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forum.math.uoa.gr • Προβολή θέματος - Διδακτορικό με υποτροφία στη Γαλλία

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 Θέμα δημοσίευσης: Διδακτορικό με υποτροφία στη Γαλλία
ΔημοσίευσηΔημοσιεύτηκε: 11 Απρ 2017, 18:01 
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Εγγραφή: 09 Δεκ 2014, 14:11
Δημοσ.: 51
Ακολουθεί μία δυνατότητα διδακτορικού στη Γαλλία με υποτροφία από το Σεπτέμβρη 2017.
H υποτροφία είναι για τρία χρόνια ύψους περίπου 1700 ευρώ (καθαρά)
Οι ενδιαφερόμενοι μπορούν να επικοινωνήσουν μαζί μου μέχρι τις 23 Απριλίου (τα χρονικά όρια είναι στενά) στο strevezas@math.uoa.gr
όπου θα χρειαστεί και ένα βιογραφικό στα Αγγλικά για να εξεταστεί η καταλληλότητα της υποψηφιότητας.
Η υποτροφία αυτή δίνεται απο την grande ecole CentraleSupelec στη Γαλλία μέσα απο διαγωνισμό, και
η πιθανότητα επιτυχίας θα είναι πιο μεγάλη όσο καλύτερο είναι το προφίλ του υποψηφίου.
Οι απαιτήσεις είναι κάποια εξοικείωση με στοχαστική και στατιστική μοντελοποίηση και μία
όρεξη για προγραμματισμό. Οι ενδιαφερόμενοι θα πρέπει να έχουν με το τέλος αυτής της ακαδημαικής
χρονιάς ένα μεταπτυχιακό σε συναφή κλάδο με το θέμα της διατριβής (Στατιστική, Βιοστατιστική, Εφαρμοσμένα Μαθηματικά, Βιοπληροφορική, Επιστήμη Δεδομένων, ή άλλο συναφές). Αν το μεταπτυχιακό είναι διετές τότε η υποψηφιότητα ενός πρωτοετούς φοιτητή θα εξεταστεί κατά περίπτωση.

Title : Parameter Estimation for Stochastic models of Protein Reaction

PhD Supervision: Paul-Henry Cournede, Paolo Ballarini
Laboratory: MICS Lab (Mathematiques et Informatique pour la Com-
plexite et les Systemes), CentraleSupelec, France.

PhD Co-supervision: Samis Trevezas, National and Kapodistrian Uni-
versity of Athens

1 Summary
The PhD objective is to develop parameter estimation methods and algo-
rithms for a class of stochastic dynamic models in biology. Among several
possibilities, the generalised semi-Markov Processes (GSPM) offer a very
versatile modeling approach for the stochastic dynamics of the system and
Sequential Monte-Carlo Approximate Bayesian Computation (SMC-ABC)
promising perspectives for parameter estimation in these type of models.
A real-case biological study will also be conducted for a model of protein
reaction (Wnt pathway) in collaboration with Hopital Debre (Paris).
2 Context
A reaction network is a chemical system involving several potential reactions
(say R) among different chemical species (say M). If an M-dimensional state
vector X(t) represents the number of molecules of each species (for example,
proteins) at time t, then the simplest modeling approach is to assume that
(X(t)) evolves as a continuous time Markov chain (CTMC, Gillespie (2007)).
A transition takes place when a reaction occurs and the transition rates of
the Markov chain are in correspondence with the intensities (mass kinetic
rates) of the chemical reactions (see, e.g., Anderson and Kurtz (2011) for
a mathematical survey of this modeling approach). Each intensity is mod-
eled by a state dependent and reaction specific function and is assumed
to be proportional to one kinetic rate constant, characterizing the speed
of interaction. These proportionality constants are generally unknown and
have to be estimated from the data Y which correspond to measurements
[unparseable or potentially dangerous latex formula] at speci c time epochs
[unparseable or potentially dangerous latex formula] .
If the system is very frequently observed, then the estimation problem is eas-
ier and approximate maximum likelihood or Bayesian type inference meth-
ods have already been proposed (e.g., Reinker et al. (2006), Boys et al.
(2008)). However, in several cases of interest the state space of (X(t))
could be prohibitively large and/or much information could be lost from
unobserved transitions. Since the resulting data are incomplete, Angius
and Horvath (2011) proposed a Monte Carlo Expectation-Maximization
(MCEM, Wei and Tanner (1990)) algorithm to make parameter estimation
feasible by formulating the model as an incomplete data model. Neverthe-
less, the application of this method was limited to very simple situations
and involved several approximations. Additionally, the underlying assump-
tion that (X(t)) evolves as a CTMC is very restrictive, since it implies
exponentially distributed sojourn times in the different states of the system.
Generalised semi-Markov processes (GSMP, e.g., Whitt (1980)) is a fairly
general class of stochastic processes, which include semi-Markov processes
and Markov Regerative Processes (MRP) as a special case, and are among
the most promising stochastic processes for modeling complex phenomena
which can be described as stochastic event-driven systems. They have been
applied successfully in operations research, including queuing networks (e.g.,
Barbour (1982)) and seem very appropriate to model the complexity of bi-
ological phenomena. Each occupied state is associated with some possible
events and the sojourn time in the current state as well as the next visited
state depend on which event occurs first.
3 Research Objective
In such a context, the objective of this project is to make a more general
formulation of protein reaction models by using the GSMP approach and to
develop the proper estimation methodology adapted to this kind of models.
Promising perspectives from this point of view are offered by likelihood-
free methods, among which the Approximate Bayesian computation theory
proposes an effcient and versatile framework (Marin et al. (2012)). ABC
methods have been successfully used for biological dynamical systems (see,
e.g., Toni et al. (2009) or more recently Koutroumpas et al. (2016)) modelled
as deterministic systems of ordinary dierential equations. The PhD work
will extend the ABC methodology to stochastic models of protein reactions,
develop the proper computational tools and test the methods to a real-case
biological study.

