Hindgut specification and cell-adhesion functions of Sphox11/13b in the endoderm of the sea urchin embryo

Sphox11/13b is one of the two hox genes of Strongylocentrotus purpuratus expressed in the embryo. Its dynamic pattern of expression begins during gastrulation, when the transcripts are transiently located in a ring of cells at the edge of the blastopore. After gastrulation, expression is restricted to the anus–hindgut region at the boundary between the ectoderm and the endoderm. The phenotype that results when translation of Sphox11/13b mRNA is knocked down by treatment with morpholino antisense oligonucleotides (MASO) suggests that this gene may be indirectly involved in cell adhesion functions as well as in the proper differentiation of the midgut–hindgut and midgut–foregut sphincters. The MASO experiments also reveal that Sphox11/13b negatively regulates several downstream endomesoderm genes. For some of these genes, Sphox11/13b function is required to restrict expression to the midgut by preventing ectopic expression in the hindgut. The evolutionary conservation of these functions indicates the general roles of posterior Hox genes in regulating cell-adhesion, as well as in spatial control of gene regulatory network subcircuits in the regionalizing gut

Spatial expression of Hox cluster genes in the ontogeny of a sea urchin

The Hox cluster of the sea urchin Strongylocentrous purpuratus contains ten genes in a 500 kb span of the genome. Only two of these genes are expressed during embryogenesis, while all of eight genes tested are expressed during development of the adult body plan in the larval stage. We report the spatial expression during larval development of the five 'posterior' genes of the cluster: SpHox7, SpHox8, SpHox9/10, SpHox11/13a and SpHox11/13b. The five genes exhibit a dynamic, largely mesodermal program of expression. Only SpHox7 displays extensive expression within the pentameral rudiment itself. A spatially sequential and colinear arrangement of expression domains is found in the somatocoels, the paired posterior mesodermal structures that will become the adult perivisceral coeloms. No such sequential expression pattern is observed in endodermal, epidermal or neural tissues of either the larva or the presumptive juvenile sea urchin. The spatial expression patterns of the Hox genes illuminate the evolutionary process by which the pentameral echinoderm body plan emerged from a bilateral ancestor

Matching of spatially homogeneous non-stationary space--times to vacuum in cylindrical symmetry

We study the matching of LRS spatially homogeneous collapsing dust space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior. The matched solutions contain trapped surfaces, singularities and Cauchy horizons. The solutions cannot be asymptotically flat and we present evidence that they are singular on the Cauchy horizons.Comment: LaTeX, 15 pages, 1 figure, submitted for publicatio

High-order gauge-invariant perturbations of a spherical spacetime

We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l=0,1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants

Plane waves in quantum gravity: breakdown of the classical spacetime

Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees of freedom can be interpreted as an infinite and continuous set of annihilation and creation like variables. We also consider a simplified version of the model, in which the number of modes is restricted to a discrete set. In both cases, the quantization is achieved by introducing a Fock representation. We find regularized operators to represent the metric and discuss whether the coherent states of the quantum theory are peaked around classical spacetimes. It is shown that, although the expectation value of the metric on Killing orbits coincides with a classical solution, its relative fluctuations become significant when one approaches a region where null geodesics are focused. In that region, the spacetimes described by coherent states fail to admit an approximate classical description. This result applies as well to the vacuum of the theory.Comment: 11 pages, no figures, version accepted for publication in Phys. Rev.

Canonical Quantization of the Gowdy Model

The family of Gowdy universes with the spatial topology of a three-torus is studied both classically and quantum mechanically. Starting with the Ashtekar formulation of Lorentzian general relativity, we introduce a gauge fixing procedure to remove almost all of the non-physical degrees of freedom. In this way, we arrive at a reduced model that is subject only to one homogeneous constraint. The phase space of this model is described by means of a canonical set of elementary variables. These are two real, homogeneous variables and the Fourier coefficients for four real fields that are periodic in the angular coordinate which does not correspond to a Killing field of the Gowdy spacetimes. We also obtain the explicit expressions for the line element and reduced Hamiltonian. We then proceed to quantize the system by representing the elementary variables as linear operators acting on a vector space of analytic functionals. The inner product on that space is selected by imposing Lorentzian reality conditions. We find the quantum states annihilated by the operator that represents the homogeneous constraint of the model and construct with them the Hilbert space of physical states. Finally, we derive the general form of the quantum observables of the model.Comment: 13 pages, Revte

On the inferential implications of decreasing weight structures in mixture models

Bayesian estimation of nonparametric mixture models strongly relies on available representations of discrete random probability measures. In particular, the order of the mixing weights plays an important role for the identifiability of component-specific parameters which, in turn, affects the convergence properties of posterior samplers. The geometric process mixture model provides a simple alternative to models based on the Dirichlet process that effectively addresses these issues. However, the rate of decay of the mixing weights for this model may be too fast for modeling data with a large number of components. The need for different decay rates arises. Some variants of the geometric process featuring different decay behaviors, while preserving the decreasing structure, are presented and investigated. An asymptotic characterization of the number of distinct values in a sample from the corresponding mixing measure is also given, highlighting the inferential implications of different prior specifications. The analysis is completed by a simulation study in the context of density estimation. It shows that by controlling the decaying rate, the mixture model is able to capture data with a large number of components

Non-radial null geodesics in spherical dust collapse

The issue of the local visibility of the shell-focussing singularity in marginally bound spherical dust collapse is considered from the point of view of the existence of future-directed null geodesics with angular momentum which emanate from the singularity. The initial data (i.e. the initial density profile) at the onset of collapse is taken to be of class $C^3$. Simple necessary and sufficient conditions for the existence of a naked singularity are derived in terms of the data. It is shown that there exist future-directed non-radial null geodesics emanating from the singularity if and only if there exist future-directed radial null geodesics emanating from the singularity. This result can be interpreted as indicating the robustness of previous results on radial geodesics, with respect to the presence of angular momentum.Comment: 26 pages, 1 figur

Second Order Perturbations of Flat Dust FLRW Universes with a Cosmological Constant

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $\Lambda\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.Comment: 6 pages, 1 figure. to be published in "Proceedings of the 5th Alexander Friedmann Seminar on Gravitation and Cosmology", Int. Journ. Mod. Phys. A (2002). Macros: ws-ijmpa.cls, ws-p9-75x6-50.cl