Institute for Systems Research

The collection of responses to all elementary ripples is the spectro-temporal transfer function. Previous experiments using ripples with downward drifting spectra suggested that the transfer function is separable, i.e., it is reducible into a product of purely temporal and purely spectral functions.

Here we compare the responses to upward and downward drifting ripples, assuming separability within each direction, to determine if the total bi-directional transfer function is fully separable. In general, the combined transfer function for two directions is not symmetric, and hence units in AI are not, in general, fully separable. Consequently, many AI units have complex response properties such as sensitivity to direction of motion, though most inseparable units are not strongly directionally selective.

We show that for most neurons the lack of full separability stems from differences between the upward and downward spectral cross-sections, not from the temporal cross-sections; this places strong constraints on the neural inputs of these AI units.

In this paper, the relationship betweenthe spectro-temporal structure of any given stimulus and the quality ofthe STRF estimate is explored and exploited. Invoking the Fouriertheorem, arbitrary dynamic spectra are described as sums of basicsinusoidal components, i.e., "moving ripples." Accurate estimation isfound to be especially reliant on the prominence of components whosespectral and temporal characteristics are of relevance to the auditorylocus under study, and is sensitive to the phase relationships betweencomponents with identical temporal signatures.

These and otherobservations have guided the development and use of stimuli withdeterministic dynamic spectra composed of the superposition of many"temporally orthogonal" moving ripples having a restricted, relevant rangeof spectral scales and temporal rates.

The method, termedsum-of-ripples, is similar in spirit to the "white-noise approach," butenjoys the same practical advantages--which equate to faster and moreaccurate estimation--attributable to the time-domain sum-of-sinusoidsmethod previously employed in vision research. Application of the methodis exemplified with both modeled data and experimental data from ferretprimary auditory cortex (AI).

However, it has been a mystery where andhow such harmonic templates can come about. Here we present a biologicallyplausible model for how such templates can form in the early stages of theauditory system. The model demonstrates that {it any} broadband stimulussuch as noise or random click trains, suffices for generating thetemplates, and that there is no need for any delay-lines, oscillators, orother neural temporal structures.

The model consists of two key stages:cochlear filtering followed by coincidence detection. The cochlear stageprovides responses analogous to those seen on the auditory-nerve andcochlear nucleus. Specifically, it performs moderately sharp frequencyanalysis via a filter-bank with tonotopically ordered center frequencies(CFs); the rectified and phase-locked filter responses are further enhancedtemporally to resemble the synchronized responses of cells in the cochlearnucleus.

The second stage is a matrix of coincidence detectors thatcompute the average pair-wise instantaneous correlation (or product)between responses from all CFs across the channels. Model simulations showthat for any broadband stimulus, high coincidences occur between cochlearchannels that are exactly harmonic distances apart. Accumulatingcoincidences over time results in the formation of harmonic templates forall fundamental frequencies in the phase-locking frequency range.

Themodel explains the critical role played by three subtle but importantfactors in cochlear function: the nonlinear transformations following thefiltering stage; the rapid phase-shifts of the traveling wave near itsresonance; and the spectral resolution of the cochlear filters. Finally, wediscuss the physiological correlates and location of such a process and itsresulting templates.

The work is initially planned to be divided in five parts: assessment of the raw data (measurements from the network), feature extraction (data preprocessing), classification (data clustering according to the network potential problems), system training (tuning methods) and self-improving (module learning capability).

Raw data analysis: The network database will be accessed to identify the, measurement being performed. The data context and problem definition are, also part of the data analysis process. The problem, the solution to the problem and strategies for solving such problems will be defined according to the network management standards. The data organization, parameters being monitored, data context and its amount are the targets at this level of the research.

Feature extraction: The data is preprocessed in such a way that events in the network are converted into a vector of parameters. The vector that is obtained is called "feature vector". The objective at this level is to transform data into information to be used further in the network monitoring system.

We also provide a constructive procedure to build networks based on wavelet theory. Moreover, cognizant of the problems usually encountered in practical implementations of these ideas, we develop a heuristic methodology, inspired by similar work in the area of Radial Basis Function (RBF) networks (Moody & Darken, Platt), to build a network sequentially on-line as well as off-line.

We show some connections of our method to some existing methods such as Projection Pursuit Regression (Friedman), Hyper Basis Functions (Poggio & Girosi) and other methods that have been proposed in the literature on neural- networks as well as statistics. In particular, some classes of wavelets can also be derived from the regularization theoretical framework given by Poggio & Girosi.

Finally, we choose direct nonlinear adaptive control to demonstrate the utility of the network in the context of local learning. Stability analysis is carried out within a standard Lyapunov formulation. Simulation studies show the effectiveness of these methods. We compare and contrast these methods with some recent results obtained by other researchers using Back Propagation (Feed-Forward) Networks, and Gaussian Networks.

The ripples parameters that characterize cortical cells are distributed somewhat evenly, with the characteristic ripple frequencies ranging from 0.2 to over 2 cycles/octave and the characteristic angular frequency typically ranging from 2 to 20 Hz. Many responses exhibit periodicities not found in the spectral envelope of the stimulus. These periodicities are of two types. Slow rebounds with a period of about 150 ms appear with various strengths in about 30 % of the cells. Fast regular firings, with interspike intervals of the order of 10 ms are much less common and may reflect the ability of certain cells to follow the fine structure of the stimulus.