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Modeling and Decoding Motor Cortical Activity Using a Switching Kalman Filter
We present a switching Kalman filter model for the real-time inference of hand kinematics from a population of motor cortical neurons. Firing rates are modeled as a Gaussian mixture where the mean of each Gaussian component is a linear function of hand kinematics. A "hidden state" models the probability of each mixture component and evolves over time in a Markov chain. The model generalizes previous encoding and decoding methods, addresses the non-Gaussian nature of firing rates, and can cope with crudely sorted neural data common in on-line prosthetic applications.Mathematic
Fourier-Space Crystallography as Group Cohomology
We reformulate Fourier-space crystallography in the language of cohomology of
groups. Once the problem is understood as a classification of linear functions
on the lattice, restricted by a particular group relation, and identified by
gauge transformation, the cohomological description becomes natural. We review
Fourier-space crystallography and group cohomology, quote the fact that
cohomology is dual to homology, and exhibit several results, previously
established for special cases or by intricate calculation, that fall
immediately out of the formalism. In particular, we prove that {\it two phase
functions are gauge equivalent if and only if they agree on all their
gauge-invariant integral linear combinations} and show how to find all these
linear combinations systematically.Comment: plain tex, 14 pages (replaced 5/8/01 to include archive preprint
number for reference 22
Random Walks for Spike-Timing Dependent Plasticity
Random walk methods are used to calculate the moments of negative image
equilibrium distributions in synaptic weight dynamics governed by spike-timing
dependent plasticity (STDP). The neural architecture of the model is based on
the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which
forms a negative image of the reafferent signal from the fish's own electric
discharge to optimize detection of sensory electric fields. Of particular
behavioral importance to the fish is the variance of the equilibrium
postsynaptic potential in the presence of noise, which is determined by the
variance of the equilibrium weight distribution. Recurrence relations are
derived for the moments of the equilibrium weight distribution, for arbitrary
postsynaptic potential functions and arbitrary learning rules. For the case of
homogeneous network parameters, explicit closed form solutions are developed
for the covariances of the synaptic weight and postsynaptic potential
distributions.Comment: 18 pages, 8 figures, 15 subfigures; uses revtex4, subfigure, amsmat
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