Additional Acceleration of Protons and Energetic Neutrino Production in a Filamentary Jet of the Blazar Markarian 501

Blazars have been regarded as one of the most powerful sources of the highest energy cosmic rays and also their byproducts, neutrinos. Provided that a magnetized filamentary system is established in a blazar jet as well, we could apply the mechanism of multi-stage diffusive shock acceleration to a feasible TeV emitter, Mrk 501 to evaluate the achievable maximum energy of protons. Taking conceivable energy restriction into account systematically, it seems adequate to say that EeV-protons are produced at this site by our present model. We also estimate neutrino fluxes generated by these accelerated protons and discuss the detectability based on an updated kilometre-scale telescope such as IceCube.Comment: 17 pages, 3 Postscript figure

Sutured Floer homology, sutured TQFT and non-commutative QFT

We define a "sutured topological quantum field theory", motivated by the study of sutured Floer homology of product 3-manifolds, and contact elements. We study a rich algebraic structure of suture elements in sutured TQFT, showing that it corresponds to contact elements in sutured Floer homology. We use this approach to make computations of contact elements in sutured Floer homology over $\Z$ of sutured manifolds $(D^2 \times S^1, F \times S^1)$ where $F$ is finite. This generalises previous results of the author over $\Z_2$ coefficients. Our approach elaborates upon the quantum field theoretic aspects of sutured Floer homology, building a non-commutative Fock space, together with a bilinear form deriving from a certain combinatorial partial order; we show that the sutured TQFT of discs is isomorphic to this Fock space.Comment: v.2: 49 pages, 13 figures. Improved and expanded exposition, some minor corrections. Sections on torsion, annuli, and tori moved to a separate pape

Exact Asymptotics for the Random Coding Error Probability

Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap between the achievable error probability and its bound than to discuss the absolute gap. Scarlett et al. derived a good upper bound of a random coding union bound based on the technique of saddlepoint approximation but it is not proved that the relative gap of their bound converges to zero. This paper derives a new bound on the achievable error probability in this viewpoint for a class of memoryless channels. The derived bound is strictly smaller than that by Scarlett et al. and its relative gap with the random coding error probability (not a union bound) vanishes as the block length increases for a fixed coding rate.Comment: Full version of the paper in ISIT2015 with some corrections and refinement