laboratoire de physique statistique
laboratoire de physique statistique




P A R M I :

From Spiking Neuron Models to Linear-Nonlinear Models - Ostojic, Srdjan and Brunel, Nicolas

Abstract : Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsaki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsaki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
Orientation profiles of the trapezium and the square-diamond geometrical illusions - Ninio, J.
PERCEPTION 4045 (2011)
Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators - Brau, Fabian and Vandeparre, Hugues and Sabbah, Abbas and Poulard, Christophe and Boudaoud, Arezki and Damman, Pascal
NATURE PHYSICS 756-60 (2011)

Abstract : Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy(1), whereas compressing a membrane resting on a soft foundation creates a regular pattern of sinusoidal wrinkles with a broad distribution of energy(2-8). Here, we study the energy distribution for highly confined membranes and show the emergence of a new morphological instability triggered by a period-doubling bifurcation. A periodic self-organized focalization of the deformation energy is observed provided that an up-down symmetry breaking, induced by the intrinsic nonlinearity of the elasticity equations, occurs. The physical model, exhibiting an analogy with parametric resonance in a nonlinear oscillator, is a new theoretical toolkit to understand the morphology of various confined systems, such as coated materials or living tissues, for example wrinkled skin(3), internal structure of lungs(9), internal elastica of an artery(10), brain convolutions(11,12) or formation of fingerprints(13). Moreover, it opens the way to a new kind of microfabrication design of multiperiodic or chaotic (aperiodic) surface topography through self-organization.
Microscopic versus macroscopic approaches to non-equilibrium systems - Derrida, Bernard

Abstract : The one-dimensional symmetric simple exclusion process (SSEP) is one of the very few exactly soluble models of non-equilibrium statistical physics. It describes a system of particles which diffuse with hard core repulsion on a one-dimensional lattice in contact with two reservoirs of particles at unequal densities. The goal of this paper is to review the two main approaches which lead to the exact expression of the large deviation functional of the density of the SSEP in its steady state: a microscopic approach (based on the matrix product ansatz and an additivity property) and a macroscopic approach (based on the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim).
Effect of Helium Elasticity on Torsional Oscillator Measurements - Maris, Humphrey J. and Balibar, Sebastien

Abstract : In 2004 Kim and Chan performed a torsional oscillator measurement of the rotational inertia of solid helium-4. They found frequency changes which were interpreted in terms of a non-classical rotational inertia, that is a partial superfluidity or ``supersolidity'' of solid helium-4. Since then there have been many further studies using various versions of this technique. One important question that arises in these experiments is the possible effect on the oscillator frequency of changes in the elasticity of the solid helium; this can produce a change in frequency that adds to any effect due to superfluidity. In this paper we give a general discussion of the effect of changes in elasticity on the oscillator frequency and consider how the magnitude of the effect is influenced by the oscillator design. Our results should help make it possible to discriminate between frequency changes due to changes in elasticity and changes due to supersolidity.
Alternation frequency thresholds for stereopsis as a technique for exploring stereoscopic difficulties - Rychkova, Svetlana and Ninio, Jacques
I-PERCEPTION 250-68 (2011)

Abstract : When stereoscopic images are presented alternately to the two eyes, stereopsis occurs at F >= 1 Hz full-cycle frequencies for very simple stimuli, and F >= 3 Hz full-cycle frequencies for random-dot stereograms (eg Ludwig I, Pieper W, Lachnit H, 2007 ``Temporal integration of monocular images separated in time: stereopsis, stereoacuity, and binocular luster'' Perception \& Psychophysics 69 92-102). Using twenty different stereograms presented through liquid crystal shutters, we studied the transition to stereopsis with fifteen subjects. The onset of stereopsis was observed during a stepwise increase of the alternation frequency, and its disappearance was observed during a stepwise decrease in frequency. The lowest F values (around 2.5 Hz) were observed with stimuli involving two to four simple disjoint elements (circles, arcs, rectangles). Higher F values were needed for stimuli containing slanted elements or curved surfaces (about 1 Hz increment), overlapping elements at two different depths (about 2.5 Hz increment), or camouflaged overlapping surfaces (> 7 Hz increment). A textured cylindrical surface with a horizontal axis appeared easier to interpret (5.7 Hz) than a pair of slanted segments separated in depth but forming a cross in projection (8 Hz). Training effects were minimal, and F usually increased as disparities were reduced. The hierarchy of difficulties revealed in the study may shed light on various problems that the brain needs to solve during stereoscopic interpretation. During the construction of the three-dimensional percept, the loss of information due to natural decay of the stimuli traces must be compensated by refreshes of visual input. In the discussion an attempt is made to link our results with recent advances in the comprehension of visual scene memory.
Effective line tension and contact angles between membrane domains in biphasic vesicles - Trejo, M. and Ben Amar, M.

