The adapted solution and comparison theorem for backward stochastic differential equations with Poisson jumps and applications

This paper deals with a class of backward stochastic differential equations with Poisson jumps and with random terminal times. We prove the existence and uniqueness result of adapted solution for such a BSDE under the assumption of non-Lipschitzian coefficient. We also derive two comparison theorems by applying a general Girsanov theorem andthe linearized technique on the coefficient. By these we first show the existence and uniqueness of minimal solution for one-dimensional BSDE with jumps when its coefficient is continuous and has a linear growth. Then we give a general Feynman-Kac formula for a class of parabolic types of second-order partial differential and integral equations (PDIEs) by using the solution of corresponding BSDE with jumps. Finally, we exploit above Feynman-Kac formula and related comparison theorem to provide a probabilistic formula for the viscosity solution of a quasi-linear PDIE of parabolic type

Control of spiral waves and turbulent states in a cardiac model by travelling-wave perturbations

We propose a travelling-wave perturbation method to control the spatiotemporal dynamics in a cardiac model. It is numerically demonstrated that the method can successfully suppress the wave instability (alternans in action potential duration) in the one-dimensional case and convert spiral waves and turbulent states to the normal travelling wave states in the two-dimensional case. An experimental scheme is suggested which may provide a new design for a cardiac defibrillator.Comment: 9 pages, 5 figure

Prospects for Detecting Neutrino Signals from Annihilating/Decaying Dark Matter to Account for the PAMELA and ATIC results

Recent PAMELA data show that positron fraction has an excess above several GeV while anti-proton one is not. Moreover ATIC data indicates that electron/positron flux have a bump from 300 GeV to 800 GeV. Both annihilating dark matter (DM) with large boost factor and decaying DM with the life around $10^{26} s$ can account for the PAMELA and ATIC observations if their main final products are charged leptons ($e$, $\mu$ and $\tau$). In this work, we calculated the neutrino flux arising from $\mu$ and $\tau$ which originate from annihilating/decaying DM, and estimated the final muon rate in the neutrino telescopes, namely Antares and IceCube. Given the excellent angular resolution, Antares and IceCube are promising to discover the neutrino signals from Galactic center and/or large DM subhalo in annihilating DM scenario, but very challenging in decaying DM scenario.Comment: 21 pages, 7 figures, 2 tables. V2: references added. V3: the number density of massive subhalo has been discussed in the appendix; accepted by PR