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How do sensory systems optimize detection of behaviorally relevant stimuli when the sensory environment is constantly changing? We addressed the role of spike timing-dependent plasticity (STDP) in driving changes in synaptic strength in a sensory pathway and whether those changes in synaptic strength could alter sensory tuning. It is challenging to precisely control temporal patterns of synaptic activity in vivo and replicate those patterns in vitro in behaviorally relevant ways. This makes it difficult to make connections between STDP-induced changes in synaptic physiology and plasticity in sensory systems. Using the mormyrid species Brevimyrus niger and Brienomyrus brachyistius, which produce electric organ discharges for electrolocation and communication, we can precisely control the timing of synaptic input in vivo and replicate these same temporal patterns of synaptic input in vitro. In central electrosensory neurons in the electric communication pathway, using whole cell intracellular recordings in vitro, we paired presynaptic input with postsynaptic spiking at different delays. Using whole cell intracellular recordings in awake, behaving fish, we paired sensory stimulation with postsynaptic spiking using the same delays. We found that Hebbian STDP predictably alters sensory tuning in vitro and is mediated by NMDA receptors. However, the change in synaptic responses induced by sensory stimulation in vivo did not adhere to the direction predicted by the STDP observed in vitro. Further analysis suggests that this difference is influenced by polysynaptic activity, including inhibitory interneurons. Our findings suggest that STDP rules operating at identified synapses may not drive predictable changes in sensory responses at the circuit level. NEW & NOTEWORTHY We replicated behaviorally relevant temporal patterns of synaptic activity in vitro and used the same patterns during sensory stimulation in vivo. There was a Hebbian spike timing-dependent plasticity (STDP) pattern in vitro, but sensory responses in vivo did not shift according to STDP predictions. Analysis suggests that this disparity is influenced by differences in polysynaptic activity, including inhibitory interneurons. These results suggest that STDP rules at synapses in vitro do not necessarily apply to circuits in vivo. 

The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability. However, this usefulness begins to falter when the data cloud contains sufficiently many outliers corresponding to stray elements from another class or when the number of data points is larger than the number of features. We illustrate how nested subspace methods, utilizing flag manifolds, can help to deal with such additional confounding factors. Flag manifolds, which are parameter spaces for nested sequences of subspaces, are a natural geometric generalization of Grassmann manifolds. We utilize and extend known algorithms for determining the minimal length geodesic, the initial direction generating the minimal length geodesic, and the distance between any pair of points on a flag manifold. The approach is illustrated in the context of (hyper) spectral imagery showing the impact of ambient dimension, sample dimension, and flag structure. 

A flag is a nested sequence of vector spaces. The type of the flag encodes the sequence of dimensions of the vector spaces making up the flag. A flag manifold is a manifold whose points parameterize all flags of a fixed type in a fixed vector space. This paper provides the mathematical framework necessary for implementing self-organizing mappings on flag manifolds. Flags arise implicitly in many data analysis contexts including wavelet, Fourier, and singular value decompositions. The proposed geometric framework in this paper enables the computation of distances between flags, the computation of geodesics between flags, and the ability to move one flag a prescribed distance in the direction of another flag. Using these operations as building blocks, we implement the SOM algorithm on a flag manifold. The basic algorithm is applied to the problem of parameterizing a set of flags of a fixed type. 

We propose a sequential algorithm for learning sparse radial basis approximations for streaming data. The initial phase of the algorithm formulates the RBF training as a convex optimization problem with an objective function on the expansion weights while the data fitting problem imposed only as an ℓ∞-norm constraint. Each new data point observed is tested for feasibility, i.e., whether the data fitting constraint is satisfied. If so, that point is discarded and no model update is required. If it is infeasible, a new basic variable is added to the linear program. The result is a primal infeasible-dual feasible solution. The dual simplex algorithm is applied to determine a new optimal solution. A large fraction of the streaming data points does not require updates to the RBF model since they are similar enough to previously observed data and satisfy the data fitting constraints. The structure of the simplex algorithm makes the update to the solution particularly efficient given the inverse of the new basis matrix is easily computed from the old inverse. The second phase of the algorithm involves a non-convex refinement of the convex problem. Given the sparse nature of the LP solution, the computational expense of the non-convex algorithm is greatly reduced. We have also found that a small subset of the training data that includes the novel data identified by the algorithm can be used to train the non-convex optimization problem with substantial computation savings and comparable errors on the test data. We illustrate the method on the Mackey-Glass chaotic time-series, the monthly sunspot data, and a Fort Collins, Colorado weather data set. In each case we compare the results to artificial neural networks (ANN) and standard skew-RBFs.