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Let $G$ be a non-elementary hyperbolic group. Let $w$ be a proper group word. We show that the width of the verbal subgroup $w(G)=\langle w[G]\rangle$ is infinite. That is, there is no $l\in \mathbb Z$ such that any $g\in w(G)$ can be represented as a product of at most $l$ values of $w$ and their inverses. As a consequence, we obtain the same result for a wide class of relatively hyperbolic groups. [ABSTRACT FROM PUBLISHER]

Phase patterns of human scalp alpha EEG activity show spontaneous transitions between different globally phase-synchronized states. We studied the dynamical properties of these transitions using the method of symbolic dynamics. We found greater predictability (deterministicity) and heterogeneity in the dynamics than what was expected from corresponding surrogate series in which linear correlations are retained. A possible explanation of these observations within the framework of chaotic itinerancy is discussed. Hum Brain Mapp, 2007. © 2007 Wiley-Liss, Inc. [ABSTRACT FROM AUTHOR]

In this study we investigate the possibility of a-GaN ELOG process and its peculiarities for stripes of various orientations. It is shown that stripe orientation allows governing such important parameters of ELOG-process as lateral growth rate, voids high, fast growth direction. The intermediate orientations of stripe windows (differ from conventional (0001) and (1-100)) can be effectively used for double-cross ELOG process. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

While viewing a scene, the eyes are attracted to salient stimuli. We set out to identify the brain signals controlling this process. In a contour integration task, in which participants searched for a collinear contour in a field of randomly oriented Gabor elements, a previously established model was applied to calculate a visual saliency value for each fixation location. We studied brain activity related to the modeled saliency values, using coregistered eye tracking and EEG. To disentangle EEG signals reflecting salience in free viewing from overlapping EEG responses to sequential eye movements, we adopted generalized additive mixed modeling (GAMM) to single epochs of saccade‐related EEG. We found that, when saliency at the next fixation location was high, amplitude of the presaccadic EEG activity was low. Since presaccadic activity reflects covert attention to the saccade target, our results indicate that larger attentional effort is needed for selecting less salient saccade targets than more salient ones. This effect was prominent in contour‐present conditions (half of the trials), but ambiguous in the contour‐absent condition. Presaccadic EEG activity may thus be indicative of bottom‐up factors in saccade guidance. The results underscore the utility of GAMM for EEG—eye movement coregistration research. [ABSTRACT FROM AUTHOR]