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Cross-frequency synchronization (CFS) has been proposed as a mechanism for integrating spatially and spectrally distributed information in the brain. However, investigating CFS in Magneto- and Electroencephalography (MEG/EEG) is hampered by the presence of spurious neuronal interactions due to the non-sinusoidal waveshape of brain oscillations. Such waveshape gives rise to the presence of oscillatory harmonics mimicking genuine neuronal oscillations. Until recently, however, there has been no methodology for removing these harmonics from neuronal data. In order to address this long-standing challenge, we introduce a novel method (called HARMOnic miNImization - Harmoni) that removes the signal components which can be harmonics of a non-sinusoidal signal. Harmoni’s working principle is based on the presence of CFS between harmonic components and the fundamental component of a non-sinusoidal signal. We extensively tested Harmoni in realistic EEG simulations. The simulated couplings between the source signals represented genuine and spurious CFS and within-frequency phase synchronization. Using diverse evaluation criteria, including ROC analyses, we showed that the within- and cross-frequency spurious interactions are suppressed significantly, while the genuine activities are not affected. Additionally, we applied Harmoni to real resting-state EEG data revealing intricate remote connectivity patterns which are usually masked by the spurious connections. Given the ubiquity of non-sinusoidal neuronal oscillations in electrophysiological recordings, Harmoni is expected to facilitate novel insights into genuine neuronal interactions in various research fields, and can also serve as a steppingstone towards the development of further signal processing methods aiming at refining within- and cross-frequency synchronization in electrophysiological recordings.

In contemporary discourse, international investment law and investor-state dispute settlement (ISDS) are often perceived as threats to community interests in one-sidedly protecting foreign investors and undermining public policies that are to the benefit of the local population and the international community. The chapter promotes a different perspective. First, it argues that international investment law properly construed can be conceptualized as protecting community interests, because it is part of the legal infrastructure necessary for the functioning of the global economy under a rule of law framework. Aimed at supporting economic growth, this helps further economic and noneconomic community interests, including sustainable development. Second, the chapter argues that international investment law and ISDS do not turn a blind eye to the conflicts that can arise between economic and noneconomic community interests, such as environmental protection or human rights. Instead, international investment law and ISDS have numerous mechanisms at their disposal for alleviating tensions with noneconomic community interests.

Objective. Neurophysiological correlates of vertical disparity in 3D images are studied in an objective approach using EEG technique. These disparities are known to negatively affect the quality of experience and to cause visual discomfort in stereoscopic visualizations. Approach. We have presented four conditions to subjects: one in 2D and three conditions in 3D, one without vertical disparity and two with different vertical disparity levels. Event related potentials (ERPs) are measured for each condition and the differences between ERP components are studied. Analysis is also performed on the induced potentials in the time frequency domain. Main results. Results show that there is a significant increase in the amplitude of P1 components in 3D conditions in comparison to 2D. These results are consistent with previous studies which have shown that P1 amplitude increases due to the depth perception in 3D compared to 2D. However the amplitude is significantly smaller for maximum vertical disparity (3D-3) in comparison to 3D with no vertical disparity. Our results therefore suggest that the vertical disparity in 3D-3 condition decreases the perception of depth compared to other 3D conditions and the amplitude of P1 component can be used as a discriminative feature. Significance. The results show that the P1 component increases in amplitude due to the depth perception in the 3D stimuli compared to the 2D stimulus. On the other hand the vertical disparity in the stereoscopic images is studied here. We suggest that the amplitude of P1 component is modulated with this parameter and decreases due to the decrease in the perception of depth.

The accuracy of EEG source localization depends on the choice of the inverse method, the resolution of the forward model, and the signal to noise ratio (SNR) of the recordings. Since we are interested in disentangling sources in proximity, the goal of our study is to examine the sensitivity of spatial resolution of EEG source reconstruction to a wide variety of factors like reconstruction method, SNR, orientation, inter-dipole distance and depth of the simulated dipoles, etc.We simulated time series to resemble waveforms of somatosensory evoked potentials. Inter-dipole distances and different dipole orientations were investigated as well as the effect of (realistic) noise. We employed both spherical and realistic head models. Source reconstruction was realized using a conventional stationary dipole model, MUSIC, self-consistent MUSIC (SC-MUSIC) algorithm, and e-LORETA. In addition to the above mentioned methods, a new approach is tested building upon the e-LORETA solution: the topography of the maximum of the e-LORETA distribution is projected out of the data before calculating the next e-LORETA inverse solution in a iterative process. The quality of fit (or localization) was defined as the distance between the simulated point- sources and either the estimated point-sources or the activity distributions by means of the Euclidean distance or of the Earth Mover’’s Distance, respectively. As expected, inter-dipole distances played an important role in the ability of every method to disentangle the simulated sources. Overall, SC-MUSIC appeared best suited for disentangling the two simulated sources even at high-noise simulations.

