Complexity reduction of astrochemical networks

We present a new computational scheme aimed at reducing the complexity of the chemical networks in astrophysical models, one which is shown to markedly improve their computational efficiency. It contains a flux-reduction scheme that permits to deal with both large and small systems. This procedure is shown to yield a large speed-up of the corresponding numerical codes and provides good accord with the full network results. We analyse and discuss two examples involving chemistry networks of the interstellar medium and show that the results from the present reduction technique reproduce very well the results from fuller calculations.Comment: 9 pages, 7 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journa

Complexity reduction of C-algorithm

The C-Algorithm introduced in [Chouikha2007] is designed to determine isochronous centers for Lienard-type differential systems, in the general real analytic case. However, it has a large complexity that prevents computations, even in the quartic polynomial case. The main result of this paper is an efficient algorithmic implementation of C-Algorithm, called ReCA (Reduced C-Algorithm). Moreover, an adapted version of it is proposed in the rational case. It is called RCA (Rational C-Algorithm) and is widely used in [BardetBoussaadaChouikhaStrelcyn2010] and [BoussaadaChouikhaStrelcyn2010] to find many new examples of isochronous centers for the Li\'enard type equation

Complexity Reduction for Parameter-Dependent Linear Systems

We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with fewer parameters or state variables. To do so, it minimizes the distance (i.e., H-infinity-norm of the difference) between the original system and its reduced version. We present a sub-optimal solution to this problem using sum-of-squares optimization methods. We present the results for both continuous-time and discrete-time systems. Lastly, we illustrate the applicability of our proposed algorithm on numerical examples

Geometrical relations between space time block code designs and complexity reduction

In this work, the geometric relation between space time block code design for the coherent channel and its non-coherent counterpart is exploited to get an analogue of the information theoretic inequality $I(X;S)\le I((X,H);S)$ in terms of diversity. It provides a lower bound on the performance of non-coherent codes when used in coherent scenarios. This leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced sub tasks. Moreover a geometrical criterion for high performance space time code design is derived.Comment: final version, 11 pages, two-colum