Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives

Poster Session

The prefered size of the posters is A0 or ArchE portrait (i.e. higher than wide). A hook will be available for hanging as well as material for fixing the posters in the support.

General schedule

Poster presentation is grouped by topics.

Session 1: Wednesday, March 15th, 18:20–21:00
Groups I, P, C, T
Session 2: Thursday, March 16th, 10:45–12:15
Groups B, S, M, W

Session 1: Wednesday, March 15th, 18:20–21:00

Group C: Concepts from complex systems – networks, synchronisation, recurrence


C1	A. Tiganouria, M. Pavlidou, D. Valavanis, D. Spanoudaki, Ch. Gkili, D. Sazou	Recurrence analysis of the complex dynamics of an electrochemical oscillator comprising the destabilization of iron induced by halides under current-controlled conditions
			The potential oscillations assigned to the halide-induced destabilization of the protective iron oxide observed, under current-controlled conditions, were analyzed using recurrence plots (RPs) and recurrence quantification analysis (RQA). It was found that RQA is efficient in identifying the transitions between different states of the passivation mechanism, determined by the rate of oxide growth and its breakdown. Breakdown of the oxide is initiated by halides acting competitively to the oxide growth. At relatively low halide concentrations (<30 mM) the passive state is rapidly established, and its destabilization appears to be a relatively slow process, which at a critical moment causes a major collapse of the protective oxide film. This step occurs suddenly and leads to the transition of iron to its active state. An oxide-free surface is then exposed to the aggressive environment for a while, before its repassivation. At relatively high halide concentrations (>30 mM), full iron passivation is prevented. Instead, rhythmic passivation events now occur, depending on the localized conditions established on the iron surface. It is shown that in both cases, increasing the applied current facilitates repassivation and increases the time the system spent in the passive state. A correlation between either the instant collapse of the passive state or the instant attainment of the passive state and RQA measures was found. In summary, this investigation shows that RQA measures may distinguish between two distinct situations associated with the stability of the iron: (i) a mostly passive state regime, with passive-active transitions, during which the active state is reached for a very short time; and (ii) a reversed behavior, with the active-passive transitions prevailing, and the iron reaching the passive state only briefly. The latter case is characterized by worse metal stability and increased metal weight loss. Finally, the greater aggressiveness of chlorides in comparison with bromides, as well as their notable effect on the stability of the iron passive state, are reflected in RQA measures.
C2	Abinesh Ganapathy, Ankit Agarwal	Multi-scale SST-Streamflow connectivity: A complex network approach
			The current study examines the association of global SST and streamflow in Germany at different timescales, ranging from seasonal to interannual, by integrating wavelet transform and complex network techniques. Most studies exploring this connection only focus on a single timescale; however, consideration of various atmospheric and oceanic large-scale phenomena occurring at different temporal scales is important. Germany is divided into three regions, viz. Alpine, Atlantic and Continental, based on its streamflow regime. The decomposition of the time series into multiple frequency signals is carried out using wavelet transform, and the network theory is employed on these decomposed signals to identify the spatial connections based on the 99 percentile correlation coefficient. The degree centrality metric is used to evaluate the characteristics of the spatially embedded networks. Our results re-establish known SST regions that have a potential connection with the various streamflow regions of Germany. Spatial patterns that resemble the North Atlantic SST tripole-like pattern is predominant for Alpine streamflow regions at finer timescale. Equatorial Atlantic Mode regions observed for Atlantic streamflow at interannual timescale and Vb weather system connected regions in the Mediterranean Sea have appeared for all the streamflow regions of Germany. Besides, continental streamflow regions exhibited combined characteristics of the Alpine and Atlantic streamflow spatial patterns. In addition to the above regions, we also identify the scale-specific patterns in the Pacific, Indian and Southern Ocean regions at different timescales.
