challenges in the optimization of bio-systems gerhard-wilhelm weber institute of applied...
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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
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 Ankara
CUBIC, Uni Cologne
IAM, METU Ankara
CUBIC, Uni Cologne
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
Conclusion and Perspectives
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
Bad Berleburg,Wemlighausen
Ankara
Bio-Systems
IAM, METU Ankara
CUBIC, Uni Cologne
DNA microarray chip experiments
Comp. Bio. & Med.
anticipation of gene patterns based on
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
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CUBIC, Uni Cologne
least squares – ML
statistical learning
time-contin.
EEME )(
Expression data
time-discr.
kkk EE M1
)(Μ jik em M
Gene Patterns Modeling & Prediction
0)0( EE
Ex.: Euler, Runge-Kutta
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For which parameters, i.e., for which set M (or: dynamics), is stability guaranteed ?
Def.: M is stable : B : (compl.) bounded neighbourhood of ,n
M : 110 M,...,M,M, mΙΝm
.)M...MM( 021 mm
development of processits feasibilitygoodness-of-fit (model) test
Gene Patterns Model. & Pred.
IAM, METU Ankara
CUBIC, Uni Cologne
Analysis with Polytopes
Theorem (Brayton, Tong 1979) :
Given a set M : of m distinct complex matrices.
Then,
M is stable is bounded .
0B n0
:kB H
,mod)1(: mkk H : convex hull .
kk
BB
0
* U
,M 1'0
kik
iBU
0 1M ,...,Mm
Here, is a bounded neighbourhood of ,
and for k > 0
where
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The ‘‘discrete” power of the algorithm is based on using
polyhedra and focussing on the extremal points
of the sets .
kB
kB
Theorem 1 : If z is an extremal point of , then there
exist and an extremal point u of , such that
z
kB
0j
.M uj
k
1kB
Extremal Points
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Construction Principle
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Stopping Criterion
Theorem 2 :
Let ( as above,
Then,
}).,...,2,1{M riuz ijki
1 1{ } M { } 1,2,..., .r k k i rz ,...,z B z z ,...,z i r H H
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Construction Principle
stability
unboundedBBB k 00
dynamicsmatricesof
boundedBB
kstepatstopping
kkBB ii
kk
/
,
,)(""
)(0
0
00U
stability
in
Gebert, Laetsch, Pickl, W., Wünschiers 2005
Ergenç, W. 2004
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Numerical Example
Ex. (Pickl 1999) :
M = }M,M{ 10 ,0
1M0
b
a
0
10M1 b
algorithm
instability
region of stability
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CUBIC, Uni Cologne
A
)()()()(
)()()()(
)()()()(
)()()()(
34333231
24232221
14131211
04030201
tEtEtEtE
tEtEtEtE
tEtEtEtE
tEtEtEtE
080170255
25570180255
050200255
2550250255
2001
039.02.00
0061.04.0
0000
M
Gene Network
Ex. : 1
h kEME
Ė 4Ė 2
Ė 0
Ė 5
Ė 1
Ė 3
0123456789
0 2 4 6 8
Time, t
Ex
pre
ss
ion
lev
el,
Ė
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Gene Network
gene2
gene3
gene1
gene4
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0.4 x1
0.2 x2 1 x1
Comp. Bio. & Med.
F.B. Yilmaz 2004
: exper. data
: approx. increase/decrease
Ex.:
nonlinearities
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Inference of Gene Regulatory Networks
genes mRNA proteins
disintegration disintegration
protein complexes
cellularprocesses
Gene transcription also regulates the transcription factors defining a dynamic regulatory network involving highly nonlinear feedback mechanisms.
externalfactors
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CUBIC, Uni Cologne
Proposed Model Class
)()( )(M)1( ksks bkEkE
else0
)(if1))((
))1(()(
iii
B
kEkEQ
kEQFks
ipi
p
qEEEQ
tEtEtEQFts
,...,1,0),...,,(
)))(),...,(),((()(121
1
piecewise linear:
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Akhmet, Gebert, Pickl, Öktem, W. 2004
Gebert, Radde, W. 2004
Dynamics and Variation
population dynamics
M.U. Akhmet , V. Tkachenko H. Öktem, S.W. Pickl, W., et al.
gene dyn. & variation
I. Togan A. Kence C. Berkman et al.
et al.
with delay and impulse
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time
( ) ( , ( ), ([ ]))E t f t E t E t
anticipation
... Tomography
inverse problems
Ö. Yaşar, O. Özgür, W.
