Geometric phases and criticality in spin systems

A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study regions of criticality without having to undergo a quantum phase transition. As a concrete example a spin-1/2 chain with XY interactions is presented and the corresponding geometric phases are analyzed. The generalization of these results to the case of an arbitrary spin system provides an explanation for the existence of such a relation.Comment: 12 pages, 4 figure

Space Time Defects as a Source of Curvature and Torsion

Space time is described as a continuum four-dimensional medium similar to ordinary elastic continua. Exploiting the analogy internal stress states are considered. The internal ''stress'' is originated by the presence of defects. The defects are described according to the typical Volterra process. The case of a point defect in an otherwise isotropic four-dimensional medium is discussed showing that the resulting metric tensor corresponds to an expanding (or contracting) universe filled up with a non-zero energy-momentum density.Comment: Presentation at the Sixth Friedman seminar in Cargese 28/6-3/7/2004. Submitted for the proceedings of the seminar to appear in the International Journal of Modern Physics

Biodiversity in model ecosystems, II: Species assembly and food web structure

This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models thecoexistence condition derived for systems at the fixed point. The ecological overlap between species with shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies

Harnessing the power of cell transplantation to target respiratory dysfunction following spinal cord injury.

The therapeutic benefit of cell transplantation has been assessed in a host of central nervous system (CNS) diseases, including disorders of the spinal cord such as traumatic spinal cord injury (SCI). The promise of cell transplantation to preserve and/or restore normal function can be aimed at a variety of therapeutic mechanisms, including replacement of lost or damaged CNS cell types, promotion of axonal regeneration or sprouting, neuroprotection, immune response modulation, and delivery of gene products such as neurotrophic factors, amongst other possibilities. Despite significant work in the field of transplantation in models of SCI, limited attention has been directed at harnessing the therapeutic potential of cell grafting for preserving respiratory function after SCI, despite the critical role pulmonary compromise plays in patient outcome in this devastating disease. Here, we will review the limited number of studies that have demonstrated the therapeutic potential of intraspinal transplantation of a variety of cell types for addressing respiratory dysfunction in SCI

Biodiversity in model ecosystems, I: Coexistence conditions for competing species

This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is (Chesson, 1994). Here we review and generalize this analysis, beyond the ``mean-field''-like approximation of the competition matrix used in previous works, and extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between biodiversity and competition: the narrower the productivity distribution is, the more species can stably coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal biodiversity that a trophic level can host