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

On trisecant lines to White surfaces

In this work we show that the only White surface in the projective 5-space having an excess of trisecant lines is the polygonal surface constructed by C. Segre. The proof follows the line of B.Gambier's beautiful approach to this question and is intended to give it modern rigour. This has some implications on the geometry of the generic point of the principal componant of the Hilbert scheme of 18 points in the projective plane special in degree 5.Comment: 25 page

Non-Involutive Constrained Systems and Hamilton-Jacobi Formalism

In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the integrability conditions leads to the reduction of degrees of freedom of these systems and, as consequence, naturally defines a dynamics in a reduced phase space.Comment: 12 page

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

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. 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 visually 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 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