Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached.

PCA 4 DCA: the application of principal component analysis to the Dendritic Cell Algorithm

As one of the newest members in the field of articial immune systems (AIS), the Dendritic Cell Algorithm (DCA) is based on behavioural models of natural dendritic cells (DCs). Unlike other AIS, the DCA does not rely on training data, instead domain or expert knowledge is required to predetermine the mapping between input signals from a particular instance to the three categories used by the DCA. This data preprocessing phase has received the criticism of having manually over-fitted the data to the algorithm, which is undesirable. Therefore, in this paper we have attempted to ascertain if it is possible to use principal component analysis (PCA) techniques to automatically categorise input data while still generating useful and accurate classication results. The integrated system is tested with a biometrics dataset for the stress recognition of automobile drivers. The experimental results have shown the application of PCA to the DCA for the purpose of automated data preprocessing is successful.