A one-day workshop
The Lab of Mathematics of Le Havre university (LMAH), supported by several structures
(Federation Normandy Mathematics FR-CNRS-3335 FNM ,
the ISCN ,
the High-Normandie region R-HN,
and by a network of researchers from Normandy), develops as a
unifying theme: complex systems, in particular dynamical systems and applications to the living systems,
(Brain dynamics, Ecosystems, ...).
It organizes regularly workshops on these topics.
By the day of Thursday, May 16, 2013, the speakers come from different institutions:
-- Brain Day --
-- La Journée du Cerveau --
- CHAVEZ Mario (CNRS-UMR 7225, Institute for Brain and Spinal Cord, Paris, http://cogimage.dsi.cnrs.fr/oldsite/equipes/adn/index.htm),
- DEMONGEOT Jacques (AGIM CNRS/UJF 3405, Faculté de Médecine, Univ. J. Fourier Grenoble I, France, http://membres-timc.imag.fr/Jacques.Demongeot/),
- FRANCOISE Jean-Pierre (Prof. Laboratoire J.-L. Lions, UMR 7598 CNRS, Paris-6, http://www.ann.jussieu.fr/~francoise/),
- JIRSA Viktor, (DR-CNRS, Institut de Neurosciences des Systèmes, Aix-Marseille,
- KRUPA (Martin) Maciej (INRIA, Paris Roquencourt Centre, https://who.rocq.inria.fr/Maciej.Krupa/index.html)
- POPOVIC Nikola (School of Math. & Maxwell Institute of Math.Sciences
Univ. Edinburgh, UK, http://www.maths.ed.ac.uk/~npopovic/)
You are cordially invited to participate in this one-day workshop, scheduled on 16th May, 2013,
(09h45 - 17h15).
The workshop is FREE, .
Location of Le Havre University:
University of Le Havre, UFR-ST, LMAH (Applied Math Lab.),
25 Rue Philippe Lebon, Le Havre, France.
The university is located 5 minutes walk from the train station
(plan to go to ULH university or Kyriad hotel HERE.
See train schedules at the bottom of this page).
- Neuroscience (multidisciplinary approach, mainly theoretical, but also experimental)
- Brain dynamics and mathematical modeling,
- Brain network dynamics and complex systems
- 09h00 : Welcome, Coffee, (posters)
- 10h10-10h55, FRANCOISE Jean-Pierre (Lab. J.-L. Lions, UMR 7598 CNRS, Paris-6)
Title: Dip and Buffering in a fast-slow system associated to Brain Lactate Kinetics
Abstract: This is a joint work with M. Lahutte-Auboin, R. Costalat and R. Guillevin.
This work is devoted to a mathematical analysis of a fast-slow impulsive system with control inspired
by a physiological model introduced by A. Aubert, R. Costalat, P. Magistretti and L. Pellerin(2005).
The model is based on transport theory through membranes from capillary to an extracellular compartment
with a control term which yields the exchange with an intracellular compartment. The methods are quite
classical (existence of a slow manifold, averaging theory) although they are applied to a less classical
situation (perturbation of an integrable impulsive dynamics). It is interesting to note that the mathematical
interpretation fits quite well the experimental results obtained by Hu and Wilson, further confirmed
by IRMf imaging techniques.
- 10h55-11h40, JIRSA Viktor (DR-CNRS, Institut de Neurosciences des Systèmes, Aix-Marseille)
Title: Invariances and bifurcations of epileptic seizures
Despite many decades of research to identify mechanisms and treatments for specific epileptic pathologies,
many patients continue to have unpredictable and uncontrolled seizures. The lack of a clear understanding
of the nature of seizures contributes to the challenge of improving clinical care. Here, we analyzed
seizure dynamics mathematically to identify characteristics that are conserved across many different
syndromes, brain regions, and species. We characterized the onset, time course, and offset of focal
seizures in humans, rodents and zebrafish. We found that focal seizures necessitate a DC baseline
shift at onset and logarithmic scaling of interspike intervals at offset. This enabled us to build
a general phenomenological model of seizure dynamics composed of five state variables. We then
identified possible biophysical correlates of these state variables, and verified the theoretical
predictions experimentally. Finally, we found how seizure onset can be reached via very different
routes, which may explain why seizures are difficult to treat and predict. Our results demonstrate
that seizures are a simple form of activity, generic to different neuronal networks across species.
Seizure threshold is defined by the interaction and distance between the current brain state
and a permittivity variable, both of which are dynamic processes. Seizure susceptibility
is thus affected by various internal and external factors that are present under many
different conditions, a concept that may become central to the design of future anti-seizure
- 11h40-12h25, CHAVEZ Mario (CNRS-UMR 7225, Institut du Cerveau et de la Moelle Epinière, Institute for Brain and Spinal Cord, Paris)
Title: Simple introduction to complex brain networks
In the last years, network science has became a comprehensive framework to investigate, model and understand
the structure and function of the complex interaction patterns observed in diverse biological, physical,
social and technological systems. In neurosciences, experimental works have recently suggested that brain
connectivity can be modeled as networks, i.e. mathematical objects whose nodes represent different brain
regions and links stand for functional or anatomical connections between them. I'll present provide a an overview
of how this general framework, known as complex network theory, and I'll introduce various metrics to characterize
the wiring structure at both local (the neighborhood of a node) and global (full network) level. I'll show how
network theory provides a robust tool allows anyone to classify in a simple and straight way the functional
brain network and to compare connectivity patterns obtained from different pathological and cognitive states.
