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Path Integral Techniques for Estimating Neural Network Connectivity


Characterizing the behavior of networks of neurons requires accounting for the differing levels of measurements at different scales. At the single neuron level, intracellular recordings allow for highly accurate membrane potential measurements in response to an designed applied current. Because the probes used for the single neuron experiments are large compared to the cells themselves, these voltage measurements cannot be assumed to be available for any more than a few cells at a time. Instead of voltage measurements of the potential across the cell membrane, extracellular voltage measurements combined with spike sorting algorithms allow for measurements of spike times on orders of magnitude more neurons. This spike timing information provides much less information per neuron, requiring the development of new methods to estimate the states and connectivity of a network of neurons. Previous work̃\cite{biocyb1,biocyb2, cdm1} has demonstrated the ability of a path integral formulation to characterize the behavior of individual neurons given time series voltage data. We expand on this to potential future experiments to characterize the behavior of synaptic connections, and other external currents acting on neurons and two possible means for determining the connectivity of a network of neurons given spike timing information

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