Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognized that more realistic models of neural tissue can be obtained with the introduction of state-dependent dynamic thresholds. In this paper we treat a specific phenomenological model of threshold accommodation that mimics many of the properties originally described by Hill. Importantly we explore the consequences of this dynamic threshold at the tissue level, by modifying a standard neural field model of Wilson-Cowan type. As in the case without threshold accommodation classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps) in both one and two dimensions. Importantly an analysis of bump stability in one dimension, using recent Evans function techniques, shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. In the regime where a bump solution does not exist direct numerical simulations show the possibility of self-replicating bumps via a form of bump splitting. Simulations in two space dimensions show analogous localized and traveling solutions to those seen in one dimension. Indeed dynamical behavior in this neural model appears reminiscent of that seen in other dissipative systems that support localized structures, and in particular those of coupled cubic complex Ginzburg-Landau equations. Further numerical explorations illustrate that the traveling pulses in this model exhibit particle like properties, similar to those of dispersive solitons observed in some three component reaction-diffusion systems. A preliminary account of this work first appeared in S Coombes and M R Owen, Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters 94 (2005), 148102(1-4).

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

The Application of a Dendric Cell Algorithm to a Robotic Classifier

The dendritic cell algorithm is an immune-inspired technique for processing time-dependant data. Here we propose it as a possible solution for a robotic classification problem. The dendritic cell algorithm is implemented on a real robot and an investigation is performed into the effects of varying the migration threshold median for the cell population. The algorithm performs well on a classification task with very little tuning. Ways of extending the implementation to allow it to be used as a classifier within the field of robotic security are suggested.

The Application of a Dendric Cell Algorithm to a Robotic Classifier

The dendritic cell algorithm is an immune-inspired technique for processing time-dependant data. Here we propose it as a possible solution for a robotic classification problem. The dendritic cell algorithm is implemented on a real robot and an investigation is performed into the effects of varying the migration threshold median for the cell population. The algorithm performs well on a classification task with very little tuning. Ways of extending the implementation to allow it to be used as a classifier within the field of robotic security are suggested.

The Application of a Dendric Cell Algorithm to a Robotic Classifier

The dendritic cell algorithm is an immune-inspired technique for processing time-dependant data. Here we propose it as a possible solution for a robotic classification problem. The dendritic cell algorithm is implemented on a real robot and an investigation is performed into the effects of varying the migration threshold median for the cell population. The algorithm performs well on a classification task with very little tuning. Ways of extending the implementation to allow it to be used as a classifier within the field of robotic security are suggested.

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Genetic algorithm seeding of idiotypic networks for mobile-robot navigation

Robot-control designers have begun to exploit the properties of the human immune system in order to produce dynamic systems that can adapt to complex, varying, real-world tasks. Jerne’s idiotypic-network theory has proved the most popular artificial-immune-system (AIS) method for incorporation into behaviour-based robotics, since idiotypic selection produces highly adaptive responses. However, previous efforts have mostly focused on evolving the network connections and have often worked with a single, preengineered set of behaviours, limiting variability. This paper describes a method for encoding behaviours as a variable set of attributes, and shows that when the encoding is used with a genetic algorithm (GA), multiple sets of diverse behaviours can develop naturally and rapidly, providing much greater scope for flexible behaviour-selection. The algorithm is tested extensively with a simulated e-puck robot that navigates around a maze by tracking colour. Results show that highly successful behaviour sets can be generated within about 25 minutes, and that much greater diversity can be obtained when multiple autonomous populations are used, rather than a single one.