![]() |
|
|||
![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() |
|
![]() |
[an error occurred while processing this directive]
3.2.3 Neural field theoryThe spatiotemporal activity in randomly interconnected neurons refers to the neurodynamics or neural field theory in which a set of differential equations describe activity patterns in bulk neural continuum [11,12]. For example, the fluid mechanics based visualization of neuron flow has two perspectives: The governing differential equations could be derived on the continuum point of view or on the basis of a large number of interacting particles. (The later consideration refers to statistical mechanics principles which will be discussed in Chapter 5 in detail.) The earliest continuum model of neuronal spatiotemporal activity is due to Beurle [42] who deduced the following set of differential equations governing the random activity in a neuronal network in terms of the level of sustained activity (F) and the proportion of cells which are nonrefractory (R): where Φ is the probability that a sensitive cell will be energized above its threshold in unit time. The solution of the above equations represent the proliferation of the neuronal activity (in time and space) as traveling waves. Considering the neuronal excitation (ψ) is regarded as being carried by a continual shuffling between sources and fields (Fa), Griffith in 1963 proposed [11-14] that Fa creates ψ and so on by an operation specified by: where He is an undefined operation and k is a constant. The spatiotemporal distribution of the overall excitation (ψ) has hence been derived in terms of the activity of some on neurons (Fa) as: where α, β, γ, are system coefficients. Another continuum model of spatiotemporal activity of neurons is due to Wilson and Cowan [43,44] who described the spatiotemporal development in terms of the proportion of excitatory cells (Le) becoming active per unit time; or proportion of inhibitory cells (Li) becoming active per unit time. Representing the excitatory activity of the neurons by a function Ee and the inhibitory activity by Ei: are derived as the functions to denote the spatiotemporal activity of the neurons. Here, μ, γe, γi are system coefficients and De, Di are densities of excitatory and inhibitory cells participating in the regime of activity. Solutions of the above equations involve convolutions, and simplification of these equations leads to system description in terms of coupled van der Pohl oscillators. A more involved description of the neuronal activity continuum refers to nonlinear integro-differential equations as elucidated by Orguztoreli [45] and Kawahara et al. [46]. Another modeling technique due to Ventriglia [47] incorporating intraneuron excitation, proportion of neurons in refractory state, velocity of impulses, neuronal density, synaptic density, axonic branching, and fraction of excitatory neurons in the continuum description of spatiotemporal neuronal activity has led to the study of informational waves, dynamic activities, and memory effect. 3.3 Models of Memory in Neural NetworksThe memory associated with neural system is twofold: Long-term and short-term memories. The short-term memory refers to a transient activity; and if that persists long enough, it would constitute the long-term memory. The short-term memory corresponds to the input firing at a modular net stored by the impulse reverberating in the loop as illustrated in Figure 3.5. The net has a long-term memory if the short-term memory could cause its threshold to drop from 1 to 0, for example; for the memory would then be preserved and persistent even if the reverberation dies down. The concept of memory involves a storage mechanism which utilizes a storage medium; the associated operation is termed as memory function which operates with the other functions of the neural network and/or the biological system. Storage and recall of information by association with other information refers to the most basic application of collective computation on a neural network. The information storing device is known as the associative memory, if it permits the recall of information on the basis of partial knowledge of its content, but without knowing its storage location. It depicts a content addressable memory.
Copyright © CRC Press LLC
![]() |
![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() |
![]() |