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**Vendredi 7 Juin 2019 à 11 heures en salle de Conférences du LJAD**

**Invité Franck (Lyon)**

**"**** Title "**

Résumé

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Archives séminaires (2011-2018)

**Lundi 5 Novembre 2018 à 11 h (salle de conf du LJAD)**

**Boris Gutkin (Paris/Moscou)**

**'Intrinsic and Synaptic Properties Determine Macroscopic Phase Response
Curves and Coherence States of Inter-communicating Gamma Oscillatory
Neural Circuits'**

**Abstract:** Macroscopic oscillations of different brain regions show

multiple phase relations that are persistent across time [5]. Such phase

locking is believed to be implicated in a number of cognitive functions

and is key to the so-called Communication Through Coherence (CTC) theory

for neural information transfer [7]. The question is then to identify

the biophysical neuronal and synaptic properties that permit such motifs

to arise.

We investigate the dynamical emergence of phase locking within two

bidirectionally delayed-coupled spiking circuits with emergent gamma

band oscillations. Internally the circuits consist of excitatory and

inhibitory cells coupled synaptically in an all-to-all fashion and

parameterized to give either the pyramidal-interneuron (PING) or

interneuron gamma (ING) rhythm activity to emerge. Multiple circuits can

also be intercoupled together with reciprocal synaptic connections with

variable delays and targeting excitatory and/or inhibitory neurons.

Using mean-field approach combined with an exact reduction method [3,8],

we break down the description of each spiking network into a low

dimensional nonlinear system. The adjoint method can be applied to

derive semi-analytical expressions for the macroscopic infinitesimal

phase resetting-curves (mPRCs) [2,4]. Using the mPRCs we determine how

the phase of the global oscillation responds to incoming perturbations.

In fact, we find that depending on wether PING or ING is expressed and

wether the excitatory of inhibitory neurons are perturbed, the mPRC can

be either class I (purely positive) or class II (by-phasic). Hence we

show analytically how incoming excitation can either promote spiking

(advancing the phase) or retard the oscillation.

We further study the dynamical emergence of macroscopic phase locking of

two bidirectionally delayed-coupled spiking networks within the

framework of weakly coupled oscillators [1,9]. Using the weak coupling

ansatz we abbreviate the bidirectionally coupled circuits description

into a phase equation [1,9]. An analysis of the phase equation shows

that the delay is a necessary condition to get a symmetry breaking. We

find that a whole host of phase-locking relationships can exist,

depending on the coupling strength and delay. Our analysis further

allows us to track how the perturbation of on the interacting circuits

is transferred to its coupled partner. We find that such transfer is

phase-locking state dependent. We show that this transfer of signals can

be directional in the symmetrically coupled network.

[1] Ashwin, P., Coombes, S., Nicks, R.: Mathematical frameworks for

oscillatory network dynamics in neuroscience. The Journal of

Mathematical Neuroscience 6(1), 2 (2016).

[2] Brown, E., Moehlis, J., Holmes, P.: On the phase reduction and

response dynamics of neural oscillator populations. Neural Computation

16(4), 673{715 (2004).

[3] Deco, G., Jirsa, V.K., Robinson, P.A., Breakspear, M., Friston, K.:

The dynamic brain: From spiking neurons to neural masses and cortical

fields. PLoS Comput Biol 4(8), 1{35 (2008). DOI

10.1371/journal.pcbi.1000092. Neural Computation 25(12), 3207{3234

(2013).

[4] Dumont, G., Ermentrout, G.B., Gutkin, B.: Macroscopic

phase-resetting curves for spiking neural networks. Phys. Rev. E 96,

042,311 (2017).

[5] Fries, P.: Neuronal gamma-band synchronization as a fundamental

process in cortical computation. Annual review of neuroscience 32,

209–224 (2009)

[7] Maris, E., Fries, P., van Ede, F.: Diverse phase relations among

neuronal rhythms and their potential function. Trends in Neurosciences

39(2), 86{99. DOI 10.1016/j.tins.2015.12.004.

[8] Montbrio, E., Pazo, D., Roxin, A.: Macroscopic description for

networks of spiking neurons. Phys. Rev. X 5, 021,028 (2015).

[9] Nakao, H.: Phase reduction approach to synchronisation of nonlinear

oscillators. Contemporary Physics 57(2), 188{214 (2016).

**Mercredi 7 Novembre 2018 à 11 h (salle III du LJAD)**

**Yohann Scribano (Montpellier)**

**"Quantum trajectories approach for low-temperature molecular reactive processes"**

Based on the de Broglie-Bohm formulation of quantum mechanics [1], quantum trajectories have seen a growing

interest in the chemical dynamics community over the past ten years or so [2]. As the name suggests, quantum

trajectories (QTs),are able to capture quantum dynamical effects—tunneling, in particular—which are known or

suspected to be important for many processes of current interest: tunneling effect in reactive processes (in gas or

condensed phases), non-adiabatic effects, quantum coherence, proton transfers in biochemistry, . . . .

