MODA

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Numerical toolbox developed by the Nonlinear & Biomedical Physics group at Lancaster University for analysing real-life time-series.

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## Table of Contents

- [MODA](#moda)
  - [Purpose](#purpose)
  - [Getting started](#getting-started)
- [References](#references)
- [Example applications](#example-applications)

# MODA

[![DOI](https://zenodo.org/badge/194114858.svg)](https://zenodo.org/badge/latestdoi/194114858)

MODA (Multiscale Oscillatory Dynamics Analysis) is a numerical toolbox developed by the
[Nonlinear & Biomedical Physics group](https://www.lancaster.ac.uk/physics/research/experimental-condensed-matter/nonlinear-and-biomedical-physics/) at [Lancaster University](https://www.lancaster.ac.uk/physics/) and the Nonlinear Dynamics and Synergetic Group at the Faculty of Electrical
Engineering, University of Ljubljana, Slovenia under the supervision of Aneta Stefanovska.

> **Note:** A Python implementation of MODA, [PyMODA](https://github.com/luphysics/PyMODA), is currently in development. PyMODA does not require a MATLAB license.

## Purpose

MODA is designed for analysing real-life time-series
that are assumed to be the output of some *a priori* unknown non-autonomous dynamical system,
and deriving important properties about this dynamical system from the time-series.

MODA includes
methods both for analysing the recordings of a single signal over time, and for analysing a set
of recordings of multiple different signals over time. In particular, it has tools for analysing
bivariate time-series consisting of the simultaneous recordings of two different signals over time,
with a view to examining possible connections between the two signals.

## Getting started

To get started, please see the [User Guide](/docs/user-guide.md).

# References

#### Overview
1. J Newman, G Lancaster and A Stefanovska, “Multiscale Oscillatory Dynamics
Analysis”, v1.01, User Manual, 2018.
2. P Clemson, G Lancaster, A Stefanovska, “Reconstructing time-dependent dynamics”, *Proc IEEE*
**104**, 223–241 (2016).
3. P Clemson, A Stefanovska, “Discerning non-autonomous dynamics”, *Phys Rep* **542**, 297-368 (2014).

#### Time-Frequency Analysis
1. D Iatsenko, P V E McClintock, A Stefanovska, “Linear and synchrosqueezed time-frequency
representations revisited: Overview, standards of use, resolution, reconstruction, concentration, and
algorithms”, *Dig Sig Proc* **42**, 1–26 (2015).
2. P Clemson, G Lancaster, A Stefanovska, “Reconstructing time-dependent dynamics”, *Proc IEEE*
**104**, 223–241 (2016).
3. G Lancaster, D Iatsenko, A Pidde, V Ticcinelli, A Stefanovska, “Surrogate data for hypothesis testing of
physical systems”, *Phys Rep* **748**, 1–60 (2018).

#### Wavelet Phase Coherence
1. Bandrivskyy A, Bernjak A, McClintock P V E, Stefanovska A, “Wavelet phase coherence analysis:
Application to skin temperature and blood flow”, *Cardiovasc Engin* **4**, 89–93 (2004).
2. Sheppard L W, Stefanovska A, McClintock P V E, “Testing for time-localised coherence in bivariate
data”, *Phys. Rev. E* **85**, 046205 (2012).

#### Ridge Extraction & Filtering
1.  D Iatsenko, P V E McClintock, A Stefanovska, “Nonlinear mode decomposition: A noise-robust,
adaptive decomposition method”, *Phys Rev E* **92**, 032916 (2015).
2. D Iatsenko, P V E McClintock, A Stefanovska, “Extraction of instantaneous frequencies from ridges in
time-frequency representations of signals”, *Sig Process* **125**, 290–303 (2016).

#### Wavelet Bispectrum Analysis
1. J Jamšek, A Stefanovska, P V E McClintock, “Wavelet bispectral analysis for the study of interactions
among oscillators whose basic frequencies are significantly time variable”, *Phys Rev E* **76**, 046221
(2007).
2. J Jamšek, M Paluš, A Stefanovska, “Detecting couplings between interacting oscillators with
time-varying basic frequencies: Instantaneous wavelet bispectrum and information theoretic approach”,
*Phys Rev E* **81**, 036207 (2010).
3. J Newman, A Pidde, A Stefanovska, “Defining the wavelet bispectrum”, submitted (2019).

