1 / 42

Challenges in the Optimization of Bio-Systems Gerhard-W ilhelm Weber

Challenges in the Optimization of Bio-Systems Gerhard-W ilhelm Weber Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey http://www.iam.metu.edu.tr/research/groups/compbio/index.html.

seven
Download Presentation

Challenges in the Optimization of Bio-Systems Gerhard-W ilhelm Weber

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Challenges in the Optimization of Bio-Systems Gerhard-Wilhelm Weber Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey http://www.iam.metu.edu.tr/research/groups/compbio/index.html IAM, METU AnkaraCUBIC, Uni Cologne

  2. Content • Motivation: Bio-Systems • Computational Biology • Modeling and Prediction of Gene Expression Patterns • Population Dynamics, Gene Dynamics and Variation • Optimization • Computational Metabolism, Medicine and Tomography • Earth Warming and Sustainable Development • Conclusionand Perspectives IAM, METU AnkaraCUBIC, Uni Cologne

  3. Bio-Systems Bad Berleburg, Wemlighausen IAM, METU AnkaraCUBIC, Uni Cologne

  4. Bio-Systems Bad Berleburg, Wemlighausen IAM, METU AnkaraCUBIC, Uni Cologne

  5. Bio-Systems Bad Berleburg, Wemlighausen IAM, METU AnkaraCUBIC, Uni Cologne

  6. Bio-Systems Bad Berleburg, Wemlighausen IAM, METU AnkaraCUBIC, Uni Cologne

  7. Bio-Systems Bad Berleburg, Wemlighausen IAM, METU AnkaraCUBIC, Uni Cologne

  8. Bio-Systems Bad Berleburg, Wemlighausen IAM, METU AnkaraCUBIC, Uni Cologne

  9. Bio-Systems Bad Berleburg, Wemlighausen IAM, METU AnkaraCUBIC, Uni Cologne

  10. Bio-Systems Bad Berleburg, Wemlighausen IAM, METU AnkaraCUBIC, Uni Cologne

  11. Bio-Systems Bad Berleburg, Wemlighausen Ankara IAM, METU AnkaraCUBIC, Uni Cologne

  12. Bio-Systems IAM, METU AnkaraCUBIC, Uni Cologne

  13. Comp. Bio. & Med. anticipationof gene patterns based on DNA microarraychip experiments M.U. Akhmet, H. Öktem S.W. Pickl, E. Quek Ming Poh T. Ergenç, B. Karasözen J. Gebert, N. Radde, W. Ö. Uğur, R. Wünschiers M. Taştan, F.B. Yılmaz IAM, METU AnkaraCUBIC, Uni Cologne

  14. Gene Patterns Modeling & Prediction least squares – ML statistical learning time-contin. Expression data time-discr. Ex.: Euler, Runge-Kutta M IAM, METU AnkaraCUBIC, Uni Cologne

  15. Gene Patterns Model. & Pred. For which parameters, i.e., for which setM(or: dynamics), isstabilityguaranteed ? development of process its feasibility goodness-of-fit (model) test Def.:Mis stable : B : (compl.) bounded neighbourhood of M : IAM, METU AnkaraCUBIC, Uni Cologne

  16. Analysis with Polytopes Theorem(Brayton, Tong 1979): Given a set M: of m distinct complexmatrices. Then, M is stable is bounded . Here, is a bounded neighbourhoodof , and for k > 0 where H H: convex hull . IAM, METU AnkaraCUBIC, Uni Cologne

  17. Extremal Points The ‘‘discrete”power of the algorithm is based on using polyhedra and focussing on the extremal points of the sets . Theorem 1 :If z is an extremalpoint of , then there existand an extremal point u of , such that z IAM, METU AnkaraCUBIC, Uni Cologne

  18. Construction Principle IAM, METU AnkaraCUBIC, Uni Cologne

  19. Stopping Criterion Theorem 2 : Let ( as above, Then, IAM, METU AnkaraCUBIC, Uni Cologne

  20. Construction Principle stability in Gebert, Laetsch, Pickl, W., Wünschiers 2005 Ergenç, W. 2004 IAM, METU AnkaraCUBIC, Uni Cologne

  21. Numerical Example Ex.(Pickl 1999): M = region of stability algorithm instability IAM, METU AnkaraCUBIC, Uni Cologne

  22. Gene Network Ex. : IAM, METU AnkaraCUBIC, Uni Cologne

  23. Gene Network 0.4x1 gene1 gene2 0.2 x2 1 x1 gene3 gene4 IAM, METU AnkaraCUBIC, Uni Cologne

  24. Comp. Bio. & Med. F.B. Yilmaz 2004 nonlinearities Ex.: : exper. data : approx. increase/decrease IAM, METU AnkaraCUBIC, Uni Cologne

