Spin-Spin Interaction In Matrix Theory

We calculate the spin dependent static force between two D0-branes in Matrix theory. Supersymmetry relates velocity dependent potentials to spin dependent potentials. The well known v^4/r^7 term is related to a theta^8/r^11 term, where theta is the relative spin of the D0-branes. We calculate this term, confirming that it is the lowest order contribution to the static potential, and find its structure consistent with supergravity.Comment: 15 pages, LaTeX, uses feynmf.sty for diagrams. Reference added and some labels on the diagrams restore

Size dependent symmetry breaking in models for morphogenesis

A general property of dynamical systems is the appearance of spatial and temporal patterns due to a change of stability of a homogeneous steady state. Such spontaneous symmetry breaking is observed very frequently in all kinds of real systems, including the development of shape in living organisms. Many nonlinear dynamical systems present a wide variety of patterns with different shapes and symmetries. This fact restricts the applicability of these models to morphogenesis, since one often finds a surprisingly small variation in the shapes of living organisms. For instance, all individuals in the Phylum Echinodermata share a persistent radial fivefold symmetry. In this paper, we investigate in detail the symmetry-breaking properties of a Turing reaction–diffusion system confined in a small disk in two dimensions. It is shown that the symmetry of the resulting pattern depends only on the size of the disk, regardless of the boundary conditions and of the differences in the parameters that differentiate the interior of the domain from the outer space. This study suggests that additional regulatory mechanisms to control the size of the system are of crucial importance in morphogenesis

The relative dependence of Spanish landscape pattern on environmental and geographical variables over time

The analysis of the dependence of landscape patterns on environment was carried out in order to investigate the landscape structure evolution of Spain. The underlying concept was that the dependence between landscape spatial structure and environmental factors could be gradually decreasing over time. Land cover data were recorded from aerial photo interpretation of 206 4 x 4 km(2) samples from three different years: 1956, 1984 and 1998. Geographical variables were taken into consideration together with the purely environmental ones. General Linear Models of repeated measures were then used to segregate environmental from geographical effects on the pattern of the land cover patches of the samples. Aridity, lithology and topography were the environmental factors used to analyse structural indices of landscape. Landscape composition has a higher dependence on environment than configuration. Environmental variables showed higher correlations with landscape composition and configuration than geographical variables. Ail-long them, overall the climatic aridity and topography significantly accounted for more variation than did lithology. There was a high degree of stability in land cover composition over time, with some significant exceptions. Nevertheless, the registered increase of fragmentation over time has demonstrated that configuration measures are needed to fully assess landscape change

Bregman Proximal Gradient Algorithm with Extrapolation for a class of Nonconvex Nonsmooth Minimization Problems

In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a Bregman Proximal Gradient algorithm with extrapolation(BPGe). This algorithm extends and accelerates the Bregman Proximal Gradient algorithm (BPG), which circumvents the restrictive global Lipschitz gradient continuity assumption needed in Proximal Gradient algorithms (PG). The BPGe algorithm has higher generality than the recently introduced Proximal Gradient algorithm with extrapolation(PGe), and besides, due to the extrapolation step, BPGe converges faster than BPG algorithm. Analyzing the convergence, we prove that any limit point of the sequence generated by BPGe is a stationary point of the problem by choosing parameters properly. Besides, assuming Kurdyka-{\'L}ojasiewicz property, we prove the whole sequences generated by BPGe converges to a stationary point. Finally, to illustrate the potential of the new method BPGe, we apply it to two important practical problems that arise in many fundamental applications (and that not satisfy global Lipschitz gradient continuity assumption): Poisson linear inverse problems and quadratic inverse problems. In the tests the accelerated BPGe algorithm shows faster convergence results, giving an interesting new algorithm.Comment: Preprint submitted for publication, February 14, 201

El sistema escolar a les Illes Balears en xifres (2009)

En aquest article presentam dades referides al sistema educatiu no universitari de les Illes Balears. La lectura i anàlisi de les darreres dades del MEC i de la Conselleria d’Educació ens permeten de!nir el per!l del sistema educatiu actual i, des d’una visió retrospectiva, observar-ne les tendències i els canvis més signi!catius.En el artículo presentamos datos referidos al sistema educativo no universitario de las Islas Baleares. La lectura y el análisis de los últimos datos del MEC y de la Conselleria d’Educació, nos permite de!nir el per!l del sistema educativo y, desde una visión retrospectiva, observar las tendencias y los cambios más signi!cativos

El sistema escolar de les Illes Balears en xifres

En aquest article presentam algunes dades referides al sistema educatiu no universitari de les Illes Balears. Per una banda, mostram la situació educativa del curs actual i, per una altra, n’oferim una lectura evolutiva amb les variacions dels darrers cursos. Presentam dades del MEC, de la Conselleria d’Educació i Cultura, i informes socials i educatius diversos.En el artículo presentamos datos referidos al sistema educativo no universitario de las Islas Baleares. Por una parte mostramos la situación educativa en el curso actual y por otra ofrecemos una lectura evolutiva con las variaciones que se han dado en los últimos cursos. Presentamos datos del MEC, de la Conselleria d’Educació i Cultura de la CAIB y diferentes informes sociales y educativos

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detect their organizing centers - codimension-two T-points and separating saddles in the kneading-based scans of the iconic Lorenz equation from hydrodynamics, a normal model from mathematics, and a laser model from nonlinear optics.Comment: Journal of Bifurcations and Chaos, 201