Interpretive practices between legal systems and domestic courts vary widely. This inevitably will affect the interpretation of rules of international law by domestic courts. The question is whether there are good grounds for national courts to limit divergence of interpretations, by relying on international principles of interpretation. This chapter explores three possible grounds on the basis of which domestic courts can resort to an application of international rules of interpretation: the effective performance of treaty obligations, the international quality of domesticated norms, and the external authority of decisions of domestic courts. The chapter argues that, depending on the context, each of these grounds may offer a justification for relying on international rules of interpretation, but that competing considerations may pull in diverging directions, and that the international rules of treaty interpretation do not necessarily preclude this.

MUltiple SIgnal Classification (MUSIC) is a standard localization method which is based on the idea of dividing the vector space of the data into two subspaces: signal subspace and noise subspace. The brain, divided into several grid points, is scanned entirely and the grid point with the maximum consistency with the signal subspace is considered as the source location. In one of the MUSIC variants called Recursively Applied and Projected MUSIC (RAP-MUSIC), multiple iterations are proposed in order to decrease the location estimation uncertainties introduced by subspace estimation errors. In this paper, we suggest a new method called Self-Consistent MUSIC (SC-MUSIC) which extends RAP-MUSIC to a self-consistent algorithm. This method, SC-MUSIC, is based on the idea that the presence of several sources has a bias on the localization of each source. This bias can be reduced by projecting out all other sources mutually rather than iteratively. While the new method is applicable in all situations when MUSIC is applicable we will study here the localization of interacting sources using the imaginary part of the cross-spectrum due to the robustness of this measure to the artifacts of volume conduction. For an odd number of sources this matrix is rank deficient similar to covariance matrices of fully correlated sources. In such cases MUSIC and RAP-MUSIC fail completely while the new method accurately localizes all sources. We present results of the method using simulations of odd and even number of interacting sources in the presence of different noise levels. We compare the method with three other source localization methods: RAP-MUSIC, dipole fit and MOCA (combined with minimum norm estimate) through simulations. SC-MUSIC shows substantial improvement in the localization accuracy compared to these methods. We also show results for real MEG data of a single subject in the resting state. Four sources are localized in the sensorimotor area at f = 11 Hz which is the expected region for the idle rhythm.

Einleitung und Fragestellung: In beiden Häusern der Maximalversorgung ist eine komplexe Kombination aus KIS und weiteren klinischen Informationssystemen im Einsatz. Eine Vielzahl an Abteilungen hat spezifische Anforderungen an Datenaustausch und Präsentation in ihren Fachbereichen, welche [for full text, please go to the a.m. URL], GMDS 2014; 59. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e.V. (GMDS)

Considering that many biological systems including the brain are complex non-linear systems, suitable methods capable of detecting these non-linearities are required to study the dynamical properties of these systems. One of these tools is the third order cummulant or cross-bispectrum, which is a measure of interfrequency interactions between three signals. For convenient interpretation, interaction measures are most commonly normalized to be independent of constant scales of the signals such that its absolute values are bounded by one, with this limit reflecting perfect coupling. Although many different normalization factors for cross-bispectra were suggested in the literature these either do not lead to bounded measures or are themselves dependent on the coupling and not only on the scale of the signals. In this paper we suggest a normalization factor which is univariate, i.e., dependent only on the amplitude of each signal and not on the interactions between signals. Using a generalization of Holder's inequality it is proven that the absolute value of this univariate bicoherence is bounded by zero and one. We compared three widely used normalizations to the univariate normalization concerning the significance of bicoherence values gained from resampling tests. Bicoherence values are calculated from real EEG data recorded in an eyes closed experiment from 10 subjects. The results show slightly more significant values for the univariate normalization but in general, the differences are very small or even vanishing in some subjects. Therefore, we conclude that the normalization factor does not play an important role in the bicoherence values with regard to statistical power, although a univariate normalization is the only normalization factor which fulfills all the required conditions of a proper normalization.

Neurological disorders and physiological aging can lead to a decline of perceptual abilities. In contrast to the conventional therapeutic approach that comprises intensive training and practicing, passive repetitive sensory stimulation (RSS) has recently gained increasing attention as an alternative to countervail the sensory decline by improving perceptual abilities without the need of active participation. A particularly effective type of high-frequency RSS, utilizing Hebbian learning principles, improves perceptual acuity as well as sensorimotor functions and has been successfully applied to treat chronic stroke patients and elderly subjects. High-frequency RSS has been shown to induce plastic changes of somatosensory cortex such as representational map reorganization, but its impact on the brain's ongoing network activity and resting-state functional connectivity has not been investigated so far. Here, we applied high-frequency RSS in healthy human subjects and analyzed resting state Electroencephalography (EEG) functional connectivity patterns before and after RSS by means of imaginary coherency (ImCoh), a frequency-specific connectivity measure which is known to reduce over-estimation biases due to volume conduction and common reference. Thirty minutes of passive high-frequency RSS lead to significant ImCoh-changes of the resting state mu-rhythm in the individual upper alpha frequency band within distributed sensory and motor cortical areas. These stimulation induced distributed functional connectivity changes likely underlie the previously observed improvement in sensorimotor integration.