C3	Akhilesh Nandan, Aneta Koseska	Role of transient dynamics versus fixed points in cellular sensing and responsiveness to dynamic spatial-temporal signals
			Under physiological conditions, cells continuously sense and migrate in response to local gradient cues which are irregular, conflicting, and changing over time and space. This suggests cells exhibit seemingly opposed characteristics, such as robust maintenance of polarized state longer than the signal duration while remaining adaptive to novel signals. However, the dynamical mechanism that enables such sensing capabilities is still unclear. Here we propose a generic dynamical mechanism based on the critical positioning of the receptor signaling network in the vicinity of saddle node of a sub critical pitchfork bifurcation (SubPB mechanism). The dynamical ghost that emerges at the critical organization gives transient memory in the polarized response, as well as the ability to continuously adapt to changes in signal localization. Using weakly nonlinear analysis, an analytical description of the necessary conditions for the existence of this mechanism in a general receptor network is provided. By using a physical model that couples signaling to morphology, we demonstrate how this mechanism enables cells to navigate in changing environments. Comparing to three classes of existing mathematical models for the polarization that operate on the principle of stable attractors (Wave pinning, Turing, and LEGI models), we show that the metastability arising from ghost in the SubPB mechanism uniquely enables sensing dynamic spatial-temporal signals in a history dependent manner.
C4	Alexander Schlemmer, Inga Kottlarz, Baltasar Rüchardt, Ulrich Parlitz, Stefan Luther	Improving Findability and Reproducibility of Research Data using Semantic Data Management with CaosDB
			Semantic data management is a powerful concept for managing complex heterogeneous data. The open source project CaosDB provides a framework that is especially suited for scientific data and has been successfully applied in different fields of research. Here we would like to focus on two important aspects of data-intensive research: Findability and Reproducibility. To allow reproducibility, it must be ensured that software, data and meta data are sufficiently documented. This documentation must also be easily findable in order to perform continued research on this data. We show how simple guidelines for creating a human- and machine-readable documentation of digital scientific workflows can lead to a high degree of reproducibility. We demonstrate, how this approach can be combined with semantic data management using CaosDB to simplify findability and interoperability. References: Fitschen, T.; Schlemmer, A.; Hornung, D.; tom Woerden, H.; Parlitz, U.; Luther, S.: CaosDB -- Research Data Management for Complex, Changing, and Automated Research Workflows. Data 2019, 4, 83
C5	Matheus Hansen, Paulo R. Protachevicz, Kelly C. Iarosz, Ibere L. Caldas, Antonio M. Batista, Elbert E. N. Macau	The effect of time delay for synchronisation suppression in neuronal networks
			We study the time delay in the synaptic conductance for suppression of spike synchronisation in a random network of Hodgkin Huxley neurons coupled by means of chemical synapses. In the first part, we examine in detail how the time delay acts over the network during the synchronised and desynchronised neuronal activities. We observe a relation between the neuronal dynamics and the synaptic conductance distributions. We find parameter values in which the time delay has high effectiveness in promoting the suppression of spike synchronisation. In the second part, we analyse how the delayed neuronal networks react when pulsed inputs with different profiles (periodic, random, and mixed) are applied to the neurons. We show the main parameters responsible for inducing or not synchronous neuronal oscillations in delayed networks.
C6	Gonzalo Contreras, Miguel Romance, Regino Criado	Parametric control of PageRank on real network data
