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DAMOCO: Data Analysis with Models Of Coupled OscillatorsMATLAB Toolbox for multivariate time series analysisBjörn Kralemann, Michael Rosenblum, Arkady
Pikovsky
Version
2.0 (2014)
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Last modification 05.06.18
This toolbox is a collection of functions for multivariate data analysis,
based on the coupled oscillator approach, developed in our publications.
With the help of this toolbox you can:
· compute protophases (initial phase estimates) from time series by means of the Hilbert Transform
· transform protophases into true phases
· reconstruct phase dynamics of coupled oscillators from data
· compute synchronization and directionality indices
A description of the toolbox and of how to use it can be found in this manual. Sorry, the manual for Version 2 is not ready yet.
You can download the whole toolbox as an archive here
or as separate files from the list of functions below.
Main functions are illustrated by examples.
Please mail us if you encounter any bug or problem in using
the toolbox! Any questions/suggestions are highly welcome.
Please cite our publications if you use this
software.
DAMOCO Version 1.0 can be found here.
Brief
illustration to the theory
o Coupled
oscillators approach: main ideas and assumptions
o Phase
dynamics of coupled oscillators
o Synchronization
and its quantification
o Direction
of coupling and its quantification
o Protophase →
phase transformation: why do we need it?
The
current version 2.0 of the toolbox contains the following functions:
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Function |
What it does |
Version |
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Protophase computation |
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Protophase from a scalar time series, using the Hilbert transform |
27.02.2014 |
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Protophase from a scalar time series, using the
length of the trajectory in the state space |
10.04.2014 |
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Protophase from a scalar time series via markers
(minima, maxima, zero-crossings) |
06.05.2014 |
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Protophase from a scalar time series, via the
average cycle |
18.05.2014 |
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Univariate protophase → phase transformation |
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Protophase → phase transformation plus computation of the transformation function |
02.03.2014 |
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Protophase → phase
transformation with optimization (recommended) |
02.03.2014 |
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Synchronization analysis |
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n:m synchronization index |
17.01.2011 |
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Maximal n:m synchronization index for a given range of n, m |
27.02.2014 |
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n:m:p triplet synchronization index |
06.03.2014 |
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Maximal n:m:p synchronization index for a given range of n, m, p |
06.03.2014 |
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Two interacting oscillators: coupling functions |
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Fourier-based technique, coupling functions for both
oscillators |
04.03.2014 |
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Fourier-based technique, coupling function for one
oscillator only |
04.03.2014 |
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Kernel estimation, coupling functions for both
oscillators |
03.03.2014 |
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Kernel estimation, coupling function for one
oscillator only |
03.03.2014 |
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Analysis of two-dimensional coupling functions |
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Norm and constant term (frequency) of the coupling function, given by the Fourier coefficients |
05.03.2014 |
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Norm and constant term (frequency) of the coupling function, given on the grid |
04.03.2014 |
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Correlation between two coupling functions (Fourier-based) |
06.03.2014 |
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Maximal correlation between two coupling functions
(Fourier-based) |
06.03.2014 |
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Correlation between two coupling functions, given on a grid |
06.03.2014 |
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Maximal correlation between two coupling functions,
given on a grid |
06.03.2014 |
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Correlation and difference measure for two coupling
functions on a grid |
02.03.2014 |
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Directionality index from norms of the coupling functions |
26.02.2014 |
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Directionality index from partial derivatives of the coupling functions |
26.02.2014 |
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Phase Response Curve via decomposition of the
coupling function |
28.02.2014 |
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More than two interacting oscillators |
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Three coupled oscillators, coupling functions via a
Fourier-based technique |
06.03.2014 |
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Coupling structure of the triplet |
12.03.2014 |
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Triplet analysis of a network with N>3
oscillators |
12.03.2014 |
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Plot of the triplet coupling structure |
05.04.2014 |
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Additional functions |
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Derivative of the phase via the Savitzky-Golay
filter |
06.03.2014 |
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Derivatives of two phases via the Savitzky-Golay filter (for bivariate
analysis) |
06.03.2014 |
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Derivatives of three phases via the Savitzky-Golay filter (for triplet analysis) |
06.03.2014 |
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Plot of the coupling function |
17.01.2011 |
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Plot of two coupling functions in the same window |
17.01.2011 |
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Plot of the Fourier coefficients of the coupling function |
17.01.2011 |
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Plot of the Fourier coefficients of two coupling functions |
17.01.2011 |
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Auxiliary function which checks the input data |
17.01.2011 |
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Publications
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Reference |
What it is about |
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1 |
M. Rosenblum and A. Pikovsky |
Notion of directionality in coupled oscillatory systems, directionality index via partial derivatives |
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2,3 |
B. Kralemann, L. Cimponeriu, M. Rosenblum, A.
Pikovsky, and R. Mrowka Phase
dynamics of coupled oscillators reconstructed from data, |
Notion of protophases, phase to protophase transformation, protophaase
via the length of the trajectory, recovery of autonomous frequencies |
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4 |
B. Kralemann, A. Pikovsky, and M. Rosenblum,
Reconstructing
phase dynamics of oscillator networks,
Chaos, 21, p. 025104, 2011 |
Reconstruction of small networks, coupling functions for
three coupled oscillators, directionality index via partial norms, recovery
of autonomous frequencies |
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5 |
B. Kralemann, M. Frühwirth, A. Pikovsky, M. Rosenblum,
T. Kenner,
J. Schaefer, and M. Moser In vivo
cardiac phase response curve elucidates human respiratory heart rate
variability, Nature Communications, 4, 2418, 2013 |
Protophase via average cycle, phase response
curve from the coupling function |
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6 |
B. Kralemann, A. Pikovsky, and M. Rosenblum, Detecting
triplet locking by triplet synchronization indices, Phys. Rev. E, 87, p. 052904, 2013. |
Computation of the triplet index, quantification of the
triplet locking from data |
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7 |
B. Kralemann, A. Pikovsky, and M. Rosenblum, Reconstructing effective phase
connectivity of oscillator networks from observations, New Journal of Physics, 16, p. 085013, 2014 |
Extension of the approach from Ref. [4]; here triplet
analysis of the N-oscillator network (N>3) is used instead of traditional pair-wise
analysis. Improved differentiation between structurally existing and
non-existing links. |
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The
toolbox is illustrated by the following examples: new
examples are coming
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Example |
Function |
Sample data |
Output |
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Two coupled van der Pol oscillators |
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High-level Fourier-based function |
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Fourier-based technique, step-by-step with plots of intermediate results |
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High-level function, iteration technique |
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Iteration technique, step-by-step with plots of intermediate results |
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Related links
|
HERMES: Integrated Toolbox to Characterize Functional
and Effective Brain Connectivity |
G. Niso, R. Bruña,
E. Pereda, R. Gutiérrez, R.
Bajo, F.
Maestú,
and F. del-Pozo. Neuroinform (2013) 11:405–434 |
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Trentool: an open source toolbox to estimate
neural directed interactions with transfer entropy |
M. Wibral, R. Vicente, V. Priesemann, and M. Lindner. BMC Neuroscience, 12 (Suppl 1): P200, 2011. |
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L.
Barnett, A.K. Seth. J. Neurosci Methods, 223:50-68, 2014 |
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