A bistable reaction-diffusion system in a stretching flow

We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODEs) for the dynamics of the governing advection-reaction-diffusion partial differential equations (PDE), for pulse-like and for plateau-like solutions, based on a non-perturbative approach. This reduction allows us to study the dynamics in two cases: first, close to a saddle-node bifurcation at which a pair of nontrivial steady states are born as the dimensionless reaction rate (Damkoehler number) is increased, and, second, for large Damkoehler number, far away from the bifurcation. The main aim is to investigate the initial-value problem and to determine when an initial condition subject to chaotic stirring will decay to zero and when it will give rise to a nonzero final state. Comparisons with full PDE simulations show that the reduced pulse model accurately predicts the threshold amplitude for a pulse initial condition to give rise to a nontrivial final steady state, and that the reduced plateau model gives an accurate picture of the dynamics of the system at large Damkoehler number. Published in Physica D (2006)

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.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular we are able to treat "patchy'" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice-directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs. Article published and (c) American Physical Society 2007

Detecting Motifs in System Call Sequences

The search for patterns or motifs in data represents an area of key interest to many researchers. In this paper we present the Motif Tracking Algorithm, a novel immune inspired pattern identification tool that is able to identify unknown motifs which repeat within time series data. The power of the algorithm is derived from its use of a small number of parameters with minimal assumptions. The algorithm searches from a completely neutral perspective that is independent of the data being analysed and the underlying motifs. In this paper the motif tracking algorithm is applied to the search for patterns within sequences of low level system calls between the Linux kernel and the operating system’s user space. The MTA is able to compress data found in large system call data sets to a limited number of motifs which summarise that data. The motifs provide a resource from which a profile of executed processes can be built. The potential for these profiles and new implications for security research are highlighted. A higher level system call language for measuring similarity between patterns of such calls is also suggested.

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.