Construction of neural networks and computational neuroscience
The aim of this work is to address a common set of problems concerning the ways in which networks of neurons may become interconnected and the computations that such networks may carry out. The problems are those of producing explanatory models for (i) the elimination of superinnervation in developing muscle, and (ii) the development and functioning of the visual system, particularly the formation of binocular visual connections where the target area is divided up into eye-specific regions yet the monocular part-projections are retinotopically ordered. (iii) Finally, an investigation is being made into the capacity of certain parts of the brain, principally hippocampus and cerebellum, to support particular memory functions.
The following projects have been completed or are underway:
- A new theory for the development of innervation of neonatal muscle has been developed. According to this theory the elimination of superinnervation involves competition for a factor released at motor neuron terminals and competition for a different factor available at muscle end-plates. Stability analysis has shown that according to this theory intrinsical withdrawal of contacts is not a separate non-competitive phenomenon, but rather a by-product of the competition (Rasmussen and Willshaw, 1993).
- A full scale simulation model of the connections to one Purkinje cell of the cerebellum has been built which was used for testing of Marr's theory of cerebellar cortex (J. Physiol., 1969) (Tyrrell and Willshaw, 1992).
- In ongoing theoretical work on the relevance of the neural network model called the Associative Net (Willshaw et al, 1969), to hippocampal function,the current focus is on the biological relevance of the mechanisms proposed for the storage and retrieval of information in the Associative Net (Buckingham and Willshaw 1992, 1993).
- One defect of the Associative Net in its pure form is that once it is overloaded, its performance deteriorates catastrophically. A possible solution isto adapt its characteristics so that new memories are stored at the expense of old memories being forgotten - the system acts as a short-term memory. With Rik Henson, I have examined the possible ways in which the Associative Net can be used in this fashion (Henson, MSc thesis 1993). This work is continuing.
- With Dr Goodhill (Joint Councils' Fellow) and Dr Simmen (MRC Brain and Behaviour, Oxford), we have been examining the use of quantitative methods (such as that proposed recently by M P Young, Nature, 358: 152-155, 1992) for analysing brain connectivity.
- Buckingham, J T and Willshaw, D J (1992). Performance characteristics of the associative net. Network 3: 407-414.
- Buckingham, J T and Willshaw, D J (1993). On setting unit thresholds in an incompletely connected associative net. Network 4: 441-459.
- Tyrrell, L R T and Willshaw, D J (1992). Cerebellar cortex: Its simulation and the relevance of Marr's theory. Phil. Trans. Roy. Soc. B. 336: 239-257.
- Rasmussen, C E and Willshaw, D J (1993). Presynaptic and postsynaptic competition in models for the development of neuromuscular connections. Biol. Cybern., 68: 409-419.
- Willshaw, D J, Buneman, O P and Longuet-Higgins, H C (1969). Non-holographic associative memory. Nature, 222: 960-962.
- Willshaw, D J (1993). Models for the formation of ordered retino-tectal connections. In: Formation and Regeneration of nerve connections, Sharma and Fawcett (Eds) Birkhauser.