Limit curve theorems in Lorentzian geometry

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causality holds at their points. Finally, it is proved that two distinct components of the chronology violating set have disjoint closures or there is a lightlike line passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio

Distributional fixed point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling

The distributions of inter-island gaps and captures zones for islands nucleated on a one-dimensional substrate during submonolayer deposition are considered using a novel retrospective view. This provides an alternative perspective on why scaling occurs in this continuously evolving system. Distributional fixed point equations for the gaps are derived both with and without a mean field approximation for nearest neighbour gap size correlation. Solutions to the equations show that correct consideration of fragmentation bias justifies the mean field approach which can be extended to provide closed-from equations for the capture zones. Our results compare favourably to Monte Carlo data for both point and extended islands using a range of critical island size $i=0,1,2,3$. We also find satisfactory agreement with theoretical models based on more traditional fragmentation theory approaches.Comment: 9 pages, 7 figures and 1 tabl

Seasonal variations of the vagile fauna associated with Ectopleura crocea (Cnidaria, Hydrozoa) in El Rompido marina (Huelva)

El desarrollo urbano en las zonas costeras se ha visto incrementado notablemente en los últimos años, resultando en un mayor número de estructuras artificiales en los ambientes marinos. Diversos organismos han sido capaces de colonizar las superficies de estos nuevos hábitats, incluyendo al hidrozoo Ectopleura crocea (Agassiz, 1862). Se estudió la epifauna asociada a esta especie a lo largo de un año en Puerto Marina, El Rompido, Huelva, con el objetivo de describir su composición y fluctuaciones temporales. En total, se encontraron 22 especies, mayoritariamente crustáceos anfípodos, siendo los más abundantes Stenothoe tergestina (Nebeski, 1881) y Apocorophium acutum (Chevreux, 1908). No se encontraron diferencias significativas a lo largo del ciclo anual en los valores de abundancia y diversidad, si bien se detectaron cambios en la composición faunística. En general, la diversidad de especies encontrada en Ectopleura crocea fue menor que la citada en otros estudios en hábitats naturales. Se sugiere que ello puede ser debido a características intrínsecas del hábitat artificial, tales como una menor heterogeneidad de sus superficies o a un mayor estrés ambiental. Por ello, para contrastar la consistencia a lo largo del tiempo y la causa de tales patrones, sería necesario estudios futuros que abarcasen un mayor rango temporal.Urban development in coastal areas has increased considerably in recent years, which has resulted in a larger number of artificial structures in coastal marine environments. However, various organisms have been able to colonize the surfaces of these new habitats, including the hydrozoan Ectopleura crocea (Agassiz, 1862). We studied the epifauna associated with this species over a year in Puerto Marina, El Rompido, Huelva, with the objective of describing its composition and temporal fluctuations. In total, 22 species were found, mostly amphipod crustaceans, the most abundant of these being Stenothoe tergestina (Nebeski, 1881) and Apocorophium acutum (Chevreux, 1908). No significant differences were found between the abundance and diversity of epifauna throughout the year, although changes in epifauna composition were detected over time. In general, the diversity found on Ectopleura crocea in the present study was lower than that reported by other studies in natural habitats. It is suggested that this could be due to intrinsic characteristics of the artificial habitat, such as lower heterogeneity of its surfaces or greater environmental stress. To contrast consistency over time and the causes of these patterns future studies carried out over a larger time period will be necessar

Rapid Evolutionary Rates and Unique Genomic Signatures Discovered in the First Reference Genome for the Southern Ocean Salp, Salpa thompsoni (Urochordata, Thaliacea)

