Quadri-tilings of the plane

We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called {\em triangular quadri-tilings}, as an interface model in dimension 2+2. Assigning "critical" weights to edges of $R^*$, we prove an explicit expression, only depending on the local geometry of the graph $R^*$, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of \cite{Kenyon1}. We also show that when edges of $R^*$ are asymptotically far apart, the probability of their occurrence only depends on this set of edges. Finally, we give an expression for a Gibbs measure on the set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs measures, and conjecture it to be that of minimal free energy per fundamental domain.Comment: Revised version, minor changes. 30 pages, 13 figure

Circumbinary Chaos: Using Pluto's Newest Moon to Constrain the Masses of Nix & Hydra

The Pluto system provides a unique local laboratory for the study of binaries with multiple low mass companions. In this paper, we study the orbital stability of P4, the most recently discovered moon in the Pluto system. This newfound companion orbits near the plane of the Pluto-Charon binary, roughly halfway between the two minor moons Nix and Hydra. We use a suite of few body integrations to constrain the masses of Nix and Hydra, and the orbital parameters of P4. For the system to remain stable over the age of the Solar System, the masses of Nix and Hydra likely do not exceed 5e16 kg and 9e16 kg, respectively. These upper limits assume a fixed mass ratio between Nix and Hydra at the value implied by their median optical brightness. Our study finds that stability is more sensitive to their total mass and that a downward revision of Charon's eccentricity (from our adopted value of 0.0035) is unlikely to significantly affect our conclusions. Our upper limits are an order of magnitude below existing astrometric limits on the masses of Nix and Hydra. For a density at least that of ice, the albedos of Nix and Hydra would exceed 0.3. This constraint implies they are icy, as predicted by giant impact models. Even with these low masses, P4 only remains stable if its eccentricity e < 0.02. The 5:1 commensurability with Charon is particularly unstable, Combining stability constraints with the observed mean motion places the preferred orbit for P4 just exterior to the 5:1 resonance. These predictions will be tested when the New Horizons satellite visits Pluto. Based on the results for the Pluto-Charon system, we expect that circumbinary, multi-planet systems will be more widely spaced than their singleton counterparts. Further, circumbinary exoplanets close to the three-body stability boundary, such as those found by Kepler, are less likely to have other companions nearby.Comment: 12 pages, 7 figure

Vacancy localization in the square dimer model

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1/4. The resultant weak localization of vacancies still allows for unbounded diffusion, characterized by a diffusion exponent that we relate to that of diffusion on spanning trees. We also implement numerical simulations of the model with both free and periodic boundary conditions.Comment: 35 pages, 24 figures. Improved version with one added figure (figure 9), a shift s->s+1 in the definition of the tree size, and minor correction

The TAOS Project: Upper Bounds on the Population of Small KBOs and Tests of Models of Formation and Evolution of the Outer Solar System

We have analyzed the first 3.75 years of data from TAOS, the Taiwanese American Occultation Survey. TAOS monitors bright stars to search for occultations by Kuiper Belt Objects (KBOs). This dataset comprises 5e5 star-hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this dataset. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari (2005), Kenyon & Bromley (2004), Benavidez & Campo Bagatin (2009), and Fraser (2009). A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is comprised of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.Comment: 18 pages, 16 figures, Aj submitte

Generalized Integer Partitions, Tilings of Zonotopes and Lattices

In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of two dimensional zonotopes, using dynamical systems and order theory. We show that the sets of partitions ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of zonotopes, ordered with a simple and classical dynamics, is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical systems exist. These results give a better understanding of the behaviour of tilings of zonotopes with flips and dynamical systems involving partitions.Comment: See http://www.liafa.jussieu.fr/~latapy

Optical and infrared properties of V1647 Orionis during the 2003-2006 outburst. I The reflection nebula

