. In a number of systems including wind detection in the cricket, visual motion perception and coding of arm movement direction in the monkey and place cell response to position in the rat hippocampus, firing rates in a population of tuned neurons are correlated with a vector quantity. We examine and compare several methods that allow the coded vector to be reconstructed from measured firing rates. In cases where the neuronal tuning curves resemble cosines, linear reconstruction methods work as well as more complex statistical methods requiring more detailed information about the responses of the coding neurons. We present a new linear method, the optimal linear estimator (OLE), that on average provides the best possible linear reconstruction. This method is compared with the more familiar vector method and shown to produce more accurate reconstructions using far fewer recorded neurons. Introduction To determine how information is represented by nervous systems, we need to understand ...

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Introduction Biological neural networks are large systems of complex elements interacting through a complex array of connections. Individual neurons express a large number of active conductances (Connors et al., 1982; Adams & Gavin, 1986; Llin'as, 1988; McCormick, 1990; Hille, 1992) and exhibit a wide variety of dynamic behaviors on time scales ranging from milliseconds to many minutes (Llin'as, 1988; Harris-Warrick & Marder, 1991; Churchland & Sejnowski, 1992; Turrigiano et al., 1994). Neurons in cortical circuits are typically coupled to thousands of other neurons (Stevens, 1989) and very little is known about the strengths of these synapses (although see Rosenmund et al., 1993; Hessler et al., 1993; Smetters & Nelson, 1993). The complex firing patterns of large neuronal populations are difficult to describe let alone understand. There is little point in accurately modeling each membrane potential in a large neural

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This paper investigates the influence of reflex blinks on the discharge properties of saccade-related burst neurons (SRBNs) in intermediate and deep layers of the monkey superior colliculus (SC). Twenty-nine SRBNs, recorded in three monkeys, were tested in the blink-perturbation paradigm. We report that the air puff stimuli, used to elicit blinks, resulted in a short-latency (;10 ms) transient suppression of saccaderelated SRBN activity. Shortly after this suppression (within 10 --30 ms), all neurons resumed their activity, and their burst discharge then continued until the perturbed saccade ended near the extinguished target. This was found regardless whether the compensatory movement was into the cell's movement field or not. In the limited number of trials where no compensation occurred, the neurons typically stopped firing well before the end of the eye movement. Several aspects of the saccade-related activity could be further quantified for 25 SRBNs. It appeared that 1) the increase in duration of the highfrequency burst was well correlated with the (two- to threefold) increase in duration of the perturbed movement. 2) The number of spikes in the burst for control and perturbed saccades was quite similar. On average, the number of spikes increased only 14%, whereas the mean firing rate in the burst decreased by 52%. 3)An identical number of spikes were obtained between control and perturbed responses when burst and postsaccadic activity were both included in the spike count. 4) The decrease of the mean firing rate in the burst was well correlated with the decrease in the velocity of perturbed saccades. 5) Monotonic relations between instantaneous firing rate and dynamic motor error were obtained for control responses but not for perturbed responses. And 6) the hig...

. In a number of systems including wind detection in the cricket, visual motion perception and coding of arm movement direction in the monkey and place cell response to position in the rat hippocampus, firing rates in a population of tuned neurons are correlated with a vector quantity. We examine and compare several methods that allow the coded vector to be reconstructed from measured firing rates. In cases where the neuronal tuning curves resemble cosines, linear reconstruction methods work as well as more complex statistical methods requiring more detailed information about the responses of the coding neurons. We present a new linear method, the optimal linear estimator (OLE), that on average provides the best possible linear reconstruction. This method is compared with the more familiar vector method and shown to produce more accurate reconstructions using far fewer recorded neurons. Introduction To determine how information is represented by nervous systems, we need to understand...

This paper reports on single-unit activity of saccade -related burst neurons (SRBNs) in the intermediate and deep layers of the monkey superior colliculus (SC), evoked by bimodal sensory stimulation. Monkeys were trained to generate saccadic eye movements towards visual stimuli, in either a unimodal visual saccade task, or in a bimodal visual-auditory task. In the latter task, the monkeys were required to make an accurate saccade towards a visual target, while ignoring an auditory stimulus. The presentation of an auditory stimulus in temporal and spatial proximity of the visual target influenced neither the accuracy nor the kinematic properties of the evoked saccades. However, it had a significant effect on the activity of 90% (45/50) of the SRBNs. The motor-related burst increased significantly in some neurons, but was suppressed in others. In visual-movement cells, comparable bimodal interactions were observed in both the visually evoked burst and the movementrelated burst. The large differences observed in the movementrelated activity of SRBNs for identical saccades under different sensory conditions do not support the hypothesis that such cells encode dynamic motor error. The only behavioral parameter that was affected by the presentation of the auditory stimulus was saccade latency. Auditory stimulation caused saccade latency changes in the majority of the experiments. Meanwhile, the timing of peak collicular motor activity and saccade onset remained tightly coupled for all stimulus configurations. In addition, saccade latency varied as function of the distance between the stimuli in 36% of the recordings. Interestingly, the occurrence of a spatial latency effect covaried significantly with a similar spatial influence on the SRBNs firing rate. These cells were al...