		One of the sparks which ignited the study of complex networks of the last two decades was the invention of the PageRank algorithm in 1998 by Brin and Page. This algorithm to the Internet by storm, and soon attracted a lot of attention of attention from the network science community. Initially, a vast amount of research was poured in the understanding of the role of the damping factor $\alpha$. However, one quickly realizes that the behavior of the different rankings one can obtain is highly dependent on the personalization vector $\mathbf{v}$ too. In this poster we study the extent of the control one can exert on the network centrality defined by the PageRank centrality measure. In order to present these results, we resort to a geometrical description of the PageRank algorithm, which shines a light on the problem of centrality ranking control. We later numerically examine the consequences of the proven theorems, which confirm the reliability of the PageRank algorithm as a source of trustworthy importance, and we apply this new methodology to several real network data sets.
C7	J. S. Armand Eyebe Fouda, Wolfram Koepf	The permutation largest slope network: Concept and applications
		The permutation largest slope entropy (PLSE) has been shown effective to distinguish between regular and non-regular dynamics and estimate the period of limit-cycles. However, it fails to detect limit-cycles with large periods under the embedding dimension constraint. This talk presents the concept of the permutation largest slope network (PLSN) as a complementary tool for the interpretation of the entropy values. Permutation largest slopes derived from embedding vectors of the underlying time series are considered as the network nodes. The PLSN is then constructed by considering connections between the different nodes. Likewise, as the PLSE is computed from node probability, we defined the PLSN entropy (PLSNE) by considering the node edge probability. Thereby, we observed that limit-cycles are represented by a network with proportionally distributed edge weights, whereas non-regular dynamics do by randomly distributed edge weights. Some examples of applications using well-known dynamical systems are presented to show how far is enhanced the interpretation of entropy results by the network plot, hence the characterization of the underlying dynamics.
C8	Jonathan F. Donges, Jakob Lochner, Niklas Kitzmann, Jobst Heitzig, Sune Lehmann, Marc Wiedermann, Jürgen Vollmer	Dose-response functions and surrogate data models for exploring complex social contagion and tipping dynamics
			Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other non-linear phenomena in complex human and natural systems. Increasing amounts of temporal network data are now becoming available to study such spreading processes of behaviours, opinions, ideas, diseases and innovations to test hypotheses regarding their specific properties. To this end, we here present a methodology based on dose-response functions and hypothesis testing using surrogate network data models that randomise most aspects of the empirical data while conserving certain structures relevant to contagion, group or homophily dynamics. We demonstrate this methodology for synthetic temporal network data of spreading processes generated by the adaptive voter model. Furthermore, we apply it to empirical temporal network data from the Copenhagen Networks Study and to study the global spreading dynamics of bus rapid transport systems, a sustainability innovation in the transport sector. The proposed methodology is generic and promising also for applications to a broader set of temporal network data sets and traits of interest.
C9	José Angel Mercado Uribe, Jesus Mendoza Avila, Denis Efimov, Johannes Schiffer	Global Synchronization Analysis of Acyclic Networks of Heterogeneous Kuramoto Oscillators
		Global synchronization properties of acyclic networks of Kuramoto oscillators with heterogeneous coupling strengths and natural frequencies are established. To this end, we employ the Leonov function framework, which can be applied to systems whose dynamics are periodic with respect to some or all state variables. By using this approach, we construct a suitable Leonov function for the Kuramoto model and obtain sufficient conditions for almost global synchronization of the system. The result is accompanied by necessary and sufficient conditions to guarantee the existence of equilibria. The implications of the proposed conditions on the network topology as well as the oscillator's coupling strengths and natural frequencies are discussed. Furthermore, the results are illustrated via a numerical example.
C10	L. Alexandre, W. Duch, L. Furman, K. Tolpa	Recurrence analysis of brain neurodynamics

