Dietrich Lehmann

Publications (161) View all

• Article: A measure of association between vectors based on "similarity covariance"

  Roberto D. Pascual-Marqui, Dietrich Lehmann, Kieko Kochi, Toshihiko Kinoshita, Naoto Yamada
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  ABSTRACT: The "maximum similarity correlation" definition introduced in this study is motivated by the seminal work of Szekely et al on "distance covariance" (Ann. Statist. 2007, 35: 2769-2794; Ann. Appl. Stat. 2009, 3: 1236-1265). Instead of using Euclidean distances "d" as in Szekely et al, we use "similarity", which can be defined as "exp(-d/s)", where the scaling parameter s>0 controls how rapidly the similarity falls off with distance. Scale parameters are chosen by maximizing the similarity correlation. The motivation for using "similarity" originates in spectral clustering theory (see e.g. Ng et al 2001, Advances in Neural Information Processing Systems 14: 849-856). We show that a particular form of similarity correlation is asymptotically equivalent to distance correlation for large values of the scale parameter. Furthermore, we extend similarity correlation to coherence between complex valued vectors, including its partitioning into real and imaginary contributions. Several toy examples are used for comparing distance and similarity correlations. For instance, points on a noiseless straight line give distance and similarity correlation values equal to 1; but points on a noiseless circle produces near zero distance correlation (dCorr=0.02) while the similarity correlation is distinctly non zero (sCorr=0.36). In distinction to the distance approach, similarity gives more importance to small distances, which emphasizes the local properties of functional relations. This paper represents a preliminary empirical study, showing that the novel similarity association has some distinct practical advantages over distance based association.For the sake of reproducible research, the software code implementing all methods here (using lazarus free-pascal "www.lazarus.freepascal.org"), including all test data, are freely available at: "sites.google.com/site/pascualmarqui/home/similaritycovariance".
  01/2013;
• Article: EEG source imaging during two Qigong meditations.

  Pascal L Faber, Dietrich Lehmann, Shisei Tei, Takuya Tsujiuchi, Hiroaki Kumano, Roberto D Pascual-Marqui, Kieko Kochi
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  ABSTRACT: Experienced Qigong meditators who regularly perform the exercises "Thinking of Nothing" and "Qigong" were studied with multichannel EEG source imaging during their meditations. The intracerebral localization of brain electric activity during the two meditation conditions was compared using sLORETA functional EEG tomography. Differences between conditions were assessed using t statistics (corrected for multiple testing) on the normalized and log-transformed current density values of the sLORETA images. In the EEG alpha-2 frequency, 125 voxels differed significantly; all were more active during "Qigong" than "Thinking of Nothing," forming a single cluster in parietal Brodmann areas 5, 7, 31, and 40, all in the right hemisphere. In the EEG beta-1 frequency, 37 voxels differed significantly; all were more active during "Thinking of Nothing" than "Qigong," forming a single cluster in prefrontal Brodmann areas 6, 8, and 9, all in the left hemisphere. Compared to combined initial-final no-task resting, "Qigong" showed activation in posterior areas whereas "Thinking of Nothing" showed activation in anterior areas. The stronger activity of posterior (right) parietal areas during "Qigong" and anterior (left) prefrontal areas during "Thinking of Nothing" may reflect a predominance of self-reference, attention and input-centered processing in the "Qigong" meditation, and of control-centered processing in the "Thinking of Nothing" meditation.
  Cognitive Processing 05/2012; 13(3):255-65. · 1.57 Impact Factor
• Article: Reduced functional connectivity between cortical sources in five meditation traditions detected with lagged coherence using EEG tomography.

  Dietrich Lehmann, Pascal L Faber, Shisei Tei, Roberto D Pascual-Marqui, Patricia Milz, Kieko Kochi
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  ABSTRACT: Brain functional states are established by functional connectivities between brain regions. In experienced meditators (13 Tibetan Buddhists, 15 QiGong, 14 Sahaja Yoga, 14 Ananda Marga Yoga, 15 Zen), 19-channel EEG was recorded before, during and after that meditation exercise which their respective tradition regards as route to the most desirable meditative state. The head surface EEG data were recomputed (sLORETA) into 19 cortical regional source model time series. All 171 functional connectivities between regions were computed as 'lagged coherence' for the eight EEG frequency bands (delta through gamma). This analysis removes ambiguities of localization, volume conduction-induced inflation of coherence, and reference-dependence. All significant differences (corrected for multiple testing) between meditation compared to no-task rest before and after meditation showed lower coherence during meditation, in all five traditions and eight (inhibitory as well as excitatory) frequency bands. Conventional coherence between the original head surface EEG time series very predominantly also showed reduced coherence during meditation. The topography of the functional connectivities was examined via PCA-based computation of principal connectivities. When going into and out of meditation, significantly different connectivities revealed clearly different topographies in the delta frequency band and minor differences in the beta-2 band. The globally reduced functional interdependence between brain regions in meditation suggests that interaction between the self process functions is minimized, and that constraints on the self process by other processes are minimized, thereby leading to the subjective experience of non-involvement, detachment and letting go, as well as of all-oneness and dissolution of ego borders during meditation.
  NeuroImage 01/2012; 60(2):1574-86. · 5.89 Impact Factor
• Article: EEG sLORETA functional imaging during hypnotic arm levitation and voluntary arm lifting.

  Etzel Cardeña, Dietrich Lehmann, Pascal L Faber, Peter Jönsson, Patricia Milz, Roberto D Pascual-Marqui, Kieko Kochi
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  ABSTRACT: This study (N = 37 with high, medium, and low hypnotizables) evaluated depth reports and EEG activity during both voluntary and hypnotically induced left-arm lifting with sLORETA functional neuroimaging. The hypnotic condition was associated with higher activity in fast EEG frequencies in anterior regions and slow EEG frequencies in central-parietal regions, all left-sided. The voluntary condition was associated with fast frequency activity in right-hemisphere central-parietal regions and slow frequency activity in left anterior regions. Hypnotizability did not have a significant effect on EEG activity, but hypnotic depth correlated with left hemisphere increased anterior slow EEG and decreased central fast EEG activity. Hypnosis had a minimal effect on depth reports among lows, a moderate one among mediums, and a large one among highs. Because only left-arm data were available, the full role of the hemispheres remains to be clarified.
  International Journal of Clinical and Experimental Hypnosis 01/2012; 60(1):31-53. · 1.52 Impact Factor
• Article: Assessing interactions in the brain with exact low-resolution electromagnetic tomography.

  Roberto D Pascual-Marqui, Dietrich Lehmann, Martha Koukkou, Kieko Kochi, Peter Anderer, Bernd Saletu, Hideaki Tanaka, Koichi Hirata, E Roy John, Leslie Prichep, Rolando Biscay-Lirio, Toshihiko Kinoshita
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  ABSTRACT: Scalp electric potentials (electroencephalogram; EEG) are contingent to the impressed current density unleashed by cortical pyramidal neurons undergoing post-synaptic processes. EEG neuroimaging consists of estimating the cortical current density from scalp recordings. We report a solution to this inverse problem that attains exact localization: exact low-resolution brain electromagnetic tomography (eLORETA). This non-invasive method yields high time-resolution intracranial signals that can be used for assessing functional dynamic connectivity in the brain, quantified by coherence and phase synchronization. However, these measures are non-physiologically high because of volume conduction and low spatial resolution. We present a new method to solve this problem by decomposing them into instantaneous and lagged components, with the lagged part having almost pure physiological origin.
  Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 10/2011; 369(1952):3768-84. · 2.77 Impact Factor