Local field potentials (LFPs) reflect subthreshold integrative processes that complement spike train measures. However, little is yet known about the differences between how LFPs and spikes encode rich naturalistic sensory stimuli. We addressed this question by recording LFPs and spikes from the primary visual cortex of anesthetized macaques while presenting a color movie. We then determined how the power of LFPs and spikes at different frequencies represents the visual features in the movie. We found that the most informative LFP frequency ranges were 1-8 and 60 -100 Hz. LFPs in the range of 12-40 Hz carried little information about the stimulus, and may primarily reflect neuromodulatory inputs. Spike power was informative only at frequencies Ͻ12 Hz. We further quantified "signal correlations" (correlations in the trial-averaged power response to different stimuli) and "noise correlations" (trial-by-trial correlations in the fluctuations around the average) of LFPs and spikes recorded from the same electrode. We found positive signal correlation between high-gamma LFPs (60 -100 Hz) and spikes, as well as strong positive signal correlation within high-gamma LFPs, suggesting that high-gamma LFPs and spikes are generated within the same network. LFPs Ͻ24 Hz shared strong positive noise correlations, indicating that they are influenced by a common source, such as a diffuse neuromodulatory input. LFPs Ͻ40 Hz showed very little signal and noise correlations with LFPs Ͼ40 Hz and with spikes, suggesting that low-frequency LFPs reflect neural processes that in natural conditions are fully decoupled from those giving rise to spikes and to high-gamma LFPs.

Several neural codes have been proposed in order to explain how neurons encode sensory information. Here we tested the hypothesis that different codes might be employed concurrently and provide complementary stimulus information. Quantifying the information encoded about natural sounds in the auditory cortex of alert animals, we found that temporal spike-train patterns and spatial populations were both highly informative. However, the relative phase of slow ongoing rhythms at which these (temporal or population) responses occurred provided much additional and complementary information. Such nested codes combining spike-train patterns with the phase of firing were not only most informative, but also most robust to sensory noise added to the stimulus. Our findings suggest that processing in sensory cortices could rely on the concurrent use of several codes that combine information across different spatiotemporal scales. In addition, they propose a role of slow cortical rhythms in stabilizing sensory representations by reducing effects of noise.

Information Theory enables the quantification of how much information a neuronal response carries about external stimuli and is hence a natural analytic framework for studying neural coding. The main difficulty in its practical application to spike train analysis is that estimates of neuronal information from experimental data are prone to a systematic error (called "bias"). This bias is an inevitable consequence of the limited number of stimulus-response samples that it is possible to record in a real experiment. In this paper, we first explain the origin and the implications of the bias problem in spike train analysis. We then review and evaluate some recent general-purpose methods to correct for sampling bias: the Panzeri-Treves, Quadratic Extrapolation, Best Universal Bound, Nemenman-Shafee-Bialek procedures, and a recently proposed shuffling bias reduction procedure. Finally, we make practical recommendations for the accurate computation of information from spike trains. Our main recommendation is to estimate information using the shuffling bias reduction procedure in combination with one of the other four general purpose bias reduction procedures mentioned in the preceding text. This provides information estimates with acceptable variance and which are unbiased even when the number of trials per stimulus is as small as the number of possible discrete neuronal responses.

We investigated the hypothesis that neurons encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. We recorded local field potentials (LFPs) and multiunit spikes from the primary visual cortex of anaesthetized macaques while binocularly presenting a color movie. We found that both the spike counts and the low-frequency LFP phase were reliably modulated by the movie and thus conveyed information about it. Moreover, movie periods eliciting higher firing rates also elicited a higher reliability of LFP phase across trials. To establish whether the LFP phase at which spikes were emitted conveyed visual information that could not be extracted by spike rates alone, we compared the Shannon information about the movie carried by spike counts to that carried by the phase of firing. We found that at low LFP frequencies, the phase of firing conveyed 54% additional information beyond that conveyed by spike counts. The extra information available in the phase of firing was crucial for the disambiguation between stimuli eliciting high spike rates of similar magnitude. Thus, phase coding may allow primary cortical neurons to represent several effective stimuli in an easily decodable format.

In this paper the Zipf-Mandelbrot law is revisited in the context of linguistics. Despite its widespread popularity the Zipf-Mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of words contained in some given corpus. In particular, we focus our attention on the important deviations that become statistically relevant as larger corpora are considered and that ultimately could be understood as salient features of the underlying complex process of language generation. Finally, it is shown that all the di erent observed regimes can be accurately encompassed within a single mathematical framework recently introduced by C. Tsallis.