Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

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DEncuesta

En aquest treball es realitza la planificació, anàlisi, disseny i implementació de un sistema que gestiona enquestes. El projecte es titula DEncuesta i permet crear i respondre enquestar, així com visualitzar les seves resultats. Gran part del treball està dedicat a l'estudi de Java Enterprise Edition ja que el projecte es desenvolupa amb aquesta tecnologia. En concret s'utilitza JSPs, servlets i EJBs amb un patró MVC per desenvolupar el sistema. A part d'utilitzar el llenguatge Java també s'utilitza HTML i CSS.

Color differences among feral pigeons (Columba livia) are not attributable to sequence variation in the coding region of the melanocortin-1 receptor gene (MC1R)

Genetic variation at the melanocortin-1 receptor (MC1R) gene is correlated with melanin color variation in many birds. Feral pigeons (Columba livia) show two major melanin-based colorations: a red coloration due to pheomelanic pigment and a black coloration due to eumelanic pigment. Furthermore, within each color type, feral pigeons display continuous variation in the amount of melanin pigment present in the feathers, with individuals varying from pure white to a full dark melanic color. Coloration is highly heritable and it has been suggested that it is under natural or sexual selection, or both. Our objective was to investigate whether MC1R allelic variants are associated with plumage color in feral pigeons.We sequenced 888 bp of the coding sequence of MC1R among pigeons varying both in the type, eumelanin or pheomelanin, and the amount of melanin in their feathers. We detected 10 non-synonymous substitutions and 2 synonymous substitution but none of them were associated with a plumage type. It remains possible that non-synonymous substitutions that influence coloration are present in the short MC1R fragment that we did not sequence but this seems unlikely because we analyzed the entire functionally important region of the gene.Our results show that color differences among feral pigeons are probably not attributable to amino acid variation at the MC1R locus. Therefore, variation in regulatory regions of MC1R or variation in other genes may be responsible for the color polymorphism of feral pigeons.

A carboxylesterase, Esterase-6, modulates sensory physiological and behavioural response dynamics to pheromone in Drosophila

Background: Insects respond to the spatial and temporal dynamics of a pheromone plume, which implies not only a strong response to"odor on", but also to"odor off". This requires mechanisms geared toward a fast signal termination. Several mechanisms may contribute to signal termination, among which odorant-degrading enzymes. These enzymes putatively play a role in signal dynamics by a rapid inactivation of odorants in the vicinity of the sensory receptors, although direct in vivo experimental evidences are lacking. Here we verified the role of an extracellular carboxylesterase, esterase-6 (Est-6), in the sensory physiological and behavioral dynamics of Drosophila melanogaster response to its pheromone, cis-vaccenyl acetate (cVA). Est-6 was previously linked to post-mating effects in the reproductive system of females. As Est-6 is also known to hydrolyze cVA in vitro and is expressed in the main olfactory organ, the antenna, we tested here its role in olfaction as a putative odorant-degrading enzyme. Results: We first confirm that Est-6 is highly expressed in olfactory sensilla, including cVA-sensitive sensilla, and we show that expression is likely associated with non-neuronal cells. Our electrophysiological approaches show that the dynamics of olfactory receptor neuron (ORN) responses is strongly influenced by Est-6, as in Est-6° null mutants (lacking the Est-6 gene) cVA-sensitive ORN showed increased firing rate and prolonged activity in response to cVA. Est-6° mutant males had a lower threshold of behavioral response to cVA, as revealed by the analysis of two cVAinduced behaviors. In particular, mutant males exhibited a strong decrease of male-male courtship, in association with a delay in courtship initiation. Conclusions: Our study presents evidence that Est-6 plays a role in the physiological and behavioral dynamics of sex pheromone response in Drosophila males and supports a role of Est-6 as an odorant-degrading enzyme (ODE) in male antennae. Our results also expand the role of Est-6 in Drosophila biology, from reproduction to olfaction, and highlight the role of ODEs in insect olfaction. Keywords: carboxylesterase, esterase 6, olfaction, pheromone, signal termination