Analytic Torsion on Hyperbolic Manifolds and the Semiclassical Approximation for Chern-Simons Theory

The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of hyperbolic 3-manifolds is presented. We discuss briefly L^2 - analytical and topological torsions of a manifold with boundary.Comment: 12 pages, LaTeX fil

S5 0716+714 : GeV variability study

The GeV observations by Fermi-LAT give us the opportunity to characterize the high-energy emission (100 MeV - 300 GeV) variability properties of the BL Lac object S5 0716+714. In this study, we performed flux and spectral analysis of more than 3 year long (August 2008 to April 2012) Fermi-LAT data of the source. During this period, the source exhibits two different modes of flux variability with characteristic timescales of ~75 and ~140 days, respectively. We also notice that the flux variations are characterized by a weak spectral hardening. The GeV spectrum of the source shows a clear deviation from a simple power law, and is better explained by a broken power law. Similar to other bright Fermi blazars, the break energy does not vary with the source flux during the different activity states. We discuss several possible scenarios to explain the observed spectral break.Comment: 21 pages, 10 figures, Accepted for publication in Advances in Space Research journa

New holomorphically closed subalgebras of C∗C^*-algebras of hyperbolic groups

We construct dense, unconditional subalgebras of the reduced group $C^*$-algebra of a word-hyperbolic group, which are closed under holomorphic functional calculus and possess many bounded traces. Applications to the cyclic cohomology of group $C^*$-algebras and to delocalized $L^2$-invariants of negatively curved manifolds are given

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

A network-based ranking system for American college football

American college football faces a conflict created by the desire to stage national championship games between the best teams of a season when there is no conventional playoff system to decide which those teams are. Instead, ranking of teams is based on their record of wins and losses during the season, but each team plays only a small fraction of eligible opponents, making the system underdetermined or contradictory or both. It is an interesting challenge to create a ranking system that at once is mathematically well-founded, gives results in general accord with received wisdom concerning the relative strengths of the teams, and is based upon intuitive principles, allowing it to be accepted readily by fans and experts alike. Here we introduce a one-parameter ranking method that satisfies all of these requirements and is based on a network representation of college football schedules.Comment: 15 pages, 3 figure

In vivo potassium MRI of the human heart

PURPOSE: Potassium ions (K(+)) play a critical role in cardiac electrophysiology, and changes in their concentration reflect pathophysiological processes related to cardiovascular diseases. Here, we investigated the feasibility of in vivo (39)K MRI of the human heart. To achieve this, we developed, evaluated, and applied a (39)K/(1)H RF coil, which is tailored for (39)K MRI of human heart at 7.0T. METHODS: The performance of the (39)K/(1)H RF coil was evaluated by electromagnetic field and specific absorption ratio simulations using 2 (male/female) human voxel models. The RF coil was evaluated at the bench and applied in an in vivo proof-of-principle study involving 7 healthy volunteers. The experiments were performed using a 7.0T whole-body MR system in conjunction with a 3D density-adapted projection reconstruction imaging technique. RESULTS: For in vivo (39)K MRI of the human heart, a nominal spatial resolution of 14.5 × 14.5 × 14.5 mm(3) within a total scan time of 30 min was achieved. The average SNR within the heart was 9.6 ± 2.4. CONCLUSION: This work validates the design of a (39)K/(1)H RF coil for cardiac MR at 7.0T and demonstrates for the first time in vivo the feasibility of (39)K MRI of the human heart