Simulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations

We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set of five distinct vertexes, we allow triangulations containing multiply connected simplexes and distinct simplexes defined by the same set of vertexes. We demonstrate numerically that including degenerated triangulations substantially reduces the finite-size effects in the model. In particular, we provide a strong numerical evidence for an exponential bound on the entropic growth of the ensemble of degenerate triangulations, and show that a discontinuous crumpling transition is already observed on triangulations of volume N_4 ~= 4000.Comment: Latex, 8 pages, 4 eps-figure

BSSN in Spherical Symmetry

The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in the context of a single Schwarzschild black hole. One of the benefits of spherical symmetry is that the numerical grid points can be tracked on a Kruskal--Szekeres diagram. Boundary conditions suitable for puncture evolution of a Schwarzschild black hole are presented. Several results are shown for puncture evolution using a fourth--order finite difference implementation of the equations.Comment: This is the final version to be published in CQG. It contains much more information and detail than the original versio

The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analized in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.Comment: The resubmited paper contains the title and abstract, that were omitted in the previous version. 42 pages, report IFFI/93.0

Defects in the Fanconi Anemia Pathway in Head and Neck Cancer Cells Stimulate Tumor Cell Invasion through DNA-PK and Rac1 Signaling

PURPOSE: Head and neck squamous cell carcinoma (HNSCC) remains a devastating disease, and Fanconi anemia (FA) gene mutations and transcriptional repression are common. Invasive tumor behavior is associated with poor outcome, but relevant pathways triggering invasion are poorly understood. There is a significant need to improve our understanding of genetic pathways and molecular mechanisms driving advanced tumor phenotypes, to develop tailored therapies. Here we sought to investigate the phenotypic and molecular consequences of FA pathway loss in HNSCC cells. EXPERIMENTAL DESIGN: Using sporadic HNSCC cell lines with and without FA gene knockdown, we sought to characterize the phenotypic and molecular consequences of FA deficiency. FA pathway inactivation was confirmed by the detection of classic hallmarks of FA following exposure to DNA cross-linkers. Cells were subjected to RNA sequencing with qRT-PCR validation, followed by cellular adhesion and invasion assays in the presence and absence of DNA-dependent protein kinase (DNA-PK) and Rac1 inhibitors. RESULTS: We demonstrate that FA loss in HNSCC cells leads to cytoskeletal reorganization and invasive tumor cell behavior in the absence of proliferative gains. We further demonstrate that cellular invasion following FA loss is mediated, at least in part, through NHEJ-associated DNA-PK and downstream Rac1 GTPase activity. CONCLUSIONS: These findings demonstrate that FA loss stimulates HNSCC cell motility and invasion, and implicate a targetable DNA-PK/Rac1 signaling axis in advanced tumor phenotypes

Loop quantum gravity and light propagation

Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined as the expectation value of the electromagnetic term in the Einstein-Maxwell Hamiltonian constraint, regularized a la Thiemann, with respect to a would-be semiclassical state. The resulting energy dispersion relations entail Planck scale corrections to those in flat spacetime. Both the helicity dependent contribution of Gambini and Pullin [GP] and, for a value of a parameter of our approximation, that of Ellis et. al. [ELLISETAL] are recovered. The electric/magnetic asymmetry in the regularization procedure yields nonlinearities only in the magnetic sector which are briefly discussed. Observations of cosmological Gamma Ray Bursts might eventually lead to the needed accuracy to study some of these quantum gravity effects.Comment: Latex, 45 pages, shorter abstract, additional reference

A Cross-Species Analysis of MicroRNAs in the Developing Avian Face

Higher vertebrates use similar genetic tools to derive very different facial features. This diversity is believed to occur through temporal, spatial and species-specific changes in gene expression within cranial neural crest (NC) cells. These contribute to the facial skeleton and contain species-specific information that drives morphological variation. A few signaling molecules and transcription factors are known to play important roles in these processes, but little is known regarding the role of micro-RNAs (miRNAs). We have identified and compared all miRNAs expressed in cranial NC cells from three avian species (chicken, duck, and quail) before and after species-specific facial distinctions occur. We identified 170 differentially expressed miRNAs. These include thirty-five novel chicken orthologs of previously described miRNAs, and six avian-specific miRNAs. Five of these avian-specific miRNAs are conserved over 120 million years of avian evolution, from ratites to galliforms, and their predicted target mRNAs include many components of Wnt signaling. Previous work indicates that mRNA gene expression in NC cells is relatively static during stages when the beak acquires species-specific morphologies. However, miRNA expression is remarkably dynamic within this timeframe, suggesting that the timing of specific developmental transitions is altered in birds with different beak shapes. We evaluated one miRNA:mRNA target pair and found that the cell cycle regulator p27KIP1 is a likely target of miR-222 in frontonasal NC cells, and that the timing of this interaction correlates with the onset of phenotypic variation. Our comparative genomic approach is the first comprehensive analysis of miRNAs in the developing facial primordial, and in species-specific facial development

Utilizing the chicken as an animal model for human craniofacial ciliopathies

The chicken has been a particularly useful model for the study of craniofacial development and disease for over a century due to their relatively large size, accessibility, and amenability for classical bead implantation and transplant experiments. Several naturally occurring mutant lines with craniofacial anomalies also exist and have been heavily utilized by developmental biologist for several decades. Two of the most well known lines, talpid(2) (ta(2)) and talpid(3) (ta(3)), represent the first spontaneous mutants to have the causative genes identified. Despite having distinct genetic causes, both mutants have recently been identified as ciliopathic. Excitingly, both of these mutants have been classified as models for human craniofacial ciliopathies: Oral-facial-digital syndrome (ta(2)) and Joubert syndrome (ta(3)). Herein, we review and compare these two models of craniofacial disease and highlight what they have revealed about the molecular and cellular etiology of ciliopathies. Furthermore, we outline how applying classical avian experiments and new technological advances (transgenics and genome editing) with naturally occurring avian mutants can add a tremendous amount to what we currently know about craniofacial ciliopathies

Apoptosis and proliferation in the trigeminal placode

The neurogenic trigeminal placode develops from the crescent-shaped panplacodal primordium which delineates the neural plate anteriorly. We show that, in Tupaia belangeri, the trigeminal placode is represented by a field of focal ectodermal thickenings which over time changes positions from as far rostral as the level of the forebrain to as far caudal as opposite rhombomere 3. Delamination proceeds rostrocaudally from the ectoderm adjacent to the rostral midbrain, and contributes neurons to the trigeminal ganglion as well as to the ciliary ganglion/oculomotor complex. Proliferative events are centered on the field prior to the peak of delamination. They are preceded, paralleled and, finally, outnumbered by apoptotic events which proceed rostrocaudally from non-delaminating to delaminating parts of the field. Apoptosis persists upon regression of the placode, thereby exhibiting a massive “wedge” of apoptotic cells which includes the postulated position of the “ventrolateral postoptic placode” (Lee et al. in Dev Biol 263:176–190, 2003), merges with groups of lens-associated apoptotic cells, and disappears upon lens detachment. In conjunction with earlier work (Washausen et al. in Dev Biol 278:86–102, 2005) our findings suggest that apoptosis contributes repeatedly to the disintegration of the panplacodal primordium, to the elimination of subsets of premigratory placodal neuroblasts, and to the regression of placodes