Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Family dynasties in the Tasmanian native hen (Gallinula mortierii)

For species that form multi-generational and territorial family groups, resource-rich areas are predicted to support family dynasties in which one genetic lineage continuously occupies an area and may even expand to occupy surrounding areas. Data from a long-term study of Tasmanian native hens (Gallinula mortierii) support this prediction. The reproductive success and dispersal patterns of 18 hen lineages were monitored for seven breeding seasons and over several generations. The founder group with the highest average territory quality produced the highest total number of fledged young and the highest number of fledged linear descendants, accounting for 24% of the combined reproductive output of these 18 lineages. In the space of 6 years, this single genetic lineage expanded from one territory to occupy 12 of the 47 territories present in the population. This rate of expansion was over four times the population average for the same period. A multivariate analysis revealed that the success of a genetic lineage depended only on the number of high-quality territories surrounding the founder group. These results further demonstrate the resource-dependent nature of reproductive success in this species, and also highlight the potential importance of family dynasties in other cooperative species with complex social dynamics and dispersal patterns.

Exploring complex fitness surfaces: Multiple ornamentation and polymorphism in male guppies

The sexual ornamentation used by male guppies to attract females comprises many components, each of which varies considerably among males. Although natural and sexual selection have been shown to contribute to divergence among populations in male sexual ornaments, the role of sexual selection in maintaining polymorphism within populations is less clear. We used both parametric quadratic regression and nonparametric projection pursuit regression techniques to reveal the major axes of non-linear sexual selection on male ornaments. We visualized the fitness surfaces defined by these axes using thin-plate splines to allow a direct comparison of the two methodologies. Identification of the major axes of selection and their visualization was critical in determining the form and strength of nonlinear selection. Both types of analysis revealed fitness surfaces comprising three peaks, suggesting that there is more than one way to make an attractive guppy. Disruptive selection may be an important process underlying the presence of multiple sexual ornaments and may contribute to the maintenance of the high levels of polymorphism in male sexual ornaments found in guppy populations.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.