Originally considered an interpretative tool for quantum mechanics, QTs have been recently rediscovered as a

computational method for doing quantum reaction dynamics [2]. Traditionally, analytic quantum trajectories, often

used as an interpretative tool, were extracted from conventional wave packets. In the more recent synthetic

quantum trajectory methods, both the trajectories and the wave function are computed on the fly, each affecting the

propagation of the other [2].

We recently investigate the most recent formulation of QTs proposed by Bill Poirier and coworkers [3, 4],

which regards the trajectory ensemble itself as the fundamental quantum state entity, rather than the wavefunction.

Similarly to classical trajectories, QTs obey Hamiltonian equations of motion, albeit special ones. The resultant

quantum trajectory simulation scheme so obtained is identical to a classical trajectory simulation, apart from the

addition of one extra “quantum” coordinate. Using standard techniques to integrate the equations of motion,

quantum trajectory simulations is indeed capable of providing accurate quantum dynamical information, but with

the same ease-use and computational effort as classical trajectory simulation. In this QTs formulation, a 4th-order

Newtonian-like ordinary differential equation (ODE) was derived that describes 1D stationary scattering states

exactly, solely in terms of quantum trajectories. The concept of those QTs will be presented and illustrated by our

application for a 1D Eckart barrier system [5] as well as its application in a capture model of the cold and ultra-cold

Li + CaH reaction [6]. Some perpectives will also presented on the way to perform quantum-classical trajectories

simulations for chemical reaction involving many degree of freedom (high dimensional reaction dynamics).

References

[1] D. Bohm, Phys.Rev. 85, 85.

[2] R. E. Wyatt, Quantum Dynamics with Trajectories (Springer, New York, 2005).

[3] B. Poirier, Chem. Phys. 370, 4 (2010).

[4] J. Schiff and B. Poirier. J. Chem. Phys., 136, 031102 (2012).

[5] G. Parlant, Y.-C. Ou, K. Park, and B. Poirier, Comp. Theor. Chem. 990, 3 (2012).

[6] Y. Scribano, G. Parlant, and B. Poirier, J. Chem. Phys. 149, 021101 (2018).

**Vendredi 30 novembre 2018 à 11 heures en salle de Conférences du LJAD**

**Daniele Avitabile (Nottingham)**

**"****Analysing waves and bumps with interfacial dynamics: spatio-temporal canards and
localised spatiotemporal chaos in neural networks"**

We will discuss level-set based approaches to study the existence and

bifurcation structure of spatio-temporal patterns in biological neural

networks. Using this framework, which extends previous ideas in the

study of neural field models, we study the first example of canards in

an infinite-dimensional dynamical system, and we give a novel

characterisation of localised structures, informally called “bumps”,

supported by spiking neural networks.

We will initially consider a spatially-extended network with heterogeneous

synaptic kernel. Interfacial methods allow for the explicit

construction of a bifurcation equation for localised steady states. When

the model is subject to slow variations in the control parameters,

a new type of coherent structure emerges: the structure displays a

spatially-localised pattern, undergoing a slow-fast modulation at the

core. Using interfacial dynamics and geometric singular perturbation

theory, we show that these patterns follow an invariant repelling slow

manifold, hence we name them "spatio-temporal canards". We classify

spatio-temporal canards and give conditions for the existence of

folded-saddle and folded-node canards. We also find that these

structures are robust to changes in the synaptic connectivity and firing

rate. The theory correctly predicts the existence of spatio-temporal

canards with octahedral symmetries in a neural field model posed on a spherical domain.

synaptic kernel. Interfacial methods allow for the explicit

construction of a bifurcation equation for localised steady states. When

the model is subject to slow variations in the control parameters,

a new type of coherent structure emerges: the structure displays a

spatially-localised pattern, undergoing a slow-fast modulation at the

core. Using interfacial dynamics and geometric singular perturbation

theory, we show that these patterns follow an invariant repelling slow

manifold, hence we name them "spatio-temporal canards". We classify

spatio-temporal canards and give conditions for the existence of

folded-saddle and folded-node canards. We also find that these

structures are robust to changes in the synaptic connectivity and firing

rate. The theory correctly predicts the existence of spatio-temporal

canards with octahedral symmetries in a neural field model posed on a spherical domain.

