Biomathematics
Department of Mathematics and Statistics
Texas Tech University
Abstract pdf
The Biomath seminar may be attended virtually Friday at 11:00 AM CST (UTC-6) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
Abstract pdf
The Biomath seminar may be attended virtually Friday at 11:00 AM CST (UTC-6) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
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 insight. Previously, graph theory has been used with functional magnetic resonance imaging (fMRI) 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 recordings from the freely behaving wild type and Shank3fx mice (a mouse model of autism), and compared their functional connections among individual neurons in the prefrontal cortical microcircuits during social behavior tasks. We demonstrated that Shank3fx mice displayed reduced neural activity, a 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 Shank3fx and WT mice. Our results indicate a strong link between altered prefrontal microcircuits and social behavior differences in an ASD mouse model, highlighting prefrontal microcircuitry as a potential diagnostic and therapeutic target for ASD.
The Biomath seminar may be attended virtually Friday at 11:00 AM CST (UTC-6) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
Ixodes scapularis, the blacklegged tick, is the main North American vector for the bacteria Borrelia burgdorferi, which causes Lyme disease, the most prevalent vector-borne disease on the continent. Tick demographics are influenced by many factors which vary geographically, including its community of hosts and its questing behavior. Both of these factors differ significantly from the northeastern US to the southeastern US: southern ecosystems contain greater biodiversity, including higher reptile abundance, while northern communities are dominated by small mammals. Questing behavior also differs regionally, with southern populations more likely to seek hosts below the leaf litter, while northern ticks quest above it. This talk uses a stage-structured nonlinear system of difference equations that is the first to incorporate questing behavior and ratio-dependent host-attachment success. Excessive effective tick reproduction levels destabilize tick population density while questing more above the leaf litter stabilizes it; the alternative is a 2-cycle in which one cohort of ticks is lost but the other becomes more than twice as large as either cohort would normally be. The impact of this 1-cohort vs. 2-cohort outcome in population dynamics carries over into B. burgdorferi transmission dynamics and Lyme disease risk as well.
The Biomath seminar may be attended virtually Friday at 11:00 AM CST (UTC-6) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472