Detecting coherence between oscillators in heavy-noise environments with a moving block bootstrap

In this paper, a novel algorithm based on the moving block-bootstrap (MBB) technique for the detection of coherence between oscillators in heavy-noise environments is proposed. To verify the null hypothesis of absent significant coherence against the alternative, the average coherence of MBB resampled data is compared with a certain threshold over all frequencies. The threshold is defined as the upper bound of a 95 % confidence interval for bootstrapping coherence performed with independent resampling indexes for both time series, so the dependence between the time series under consideration is destroyed. The benefits of the proposed method are illustrated by simulations of the phase synchronization effects of two linearly coupled chaotic Rössler oscillators

Synchronization of a Self-Sustained Cold Atom Oscillator

Nonlinear oscillations and synchronisation phenomena are ubiquitous in nature. We study the synchronization of self oscillating magneto-optically trapped cold atoms to a weak external driving. The oscillations arise from a dynamical instability due the competition between the screened magneto-optical trapping force and the inter-atomic repulsion due to multiple scattering of light. A weak modulation of the trapping force allows the oscillations of the cloud to synchronize to the driving. The synchronization frequency range increases with the forcing amplitude. The corresponding Arnold tongue is experimentally measured and compared to theoretical predictions. Phase-locking between the oscillator and drive is also observed.Comment: Corrected typo

Detecting coherence between oscillators in heavy-noise environments with a moving block bootstrap

In this paper, a novel algorithm based on the moving block-bootstrap (MBB) technique for the detection of coherence between oscillators in heavy-noise environments is proposed. To verify the null hypothesis of absent significant coherence against the alternative, the average coherence of MBB resampled data is compared with a certain threshold over all frequencies. The threshold is defined as the upper bound of a 95 % confidence interval for bootstrapping coherence performed with independent resampling indexes for both time series, so the dependence between the time series under consideration is destroyed. The benefits of the proposed method are illustrated by simulations of the phase synchronization effects of two linearly coupled chaotic Rössler oscillators

Quasi-biennial oscillations extracted from the monthly NAO index and temperature records are phase-synchronized

Using the extension of Monte Carlo Singular System Analysis (MC SSA), based on evaluating and testing the regularity of the dynamics of the SSA modes against the colored noise null hypothesis, we demonstrate detection of oscillatory modes with period of about 27 months in records of monthly average near-surface air temperature from several European locations, as well as in the monthly North Atlantic Oscillation index. According to their period, the detected modes can be attributed to the quasi-biennial oscillations (QBO). The QBO modes extracted from the temperature and from the NAO index underwent synchronization analysis and their phase synchronization has been confirmed with high statistical significance

The blessing of Dimensionality : feature selection outperforms functional connectivity-based feature transformation to classify ADHD subjects from EEG patterns of phase synchronisation

Functional connectivity (FC) characterizes brain activity from a multivariate set of N brain signals by means of an NxN matrix A, whose elements estimate the dependence within each possible pair of signals. Such matrix can be used as a feature vector for (un)supervised subject classification. Yet if N is large, A is highly dimensional. Little is known on the effect that different strategies to reduce its dimensionality may have on its classification ability. Here, we apply different machine learning algorithms to classify 33 children (age [6-14 years]) into two groups (healthy controls and Attention Deficit Hyperactivity Disorder patients) using EEG FC patterns obtained from two phase synchronisation indices. We found that the classification is highly successful (around 95%) if the whole matrix A is taken into account, and the relevant features are selected using machine learning methods. However, if FC algorithms are applied instead to transform A into a lower dimensionality matrix, the classification rate drops to less than 80%. We conclude that, for the purpose of pattern classification, the relevant features should be selected among the elements of A by using appropriate machine learning algorithms

О работе НОЦ «Нелинейная динамика»

В ноябре–декабре 2012 г. в научно-образовательном центре «Нелинейная динамика» при поддержке Министерства образования и науки Российской Федерации осуществлялась научно-исследовательская работа приглашенных молодых ученых из научных учреждений и университетов РФ. В ходе проведения работ по проекту научно-образовательный центр посетили молодые специалисты из Ижевска, Нижнего Новгорода, Москвы и Саратова. Ниже представлены аннотации некоторых из состоявшихся научных исследований