2,112 research outputs found
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 obtained
by adding a translation part to a subgroup of 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 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
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