Reply to "Comment on `Performance of different synchronization measures in real data: A case study on electroencephalographic signals'"

We agree with the Comment by Nicolaou and Nasuto about the utility of mutual information (MI) when properly estimated and we also concur with their view that the estimation based on k nearest neighbors gives optimal results. However, we claim that embedding parameters can indeed change MI results, as we show for the electroencephalogram data sets of our original study and for coupled chaotic systems. Furthermore, we show that proper embedding can actually improve the estimation of MI with the k nearest neighbors algorithm

Hierarchically nested factor model from multivariate data

We show how to achieve a statistical description of the hierarchical structure of a multivariate data set. Specifically we show that the similarity matrix resulting from a hierarchical clustering procedure is the correlation matrix of a factor model, the hierarchically nested factor model. In this model, factors are mutually independent and hierarchically organized. Finally, we use a bootstrap based procedure to reduce the number of factors in the model with the aim of retaining only those factors significantly robust with respect to the statistical uncertainty due to the finite length of data records.Comment: 7 pages, 5 figures; accepted for publication in Europhys. Lett. ; the Appendix corresponds to the additional material of the accepted letter

Advances in Feature Selection with Mutual Information

The selection of features that are relevant for a prediction or classification problem is an important problem in many domains involving high-dimensional data. Selecting features helps fighting the curse of dimensionality, improving the performances of prediction or classification methods, and interpreting the application. In a nonlinear context, the mutual information is widely used as relevance criterion for features and sets of features. Nevertheless, it suffers from at least three major limitations: mutual information estimators depend on smoothing parameters, there is no theoretically justified stopping criterion in the feature selection greedy procedure, and the estimation itself suffers from the curse of dimensionality. This chapter shows how to deal with these problems. The two first ones are addressed by using resampling techniques that provide a statistical basis to select the estimator parameters and to stop the search procedure. The third one is addressed by modifying the mutual information criterion into a measure of how features are complementary (and not only informative) for the problem at hand

Starting and stopping movement by the primate brain

We review the current knowledge about the part that motor cortex plays in the preparation and generation of movement, and we discuss the idea that corticospinal neurons, and particularly those with cortico-motoneuronal connections, act as ‘command’ neurons for skilled reach-to-grasp movements in the primate. We also review the increasing evidence that it is active during processes such as action observation and motor imagery. This leads to a discussion about how movement is inhibited and stopped, and the role in these for disfacilitation of the corticospinal output. We highlight the importance of the non-human primate as a model for the human motor system. Finally, we discuss the insights that recent research into the monkey motor system has provided for translational approaches to neurological diseases such as stroke, spinal injury and motor neuron disease

Ventral Premotor-Motor Cortex Interactions in the Macaque Monkey during Grasp: Response of Single Neurons to Intracortical Microstimulation

Recent stimulation studies in monkeys and humans have shown strong interactions between ventral premotor cortex (area F5) and the hand area of primary motor cortex (M1). These short-latency interactions usually involve facilitation from F5 of M1 outputs to hand muscles, although suppression has also been reported. This study, performed in three awake macaque monkeys, sought evidence that these interactions could be mediated by short-latency excitatory and inhibitory responses of single M1 neurons active during grasping tasks. We recorded responses of these M1 neurons to single low-threshold (<= 40 mu A) intracortical microstimuli delivered to F5 sites at which grasp-related neurons were recorded. In 29 sessions, we tested 232 M1 neurons with stimuli delivered to between one and four sites in F5. Of the 415 responses recorded, 142 (34%) showed significant effects. The most common type of response was pure excitation (53% of responses), with short latency (1.8-3.0 ms) and brief duration (similar to 1 ms); purely inhibitory responses had slightly longer latencies (2-5 ms) and were of small amplitude and longer duration (5-7 ms). They accounted for 13% of responses, whereas mixed excitation then inhibition was seen in 34%. Remarkably, a rather similar set of findings applied to 280 responses of 138 F5 neurons to M1 stimulation; 109 (34%) responses showed significant effects. Thus, with low-intensity stimuli, the dominant interaction between these two cortical areas is one of short-latency, brief excitation, most likely mediated by reciprocal F5-M1 connections. Some neurons were tested with stimuli at both 20 and 40 mu A; inhibition tended to dominate at the higher intensity

