09:00  09:30

Alejandro Frery
(Victoria University of Wellington)
A Test for White Noise in the EntropyComplexity Plane (virtual)
We seek for a better understanding of the statistical properties of points in the EntropyComplexity plane by proposing a test for the white noise hypothesis. Our test is based on true white noise sequences obtained from physical devices. The proposed methodology provides consistent results: it assesses sequences of true random samples as random (adequate test size), rejects correlated and contaminated sequences (sound test power), and captures the randomness of generators previously analyzed in the literature.

09:30  10:00

Hiroshi Gotoda
(Tokyo University of Science)
Ordinal patternbased analysis of spatiotemporal dynamics in flame and combustion instabilities (virtual)
Recent progress in the ordinal patternbased analysis has opened up a new pathway as an important platform for understanding various dynamic behavior emerging in nonlinear systems, and has yielded significant success in the field of combustion physics and science, mainly achieving two aims: (i) an indepth physical interpretation of nonlinear dynamics and (ii) the development of substitute detectors for capturing the onset of combustion instabilities. Gotoda and coworkers have adopted the ordinal patternbased analysis for wide spectrum of combustion phenomena including fame instability induced by swirl/buoyancy coupling (H. Gotoda et al., Phys. Rev. E 95, 022201, 2017), a buoyant turbulent fire (K. Takagi et al., Phys. Rev. E 96, 052223, 2017; K. Takagi and H. Gotoda, Phys. Rev. E, 98, 032207, 2018), a propagating flame in a HeleShaw cell (Y. Nomi et al., Phys. Rev. E 103, 022218, 2021; Y. Nomi et al., Chaos 31, 123133, 2021), and thermoacoustic combustion oscillations (S. Murayama et al., Phys. Rev. E 97, 022223, 2018; T. Hachijo et al., Chaos 29, 103123, 2019; C. Aoki et al., J. Appl. Phys. 127, 224903, 2020). In this workshop, we present the usefulness of the ordinal patternbased analysis for dealing with nonlinear dynamics of flame front and combustion instabilities.

10:00  10:30

Piergiulio Tempesta
(Complutense University of Madrid)
A unified approach to the ordinal analysis of deterministic and random processes I: complexity classes and group entropies (virtual)
Generalized entropies can play a crucial role in the characterization of the complexity of a large class of deterministic and random processes.
In the first part of this talk, we will show that an intrinsic group¬theoretical structure is at the heart of the notion of generalized entropy. This structure emerges when imposing the requirement of composability of an entropy with respect to the union of two statistically independent systems. A generalization of the celebrated Shannon¬Khinchin set of axioms is proposed, obtained by replacing the additivity axiom with that of composability. This formulation, which makes use of the theory of formal groups of algebraic topology, leads to the new, infinite family of nontraceform entropies called group entropies. The first example of this class is represented by the classical Renyi entropy.
We will show that complex systems can be classified into universality classes, each characterized by a specific phase space growth rate, and described by a suitable group entropy, representing the complexity measure associated to the universality class. The volume of phase space may also grow superexponentially with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. We discuss how the axiomatically based group entropies are able to ensure extensivity in the microcanonical ensemble for superexponentially growing phase spaces and in fact for any monotonously increasing phase space volume.
Group entropies are also relevant in information geometry, since they allow to define a new class of divergences generalizing the KullbackLeibler one.
The applications of the new theory of group entropies to the ordinal analysis of a wide class of random processes will be presented by J. M. Amigó in the second part of the talk.
Joint work in collaboration with J. M. Amigó (CIOElche), R. Dale (CIOElche), H. Jensen (Imperial College, London).

10:30  11:00

Coffee break

11:00  11:30

Ulrich Parlitz
(Max Planck Institute for Dynamics and SelfOrganization)
Characterizing multivariate time series in live sciences using ordinal patterns (onsite)
Multimodal measurements in biomedical physics provide ample multivariate and spatiotemporal time series of cardiac and neural activities, including EEG and ECG time series, optical mapping (using fluorescent dyes), 4D Ultrasound, and realtime MRI. To analyze and classify these data in clinical diagnosis and preclinical experiments fast algorithms are required which are robust with respect to observational noise and other artifacts. In this presentation we will discuss how statistics of spatiotemporal ordinal patterns may address these (medical) needs using practical examples.

