Matrix-correlated random variables: a dialogue between statistical physics and signal processing

Florian Angeletti, National Institute for Theoretical Physics, Stellenbosch

 Stochastic flow models

Pascal Viot (LPTMC, UPMC)

Filtration, and flow in micro/nano-channels and traffic flow are examples of processes subject to blocking when the channel conveying the particles becomes too crowded. We investigate a concurrent flow model where particles enter a channel randomly. If at any time two particles are simultaneously present in the channel, failure occurs. We obtain the exact solution for the survival probability, the distribution of the number of particles that pass before failure, and the instantaneous flux exiting the channel. Several generalizations of this simple model are also studied. We also consider  a counterflow model with two opposing Poisson streams. There is no restriction on the number of particles passing in the same direction, but blockage occurs if, at any time, two opposing particles are simultaneously present in the passage. All relevant quantities have been obtained exactly.

Shape controlled filaments suspensions – rheology and dynamics

Thomas Gibaud (ENS Lyon)

The mechanical behavior of a suspension of rigid and semiflexible filaments has been studied in great detail. In comparison the effect of the filament geometry has been relatively unexplored. Here, we hijack flagellar filaments from their original purpose in order to develop a versatile model rod-like bio-colloid whose shape and length can be tuned. We present experimental results on the rheological behavior of suspensions of (1) straight, (2) curly and (3) semi-straight/semi-curly flagella with an identical average contour length. We find that (1) and (2) show an elastic behavior at intermediate time but that (3) remains elastic and does not flow at long times. Using fluorescence microscopy, we track individual filament and find that this elastic plateau is related to a cage in which the filament is trapped for a certain among of time. Taken together, this highlights the role of filament geometry in suspension mechanics.

Chiral Random Matrix Theories for Wilson Fermions

Savvas Zafeiropoulos, Institut für Theoretische Physik - Goethe-Universität Frankfurt

Electromagnetic properties of viscous charged fluids

Davide Forcella (Université Libre de Bruxelles)

Recently the gauge/gravity correspondence has provided new interesting applications to high energy strongly coupled plasmas and strongly correlated condensed matter systems. At the same time, in an apparently unrelated field, there have been enormous progresses in the ability to engineer electromagnetic devices with exotic properties: such as negative refraction (energy and phase velocity for the electromagnetic field in the medium are in opposite directions), cloaking, photonics black-holes, etc. In the talk, building on these two recent developments, I will discuss the electromagnetic properties of viscous charged fluids, consisting for example of electrons in certain solids or high energy physics plasmas. In particular I will show that finite viscosity leads to multiple modes of evanescent electromagnetic waves at a given frequency, one of which is characterised by a negative index of refraction. I will then underline the concept of electron viscosity in actual electron systems (rarely discussed in literature and not measured in experiments yet) in condensed matter and its consequences on the electromagnetic response. In particular I will discuss how optical spectroscopy can be used to probe the electron viscosity. Indeed finite viscosity has the effect to decrease the reflectivity of a metallic surface, and support the occurrence, in a half-infinite sample, of oscillations of the electromagnetic field intensity as a function of distance from the interface. I will conclude with some comments on future perspectives and applications.

Lieb's soliton-like excitations in harmonic traps

Grigory Astrakharchik (Universitat Politècnica de Catalunya, Barcelona)

We study the solitonic Lieb II branch of excitations the in one-dimensional Bose gas in homogeneous and trapped geometry. Using Bethe-ansatz Lieb's equations we calculate the "effective number of atoms'' and the "effective mass'' of the excitation. The equations of motion of the excitation are defined by the ratio of these quantities. The frequency of oscillations of the excitation in a harmonic trap is calculated. It changes continuously from its "soliton-like'' value $omega_h/sqrt{2}$ in the high density mean field regime to $omega_h$ in the low density Tonks-Girardeau regime with $omega_h$ the frequency of the harmonic trapping. Particular attention is paid to the effective mass of a soliton with velocity near the speed of sound.

How history shapes geometry in a model of protein evolution

Olivier Rivoire (Laboratoire interdisciplinaire de Physique, UJF Grenoble)

The interactions between amino acids in a protein are heterogeneous but not arbitrary: they enable proteins to perform specific biochemical "functions". Understanding these interactions may require, however, looking beyond current functional requirements, to the evolutionary history of proteins. I will illustrate this point with a simple statistical mechanics model, which I will motivate with observations and experiments on natural proteins. The model relates the parameters controlling the evolution of a protein to the organization of the interactions inside its structure.

Dynamics of synaptic domains: scaffold-protein aggregation at the postsynaptic membrane

Jonas Ranft, Laboratoire de Physique Statistique de l'ENS

Fluctuations of the current and optimal profiles in the open Asymmetric Simple Exclusion Process

Alexandre Lazarescu, Institute for Theoretical Physics, KU Leuven

The Self-Journal of Science : an ethical and realistic alternative for scientific publishing

Michaël Bon, CEA Saclay

The Cytoskeleton as an Active Gel: Modelling Cell Polarization, Shape Change, and Migration

Andrew Callan-Jones (Université Paris-Diderot)

Driven-dissipative phyics: the relaxing virtues of a bath

Camille Aron (Princeton University)

Despite being ubiquitous from nano to macroscale, far-from-equilibrium physics remains largely an uncharted territory in which the standard toolbox of equilibrium statistical mechanics is a priori unavailable. Besides its fundamental relevance, nonequilibrium physics can also be viewed as a resource to achieve a new type of control over matter. In this talk, I will review recent developments in our understanding of driven-dissipative physics and illustrate how "bath engineering" offers a promising route to realize exotic many-body states in a nonequilibrium fashion, such as large-scale long-lived quantum entanglement or high-temperature superconductivity.