Abstract : Inhomogeneities in membranes give rise to localized interactions at the interface between domains in two-component vesicles. The corresponding energy is expressed as a line tension between the two phases. In this paper we study the implications of the thickness mismatch between domains which has been experimentally reported to be of order 20-30\% and the conditions under which the induced line tension can destabilize the domains in inhomogeneous vesicles. For asymmetric lipidic membranes we prove an increase of the line tension and the existence of a contact angle. Adsorption of impurities is also examined, our scope being the extension of the Canham-Helfrich model to describe elastic deformations and chemical interactions arising at microscopic scales. This mismatch effect may have important consequences for the stability of very small domains.
Micro helical polymeric structures produced by variable voltage direct electrospinning - Shariatpanahi, S. P. and Zad, A. Iraji and Abdollahzadeh, I. and Shirsavar, R. and Bonn, D. and Ejtehadi, R.
SOFT MATTER 710548-10551 (2011)

Abstract : Direct near field electrospinning is used to produce very long helical polystyrene microfibers in water. The pitch length of helices can be controlled by changing the applied voltage, allowing the production of both microsprings and microchannels. Using a novel high frequency variable voltage electrospinning method we determined the helix formation speed and compared the experimental buckling frequency to theoretical expressions for viscous and elastic buckling. Finally we showed that the new method can be used to produce new periodic micro and nano structures.
Mutual Adaptation of a Faraday Instability Pattern with its Flexible Boundaries in Floating Fluid Drops - Pucci, G. and Fort, E. and Ben Amar, M. and Couder, Y.

Abstract : Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This is implemented by triggering this instability in floating fluid drops. An interaction of Faraday waves with the shape of the drop is observed, the radiation pressure of the waves exerting a force on the surface tension held boundaries. Two regimes are observed. In the first one there is a coadaptation of the wave pattern with the shape of the domain so that a steady configuration is reached. In the second one the radiation pressure dominates and no steady regime is reached. The drop stretches and ultimately breaks into smaller domains that have a complex dynamics including spontaneous propagation.
Cell motility: A viscous fingering analysis of active gels - Ben Amar, M. and Manyuhina, O. V. and Napoli, G.

Abstract : The symmetry breaking of the actin network from radial to longitudinal symmetry has been identified as the major mechanism for keratocytes (fish cells) motility on solid substrate. For strong friction coefficient, the two-dimensional actin flow which includes the polymerisation at the edge and depolymerisation in the bulk can be modelled as a Darcy flow, the cell shape and dynamics being then modelled by standard complex analysis methods. We use the theory of active gels to describe the orientational order of the filaments which varies from the border to the bulk. We show analytically that the reorganisation of the cortex is enough to explain the motility of the cell and find the velocity as a function of the orientation order parameter in the bulk.
A versatile Bilayer Phase for the Studies of Transmembrane Proteins' Association - Rayan, Gamal and Reffay, Myriam and Picard, Martin and Taulier, Nicolas and Ducruix, Arnaud and Urbach, Wladimir
Sudden Chain Energy Transfer Events in Vibrated Granular Media - Rivas, Nicolas and Ponce, Suomi and Gallet, Basile and Risso, Dino and Soto, Rodrigo and Cordero, Patricio and Mujica, Nicolas

