The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

A cell-based model of extracellular-matrix-guided endothelial cell migration during angiogenesis.

Angiogenesis, the formation of new blood vessels sprouting from existing ones, occurs in several situations like wound healing, tissue remodeling, and near growing tumors. Under hypoxic conditions, tumor cells secrete growth factors, including VEGF. VEGF activates endothelial cells (ECs) in nearby vessels, leading to the migration of ECs out of the vessel and the formation of growing sprouts. A key process in angiogenesis is cellular self-organization, and previous modeling studies have identified mechanisms for producing networks and sprouts. Most theoretical studies of cellular self-organization during angiogenesis have ignored the interactions of ECs with the extra-cellular matrix (ECM), the jelly or hard materials that cells live in. Apart from providing structural support to cells, the ECM may play a key role in the coordination of cellular motility during angiogenesis. For example, by modifying the ECM, ECs can affect the motility of other ECs, long after they have left. Here, we present an explorative study of the cellular self-organization resulting from such ECM-coordinated cell migration. We show that a set of biologically-motivated, cell behavioral rules, including chemotaxis, haptotaxis, haptokinesis, and ECM-guided proliferation suffice for forming sprouts and branching vascular trees.

A three dimensional signed small ball inequality

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

Gains from switching and evolutionary stability in multi-player matrix games.

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.

Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞

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

Effect of magnesium chloride and guanidinum chloride on the extraction of components of extracellular matrix from chicken cartilage

In order to evaluate the effect of chaotropic agents on proteoglycan and non-collagenous proteins, chicken xiphoid cartilage was treated with guanidine-HCI and MgCl2 in different concentrations (1M to 5M), and different periods of time (12, 24, 48 and 72hr). The maximum yield of uronic acid was obtained with 3M MgCl2 (73.3 per cent). Concentrations of 4M and 5M of MgCl2 showed that much less uronic acid was removed, 55.3 per cent and 38.1 respectively. Extraction with 3M MgCl2 and 3M guanidine-HCl resulted better efficiency when performed for 48 hr. Analysis by SDS-PAGE of the extracts obtained with guanidine-HCl and MgCl, in different concentrations pointed out that most components are equally removed with the two solvents, showing that the extraction with MgCl2 is an alternative assay to remove non-collagenous proteins from extracellular matrix.

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.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.