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Structure, dynamics and computation [electronic resource] : diverse applications of theory in neuroscience

How do the structure and dynamics of neural circuits conspire with circuit inputs to solve specific computational problems in the brain? In this thesis we use theory, often in coordination with experiment, to study several problems with relevance to this question. First, we use estimation theory to develop a measure of spatial resolution for stochastic localization microscopy that jointly depends on the density of fluorescent emitters, the precision of emitter localization, and prior information regarding the labeled object. This resolution measure clarifies the conditions under which optical methods suffice to measure neural circuit structure. Second, we use signal detection and estimation theory to quantify the physical limits set by photon shot noise for the optical detection and timing of neural spikes. This framework provides a quantitative benchmark for optical methods that measure the dynamics of neural circuits. Third, we combine time-lapse two-photon microendoscopy and mathematical modeling to track and quantify the dynamics of dendritic spines in the CA1 hippocampal area of living mice. Our results suggest new relationships between structure, dynamics, and function in the hippocampal circuit. Fourth, we treat visual motion estimation as a problem of Bayesian inference to determine how the optimal algorithm for motion estimation depends on the statistics of visual inputs. Our theory reveals that dark-light contrast asymmetries facilitate motion estimation with triple correlations. Finally, we show that fly and human visual systems jointly encode the direction and contrast polarity of moving edges using triple correlations that enhance motion estimation of natural stimuli. This striking convergence argues that the statistics of natural inputs have driven a common computational strategy for motion estimation across 500 million years of evolution. Collectively, these projects demonstrate several distinct and complementary ways that the integration of theory and experiment can accelerate progress in neuroscience.