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.

Investor protection and income inequality: risk sharing vs risk taking

This paper studies the relationship between investor protection, entrepreneurial risk taking and income inequality. In the presence of market frictions, better protection makes investors more willing to take on entrepreneurial risk when lending to firms, thereby improving the degree of risk sharing between financiers and entrepreneurs. On the other hand, by increasing risk sharing, investor protection also induces more firms to undertake risky projects. By increasing entrepreneurial risk taking, it raises income dispersion. By reducing the risk faced by entrepreneurs, it reduces income volatility. As a result, investor protection raises income inequality to the extent that it fosters risk taking, while it reduces it for a given level of risk taking. Empirical evidence from a panel of forty-five countries spanning the period 1976-2000 supports the predictions of the model.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Estils d'aprenentatge i rendiment acadèmic. Un estudi sobre alumnat de la Diplomatura de mestres de la Universitat de Vic

Com a part inicial d'un procés més ampli d’implementació dels principis del Disseny Instruccional Universal a la Universitat de Vic, aquest estudi ha examinat i explorat els estils d'aprenentatge dels estudiants de primer curs de la Diplomatura de Mestre a la Universitat de Vic. Els objectius han estat, analitzar els perfils dels estils d’aprenentatge dels alumnes de primer curs d'educació per determinar si hi havia diferències significatives en l'estil d'aprenentatge preferit en base a especialitat escollida, edat i sexe, així com també detectar correlacions entre estilsd'aprenentatge i rendiment acadèmic. S’ha estudiat una mostra de 243 estudiants. L'instrument de mesura ha estat el “Index of Learning Styles Questuinnaire”. S’ha procedit a fer un anàlisi descriptiu i ANOVA. Els resultats mostren una distribució de les quatre dimensions del ILS similars als perfils d’altres poblacions d'altres universitats. La immensa majoria dels estudiants resulten visuals i sensorial i indiferents per a les dimensions actiu-reflexiu i seqüencial-global. Per especialitat i edat només les dimensions actiureflexiu ivisual-verbal han mostrat diferències significatives. Per gènere no s'han trobat diferèncie significatives . Pel que respecta al rendiment acadèmic, només la dimensió visual-verbal sembla tenir una relació significativa, obtenint qualificacions sensiblement més altes aquells estudiants amb un perfil verbal més alts que els efectes visuals. S’ha generat dues noves variables "nivell de dispersió" i "grau de risc". No s’ha trobat cap relació entre aquests dos factors i el rendiment acadèmic. S’han discutit els resultats. L’instrument ILSQ sembla presentar un valor moderat com a element predictiu de dificultats l'aprenentatge de l’alumnat i el seu rendiment acadèmic.

Spatio-temporal variations in reproductive patterns and population structure of Pasiphaea multidentata (Decapoda: Caridea) in the Blanes canyon and adjacent margin, North-western Mediterranean Sea

The bathyal faunal communities of the NW Mediterranean slopes have been studied consistently in the last two decades, with a special focus on population structure, trophic dynamics and benthopelagic coupling of commercial deep-sea decapod crustaceans and fishes (reviewed in Sardà et al. 2004) and associated species (Cartes and Sardà, 1993; Company and Sardà, 1997, 2000; Cartes et al., 2001; Company et al., 2001, 2003, 2004). One of the major topographic features in the North-western Mediterranean slope is the presence of submarine canyons. Canyons play a major role in funnelling energy and organic matter from the shelf to bathyal and abyssal depths (Puig et al., 2000), but the implications of this enhanced organic supply in the deep-sea benthic communities is still mostly unknown. Trophic supply can follow two major pathways – vertical deposition in the water column (Billett et al., 1983; Baldwin et al., 1998; Lampitt et al., 2001) or down-slope advection on the margins (Puig et al., 2001; Bethoux et al., 2002; Canals et al., 2006) – and can be a limiting factor in the deep-sea, being especially important in the oligotrophic Mediterranean Sea (Sardà et al., 2004). Differences in the quantity, quality and timing of organic matter input to the deep seafloor have been used to explain patterns of biomass and abundance in benthic communities (Levin et al., 1994; Gooday & Turley, 1990; Billett et al., 2001; Galéron et al., 2001; Puig et al., 2001; Gage, 2003) as well as other biological process and in particular the existence of seasonal reproduction (Tyler et al., 1994; Company et al., 2004 (MEPS). Reproduction is a highly energetic process tightly linked to food availability and quality.