Inductive Theorem Proving and Computer Algebra in the Mathweb Software Bus

Reasoning systems have reached a high degree of maturity in the last decade. However, even the most successful systems are usually not general purpose problem solvers but are typically specialised on problems in a certain domain. The MathWeb SOftware Bus (Mathweb-SB) is a system for combining reasoning specialists via a common osftware bus. We described the integration of the lambda-clam systems, a reasoning specialist for proofs by induction, into the MathWeb-SB. Due to this integration, lambda-clam now offers its theorem proving expertise to other systems in the MathWeb-SB. On the other hand, lambda-clam can use the services of any reasoning specialist already integrated. We focus on the latter and describe first experimnents on proving theorems by induction using the computational power of the MAPLE system within lambda-clam.

Toxicity of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) in the developing male Wistar(Han) rat II: chronic dosing causes developmental delay

We have investigated whether fetal exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) causes defects in the male reproductive system of the rat, using chronically exposed rats to ensure continuous exposure of the fetus. 5-6 week old rats were exposed to control diet, or diet containing TCDD, to attain an average dose of 2.4, 8 and 46 ng TCDD kg-1 day-1 for twelve weeks, whereupon the rats were mated, and allowed to litter; rats were switched to control diet after parturition. Male offspring were allowed to develop until kills on PND70 (25 per group), or PND120 (all remaining animals). Offspring from the high dose group showed an increase in total litter loss, and the number of animals alive on post-natal day (PND) 4 in the high dose group was ~26% less than control. The high and medium dose offspring showed decreased weights at various ages. Balano-preputial separation was significantly delayed in all three dose groups, compared to control. There were no significant effects of maternal treatment when the offspring were subjected to a functional observational battery, or learning tests, with the exception that the high dose group showed a deficit in motor activity. 20 rats per group were mated to females, and there were no significant effects of maternal treatment on the fertility of these rats, nor on the F1 or F2 sex ratio. Sperm parameters at PND70 and 120 showed no significant effect of maternal treatment, with the exception that there was an increase in the proportion of abnormal sperm in the high dose group at PND70; this is associated with the developmental delay in puberty in this dose group. There were no remarkable findings of maternal treatment on organ weights, with the exception that testis weights were reduced by ~10% at PND70 (but not PND120), and although the experiment was sufficiently powered to detect small changes, ventral prostate weight was not reduced. There were no significant effects of maternal treatment upon histopathological comparison of high dose and control group organs. These data confirm that developmental exposure to TCDD shows no potent effect on adult sperm parameters or accessory sexual organs, but show that delay in BPS occurs after exposure to low doses of TCDD, and this is dependent upon whether TCDD is administered acutely or chronically.

Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio-temporal chaos. In this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.