Multiplicative auditory spatial receptive fields created by a hierarchy of population codes.

A multiplicative combination of tuning to interaural time difference (ITD) and interaural level difference (ILD) contributes to the generation of spatially selective auditory neurons in the owl's midbrain. Previous analyses of multiplicative responses in the owl have not taken into consideration the frequency-dependence of ITD and ILD cues that occur under natural listening conditions. Here, we present a model for the responses of ITD- and ILD-sensitive neurons in the barn owl's inferior colliculus which satisfies constraints raised by experimental data on frequency convergence, multiplicative interaction of ITD and ILD, and response properties of afferent neurons. We propose that multiplication between ITD- and ILD-dependent signals occurs only within frequency channels and that frequency integration occurs using a linear-threshold mechanism. The model reproduces the experimentally observed nonlinear responses to ITD and ILD in the inferior colliculus, with greater accuracy than previous models. We show that linear-threshold frequency integration allows the system to represent multiple sound sources with natural sound localization cues, whereas multiplicative frequency integration does not. Nonlinear responses in the owl's inferior colliculus can thus be generated using a combination of cellular and network mechanisms, showing that multiple elements of previous theories can be combined in a single system.

Time and frequency characteristics of Purkinje cell complex spikes in the awake monkey performing a nonperiodic task.

A number of studies have been interpreted to support the view that the inferior olive climbing fibers send periodic signals to the cerebellum to time and pace behavior. In a direct test of this hypothesis in macaques performing nonperiodic tasks, we analyzed continuous recordings of complex spikes from the lateral cerebellar hemisphere. We found no periodicity outside of a 100-ms relative refractory period.

Solving the problem of negative synaptic weights in cortical models.

In cortical neural networks, connections from a given neuron are either inhibitory or excitatory but not both. This constraint is often ignored by theoreticians who build models of these systems. There is currently no general solution to the problem of converting such unrealistic network models into biologically plausible models that respect this constraint. We demonstrate a constructive transformation of models that solves this problem for both feedforward and dynamic recurrent networks. The resulting models give a close approximation to the original network functions and temporal dynamics of the system, and they are biologically plausible. More precisely, we identify a general form for the solution to this problem. As a result, we also describe how the precise solution for a given cortical network can be determined empirically.

A logarithmic, scale-invariant representation of speed in macaque middle temporal area accounts for speed discrimination performance.

Human speed discrimination thresholds follow Weber's law over a large range of reference (i.e., pedestal) speeds, that is, the just-noticeable-difference in speed scales in proportion to the reference speed. We analyzed the neural representation of speed information in macaque middle temporal visual area (MT) to determine whether this representation can account for the basic form of psychophysical data. Based on theoretical considerations, we hypothesized: (1) that the speed tuning curves of MT neurons should be bell-shaped (Gaussian) as a function of the logarithm of speed, (2) that the set of speed-tuning curves should be approximately scale-invariant, (3) that the distribution of speed preferences should be approximately uniform in log speed, and (4) that response variability should be independent of speed preference. Our quantitative analysis of data from 501 MT neurons shows that the neural representation of speed approximately obeys these constraints, with modest deviations particularly at slow speeds. We then used the MT data to predict how speed discrimination thresholds should depend on pedestal speed. The shape of this prediction matches very closely to that of human psychophysical data, accounting for constant Weber fractions over a large range of intermediate speeds as well as a marked departure from Weber's law at slow speeds. Moreover, we show that deviations of the MT representation from the above constraints are important for predicting how psychophysical thresholds depart from Weber's law at slow speeds. These findings support the notion that a logarithmic, approximately scale-invariant representation of speed in area MT limits perceptual speed discrimination.

Layer 4C in monkey V1 may linearize the output of the LGN.

In primates, most LGN fibers terminate in cortical layer 4C, an anatomically prominent structure of unexplained function. We hypothesize that the enormous number of cells in layer 4C of monkey primate visual cortex functions as a neural network "hidden layer" that inverts distortions introduced by transmitting visual signals through the LGN. This hypothesis helps explain how simple cells respond (quasi-) linearly to visual inputs in spite of nonlinearities present in LGN responses. Linearization averts prematurely discarding visual information, in keeping with the role of primary visual cortex as the source of raw visual information to the rest of the brain.

Linearly decodable functions from neural population codes.

The population vector is a linear decoder for an ensemble of neurons, whose response properties are nonlinear functions of the input vector. However, previous analyses of this decoder seem to have missed the observation that the population vector can also be used to estimate functions of the input vector. We explore the use of singular value decomposition to delineate the set of functions which are linearly decodable from a given population of noisy neurons.