Tipping points and monetary policy in a stylized macroeconomic agent-based model

Stanislao Gualdi, Centrale Supélec

Breathing modes of one-dimensional trapped BEC

Andrii Gudyma (LPTMS)

We calculate the breathing mode frequency in a one-dimensional Bose gas confined to a harmonic trap. We predict a smooth crossover from Thomas–Fermi Bose–Einstein condensate (BEC) regime to Gaussian BEC regime using Hartree approximation and sum rules approach, adopted to small system sizes. Local density approximation (LDA) correctly captures the crossover from Tonks-Girardeau to Thomas-Fermi BEC regimes. Hartree and LDA predictions can be continuously matched for N > 25 particles, providing a complete zero-temperature description for large number of particles and resulting in a non-monotonic reentrant behavior of the breathing frequency. For smaller number of particles (ranging from N = 2 to N = 25) we perform extensive diffusion Monte Carlo simulations. This permits us to obtain a complete picture, applicable to arbitrary number of particles and any repulsive interaction strength. We provide perturbative analysis for both weak and strong coupling regimes. We revisit Innsbrick group experiment [Science 325, 1224 (2009)], analyzing the measurements done in Thomas–Fermi Gaussian BEC crossover, and demonstrate that the breathing frequency follows a reentrant behavior as a function of the interaction strength in full agreement with our theory.

Latent liquidity models: an universal mechanism for the anomalous response of financial markets

Iacopo Mastromatteo, CMAP Ecole polytechnique

Collective cell motion and statistical mechanics : global modes and fluctuations in confined cell assemblies.

Vincent Hakim (Laboratoire de Physique Statistique, ENS, Paris)

Non-Equilibrium long-range interacting systems : kinetic theory and large deviations

Cesare Nardini, Edinburgh University

Few- and many-body quantum physics of p-wave interacting fermions in two dimensions

Sergej Moroz, University of Colorado, Boulder

Stochasticity and robustness in growth and morphogenesis

Arezki Boudaoud (ENS Lyon)

How do organisms cope with natural variability to achieve well-defined morphologies and architectures? We addressed this question by combining experiments with live plants and analyses of stochastic models that integrate cell-cell communication and tissue mechanics. This led us to counterintuitive results on the role of noise in development, whereby noise is either filtered or enhanced according to the level at which it is acting.

Dynamics at a Quantum Critical Point: Combining Quantum Monte Carlo and Holography

Erik Sorensen, LPT Toulouse

Pensée antique et science contemporaine

Pierre Charles (UPMC)

La science contemporaine nous amène à reconsidérer certains textes anciens. La mécanique quantique, tout particulièrement, utilise de nombreux concepts que l’on retrouve dans les philosophies de Pythagore, Héraclite, Platon, Aristote et Carnéade. Les théories modernes du langage et de la signification, la nature des nombres et des propositions logiques, nous offrent l’opportunité d’une confrontation.

Many-body physics of bosons in (quasi)disorder

Vincent Michal (LPTMS)

Critical systems and quantum multifractality

Economic inequality from statistical physics point of view

Victor Yakovenko (Department of Physics, University of Maryland, College Park, USA)

Similarly to the probability distribution of energy in physics, the probability distribution of money among the agents in a closed economic system is also expected to follow the exponential Boltzmann-Gibbs law, as a consequence of entropy maximization. Analysis of empirical data shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structure. The majority of the population (about 97%) belongs to the lower class characterized by the exponential ("thermal") distribution. The upper class (about 3% of the population) is characterized by the Pareto power-law ("superthermal") distribution, and its share of the total income expands and contracts dramatically during booms and busts in financial markets. Globally, data analysis of energy consumption per capita around the world shows decreasing inequality in the last 30 years and convergence toward the exponential probability distribution, in agreement with the maximal entropy principle. Similar results are found for the global probability distribution of CO2 emissions per capita. All papers are available at http://physics.umd.edu/~yakovenk/econophysics/. For recent coverage in Science magazine, see http://www.sciencemag.org/content/344/6186/828

Energetic reduction of elastic knots to normal form: Gradient descent along the Euler functional

 Alexey Sossinsky, Independent University of Moscow, Laboratoire Poncelet

The Dynamics of Two Biological Interfaces

Gerald G. Fuller (Stanford University)

Seminar co-hosted by Éric Raspaud—SPECIAL TIME

Biological systems are normally high-interface systems and these surfaces are laden with biological molecules and cells that render them mechanically complex. The resulting nonlinearities with response to surface stresses and strain are often essential to their proper function and these are explored using recently developed methods that reveal an intricate interplay between applied stress and dynamic response. Two applications are discussed.

1. Vascular endothelial cells are nature's "rheologists" and line the interior walls of our blood vessels and are sensitive to surface shear stresses. These stresses are known to affect the shape and orientation of endothelial cells. It is evident that the spatial homogeneity of flow can affect vascular health and it is well-documented that lesions form in regions of high curvature, bifurcations, and asperities in blood vessels. Experiments are described where stagnation point flows are used to create regions of well controlled flow stagnation and spatial variation of wall shear stresses. Live-cell imaging is used to monitor the fate of cells attached to surfaces experiencing flow impingement and it is revealed that endothelial cells migrate and orient in such flows to create remarkable patterns of orientation and cell densification. This response, termed "rheotaxis", is used to explore mechano-transduction pathways within these cells.

