B0720
Title: Modeling trajectories using functional first-order linear differential equations
Authors: Jeff Goldsmith - Columbia University (United States)
Julia Wrobel - Colorado School of Public Health (United States) [presenting]
Abstract: The motivation is to seek a better understanding of the role of the motor cortex in driving goal-oriented reaching movements in mice. For each trial in this experiment, neural firing rates and paw position were measured continuously as the mouse, in reaction to an auditory cue, reached for a food pellet. An innovative general regression method is proposed that draws from both ordinary differential equations and functional data analysis to model the relationship between these functional inputs and responses as a dynamical system that evolves over time. Specifically, the model addresses gaps in the literature and borrows strength across curves, estimating ODE parameters across all curves simultaneously rather than separately modelling each functional observation. The approach compares favourably to related functional data methods in simulations. In the analysis of reaching movements, it is found that increased cortical activation is associated with greater changes in paw velocity and that the effect of activation persists beyond the activation itself.
