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

"Vegeu el resum a l'inici del document del fitxer adjunt."

Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension

"Vegeu el resum a l'inici del document del fitxer adjunt."

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities

We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a proof of the logarithmic Hardy-Littlewood-Sobolev inequality in the one dimensional and radially symmetric two dimensional case based on optimal transport arguments. In addition we prove that the onedimensional equation is a contraction with respect to Fourier distance in the subcritical case.

Desenvolupament futur de les revistes electròniques: una enquesta Delphi

Aquest article presenta els resultats d'una enquesta Delphi internacional i interdisciplinària sobre el desenvolupament futur de les revistes electròniques. El quadre d'experts constà de 45 científics, editors, bibliotecaris, agents de revistes i consultors. L'enquesta cobria cinc àrees d'interès sobre revistes electròniques: el futur rol de la literatura erudita en suport revista, escenaris per a les revistes del futur; crisi en les publicacions en sèrie; arxiu de revistes electròniques i nous models en l'adquisició i l'accés. L'enquesta Delphi va estudiar els canvis esperats durant els propers cinc a deu anys. Els resultats són analitzats i indiquen que, durant els seus 300 anys d'història, les revistes mai no han afrontat tants de canvis com els que experimenten ara, o els que s'esperen durant els propers cinc a deu anys.

On two examples by Iyama and Yoshino

In a recent paper Iyama and Yoshino consider two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen-Macaulay modules in terms of linear algebra data. In this paper we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov's result on the graded singularity category. We obtain some new results on the singularity category of isolated singularities which may be interesting in their own right.

Cluster algebras, quiver representations and triangulated categories

This is an introduction to some aspects of Fomin-Zelevinsky’s cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer schools held in 2006 (Bavaria)and 2008 (Jerusalem). In addition to by now classical material, we present the outline of a proof of the periodicity conjecture for pairs of Dynkin diagrams (details will appear elsewhere) and recent results on the interpretation of mutations as derived equivalences.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

Cost system design and cost management in the Spanish public sector

Cost systems have been shown to have developed considerably in recent years andactivity-based costing (ABC) has been shown to be a contribution to cost management,particularly in service businesses. The public sector is composed to a very great extentof service functions, yet considerably less has been reported of the use of ABC tosupport cost management in this sector.In Spain, cost systems are essential for city councils as they are obliged to calculate thecost of the services subject to taxation (eg. waste collection, etc). City councils musthave a cost system in place to calculate the cost of services, as they are legally requirednot to profit , from these services.This paper examines the development of systems to support cost management in theSpanish Public Sector. Through semi-structured interviews with 28 subjects within oneCity Council it contains a case study of cost management. The paper contains extractsfrom interviews and a number of factors are identified which contribute to thesuccessful development of the cost management system.Following the case study a number of other City Councils were identified where activity-based techniques had either failed or stalled. Based on the factors identified inthe single case study a further enquiry is reported. The paper includes a summary usingstatistical analysis which draws attention to change management, funding and politicalincentives as factors which had an influence on system success or failure.

Residual Stress Measurement on a MEMS Structure With High-Spatial Resolution

A new approach to the local measurement of residual stress in microstructures is described in this paper. The presented technique takes advantage of the combined milling-imaging features of a focused ion beam (FIB) equipment to scale down the widely known hole drilling method. This method consists of drilling a small hole in a solid with inherent residual stresses and measuring the strains/displacements caused by the local stress release, that takes place around the hole. In the presented case, the displacements caused by the milling are determined by applying digital image correlation (DIC) techniques to high resolution micrographs taken before and after the milling process. The residual stress value is then obtained by fitting the measured displacements to the analytical solution of the displacement fields. The feasibility of this approach has been demonstrated on a micromachined silicon nitride membrane showing that this method has high potential for applications in the field of mechanical characterization of micro/nanoelectromechanical systems.

El secreto de Vera Drake (2004) y Las Normas de la Casa de la Sidra (1999): el aborto en el cine y su utilización en la docencia

El Secreto de Vera Drake (2004) de Mike Leigh y de Las Normas de la Casa de la Sidra (1999) de Lasse Hallström presentan la interrupción voluntaria del embarazo y las circunstancias que la rodean en un total de diez abortos y un parto. El Secreto de Vera Drake nos muestra a una mujer de clase media-baja que"ayuda a chicas jóvenes" a poner fin a embarazos no deseados sin aceptar dinero a cambio. Su secreto se desvelará cuando una de las jóvenes a la que practicó un aborto sufre complicaciones y es condenada. Las Normas de la Casa de la Sidra presenta la historia de Homer Wells, un joven que nace y crece en un orfanato donde su responsable, el Dr. Larch, le enseña a asistir partos y a practicar abortos. Un día Homer siente la necesidad de volar libre fuera del orfanato e inicia un viaje que le acercará a otras realidades que le llevarán a reconsiderar su postura en contra del aborto. Ambas películas pueden ser un material útil para estudiar aspectos clínicos, éticos y sociodemográficos del aborto inducido en las enseñanzas de medicina, enfermería y matrona.

El secreto de Vera Drake (2004) y Las Normas de la Casa de la Sidra (1999): el aborto en el cine y su utilización en la docencia

El Secreto de Vera Drake (2004) de Mike Leigh y de Las Normas de la Casa de la Sidra (1999) de Lasse Hallström presentan la interrupción voluntaria del embarazo y las circunstancias que la rodean en un total de diez abortos y un parto. El Secreto de Vera Drake nos muestra a una mujer de clase media-baja que"ayuda a chicas jóvenes" a poner fin a embarazos no deseados sin aceptar dinero a cambio. Su secreto se desvelará cuando una de las jóvenes a la que practicó un aborto sufre complicaciones y es condenada. Las Normas de la Casa de la Sidra presenta la historia de Homer Wells, un joven que nace y crece en un orfanato donde su responsable, el Dr. Larch, le enseña a asistir partos y a practicar abortos. Un día Homer siente la necesidad de volar libre fuera del orfanato e inicia un viaje que le acercará a otras realidades que le llevarán a reconsiderar su postura en contra del aborto. Ambas películas pueden ser un material útil para estudiar aspectos clínicos, éticos y sociodemográficos del aborto inducido en las enseñanzas de medicina, enfermería y matrona.