11:30  12:00

Reik Donner
(Hochschule MagdeburgStendal)
Causal inference from multivariate time series using transition network representations based on ordinal patterns, graphlets and event synchrony (onsite)
In recent years, the construction and analysis of ordinal pattern transition networks (OPTNs) from time series has provided new means for complexity characterization and coupling inference from observational time series.
In my presentation, I will demonstrate an extension of the recently developed bivariate OPTN analysis framework to multivariate situations based on proper conditioning on the occurrence of patterns obeyed by any third time series. The presented methodology does not only allow identifying coupling directions and delays, but also distinguishing direct from indirect coupling configurations. The power of the proposed methodology is investigated based on numerical studies of different types of examples including coupled linear stochastic processes, Lorenz63 systems and networks of neural mass models.
Finally, I will discuss some recent ideas on combining concepts used in the analysis of ordinal patterns with alternative approaches, including the replacement of classical ordinal patterns by other types of subsequence specific discrete graphlets (e.g. visibility graphlets) and the exploitation of synchronous occurrences of specific (ordinal or graphlet) patterns in a time series using event coincidence analysis.

12:00  12:30

Inga Kottlarz
(Max Planck Institute for Dynamics and SelfOrganization)
Ordinal Patterns as Robust Biomarkers in Multichannel EEG Time Series (onsite)
By: Inga Kottlarz, Sebastian Berg, Diana ToscanoTejeida, Iris Steinmann, Mathias Bähr, Stefan Luther, Melanie Wilke, Ulrich Parlitz and Alexander Schlemmer
We extract ordinal pattern based features from multichannel EEG time series to differentiate between different age groups and individuals. We consider functional connectivity in the form of ordinal patternbased mutual information and single channel features in the form of the pattern distributions in each individual EEG channel. Both functional connectivity and singlechannel features are subjected to nonlinear dimensionality reduction using tdistributed stochastic neighbor embedding. We analyze the separation of EEGs from different age groups and individuals and demonstrate that ordinal patternbased measures yield results comparable to frequencybased measures applied to preprocessed data, and outperform them if applied to raw data. Our analysis yields no significant differences in performance between singlechannel features and functional connectivity features regarding the question of age group separation.
References:
I. Kottlarz et al. “Extracting Robust Biomarkers From Multichannel EEG Time Series Using Nonlinear Dimensionality Reduction Applied to Ordinal Pattern Statistics and Spectral Quantities”. In: Front. Physiol. 11 (2021), p. 1790. doi: 10.3389/fphys.2020.614565.

12:30  13:30

Lunch break

13:30  14:30

Informal discussions

14:30  15:00

Luciano Zunino
(National Scientific and Technical Research Council, Buenos Aires)
A versatile ordinal distance for time series analysis (virtual)
In this presentation, the permutation JensenShannon distance (PJSD) is introduced. It is a symbolic metric able to quantify the ordinal similarity between two arbitrary time series. Based on the fusion of two wellknown concepts, namely, the JensenShannon divergence and the ordinal encoding scheme, the PJSD inherits all the important advantages associated with them: simplicity, low computational cost, noise robustness and wide applicability. Consequently, large amounts of data with outliers and artifacts can be efficiently handled with this quantifier, making it especially suited to deal with the current big data challenges. It is worth emphasizing its versatility, since hypothesis tests related to the nature of an arbitrary time series can be easily carried out by estimating its PJSD to reference time series appropriately generated according to the null model. Several numerical and experimental analyses illustrate this versatility as well as the robustness for characterizing and classifying time series. For all these reasons, the proposed ordinal distance seems to be a promising addition to the repertoire of existing methods for complex signals analysis.