2. The tear film of the eye is a composite structure of an aqueous solution of protein and biomacromolecules. This thin layer is further covered by a film comprised of meibomian lipids excreted during each blink. The purpose of the meibum has been largely unexplained although one prevailing suggestion is that it suppresses evaporation. Recent measurements in our laboratory demonstrate that this layer is strongly viscoelastic and this property has dramatic effects on the dynamics of the moving contact line and stability against dewetting.

—

Gerald Fuller is the Fletcher Jones Professor of Chemical Engineering at Stanford University. He joined Stanford in 1980 following his graduate work at Caltech where he acquire his MS and PhD degrees. His undergraduate education was obtained at the University of Calgary, Canada. Professor Fuller's interests lie in studies of rheology and interfacial fluid mechanics. His work has been recognized by receipt of the Bingham Medal of The Society of Rheology, membership in the National Academy of Engineering, and honorary doctorates from the Universities of Crete, Greece, and Leuven, Belgium.

Matrix optimization under random external fields

Amir Dembo, Stanford University

Consider the problem of maximizing the quadratic form <x,Wx> + <h,x> over unit norm n-dimensional vectors x, where W is a Wigner matrix which is independent of the Gaussian vector h whose entries are independent and identically distributed. Two recent studies of the large n asymptotic probability of deviations of such maximum from its typical value, take very different approaches. Fyodorov and Le Doussal (2014) use the replica method of statistical physics, whereas Dembo and Zeitouni (2015) rely instead on the mathematical theory of large deviations. I will describe the main points of the latter, using this specific example also to illustrate some of the differences, strength and weaknesses of each approach.

Semiclassical evolution of correlations between observables

Alfredo Ozorio de Almeida, Centro brasileiro de pesquisas físicas

Actomyosin Force Generation and Pattern Formation

Stephan Grill (MPI-CBG Dresden)

Learning to discover: signal/background separation and the Higgs boson challenge

Balázs Kégel (Laboratoire de l'Accélérateur Linéaire, Univ. d'Orsay)

Classification algorithms have been routinely used since the 90s in high-energy physics to separate signal and background in particle detectors. The goal of the classifier is to maximize the sensitivity of a counting test in a selection region. It is similar in spirit but formally different from the classical objectives of minimizing misclassification error or maximizing AUC. We start the talk by motivating the problem on an ongoing example of detecting the Higgs boson in the tau-tau decay channel in the ATLAS detector of the LHC. We formalize the problem, then go on by describing the usual analysis chain, and explain some of the choices physicists make when designing a classifier for optimizing the discovery significance. We derive different surrogates that capture this goal and show some simple techniques to optimize them, raising some questions both on the statistical and on the algorithmic side. We end the talk by presenting a data challenge we organized to draw the attention of the machine learning and statistics communities to this important application and to improve the techniques used to optimize the discovery significance. With a PhD in computer science, Balázs Kégl has been a researcher in the Linear Accelerator Laboratory of the CNRS and the chair of the Center for Data Science of the Université Paris-Saclay since 2014. He has published more than hundred papers on unsupervised and supervised learning, large-scale Bayesian inference and optimization, and on various applications. At his current position he has been the head of the AppStat team working on machine learning and statistical inference problems motivated by applications in high-energy particle and astroparticle physics.

Realization of strongly interacting topological phases on lattices

Antoine Sterdyniak, Universität Innsbruck

Broken symmetries in spin-orbit coupled Bose Einstein condensed gases

Sandro Stringari (University of Trento and BEC Center)

In the seminar I will focus on the symmetries characterizing the 1D spin-orbit coupled hamiltonian first realized experimentally by the team of Ian Spielman at Nist. The nature of the new quantum phases and their dynamic properties will be discussed. Special focus will be given on the recently observed rotonic excitation, which follows from the breaking of time reversal and parity symmetry, on the emergence of stripes which follows from the spontaneous breaking of translational invariance, and on the dynamic instability of large amplitude oscillations which is the consequence of the violation of Galilean invariance.

Statistique d’extrêmes de variables aléatoires fortement corrélées

Anthony Perret

La statistique des valeurs extrêmes est une question majeure dans divers domaines des sciences. Dans ce contexte, une question naturelle qui se pose alors est la suivante: ces valeurs extrêmes sont-elles isolées, loin des autres variables ou bien au contraire existe-t-il un grand nombre d'autres variables proches de ces valeurs extrêmes ? Cette question a suscité l'étude de la densité d'état de ces événements quasi-extrêmes. Il existe pour cette quantité peu de résultats pour des variables fortement corrélées, qui pourtant est le cas dans de nombreux modèles d'intérêt en physique statistique. Deux pistes de modèles physiques de variables fortement corrélées pouvant être étudiés analytiquement se démarquent : les positions d’une marche aléatoire et les valeurs propres de matrice aléatoire. Ce sont les deux modèles que j'ai étudiés dans ma thèse. Après avoir très brièvement discuté le cas des marches aléatoires, je me concentrerai dans cet exposé au cas où la collection de variables aléatoires est l'ensemble des valeurs propres d'une matrice aléatoire gaussienne hermitienne de grande taille. Je discuterai plus particulièrement la distribution de l’écart entre les deux plus grandes valeurs propres pour laquelle j’ai obtenu une formule faisant intervenir des fonctions transcendantes de Painlevé. Les comportements asymptotiques de cette formule permettent par exemple de trouver des nouveaux régimes intéressants dans le modèle de Sherrington-Kirkpatrick sphérique.

