Equivalence between various versions of the self-dual action of the Ashtekar formalism

Different aspects of the self-dual (anti-self-dual) action of the Ashtekar canonical formalism are discussed. In particular, we study the equivalences and differences between the various versions of such an action. Our analysis may be useful for the development of an Ashtekar formalism in eight dimensions.Comment: 10 pages, Latex, minor correction

On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity

We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical simulation we find that the number of such triangulations containing $V$ simplices grows faster than exponentially with $V$. This property ensures that the model has no thermodynamic limit.Comment: 8 pages, 2 figure

Random manifolds and quantum gravity

The non-perturbative, lattice field theory approach towards the quantization of Euclidean gravity is reviewed. Included is a tentative summary of the most significant results and a presentation of the current state of art.Comment: invited plenary talk at LATTICE '99 (Pisa), latex 5p

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

Classical Loop Actions of Gauge Theories

Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.Comment: LaTeX 14 page

Gli3 utilizes Hand2 to synergistically regulate tissue-specific transcriptional networks.

Despite a common understanding that Gli TFs are utilized to convey a Hh morphogen gradient, genetic analyses suggest craniofacial development does not completely fit this paradigm. Using the mouse model (Mus musculus), we demonstrated that rather than being driven by a Hh threshold, robust Gli3 transcriptional activity during skeletal and glossal development required interaction with the basic helix-loop-helix TF Hand2. Not only did genetic and expression data support a co-factorial relationship, but genomic analysis revealed that Gli3 and Hand2 were enriched at regulatory elements for genes essential for mandibular patterning and development. Interestingly, motif analysis at sites co-occupied by Gli3 and Hand2 uncovered mandibular-specific, low-affinity, \u27divergent\u27 Gli-binding motifs (dGBMs). Functional validation revealed these dGBMs conveyed synergistic activation of Gli targets essential for mandibular patterning and development. In summary, this work elucidates a novel, sequence-dependent mechanism for Gli transcriptional activity within the craniofacial complex that is independent of a graded Hh signal

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

The Cyprinodon variegatus genome reveals gene expression changes underlying differences in skull morphology among closely related species

Genes in durophage intersection set at 15 dpf. This is a comma separated table of the genes in the 15 dpf durophage intersection set. Given are edgeR results for each pairwise comparison. Columns indicating whether a gene is included in the intersection set at a threshold of 1.5 or 2 fold are provided. (CSV 13 kb

Identification of a heterogeneous and dynamic ciliome during embryonic development and cell differentiation.

Primary cilia are nearly ubiquitous organelles that transduce molecular and mechanical signals. Although the basic structure of the cilium and the cadre of genes that contribute to ciliary formation and function (the ciliome) are believed to be evolutionarily conserved, the presentation of ciliopathies with narrow, tissue-specific phenotypes and distinct molecular readouts suggests that an unappreciated heterogeneity exists within this organelle. Here, we provide a searchable transcriptomic resource for a curated primary ciliome, detailing various subgroups of differentially expressed genes within the ciliome that display tissue and temporal specificity. Genes within the differentially expressed ciliome exhibited a lower level of functional constraint across species, suggesting organism and cell-specific function adaptation. The biological relevance of ciliary heterogeneity was functionally validated by using Cas9 gene-editing to disrupt ciliary genes that displayed dynamic gene expression profiles during osteogenic differentiation of multipotent neural crest cells. Collectively, this novel primary cilia-focused resource will allow researchers to explore longstanding questions related to how tissue and cell-type specific functions and ciliary heterogeneity may contribute to the range of phenotypes associated with ciliopathies