**1. Introduction**

Our brain is an extraordinary microsome and has been completely shrouded in mystery. However, its mystery has been just a little bit by bit solved owing to recent advances in experimental technologies and tremendous development of computers. Many people can simply say "brain," but it is a general term for a collection of six main regions, that is, cerebrum, diencephalon, midbrain, cerebellum, pons, and medulla oblongata. The brain is an organ that

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takes the central role in advanced information processing, such as visual, auditory, speech or language faculties, motion control, recognition, emotion, and so on. According to advances of experiment and computer technology, the research of brain science or neuroscience has been made not only in the fields of medicine, biology, biochemistry, pharmacology, and psycholo‐ gy but also in the field of engineering.

The present-day computers have outstanding processing capacity. For example, they can find the data that satisfy some requirements among huge quantities of data (database) or can calculate over five trillion figures of pi(π). Therefore, many people are inclined to think that our brain will be able to be replaced by computer in near future. Surely, computers excel at processing of digitized data and processing by following a standard algorithm. However, it can hardly execute processing, such as recognition of ambiguity figures (such as illusionism) or inference based on imperfect information, which our brain can instantaneously carry out. Reason for this comes from differences in ways of information processing of the computer and our brain. The current computers, called von Neumann computer, are grounded in sequential processing by using central processing units (CPUs) and memory storages, while on the other hand, our brain bases on parallel and distributed processing through neural networks whose components are neurons.

There exist tens of billions of neurons in our brain, which build neural networks in complicated arrangement. All information processing in the brain is accomplished by neural activity in the form of neural oscillations that cause cortical oscillations (delta, theta, alpha, beta, or gamma oscillation). In order to clarify the mechanisms of advanced information processing in the brain, such as learning and memory, it is necessary to understand functions and features of neurons and neural networks. Although the current progress in experiment technology and measuring system is remarkable, only experiments by themselves cannot uncover the behavior of only a single neuron, because even a single neuron has complex biophysical characteristics and never stops growth. Computational neuroscience is a research field which fills up such a deficiency in experiments. By modeling the essential features of a neuron or a neural network at multiple spatial-temporal scales, we can capture and analyze the fundamental properties of a neuron or a neural network by computer simulation. Moreover, we can even offer some suggestions to experimental study by taking into account the probable results obtained from the simulation.