C. Diner, A. DoğanF. Özbudak, A. Tiefenbach
M. Eyüboğlu, N. Gençer Y. Serinağoğlu, A. KurtS. Sarıkaya, W.
VLSI chip design
medicial imaging
inverse
Discrete ...
Brain / Heart ...
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Metabolic Engineering
object oriented
modules
DAE ODE
training program
math. modeling
parameter estimation
sports (and general) medicine
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A. Schulte Thomas 2004
S. Özöğür 2005
Generalized Semi-Infinite Opt.
I, K, L finite
2C
W. 2003
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Reverse Chebychev Approx.
Ex.: approx. of a thermo-couple characteristic Hoffmann, Reinhard
thermo-couple f (y) : spline of polynomials with deg. 3 – 13, on [a,b]
to be approx. by :
bounds on error
some interpol.
(= y)
Bernhard
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Reverse Chebychev Approx.
Ex.: approx. of a thermo-couple characteristic
thermo-couple f (y) : spline of polynomials with deg. 3 – 13, on [a,b]
to be approx. by :
bounds on error
some interpol.
(= y)
IAM, METU Ankara
CUBIC, Uni Cologne
Reverse Chebychev Approx.
Ex.: approx. of a thermo-couple characteristic
thermo-couple f (y) : spline of polynomials with deg. 3 – 13, on [a,b]
to be approx. by :
bounds on error
some interpol.
(= y)
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time
Time-Optimal Control
r R
B
Ex.: time-minimal cooling (or heating) of
!0 T
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Anticipation
Ex.’s.: thermo-regulation
control of earth warming
Pickl, W.
),,( txr local-global
anticipation
maximization of time-horizon longest term approximation / description
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TEM Model
Z. Alparslan
B. K., W.
S.W. Pickl
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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 Management H. Körezlioğlu et al.
ValidiertesEmissionsreduktions-
projekt
common learning
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improvement of living conditions learning
modeling
optimization
data mining
Sustainable Living
D. DeTombe, A., I., H. Gökmen
S. Kayalığil, M., Y. Ecevit
T. Bali, W. et al.
IAM, METU Ankara
CUBIC, Uni Cologne
Balaban Valley
METU
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Turkey
Conclusions and Perspectives
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CUBIC, Uni Cologne
Association of European
Operational Research Societies
Operations Research Society
of Germany
EURO Working Group
on Continuous Optimization
Operations Research Society
of Israel
Operations Research
Society of Turkey
Operations Research Society
of Hungary
EURO XXI in Iceland July 2-5, 2006
21st European Conference on Operational Research
OR for Better Management of Sustainable Development
5th EUROPT Workshop
“Advances in
Continuous Optimization”
Reykjavik, Iceland
June 29 – July 1, 2006
Conclusions and Perspectives
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CUBIC, Uni Cologne
EURO Summer Institute
“Optimization Challenges in Engineering: Methods, Software, and Applications”
Wittenberg, Germany August 18 – September 2, 2006
Earth Institute
Young People for OR in Developing Countries
Balaban Valley Project
to
EURO Working Group
in Continuous Optimization
http://www.iam.metu.edu.tr/EUROPT/
and Computational Biology and Medicine Group
Sincere invitation ...
http://www.iam.metu.edu.tr/research/groups/compbio/index.html
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CUBIC, Uni Cologne
two new EURO WGs planned:
Computational Biology & Bioinformatics
OR for Development