We will then discuss how the insight gained with interfacial dynamics may

be used to perform coarse-grained bifurcation analysis on neural

networks, even in models where the network does not evolve according to

an integro-differential equation. As an example I will consider a

well-known event-driven network of spiking neurons, proposed by Laing

and Chow. In this setting, we construct numerically travelling waves

whose profiles possess an arbitrary number of spikes. An open question

is the origin of the travelling waves, which have been conjectured to

form via a destabilisation of a bump solution. We provide numerical

evidence that this mechanism is not in place, by showing that

disconnected branches of travelling waves with countably many spikes

exist, and terminate at grazing points; the grazing points correspond to

travelling waves with an increasing number of spikes, a well-defined

width, and decreasing propagation speed. We interpret the so called

“bumps” and “meandering bumps”, supported by this model as localised

states of spatiotemporal chaos, whereby the dynamics visits a large

number of unstable localised travelling wave solutions.

be used to perform coarse-grained bifurcation analysis on neural

networks, even in models where the network does not evolve according to

an integro-differential equation. As an example I will consider a

well-known event-driven network of spiking neurons, proposed by Laing

and Chow. In this setting, we construct numerically travelling waves

whose profiles possess an arbitrary number of spikes. An open question

is the origin of the travelling waves, which have been conjectured to

form via a destabilisation of a bump solution. We provide numerical

evidence that this mechanism is not in place, by showing that

disconnected branches of travelling waves with countably many spikes

exist, and terminate at grazing points; the grazing points correspond to

travelling waves with an increasing number of spikes, a well-defined

width, and decreasing propagation speed. We interpret the so called

“bumps” and “meandering bumps”, supported by this model as localised

states of spatiotemporal chaos, whereby the dynamics visits a large

number of unstable localised travelling wave solutions.

This is joint work with Mathieu Desroches, Edgar Knobloch, Joshua Davis and Kyle Wedgwood.

**Vendredi 11 janvier 2019 à 11 heures en salle 2 du LJAD**

**Giovanni Manfredi (Strasbourg)**

**"Self-gravitating systems: quantum and classical"**

In recent years, there has been a renewal of interest in the set of nonlinear equations known as the

Schrödinger–Newton equations (SNEs). These consist of the ordinary Schrödinger equation endowed with

a gravitational potential that is obtained self-consistently from Poisson’s equation. The source term in

Poisson’s equation is provided by a matter density

ρ ( r , t )= | ψ |^2 that is proportional to the probability

density as given by the wave function ψ (r , t) .

The SNEs were originally put forward by Diosi [1] and Penrose [2] as a fundamental modification of

quantum mechanics for massy objects. The SNE equations may also represent the weak-field limit of

semiclassical gravity [3]. Finally, in an astrophysical context, they were used to study self-gravitating

objects (boson stars) [4] or to describe dark matter by means of a scalar field [5].

Here, I will first revisit the SNEs using a variational method [6]. With this approach, one can arrive at a

single ODE that describes the evolution of the width of the mass density. This method reproduces all the

results for the ground state and linear dynamics derived previously. In addition, it is not restricted to linear

theory and can be used to investigate nonlinear oscillations or the long-time dynamics.

Second, I will present a general-relativistic extension of the SNEs. The strategy adopted here is to first

replace Poisson’s equation with the equations of gravitoelectromagnetism (GEM). These are a linearized

approximation of the Einstein equations, which is formally almost identical to Maxwell’s equations of

ordinary electromagnetism. Next, we derive the nonrelativistic limit of the GEM equations using the

methods developed in [6]. The resulting equations can be coupled to the Schrödinger equation to obtain a

new set of SNEs augmented by a gravitomagnetic field. Such modified SNEs, though still Galilei covariant,

incorporate all three fundamental constants (G, h, c) and can be conveniently expressed in Planck’s units.

Finally, I will discuss some recent results on a class of idealized 1D models for cosmological applications.

Most existing results rely on N-body simulations, which solve the equations of motion of many particles

interacting via Newton’s force. N-body simulations show the formation of a hierarchical structure [7] that

suggests a fractal distribution of mass. The analyses are robust for high-density regions, but noisy in the

low-density ones. To gain a better insight, we propose to use a continuous probability distribution in the

phase space, which evolves according to the Vlasov-Poisson equations. As the entire phase space is

covered with a uniform mesh, regions of high and low density are sampled with equal precision and the

numerical noise remains low. Here, I will present the results of these Vlasov-Poisson simulations [8].

[1] Diosi, L.: Phys. Lett. A 105, 199 (1984)

[2] Penrose, R.: Gen. Relativ. Gravit. 28, 581 (1996)

[3] Carlip, S.: Class. Quantum Gravit. 25, 154010 (2008)

[4] Schunck, F.E., Mielke, E.W.: Class. Quantum Gravit. 20, R301 (2003)

[5] Guzman, F.S., Urena-Lopez, L.A.: Phys. Rev. D 68, 024023 (2003)

[6] Manfredi, G.: Eur. J. Phys. 34, 859 (2013)

[7] B. N. Miller and J.-L. Rouet. J. Stat. Mech. P12028 (2010); Phys. Rev. E 82, 066203 (2010).

