From coinductive proofs to exact real arithmetic: theory and applications

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. We discuss several examples including the extraction of programs for polynomials up to degree two and the definite integral of continuous maps

Randall-Sundrum black holes and strange stars

It has recently been suggested that the existence of bare strange stars is incompatible with low scale gravity scenarios. It has been claimed that in such models, high energy neutrinos incident on the surface of a bare strange star would lead to catastrophic black hole growth. We point out that for the flat large extra dimensional case, the parts of parameter space which give rise to such growth are ruled out by other methods. We then go on to show in detail how black holes evolve in the the Randall-Sundrum two brane scenario where the extra dimensions are curved. We find that catastrophic black hole growth does not occur in this situation either. We also present some general expressions for the growth of five dimensional black holes in dense media.Comment: 16 pages, more numerics has lead to different path to same conclusion. Accepted in PR

Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. The numerical evolutions have been carried out in full general relativity using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.Comment: 19 pages, 17 figure

Variação sazonal na riqueza e na abundância de pequenos mamíferos, na estrutura da floresta e na disponibilidade de artrópodes em fragmentos florestais no Mato Grosso, Brasil

We captured small mammals in eight forest fragments (43 a 1.411 ha.) during the dry and wet seasons, in southwest Mato Grosso, Brazil, and investigated the variation in small mammal richness and abundance, as well as in forest structure variables (litter volume and canopy openness) and arthropod availability, between the two seasons. Sampling was carried out during the wet season between 2002 and 2003 and in the dry season of 2003. In each fragment, we used Sherman, Tomahawk, snap, and pitfall traps during 10 consecutive days per season, totaling 17,600 trap x nights. In total, we obtained 379 captures of 20 species, seven of marsupials and 13 of rodents. Overall capture success was 2.2% (1.6% during the wet season and 2.7% during the dry season). Total richness, richness of rodents, richness of marsupials, total abundance and abundance of rodents did not varied significantly between seasons. However, marsupial abundance was significantly lower in the dry season, when rainfall is high. Litter volume was significantly higher during the dry season, while arthropod availability was significantly higher during the wet season. Therefore, higher food availability during the wet season may have made trap baits less attractive. In general, the observed variations between dry and wet seasons are in accordance with patterns described in other studies

Rho GTPase function in flies: insights from a developmental and organismal perspective.

Morphogenesis is a key event in the development of a multicellular organism and is reliant on coordinated transcriptional and signal transduction events. To establish the segmented body plan that underlies much of metazoan development, individual cells and groups of cells must respond to exogenous signals with complex movements and shape changes. One class of proteins that plays a pivotal role in the interpretation of extracellular cues into cellular behavior is the Rho family of small GTPases. These molecular switches are essential components of a growing number of signaling pathways, many of which regulate actin cytoskeletal remodeling. Much of our understanding of Rho biology has come from work done in cell culture. More recently, the fruit fly Drosophila melanogaster has emerged as an excellent genetic system for the study of these proteins in a developmental and organismal context. Studies in flies have greatly enhanced our understanding of pathways involving Rho GTPases and their roles in development

Gene expression profiling of mucinous ovarian tumors and comparison with upper and lower gastrointestinal tumors identifies markers associated with adverse outcomes.

PURPOSE: Advanced-stage mucinous ovarian carcinoma (MOC) has poor chemotherapy response and prognosis and lacks biomarkers to aid stage I adjuvant treatment. Differentiating primary MOC from gastrointestinal (GI) metastases to the ovary is also challenging due to phenotypic similarities. Clinicopathologic and gene-expression data were analyzed to identify prognostic and diagnostic features. EXPERIMENTAL DESIGN: Discovery analyses selected 19 genes with prognostic/diagnostic potential. Validation was performed through the Ovarian Tumor Tissue Analysis consortium and GI cancer biobanks comprising 604 patients with MOC (n = 333), mucinous borderline ovarian tumors (MBOT, n = 151), and upper GI (n = 65) and lower GI tumors (n = 55). RESULTS: Infiltrative pattern of invasion was associated with decreased overall survival (OS) within 2 years from diagnosis, compared with expansile pattern in stage I MOC [hazard ratio (HR), 2.77; 95% confidence interval (CI), 1.04–7.41, P = 0.042]. Increased expression of THBS2 and TAGLN was associated with shorter OS in MOC patients (HR, 1.25; 95% CI, 1.04–1.51, P = 0.016) and (HR, 1.21; 95% CI, 1.01–1.45, P = 0.043), respectively. ERBB2 (HER2) amplification or high mRNA expression was evident in 64 of 243 (26%) of MOCs, but only 8 of 243 (3%) were also infiltrative (4/39, 10%) or stage III/IV (4/31, 13%). CONCLUSIONS: An infiltrative growth pattern infers poor prognosis within 2 years from diagnosis and may help select stage I patients for adjuvant therapy. High expression of THBS2 and TAGLN in MOC confers an adverse prognosis and is upregulated in the infiltrative subtype, which warrants further investigation. Anti-HER2 therapy should be investigated in a subset of patients. MOC samples clustered with upper GI, yet markers to differentiate these entities remain elusive, suggesting similar underlying biology and shared treatment strategies