Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature

We show how an operation of inf-convolution can be used to approximate convex functions with $C^{1}$ smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications.Comment: 17 page

A simple method to identify significant effects in unreplicated two-level factorial designs

This article proposes a generalization and improvement on the method of Lenth (1989). The problem is solved by fixing outliers in highly contaminated samples. To do this a scale robust estimator is obtained and its performance is analyzed using computer simulations. The method is extremely simple to use and leads to the same results as the more complex one proposed by Box and Meyer (1986)

Reciprocal interactions between tumor and endothelial cells: Effects of selective vasopressin V2 receptor peptide agonists

Recent experimental evidence suggested that the synthetic peptide desmopressin (DDAVP) interferes tumor angiogenesis by inducing the formation of angiostatin. It is also known that DDAVP stimulates the endothelial release of von Willebrand factor, a key element in resistance to metastasis. Vasopressin V2 receptor agonists such as DDAVP seem to evoke dual angiostatic and antimetastatic effects, breaking cooperative interactions of tumor and endothelial cells during tumor progression.Fil: Garona, Juan. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Oncología Molecular; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Alonso, Daniel Fernando. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Oncología Molecular; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Sensitive dependence of geometric Gibbs states

For quadratic-like maps, we show a phenomenon of sensitive dependence of geometric Gibbs states: There are analytic families of quadratic-like maps for which an arbitrarily small perturbation of the parameter can have a definite effect on the low-temperature geometric Gibbs states. Furthermore, this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit sensitive dependence of geometric Gibbs states. We introduce a geometric version of the Peierls condition for contour models ensuring that the low-temperature Gibbs states are concentrated near the critical orbit.Comment: Minor change

ON THE PERFORMANCE OF NONPARAMETRIC SPECIFICATION TESTS IN REGRESSION MODELS

Some recently developed nonparametric specification tests for regression models are described in a unified way. The common characteristic of these tests is that they are consistent against any alternative hypothesis. The performance of the test statistics is compared by means of Monte Carlo simulations, analysing how heteroskedasticity, number of regressors and bandwidth selection influence the results. The statistics which do not use a bandwidth perform slightly better if the regression model has only one regressor; otherwise, some of the statistics which use a bandwidth behave better if the bandwidth is chosen adequately. These statistics are applied to test the specification of three commonly used Mincer-type wage equations with Uruguayan and Spanish data; all of them are rejected.

A new gravitational wave background from the Big Bang

The reheating of the universe after hybrid inflation proceeds through the nucleation and subsequent collision of large concentrations of energy density in the form of bubble-like structures moving at relativistic speeds. This generates a significant fraction of energy in the form of a stochastic background of gravitational waves, whose time evolution is determined by the successive stages of reheating: First, tachyonic preheating makes the amplitude of gravity waves grow exponentially fast. Second, bubble collisions add a new burst of gravitational radiation. Third, turbulent motions finally sets the end of gravitational waves production. From then on, these waves propagate unimpeded to us. We find that the fraction of energy density today in these primordial gravitational waves could be significant for GUT scale models of inflation, although well beyond the frequency range sensitivity of gravitational wave observatories like LIGO, LISA or BBO. However, low-scale models could still produce a detectable signal at frequencies accessible to BBO or DECIGO. For comparison, we have also computed the analogous background from some chaotic inflation models and obtained similar results to those of other groups. The discovery of such a background would open a new observational window into the very early universe, where the details of the process of reheating could be explored. Thus, it could also serve as a new experimental tool for testing the Inflationary Paradigm.Comment: 20 pages, 8 figures, to appear in the Proceedings of JGRG17, Nagoya (Japan), 3-7 December 200

Viscosity solutions to second order partial differential equations on Riemannian manifolds

We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations $F(x, u, du, d^{2}u)=0$ defined on a finite-dimensional Riemannian manifold $M$. Finest results (with hypothesis that require the function $F$ to be degenerate elliptic, that is nonincreasing in the second order derivative variable, and uniformly continuous with respect to the variable $x$) are obtained under the assumption that $M$ has nonnegative sectional curvature, while, if one additionally requires $F$ to depend on $d^{2}u$ in a uniformly continuous manner, then comparison results are established with no restrictive assumptions on curvature.Comment: Final version: the domain of F in the equation F=0 has been changed in order to get more generality and simplicity in the definitions and assumptions, and several important misprints have been correcte