[8] G. Manfredi, J.-L. Rouet, B. Miller, and Y. Shiozawa, Phys. Rev. E 93, 042211 (2016).

**Vendredi 25 janvier 2019 à 14 heures en salle 2 du LJAD**

**Marco Martins Afonso (Centro de Matemática da Universidade do Porto)**

**"EFFECTIVE TRANSPORT OF INERTIAL PARTICLES IN FLUID FLOWS"**

We study how an imposed fluid flow - laminar or turbulent - modifies

the transport properties of inertial particles (e.g. aerosols,

droplets or bubbles), namely their terminal velocity, effective

diffusivity, and concentration following a point-source emission.

Such quantities are investigated by means of analytical and

numerical computations, as functions of the control parameters of

both flow and particle; i.e., density ratio, inertia, Brownian

diffusivity, gravity (or other external forces), turbulence

intensity, compressibility degree, space dimension, and

geometric\temporal properties.

The complex interplay between these parameters leads to the

following conclusion of interest in the realm of applications: any

attempt to model dispersion and sedimentation processes - or

equivalently the wind-driven surface transport of floaters -

cannot avoid taking into account the full details of the flow

field and of the inertial particle.

**Mardi 26 mars 2019 à 14 heures en salle de conférence du LJAD**

**Prof. Katsuhiko Sato (Hokkaido Univ.)**

**"Left-right asymmetric cell intercalation drives directional collective cell movement in epithelial morphogenesis"**

abstract:

During early development and wound healing, epithelial cells (cohesive cells)

that form a monolayer sheet sometimes move collectively in a definite direction in the sheet; that is, the

cohesive cells move unidirectionally while maintaining the attachments with adjacent cells. This phenomenon is

called collective migration of epithelial cells [1], and is considered to be an essential factor for

morphological changes of multicellular organisms [2]. While the molecular mechanisms underlying this

phenomenon are becoming understood, much of the mechanical mechanisms remain still unclear. In the present

talk, I will provide one possible mechanism for collective migration from a theoretical point of view [3]: If

the cell boundaries contract depending on their orientation (generalized planar polarity), and spatial

inhomogeneity about the cell properties, such as strength of cell adhesion, exists, then the cohesive cells

collectively move in the direction perpendicular to that of spatial inhomogeneity, by repeating rearrangement

of neighbor relationships. I will demonstrate this scenario by using the vertex model, and reproduce the

behaviors of typical collective cell migration such as that seen in zebrafish lateral line primordium. I also

provide experimental evidence for this type of movement by investigating a phenomenon in development of fly,

where monolayer epithelial sheets move 360 degrees clockwise around the genital disc [4].

Refs:

1. P. Friedl and D. Gilmour, (2009) Nat. Rev. Mol. Cell Biol. 10, 445-457.

2. J. Davies, Mechanisms of Morphogenesis (Academic Press, Second Edition, 2013).

3. K. Sato, T. Hiraiwa, and T. Shibata, Phys. Rev. Lett. 115, 188102 (2015).

4. K. Sato, T. Hiraiwa, E. Maekawa, A. Isomura, T. Shibata, and E. Kuranaga, Nat. Commun. 6, 10074 (2015).

**Vendredi 5 avril 2019 à 14 heures en salle 1 du LJAD**

**Giorgio Krstulovic (Laboratoire Lagrange, OCA)**

**"Non-linear wave interaction and cascades in thin elastic plates"**

In fluid turbulence, energy is transferred from one scale to another by

an energy cascade that depends only on the energy dissipation rate.

Remarkably, a similar phenomenon takes place in thin elastic plates. In

the limit where the non-linearity in the equations governing the

vibrations of a plate is weak, the theory of wave turbulence (WT) can be

safely applied. Over the last ten years this cascade has been

extensively studied theoretically and numerically. This system has

revealed itself as a useful prototype to study wave interactions and

turbulence.

In this seminar, I will start by explaining how the theory of weak wave

turbulence applies to this problem, what are the corresponding

theoretical predictions and how well experimental results confirm such

predictions. Then, I will show that for this system, it is possible to

derive the analogous of the 4/5-law of hydrodynamic turbulence, which

provides an exact result concerning the energy transfers. Moreover, I

will show than in the fully non-linear regime, elastic deformations

present large “eddies” together with a myriad of small “crumpling

eddies”, such that folds, developable cones, and more complex stretching

structures, in close analogy with swirls, vortices and other structures

in hydrodynamic turbulence. This deformations lead to the same

Kolmogorov spectrum observed in hydrodynamic turbulence. To finish, if

time allows it, I will discuss the non-dispersive limit and explain what

are the mathematical difficulties of applying WT theory in this case.