Towards Support for Reverse Engineering of Neural Circuits and Non-Linear Dimensionality Reduction in Fovea and PyDSTool

Computational models of neural circuitry are increasingly superseding single neuron models for understanding dynamic processes in the brain. Recurrent Neural Networks offer an attractive method for simulating, replicating, and characterizing these circuits. PyDSTool currently supports simulation of neural circuity dynamics and linear methods of dimensionality reduction such as Principle Component Analysis for normalizing complex data; however, such methods are insufficiently tailored to working with non-linearly distributed data. I propose the implementation of a module targeted at providing non-linear dimensionality reduction via Sammon mappings, principal curves, and locally linear embeddings. In addition, I will create tools in Fovea that will allow for the intuitive visualization of datasets resolved by these methods.

I also seek to provide a suite of tools to PyDSTool for constructing and training Recurrent Neural Networks and corresponding solutions for visualizing the operation, feedback mechanisms, network structure, and dynamical systems characteristics (e.g. attractors) of these models.