Efficient Kernel Computation for Volterra Filter Structure Evaluation

Despite their generality, conventional Volterra filters are inadequate for some applications, due to the huge number of parameters that may be needed for accurate modelling. When a state-space model of the target system is known, this can be assessed by computing its kernels, which also provides valuable information for choosing an adequate alternate Volterra filter structure, if necessary, and is useful for validating parameter estimation procedures. In this letter, we derive expressions for the kernels by using the Carleman bilinearization method, for which an efficient algorithm is given. Simulation results are presented, which confirm the usefulness of the proposed approach.

Coupled Boltzmann calculation of mixed axion/neutralino cold dark matter production in the early universe

We calculate the relic abundance of mixed axion/neutralino cold dark matter which arises in R-parity conserving supersymmetric (SUSY) models wherein the strong CP problem is solved by the Peccei-Quinn (PQ) mechanism with a concommitant axion/saxion/axino supermultiplet. By numerically solving the coupled Boltzmann equations, we include the combined effects of 1. thermal axino production with cascade decays to a neutralino LSP, 2. thermal saxion production and production via coherent oscillations along with cascade decays and entropy injection, 3. thermal neutralino production and re-annihilation after both axino and saxion decays, 4. gravitino production and decay and 5. axion production both thermally and via oscillations. For SUSY models with too high a standard neutralino thermal abundance, we find the combined effect of SUSY PQ particles is not enough to lower the neutralino abundance down to its measured value, while at the same time respecting bounds on late-decaying neutral particles from BBN. However, models with a standard neutralino underabundance can now be allowed with either neutralino or axion domination of dark matter, and furthermore, these models can allow the PQ breaking scale f(a) to be pushed up into the 10(14) - 10(15) GeV range, which is where it is typically expected to be in string theory models.