C11	Matheus Palmero, Iberê Caldas, Igor Sokolov	Recurrence analysis of chaotic trajectories: Application in tokamaks
		In this work, we show that recurrence analysis of chaotic trajectories in non-linear Hamiltonian systems provides useful prior knowledge of their dynamical behaviour. By defining an ensemble of initial conditions, evolving them until a given maximum iteration time, and computing the recurrence rate of each orbit, it is possible to find particular trajectories that widely differ from the average behaviour. We show that orbits with high recurrence rates are the ones that experience stickiness, phenomena where the trajectories are dynamically trapped in certain regions of the system's phase space. We analyse the ergodic magnetic limiter map, or Ullmann map, a symplectic model that qualitatively describes the magnetic field lines of a tokamak assembled with an ergodic magnetic limiter, a device that periodically perturbs the magnetic configuration on the plasma edge. This selected approach is proposed as a general method for different Hamiltonian systems with diverse applications. The method is suitable to visually illustrate and characterise particular regions of the space that indicate very distinct dynamical behaviours.
C12	Matheus R. Sales, Michele Mugnaine, José D. Szezech Jr., Ricardo L. Viana, IbeIberê L. Caldas, Norbert Marwan, Jürgen Kurths	Characterizing stickiness using recurrence time entropy
			The stickiness effect is a fundamental characteristic of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and show that each mode corresponds to the motion around islands of different hierarchical levels.
C13	Matthias Wolfrum	Phase sensitive excitability of a limit cycle
			The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear threshold-like behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like response appears only after perturbations applied within a certain part of the periodic orbit, i.e the excitability happens to be phase sensitive. As a paradigmatic example of this concept we employ the classical FitzHugh-Nagumo system. The relaxation oscillations, appearing in the oscillatory regime of this system, turn out to exhibit a phase sensitive nonlinear threshold-like response to perturbations, which can be explained by the nonlinear behavior in the vicinity of the canard trajectory. Triggering the phase sensitive excitability of the relaxation oscillations by noise we find a characteristic non-monotone dependence of the mean spiking rate of the relaxation oscillation on the noise level. We explain this non-monotone dependence as a result of an interplay of two competing effects of the increasing noise: the growing efficiency of the excitationand the degradation of the nonlinear response.
C14	Miwa Fukino, Yoshito Hirata, Kazuyuki Aihara	Comparing music waveform and its MIDI by their hierarchical recurrence plots
			We introduce a method for using a recurrence plot (Marwan et al., 2007) for music analysis. A recurrence plot is one of the important tools for analyzing the nonlinear properties behind time series data. It takes the same time series for both the vertical and horizontal axes. If the distance between the points for two times is close, a dot is plotted at the corresponding two-dimensional place. If the distance is far, a dot is not plotted there. In recurrence plots, a sampling rate of the time series is usually kept at a constant interval, and 10,000 points or less is an appropriate length to ensure the visibility of the resulting plots. In this presentation, we compare two formats of recorded musical performance data, namely sampled acoustic waveforms and MIDI (Musical Instrument Digital Interface), from the viewpoints of their time series characteristics. First, we show an analysis method of acoustic waveforms of music. In the case of acoustic waveforms in CD, the sampling rate is 44.1 kHz, and thus a five-minute song contains $44100 \cdot 60 \cdot 5 = 13.23$ million points. That is too long to be represented in a recurrence plot. Instead, we proposed our method called Recurrence Plot of Recurrence Plots (RPofRPs) (Fukino et al., 2016), which uses recurrence plots hierarchically in two layers to solve this problem. Next, we show how to analyze MIDI, which is a standard format for recording performance information with electronic musical instruments and computers. In MIDI, the sampling period is not constant. It is discrete data which records such as the onset time, duration, and volume (velocity) of each pitch (note number) of each timber. We describe how to calculate RPofRPs of MIDI data as a marked point process by using the edit distance for marked point processes (Suzuki et al., 2010, Hirara et al., 2012). We regard a set of onset times of MIDI as a point process, and duration, note number, and velocity as the marks of the point process. Finally, we discuss the differences for these two types of RPofRPs obtained from the same song by varying parameters of the marked point processes and the RPofRPs.
C15	Nils Antary, Norbert Marwan	Interpolation effects an RQA measures
			The recurrence plot and recurrence quantification analysis (RQA) are well established methods for the analysis of data from complex systems. They provide import insides about the nature of the dynamics, periodicity, regime changes, and many more. This method is used in different fields of research like finance, engineering, life and earth science. In order to use this method the data has usually to be uniformly sampled. This poses a difficulty for data, which is taken from palaeoclimate archives like sediment cores or stalagmite. One frequently used solution is interpolation to generate uniform time series. However, this prepossessing changes the RQA measures like DET, LAM, or the average line length. Using auto-regression processes, we systematically analyse how these measures increase when interpolating the data. For other systems which show a smoother behavior there is only an effect if the interpolation takes place on a time scale close to the characteristic timescale of the system, like the period lengths. For the Roessler system, the RQA measures decrease when approaching this timescale and show a very irregular behavior below. For real data, we show that the course of the DET measure strongly depends on the choice of interpolation.
