Biomedical subjects

D S Broomhead

Publications and source records attributed to D S Broomhead.

6 recordsLinked to original sources

PubMed2001

Relating individual behaviour to population dynamics.

How do the behavioural interactions between individuals in an ecological system produce the global population dynamics of that system? We present a stochastic individual-based model of the reproductive cycle of the mite Varroa jacobsoni, a parasite of honeybees. The model has the interesting property in that its population level behaviour is approximated extremely accurately by the exponential logistic equation or Ricker map. We demonstrated how this approximation is obtained mathematically and how the parameters of the exponential logistic equation can be written in terms of the parameters of the individual-based model. Our procedure demonstrates, in at least one case, how study of animal ecology at an individual level can be used to derive global models which predict population change over time.

Animals↗

PubMed2001

Ants and agents: a process algebra approach to modelling ant colony behaviour.

Process algebras are widely used in the analysis of distributed computer systems. They allow formal reasoning about how the various components of a system contribute to its overall behaviour. In this paper we show how process algebras can be usefully applied to understanding social insect biology, in particular to studying the relationship between algorithmic behaviour of individual insects and the dynamical behaviour of their colony. We argue that process algebras provide a useful formalism for understanding this relationship, since they combine computer simulation, Markov chain analysis and mean-field methods of analysis. Indeed, process algebras can provide a framework for relating these three methods of analysis to each other and to experiments. We illustrate our approach with a series of graded examples of modelling activity in ant colonies.

Animals↗

PubMed2001

The Whitney reduction network: a method for computing autoassociative graphs.

This article introduces a new architecture and associated algorithms ideal for implementing the dimensionality reduction of an m-dimensional manifold initially residing in an n-dimensional Euclidean space where n >> m. Motivated by Whitney's embedding theorem, the network is capable of training the identity mapping employing the idea of the graph of a function. In theory, a reduction to a dimension d that retains the differential structure of the original data may be achieved for some d < or = 2m + 1. To implement this network, we propose the idea of a good-projection, which enhances the generalization capabilities of the network, and an adaptive secant basis algorithm to achieve it. The effect of noise on this procedure is also considered. The approach is illustrated with several examples.

Journal Article↗

PubMed2000

Shape and dynamics of thermoregulating honey bee clusters.

A model of simple algorithmic "agents" acting in a discrete temperature field is used to investigate the movement of individuals in thermoregulating honey bee (Apis mellifera) clusters. Thermoregulation in over-wintering clusters is thought to be the result of individual bees attempting to regulate their own body temperatures. At ambient temperatures above 0( degrees )C, a clustering bee will move relative to its neighbours so as to put its local temperature within some ideal range. The proposed model incorporates this behaviour into an algorithm for bee agents moving on a two-dimensional lattice. Heat transport on the lattice is modelled by a discrete diffusion process. Computer simulation of this model demonstrates qualitative behaviour which agrees with that of real honey bee clusters. In particular, we observe the formation of both disc- and ring-like cluster shapes. The simulation also suggests that at lower ambient temperatures, clusters do not always have a stable shape but can oscillate between insulating rings of different sizes and densities.

Algorithms↗

PubMed2000

Modelling of congenital nystagmus waveforms produced by saccadic system abnormalities.

Models of the mechanisms of normal eye movements are typically described in terms of the block diagrams which are used in control theory. An alternative approach to understanding the mechanisms of normal eye movements involves describing the eye movement behaviour in terms of smooth changes in state variables. The latter approach captures the burst cell firing against motor error (difference between target gaze angle and current gaze angle) phase plane behaviour which is found experimentally and facilitates the modelling of variations in burst cell behaviour. A novel explanation of several types of congenital nystagmus waveforms is given in terms of a saccadic termination abnormality.

Humans↗

PubMed1997

Dynamical systems analysis: a new method of analysing congenital nystagmus waveforms.

Congenital nystagmus is an oculomotor disorder in which fixation is disrupted by rhythmical, bilateral involuntary oscillations. Clinically these eye movements have been described with some degree of success in terms of their peak-to-peak amplitude, frequency, mean velocity and waveform shape. However, it has not proved possible to diagnose any underlying pathology from the nystagmus characteristics. Here, we propose a new approach to understanding the nystagmus using dynamical systems theory. Our approach is based on the use of delay embedding techniques, which allow one to relate a time series of scalar observations to the state space dynamics of the underlying dynamical system. Using this approach we quantify the dynamics of the nystagmus in the region of foveation and present evidence to suggest that it is low-dimensional and deterministic. Our results put new constraints on acceptable models of nystagmus and suggest a way to make a closer link between data analysis and model development. This approach raises the hope that techniques originally developed to stabilise chaotic systems, by using small perturbations, may prove useful in the control of nystagmus.

Adolescent↗