The cavity method in routing optimization problems on networks.

Caterina De Bacco

 In recent years the cavity method, or message-passing algorithm, has been successfully exploited by statistical physicists to solve combinatorial optimization problems such as the K-satisfability (K-SAT). In this talk we introduce this method and outline how it is applied to solve routing problems on communication or traffic networks. In this context the typical situation is where many users want to communicate at the same time over a given network. One then wants to optimize the overall routing by minimizing communication path length and the traffic overlap either at nodes or at edges given a set of constraints. We will show how the cavity method provides the algorithmic tools to tackle these types of optimization problems efficiently.

Growth of living fibrous tissues: from biofilms to fibrosis

Martine Ben Amar (ENS Paris)

Morphologies of soft materials in growth, swelling or drying have been extensively studied recently. Shape modifications occur as the size varies transforming ordinary spheres, cylinders and thin plates into more or less complex objects. Existence of fibers exacerbates this complexity, giving anisotropy to the growth process itself. The growth is coupled to the environment, for bacteria the substrate, in pathology the healthy tissue. In pathological situations such as wound-healing or desmoplastic tumor growth, the immune system reacts with a battery of morphogenetic gradients, making a new tissue full of collagene and eventually sending active cells. All these factors contribute to a high level of compressive stress at the origin of patterns and deformity. I will show how we can predict quantitatively these patterns on the simple drop geometry of the biofilms and on the spherical shape of tumors.

For the pathological cases, it turns out that the wrinkling process dominates the growth, deforming the tissues and exacerbating the immune system which reacts via passive (fibroblasts) and active cells (myo-fibroblasts). I will show that the consequence is a huge increase of the stiffness, which stops spontaneously when the healing is achieved but not in case of implants or tumors. Naive estimations can be given explaining difficulties encounted in drug treatments, for example.

Joint work with Min Wu.

Topological aspects of SU(N) magnetism and its cold atom realization

Thomas Quella, Universität Köln

Skyrmion Lattices in Antiferromagnetic Systems

Daniel C. Cabra  (University of La Plata)

Ordering of the frustrated classical Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions on the antiferromagnetic triangular lattice is studied under a magnetic field by means of semiclassical calculations and large-scale Monte Carlo simulations. We show that even a small DM interaction induces the formation of anAntiferromagneticSkyrmion crystal (AF-SkX) state. Unlike what is observed in ferromagnetic materials, we show that the AF-SkX state consists of three interpenetrating usual Skyrmion crystals (one by sublattice), and most importantly, the AF-SkX state survives in the limit of zero temperature. To characterize the phase diagram we compute the average of the topological order parameter, the chirality, which measures the numberof Skyrmions. As themagneticfieldincreases, this parameter presents a series of discrete jumps that may indicate transitions between different topological states. Increasing the magnetic field the model exhibits a first-order transition from a spiral phase into a three-sublattice Skyrmion structure where multiple Bragg peaks coexist in the spin structure factor.

Dynamic Nuclear Polarization and the paradox of Quantum Thermalization

Alberto Rosso (LPTMS)

Dynamic Nuclear Polarization (DNP) is to date the most  effective technique to increase the nuclear polarization up to a factor 100,000 opening disruptive perspectives for medical applications. In DNP, the nuclear spins are driven to an - out of equilibrium - hyperpolarized state by microwave saturation of the electron spins in interaction with them. Here we show that the electron dipolar interactions compete with the local magnetic fields resulting in two distinct dynamical phases: for strong interactions the electron spins equilibrate to an extremely low effective temperature that boosts  DNP  efficiency. For weak interaction this spin temperature is not defined and the polarization profile has an 'hole burning' shape characteristic of the non interacting case. The study of the many-body eigenstates reveals that these two phases are intimately related to the problem of thermalization in closed quantum systems where breaking of ergodicity is expected varying the strength of the interactions.

Instabilities in granular fluids at moderate densities

Vicente Garzo, Departamento de Fisica, Universidad de Extremadura

Physics of active contractile matter

Ulrich S. Schwarz (Heidelberg University)

Biological systems such as cells and tissue use non-equilibrium processes to actively generate mechanical stress, movement and growth. Some of these processes can actually be reconstituted in biomimetic experiments with active soft matter. In this talk, we will first discuss why and how contractile forces are generated by biological systems and how they can be measured with soft elastic substrates ("traction force microscopy"). Because kilo-Pascal stresses are typically transmitted through micrometer-sized contacts, the relevant force scale is nano-Newton. We then introduce different theoretical approaches to understand and model the contractility of biological matter. Because closed systems have to conserve momentum, the most central concept here is the one of a "force dipole", similarly as for the theoretical description of microswimmers, but now coupled to a mechanical rather than to a hydrodynamic environment. We present a stochastic theory for the biologically most relevant example of a contractile force dipole, namely the "myosin II minifilament". We then explain why on the large length scale of cells and tissue, the mechanical properties of these systems are dominated by tensions rather than by their elastic modulus, with dramatic consequences for their shape and force transmission to the environment.

