The inception of Symplectic Geometry: the works of Lagrange and Poisson during the years 1808-1810

The concept of a symplectic structure first appeared in the works of Lagrange on the so-called "method of variation of the constants". These works are presented, together with those of Poisson, who first defined the composition law called today the "Poisson bracket". The method of variation of the constants is presented using today's mathematical concepts and notations.Comment: Presented at the meeting "Poisson 2008" in Lausanne, July 2008. Published in Letters in Mathematical Physics. 22 page

Integration of Dirac-Jacobi structures

We study precontact groupoids whose infinitesimal counterparts are Dirac-Jacobi structures. These geometric objects generalize contact groupoids. We also explain the relationship between precontact groupoids and homogeneous presymplectic groupoids. Finally, we present some examples of precontact groupoids.Comment: 10 pages. Brief changes in the introduction. References update

On the linear fractional self-attracting diffusion

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized self-intersection local time exists in L^2 if $\frac12<H<\frac3{4}$.Comment: 14 Pages. To appear in Journal of Theoretical Probabilit

Effect of band filling in the Kondo lattice: A mean-field approach

The usual Kondo-lattice, including an antiferromagnetic exchange interaction between nearest-neighboring localized spins, is treated here in a mean-field scheme that introduces two mean-field parameters: one associated with the local Kondo effect, and the other related to the magnetic correlations between localized spins. Phases with short-range magnetic correlations or coexistence between those and the Kondo effect are obtained. By varying the number of electrons in the conduction band, we notice that the Kondo effect tends to be suppressed away from half filling, while magnetic correlations can survive if the Heisenberg coupling is strong enough. An enhanced linear coefficient of the specific heat is obtained at low temperatures in the metallic state.Comment: 7 pages, ReVTeX two-column, 7 figure

Why, when, and how fast innovations are adopted

When the full stock of a new product is quickly sold in a few days or weeks, one has the impression that new technologies develop and conquer the market in a very easy way. This may be true for some new technologies, for example the cell phone, but not for others, like the blue-ray. Novelty, usefulness, advertising, price, and fashion are the driving forces behind the adoption of a new product. But, what are the key factors that lead to adopt a new technology? In this paper we propose and investigate a simple model for the adoption of an innovation which depends mainly on three elements: the appeal of the novelty, the inertia or resistance to adopt it, and the interaction with other agents. Social interactions are taken into account in two ways: by imitation and by differentiation, i.e., some agents will be inclined to adopt an innovation if many people do the same, but other will act in the opposite direction, trying to differentiate from the "herd". We determine the conditions for a successful implantation of the new technology, by considering the strength of advertising and the effect of social interactions. We find a balance between the advertising and the number of anti-herding agents that may block the adoption of a new product. We also compare the effect of social interactions, when agents take into account the behavior of the whole society or just a part of it. In a nutshell, the present model reproduces qualitatively the available data on adoption of innovation.Comment: 11 pages, 13 figures (with subfigures), full paper (EPJB 2012) on innovation adoption mode

Star Forming Objects in the Tidal Tails of Compact Groups

A search for star forming objects belonging to tidal tails has been carried out in a sample of deep Halpha images of 16 compact groups of galaxies. A total of 36 objects with Halpha luminosity larger than 10^38 erg s-1 have been detected in five groups. The fraction of the total Halpha luminosity of their respective parent galaxies shown by the tidal objects is always below 5% except for the tidal features of HCG95, whose Halpha luminosity amounts to 65% of the total luminosity. Out of this 36 objects, 9 star forming tidal dwarf galaxy candidates have been finally identified on the basis of their projected distances to the nuclei of the parent galaxies and their total Halpha luminosities. Overall, the observed properties of the candidates resemble those previously reported for the so-called tidal dwarf galaxies.Comment: 5 gif figures. Accepted for publication in Astrophysical Journa

Poisson-Jacobi reduction of homogeneous tensors

The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold $M$, homogeneous with respect to a vector field $\Delta$ on $M$, and first-order polydifferential operators on a closed submanifold $N$ of codimension 1 such that $\Delta$ is transversal to $N$. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on $M$ to the Schouten-Jacobi bracket of first-order polydifferential operators on $N$ and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can be also understood as a sort of reduction; in the standard case -- a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between $\Delta$-homogeneous symplectic structures on $M$ and contact structures on $N$.Comment: 19 pages, minor corrections, final version to appear in J. Phys. A: Math. Ge

Twice Bitten, Thrice Shy: A Case of Recurrent Isolated Cardiac Sarcoidosis in the Transplanted Heart.

We present a case of recurrent isolated cardiac sarcoidosis, 3 years post-heart transplantation. The case highlights the scarcity of data on the utility of immunosuppression in cardiac sarcoidosis and, in particular, raises questions about the optimal immunosuppression regimen in transplant recipients. (Level of Difficulty: Advanced.)

Universal features of cell polarization processes

Cell polarization plays a central role in the development of complex organisms. It has been recently shown that cell polarization may follow from the proximity to a phase separation instability in a bistable network of chemical reactions. An example which has been thoroughly studied is the formation of signaling domains during eukaryotic chemotaxis. In this case, the process of domain growth may be described by the use of a constrained time-dependent Landau-Ginzburg equation, admitting scale-invariant solutions {\textit{\`a la}} Lifshitz and Slyozov. The constraint results here from a mechanism of fast cycling of molecules between a cytosolic, inactive state and a membrane-bound, active state, which dynamically tunes the chemical potential for membrane binding to a value corresponding to the coexistence of different phases on the cell membrane. We provide here a universal description of this process both in the presence and absence of a gradient in the external activation field. Universal power laws are derived for the time needed for the cell to polarize in a chemotactic gradient, and for the value of the smallest detectable gradient. We also describe a concrete realization of our scheme based on the analysis of available biochemical and biophysical data.Comment: Submitted to Journal of Statistical Mechanics -Theory and Experiment

The Local Universe as Seen in Far-Infrared and in Far-Ultraviolet: A Global Point of View on the Local Recent Star Formation

We select far-infrared (FIR-60 microns) and far-ultraviolet (FUV-1530 A) samples of nearby galaxies in order to discuss the biases encountered by monochromatic surveys (FIR or FUV). Very different volumes are sampled by each selection and much care is taken to apply volume corrections to all the analyses. The distributions of the bolometric luminosity of young stars are compared for both samples: they are found to be consistent with each other for galaxies of intermediate luminosities but some differences are found for high (>5 10^{10} L_sun) luminosities. The shallowness of the IRAS survey prevents us from securing comparison at low luminosities (<2 10^9 L_sun). The ratio of the total infrared (TIR) luminosity to the FUV luminosity is found to increase with the bolometric luminosity in a similar way for both samples up to 5 10^{10} L_sun. Brighter galaxies are found to have a different behavior according to their selection: the L_TIR/L_FUV ratio of the FUV-selected galaxies brighter than 5 10^{10} L_sun reaches a plateau whereas L_TIR/L_FUV continues to increase with the luminosity of bright galaxies selected in FIR. The volume-averaged specific star formation rate (SFR per unit galaxy stellar mass, SSFR) is found to decrease toward massive galaxies within each selection. The SSFR is found to be larger than that measured for optical and NIR-selected sample over the whole mass range for the FIR selection, and for masses larger than 10^{10} M_sun for the FUV selection. Luminous and massive galaxies selected in FIR appear as active as galaxies with similar characteristics detected at z ~ 0.7.Comment: 32 pages, 9 figures, to be published in the Astrophysical Journal Supplement series dedicated to GALEX result