Laboratoire de Physique Théorique et Modèles Statistiques

Quantum Chaos and Combinatorics on discrete graphs

Uzy Smilansky, Weizmann Institute, Israel

I shall discuss the spectrum and eigenfunctions of the discrete Laplacian on d-regular graphs. After presenting some trace formulae, I shall show the intimate connection between spectral statistics and the statistics of the number of cycles on the graphs. Finally I shall discuss nodal domains and percolation of level-sets of the eigenvectors. Using a "random waves conjecture" I will compute the nodal distribution and the critical level as a function of the degree and the eigenvalue.

Mardi 1 juin à 16h

LPTMS-batiment 100, salle 201, Orsay

Belief propagation for graph partitioning

Petr Sulc, Los Alamos National Laboratory

We study the belief propagation algorithm for the graph bi-partitioning problem, i.e. the ground state of the ferromagnetic Ising model at a fixed magnetization. Application of a message passing scheme to a model with a fixed global parameter is not banal and we show that the magnetization can in fact be fixed in a local way within the belief propagation equations. Our method provides the full phase diagram of the bi-partitioning problem on random graphs, as well as an efficient heuristic solver that we anticipate to be useful in a wide range of application of the partitioning problem.
Work done in collaboration with L. Zdeborova

Jeudi 3 juin à 14h

LPTMS-batiment 100, salle 201, Orsay

A statistical mechanical approach to compressed sensing

Yoshiyuki Kabashima, Tokyo Institute of Technology, Japan

We consider the problem of reconstructing an N-dimensional continuous vector x from P constraints which are generated from its linear transformation under the assumption that the number of non-zero elements of x is typically limited to \rho N (0 \le \rho \le 1). Problems of this kind are very relevant for various modern sensing (sampling, imaging, etc.) techniques such as radar measurement, computed tomography and so on. In efforts toward designing efficient reconstruction schemes exploiting the prior knowledge of sparsity, minimization of a cost function with respect to the so-called Lp-norm of x under the P constraints has been actively studied these days [1].In this talk, we introduce our recent attempt [2], which is based on the replica method of statistical mechanics, for evaluating a critical relation between \alpha = P/N and \rho for successfully reconstructing the original vector x by the minimization.

References:
[1] http://en.wikipedia.org/wiki/Compressed_sensing
[2] YK, T. Wadayama and T. Tanaka, J. Stat. Mech. (2009) L09003 (12 pages)

Vendredi 4 juin à 11h

LPTMS-batiment 100, salle 201, Orsay

Random Matrices and Number Theory

Jon KEATING (University of Bristol, Department of Mathematics)

The Riemann zeta function encodes information about the primes through the positions of its zeros. These zeros are the subject of the
Riemann Hypothesis. Remarkably, everything we know about them is consistent with their being distributed like the eigenvalues of random
matrices. They thus exhibit the characteristics of the energy levels of complex quantum systems. This connection extends to generalizations of
the zeta function and has shed new light on several long-standing problems in number theory. I shall review these ideas.

Un café sera servi a 13h30.

Lundi 7 juin à 14h

LPTMS-batiment 100, salle 201, Orsay

Proof of the Razumov-Stroganov conjecture

Luigi Cantini (LPT ENS)

In 2001 Razumov and Stroganov conjectured that the (properly normalized) components of
the ground state of the dense O(1) loop model on a semi-infinite cylinder enumerate fully-packed
loop (FPL) configurations on the square, with alternating boundary conditions, refined according
to the link pattern for the boundary points. This conjecture has arisen a lot of interest both in
the physics and in the mathematics community.
In this talk, after reviewing the main background, I will present a proof of this conjecture. The main idea is to recognize the fundamental role of ?gyration?, an operation that can be performed on FPL, which was already the key in Wieland?s proof of the rotational symmetry of the FPL enumerations.

