On Neuroinformatics: Mathematical Models of Neuroscience and Neurocomputing

Neuroinformatics is a broad and rapidly evolving discipline concerned with applying information technology and computer science to solve challenges and answer pressing questions in the field of neuroscience. An emerging field of neuroinformatics attempts to model the cellular structures, properties, and functions of neural networks and their applications in neurocomputing and cognitive information systems. This paper presents a set of theories and mathematical models in neuroinformatics for neuroscience and neurocomputing. The neurological foundations of neural clusters and nervous systems are explored. A mathematical treatment of the neurological models and neural signal theories is formally described covering neural signal generation, pulse frequency modulation, and the multiplexer/demultiplexer for neural signal transmissions. Formal models of association, sensory, and motor neurons are established that explain the neurological foundation of applied artificial neural networks. Engineering applications of this neuroinformatics theory and formal neural models are elaborated in cognitive computing, neurocomputing, and neural network analyses.