Abstract : In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost. The process repeats once segregation has taken place again, either randomly or with some regularity in time depending on the experimental or numerical parameters. An explanation for these events is provided based on the existence of a fixed point for an isolated particle bouncing with only vertical motion. The horizontal energy peaks occur when the energy stored in the vertical motion is partly transferred into horizontal energy through a chain reaction of collisions between heavy particles.
Two-dimensional simulation of linear wave propagation in a suspension of polymeric microcapsules used as ultrasound contrast agents - Haiat, Guillaume and Berti, Romain and Galaz, Belfor and Taulier, Nicolas and Amman, Jean-Jacques and Urbach, Wladimir

Abstract : A generation of tissue-specific stable ultrasound contrast agent (UCA) composed of a polymeric capsule with a perfluorocarbone liquid core has become available. Despite promising uses in clinical practice, the acoustical behavior of such UCA suspensions remains unclear. A simulation code (2-D finite-difference time domain, FDTD) already validated for homogeneous particles [Galaz Haiat, Berti, Taulier, Amman and Urbach, (2010). J. Acoust. Soc. Am. 127, 148-154] is used to model the ultrasound propagation in such UCA suspensions at 50 MHz to investigate the sensitivity of the ultrasonic parameters to physical parameters of UCA. The FDTD simulation code is validated by comparison with results obtained using a shell scatterer model. The attenuation coefficient (respectively, the sound velocity) increases (respectively, decreases) from 4.1 to 58.4 dB/cm (respectively, 1495 to 1428 m/s) when the concentration varies between 1.37 and 79.4 mg/ml, while the backscattered intensity increases non-linearly, showing that a concentration of around 30 mg/ml is sufficient to obtain optimal backscattering intensity. The acoustical parameters vary significantly as a function of the membrane thickness, longitudinal and transverse velocity, indicating that mode conversions in the membrane play an important role in the ultrasonic propagation. The results may be used to help manufacturers to conceive optimal liquid-filled UCA suspensions. (C) 2011 Acoustical Society of America. [DOI: 10.1121/1.3543966]
Buckling condensation in constrained growth - Dervaux, Julien and Ben Amar, Martine

Abstract : The multiple complexities inherent to living objects have motivated the search for abiotic substitutes, able to mimic some of their relevant physical properties. Hydrogels provide a highly monitorable counterpart and have thus found many applications in medicine and bioengineering. Recently, it has been recognized that their ability to swell could be used to unravel some of the universal physical processes at work during biological growth. However, it is yet unknown how the microscopic distinctions between swelling and biological growth affect macroscopic changes (shape, stresses) induced by volume variations. To answer this question, we focus on a clinically motivated example of growth. Some solid tumors such as melanoma or glioblastoma undergo a shape transition during their evolution. This bifurcation appears when growth is confined at the periphery of the tumor and is concomitant with the transition from the avascular to the vascular stage of the tumor evolution. To model this phenomenon, we consider in this paper the deformation of an elastic ring enclosing a core of different stiffness. When the volume of the outer ring increases, the system develops a periodic instability. We consider two possible descriptions of the volume variation process: either by imposing a homogeneous volumetric strain (biological growth) or through migration of solvent molecules inside a solid network (swelling). For thin rings, both theories are in qualitative agreement. When the interior is soft, we predict the emergence of a large wavelength buckling. Upon increasing the stiffness of the inner disc, the wavelength of the instability decreases until a condensation of the buckles occurs at the free boundary. This short wavelength pattern is independent of the stiffness of the disc and is only limited by the presence of surface tension. For thicker rings, two scenarios emerge. When a volumetric strain is prescribed, compressive stresses accumulate in the vicinity of the core and the deformation localizes itself at the boundary between the disc and the ring. On the other hand, swelling being an instance of stress-modulated growth, elastic stretches near the core saturate and the instability occurs primarily at the free boundary. Besides its implications for the mechanical stability of avascular tumors, this work provides important results concerning layered tissues growth and the role of hydrogels as biological tissues substitutes. (C) 2010 Elsevier Ltd. All rights reserved.
Soft magnetic tweezers: A proof of principle - Mosconi, Francesco and Allemand, Jean Francois and Croquette, Vincent

