General representation of collective neural dynamics with columnar   modularity
  We exhibit a mathematical framework to represent the neural dynamics at cortical level. Our description of neural dynamics with columnar and functional modularity, named fibre bundle representation (FBM) method, is based both on neuroscience and informatics, whereas they correspond with the conventional formulas in statistical physics. In spite of complex interactions in neural circuitry and various cortical modification rules per models, some significant factors determine the typical phenomena in cortical dynamics. The FBM representation method reveals them plainly and gives profit in building or analyzing the cortical dynamic models. Not only the similarity in formulas, the cortical dynamics can share the statistical properties with other physical systems, which validated in primary visual maps. We apply our method to proposed models in visual map formations, in addition our suggestion using the lateral interaction scheme. In this paper, we will show that the neural dynamic procedures can be treated through conventional physics expressions and theories. 
Myoung Won Cho, Seunghwan Kim