  25. Inference of Gene Regulatory Networks disintegration disintegration cellular processes genes mRNA proteins external factors protein complexes Gene transcription also regulates the transcriptionfactors defining a dynamic regulatory network involving highly nonlinearfeedback mechanisms. IAM, METU AnkaraCUBIC, Uni Cologne

  26. Proposed Model Class piecewise linear: Akhmet, Gebert, Pickl, Öktem, W. 2004 Gebert, Radde, W. 2004 IAM, METU AnkaraCUBIC, Uni Cologne

  27. population dynamics M.U. Akhmet , V. Tkachenko H. Öktem, S.W. Pickl, W., et al. genedyn.&variation I. Togan A. Kence C. Berkman et al. et al. Dynamics and Variation with delay and impulse anticipation time IAM, METU AnkaraCUBIC, Uni Cologne

  28. inverse ... Tomography Discrete ... Ö. Yaşar, O. Özgür, W. C. Diner, A. Doğan F. Özbudak, A. Tiefenbach M. Eyüboğlu, N. Gençer Y. Serinağoğlu, A. Kurt S. Sarıkaya, W. VLSI chip design medicial imaging Brain / Heart ... inverse problems IAM, METU AnkaraCUBIC, Uni Cologne

  29. Metabolic Engineering math. modeling parameter estimation sports (and general) medicine object oriented modules DAE ODE training program A. Schulte Thomas 2004 S. Özöğür 2005 IAM, METU AnkaraCUBIC, Uni Cologne

  30. Generalized Semi-Infinite Opt. I, K, L finite W. 2003 IAM, METU AnkaraCUBIC, Uni Cologne

  31. Reverse Chebychev Approx. Ex.:approx. of a thermo-couple characteristic Hoffmann, Reinhard thermo-couple f(y) : splineof polynomials with deg. 3 – 13, on [a,b] to be approx. by : bounds on error some interpol. Bernhard (= y) IAM, METU AnkaraCUBIC, Uni Cologne

  32. Reverse Chebychev Approx. Ex.:approx. of a thermo-couple characteristic thermo-couple f(y) : splineof polynomials with deg. 3 – 13, on [a,b] to be approx. by : bounds on error some interpol. (= y) IAM, METU AnkaraCUBIC, Uni Cologne

  33. Reverse Chebychev Approx. Ex.:approx. of a thermo-couple characteristic thermo-couple f(y) : splineof polynomials with deg. 3 – 13, on [a,b] to be approx. by : bounds on error some interpol. (= y) time IAM, METU AnkaraCUBIC, Uni Cologne

  34. Time-Optimal Control Ex.:time-minimalcooling (orheating)of B r R IAM, METU AnkaraCUBIC, Uni Cologne

  35. Anticipation Ex.’s.:thermo-regulation control of earth warming Pickl, W. local-global maximizationof time-horizonlongest term approximation / description anticipation IAM, METU AnkaraCUBIC, Uni Cologne

  36. TEM Model S.W. Pickl Z. Alparslan B. K., W. IAM, METU AnkaraCUBIC, Uni Cologne

  37. JET EU project application “Joint International Emissions Trading, Analysis, Forecast, and Optimal Strategies in Sustainable Low Carbon Energy Management” U. Leopold-W., B. K., S.W. P., M. Türkay, W. Risk ManagementH. Körezlioğlu et al. common learning IAM, METU AnkaraCUBIC, Uni Cologne

  38. Sustainable Living Balaban Valley improvement of living conditionslearning modeling optimization data mining D. DeTombe, A., I., H. Gökmen S. Kayalığil, M., Y. Ecevit T. Bali, W. et al. IAM, METU AnkaraCUBIC, Uni Cologne

  39. Turkey METU IAM, METU AnkaraCUBIC, Uni Cologne

  40. Conclusions and Perspectives Operations Research Society of Hungary Operations Research Society of Israel Association of European Operational Research Societies Operations Research Society of Turkey Operations Research Society of Germany EURO Working Group on Continuous Optimization IAM, METU AnkaraCUBIC, Uni Cologne

  41. Conclusions and Perspectives 5th EUROPT Workshop “Advances in Continuous Optimization” Reykjavik, Iceland June 29 – July 1, 2006 EURO Summer Institute “Optimization Challenges in Engineering: Methods, Software, and Applications” Wittenberg, Germany August 18 – September 2, 2006 OR for Better Management of Sustainable Development EURO XXI in IcelandJuly 2-5, 200621st European Conference on Operational Research Earth Institute Young People for OR in Developing Countries Balaban Valley Project IAM, METU AnkaraCUBIC, Uni Cologne

  42. Sincere invitation ... to EURO Working Group in Continuous Optimization http://www.iam.metu.edu.tr/EUROPT/ andComputational Biology and Medicine Group two new EURO WGs planned: Computational Biology & Bioinformatics OR for Development http://www.iam.metu.edu.tr/research/groups/compbio/index.html gweber@metu.edu.tr IAM, METU AnkaraCUBIC, Uni Cologne

More Related