Dimensionality reduction method of dynamic networks for evolutionary mechanism of neuronal systems

Understanding the development process of biological neuronal systems is one of the major challenges to explore the formation mechanism of human brain intelligence and biological behaviors, which is of great importance to enlighten the designing of various artificial neural network algorithms as well. Here, with the whole neural connection map of C.elegans, we explore the evolutionary mechanism of its neuronal system based on mean-field theory and network dimension reduction method. Firstly, we use a set of activation equations to capture the neurons’ interaction in the networks, and adopt the dimensionality reduction framework to decouple the nematode’s multi-dimensional neural network into an one-dimensional system. Then we propose two control index after the system is decoupled, which can be used to describe the structure and stable state of the whole neural network, as well as the development of an organism on the basis of birth time and process length. Our theoretical approach of multidimensional system to the one-dimensional system can help distract our attention from the micro-dynamics of a single neuron to the macro-dynamics of the whole network. Our results reveal some factors that influence the evolution of neural system, explore the evolutionary constraints and contribution of these factors at the level of neural networks function and topology. In conclusion, our analytical framework provides an overview of quantitative understanding of the growth process and the evolutionary constraints in the neural system.