Abstract : We present here the principle of soft magnetic tweezers which improve the traditional magnetic tweezers allowing the simultaneous application and measurement of an arbitrary torque to a deoxyribonucleic acid (DNA) molecule. They take advantage of a nonlinear coupling regime that appears when a fast rotating magnetic field is applied to a superparamagnetic bead immersed in a viscous fluid. In this work, we present the development of the technique and we compare it with other techniques capable of measuring the torque applied to the DNA molecule. In this proof of principle, we use standard electromagnets to achieve our experiments. Despite technical difficulties related to the present implementation of these electromagnets, the agreement of measurements with previous experiments is remarkable. Finally, we propose a simple way to modify the experimental design of electromagnets that should bring the performances of the device to a competitive level. (C) 2011 American Institute of Physics. [doi:10.1063/1.3531959]
Fiber optic probe hydrophone for the study of acoustic cavitation in water - Arvengas, Arnaud and Davitt, Kristina and Caupin, Frederic

Abstract : We use focused ultrasound bursts to submit a liquid to mechanical tension. When the pressure in the sound wave reaches a sufficiently low value, vapor bubbles are nucleated in the bulk liquid. According to nucleation theory, increasing the ultrasound frequency increases the cavitation threshold by a calculable amount. To check this, we have built a fiber optic probe hydrophone based on one originally proposed by Staudenraus and Eisenmenger [Ultrasonics 31, 267 (1993)]. We have adapted the pressure calibration and data analysis of this tool to make it appropriate for precise measurements of tension in liquids. We are able to resolve the fractional change in the pressure threshold for cavitation in water that results from a twofold increase in the frequency. This provides a test of nucleation theory in general. (C) 2011 American Institute of Physics. [doi:10.1063/1.3557420]
Adaptive Cluster Expansion for Inferring Boltzmann Machines with Noisy Data - Cocco, S. and Monasson, R.

Abstract : We introduce a procedure to infer the interactions among a set of binary variables, based on their sampled frequencies and pairwise correlations. The algorithm builds the clusters of variables contributing most to the entropy of the inferred Ising model and rejects the small contributions due to the sampling noise. Our procedure successfully recovers benchmark Ising models even at criticality and in the low temperature phase, and is applied to neurobiological data.
Nonlinear dynamos at infinite magnetic Prandtl number - Alexakis, Alexandros

Abstract : The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior.
The radial growth phase of malignant melanoma: multi-phase modelling, numerical simulations and linear stability analysis - Ciarletta, P. and Foret, L. and Ben Amar, M.

Abstract : Cutaneous melanoma is disproportionately lethal despite its relatively low incidence and its potential for cure in the early stages. The aim of this study is to foster understanding of the role of microstructure on the occurrence of morphological changes in diseased skin during melanoma evolution. The authors propose a biomechanical analysis of its radial growth phase, investigating the role of intercellular/stromal connections on the initial stages of epidermis invasion. The radial growth phase of a primary melanoma is modelled within the multi-phase theory of mixtures, reproducing the mechanical behaviour of the skin layers and of the epidermal-dermal junction. The theoretical analysis takes into account those cellular processes that have been experimentally observed to disrupt homeostasis in normal epidermis. Numerical simulations demonstrate that the loss of adhesiveness of the melanoma cells both to the basal laminae, caused by deregulation mechanisms of adherent junctions, and to adjacent keratynocytes, consequent to a downregulation of E-cadherin, are the fundamental biomechanical features for promoting tumour initiation. Finally, the authors provide the mathematical proof of a long wavelength instability of the tumour front during the early stages of melanoma invasion. These results open the perspective to correlate the early morphology of a growing melanoma with the biomechanical characteristics of its micro-environment.
Single molecule actuation and detection on a lab-on-a-chip magnetoresistive platform - Chaves, R. C. and Bensimon, D. and Freitas, P. P.

Abstract : On-chip magnetic tweezers based on current loops were integrated with magnetoresistive sensors. Magnetic forces up to 1.0 +/- 0.3 pN are produced to actuate on DNA anchored to the surface of a flow cell and labeled with micrometer-sized magnetic beads. The levitation of the beads stretches the immobilized DNA. The relative position of the magnetic beads is monitored using spin-valve sensors. A bead vertical displacement resolution of 60 nm is derived for DNA molecular motor activity in a tweezer steady current regime. (C) 2011 American Institute of Physics. [doi:10.1063/1.3560853]