Ratio control in a cascade model of cell differentiation

We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a global feedback term. The size ratio of each cell type is controlled by a system parameter in the model. Finally, we extend the model to a cascade model of cell differentiation. A hierarchical spatial structure appears as a result of the cell differentiation. The size ratio of each cell type is also controlled by the system parameter.Comment: 13 pages, 7 figure

Thermal gravity, black holes and cosmological entropy

Taking seriously the interpretation of black hole entropy as the logarithm of the number of microstates, we argue that thermal gravitons may undergo a phase transition to a kind of black hole condensate. The phase transition proceeds via nucleation of black holes at a rate governed by a saddlepoint configuration whose free energy is of order the inverse temperature in Planck units. Whether the universe remains in a low entropy state as opposed to the high entropy black hole condensate depends sensitively on its thermal history. Our results may clarify an old observation of Penrose regarding the very low entropy state of the universe.Comment: 5 pages, 2 figures, RevTex. v4: to appear in Phys. Rev.

Modelling spatially regulated B-catenin dynamics & invasion in intestinal crypts

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from mouse and rat to human) and throughout the different regions of the small and large intestines. In this article, we construct a partial differential equation model of a single colonic crypt that describes the spatial distribution of Wnt pathway proteins along the crypt axis. The novelty of our continuum model is that it is based upon assumptions that can be directly related to processes at the cellular and subcellular scales. We use the model to predict how the distributions of Wnt pathway proteins are affected by mutations. The model is then extended to investigate how mutant cell populations can invade neighboring crypts. The model simulations suggest that cell crowding caused by increased proliferation and decreased cell loss may be sufficient for a mutant cell population to colonize a neighboring healthy crypt

Search for an Near-IR Counterpart to the Cas A X-ray Point Source

We report deep near-infrared and optical observations of the X-ray point source in the Cassiopeia A supernova remnant, CXO J232327.9+584842. We have identified a J=21.4 +/- 0.3 mag and Ks=20.5 +/- 0.3 mag source within the 1-sigma error circle, but we believe this source is a foreground Pop II star with Teff=2600-2800 K at a distance of ~2 kpc, which could not be the X-ray point source. We do not detect any sources in this direction at the distance of Cas A, and therefore place 3-sigma limits of R >~ 25 mag, F675W >~ 27.3 mag, J >~ 22.5 mag and Ks >~ 21.2 mag (and roughly H >~ 20 mag) on emission from the X-ray point source, corresponding to M_{R} >~ 8.2 mag, M_{F675W} >~ 10.7 mag, M_{J} >~ 8.5 mag, M_{H} >~ 6.5 mag, and M_{Ks} >~ 8.0 mag, assuming a distance of 3.4 kpc and an extinction A_{V}=5 mag.Comment: 14 pages, 7 figures. Accepted by Ap

Effect of heat treatment and aging on the mechanical loss and strength of hydroxide catalysis bonds between fused silica samples

Hydroxide catalysis bonds are used in the aLIGO gravitational wave detectors and are an essential technology within the mirror suspensions which allowed for detector sensitivities to be reached that enabled the first direct detections of gravitational waves. Methods aimed at further improving hydroxide catalysis bonds for future upgrades to these detectors, in order to increase detection rates and the number of detectable sources, are explored. Also, the effect on the bonds of an aLIGO suspension construction procedure involving heat, the fibre welding process, is investigated. Here we show that thermal treatments can be beneficial to improving some of the bond properties important to the mirror suspensions in interferometric gravitational wave detectors. It was found that heat treating bonds at 150\,^\circC increases bond strength by a factor of approximately 1.5 and a combination of bond ageing and heat treatment of the optics at 150\,\circC reduces the mechanical loss of a bond from 0.10 to 0.05. It is also shown that current construction procedures do not reduce bond strength

A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys