Entropic aging and extreme value statistics

Entropic aging consists in a progressive slowing down of the low-temperature dynamics of a glassy system due to the rarefaction of downwards directions on the energy landscape, as lower and lower energy levels are reached. A prototypical model exhibiting this scenario is the Barrat-M\'ezard model. We argue that in the zero-temperature limit, this model precisely corresponds to a dynamical realization of extreme value statistics, providing an interesting connection between the two fields. This mapping directly yields the long-time asymptotic shape of the dynamical energy distribution, which is then one of the standard extreme value distributions (Gumbel, Weibull or Fr\'echet), thus restricting the class of asymptotic energy distributions with respect to the original preasymptotic results. We also briefly discuss similarities and differences between the Barrat-M\'ezard model and undriven dissipative systems like granular gases.Comment: 8 pages, to appear in J. Phys.

Weak Homology of Bright Elliptical Galaxies

Studies of the Fundamental Plane of early-type galaxies, from small to intermediate redshifts, are often carried out under the guiding principle that the Fundamental Plane reflects the existence of an underlying mass-luminosity relation for such galaxies, in a scenario where elliptical galaxies are homologous systems in dynamical equilibrium. Here I will re-examine the issue of whether empirical evidence supports the view that significant systematic deviations from strict homology occur in the structure and dynamics of bright elliptical galaxies. In addition, I will discuss possible mechanisms of dynamical evolution for these systems, in the light of some classical thermodynamical arguments and of recent N-body simulations for stellar systems under the influence of weak collisionality.Comment: 13 pages, 7 figures, to appear in "Galaxies and Chaos", Contopoulos, G. and Voglis, N. (eds), Lecture Notes in Physics, Springer-Verlag, Heidelber

Optic flow based perception of two-dimensional trajectories and the effects of a single landmark.

It is well established that human observers can detect their heading direction on a very short time scale on the basis of optic flow (500ms; Hooge et al., 2000). Can they also integrate these perceptions over time to reconstruct a 2D trajectory simulated by the optic flow stimulus? We investigated the visual perception and reconstruction of passively travelled two-dimensional trajectories from optic flow with and without a single landmark. Stimuli in which translation and yaw are unyoked can give rise to illusory percepts; using a structured visual environment instead of only dots can improve perception of these stimuli. Does the additional visual and/or extra-retinal information provided by a single landmark have a similar, beneficial effect? Here, seated, stationary subjects wore a head-mounted display showing optic flow stimuli that simulated various manoeuvres: linear or curvilinear 2D trajectories over a horizontal ground plane. The simulated orientation was either fixed in space, fixed relative to the path, or changed relative to both. Afterwards, subjects reproduced the perceived manoeuvre with a model vehicle, of which we recorded position and orientation. Yaw was perceived correctly. Perception of the travelled path was less accurate, but still good when the simulated orientation was fixed in space or relative to the trajectory. When the amount of yaw was not equal to the rotation of the path, or in the opposite direction, subjects still perceived orientation as fixed relative to the trajectory. This caused trajectory misperception because yaw was wrongly attributed to a rotation of the path. A single landmark could improve perception

Visuo-vestibular interaction in the reconstruction of travelled trajectories

We recently published a study of the reconstruction of passively travelled trajectories from optic flow. Perception was prone to illusions in a number of conditions, and not always veridical in the others. Part of the illusionary reconstructed trajectories could be explained by assuming that subjects base their reconstruction on the ego-motion percept built during the stimulus' initial moments . In the current paper, we test this hypothesis using a novel paradigm: if the final reconstruction is governed by the initial percept, providing additional, extra-retinal information that modifies the initial percept should predictably alter the final reconstruction. The extra-retinal stimulus was tuned to supplement the information that was under-represented or ambiguous in the optic flow: the subjects were physically displaced or rotated at the onset of the visual stimulus. A highly asymmetric velocity profile (high acceleration, very low deceleration) was used. Subjects were required to guide an input device (in the form of a model vehicle; we measured position and orientation) along the perceived trajectory. We show for the first time that a vestibular stimulus of short duration can influence the perception of a much longer lasting visual stimulus. Perception of the ego-motion translation component in the visual stimulus was improved by a linear physical displacement: perception of the ego-motion rotation component by a physical rotation. This led to a more veridical reconstruction in some conditions, but to a less veridical reconstruction in other conditions

A fast direct method of mass reconstruction for gravitational lenses

Statistical analyses of observed galaxy distortions are often used to reconstruct the mass distribution of an intervening cluster responsible for gravitational lensing. In current projects, distortions of thousands of source galaxies have to be handled efficiently; much larger data bases and more massive investigations are envisaged for new major observational initiatives. In this article we present an efficient mass reconstruction procedure, a direct method that solves a variational principle noted in an earlier paper, which, for rectangular fields, turns out to reduce the relevant execution time by a factor from 100 to 1000 with respect to the fastest methods currently used, so that for grid numbers N = 400 the required CPU time on a good workstation can be kept within the order of 1 second. The acquired speed also opens the way to some long-term projects based on simulated observations (addressing statistical or cosmological questions) that would be, at present, practically not viable for intrinsically slow reconstruction methods.Comment: 6 pages, 2 figures. Uses A&A macros. Accepted for pubblication on A&

Dynamical properties of a family of collisionless models of elliptical galaxies

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation, that is to a quasi-equilibrium configuration characterized by isotropic, quasi-Maxwellian distribution of stellar orbits in the inner regions and by radially biased anisotropic pressure in the outer parts. In earlier studies, as illustrated in a number of papers several years ago (see Bertin et al. 1993 and references therein), the attention was largely focused on the successful comparison between the models (constructed under the qualitative clues offered by the N-body simulations mentioned above) and the observations. In this paper we revisit the problem of incomplete violent relaxation, by making a direct comparison between the detailed properties of a family of distribution functions and those of the products of collisionless collapse found in N-body simulations.Comment: to appear in "Plasmas in the Laboratory and in the Universe: new insights and new challenges", G. Bertin, D. Farina, R. Pozzoli eds., AIP Conference Proceedings, Vol. XXX, pp. YY

On the Mahler measure of hyperelliptic families

We prove Boyd’s “unexpected coincidence” of the Mahler measures for two families of two-variate polynomials defining curves of genus 2. We further equate the same measures to the Mahler measures of polynomials y³ − y + x³ − x + kxy whose zero loci define elliptic curves for k ≠ 0, ± 3

Septin filament organization in Saccharomyces cerevisiae.

Septins are a family of GTP-binding, membrane-interacting cytoskeletal proteins, highly conserved and essential in all eukaryotes (with the exception of plants). Septins play important roles in a number of cellular events that involve membrane remodeling and compartmentalization. One such event is cytokinesis, the last stage of cell division. While cytokinesis is ultimately achieved via the mechanical contraction of an actomyosin ring at the septum, determination of the location where cytokinesis will take place, and recruitment of factors involved in signaling events leading to septation requires the activity of septins. We are working towards dissecting the properties of septins from the budding yeast Saccharomyces cerevisiae, where they were first discovered as cell cycle mutants. In our studies we have employed several complementary electron microscopy techniques to describe the organization and structure of septins both in vitro and in situ