Summation neurons

The network architecture of a PNN (Figure 8.1) is similar to that of a GRNN, except that its summation layer has a neuron for each data class and the neurons sum all the pattern neurons output corresponding to members of that summation neuron s data class to obtain the estimated probability density function for that data class. The single neuron in the output layer then... 

The more synchronised the activity of the cortical neurons, the greater the summation of currents and the larger and slower the EEG wave, as in the sleep pattern (Fig. 22.4). While there are some dissociations between EEG pattern and behavioural states, the EEG offers one way of determining experimentally the pathways (and neurotransmitters) that control arousal and sleep, and can be regarded as an important objective measurement of the cortical correlates of sleep and waking. 

As previously mentioned, a single action potential at a single synapse results in a graded potential only an EPSP or an IPSP. Therefore, generation of an action potential in the postsynaptic neuron requires the addition or summation of a sufficient number of excitatory inputs to depolarize this neuron to threshold. Two types of summation may occur ... 

Temporal summation occurs when multiple EPSPs (or IPSPs) produced by a single presynaptic neuron in close sequence exert their effect on membrane potential of the postsynaptic neuron. For example, an action potential in the presynaptic neuron produces an EPSP and partial depolarization of the postsynaptic neuron (see Figure 5.2). While the postsynaptic neuron is still depolarized, a second action potential in the presynaptic neuron produces another EPSP in the postsynaptic neuron that adds to the first and further depolarizes this neuron. 

As more EPSPs add together, the membrane depolarizes closer to threshold until an action potential is generated. Although temporal summation is illustrated in Figure 5.2 with the summation of relatively few EPSPs, in actuality, addition of up to 50 EPSPs may be necessary to reach threshold. Because a presynaptic neuron may generate up to 500 action potentials per... 

Figure 5.2 Temporal summation. Multiple excitatory postsynaptic potentials (EPSPs) produced by a single presynaptic neuron in close sequence may add together to depolarize the postsynaptic neuron to threshold and generate an action potential.

As with temporal summation, this example has been simplified to illustrate the concept clearly. In actuality, a large number of excitatory inputs from different presynaptic neurons are necessary to depolarize the postsynaptic neuron to threshold. Because a typical neuronal cell body receives thousands of presynaptic inputs, spatial summation also occurs quite readily. The number of presynaptic neurons that are active simultaneously therefore influences the strength of the signal to the postsynaptic neuron. Under normal physiological conditions, temporal summation and spatial summation may occur concurrently. 

Figure 5.3 Spatial summation. Multiple excitatory postsynaptic potentials (EPSPs) or inhibitory postsynaptic potentials (IPSPs) produced by many presynaptic neurons simultaneously may add together to alter the membrane potential of the postsynaptic neuron. Sufficient excitatory input (A and B) will depolarize the membrane to threshold and generate an action potential. The simultaneous arrival of excitatory and inhibitory inputs (A and C) may cancel each other out so that the membrane potential does not change.

Convergence occurs when the axon terminals of many presynaptic neurons all synapse with a single postsynaptic neuron. As discussed previously, spatial summation of nerve impulses relies on the presence of convergence. Divergence occurs when the axon of a single presynaptic neuron branches and synapses with multiple postsynaptic neurons. In this way, activity in a... 

Activation of ionotropic mechanisms creates postsynaptic potentials. An influx of cations or efflux of anions depolarizes the neuron, creating an excitatory-postsynaptic potential (EPSP). Conversely, an influx of anions or efflux of cations hyperpolarizes the neuron, creating an inhibitory-postsynaptic potential (IPSP). Postsynaptic potentials are summated both... 

Most neurons in the CNS receive both EPSP and IPSP input. Thus, several different types of neurotransmitters may act on the same neuron, but each binds to its own specific receptor. The overall resultant action is due to the summation of the individual actions of the various neurotransmitters on the neuron. The neurotransmitters are not uniformly distributed in the CNS but are localized in specific clusters of neurons whose axons may synapse with specific regions of the brain. Many neuronal tracts thus seem to be chemically coded, and this may offer greater opportunity for selective modulation of certain neuronal pathways. 

Practically all forms of neuron transfer functions include the summation operation, i.e., the sum of all inputs into the neuron (multiplied by their connection strength or weights) is calculated. In mathematical terms,... 

Another function common in neurons is thresholding, or changing the output signal in discrete steps depending upon the value of the summation ( ) of the input signals. The output signal of neurons can theoretically have any value between °° however, typically values range between 0 and 1. Some neurons are allowed to have only the discrete values 0 or 1 (off and on, respectively), whereas others are allowed to take any real value between 0 and 1 inclusively. A simple threshold function is of the form... 

Another common name for the threshold value 0 is bias. The idea is that each neuron may have its own built-in bias term, independent of the input. One way of handling this pictorially and computationally is to add an extra unit to the input layer that always has a value of -1. Then the weight of the connections between this unit and the neurons in the next layer is the threshold or bias values for those neurons and the summation operation includes the bias term automatically. Then the summation formula becomes... 

So, the basic neuron can be seen as having two operations, summation and thresholding, as illustrated in Figure 2.5. Other forms of thresholding and, indeed, other transfer functions are commonly used in neural network modeling some of these will be discussed later. For input neurons, the transfer function is typically assumed to be unity, i.e., the input signal is passed through without modification as output to the next layer F(x) = 1.0. 

Excitation can also result from a summation of chemical neurotransmitters released from several presy-naptic neurons that terminate on one postsynaptic neuron. In addition to such spatial control mechanisms, there are mechanisms that are time-dependent (temporal controls). Because neurotransmitters remain bound to their receptors for a time, excitation can also result from an increased rate of release of neurotransmitter from the presynaptic neuron. 

A summation operator of input signals, weighted by the respective synapses of the neuron. 

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