Entropy degeneration of convex projective surfaces

We show that the volume entropy of the Hilbert metric on a closed convex projective surface tends to zero as the corresponding Pick differential tends to infinity. The proof is based on the theorem, due to Benoist and Hulin, that the Hilbert metric and Blaschke metric are comparable.Comment: 5 page

On the Hilbert geometry of simplicial Tits sets

The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is either a point or the real line. Answering a question of M. Crampon, we prove that in the latter case, when one goes to infinity in the moduli space, the entropy of the Hilbert metric tends to 0.Comment: 18 pages, 5 figure

RELATIONSHIPS BETWEEN DIETARY FIBER STRUCTURAL FEATURES AND GROWTH AND UTILIZATION PATTERNS OF HUMAN GUT BACTERIA

Intake of dietary fiber is considered an essential strategy to influence gut microbiota, which is associated with many diet-related chronic diseases such as obesity, diabetes, and inflammatory bowel diseases. In order to make a better choice of dietary fiber for a desired microbiota shift related to a health outcome, knowledge of fiber degradation and utilization by gut bacteria is critical. However, it is still unclear how specific dietary fiber structures may influence the growth of target bacteria

On circle patterns and spherical conical metrics

The Koebe-Andreev-Thurston circle packing theorem, as well as its generalization to circle patterns due to Bobenko and Springborn, holds for Euclidean and hyperbolic metrics possibly with conical singularities, but fails for spherical metrics because of the non-uniqueness coming from M\"obius transformations. In this paper, we show that a unique existence result for circle pattern with spherical conical metric holds if one prescribes the geodesic total curvature of each circle instead of the cone angles.Comment: 9 pages, 6 figure

Association Between Obesity and Cardiometabolic Health in Asian-Canadian Sub-Groups

Purpose: To examine the association between the WHO’s Asian specific trigger points representing ‘increased risk’ (BMI ≥23 kg/m2) and ‘high risk’ (BMI ≥27.5 kg/m2) with cardiovascular-related conditions in Asian-Canadian sub-groups. Methods: Six cycles of the Canadian Community Health Survey (2001-2009; N=18 794) were pooled and weighted; multivariable logistic regression was used to estimate the odds of cardiovascular outcomes. Results: Versus South Asians, Filipinos had higher odds of ‘≥1 cardiometabolic condition’ (OR=1.29). Compared to the normal weight category in each ethnic group, the association between excess adiposity on ‘≥1 cardiometabolic condition’ was highest among Chinese (‘increased risk’: OR=3.6; ‘high risk’: OR=8.9). Compared to ‘normal weight’ South Asians, those in the ‘high risk’ groups (except Southeast Asian, Arab, and Japanese) were approximately 3-times as likely to report ‘≥1 cardiometabolic condition’. Conclusions: The relationship between overweight, obesity, and health risk varied within Asian sub-groups, and was strongest for South Asian and Filipino

Affine deformations of quasi-divisible convex cones

For any subgroup of $\mathrm{SL}(3,\mathbb{R})\ltimes\mathbb{R}^3$ obtained by adding a translation part to a subgroup of $\mathrm{SL}(3,\mathbb{R})$ which is the fundamental group of a finite-volume convex projective surface, we first show that under a natural condition on the translation parts of parabolic elements, the affine action of the group on $\mathbb{R}^3$ has convex domains of discontinuity that are regular in a certain sense, generalizing a result of Mess for globally hyperbolic flat spacetimes. We then classify all these domains and show that the quotient of each of them is an affine manifold foliated by convex surfaces with constant affine Gaussian curvature. The proof is based on a correspondence between the geometry of an affine space endowed with a convex cone and the geometry of a convex tube domain. As an independent result, we show that the moduli space of such groups is a vector bundle over the moduli space of finite-volume convex projective structures, with rank equaling the dimension of the Teichm\"uller space.Comment: 37 pages, 6 figures. Comments welcom

Gravitational Effects of Rotating Bodies

We study two type effects of gravitational field on mechanical gyroscopes (i.e. rotating extended bodies). The first depends on special relativity and equivalence principle. The second is related to the coupling (i.e. a new force) between the spins of mechanical gyroscopes, which would violate the equivalent principle. In order to give a theoretical prediction to the second we suggest a spin-spin coupling model for two mechanical gyroscopes. An upper limit on the coupling strength is then determined by using the observed perihelion precession of the planet's orbits in solar system. We also give predictions violating the equivalence principle for free-fall gyroscopes .Comment: LaTex, 6 page