Rongsong Liu

As a well-developed branch of mathematics, graph theory provides unique tools to quantifiably assess various properties of complex networks. Applied to brain circuits, network-level analyses can illustrate disruptions to brain organization that yield both mechanistic and diagnostic insights. Previously, graph theory has been used with functional magnetic resonance imaging datasets to quantify connections among different brain regions, readily capturing the macroscopic-scaled differences in brain networks between healthy and Alzheimer’s subjects. Here, we applied graph theory on the microscopic scale, using miniscope-based calcium imaging from the freely behaving wild type (WT) and Shank3 ^fx mice (a mouse model of autism), and compared functional connections among individual neurons in the prefrontal microcircuits during social behavior. We demonstrated that Shank3 ^fx mice displayed reduced neural activity, less-integrated network, and fewer network changes in the prefrontal microcircuits between the presence and absence of social targets. Furthermore, we employed machine learning to test whether graph-theoretic metrics extracted from the prefrontal microcircuits could be predictive of genotype and genotype-associated social behavior difference between Shank3 ^fx and WT mice. Our results indicate a strong link between altered prefrontal microcircuits and social behavior deficits in an autism mouse model, highlighting prefrontal microcircuitry as a potential diagnostic and therapeutic target for autism.

In this paper, we studied the stability of traveling wave solutions of a two-species Lotka-Volterra competition model in the form of a coupled system of reaction diffusion equations with nonlocal intraspecific and interspecific competitions in space at times. First, the uniform upper bounds for the solutions of the model was proved. By using the anti-weighted method and the energy estimates, the asymptotic stability of traveling waves with large wave speeds of the system was established.

In this paper, we consider a bistable monotone reaction–diffusion system in cylindrical domains. We first prove the existence of the entire solution emanating from a planar front. Then, it is proved that the entire solution converges to a planar front if the propagation is complete and the domain is bilaterally straight. Finally, we give some geometrical conditions on the domain such that the propagation of the entire solution is complete or incomplete, respectively.

Intra-specific competition in insect and amphibian species is often experienced in completely different ways in their distinct life stages. Competition among larvae is important because it can impact on adult traits that affect disease transmission, yet mathematical models often ignore larval competition. We present two models of larval competition in the form of delay differential equations for the adult population derived from age-structured models that include larval competition. We present a simple prototype equation that models larval competition in a simplistic way. Recognising that individual larvae experience competition from other larvae at various stages of development, we then derive a more complex equation containing an integral with a kernel that quantifies the competitive effect of larvae of ageāon larvae of agea. In some parameter regimes, this model and the famous spruce budworm model have similar dynamics, with the possibility of multiple co-existing equilibria. Results on boundedness and persistence are also proved.

The existences of an asymptotic spreading speed and traveling wave solutions for a diffusive model which describes the interaction of mistletoe and bird populations with nonlocal diffusion and delay effect are proved by using monotone semiflow theory. The effects of different dispersal kernels on the asymptotic spreading speeds are investigated through concrete examples and simulations.