Budding of domains in mixed bilayer membranes

J. Wolff,  Institut Charles Sadron (UPR CNRS), Strasbourg

Control of collective cell dynamics by adhesion, tension and fracking

Xavier Trepat (ICREA @ Institute for Bioengineering of Catalonia (IBEC), Barcelona)

A broad range of biological processes such as morphogenesis, tissue regeneration, and cancer invasion depend on the collective dynamics of epithelial cells. Such dynamics are determined by an exquisite balance between intercellular adhesion, cytoskeletal tension, and intracellular pressure. To study this balance in a fully quantitative manner I will present new techniques to map physical forces between and within cells. Using these techniques we studied how cellular forces are regulated and transmitted by the proteins that comprise intercellular adhesion complexes. To do so, we perturbed the main molecular players of the intercellular adhesome using RNAi and studied how these perturbations impact physical forces and cellular velocities in epithelial cell collectives. We found that perturbations targeting adherens junctions, but also tight junctions, gap junctions, and desmosomes have a significant impact on cell velocities, cell deformations, cell-matrix traction forces, and cell-cell forces. We developed a cross-validation analysis to show that concentrations of cell-cell adhesion proteins are significant predictors of cell-cell forces. Finally, I will discuss the determinants of epithelial integrity in the presence of stretching and transepithelial pressure.

Waiting times for entropic fluctuations in non-equilibrium processes

Abhishek Dhar (International centre for theoretical sciences, ICTS, Bangalore)

Nonequilibrium processes generate entropy. The total entropy generated in a fixed  finite time interval is a fluctuating variable. A  lot of recent work have looked at the probability of observing entropic fluctuations of different sizes in a fixed time interval. These distributions have been discussed in the context of fluctuation relations and large deviation functions. Here, we  ask the question: how long does one have to wait to see an entropic fluctuation of a specified size ? We present some results on the waiting time distribution,  in the context of some simple examples of non-equilibrium processes.

Reference: K. Saito and A. Dhar, arXiv:1504.02187

Universal Lyapunov Exponents from Products of Random Matrices

Gernot Akemann, Universität Bielefeld

Random Matrices find many applications in Physics and Mathematics. In particular products of random matrices can be used as a simple model for linear time evolution. In this talk I will review recent progress on an exact solution of this model for Gaussian random matrices. Both the spectral statistic of its complex eigenvalues and its real positive singular values are given by a determinantal point process with an underlying integrable kernel. In the limit of an infinite product the Lyapunov exponents become deterministic and we compute their variances and higher order cumulants. Remarkably the moduli of the complex eigenvalues and the singular values become identical in this limit. We will also discuss universality and possible extensions.

On the microstructure of active cellular processes

Eukaryotic cells use a multitude of protein machines to regulate their own structure. In this thesis, we study how the geometrical arrangement of these interacting microscopic active elements sculpt the cell's own internal microstructure and its membrane enclosure.

We first focus on the mechanisms generating actomyosin contractility, a crucial driver of cell motion and organization. We question the current position of highly organized, sarcomeric contractility as the only possible mechanism to drive contractility. We propose an alternative mechanism, and show that only it can account for the observed contractility of disordered actomyosin assemblies. It moreover yields qualitatively new effects in intracellular force transmission, including stress reversal and amplification, consistent with experimentally observations in fiber networks.

We next elucidate some of the mechanisms through which the cell deforms and cuts its own membrane, thus enabling exchanges with the extracellular medium as well as between its internal compartments. We find that the function of the proteins responsible for this remodeling is strongly influenced by the mechanics of the membrane, and use these effects to elucidate the modes of operation of proteins clathrin and dynamin, as well as of protein complex ESCRT-III.

Statistique d’extrêmes de variables aléatoires fortement corrélées

Anthony Perret

La statistique des valeurs extrêmes est une question majeure dans divers contexte scientifiques. Cependant, la description de la statistique d'un extremum global est certainement une caractéristique importante mais celle-ci ne décrit la fluctuation que d'une seule variable, parmi un grand nombre de variables aléatoires. Une question naturelle qui se pose alors est la suivante: ces valeurs extrêmes sont-elles isolées, loin des autres variables ou bien au contraire existe-t-il un grand nombre d'autres variables proches de ces valeurs extrêmes ? Ces questions ont suscité l'étude de la densité d'état de ces événements quasi-extrêmes. Il existe pour cette quantité peu de résultats pour des variables fortement corrélées, qui pourtant est le cas de nombreux modèles fondamentaux. Deux pistes de modèles physiques de variables fortement corrélées pouvant être étudiés analytiquement se démarquent alors: les positions d’une marche aléatoire et les valeurs propres de matrice aléatoire. Ce sont les deux modèles que j'ai étudiés dans ma thèse et que je vais présenter durant cette soutenance.

Pourquoi l’objectif des 2°C appartient, hélas, au passé ?

Jacques Treiner (Paris VI et Sciences Po)

Depuis la conférence de Copenhague de 2009, la référence de 2°C comme augmentation de la température moyenne de la Terre apparait comme un objectif à ne pas dépasser. Cette valeur, choisie à la suite de négociations extrêmement difficiles entre 26 pays seulement (notamment sans l’UE) n’a pas de caractère contraignant, mais c’est le seul objectif chiffré servant depuis lors de référence internationale. C’est asn doute la raison pour laquelle ce chiffre sert de référence pour la COP21 à Paris en décembre 2015. Mais il n’est pas difficile de se rendre compte que, hélas, les conditions requises pour que ce scénario se réalise sont devenue impossibles à remplir. Quelles conséquences en tirer ?

