Verification and validation of autonomous systems

NASA is working on complex future missions that require cooperation between multiple satellites or rovers. To implement these systems, developers are proposing and using intelligent and autonomous systems. These autonomous missions are new to NASA, and the software development community is just learning to develop such systems. With these new systems, new verification and validation techniques must be used. Current techniques have been developed based on large monolithic systems. These techniques have worked well and reliably, but do not translate to the new autonomous systems that are highly parallel and nondeterministic.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Practical and economic advantages of choice feeding systems for laying poultry

Poultry can be managed under different feeding systems, depending on the husbandry skills and the feed available. These systems include the following: (1) a complete dry feed offered as a mash ad libitum; (2) the same feed offered as pellets or crumbles ad libitum; (3) a complete feed with added whole grain; (4) a complete wet feed given once or twice a day; (5) a complete feed offered on a restricted basis; (6) choice feeding. Of all these, an interesting alternative to offering complete diets is choice feeding which can be applied on both a small or large commercial scale. Under choice feeding or free-choice feeding birds are usually offered a choice between three types of feedstuffs: (a) an energy source (e.g. maize, rice bran, sorghum or wheat); (b) a protein source (e.g. soyabean meal, meat meal, fish meal or coconut meal) plus vitamins and minerals and (c), in the case of laying hens, calcium in granular form (i.e. oyster-shell grit). This system differs from the modern commercial practice of offering a complete diet comprising energy and protein sources, ground and mixed together. Under the complete diet system, birds are mainly only able to exercise their appetite for energy. When the environmental temperature varies, the birds either over- or under-consume protein and calcium. The basic principle behind practising choice feeding with laying hens is that individual hens are able to select from the various feed ingredients on offer and compose their own diet, according to their actual needs and production capacity. A choice-feeding system is of particular importance to small poultry producers in developing countries, such as Indonesia, because it can substantially reduce the cost of feed. The system is flexible and can be constructed in such a way that the various needs of a flock of different breeds, including village chickens, under different climates can be met. The system also offers a more effective way to use home-produced grain, such as maize, and by-products, such as rice bran, in developing countries. Because oyster-shell grit is readily available in developing countries at lower cost than limestone, the use of cheaper oyster-shell grit can further benefit small-holders in these countries. These benefits apart, simpler equipment suffices when designing and building a feed mixer on the farm, and transport costs are lower. If whole (unground) grain is used, the intake of which is accompanied by increased efficiency of feed utilisation, the costs of grinding, mixing and many of the handling procedures associated with mash and pellet preparation are eliminated. The choice feedstuffs can all be offered in the current feed distribution systems, either by mixing the ingredients first or by using a bulk bin divided into three compartments.