Weak local rules for planar octagonal tilings

We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities, as conjectured by Thang Le in the 90s.Comment: 23 pages, 6 figure

Gamma-Ray Bursts as a Probe of the Very High Redshift Universe

We show that, if many GRBs are indeed produced by the collapse of massive stars, GRBs and their afterglows provide a powerful probe of the very high redshift (z > 5) universe.Comment: To appear in Proc. of the 5th Huntsville Gamma-Ray Burst Symposium, 5 pages, LaTe

A TQFT associated to the LMO invariant of three-dimensional manifolds

We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. It is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup ${\cal L}_g$ of the Mapping Class Group that contains the Torelli group. The N=1 truncation produces a TQFT for the Casson-Walker-Lescop invariant.Comment: 28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten, since they will constitute a separate paper. Section 4, which contained only announce of results, has been suprimated; it will appear in detail elsewhere. Consequently some statements have been re-numbered. No mathematical changes have been made.

Direct genetic demonstration of Gα13 coupling to the orphan G protein-coupled receptor G2A leading to RhoA-dependent actin rearrangement

G2A is an orphan G protein-coupled receptor (GPCR), expressed predominantly in T and B cells and homologous to a small group of GPCRs of unknown function expressed in lymphoid tissues. G2A is transcriptionally induced in response to diverse stimuli, and its ectopic expression suppresses transformation of B lymphoid precursors by BCR-ABL. G2A induces morphological transformation of NIH 3T3 fibroblasts. Microinjection of constructs encoding G2A into Swiss 3T3 fibroblasts induces actin reorganization into stress fibers that depends on RhoA, but not CDC42 or RAC. G2A elicits RhoA-dependent transcriptional activation of serum response factor. Direct evaluation of RhoA activity demonstrates elevated levels of RhoA-GTP in G2A-expressing cells. Microinjection of embryonic fibroblasts derived from various Galpha knockout mice establishes a requirement for Galpha 13 but not Galpha 12 or Galpha q/11 in G2A-induced actin rearrangement. In conclusion, G2A represents a family of GPCRs expressed in lymphocytes that may link diverse stimuli to cytoskeletal reorganization and transcriptional activation through a pathway involving Galpha 13 and RhoA