Estimating brain connectivity and especially causality between different brain regions from EEG or MEG is limited by the fact that the data are a largely unknown superposition of the actual brain activities. Any method, which is not robust to mixing artifacts, is prone to yield false positive results. We here review a number of methods that allow for addressing this problem. They are all based on the insight that the imaginary part of the cross-spectra cannot be explained as a mixing artifact. First, a joined decomposition of these imaginary parts into pairwise activities separates subsystems containing different rhythmic activities. Second, assuming that the respective source estimates are least overlapping, yields a separation of the rhythmic interacting subsystem into the source topographies themselves. Finally, a causal relation between these sources can be estimated using the newly proposed measure Phase Slope Index (PSI). This work, for the first time, presents the above methods in combination; all illustrated using a single, simulated data set.

There is no question that many believe in the power of treaties, and of the law of treaties, in the strengthening of peace. If we confide rules to paper, this will smother, or even prevent, conflicts. When my then future husband and I visited our notary for the prenuptial agreement, we told him that we did this to avoid conflict in the future: the agreement would clarify who owns what, how our shared income would be distributed, and we would not have to bicker over our possessions. Alternatively, we wanted such an agreement because it would allow us to settle the differences by legal means, since law would now cover it. Our notary looked at us and said we were wrong. In his experience, divorces of marriages based on a community of property without a prenuptial agreement caused less litigation because no special rules applied and everything would just be divided in half. Prenuptial agreements on the contrary always gave occasion for litigation: the parties would bicker over the interpretation of each and every provision. So why did we in the end decide to have the agreement? Because we believed that the alternative is worse, and because we think it may help us solve problems and avoid conflicts. While this may be a silly example, and while there may be other reasons why divorces with a prenuptial agreement are prone to more conflict than those without, this example raises questions regarding the function of a treaty for the creation and maintenance of peace.

We introduce Focal Vector Field Reconstruction (FVR), a novel technique for the inverse imaging of vector fields. The method was designed to simultaneously achieve two goals: a) invariance with respect to the orientation of the coordinate system, and b) a preference for sparsity of the solutions and their spatial derivatives. This was achieved by defining the regulating penalty function, which renders the solutions unique, as a global l(1)-norm of local l(2)-norms. We show that the method can be successfully used for solving life EEG inverse problem. In the joint localization of 2-3 simulated dipoles, FVR always reliably recovers the true sources. The competing methods have limitations in distinguishing close sources because their estimates are either too smooth (LORETA, Minimum l(1)-norm) or too scattered (Minimum l(2)-norm). In both noiseless and noisy simulations, FVR has the smallest localization error according to the Earth Mover's Distance (EMD), which is introduced here as a meaningful measure to compare arbitrary source distributions. We also apply the method to the simultaneous localization of left and right somatosensory N20 generators front real EEG recordings. Compared to its peers FVR was the only method that delivered correct location of the source in the somatosensory area of each hemisphere in accordance with neurophysiological prior knowledge.

We present a technique that identifies truly interacting subsystems of a complex system from multichannel data if the recordings are an unknown linear and instantaneous mixture of the true sources. The method is valid for arbitrary noise structure. For this, a blind source separation technique is proposed that diagonalizes antisymmetrized cross-correlation or cross-spectral matrices. The resulting decomposition finds truly interacting subsystems blindly and suppresses any spurious interaction stemming from the mixture. The usefulness of this interacting source analysis is demonstrated in simulations and for real electroencephalography data.

Nonlinearity is often deduced by showing that a dataset signi£cantly deviates from its phase randomized versions, i.e. surrogate data. For real data, however, non-stationarities like artifacts and onsets and offsets of rhythmic activity will cause false positives. We propose a new test which detects dynamical nonlinearity by measuring time-asymmetry, using surrogate data merely to estimate the standard deviation of the process. The method is applied to multi-channel MEG measurements of ongoing alpha-band activity modulated by a simple visual memory task involving motor activity. The signal to noise ratio was enhanced using ICA, and the analysis was performed on a single separated source. We found that, if the peak at 10 Hz is accompanied by a substantial higher harmonic, time asymmetry can be detected signifcantly in virtually any epoch of 3 second duration. Finally, we applied our recently proposed method to estimate correlation dimension for noisy data. We found very satisfactory scaling plots with dimension around 1.5. As a byproduct, we showed that the nondeterministic fraction can be explained almost completely by external noise.

Using Gaussian kernels to define the correlation sum we derive simple formulas that correct the noise bias in estimates of the correlation dimension and K-2 entropy of chaotic time series. The corrections are only based on the difference of correlation dimensions for adjacent embedding dimensions and hence preserve the full functional dependencies on both the scale parameter and embedding dimension. It is shown theoretically that the estimates, which are derived for additive white Gaussian noise, are also robust for moderately colored noise. Simulations underline the usefulness of the proposed correction schemes. It is demonstrated that the method gives satisfactory results also for non-Gaussian and dynamical noise.