Slowly-Conducting Pyramidal Tract Neurons in Macaque and Rat

Anatomical studies report a large proportion of fine myelinated fibers in the primate pyramidal tract (PT), while very few PT neurons (PTNs) with slow conduction velocities (CV) (2.6 ms and estimated CV 3-8 m/s, and 67 macaque PTNs (>3.9 ms, CV 6-12 m/s). Spikes of most slow PTNs were small and present on only some recording contacts, while spikes from simultaneously recorded fast-conducting PTNs were large and appeared on all contacts. Antidromic thresholds were similar for fast and slow PTNS, while spike duration was considerably longer in slow PTNs. Most slow PTNs showed no signs of failure to respond antidromically. A number of tests, including intracortical microinjection of bicuculline (GABAA antagonist), failed to provide any evidence that RI prevented antidromic invasion of slow PTNs. Our results suggest that recording bias is the main reason why previous studies were dominated by fast PTNs

Independent components in spectroscopic analysis of complex mixtures

We applied two methods of "blind" spectral decomposition (MILCA and SNICA) to quantitative and qualitative analysis of UV absorption spectra of several non-trivial mixture types. Both methods use the concept of statistical independence and aim at the reconstruction of minimally dependent components from a linear mixture. We examined mixtures of major ecotoxicants (aromatic and polyaromatic hydrocarbons), amino acids and complex mixtures of vitamins in a veterinary drug. Both MICLA and SNICA were able to recover concentrations and individual spectra with minimal errors comparable with instrumental noise. In most cases their performance was similar to or better than that of other chemometric methods such as MCR-ALS, SIMPLISMA, RADICAL, JADE and FastICA. These results suggest that the ICA methods used in this study are suitable for real life applications. Data used in this paper along with simple matlab codes to reproduce paper figures can be found at http://www.klab.caltech.edu/~kraskov/MILCA/spectraComment: 22 pages, 4 tables, 6 figure

Expression of Kv3.1b potassium channel is widespread in macaque motor cortex pyramidal cells: A histological comparison between rat and macaque

There are substantial differences across species in the organisation and function of the motor pathways. These differences extend to basic electrophysiological properties. Thus, in rat motor cortex, pyramidal cells have long duration action potentials, while in the macaque, some pyramidal neurons exhibit short duration 'thin' spikes. These differences may be related to the expression of the fast potassium channel Kv3.1b, which in rat interneurons is associated with generation of thin spikes. Rat pyramidal cells typically lack these channels, while there are reports that they are present in macaque pyramids. Here we made a systematic, quantitative comparison of the expression of Kv3.1b in sections from macaque and rat motor cortex, using two different antibodies (NeuroMab, Millipore). As our standard reference, we examined, in the same sections, Kv3.1b staining in parvalbumin-positive interneurons, which show strong Kv3.1b immunoreactivity. In macaque motor cortex, a large sample of pyramidal neurons were nearly all found to express Kv3.1b in their soma membranes. These labelled neurons were identified as pyramidal based either by expression of SMI32 (a pyramidal marker), or by their shape and size, lack of expression of parvalbumin (a marker for some classes of interneuron). Large (Betz cells), medium and small pyramidal neurons all expressed Kv3.1b. In rat motor cortex, SMI32-postive pyramidal neurons expressing Kv3.1b were very rare and weakly stained. Thus, there is a marked species difference in the immunoreactivity of Kv3.1b in pyramidal neurons, and this may be one of the factors explaining the pronounced electrophysiological differences between rat and macaque pyramidal neurons

Influence of spiking activity on cortical local field potentials.

The intra-cortical local field potential (LFP) reflects a variety of electrophysiological processes including synaptic inputs to neurons and their spiking activity. It is still a common assumption that removing high frequencies, often above 300 Hz, is sufficient to exclude spiking activity from LFP activity prior to analysis. Conclusions based on such supposedly spike-free LFPs can result in false interpretations of neurophysiological processes and erroneous correlations between LFPs and behaviour or spiking activity. Such findings might simply arise from spike contamination rather than from genuine changes in synaptic input activity. Although the subject of recent studies, the extent of LFP contamination by spikes is unclear, and the fundamental problem remains. Using spikes recorded in the motor cortex of the awake monkey, we investigated how different factors, including spike amplitude, duration and firing rate, together with the noise statistic, can determine the extent to which spikes contaminate intra-cortical LFPs. We demonstrate that such contamination is realistic for LFPs with a frequency down to ∼10 Hz. For LFP activity below ∼10 Hz, such as movement-related potential, contamination is theoretically possible but unlikely in real situations. Importantly, LFP frequencies up to the (high-) gamma band can remain unaffected. This study shows that spike-LFP crosstalk in intra-cortical recordings should be assessed for each individual dataset to ensure that conclusions based on LFP analysis are valid. To this end, we introduce a method to detect and to visualise spike contamination, and provide a systematic guide to assess spike contamination of intra-cortical LFPs