Previous studies have suggested that several types of rules govern the generation of complex arm movements. One class of rules consists of optimizing an objective function (e.g., maximizing motion smoothness). Another class consists of geometric and kinematic constraints, for instance the coupling between speed and curvature during drawing movements as expressed by the two-thirds power law. It has also been suggested that complex movements are composed of simpler elements or primitives. However, the ability to unify the different rules has remained an open problem. We address this issue by identifying movement paths whose generation according to the two-thirds power law yields maximally smooth trajectories. Using equi-affine differential geometry we derive a mathematical condition which these paths must obey. Among all possible solutions only parabolic paths minimize hand jerk, obey the two-thirds power law and are invariant under equi-affine transformations (which preserve the fit to the two-thirds power law). Affine transformations can be used to generate any parabolic stroke from an arbitrary parabolic template, and a few parabolic strokes may be concatenated to compactly form a complex path. To test the possibility that parabolic elements are used to generate planar movements, we analyze monkeys' scribbling trajectories. Practiced scribbles are well approximated by long parabolic strokes. Of the motor cortical neurons recorded during scribbling more were related to equi-affine than to Euclidean speed. Unsupervised segmentation of simulta- neously recorded multiple neuron activity yields states related to distinct parabolic elements. We thus suggest that the cortical representation of movements is state-dependent and that parabolic elements are building blocks used by the motor system to generate complex movements.

Despite many reports indicating the existence of precise firing sequences in cortical activity, serious objections have been raised regarding the statistics used to detect them and the relations of these sequences to behavior. We show that in behaving monkeys, pairs of spikes from different neurons tend to prefer certain time delays when measured in relation to a specific behavior. Single-unit activity was recorded from eight microelectrodes inserted into the motor and premotor cortices of two monkeys while they were performing continuous drawinglike hand movements. Repeated scribbling paths, termed drawing components, were extracted by data-mining techniques. The set of the least predictable relations between drawing components and pairs of neurons was determined and represented by one statistic termed the relations score. The chance probability of the relations score was evaluated by teetering the spike times: 1,000 surrogates were generated by randomly teetering the original time of each spike in a small window. In nine of 13 experimental days the precision was better than 12 ms and, in the best case, spike precision reached 0.5 ms.

A classical question in neuroscience is which features of a stimulus or of an action are represented in brain activity. When several features are interdependent either at a given point in time or at distinct points in time, neural activity related to one feature appears to be correlated with other features. Thus techniques that simultaneously consider multiple features cannot account for delayed interdependencies between features. The result is an ambiguity with respect to the encoded features. Here, we resolve this ambiguity by applying a novel statistical method based on partial cross-correlations. The method yields estimates of linear correlations between neural activity and a given feature that are not affected by linear correlations with other features at multiple time delays. The method also provides a graphical output measured on a scale that allows for comparisons between different features, neurons, and experiments. We use real movement data and neural activity simulated according to a wide range of tuning models to illustrate the method. When applied to real neural activity, the procedure yields results that indicate which of the considered features the neural activity is related to and at what time delays.

We show that times of spikes can be very precise. In the cerebral cortex, where each nerve cell is affected by thousands of others, it is the common belief that the exact time of a spike is random up to an averaged firing rate over tens of milliseconds. In a brain slice, precise time relations of several neurons have been observed. It remained unclear whether this phenomenon can also be observed in brains of behaving animals. Here we show, in behaving monkeys, that time intervals between spikes, measured in correspondence to a specific behavior, may be controlled to within the milliseconds range. data mining ͉ motor cortex ͉ neural codes ͉ precise timing ͉ single units A s known, most nerve cells in the brain communicate with each other by standard pulses called action potentials (or spikes). In the cerebral cortex, where each nerve cell is affected by thousands of others (1, 2), the common belief, so far, is that each neuron represents one aspect of the mental processes not by precise firing time, but by elevating its firing rate (3). However, if time relations among different neurons could be precisely controlled and read out, complex representations could be built from simpler ones efficiently and very fast (4-6). In a brain slice, precise time relations among several neurons have been observed (7). Could this phenomenon be also observed in brains of behaving animals? Here, we use data-mining techniques and rigorous statistic testing to test the precision of time intervals between spikes of different neurons. We show, in behaving monkeys, that when time intervals between spikes of different neurons are measured in correspondence to a specific behavior, timing may be controlled to the milliseconds range with the best case reaching 0.5 ms. Experiments Description and Drawings AnalysisIn our experiments, single unit activity was recorded from eight microelectrodes inserted into the motor and premotor cortices of a monkey while it was freely scribbling. Spike data analysis was carried for two sets of measurements. In the first set (consisting of 3 experimental days), time resolution of recording was 1 ms, whereas in the second set (consisting of 5 other days), it was 0.1 ms.Repeated scribbling paths were extracted by data-mining algorithms (8, 9). These paths are called drawing components. In a typical day there are 12-25 such drawing components. Fig. 1 illustrates the monkey's drawings and two simple drawing components. The Main IdeaTo determine whether there are any precise timing relations between the spikes of two neurons and the drawing, we selected a time slice before the start of each drawing component. For a given pair of neurons, we counted how many times a spike in the first neuron was followed by a spike in the second neuron within each of 50 particular time intervals. For the first set of measurements, these intervals were 0-1 ms, 2-3 ms, . . . , 98-99 ms, and for the second set they were 0-0.9 ms, 1-1.9 ms, 2-2.9 ms, . . . , 49-49.9 ms. The interval that repeated the largest number of times was hypot...