All Years Seminars
[INMA] 2005-11-15 (14.00 pm) : Spread of Diseases in Large Social Networks
At Auditoire Euler
Speaker :
de Kerchove D'Exaerde, Cristobald
Abstract :
This talk gives an overview of the analysis of a real
large phone calls networks. In those networks, nodes
are handsets and connections are calls, moreover its
connections change over time and each node has some evolving state.
Such a network has several interesting properties that will be discussed
like its Scale Free shape and the dynamicity of the states. The main part
will concern the identification of influent nodes in the spread of technology.
These nodes are called the leaders, and we use the background of the mathematical
theory of infectious diseases to describe the process. Three methods will be
exposed: first the algorithm of S. Brin and L. Page used by google for its Page
Rank, second an algorithm based on similarity between two graphs, and third the
definition of Social Leader. Eventually, some results will conclude the presentation.
[INMA] 2005-11-08 (14.00 pm) : Non-Negative Matrix Factorizations and Graph Clustering
At Auditoire Euler
Speaker :
Diep Ho (CESAME)
Abstract :
We present a method to approximate a non-negative matrix A by a low-rank
product UV whose factors U and V are also non-negative.
This kind of approximation is useful in applications such as face learning
and recognition, and in clustering of non-negative data.
In particular, we will focus on the application of this method to the problem
of Graph Clustering where vertices of a graph are to be grouped
into clusters with high connectivity within each cluster and low connectivity
across clusters.
We present some promising results and mention some open problems.
[INMA] 2005-10-25 (14.00 pm) : Irrigation multi-reaches regulation problem by internal model boundary control
At Auditoire Euler
Speaker :
Valérie Dos Santos (CESAME)
Abstract :
Irrigation canals regulation problem is a practical and theorical interesting problem since many decades. Many
researches deal with this control problem and, various and different approaches in modelling control were and
are used to study open surface hydraulics systems.
This paper deals with the regulation problem which is stated as a multi-reaches (several reaches in cascade)
boundary control of the nonhomogeneous hyperbolic Saint-Venant Partial Differential Equation (pde). The Internal
Model Boundary Control (IMBC) has been already used in linear control of infinite dimensional systems
describing a real plant, and for nonlinear predictive control for distributed real plant. It is extended here to
multivariable boundary control for hyperbolic systems. Moreover, spatial dependency of the operators parameters
is taken account in the regulation model around an equilibrium state.
Control synthesis and closed loop stability are done using the standard infinite dimensional operators and
semigroup perturbation theory. In this approach, the open loop system need to be carefully characterized, i.e.
the operator and associated semigroup have to be characterized and all properties to be conserved (exponential
stability e.g.) must be carried out. Finally, experimental results from Valence experimental micro-channel show
that this approach is suitable for more realistic situation.
[INMA] 2005-10-18 (14.00 pm) : Dynamical analysis of Plug Flow bioreactor nonlinear model
At Auditoire Euler
Speaker :
Abdou Dramé (CESAME)
Abstract :
This work deals with dynamical analysis of a
Plug Flow bioreactor in which occurs a growth reaction
(biomass/substrate). The dynamical modelling is based
on mass balance principles which leads to a system of
two autonomous partial differential equations. After a
linear change of variables, we prove that this system
is equivalent to an asymptotically autonomous
semilinear parabolic equation. We obtain convergence
result of solutions of the nonautonomous equation to
equilibrium solutions of its limit equation. In
addition the existence of multiple equilibrium
solutions is analyzed. The stress is laid on the non
monotonicity of the kinetic function and we prove that
the Plug Flow reactor can have one or multiple
equilibrium profiles according to the axial dispersion
and transport parameters. Numerical simulations
illustrate the bifurcation phenomena of the system.
The stability analysis of such equilibria proves that
in non degenerescence case, they are alternatively
stable, unstable, stable, etc.
[INMA] 2005-10-13 (17.00 pm) : Colloque MAPA/CESAME - Zariski-dense subgroups and number theory
At CYCL 01
Speaker :
Gopal Prasad (University of Michigan)
Abstract :
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