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Many of the most interesting functions and behaviors realized by the brain emerge from the collective activity of very large numbers of neurons of many functional types interacting in complex networks. Our long-term goal is to establish the principles underlying the structural and functional organization of such circuits in the brain.  We hope to understand how large-scale behaviors can emerge from the interaction of many individual elements, what the constraints on neural circuit architecture are, and how network functions can be impaired or improved by changes to the architecture.  We exploit theoretical and computational approaches from physics, information theory and computer science, and rely on experimental data gathered both within our lab and by collaborators at Penn and elsewhere.  We also seek to apply insights from the analysis of neural circuits to other heterogeneous living systems.
Vision: We seek to understand circuit organization in the early visual system and the cortical visual hierarchy in terms of the statistical structure of natural scenes and the theory of efficient computation. In the retina, we have addressed: (1) the diversity of cell types, and the division of resources between these types, (2) the conserved patterns of structural and functional connectivity, (3) adaptation to changing conditions, and (4) computation and communication by networks of neurons.  Our current work focuses on retinal architecture [e.g., Ratliff et al., 2010] and cortical circuits that support texture perception [e.g. Hermundstad et al., 2014].  We have assembled a large calibrated database of images, publicly available here.
Olfaction:  The olfactory system faces very different challenges from the visual system.  First, chemical space is extremely high dimensional.  Second, odor signals are highly variable and new odors are encountered all the time.  Third, odors mix together during natural olfaction and their separation is a difficult statistical problem.    We are exploring how various aspects of the olfactory circuitry are tuned to solving these challenges.  These aspects include the diffuse sensitivity of Olfactory Receptor Neurons (1st olfactory stage); the lateral inhibitory connectivity, neurogenesis of granule cells, and cortical feedback in the olfactory bulb (2nd olfactory stage); and the apparently random connectivity from the bulb to the piriform cortex (3rd olfactory stage) accompanied by diffuse inhibitory interactions within the cortex [e.g., Krishnamurthy et al., 2017].
Audition:  The theory of sensory processing and transformation by the cortex has been well developed in the visual system.  In collaboration with the Penn laboratories of Maria Geffen and Yale Cohen, we aim to understand how the hierarchy of auditory cortical areas transforms the representation of complex sounds that occur against a changing background context.  We are using data from large scale multi-electrode recordings and from optogenetic manipulations [e.g. Briguglio et al., 2017]. 
Spatial Cognition:  We are working on the theory and modeling of the entorhinal cortex (EC) and the hippocampus.  In the EC there are populations of grid cells which fire if the animal is in one of a triangular lattice of locations.  The hippocampus contains a population of place cells that fire when an animal is in a specific localized region.   Place cells are thought to provide a readout mechanism for the grid system in the entorhinal cortex.  Ongoing work considers how this integration happens, and how the place system serves goal-directed navigation by animals.   We have proposed a new theory of how such grid cells encode an animal's spatial location [Wei et al., 2015].  The theory makes a number of predictions that match experimental measurements of the anatomical and functional organization of the grid system.  We are currently working on models of dynamical self-organization of the the grid system via interactions between grid cells, border cells, head direction cells and place cells [e.g. Keinath et al., 2017].
Motor Control & Learning:  Animals learn complex skills by trial and error and repetition.   The mechanisms that support these processes provide a window into general mechanisms of learning, memory and plasticity in the brain.   We are exploring these phenomena in two systems: (a) birdsong, where mutiple brain areas coordinate to allow juvenile birds to learn to imitate adult songs [e.g. Tesileanu et al., 2017], and (b) olfaction, specifically in the olfactory bulb, where neurogenesis and cortical feedback modify the sensory representations of familiar and unfamiliar odors. 
Decision Making: A central problem in the practice of science, as well as in the day-to-day functioning of biological organisms, is deciding among competing explanations of data containing random errors. We have worked on well-founded methods for trading off complexity and accuracy of explanations in the framework of Bayesian statistics and the Minimum Description Length principle [e.g. Balasubramanian, 1997]. We are currently interested in applying ideas in statistical inference theory to learning and adaptation across levels of biological organization.   In current work we are exploring complexity-accuracy tradeoffs in the decision-making processes of humans detecting change-points in situations where the underlying process has multiple overlapping timescales. 

Spike Sorting: Multi-electrode neural recording arrays record a voltage trace from each electrode. The signals picked up are usually superpositions of extracellular electrical activity of several nearby neurons, and each neuron will likely contribute to signals on more than one neighboring electrode. Spike sorting is a data analysis technique that takes these raw signals and answers the question “Who spiked where and when?”. The result of the spike sorting is a list of neurons that left a strong signal on the array, and for each neuron, its spike times.  Solving the spike-sorting problem is critical for analysis of data from the massively parallel neural recordings that are now possible.  Our spike sorting code is available on Github [here] and is described in [Prentice et al., 2011]. 

Applications to other living systems: We also exploit techniques developed in neuroscience to address analogous problems in cell biology, specifically in the study of cell-signaling and regulatory networks and the immune system.  Theoretical neuroscience has developed many methods for understanding and analyzing adaptive sensing of the world.   In fact, living systems at every scale of organization must sense the world adaptively since they must invest their limited information processing resources wisely.  Taking this perspective, we have been constructing models and theories of the adaptive immune systems in vertebrates and bacteria (CRISPR), where organisms develop and maintain a memory of past infections to defend against future threats [e.g. Mayer et al, 2015; Bradde et al, 2017].   In ongoing work we are treating the adaptive immune apparatus as a system for making probabilistic predictions of the pathogenic landscape.