C16	Paulo R. Protachevicz, Fernando S. Borges, Kelly C. Iarosz, Iberê L. Caldas, Antonio M. Batista, Murilo S. Baptista, Jürgen Kurths	Emergence of highly synchronized firing patterns in neuronal networks
			In the brain cortex, excessive burst synchronization is a characteristic of epileptic activities. Such dynamical behaviour is associated with an unbalanced between excitatory and inhibitory signals. On the other hand, balanced excitatory and inhibitory signals could prevent such activities. For this reason, we investigated the emergence of highly synchronized bursts due to the conductance intensity and time delay in the communication of excitatory and inhibitory neurons in a random neuronal network connected by chemical synapses. As the main result, we found that synchronous burst activities can emerge via a first-order phase transition which is correlated to a hysteretic behaviour of the synchronization and firing pattern. In such a regime, both synchronous and non-synchronous patterns can occur depending on the initial conditions and external perturbations. In this framework, synchronized bursts are associated with epileptic activities, while non-synchronous spikes with non-epileptic ones. Besides that, we found that not only the excitatory and inhibitory balance is sufficient to avoid the highly synchronized behaviour, but also short time delays in the transmission of inhibitory signals. Our results improve the comprehension of how synchronized activities emerge in neuronal networks, pointing some routes to the appearance of epileptic activities, as well as proposing some possible treatments. References P. R. Protachevicz, F. S. Borges, E. L. Lameu, P. Ji, K. C. Iarosz, A. H. Kihara, I. L. Caldas, J. D. Szezech Jr, M. S. Baptista, E. E. N. Macau, C. G. Antonopoulos, A. M. Batista, J. Kurths. Bistable firing pattern in a neural network model. Front Comput Neurosci., 13:19 (2019). P. R. Protachevicz, F. S. Borges, K. C. Iarosz, M. S. Baptista, E. L. Lameu, M. Hansen, I. L. Caldas, J. D. Szezech Jr, A. M. Batista, J. Kurths. Influence of delayed conductance on neuronal synchronization. Front Physiol., 11:1053 (2020).
C17	Rubens Sautter, Reinaldo Rosa, Luan Barauna	Characterizing Nonlinear Spatiotemporal Dynamics by Gradient Pattern Analysis¬†
C18	Shruti Tandon, R. I. Sujith	Multilayer network analysis of turbulent thermoacoustic system
			Thermoacoustic systems are complex systems that comprise acoustic, hydrodynamic and combustion subsystems. Inter-subsystem nonlinear interactions between the acoustic field, heat release rate fluctuations and the underlying turbulent flow leads to a variety of rich dynamics. We study the spatio-temporal dynamics in a turbulent bluff-body stabilized dump combustor. The system exhibits a transition from chaotic to periodic (thermoacoustic instability) dynamics with increase in the Reynolds number of the inlet flow. Such a transition occurs via the state of intermittent spatio-temporal patterns. In order to capture the higher-order complexities in the system arising due to the interaction between the various subsystems we use multi-layered complex networks. We construct a two layered network, where one layer represents the vorticity dynamics and the other layer represents the acoustically-driven combustion subsystem. The nodes of the network are spatial locations in the combustion chamber. The inter-layer links between any two nodes is established using cross-variable short-window correlation between vorticity and thermoacoustic power fluctuations at the corresponding locations. The inter-layer node strength represents the strength of the inter-subsystem interactions. Further, we analyze the topology of the inter-layer network using inter-layer network assortativity and link-rank distribution during various dynamical states to infer the pattern of inter-subsystem interactions. During chaotic dynamics, the inter-subsystem interactions occur predominantly in the wake of the bluff-body in a non-localized manner. On the other hand, during periodic dynamics, the inter-subsystem interactions are intense in regions of coherent vortex shedding. Interestingly, prior to the emergence of such ordered dynamics, we obtain localized pockets of inter-subsystem interactions in the recirculation zone during the state of intermittency. These regions are identified as the hubs of the inter-layer network. The influence of interactions in such localized pockets is also spread across the entire combustion chamber as identified via disassortative network topology. Targeted attack on these hub locations using microjet secondary flow injections can cause disruption of the feedback interactions and help in mitigating the occurrence of thermoacoustic instability. Multilayer network analysis thus reveals the rich pattern of inter-subsystem interactions and helps identify critical regions for passive control of thermoacoustic instability.
C19	Teddy Craciunescu, Andrea Murari	Time series analysis for fusion plasma disruption prediction
			Tokamak plasmas are very complex systems, from both a technological and physical point of view. They are kept well out of equilibrium by continuous injection of matter and megawatts of power. One of the major issues on the route of a commercial tokamak reactor is the occurrence of macroscopic instabilities called disruptions, which cause a complete loss of confinement, the abrupt extinction of the discharge, high thermal loads on the plasma facing components,strong forces on the electromagnetic structures and the generation of beams of runaway electrons in the MeV range. Therefore, preventing disruptions or, at least, mitigating their detrimental effects is extremely important. A series of methods based on the time series analysis of the main plasma diagnostic signals are used to determine when significant changes in the plasma dynamics of the tokamak configuration occur, indicating the onset of drifts towards the plasma disruption. The main changes monitored are related to the embedding dimensions, the structure of the recurrence plots and the transition to chaotic dynamics. A good estimation of the intervals, in which the anomalous behaviours manifest themselves, is very useful for building significantly more appropriate training sets for various kinds of disruption predictors. Some of these methods presented may also be implemented themselves as stand-alone predictors for real time deployment.
