To understand the neural representation of broadband, dynamic sounds in primary auditory cortex (AI), we characterize responses using the spectro-temporal response field (STRF). The STRF describes, predicts, and fully characterizes the linear dynamics of neurons in response to sounds with rich spectro-temporal envelopes. It is computed from the responses to elementary "ripples," a family of sounds with drifting sinusoidal spectral envelopes. The collection of responses to all elementary ripples is the spectro-temporal transfer function. The complex spectro-temporal envelope of any broadband, dynamic sound can expressed as the linear sum of individual ripples. 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 measure the responses to upward and downward drifting ripples, assuming reparability within each direction, to determine if the total bidirectional 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 but not from the temporal cross-sections; this places strong constraints on the neural inputs of these AI units.

1. Auditory stimuli referred to as moving ripples are used to characterize the responses of both single and multiple units in the ferret primary auditory cortex. Moving ripples are broadband complex sounds with a sinusoidal spectral profile that drift along the logarithmic frequency axis at a constant velocity. 2. Neuronal responses to moving ripples are locked to the phase of the ripple, i.e., they exhibit the same periodicity as that of the moving ripple profile. Neural responses are characterized as a function of ripple velocity (temporal property) and ripple frequency (spectral property). Transfer functions describing the response to these temporal and spectral modulations are constructed. Temporal transfer functions are inverse Fourier transformed to obtain impulse response functions that reflect the cell's temporal characteristics. Ripple transfer functions are inverse Fourier transformed to obtain the response field, a measure analogous to the cell's response area. These operations assume linearity in the cell's response to moving ripples. 3. Transfer functions and other response functions are shown to be fairly independent on the overall level or depth of modulation of the ripple stimuli. Only downward moving ripples were used in this study. 4. The temporal and ripple transfer functions are found to be separable, in that their shapes remain unchanged for different test parameters. Thus ripple transfer functions and response fields remain statistically similar in shape (to within an overall scale factor) regardless of the ripple velocity or whether stationary or moving ripples are used in the measurement. The same stability in shape holds for the temporal transfer functions and the impulse response functions measured with different ripple frequencies. Separability implies that the combined spectrotemporal transfer function of a cell can be written as the product of a purely ripple and a purely temporal transfer functions, and thus that the neuron can be computationally modeled as processing spectral and temporal information in two separate and successive stages. 5. The ripple parameters that characterize cortical cells are distributed somewhat evenly, with the characteristic ripple frequencies ranging from 0.2 to > 2 cycles/octave and the characteristic angular frequency typically ranging from 2 to 20 Hz. 6. Many responses exhibit periodicities in the spectral envelope of the stimulus. These periodicities are of two types. Slow rebounds, not found in the spectral envelope, and with a period of approximately 150 ms, appear with various strengths in approximately 30% of the cells. Fast regular firings with interspike intervals of approximately 10 ms are much less common and appear to correspond to interactions between the component tones that make up a ripple.

The ability of rats to use their whiskers for fine tactile discrimination rivals that of humans using their fingertips. Rats perform discriminations rapidly and accurately while palpating the environment with their whiskers. This suggests that whisker deflections produce a robust and reliable neural code. Whisker primary afferents respond with highly reproducible temporal spike patterns to transient stimuli. Here we show that, with the use of a linear kernel, any of these reproducible response trains recorded from an individual neuron can reliably predict complex whisker deflections. These predictions are significantly improved by integrating responses from neurons with opposite angular preferences.

We construct a new system of integrable nonlinear differential equations associated with. the operator algebra [Formula: see text] of Polyakov. Its members are fractional generalizations of KdV type flows corresponding to an alternative set of constraints on the 2-dim. SL(3) gauge connections. We obtain the first non-trivial examples by dimensional reductiion from self-dual Yang–Mills and then generate recursively the entire hierarchy and its conserved quantities using a bi-Hamiltonian structure. Certain relations with the Boussinesq equation are also discussed together with possible generalizations of the formalism to SL (N) gauge groups and [Formula: see text] operator algebras with arbitrary N and l.