#### Dynamical Bayesian Inference
1. V N Smelyanskiy, D G Luchinsky, A Stefanovska, P V E McClintock, “Inference of a nonlinear stochastic model of the cardiorespiratory
interaction”, *Phys Rev Lett* **94**, 098101 (2005).
2. T Stankovski, A Duggento, P V E McClintock, A Stefanovska, “Inference of time-evolving coupled dynamical systems in the presence of noise”,
*Phys Rev Lett* **109**, 024101 (2012).
3. T Stankovski, A Duggento, P V E McClintock, A Stefanovska, “A tutorial on time-evolving dynamical Bayesian inference”, *Eur Phys J – Special
Topics* **223**, 2685-2703 (2014).
4. T Stankovski, T Pereira, P V E McClintock, A Stefanovska, “Coupling functions: Universal insights into dynamical interaction mechanisms”, *Rev
Mod Phys* **89**, 045001 (2017).
5. Special issue of the *Philos Trans Royal Soc A* (2019) with contributions by Kuramoto and others.

# Example applications

#### Wavelet Phase Coherence
1. Sheppard L W, Vuksanović V, McClintock P V E, Stefanovska A, Oscillatory dynamics of
vasoconstriction and vasodilation identified by time-localized phase coherence *Phys Med Biol*
**56**, 3583–3601 (2011).
2. A Bernjak, J Cui, S Iwase, T Mano, A Stefanovska, D L Eckberg, “Human sympathetic outflows to skin
and muscle target organs fluctuate concordantly over a wide range of time-varying frequencies”, *J
Physiol* **590**, 363–375 (2012).
3. P Kvandal, L Sheppard, S A Landsverk, A Stefanovska, K A Kirkebøen, “Impaired cerebrovascular
reactivity after acute traumatic brain injury can be detected by wavelet phase coherence analysis of the
intracranial and arterial blood pressure signals”, *J Clin Monit Comput* **27**, 375-383 (2013).

#### Ridge Extraction & Filtering
1. D Iatsenko, A Bernjak, T Stankovski, Y Shiogai, P J Owen-Lynch, P B M Clarkson, P V E McClintock,
A Stefanovska, “Evolution of cardiorespiratory interactions with age”, *Phil Trans R Soc A* **371**,
20110622 (2013).
2. V Ticcinelli, T Stankovski, D Iatsenko, A Bernjak, A E Bradbury, A R Gallagher, P B M Clarkson, P V
E McClintock, A Stefanovska, “Coherence and coupling functions reveal microvascular impairment in
treated hypertension”, *Front Physiol* **8**, 749 (2017).
3. YA Abdulhameed, G Lancaster, PVE McClintock, A Stefanovska, “On the suitability of laser-Doppler
flowmetry for capturing microvascular blood flow dynamics from darkly pigmented skin”, *Physiol Meas*,
**40**, 074005 (2019).

#### Wavelet Bispectrum Analysis
1. J Jamšek, A Stefanovska, P V E McClintock, “Nonlinear cardio-respiratory interactions revealed by
time-phase bispectral analysis”, *Phys Medicine Biol* **49**, 4407 (2004).

#### Dynamical Bayesian Inference
1. B Musizza, A Stefanovska, P V E McClintock, M Paluš, J Petrovčič, S Ribarič, F F Bajrović, “Interactions between cardiac, respiratory and
EEG-delta oscillations in rats during anaesthesia”, *J Physiol* **580** 315–326 (2007).
2. T Stankovski, V Ticcinelli, P V E McClintock, A Stefanovska, “Coupling functions in networks of oscillators”, *New J Phys* **17**, 035002 (2015).
3. T Stankovski, S Petkoski, J Ræder, A F Smith, P V E McClintock, A Stefanovska, “Alterations in the coupling functions between cortical and
cardio-respiratory oscillations due to anaesthesia with propofol and sevoflurane”, *Philos Trans Royal Soc A* **374**, 20150186 (2016).
4. V Ticcinelli, T Stankovski, D Iatsenko, A Bernjak, A E Bradbury, A R Gallagher, P B M Clarkson, P V E McClintock, A Stefanovska, “Coherence
and coupling functions reveal microvascular impairment in treated hypertension”, *Front Physiol* **8**, 749 (2017).

MODA

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