Mardi 8 juin à 11h

LPTMS-batiment 100, salle 201, Orsay

Mécanisme physiques de motilité et de polarisation cellulaire

Rhoda Hawkins, LPTMC, Jussieu

Nous présentons deux mécanismes physiques permettant de modéliser deux fonctions cellulaires essentielles: la motilité; et la polarisation cellulaire. Dans un premier temps, Nous proposons un nouveau mécanisme de la motilité; cellulaire, qui repose sur le couplage de la polymérisation de l'actine avec le confinement géométrique. Nous montrons que le confinement joue un rôle crucial et peut donner lieu à des vitesses de déplacement des cellules potentiellement plus grandes que la vitesse de polymérisation, et ce même en absence d'adhésion spécifique. Notre modèle correspond qualitativement à des expériences récentes qui montrent que des cellules sans protéines d'adhésion sont mobiles dans des environnements confinés (comme les canaux micro fluidique) alors qu'elles sont incapables de se déplacer sur un substrat plan. Il pourrait nous aider à comprendre les mécanismes de migration cellulaire dans des géométries plus complexes tels que les tissus vivants où les effets de confinements sont omniprésents.



Dans un deuxième temps, nous présentons un mécanisme général de polarisation cellulaire - c'est à dire conduisant à l'émergence d'une distribution inhomogène des marqueurs de polarité - reposant sur un couplage des marqueurs moléculaires avec le cytosquelette. Notre modèle montre que la géométrie des filaments du cytosquelette, qui peuvent être nucléés soit sur la membrane (e.g. actine) soit au centre de la cellule (e.g. microtubules) détermine si le système est capable de se polariser spontanément ou seulement grâce à des signaux asymétriques extérieurs. Ce modèle est en accord avec des expériences récentes de polarisation cellulaire pour deux systèmes biologiques très différents: la levure et le neurone.

Mardi 15 juin à 11h

LPTMS-batiment 100, salle 201, Orsay

Actin dynamics and mechanics : from single filaments to networks.

Guillaume Romet-Lemonne , LEBS, Gif

Actin proteins assemble to form filaments, which can elongate and disassemble from both ends, with different reaction rates. Each actin monomer binds an ATP, which is hydrolyzed into ADP after incorporation of the monomer into the filament. This results in a complex system, where ATP hydrolysis is coupled to the dynamics of assembly/disassembly, and modulates the interaction of the filament with regulatory proteins. I will present experimental data and theoretical analysis on the dynamics of individual filaments in vitro,and show that we can determine the ATP/ADP profile in the filament,and get information on this complex mechanism.
In cells, actin filaments are organized in a variety of networks, as they interact with regulatory proteins. Branched networks for example, can generate a force as they grow against a surface, such as the leading edge of a migrating cell, or the rear of an endosome or a bacterium within the cytoplasm. By reconstituting this machinery in vitro, to propel artificial vesicles, we get valuable insight in the underlying mechanism. I will show how the diffusion of proteins bound to a the lipid membrane plays an important role in regulating the growing network and the resulting movement, and how this provides a better understanding of protein-protein interactions in this system.

Vendredi 18 Juin à 14h

LPTMS-batiment 100, salle 201, Orsay

Cross-linking actin into function

Martin Lenz, James Franck Institute, Université de Chicago

Actin filaments are paramount players in the shaping and dynamics of eukaryotic cells, and can form a variety of structures as they are regulated by a host of associated proteins. Here we focus on some spectacular examples of such constructs: stereocilia and stress fibers, which are bundles formed under the influence of actin cross-linking proteins. The relatively large scale of these structures implies that their overall organization crucially involves the collective behavior of actin and its cross-linkers, into which a theoretical approach yields some interesting insights.

