Gui-Yuan Shi

Neural network architecture determines its functional output. However, the detailed mechanisms are not well characterized. In this study, we focused on the neural network architectures of male and hermaphrodite C. elegans and the association with sexually dimorphic behaviors. We applied graph theory and computational neuroscience methods to systematically discern the features of these two neural networks. Our findings revealed that a small percentage of sexual-specific neurons exerted dominance throughout the entire male neural net-work, suggesting male’s prioritized sexual-related behavior outputs. Based on the structural and dynamical characteristics of two complete neural networks, sub-networks containing sex-specific neurons and their immediate neighbors, or sub-networks exclusively comprising sex-shared neurons, we predicted dimorphic behavioral outcomes for males and hermaphrodites. To verify the prediction, we performed behavioral and calcium imaging experiments and dissected a circuit that is specific for the increased spontaneous local search in males for mate-searching. Our research sheds light on the neural circuits that underlie sexually dimorphic behaviors in C. elegans, and provides significant insights into the inter-connected relationship between network architecture and functional outcomes at the whole-brain level.

Many real-world complex systems, when hitting a tipping point, undergo irreversible sudden shifts that can eventually take a great toll on humanity and the natural world, such as ecosystem collapses, disease outbreaks, etc. Previous work has adopted approximations to predict the tipping points, but due to the nature of nonlinearity, this may lead to unexpected errors in predicting real-world systems. Here we obtain the rigorous bounds of the tipping points for general nonlinear cooperative networks. Our results offer two rigorous criteria that determine the collapse and survival of such a system. These two criteria are decided by the combined effect of dynamical parameters and interaction topology.

Multiplex networks are generally considered as networks that have the same set of vertices but different types of edges. Multiplex networks are especially useful when describing systems with several kinds of interactions. In this paper, we study the analytical solution of the k-core pruning process on multiplex networks. k-Core decomposition is a widely used method to find the dense core of the network. Previously, the Non-Backtracking Expansion Branch (NBEB) has been found to be able to easily derive the exact analytical results in the k-core pruning process. Here, we further extend this method to solve the k-core pruning process on multiplex networks by designing a variation of the method called the Multicolor Non-Backtracking Expansion Branch (MNEB). Our results show that, given any uncorrelated multiplex network, the Multicolor Non-Backtracking Expansion Branch can offer the exact solution for each intermediate state of the pruning process.

Finding the critical factor and possible “Newton’s laws” in financial markets has been an important issue. However, with the development of information and communication technologies, financial models are becoming more realistic but complex, contradicting the objective law “Greatest truths are the simplest.” Therefore, this paper presents an evolutionary model independent of micro features and attempts to discover the most critical factor. In the model, information is the only critical factor, and stock price is the emergence of collective behavior. The statistical properties of the model are significantly similar to the real market. It also explains the correlations of stocks within an industry, which provides a new idea for studying critical factors and core structures in the financial markets.

The outbreak of epidemics, the emergence of the financial crisis, the collapse of ecosystem, and the explosive spreading of rumors, we face many challenges in today's world. These real-world problems can be abstracted into a sequential break down of a complex system in an increasingly stressful environment. Because both the system and the environment require a large number of parameters to describe, the break down conditions has been difficult to estimate. We use a highly symmetric system to gauge a complex environment, which enables us to propose a scalar benchmark to describe the environment. This allows us to prove that all the tipping points of a complex network fall between the maximum k-core and maximum eigenvalue of the network.