Measurements and Information in Spin Foam Models

We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy associated to the corresponding information. We present a general definition, compute the Shannon entropy of some examples, and find some interesting inequalities.Comment: 15 pages, 3 figures. Improved versio

Rogue waves and downshifting in the presence of damping

Recently Gramstad and Trulsen derived a new higher order nonlinear Schrodinger (HONLS) equation which is Hamiltonian (Gramstad and Trulsen, 2011). We investigate the effects of dissipation on the development of rogue waves and downshifting by adding an additonal nonlinear damping term and a uniform linear damping term to this new HONLS equation. We find irreversible downshifting occurs when the nonlinear damping is the dominant damping effect. In particular, when only nonlinear damping is present, permanent downshifting occurs for all values of the nonlinear damping parameter beta. Significantly, rogue waves do not develop after the downshifting becomes permanent. Thus in our experiments permanent downshifting serves as an indicator that damping is sufficient to prevent the further development of rogue waves. We examine the generation of rogue waves in the presence of damping for sea states characterized by JONSWAP spectrum. Using the inverse spectral theory of the NLS equation, simulations of the NLS and damped HONLS equations using JONSWAP initial data consistently show that rogue wave events are well predicted by proximity to homoclinic data, as measured by the spectral splitting distance delta. We define delta(cutoff) by requiring that 95% of the rogue waves occur for delta \u3c delta(cutoff). We find that delta(cutoff) decreases as the strength of the damping increases, indicating that for stronger damping the JONSWAP initial data must be closer to homoclinic data for rogue waves to occur. As a result when damping is present the proximity to homoclinic data and instabilities is more crucial for the development of rogue waves

Predicting rogue waves in random oceanic sea states

Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the Joint North Sea Wave Project (JONSWAP) spectrum with the proximity to homoclinic solutions of the NLS equation. We find in numerical simulations of the NLS equation that rogue waves develop for JONSWAP initial data that are near NLS homoclinic data, while rogue waves do not occur for JONSWAP data that are far from NLS homoclinic data. We show the nonlinear spectral decomposition provides a simple criterium for predicting the occurrence and strength of rogue waves

Conservation of phase space properties using exponential integrators on the cubic Schrödinger equation

The cubic nonlinear Schrödinger (NLS) equation with periodic boundary conditions is solvable using Inverse Spectral Theory. The nonlinear spectrum of the associated Lax pair reveals topological properties of the NLS phase space that are difficult to assess by other means. In this paper we use the invariance of the nonlinear spectrum to examine the long time behavior of exponential and multisymplectic integrators as compared with the most commonly used split step approach. The initial condition used is a perturbation of the unstable plane wave solution, which is difficult to numerically resolve. Our findings indicate that the exponential integrators from the viewpoint of efficiency and speed have an edge over split step, while a lower order multisymplectic is not as accurate and too slow to compete. © 2006 Elsevier Inc. All rights reserved

Synopsis of the genus Spigelia (Loganiaceae) in North America, Central America, and the Caribbean