We first propose that the cross-linker espin may regulate the shape of stereocilia, which are protrusions of cells of the inner ear crucial for hearing. Very good agreement with a range of experimental results is obtained by fitting only one parameter: the detachment rate of espin. Our model displays a transition from finite-length structures to unbounded growth, some universal features of which could help classify cellular growth processes. We next focus on biomimetic bundles containing the cross-linking motor myosin. We show that the widely accepted filament sliding model is not sufficient to predict whether these bundles tend to extend or contract, whereas the latter is always observed experimentally. We explore the hypothesis that this symmetry could be broken through the nonlinear elastic behavior of actin filaments.

Mardi 22 Juin à 11h

LPTMS-batiment 100, salle 201, Orsay

Knockouts, Robustness and Cell Cycles

Gunnar Boldhaus (Bioinformatics, University of Leipzig, Germany)

The response to a knockout of a node is a characteristic feature of a networked dynamical system. Knockout resilience in the dynamics of the remaining nodes is a sign of robustness. Here we study the effect of knockouts for binary state sequences and their implementations in terms of Boolean threshold networks. Beside random sequences with biologically plausible constraints, we analyze the cell cycle sequence of the species Saccharomyces cerevisiae and the Boolean networks implementing it. Comparing with an appropriate null model we do not
find evidence that the yeast wildtype network is optimized for High knockout resilience. Our notion of knockout resilience weakly correlates with the size of the basin of attraction, which has also been considered a measure of robustness.

Jeudi 24 juin à 16h

LPTMS-batiment 100, salle 201, Orsay

On Shape abd Electrostatics: Statistical Mechanics Studies of Model Systems

Carlos Eduardo Alvarez Cabrera

This doctoral work presents a series of studies of systems in which the particles interact by means of spheroidal hard core and electrostatic interactions. We first consider a dipolar hard sphere bilayer, studied by means of Monte Carlo (MC) simulations. The pressure between the layers is found to vary as -1/h⁵, where h is the distance between layers. We observed vortex like structures, frustrated by the finite size of the system.
Next we obtained the analytical solution to the screened potential of charged spheroidal colloid particles in the Debye-Huckel regime for Neumann and Dirichlet boundary conditions. This latter result agrees with the solution of the Poisson-Boltzmann equation far from the colloid for strongly charged particles. We also perform MC simulations of spheroidal colloids with a point charge at the center and find, both analytically and in simulations, that the effective potential is stronger in the direction where the curvature of the colloid is higher.
Finally we present two studies under progress. The first one deals with the effect of the addition of small spheres to spheroidal prolate particles in the nematic phase. We have seen that for an aspect ratio of 3 this effect is mild, but for an aspect ratio of 4, the nematic to isotropic transition is shifted to higher spheroid densities. In the second work, preliminary MC results for a size bidisperse spherical charged colloidal system are provided. This allows for a test of recently proposed mean-field approaches for polydisperse charged systems (cell model and renormalized jellium). In addition, we have found that as the size difference between the colloids is increased, the screening of the smaller species increases, while the opposite effect is observed for the larger species.

Vendredi 25 juin à 10h30

LPTMS-batiment 100, salle des conseils, Orsay

Decoherence of adiabatically steered quantum system

Paolo Solinas, Aalto University, Espoo, Finland

In the seminar I will present our results about the effect of Markovian environmental noise on the dynamics of a two-level quantum system which is steered adiabatically by an external driving field. I will discuss the approximations to arrive to a master equation and, in particular, the secular approximation and its consequences on the predicted dynamics. The master equation will be used to describe the superconducting Cooper pair pumping in presence of environmental noise.
I will show how, in the adiabatic limit, the ground state Cooper pair pumping is robust against zero-temperature environment. I will also discuss the possibility to engineer the environmental noise in the above physical set-up and future experiments.

Vendredi 25 juin à 15h

LPTMS-batiment 100, salle 201, Orsay

Céline Nadal "Phase transitions in the distribution of bipartite entanglement of a random pure state".

Alvaro Rojo "Reconstruction par l'effet de champ de Dislocations d'une Jonction comportant une Onde de Densité de Charge Incommensurable"

Mardi 29 juin à 11h

LPTMS-batiment 100, salle 201, Orsay