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

Event synchronization: a simple and fast method to measure synchronicity and time delay patterns

We propose a simple method to measure synchronization and time delay patterns between signals. It is based on the relative timings of events in the time series, defined e.g. as local maxima. The degree of synchronization is obtained from the number of quasi-simultaneous appearances of events, and the delay is calculated from the precedence of events in one signal with respect to the other. Moreover, we can easily visualize the time evolution of the delay and synchronization level with an excellent resolution. We apply the algorithm to short rat EEG signals, some of them containing spikes. We also apply it to an intracranial human EEG recording containing an epileptic seizure, and we propose that the method might be useful for the detection of foci and for seizure prediction. It can be easily extended to other types of data and it is very simple and fast, thus being suitable for on-line implementations.Comment: 6 pages, including 6 figures, RevTe

Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering

This study introduces a new method for detecting and sorting spikes from multiunit recordings. The method combines the wavelet transform, which localizes distinctive spike features, with superparamagnetic clustering, which allows automatic classification of the data without assumptions such as low variance or gaussian distributions. Moreover, an improved method for setting amplitude thresholds for spike detection is proposed. We describe several criteria for implementation that render the algorithm unsupervised and fast. The algorithm is compared to other conventional methods using several simulated data sets whose characteristics closely resemble those of in vivo recordings. For these data sets, we found that the proposed algorithm outperformed conventional methods

Explicit Encoding of Multimodal Percepts by Single Neurons in the Human Brain

Different pictures of Marilyn Monroe can evoke the same percept, even if greatly modified as in Andy Warhol’s famous portraits. But how does the brain recognize highly variable pictures as the same percept? Various studies have provided insights into how visual information is processed along the ‘‘ventral pathway,’’ via both single-cell recordings in monkeys and functional imaging in humans. Interestingly, in humans, the same "concept" of Marilyn Monroe can be evoked with other stimulus modalities, for instance by hearing or reading her name. Brain imaging studies have identified cortical areas selective to voices and visual word forms. However, how visual, text, and sound information can elicit a unique percept is still largely unknown. By using presentations of pictures and of spoken and written names, we show that (1) single neurons in the human medial temporal lobe (MTL) respond selectively to representations of the same individual across different sensory modalities; (2) the degree of multimodal invariance increases along the hierarchical structure within the MTL; and (3) such neuronal representations can be generated within less than a day or two. These results demonstrate that single neurons can encode percepts in an explicit, selective, and invariant manner, even if evoked by different sensory modalities

Latency and Selectivity of Single Neurons Indicate Hierarchical Processing in the Human Medial Temporal Lobe

Neurons in the temporal lobe of both monkeys and humans show selective responses to classes of visual stimuli and even to specific individuals. In this study, we investigate the latency and selectivity of visually responsive neurons recorded from microelectrodes in the parahippocampal cortex, entorhinal cortex, hippocampus, and amygdala of human subjects during a visual object presentation task. During 96 experimental sessions in 35 subjects, we recorded from a total of 3278 neurons. Of these units, 398 responded selectively to one or more of the presented stimuli. Mean response latencies were substantially larger than those reported in monkeys. We observed a highly significant correlation between the latency and the selectivity of these neurons: the longer the latency the greater the selectivity. Particularly, parahippocampal neurons were found to respond significantly earlier and less selectively than those in the other three regions. Regional analysis showed significant correlations between latency and selectivity within the parahippocampal cortex, entorhinal cortex, and hippocampus, but not within the amygdala. The later and more selective responses tended to be generated by cells with sparse baseline firing rates and vice versa. Our results provide direct evidence for hierarchical processing of sensory information at the interface between the visual pathway and the limbic system, by which increasingly refined and specific representations of stimulus identity are generated over time along the anatomic pathways of the medial temporal lobe

Analyzing Multiple Nonlinear Time Series with Extended Granger Causality

Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such relations. In this work we consider nonlinear extensions of Granger's idea and refer to the result as Extended Granger Causality. A simple approach implementing the Extended Granger Causality is presented and applied to multiple chaotic time series and other types of nonlinear signals. In addition, for situations with three or more time series we propose a conditional Extended Granger Causality measure that enables us to determine whether the causal relation between two signals is direct or mediated by another process.Comment: 16 pages, 6 figure

Kullback-Leibler and Renormalized Entropy: Applications to EEGs of Epilepsy Patients

Recently, renormalized entropy was proposed as a novel measure of relative entropy (P. Saparin et al., Chaos, Solitons & Fractals 4, 1907 (1994)) and applied to several physiological time sequences, including EEGs of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (K-L) relative entropy, and it gives similar numerical results to the standard K-L entropy. The latter better distinguishes frequency contents of e.g. seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing we also make some critical remarks about the implementation of these methods.Comment: 15 pages, 4 Postscript figures. Submitted to Phys. Rev. E, 199