4 Methods
The first step of the project will concern the implementation and simulation
of the stochastic reaction system. This implementation will be done in the
frame of the Pygmalion platform (Cournede et al. (2013)). One objective
will be to develop a generic formalism for this type of model in the platform.
This phase will also include a feasibility study concerned with the possibil-
ity of extending the MCEM algorithm of Angius and Horvath (2011) to less
constrained classes of stochastic processes, that is, in increased level of gen-
erality, semi-Markov Chains (SMC), Markov Regenerative Processes (MRP)
and Generalized semi-Markov Processes (GSMP).
The second phase will consist in studying the extension of the ABC method-
ology to stochastic models like CTMC and to the aforementioned classes of
stochastic processes, that is, SMC, MRP and GSMP. The adaptive Sequen-
tialMonte-Carlo ABC proposed by DelMoral et al. (2012) seems particularly
adapted for this purpose.
Regarding the dimension and complexity of the system, the computational
aspects are also critical issues. Therefore, we will also consider the com-
putational performances of the methods, and their portability on high-
performance computing architectures, namely parallel CPU and GPU, using
the computing mesocentre of CentraleSupelec - ENS Paris-Saclay for this
purpose.
Finally, the methods will be tested on a relevant biological case study, that is
a model of the Wnt pathway (Mazemondet et al. (2012)), i.e., a fundamental
molecular mechanism believed to be involved in white matter pathologies
of preterm infants. The parameter estimation tools developed as result of
this project will be tested against actual experimental data resulting from
measurements performed on cell cultures performed by Dr. Pierre Gressen's
team of the H^opital Debre Paris.
5 Collaborations
The collaborators of this project will principally involve a medical research
institute which will participate to the project by providing data at cellular
level and defining biological issues of interest.
Dr. Pierre Gressen, Hopital Debre Paris
Dr. Sophie Helaine, Imperial College London, Department ofMedicine,
MRC Centre for Molecular Bacteriology and Infection.
Dr. Tommaso Mazza, Institut CSS Mendel, Roma

References
D. F. Anderson and T. G. Kurtz. Continuous time markov chain models
for chemical reaction networks. In Design and analysis of biomolecular
circuits, pages 3-42. Springer, 2011.
A. Angius and A. Horvath. The monte carlo em method for the parameter
estimation of biological models. Electronic Notes in Theoretical Computer
Science, 275:23-36, 2011.
A. Barbour. Generalized semi-markov schemes and open queueing networks.
Journal of Applied Probability, 19(02):469-474, 1982.
R. J. Boys, D. J. Wilkinson, and T. B. Kirkwood. Bayesian inference for
a discretely observed stochastic kinetic model. Statistics and Computing,
18(2):125-135, 2008.
P.-H. Cournede, Y. Chen, Q. Wu, C. Baey, and B. Bayol. Development and
evaluation of plant growth models: methodology and implementation in
the pygmalion platform. Mathematical Modelling of Natural Phenomena,
8(04):112-130, 2013.
P. Del Moral, A. Doucet, and A. Jasra. An adaptive sequential monte carlo
method for approximate bayesian computation. Statistics and Computing,
22(5):1009-1020, 2012.
D. T. Gillespie. Stochastic simulation of chemical kinetics. Annu. Rev. Phys.
Chem., 58:35-55, 2007.
K. Koutroumpas, P. Ballarini, I. Votsi, and P.-H. Cournede. Bayesian pa-
rameter estimation for the wnt pathway: an infinite mixture models ap-
proach. Bioinformatics, 32(17):i781-i789, 2016.
J.-M. Marin, P. Pudlo, C. P. Robert, and R. J. Ryder. Approximate bayesian
computational methods. Statistics and Computing, pages 1-14, 2012.
O. Mazemondet, M. John, S. Leye, A. Rolfs, and A. M. Uhrmacher. Elu-
cidating the sources of β-catenin dynamics in human neural progenitor
cells. PLOS-One, 7(8):1-12, 2012.
S. Reinker, R. Altman, and J. Timmer. Parameter estimation in stochastic
biochemical reactions. IEE Proceedings-Systems Biology, 153(4):168-178,
2006.
T. Toni, D. Welch, N. Strelkowa, A. Ipsen, and M. P. Stumpf. Approximate
bayesian computation scheme for parameter inference and model selection
in dynamical systems. Journal of the Royal Society Interface, 6(31):187-
202, 2009.

G. C. Wei and M. A. Tanner. A monte carlo implementation of the em
algorithm and the poor man's data augmentation algorithms. Journal of
the American statistical Association, 85(411):699-704, 1990.
W. Whitt. Continuity of generalized semi-markov processes. Mathematics
of operations research, 5(4):494-501, 1980.


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