General representation of collective neural dynamics with columnar modularity

We exhibit a mathematical framework to represent the neural process at the cortical level. The description of neural dynamics with columnar and functional modularity, named the fibre bundle map (FBM) representation method, is based on both neuroscience and informatics, whereas it leads to the conventional formulas in statistical physics. The possibility of analogy between the phenomena in brain and physical systems has been proposed [1, 2]. In spite of the complex circuitry and the nonlinear dynamics in neural systems, the neural behavior at high levels may be described by simple and general rules, which related to the noble theory in statistical physics. The FBM method gives profit in building or analyzing the neural models by representing essential ingredients of neural interactions by general formulas. We apply our method to the proposed models of visual map formation and show how they can share statistical properties with vortex dynamics in magnetism in spite of various development mechanisms.