baden-Wuerttemberg and www.kit.edu National Research Center of the Helmholtz Association Publishers: Department of Economics and Business Engineering Karlsruhe Institute of Technology (KIT) 76128 Karlsruhe www.wiwi.kit.edu Fakultätfür Mathematik Department of Mathematics Karlsruhe Institute of Technology (KIT) 76128 Karlsruhe www.math.kit.edu Contact: [email protected] [email protected] 2 CONTENTS CONTENTS For informational use only. For legally binding information please refer to the german version of the handbook. Contents 1 Studyplan 9 2 Helpful information 23 3 Actual Changes 25 4 Modules 27 4.1 Modules of Mathematics .......................................... 27 Riemannian Geometry- MATHMWAG04.................................. 27 Algebra- MATHMWAG05.......................................... 28 Discrete Geometry- MATHMWAG06.................................... 29 Convex Geometry- MATHMWAG07..................................... 30 Geometric Measure Theory- MATHMWAG08............................... 31 Algebraic Number Theory- MATHMWAG09................................ 32 Algebraic Geometry- MATHMWAG10................................... 33 Geometry of Schemes- MATHMWAG11.................................. 34 Geometric Group Theory- MATHMWAG12................................. 35 Lie Groups and Lie Algebras- MATHMWAG13............................... 36 Metric
    [Show full text]