Antecedentes y Objetivos: Spigelia es un género neotropical con cerca de 90 especies distribuidas desde los Estados Unidos de América hasta Argentina. La diversidad del género presenta una separación espacial entre un grupo en Norte-Centroamérica/Caribe (NA) y otro en Sudamérica (SA), cada uno con un importante centro de diversificación. Sin embargo, el conocimiento sistemático del grupo no ha sido actualizado en los últimos 10 años, por lo que el objetivo de este trabajo es generar una sinopsis sistemática para el género distribuido en la región NA. Métodos: El trabajo se realizó a través de la búsqueda de información bibliográfica para obtener la historia taxonómica, así como trabajo de campo y revisión de material herborizado, a partir del cual se realizaron descripciones diagnósticas y mapas de distribución. Resultados clave: Se encontraron 29 especies distribuidas en la región NA, lo que representa alrededor de 30% de la diversidad del género, en las zonas tropical y subtropical. En la región NA, Mesoamérica es una de las regiones en las que se concentra la diversidad vegetal, lo que la cataloga como hotspot. El trabajo incluye información novedosa sobre la morfología del grupo, como descripciones de los caracteres polínicos y carpológicos, claves de identificación por regiones en NA y mapas de distribución en el área de estudio. Conclusiones: Este estudio representa el primer tratamiento taxonómico para el género Spigelia que incluye todas las especies de la región central y norte del continente americano. La información recopilada en este trabajo puede ser útil para ser integrada en análisis filogenéticos que ayuden a resolver las relaciones intragenéricas del grupo. Asimismo, la aplicación de herramientas de modelado de distribución potencial que permitan ubicar áreas para futuras colectas, así como el desarrollo de análisis biogeográficos que ayuden a comprender la distribución de la diversidad de Spigelia a lo largo del continente.Background and Aims: Spigelia is a Neotropical genus with about 90 species distributed from the United States of America to Argentina. The diversity of the genus presents a spatial separation with a group in North-Central America/ the Caribbean (NA) and another in South America (SA), each with an important center of diversification. However, the systematic knowledge of the group has not been updated in the last 10 years, so the objective of this work is to generate a systematic synopsis for the genus distributed in the NA region. Methods: The work was carried out through the search for bibliographic information to obtain the taxonomic history, field work and review of herbarium material, based on which diagnostic descriptions and distribution maps were made. Key results: Twenty-nine species distributed in the NA region were found, which represents about 30% of the diversity of the genus, distributed in the tropical and subtropical zones. In the NA region, Mesoamerica is one of the regions in which plant diversity is concentrated, which classifies it as a hotspot. This work includes novel information on the morphology of the group, such as descriptions of the pollen and carpological characters, identification keys for regions in NA and distribution maps in the study area. Conclusions: This study represents the first taxonomic treatment for the genus Spigelia that includes all the species of the central and northern regions of the Americas. The information collected in this work may be useful to be integrated into phylogenetic analyzes that help resolve the infrageneric relationships of the group. Likewise, the application of potential distribution modeling tools that would allow locating areas for future collection, as well as the development of biogeographic analyzes that help us understand the distribution patterns of Spigelia diversity along the continent

Parasite-mediated predation determines infection in a complex predator-prey-parasite system.

The interplay of host-parasite and predator-prey interactions is critical in ecological dynamics because both predators and parasites can regulate communities. But what is the prevalence of infected prey and predators when a parasite is transmitted through trophic interactions considering stochastic demographic changes? Here, we modelled and analysed a complex predator-prey-parasite system, where parasites are transmitted from prey to predators. We varied parasite virulence and infection probabilities to investigate how those evolutionary factors determine species' coexistence and populations' composition. Our results show that parasite species go extinct when the infection probabilities of either host are small and that success in infecting the final host is more critical for the survival of the parasite. While our stochastic simulations are consistent with deterministic predictions, stochasticity plays an important role in the border regions between coexistence and extinction. As expected, the proportion of infected individuals increases with the infection probabilities. Interestingly, the relative abundances of infected and uninfected individuals can have opposite orders in the intermediate and final host populations. This counterintuitive observation shows that the interplay of direct and indirect parasite effects is a common driver of the prevalence of infection in a complex system

Supernova search at intermediate z. I. Spectroscopic analysis

We study 8 supernovae discovered as part of the International Time Programme (ITP) project ``Omega and Lambda from Supernovae and the Physics of Supernova Explosions'' at the European Northern Observatory (ENO). The goal of the project is to increase the sample of intermediate redshift (0.1<z<0.4) SNe Ia for testing properties of SNe Ia along z and for enlarging the sample in the Hubble diagram up to large z.Comment: 2 pages, 2 figures, 1 table, to appear in ``1604-2004: Supernovae as Cosmological Lighthouses'', (extended text upon request