Chaos, Solitons and Fractals: X最新文献

We consider the brain as an autonomous stochastic system, whose fundamental frequencies are locked to an external periodic stimulation. Taking into account that phase synchronization between brain response and stimulating signal is affected by noise, we propose a novel method for experimental estimation of brain noise by analyzing neurophysiological activity during perception of flickering visual stimuli. Using magnetoencephalography (MEG) we evaluate steady-state visual evoked fields (SSVEF) in the occipital cortex when subjects observe a square image with modulated brightness. Then, we calculate the probability distribution of the SSVEF phase fluctuations and compute its kurtosis. The higher kurtosis, the better the phase synchronization. Since kurtosis characterizes the distribution’s sharpness, we associate inverse kurtosis with brain noise which broadens this distribution. We found that the majority of subjects exhibited leptokurtic kurtosis (K > 3) with tails approaching zero more slowly than Gaussian. The results of this work may be useful for the development of efficient and accurate brain-computer interfaces to be adapted to individual features of every subject in accordance with his/her brain noise.

We introduce a quantum superconducting metamaterial design constituted of flux qubits that operate as artificial atoms and analyze the dynamics of an injected electromagnetic pulse in the system. Qubit-photon interaction affects dramatically the nonlinear photon pulse propagation. We find analytically that the well known atomic phenomenon of self induced transparency may occur in this metamaterial as well and may lead to significant control over the optical pulse propagating properties. Specifically, the pulse may be slowed down substantially or even be stopped. These pulse properties depend crucially on the inhomogeneous broadening of the levels of the artificial atoms.

Fractional time (non-unitary) quantum mechanics is discussed for both Schrödinger and Heisenberg representations of quantum mechanics. A correct form of the fractional Schrödinger equation is elucidated. A generic regularization procedure for the fractional Heisenberg equations of motion is suggested that makes it possible to solve these nonlinear equations in the framework of photonic and spin coherent states consideration.

From the Diagram Accuracy-Deviation and the new quantifier of chaos, this paper presents time series analysis for historical prices, volatilities and returns. The study cases are financial price series of United States Brent Oil (BNO), Wipro Limited (WIT), Nasdaq, Inc. (NDAQ) and SPDR S&P 500 ETF (SPY). Detection of chaos and randomness cover the period from November 2010 to November 2018. This work introduces the chaoticity in the Lorenz’s sense, a new measure for comparison between time series. The set of results enlights the underlying dynamics of the time evolution observed in economic indexes nowadays.

In Network Science, node neighbourhoods, also called ego-centered networks, have attracted significant attention. In particular the clustering coefficient has been extensively used to measure their local cohesiveness. In this paper, we show how, given two nodes with the same clustering coefficient, the topology of their neighbourhoods can be significantly different, which demonstrates the need to go beyond this simple characterization. We perform a large scale statistical analysis of the topology of node neighbourhoods of real networks by first constructing their clique complexes, and then computing their Betti numbers. We are able to show significant differences between the topology of node neighbourhoods of real networks and the stochastic topology of null models of random simplicial complexes revealing local organisation principles of the node neighbourhoods. Moreover we observe that a large scale statistical analysis of the topological properties of node neighbourhoods is able to clearly discriminate between power-law networks, and planar road networks.