Looking for the mechanical control of growth in plants. Is there a simple law?

Alexis Peaucelle (INRA Versailles/Cambridge University)

Plants are strikingly good at math, especially geometry. One could find parts or full plants shaped as spheres, circles, straight lines, and flat surfaces, golden and right angles and all sorts of exotic and pretty combination of shapes. These shapes are generated through complex tissue growth. We want to understand this puzzling beauty by focusing on the biophysical properties of the cell wall and its related biochemistry. We will present some of our results on dark grown hypocotyl and pavement cells demonstrating that pectin methylesterification status change is necessary for cell and tissue differentiation, growth and is related to changes in cell wall elasticity. Then we will expose puzzling results showing that cell growth rates are proportionate to the elastic stretching of the cell wall (Pressure divided by the Young modulus) and not plastic properties of the cell wall components. Finally, we will present preliminary experiments that could explain this paradox as well as some others such as microtubule partial correlation with oriented growth, and sound-induced plant growth.

Shortcutting adiabaticity : how to change rapidly the state of a trapped gas ?

Emmanuel Trizac, LPTMS

Topological phase transitions in multichannel disordered wires in the chiral  symmetry classes

Christophe Texier, LPTMS

Field theory on fuzzy spaces: effective action and phase transitions

Alexios Polychronakos (City College NY)

Marginal stability and flow in granular materials

Matthieu WYART (New York University)

Complex systems are characterized by an abundance of meta-stable states.This is the case for granular materials, that can flow until one jammed configuration (among the exponentially many possible ones) is reached. I will argue that at least in popular simplified models of granular materials, these dynamically-accessible configurations are stable, but barely so. Such marginal stability offers a new perspective on both the solid and the liquid phase. I will discuss dense suspensions and propose to describe flow as a gas of elementary excitations, corresponding to the opening and closing of contact between particles. This approach leads to a detailed scaling description of rheological properties and length scales of dense flows. If time permits I will discuss a classification of athermal glassy systems based on the stability of low-energy excitations.

Topology and fractals : waves and fields in quasicrystals (theory and experiments with polaritons)

Eric Akkermans, Technion - Israel Institute of Technology

Decentralized network control, optimization and random walks on networks

In the last years several problems been studied at the interface between statistical physics and computer science. The reason being that often these problems can be reinterpreted in the language of physics of disordered systems, where a big number of variables interacts through local fields dependent on the state of the surrounding neighborhood. Among the numerous applications of combinatorial optimisation the optimal routing on communication networks is the subject of the first part of the thesis. We will exploit the cavity method to formulate efficient algorithms of type message-passing and thus solve several variants of the problem through its numerical implementation. At a second stage, we will describe a model to approximate the dynamic version of the cavity method which allows to decrease the complexity of the problem from exponential to polynomial in time. This will be obtained by using the Matrix Product State formalism of quantum mechanics. Another topic that has attracted much interest in statistical physics of dynamic processes is the random walk on networks. The theory has been developed since many years in the case the underneath topology is a d-dimensional lattice. On the contrary the case of random networks has been tackled only in the past decade, leaving many questions still open for answers. Unravelling several aspects of this topic will be the subject of the second part of the thesis. In particular we will study the average number of distinct sites visited during a random walk and characterize its behaviour as a function of the graph topology. Finally, we will address the rare events statistics associated to random walks on networks by using the large-deviations formalism. Two types of dynamic phase transitions will arise from numerical simulations, unveiling important aspects of this problems. We will conclude outlining the main results of an independent work developed in the context of out-of-equilibrium physics. A solvable system made of two Brownian particles surrounded by a thermal bath will be studied providing details about a bath-mediated interaction arising for the presence of the bath.

Modeling and inference for biological systems: from auxin dynamics in plants to protein evolution

All biological systems are made of atoms and molecules interacting in a non-trivial manner. Such non-trivial interactions induce complex behaviours allowing organisms to fulfil their many vital functions. These features can be found in all biological systems at different levels, from molecules and genes up to cells and tissues. In the past few decades, physicists have been paying much attention to these intriguing aspects by framing them in network approaches for which a number of theoretical methods offer many powerful ways to tackle systemic problems. At least two different ways of approaching these challenges may be considered: direct modelling methods and approaches based on inverse methods. In this defence I am going to show how we made use of both approaches to study three different problems occurring on three different biological scales. The first part concerns the very early stages of tissue development in plants; it covers the model we proposed for understanding which features drive the spontaneous collective behaviour in space and time of the transporters which pump the phytohormone auxin out of plant cells. Then, at the cell level, I will go through my study of the intracellular molecular networks that implement auxin signalling in plants, examining how network structures affect network functions. Finally, I will talk about inference problems on structural properties of proteins. I will introduce a method we formulated to understand how conservation of protein function across different organisms constrains the evolution of protein sequences and their diversity.

Osmotic spreading of Bacillus subtilis biofilms

Agnese Seminara (LPMC, Université de Nice)

Bacterial biofilms are organized communities of cells living in association with surfaces. The hallmark of biofilm formation is a well defined spatio-temporal pattern of gene expression, leading to differentiation and a complex morphology. While this process resembles the development of a multicellular organism, biofilms are only transiently multicellular. More importantly the functions associated to the biofilm phenotype are largely unknown.

