Biophysical regulation of stem cell behavior within the niche.

Stem cells reside within most tissues throughout the lifetimes of mammalian organisms. To maintain their capacities for division and differentiation and thereby build, maintain, and regenerate organ structure and function, these cells require extensive and precise regulation, and a critical facet of this control is the local environment or niche surrounding the cell. It is well known that soluble biochemical signals play important roles within such niches, and a number of biophysical aspects of the microenvironment, including mechanical cues and spatiotemporally varying biochemical signals, have also been increasingly recognized to contribute to the repertoire of stimuli that regulate various stem cells in various tissues of both vertebrates and invertebrates. For example, biochemical factors immobilized to the extracellular matrix or the surface of neighboring cells can be spatially organized in their placement. Furthermore, the extracellular matrix provides mechanical support and regulatory information, such as its elastic modulus and interfacial topography, which modulate key aspects of stem cell behavior. Numerous examples of each of these modes of regulation indicate that biophysical aspects of the niche must be appreciated and studied in conjunction with its biochemical properties

Sutured Floer homology, sutured TQFT and non-commutative QFT

We define a "sutured topological quantum field theory", motivated by the study of sutured Floer homology of product 3-manifolds, and contact elements. We study a rich algebraic structure of suture elements in sutured TQFT, showing that it corresponds to contact elements in sutured Floer homology. We use this approach to make computations of contact elements in sutured Floer homology over $\Z$ of sutured manifolds $(D^2 \times S^1, F \times S^1)$ where $F$ is finite. This generalises previous results of the author over $\Z_2$ coefficients. Our approach elaborates upon the quantum field theoretic aspects of sutured Floer homology, building a non-commutative Fock space, together with a bilinear form deriving from a certain combinatorial partial order; we show that the sutured TQFT of discs is isomorphic to this Fock space.Comment: v.2: 49 pages, 13 figures. Improved and expanded exposition, some minor corrections. Sections on torsion, annuli, and tori moved to a separate pape

Similar Sublattices and Coincidence Rotations of the Root Lattice A4 and its Dual

A natural way to describe the Penrose tiling employs the projection method on the basis of the root lattice A4 or its dual. Properties of these lattices are thus related to properties of the Penrose tiling. Moreover, the root lattice A4 appears in various other contexts such as sphere packings, efficient coding schemes and lattice quantizers. Here, the lattice A4 is considered within the icosian ring, whose rich arithmetic structure leads to parametrisations of the similar sublattices and the coincidence rotations of A4 and its dual lattice. These parametrisations, both in terms of a single icosian, imply an index formula for the corresponding sublattices. The results are encapsulated in Dirichlet series generating functions. For every index, they provide the number of distinct similar sublattices as well as the number of coincidence rotations of A4 and its dual.Comment: 8 pages, paper presented at ICQ10 (Zurich, Switzerland

86 GHz Very Long Baseline Polarimetry of 3C273 and 3C279 with the Coordinated Millimeter VLBI Array

86 GHz Very Long Baseline Polarimetry probes magnetic field structures within the cores of Active Galactic Nuclei at higher angular resolutions and a spectral octave higher than previously achievable. Observations of 3C273 and 3C279 taken in April 2000 with the Coordinated Millimeter VLBI Array have resulted in the first total intensity (Stokes I) and linear polarization VLBI images reported of any source at 86 GHz. These results reveal the 86 GHz electric vector position angles within the jets of 3C273 and 3C279 to be orthogonal to each other, and the core of 3C273 to be unpolarized. If this lack of polarization is due to Faraday depolarization alone, the dispersion in rotation measure is >=90000 rad/m^2 for the core of 3C273.Comment: AASTeX v5.02; 10 pages; 4 figures; accepted for publication in the Astrophysical Journal Letter