15:00  15:30

Fernando Montani
(Universidad Nacional de La Plata)
Rhythms pattern activity and collective oscillations in neural structures: exploring the role of the different frequency bands (virtual)
The multiple sensations experienced by our body are accompanied by exchanges of information in the form of electrical signals within the brain. These electrical signals can be waves, like the way radio waves are used to broadcast music from the transmitter to the receptors. In the brain, different areas can function as transmitters or receivers of signals depending on the situation. Neural oscillations, or brain waves, are rhythmic or repetitive patterns of neural activity in the cortex. The interaction between neurons can result in oscillations with a different frequency from the one associated with the firing of individual neurons as depends on the possible rules of synaptic strength between neurons. These neuronal oscillations are a fundamental mechanism that allows synchronization of neuronal activity within and between brain regions. The mechanism facilitates precise temporal coordination of the neural processes underlying cognition, memory, perception, and behavior.
Synchronization in neural networks has attracted a lot of attention in recent years, focusing on the type of transitions of different oscillations’ patterns in the network. Whether the transition could appear as a continuous or a burst it could depend on the structure of the network, as well as synaptic plasticity rules. We consider the effect of synaptic interaction as well as structural connectivity on the synchronization transition in network models, of regularly spiking neurons, with different neuronal rhythms. Synaptic strength depresses low activation and enhances high activation of postsynaptic neurons. Importantly, triplet models of spiketimingdependent plasticity (STDP) have shown to describe accurately plasticity experiments that the classical STDP rule, based on spiking pairs, failed to capture. We consider a triplet model of STDP that depends on the interactions of three synchronized spikes with a network of excitatory and inhibitory neurons, emulating the activity of the cortex. We study the dynamic evolution of the triplet model with STDP synchronization, contrasting it to a classical pairwise model. Then the electrical recordings in patients with refractory epilepsy is investigated to discern the underlying oscillatory mechanisms during the epileptic process. For this, neuronal activity is studied for basal (far from the seizure) and preictal (immediately before the seizure) periods through recordings of intracerebral electrodes implanted in patients to achieve a greater resolution of the local field potential. We explore how the combination of pairwise and triplets STDP models can reproduce the observed dynamics. The intrinsic dynamics of the two types of records is discerned by using a time windows analysis and studying the amplitude and phase couplings for each signal. The causality of these records is quantified through information theory tools and a symbolic method of analysis that accounts for the ordinal structure of the time series, showing an enhancing of information of brain oscillations in the range of high frequencies.

15:30  16:00

Helena Bordini de Lucas
(Federal University of Alagoas)
A symbolic information approach to characterize responserelated differences in cortical activity during a Go/NoGo task (virtual)
How the brain processes information from external stimuli in order to perceive the world and act on it is one of the greatest questions in neuroscience. To address this question, different time series analyses techniques have been employed to characterize the statistical properties of brain signals during cognitive tasks. Typically, responsespecific processes are addressed by comparing the time course of average eventrelated potentials in different trials type. Here, we analyze monkey local field potentials data during visual pattern discrimination called Go/NoGo task in the light of information theory quantifiers. We show that the Bandt–Pompe symbolization methodology to calculate entropy and complexity of data is a useful tool to distinguish responserelated differences between Go and NoGo trials. We propose to use an asymmetry index to statistically validate trialtype differences. Moreover, by using the multiscale approach and embedding time delays to downsample the data we can estimate the important time scales in which the relevant information has been processed.

16:00  16:30

Coffee break

16:30  17:00

Massimiliano Zanin
(Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSICUIB))
Analysing gait through ordinal patterns (onsite)
Gait is a basic cognitive purposeful action, essential for the survival of the individual, and hence highly controlled by the Central Nervous System. When gait is altered, for instance due to neurodegenerative dementias or other lesions, a series of compensatory mechanisms are deployed to maintain this basic functionality. It is thus not surprising that gait study, and instrumental gait analysis (IGA) in particular, has been receiving increasing attention in the last few years, for being the complex result of the interactions between different brain motor areas, and thus a proxy in the understanding of the underlying neural dynamics. In spite of this, our understanding of gait, and especially of its potential use as a biomarker of initial cognitive decline, is hitherto limited. In this talk I will review some recent results on the use of ordinal patterns in the analysis of kinematic and spatiotemporal parameters obtained with IGA, in Mild Cognitive Impairment, mild Alzheimer’s Disease, and cerebral palsy.

17:00  17:30

Johann Martínez
(Spanish National Research Council)
Football & brain as simple examples of OrdPatt versatility (onsite)
Nowadays, Ordinal Patterns (OrdPatt) can be considered a crossdisciplinary field of research where scientists all along the globe work together to find new theoretical developments, challenges, and applications. Regarding the latter, applying OrdPatt for capturing the content of information of real and finite samples has been the hallmark in recent years. As an enthusiastic researcher, I have had the opportunity to work with OrdPatt in systems supposedly different from each other, and this talk goes in this line. This is just a simple talk where I want to exemplify how versatile OrdPatt are by tackling one of the main paradigms in complexity science: the bridge between topology and dynamics of a system, specifically, how the structure may influence its dynamics. I am going to talk about some common points between football and the brain from the viewpoint of complex systems, and how the OrdPatt were key at capturing both the inner dynamics of the networks’ nodes and the content of information of its evolving structure.

17:30  18:30

Discussion session on 'Ordinal Patterns and Machine Learning'

18:30  19:30

Dinner at the PKS cafeteria

19:30  20:00

Informal discussions
