Chapter 2. Prehension

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relationships are highlighted. These models act to suggest
computational models which explicitly specify details of the system by
showing solutions to mathematical systems. Computational modelling
allows one to simulate a conceptual model in order to test its validity.
However, the designer of the computational version has to make
decisions about various aspects of the conceptual model in order to
actually implement it on a computer. Some examples:
Neuronal Models. Conceptual models exist for
understanding the behavior of individual neurons. Dendrites,
acting as inputs, sum up activity coming into a neuron, and if
threshold is reached, an action potential travels down the axon to
cause neurotransmitters to be released. In order to model this on
a computer, parameters must be set using differential equations
that describe membrane potentials, thresholds, cable
propagation, etc.
Control Theoretic Models. Neuronal activity is fit into
control equations that describe feedback and feedforward control
using data transformations (e.g., integration and differentiation).
For example, neurophysiologists have shown the existence of
burst neurons, and Robinson (1981) constructed a control
theoretic models around such neurons, showing how a
computation can be performed. In another example, Allen and
Tsukahara (1974) developed a conceptual model showing the
relationship between various cerebral and cerebellar areas. From
this, Kawato and colleagues constructed a computational model
using standard feedforward-feedback control theory (Kawato et
al., 1987b) and using neurons to simulate motor cortex (Kawato
et al., 1987a).
>. Network Models. Consisting of billions of neurons making
synapses with one another, the CNS can be modelled using
massively parallel network of neurons. For example, when
looking at one’s arm, retinal inputs and eye muscle activity will
create a pattern of incoming activity into the CNS. Kuperstein
(1988) constructed a massive network that correlates retinal and
eye muscle activity to an arm configuration. Network design
decisions include: in what coordinate frame is the information,
how is it transformed, what size networks are needed, how can
learning occur. The mathematics of nonlinear dynamical
systems in high-dimensional spaces are used to construct these
models.