A common feature of biofilm formation is the secretion of a polymeric matrix rich in sugars and proteins in the extracellular space. In Bacillus subtilis, secretion of the exopolysaccharide (EPS) component of the extracellular matrix is genetically coupled to the inhibition of flagella-mediated motility. The onset of this switch results in slow expansion of the biofilm on a substrate. Different strains have radically different capabilities in surface colonization: Flagella-null strains spread at the same rate as wild type, while both are dramatically faster than EPS mutants. Multiple functions have been attributed to the EPS, but none of these provides a physical mechanism for generating spreading. We propose that the secretion of EPS drives surface motility by generating osmotic pressure gradients in the extracellular space. A simple mathematical model based on the physics of polymer solutions shows quantitative agreement with experimental measurements of biofilm growth, thickening, and spreading. We discuss the implications of this osmotically driven type of surface motility for nutrient uptake that may elucidate the reduced fitness of the matrix-deficient mutant strains.

Regulation of actin assembly and mechanotransduction in cell-matrix adhesion complexes: a biochemical study of the talin-vinculin complex

Christophe Le Clainche (I2BC, Gif-sur-Yvette)

• (1) Christophe Le Clainche and Marie-France Carlier. Regulation of actin assembly associated with protrusion and adhesion in cell migration. Physiological Reviews (2008) Apr;88(2):489-513.
• (2) Corina Ciobanasu, Bruno Faivre, Christophe Le Clainche. Integrating actin dynamics, mechanotransduction and integrin activation: The multiple functions of actin binding proteins in focal adhesions. European Journal of Cell Biology (2013) (92) 339-348.
• (3) Christophe Le Clainche, Satya P Dwivedi, Dominique Didry, Marie-France Carlier. Vinculin is a dually regulated actin filament barbed-end capping and side-binding protein. Journal of Biological Chemistry (2010) Jul 23;285(30):23420-32.
• (4) Corina Ciobanasu, Bruno Faivre, Christophe Le Clainche. Actomyosin dependent formation of the mechanosensitive talin-vinculin complex reinforces actin anchoring. Nature Communications (2014) 5:3095
• (5) Corina Ciobanasu, Bruno Faivre, Christophe Le Clainche. Reconstituting actomyosin-dependent mechanosensitive protein complexes in vitro. Nature Protocols (2015) Jan ;10(1):75-89

A random walk approach to stochastic neutron transport

Hierachical rigidities of glassy systems

Hajime Yoshino, Osaka University

Number statistics in random matrices and applications to quantum systems

Ricardo Marino

Random matrix theory has found many applications spanning a vast number of fields in physics and mathematics in the last two decades. Most recently, the equivalence between the statistics of eigenvalues of Gaussian Hermitian matrices  and the position of ground-state harmonically confined 1-D fermionic particles has been studied to obtain many interesting and universal results in cold atoms. In my thesis, I explore this connection to solve the problem of determining quantum fluctuations of cold fermions using techniques from random matrix theory, expanding previous results that were restricted only to specific scaling limits of the spectrum to yield a full picture of the behavior of fluctuations of fermionic particles in one dimensional traps.

In pure states of many-body systems, entanglement is routinely studied via the Renyi entropies, which give a complete characterization of the bipartite case. The situation becomes more complicated, if the system is composed of more than two parts, and one is interested in the entanglement between two non-complementary pieces. Such a scenario can be studied by introducing a new entanglement measure, the so-called negativity, which has been the focus of recent interest. In this talk I would like to give an overview about the available methods to calculate the negativity, and present some new results on mixed-state entanglement.

Quaternionic R transform and non-hermitian random matrices

Dr. Zdzislaw Burda (AGH University of Science and Technology)

Using the Cayley-Dickson construction we rephrase and review the non-hermitian diagrammatic formalism [R. A. Janik, M. A. Nowak, G. Papp and I. Zahed, Nucl.Phys. B 501, 603 (1997)], that generalizes the free probability calculus to asymptotically large non-hermitian random matrices. The main object in this generalization is a quaternionic extension of the R transform which is a generating function for planar (non-crossing) cumulants. We demonstrate that the quaternionic R transform generates all connected averages of all distinct powers of X and its hermitian conjugate X^†:  <<(1/N) Tr [X^a X^†b X^c …] >>  for N → ∞. We show that the R transform for Gaussian elliptic laws is given by a simple linear quaternionic map R(z+wj) = x + σ² (μ e^{2iφ} z + w j) where (z,w) is the Cayley-Dickson pair of complex numbers forming a quaternion q=(z,w)≡ z+ wj. This map has five real parameters Re[x], Im[x], φ, σ and μ. We use the R transform to calculate the limiting eigenvalue densities of several products of Gaussian random matrices.

Explosive condensation in nonequilibrium systems

Martin EVANS, School of Physics and Astronomy, Univ. of Edinburgh

In this talk I will discuss condensation in the zero range process (ZRP) and related models. The ZRP is a simple model of interacting classical particles hopping between sites of a one-dimensional lattice, but with rates that do not obey detailed balance and thus generate a nonequilibrium state. Real-space condensation is the phenomenon whereby a finite fraction of the particles are typically found at a single site in the limit of a large system size. I'll show how and why condensation arises and how it is related to large deviations of sums of random variables. I'll also discuss a variation of the model exhibiting `explosive condensation' - the condensate moves rapidly through the system and the relaxation time to the stationary state decreases to zero for large system size. This provides a first example of instantaneous gelation in a spatially extended system. If time permits I will also discuss how condensation generally arises when there are two constraints - say the sum and the variance - on a collection of random variables.

