Sparse coding via thresholding and local competition in neural circuits.

While evidence indicates that neural systems may be employing sparse approximations to represent sensed stimuli, the mechanisms underlying this ability are not understood. We describe a locally competitive algorithm (LCA) that solves a collection of sparse coding principles minimizing a weighted combination of mean-squared error and a coefficient cost function. LCAs are designed to be implemented in a dynamical system composed of many neuron-like elements operating in parallel.

Inferring the capacity of the vector Poisson channel with a Bernoulli model.

The capacity defines the ultimate fidelity limits of information transmission by any system. We derive the capacity of parallel Poisson process channels to judge the relative effectiveness of neural population structures. Because the Poisson process is equivalent to a Bernoulli process having small event probabilities, we infer the capacity of multi-channel Poisson models from their Bernoulli surrogates.

All-optical nanoscale pH meter.

We show that an Au nanoshell with a pH-sensitive molecular adsorbate functions as a standalone, all-optical nanoscale pH meter that monitors its local environment through the pH-dependent surface-enhanced Raman scattering (SERS) spectra of the adsorbate molecules. Moreover, we also show how the performance of such a functional nanodevice can be assessed quantitatively. The complex spectral output is reduced to a simple device characteristic by application of a locally linear manifold approximation algorithm.

Measuring information transfer in the spike generator of crayfish sustaining fibers.

We present a method based on information-theoretic distances for measuring the information transfer efficiency of voltage to impulse encoders. In response to light pulses, we simultaneously recorded the EPSP and spiking output of crayfish sustaining fibers. To measure the distance between analog EPSP responses, we developed a membrane noise model that accurately captures stimulus-induced nonstationarities.

Optimal stimulus coding by neural populations using rate codes.

We create a framework based on Fisher information for determining the most effective population coding scheme for representing a continuous-valued stimulus attribute over its entire range. Using this scheme, we derive optimal single- and multi-neuron rate codes for homogeneous populations using several statistical models frequently used to describe neural data. We show that each neuron's discharge rate should increase quadratically with the stimulus and that statistically independent neural outputs provides optimal coding.

Neural population structures and consequences for neural coding.

Researchers studying neural coding have speculated that populations of neurons would more effectively represent the stimulus if the neurons "cooperated:" by interacting through lateral connections, the neurons would process and represent information better than if they functioned independently. We apply our new theory of information processing to determine the fidelity limits of simple population structures to encode stimulus features. We focus on noncooperative populations, which have no lateral connections.

Visual signals in an optomotor reflex: systems and information theoretic analysis.

Compensatory optomotor reflexes were examined in crayfish (Procambarus clarkii) with oscillating sine wave gratings and step displacements of a single stripe. A capacitance transducer was used to measure the rotation of the eyestalk about its longitudinal axis. System studies reveal a spatial frequency response independent of velocity and stimulus amplitude and linear contrast sensitivity similar to that of neurons in the visual pathway.