| The field of computational neuroscience has experienced a tremendous expansion over the last several decades. Ever since the fundamental work of Hodgkin and Huxley in the early fifties, that established computational neuroscience as a discipline, scientists have been trying to attach a meaning to the process of neural “computation”.; This study will give a brief introduction as to how analog signals can be encoded using spiking neurons, and how the encoded information can be recovered from the spiky data. The discussion will start with a description of a simple circuit, so-called On/Off pair, and will be extended to a population of neurons. Such a population can be organized in a network that can perform specific computational tasks, e.g. it can encode analog variables and vectors, as well as functions of analog variables/vectors. Despite the nonlinear nature of the encoding process, the decoding algorithm can be viewed as a simple linear (weighted) sum of the neural activities. The weights are found explicitly by minimizing a suitably chosen cost functional. Furthermore, the network can be engineered to solve ordinary differential equations (ODEs), in the process where the activities of individual neurons are dynamically updated. Selected examples include solving the Van der Pol oscillator and building a memory that can hold several values of analog variable using a single set of synaptic weights.; In the second part of the thesis, a network of biophysically realistic neurons is introduced. A large scale model of turtle visual cortex is discussed in particular. The study shows that the position and velocity of a spot of light incident on the retina of a turtle are encoded in the associated spatiotemporal dynamics of the cortical wave they generate. The conjecture is verified by synthesizing a large scale model of the turtle visual cortex using GENESIS. The cortical waves are parameterized using the Principal Components Analysis, which leads to a convenient representation of the data set in a low dimensional subspace. Using standard statistical methods, the parameters of an unknown stimulus can be estimated based on the cortical response elicited by the stimulus. |