Andrii Gudyma

Insights on the regulatory principles of genome organization in unicellular microorganisms

Romain Koszul (Institut Pasteur)

Chromosomes of a broad range of kingdoms, from bacteria to mammals, are structured by large topological domains, whose precise functional roles and regulatory mechanisms remain elusive. Using chromosome conformation capture technology, we unraveled the higher-order organization of the Bacillus subtilis, Escherichia coli and Vibrio cholerae genomes, in a variety of growth and mutant conditions. Different types of topological domains were found to structure these chromosomes, ranging from a few dozens to a thousand kb. We show that the matP/matS and parB/parS systems generate specific types of topological structures, regulated by replication and cell cycle progression. We have also functionally characterized some of the global organizational principles of these domains, in link with replication/segregation during the cell cycle. Overall, the comparative analysis of these different species provide striking insights on the diversity of the regulatory mechanisms of genome structure of the bacterial world. In addition, I will also present and discuss recent data obtained during the cell cycle of the eukaryotic species Saccharomyces cerevisiae.

Random walks that generate their own environment

J.K. Percus, Courant Inst and Physics Dept, New York University

Simulating Growing Tissues

Jens Elgeti (Forschungszentrum Jülich)

Growth of solid tumors or metastasis requires, besides massive biomedical changes, also a spatial remodelling of the tissue. This remodelling, often including displacements of healthy tissue around, requires mechanical work to be done. These mechanics of growth has attracted a lot of attention in recent years, but still remains poorly understood.

We use particle based simulations to study mechanical properties and effects in growing and motile tissues. These simulations have been helpful in understanding, interpreting and designing experiments. I will present an overview of the simulation technique, and how it contributed to recent developments in three dimensional tissue growth and collective cell migration. In a recent series of simulations and close experimental collaborations we found important interfacial and surface effects that lead to novel phenomena. For example, the tissue divides favorably at a free surface, even without any nutrient effects. This leads to the possibility and stability of a negative homeostatic pressure. In turn, a negative homeostatic pressure leads to naturally to finite steady states and tensile states.

References: [1] M.Basan et al, PNAS 110:2452 (2013) [2] F. Montel et al, N. J. Phys. 14:055008 (2012) [3] F. Montel et al, Phys. Rev. Lett. 107:188102, (2011) [4] M. Basan et al, Phys. Biol. 8:026014, (2011) [5] J. Ranft et al, PNAS 107:20863, (2010)

Superfluid and quantum features in the hydrodynamic flow of a fluid of light

Pierre-Élie Larré, INO-CNR BEC Center, Dipartimento di Fisica, Università di Trento, Via Sommarive 14, 38123 Povo, Italia

Time evolution of out-of-equilibrium integrable models

Jacopo de Nardis, LPS ENS

SEMINAR CANCELLED

Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid.

Oleg Lychkovskiy, Russian Quantum Center, Moscow

We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting, the impurity is injected in the fluid with some initial velocity v_0 (which is below the critical velocity), and we enquire about its velocity at infinite time, v_inf. We derive a rigorous upper bound on |v_0 − v_inf|. In the limit of vanishing impurity-fluid coupling, this bound amounts to v_inf = v_0, which is anticipated from the Landau criterion of superfluidity. In the case of a finite coupling, the velocity of the impurity can decrease, but not to zero; the bound quantifies the maximal possible decrease.

In the second setting, a small constant force is exerted upon the impurity. We argue that two distinct dynamical regimes exist—backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. Which regime is realized depends on the mass of the impurity. A nonequilibrium quantum phase transition occurs at some critical mass.

Tracking nonequilibrium physics in living systems

Étienne Fodor (Université Paris-Diderot)

Living systems operate far from equilibrium due to the continuous injection of energy provided by ATP supply. The dynamics of the intracellular components is driven by both thermal equilibrium fluctuations and active stochastic forces generated by the molecular motors. Tracer particles are injected in living cells to study these fluctuations. Alternatively, vesicles which are already present in the cytoplasm serve as probes of the intracellular dynamics.

To sort out genuine nonequilibrium fluctuations from purely thermal effects, we combine passive and active microrheology methods. They consist in measuring the spontaneous tracer fluctuations and extracting the response from an external oscillatory perturbation. By testing the fluctuation-dissipation theorem, we quantify the deviation from equilibrium appearing at low frequency. Removing the thermal contribution in the tracer fluctuations, we estimate the spectrum of the active forces. Eventually, we report non-Gaussian tails in the tracer displacement distribution as a result of directed motion events.

We recapitulate theoretically the observed fluctuations by modeling the dynamics with a confining harmonic potential which experiences random bursts as a result of motor activity [1]. This minimal model allows us to quantify the time and length scales of the active forces, along with the energy scale injected by the ensuing fluctuations [2, 3]. Finally, we estimate the energy dissipated by the tracers in the surrounding environment, leading us to define an efficiency of the energy conversion driving the tracer dynamics [4].

• [1] É. Fodor et al., Phys. Rev. E 90, 042724 (2014)
• [2] É. Fodor et al., EPL 110, 48005 (2015)
• [3] W. W. Ahmed et al., arXiv:1510.08299
• [4] É. Fodor et al., arXiv:1511.00921

Estimating topological properties of weighted networks from limited information

Andrea Gabrielli, Dipartimento di Fisica, Università di Roma La Sapienza