Synchronization and information flow in EEGs of epileptic patients

Paulus, Michal; Komárek, Vladimı́r; Procházka, Tomáš; Hrncír, Z; Štěrbová, Katalin

doi:10.1109/51.956821

Cited by 60 publications

(46 citation statements)

References 20 publications

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“…Mutual information can be interpreted as a measure of how much information two studied systems exchange or two studied stochastic processes or data sets share. Due to these characteristics mutual information is suitable for many applications, and has been used successfully particularly enhance the understanding of the development and functioning of the brain in neuroscience [48][49][50], to characterise [51,52] and model various complex and chaotic systems [53][54][55], and also to quantify the information capacity of a communication system [56]. Additionally mutual information provides a convenient way to identify the most relevant variables with which to describe the behaviour of a complex system [57], which is of paramount importance in modelling those systems, and indeed to the methodology of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…The calculation or indeed estimation of mutual information in dynamical systems is met with three important difficulties however [52,58]. Mutual information is precisely defined only for random processes without memory.…”

Section: Introductionmentioning

confidence: 99%

“…This prevents the researchers from calculating the probabilities correctly. As a consequence, mutual information can often only be calculated with a bias [52,62,63]. Nonetheless those restrictions does not make mutual information useless, particularly the third one is true of any other similarity measure (including correlation), and the second one is a matter of careful design of methodology, while the first problem is not severe and can be contained by using methods which are asymptotically precise even for processes with memory.…”

Section: Introductionmentioning

confidence: 99%

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Networks in financial markets based on the mutual information rate

Fiedor

2014

Phys. Rev. E

117

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In the last years efforts in econophysics have been shifted to study how network theory can facilitate understanding of complex financial markets. Main part of these efforts is the study of correlation-based hierarchical networks. This is somewhat surprising as the underlying assumptions of research looking at financial markets is that they behave chaotically. In fact it's common for econophysicists to estimate maximal Lyapunov exponent for log returns of a given financial asset to confirm that prices behave chaotically. Chaotic behaviour is only displayed by dynamical systems which are either non-linear or infinite-dimensional. Therefore it seems that non-linearity is an important part of financial markets, which is proved by numerous studies confirming financial markets display significant non-linear behaviour, yet network theory is used to study them using almost exclusively correlations and partial correlations, which are inherently dealing with linear dependencies only. In this paper we introduce a way to incorporate non-linear dynamics and dependencies into hierarchical networks to study financial markets using mutual information and its dynamical extension: the mutual information rate. We estimate it using multidimensional Lempel-Ziv complexity and then convert it into an Euclidean metric in order to find appropriate topological structure of networks modelling financial markets. We show that this approach leads to different results than correlation-based approach used in most studies, on the basis of 15 biggest companies listed on Warsaw Stock Exchange in the period of 2009-2012 and 91 companies listed on NYSE100 between 2003 and 2013, using minimal spanning trees and planar maximally filtered graphs.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Networks in financial markets based on the mutual information rate

Fiedor

2014

Phys. Rev. E

117

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“…Recently we have used it in the creation of dependency networks on financial markets [20]. Mutual information measures how much information two studied stochastic processes share and has been used to enhance the understanding of the brain in neuroscience [48][49][50], to characterise [51,52] and model various complex and chaotic systems [53][54][55], and also to quantify the information capacity of a communication system [56]. Additionally mutual information provides a convenient way to identify the most relevant variables with which to describe the behaviour of a complex system [57], which is of paramount importance in modelling those systems, and indeed to the methodology of this paper [20].…”

Section: Introductionmentioning

confidence: 99%

Information-theoretic approach to lead-lag effect on financial markets

Fiedor

2014

Eur. Phys. J. B

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Abstract.Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both types of analysis are concentrated mostly on Pearson's correlation coefficient and consequently intraday lead-lag relationships (where one of the variables in a pair is time-lagged) are also associated with them. Under the Efficient-Market Hypothesis such relationships are not possible as all information is embedded in the prices, but in real markets we find such dependencies. In this paper we analyse lead-lag relationships of financial instruments and extend known methodology by using mutual information instead of Pearson's correlation coefficient. Mutual information is not only a more general measure, sensitive to non-linear dependencies, but also can lead to a simpler procedure of statistical validation of links between financial instruments. We analyse lagged relationships using New York Stock Exchange 100 data not only on an intraday level, but also for daily stock returns, which have usually been ignored.

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“…Synchronization and related phenomena have been observed in diverse physical, biological and social systems. Examples include cardio-respiratory interactions [2,3], synchronization of neural signals on various levels of organization of brain tissues [4][5][6][7], or coherent variability in the Earth atmosphere and climate [8][9][10][11][12][13]. In such systems it is not only important to detect interactions and possible synchronized states, but also to distinguish mutual interactions from a directional coupling, i.e., to identify drive-response relationships between the systems studied.…”

Section: Introductionmentioning

confidence: 99%

Cross-Scale Interactions and Information Transfer

Paluš

2014

Entropy

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An information-theoretic approach for detecting interactions and information transfer between two systems is extended to interactions between dynamical phenomena evolving on different time scales of a complex, multiscale process. The approach is demonstrated in the detection of an information transfer from larger to smaller time scales in a model multifractal process and applied in a study of cross-scale interactions in atmospheric dynamics. Applying a form of the conditional mutual information and a statistical test based on the Fourier transform and multifractal surrogate data to about a century long records of daily mean surface air temperature from various European locations, an information transfer from larger to smaller time scales has been observed as the influence of the phase of slow oscillatory phenomena with the periods around 6-11 years on the amplitudes of the variability characterized by the smaller temporal scales from a few months to 4-5 years. These directed cross-scale interactions have a non-negligible effect on interannual air temperature variability in a large area of Europe.

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Synchronization and information flow in EEGs of epileptic patients

Cited by 60 publications

References 20 publications

Networks in financial markets based on the mutual information rate

Networks in financial markets based on the mutual information rate

Information-theoretic approach to lead-lag effect on financial markets

Cross-Scale Interactions and Information Transfer

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