2.6 Graphical representation of logistic sigmoid function.
From the graphical representation, it is clear that for the large positive value of input x, the output value y tends to 1. On the other hand, for the negative value of x, y tends to 0. Again, if x approaches to −∞ or ∞, the slope of the graph becomes 0. The increment of slope occurs as x goes close to 0. These characteristics of the sigmoid graph are very crucial in ANN.
2.3.4 Single-Layer Neural Network
It is the simplest form of neural network model containing only one layer of input nodes which receives the weighted input and send it to the subsequent layer of receiving nodes. In some cases, there may be only one neuron exists at the receiving end. Even a single neuron of ANN has astonishing computational capability. As the activity of the input is limited to receiving and passing of input signal and it does not perform any computation, thus only true layer of neuron is single-layer network is the output layer. The basic model of single layer neural network is shown in Figure 2.7. The yellow nodes denote the input layer which receives x1, x2, x3, ……, xN as the input and send it to the output layer represented by green nodes. Each of the nodes in the input layer is connected with each node in the output layer through the connection weight. If the weight value is zero, then indicates no connection between the nodes. The output nodes calculate the output values and generate the output y1, y2, y3, ……, yN. Because of only one layer of link between the input and output, this model is termed as single layer network. It can only learn linear functions. The model shown in Figure 2.7 is fully connected.
2.3.5 Multilayer Neural Network
It has more computational capabilities than the previously discussed single layer neural network. Apart from single-input layer and single-output layer, it has one or more hidden layers depending on the complexity of the computational problem. Unlike to single-layer network, multi-layer network can learn non-linear functions. Computations on the weighted inputs are performed in the hidden layers and generate the net input on which activation functions are applied to produce the actual output.
Figure 2.7 Single layer neural network.
Figure 2.8 Multilayer neural network.
Figure 2.8 represents a model of fully connected multi-layer neural network. In this structure, the input layer shown by yellow nodes receive the inputs x1, x2, x3, … …, xN and pass it to the first hidden layer, represented by gray nodes in Figure 2.8. If the model has multiple hidden layers, then the output from the first hidden layer is passed to the next hidden layer and so on. Finally, when the output from the last hidden layer reaches to the output layer represented by the green nodes, it produces the final output y1, y2, y3, … …, yN. It can be said that the multi-layer network consists of a number of single layer network arrange in a cascading manner.
2.3.6 Learning Process
Learning is an impressive characteristic of human brain. But, the research on exact process of learning in human nervous system is still in its primary stage. The scientists claim that, learning in biological system occurs due to some alteration of neural structure and synaptic connections. ANN replicates the learning process of human nervous system and the ability to learn is one of the most unique features of ANN. The learning algorithms adjust the weighted connections between the neurons of neural network. The sequence of events occurs during learning process is as follows:
1 1. The environment stimulates the network in which it is embedded.
2 2. As a result of stimulation, the free parameters of the network get altered.
3 3. The system generates response to the environment in an enhanced way.
The purpose of the learning algorithm is to find an appropriate set of weight matrices so that it can generate output efficiently after mapping any input. The three classes of learning processes are listed below.
1 1. Supervised Learning: In this case, the learning algorithm provides the desired output along with the given input while training the ANN. Because of the input-output pair, the neural model becomes capable of calculating the error based on the target vs. actual output. Based on the calculated error, the model can be corrected by adjusting the weights.
2 2. Unsupervised Leaning: In unsupervised learning, the algorithm only feeds the set of input to the neural model and the weighted connection of the network is adjusted by internal monitoring system. The neural network finds some kind of pattern within the given input and accordingly the artificial is network is modified without any external assistance.
3 3. Reinforcement Learning: Reinforcement learning has some resemblance with supervised learning, but in this case no target output is given, instead, certain reward or penalties are given based on the performance of the neural model. It is a goal-oriented algorithm which receives the reward through trial-and-error method.
So far, we have given a brief overview of ANNs which a significant domain of artificial intelligence. In the next section, we will focus on the core area of this chapter, i.e., ANN using DNA computing. In the sphere of DNA computation, the logical aspect of artificial intelligence has been replaced by chemical properties and characteristics of DNA molecules.
2.4 DNA Neural Networks
DNA molecules are capable of storing and processing information which stimulates the idea of DNA computing. It is the emerging arena in the domain of computation, and gradually, we are approaching toward the paradigm shift, from silicon to carbon, where DNA computing is overcoming the drawbacks of traditional silicon-based computing. Because of the unique properties (like, Watson-Crick base pairing) of DNA molecules, it has become an influential tool of engineering at nano-scale. The models of ANNs, DNA logic gates, and DNA logic circuits, as illustrated in this chapter, inspire the basic design of DNA computer.
Set of short DNA sequences, i.e., DNA oligonucleotides can be used to design a model of ANN. These short DNA sequences are used to code input and output signal and to build the basic architecture of the neuron. In the subsequent subsections, we focus on some of the ANN models developed using DNA sequences.
2.4.1 Formation of Axon by DNA Oligonucleotide and Generation of Output Sequence
Mills [4] has developed a simple model of neural network which is capable to transport signal using DNA oligonucleotides. The states of activity of the neural model are coded by the concentrations of the neuron DNA oligonucleotides. The input and output neurons are coded by single stranded DNA sequences. Partially double-stranded DNA sequences denote the formed axons.
The DNA oligonucleotides that represent the input and output signals are used to encode the axon of the neural model. These oligonucleotides are then temporarily attached to each other by a linker oligonucleotide. The one half of the linker sequence is complementary to the half of output neuron oligonucleotide