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. For neural populations wherein each neuron has individual innervation, inter-neuron dependencies increase capacity, the opposite behavior of populations that share a single input. We use Shannon's rate-distortion theory to show that for Gaussian stimuli, the mean-squared error of the decoded stimulus decreases exponentially in both the population size and the maximal discharge rate. Detailed analysis shows that population coding is essential for accurate stimulus reconstruction. By modeling multi-neuron recordings as a sum of a neural population, we show that the resulting capacity is much less than the population's, reducing it to a level that can be less than provided with two separated neural responses. This result suggests that attempting neural control without spike sorting greatly reduces the achievable fidelity. In contrast, single-electrode neural stimulation does not incur any capacity deficit in comparison to stimulating individual neurons.

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. These algorithms use thresholding functions to induce local (usually one-way) inhibitory competitions between nodes to produce sparse representations. LCAs produce coefficients with sparsity levels comparable to the most popular centralized sparse coding algorithms while being readily suited for neural implementation. Additionally, LCA coefficients for video sequences demonstrate inertial properties that are both qualitatively and quantitatively more regular (i.e., smoother and more predictable) than the coefficients produced by greedy algorithms.

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. The average accuracy of the nano-"meter" was found to be +/-0.10 pH units across its operating range.

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. We show that they always exhibit positively correlated responses and that as population size increases, they perfectly represent the information conveyed by their inputs regardless of the individual neuron's coding scheme. Cooperative populations, which do have lateral connections, can, depending on the nature of the connections, perform better or worse than their noncooperative counterparts. We further show that common notions of synergy fail to capture the level of cooperation and to reflect the information processing properties of populations.

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. Only cooperative populations can achieve this condition in an informationally effective way.

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. By comparing the EPSP and spike responses, we found encoding efficiencies on the order of 10(-4), with interesting dynamics occurring during initial transients. A simple analog to point-process converter predicted the small information transfer efficiencies and dynamic properties we measured.

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. The reflex operates at low temporal frequencies (<0.002 Hz to 0.5 Hz) and exhibits a low-pass temporal frequency response with cut-off frequency of 0.1 Hz. Eyestalk rotation increases as a saturable function of the angular stimulus displacement. When compared to the oscillatory response, transient responses are faster, and they exhibit a lower gain for large stimulus displacements. These differences may reflect system nonlinearity and/or the presence of at least two classes of afferents in the visual pathway. Our metric for information transmission is the Kullback-Leibler (K-L) distance, which is inversely proportional to the probability of an error in distinguishing two stimuli. K-L distances are related to differences in responsiveness for variations in spatial frequency, contrast, and angular displacement. The results are interpreted in terms of the neural filters that shape the system response and the constraints that the K-L distances place on information transmission in the afferent visual pathway.