Aims: The recent outburst of the young eruptive star V1647 Orionis has produced a spectacular appearance of a new reflection nebula in Orion (McNeil's nebula). We present an optical/near infrared investigation of McNeil's nebula. This analysis is aimed at determining the morphology, temporal evolution and nature of the nebula and its connection to the outburst. Method: We performed multi epoch B, V, R, I, z, and K imaging of McNeil's nebula and V1647 Ori as well as K_S imaging polarimetry. The multiband imaging allows us to reconstruct the extinction map inside the nebula. Through polarimetric observations we attempt to disentangle the emission from the nebula from that of the accretion disk around V1647 Ori. We also attempt to resolve the small spatial scale structure of the illuminating source. Results: The energy distribution and temporal evolution of McNeil's nebula mimic that of the illuminating source. The extinction map reveals a region of higher extinction in the direction of V1647 Ori. Excluding foreground extionction, the optical extinction due to McNeil's nebula in the direction of V1647 Ori is A_V ~ 6.5 mag. The polarimetric measurement shows a compact high polarization emission around V1647 Ori. The percentage of K_S band linear polarization goes from 10 -- 20 %. The vectors are all well aligned with a position angle of 90 +/- 9 degree East of North. This may correspond to the orientation of a possible accretion disk around V1647 Ori. These findings suggest that the appearance of McNeil's nebula is due to reflection of light by pre-existing material in the surroundings of V1647 Ori. We also report on the discovery of a new candidate brown dwarf or protostar in the vicinity of V1647 Ori as well as the presence of clumpy structure within HH 22A.Comment: 8 pages, 7 figures, in pres

Microencapsulated islet allografts in diabetic NOD mice and nonhuman primates

OBJECTIVE: Our goal was to assess the efficacy of encapsulated allogeneic islets transplanted in diabetic NOD mice and streptozotocin (STZ)-diabetic nonhuman primates (NHPs).MATERIALS AND METHODS: Murine or NHP islets were microencapsulated and transplanted in non-immunosuppressed mice or NHPs given clinically-acceptable immunosuppressive regimens, respectively. Two NHPs were treated with autologous mesenchymal stem cells (MSCs) and peri-transplant oxygen therapy. Different transplant sites (intraperitoneal [i.p.], omental pouch, omental surface, and bursa omentalis) were tested in separate NHPs. Graft function was monitored by exogenous insulin requirements, fasting blood glucose levels, glucose tolerance tests, percent hemoglobin A1c (% HbA1c), and C-peptide levels. In vitro assessment of grafts included histology, immunohistochemistry, and viability staining; host immune responses were characterized by flow cytometry and cytokine/chemokine multiplex ELISAS.RESULTS: Microencapsulated islet allografts functioned long-term i.p. in diabetic NOD mice without immunosuppression, but for a relatively short time in immunosuppressed NHPs. In the NHPs, encapsulated allo-islets initially reduced hyperglycemia, decreased exogenous insulin requirements, elevated C-peptide levels, and lowered % HbA1c in plasma, but graft function diminished with time, regardless of transplant site. At necropsy, microcapsules were intact and non-fibrotic, but many islets exhibited volume loss, central necrosis and endogenous markers of hypoxia. Animals receiving supplemental oxygen and autologous MSCs showed improved graft function for a longer post-transplant period. In diabetic NHPs and mice, cell-free microcapsules did not elicit a fibrotic response.CONCLUSIONS: The evidence suggested that hypoxia was a major factor for damage to encapsulated islets in vivo. To achieve long-term function, new approaches must be developed to increase the oxygen supply to microencapsulated islets and/or identify donor insulin-secreting cells which can tolerate hypoxia.</p

Novel kinase platform for the validation of the anti-tubercular activities of Pelargonium sidoides (Geraniaceae)

Abstract Background Pelargonium sidoides is an important traditional medicine in South Africa with a well-defined history of both traditional and documented use of an aqueous-ethanolic formulation of the roots of P. sidoides (EPs 7630), which is successfully employed for the treatment of respiratory tract infections. There is also historical evidence of use in the treatment of tuberculosis. The aim of this study was to develop a platform of Mycobacterium tuberculosis (Mtb) kinase enzymes that may be used for the identification of therapeutically relevant ethnobotanical extracts that will allow drug target identification, as well as the subsequent isolation of the active compounds. Results Mtb kinases, Nucleoside diphosphokinase, Homoserine kinase, Acetate kinase, Glycerol kinase, Thiamine monophosphate kinase, Ribokinase, Aspartokinase and Shikimate kinase were cloned, produced in Escherichia coli and characterized. HPLC-based assays were used to determine the enzyme activities and subsequently the inhibitory potentials of varying concentrations of a P. sidoides extract against the produced enzymes. The enzyme activity assays indicated that these enzymes were active at low ATP concentrations. The 50% inhibitory concentration (IC50) of an aqueous root extract of P. sidoides against the kinases indicated SK has an IC50 of 1.2 μg/ml and GK 1.4 μg/ml. These enzyme targets were further assessed for compound identification from the P. sidoides literature. Conclusion This study suggests P. sidoides is potentially a source of anti-tubercular compounds and the Mtb kinase platform has significant potential as a tool for the subsequent screening of P. sidoides extracts and plant extracts in general, for compound identification and elaboration by selected extract target inhibitor profiling