- 12h25 - 14h10 : lunch (at your expense, except for speakers,
but the brewery's canteen is very good and cheap)
- 14h10-14h55, DEMONGEOT Jacques (AGIM CNRS/UJF 3405, Faculté de Médecine, Grenoble)
Title: Robustness in Neural and Genetic Regulatory Networks: Mathematical Approach and Biological Applications
Abstract: Numerous indices of complexity are used in biological networks like the number of their components,
their connectivity, or the number of the strong connected components of their interaction graph. Concerning the
stability and robustness of a biological network, they correspond to its ability to respectively recover the same
asymptotic dynamics or keep invariant the number and nature of attractors, from dynamical or structural disturbances.
The complexity will be quantified here by the evolutionary entropy, which describes the way the asymptotic presence
distribution (or equilibrium invariant measure) of a dynamical system is spread over the state space and the stability
(or robustness) will be characterized by the rate at which the system returns to its equilibrium distribution
(or the distance at which the system remains from its anterior dynamics) after a dynamical (or structural)
perturbation. Mathematical relationships between evolutionary entropy, stability rate and robustness index
will be given in the general framework of Markov chains and in the specific case of Markov chains related
to the genetic threshold Boolean random regulatory networks (getBren). It is proved that in certain
circumstances of particular connectivity, the entropy of the invariant measure can be considered both
as a complexity, stability and robustness index, by exploiting the links between these notions, fundamental
to characterize the resistance of a biological system against endogenous or exogenous perturbations.
Examples of biological networks (like m-switch or cell cycle control for different species) show the
practical interest of this approach in biology and evolution.
- 14h55-15h40, POPOVIC Nikola (School of Math. & Maxwell Institute of Math.Sciences, Univ. Edinburgh, UK) ,
Title: Three Time-Scales in an Extended Bonhoeffer-van der Pol Oscillator
We consider a three-dimensional extension of the classical Bonhoeffer-van der Pol oscillator
which exhibits dynamics on three different time-scales in certain parameter regimes. We characterise
the resulting mixed-mode oscillations in the context of a canonical three time-scale system which
was described in detail by Krupa et al. [SIAM J. Applied Dynamical Systems 7(2), 361-420, 2008].
Our asymptotics complements numerical results obtained by Sekikawa et al.
in earlier work [Phys. Lett. A 374(36), 3745-3751, 2010]; in particular, we recover the
period-doubling bifurcations of canards reported by them.
- 15h40-16h00 : Coffee break (posters)
- 16h00-16h45, KRUPA (Martin) Maciej (INRIA Paris Roquencourt Centre)
Title: Rhythmic oscillations in clusters
Rhythmic oscillations in the gamma or beta frequency range are a prominent phenomenon related to a number
of brain functions.
Data show that individual pyramidal neurons can fire at very low frequency with the population showing clear
gamma oscillations and synchrony.
An idealized model of such weak gamma is when pyramidal neurons fire in clusters. In this talk we explain
a mechanism of cluster formation in
PING (pyramidal-interneuron gamma) models with strong inhibition and weaker excitation. We also discuss
how adaptation of pyramidal neurons and inhibition coming from interneurons influence cluster formation.
- 16h45 : Closing.
- Ambrosio Benjamin, LMAH
- Aziz-Alaoui M.A., LMAH
- Corson Nathalie, LMAH
- Krupa Martin, INRIA
- Lanza Valentina, LMAH
- Verdiere Nathalie, LMAH
ULH, PRES Normandie Université, FNM-CNRS-3335, ISCN
and LMAH (Applied Math Lab., Univ. of Le Havre),
25 Rue Ph. Lebon, BP 540, Le Havre,Cedex, France.
Phone:(+33) -0- 6 70 73 76 69
Location of Le Havre University: University of Le Havre, UFR-ST, LMAH (Applied Math Lab.),
25 Rue Philippe Lebon, Le Havre, France.
The university is located 5 minutes walk from the train station, See also HERE
Schedules of trains running between Paris and Le Havre (wednesday May 15 and thursday May 16, 2013, about 2 hours trip):
PARIS SAINT-LAZARE ---> LE HAVRE,
departure from Paris at :
06h53 ; 07h53 ; 08h53 ; 10h50 ; 12h50 ; 14h50 ;
15h50 ; 16h50 ; 17h25 ; 17h50 ; 18h50 ; 19h50 ; 20h50.
LE HAVRE ---> PARIS SAINT-LAZARE,
departure from LeHavre at :
05h29 ; 06h29 ; 07h02 ; 08h01 ; 09h03 ; 10h02 ; 12h01 ;
13h02 ; 14h00 ; 16h02 ; 17h00 ; 18h02 ; 19h11 ; 20h02.
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