Unsupervised Learning Techniques for Large-Scale, Multi-Trial Neural Data
An increasingly common paradigm in neuroscience is to simultaneously record the activity of many neurons over repeated experimental trials (e.g., multiple presentations of a sensory stimulus, or a repeated motor action). The resulting datasets can be very large, potentially containing recordings from thousands of neurons over thousands of experimental trials. I'm interested in finding general statistical approaches for understanding datasets of this form.
Tensor Decomposition of Neural Data
Commonly used methods for dimensionality reduction (such as PCA) identify low-dimensional features of within-trial neural dynamics, but do not model changes in neural activity across trials. To better understand processes like learning and trial-to-trial variability, I'm exploring tensor decomposition methods to find reduced representations of multi-trial datasets.
Many animal behaviors are built as a sequence of motor primitives or decisions. The neurons that support these (and other) behaviors can also fire in repeatable sequences. Yet, statistical methods for identifying neural sequences in an unbiased manner (without pre-conceived reference to animal behavior) are not widely used. I am interested in using convolutive matrix factorization methods to address this problem.
Analysis of neural data often relies on manual alignment of neural activity to a stimulus or behavioral event on each trial. However, alignment to external events is not always possible (e.g., in cases where neural activity is locked to internal cognitive states or decisions). I'm working to develop automatic alignment methods for these cases, enabling discovery of otherwise hidden neural coding patterns.
Theoretical Molecular Neurobiology
Biology computes with both electrical and biochemical signals. I'm interested in modeling the interface of these two substrates of computation.
Neurons alter ion channel and synaptic receptor expression/activity to maintain activity levels in physiologically stable regimes. This can be modeled from a control theoretic perspective, which provides perspectives on how noisy molecular processes can nevertheless support reliable physiological behaviors.
Microtubular Transport in Complex Dendritic Trees
Neurons are remarkably complex cells. Given this, it seems an almost insurmountable challenge to transport molecular cargo reliably. I've studied a few simple models of how reliable transport can be accomplished.