A preliminary genome sequence has been assembled for the Southern Ocean salp, Salpa thompsoni (Urochordata, Thaliacea). Despite the ecological importance of this species in Antarctic pelagic food webs and its potential role as an indicator of changing Southern Ocean ecosystems in response to climate change, no genomic resources are available for S. thompsoni or any closely related urochordate species. Using a multiple-platform, multiple-individual approach, we have produced a 318,767,936-bp genome sequence, covering \u3e50% of the estimated 602 Mb (±173 Mb) genome size for S. thompsoni. Using a nonredundant set of predicted proteins, \u3e50% (16,823) of sequences showed significant homology to known proteins and ∼38% (12,151) of the total protein predictions were associated with Gene Ontology functional information. We have generated 109,958 SNP variant and 9,782 indel predictions for this species, serving as a resource for future phylogenomic and population genetic studies. Comparing the salp genome to available assemblies for four other urochordates, Botryllus schlosseri, Ciona intestinalis, Ciona savignyi and Oikopleura dioica, we found that S. thompsoni shares the previously estimated rapid rates of evolution for these species. High mutation rates are thus independent of genome size, suggesting that rates of evolution \u3e1.5 times that observed for vertebrates are a broad taxonomic characteristic of urochordates. Tests for positive selection implemented in PAML revealed a small number of genes with sites undergoing rapid evolution, including genes involved in ribosome biogenesis and metabolic and immune process that may be reflective of both adaptation to polar, planktonic environments as well as the complex life history of the salps. Finally, we performed an initial survey of small RNAs, revealing the presence of known, conserved miRNAs, as well as novel miRNA genes; unique piRNAs; and mature miRNA signatures for varying developmental stages. Collectively, these resources provide a genomic foundation supporting S. thompsoni as a model species for further examination of the exceptional rates and patterns of genomic evolution shown by urochordates. Additionally, genomic data will allow for the development of molecular indicators of key life history events and processes and afford new understandings and predictions of impacts of climate change on this key species of Antarctic pelagic ecosystems

Integration of the Friedmann equation for universes of arbitrary complexity

An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of the motion from simpler models as more species are added is stressed. It is then argued that all FLRW models admit what amounts to a unique candidate for a gravitational epoch function (a dimensionless scalar invariant derivable from the Riemann tensor without differentiation which is monotone throughout the evolution of the universe). The same relations that lead to the construction of constants of the motion allow an explicit evaluation of this function. In the simplest of all models, the $\Lambda$CDM model, it is shown that the epoch function exists for all models with $\Lambda > 0$, but for almost no models with $\Lambda \leq 0$.Comment: Final form to appear in Physical Review D1

Measures of gravitational entropy I. Self-similar spacetimes

We examine the possibility that the gravitational contribution to the entropy of a system can be identified with some measure of the Weyl curvature. In this paper we consider homothetically self-similar spacetimes. These are believed to play an important role in describing the asymptotic properties of more general models. By exploiting their symmetry properties we are able to impose significant restrictions on measures of the Weyl curvature which could reflect the gravitational entropy of a system. In particular, we are able to show, by way of a more general relation, that the most widely used "dimensionless" scalar is \textit{not} a candidate for this measure along homothetic trajectories.Comment: revtex, minor clarifications, to appear in Physical Review

Determination of Dosage Compensation of the Mammalian X Chromosome by RNA-seq is Dependent on Analytical Approach

Background An enduring question surrounding sex chromosome evolution is whether effective hemizygosity in the heterogametic sex leads inevitably to dosage compensation of sex-linked genes, and whether this compensation has been observed in a variety of organisms. Incongruence in the conclusions reached in some recent reports has been attributed to different high-throughput approaches to transcriptome analysis. However, recent reports each utilizing RNA-seq to gauge X-linked gene expression relative to autosomal gene expression also arrived at diametrically opposed conclusions regarding X chromosome dosage compensation in mammals. Results Here we analyze RNA-seq data from X-monosomic female human and mouse tissues, which are uncomplicated by genes that escape X-inactivation, as well as published RNA-seq data to describe relative X expression (RXE). We find that the determination of RXE is highly dependent upon a variety of computational, statistical and biological assumptions underlying RNA-seq analysis. Parameters implemented in short-read mapping programs, choice of reference genome annotation, expression data distribution, tissue source for RNA and RNA-seq library construction method have profound effects on comparing expression levels across chromosomes. Conclusions Our analysis shows that the high number of paralogous gene families on the mammalian X chromosome relative to autosomes contributes to the ambiguity in RXE calculations, RNA-seq analysis that takes into account that single- and multi-copy genes are compensated differently supports the conclusion that, in many somatic tissues, the mammalian X is up-regulated compared to the autosomes

Crossover from 2-dimensional to 1-dimensional collective pinning in NbSe3

We have fabricated NbSe$_3$ structures with widths comparable to the Fukuyama-Lee-Rice phase-coherence length. For samples already in the 2-dimensional pinning limit, we observe a crossover from 2-dimensional to 1-dimensional collective pinning when the crystal width is less than 1.6 $\mu$m, corresponding to the phase-coherence length in this direction. Our results show that surface pinning is negligible in our samples, and provide a means to probe the dynamics of single domains giving access to a new regime in charge-density wave physics.Comment: 4 pages, 2 figures, and 1 table. Accepted for publication in Physical Review

The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page

Yang-Mills fields on CR manifolds

We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR manifold.Comment: 52 page