C20	Yue Weng, Vishnu R. Unni, R. I. Sujith, Abhishek Saha	Transition to thermoacoustic instability: Modeling order emerging in a complex system using a synchronization framework
			In this study, we introduce a framework based on synchronization to model the transition to thermoacoustic instability in laminar and turbulent combustors. Thermoacoustic instability, which results from the positive feedback between the acoustic field and unsteady heat release rate causes large amplitude oscillations that can damage the hardware. In turbulent conditions, the transition to thermoacoustic instability corresponds to the emergence of order from disorder. Currently, flame transfer function (FTF) and flame describing function (FDF) are used to model the onset of thermoacoustic instability. However, since FTF and FDF are forcing responses, they do not capture the mutual interaction between the flame and the acoustic field. To address this lacuna, we introduce a model using the concept of synchronization and thus capture the complex behaviors and bifurcations observed in the experiment. We model the transition to thermoacoustic instability in a laminar and turbulent system. In the laminar case, we model the system as two damped simple harmonic oscillators that are nonlinearly coupled. With this model, we capture the bifurcation route from no oscillation to periodic oscillation, to quasi-periodic oscillation, to strange non-chaos, and chaos. For the turbulent case, we use two nonlinearly coupled ODEs to generate time series of the unsteady heat release rate from turbulent combustion. This unsteady heat release rate is then coupled to the acoustic oscillator with a variable coupling strength. As the coupling strength changes, the model replicates the transition from combustion noise to periodic oscillation through intermittency. Furthermore, the model captures multifractal characteristics and the power law corresponding to self-organization associated with the transition. We compare these two different transitions and show that the transition to thermoacoustic instability in a turbulent system is unique. That is the system transitions from low-amplitude chaos to high-amplitude periodic oscillations.
C21	Fred Feudel, Ulrike Feudel	The influence of a differential rotation on bifurcations of buoyancy driven spherical shell convection
			We investigate numerically the bifurcation phenomena of buoyancy driven convection in a rotating spherical shell which is heated by imposing a constant temperature difference between the inner and outer spheres, and is subject to a radially directed gravity force. Along with the overall rotation of the fluid shell the influence of a shear generated by a differential rotation between both spheres on the convection pattern is the focus of this work. This configuration is an appropriate model of convection flows in geophysical and astrophysical applications, as, e.g., in the outer cores of terrestrial planets. Due to the imposed differential rotation of both spheres the dynamics for small Rayleigh numbers generates a nonzero basic flow which possesses features of the spherical Couette flow. Increasing the Rayleigh number the axisymmetry of the flow is broken in successive Hopf bifurcations generating new stable branches of rotating waves (RWs) and modulated rotating waves (MRWs), respectively, with an azimuthal mode number m=3. However in comparison to the configuration without differential rotation, now in addition, a new RW branch with no symmetry, $m=1$, bifurcates in a saddle node bifurcation, separated from the other branches. The stable m=3 MRWs and the arising stable $m=1$ RWs are coexisting along a certain interval of the Rayleigh numbers creating a region of bistability. We demonstrate that finally the stable $m=3$ MRW branch collides with an unstable RW branch in an homoclinic bifurcation, and the $m=1$ MRW branch remains in this scenario the only stable branch for larger Rayleigh numbers. In summary, in contrast to the situation with no differential rotation in this configuration a saddle node bifurcation generates a branch with no axial subsymmetry which also enhances the heat transfer in comparison to the other branches and which forms the final attractor after the homoclinic bifurcation.

Group I: Analysis and modeling of infrastructure networks


I1	Angeles Criado-Alonso, David Aleja, Miguel Romance, Regino Criado	A new tool to analyze mesoscopic and centrality relationships in complex networks
		The existence of interactions, connections and relationships of different and simultaneous nature between nodes and edges of a complex network (e.g., group collaborations, chemical reactions in which more than two components interact, \dots) have allowed to show that hypergraphs and multilayer networks are very suitable structures for the analysis of some of these types of interactions. In this poster we present a new tool that relies on several mathematical structures such as hypergraphs, multilayer networks or the concept of derivative graph of a hypergraph to introduce a new methodology able to analyze some mesoscopic and centrality relationships in the field of complex networks. To see the scope of these ideas, we apply this methodology to a real linguistic network to computationally analyze mesoscopic relationships between words, sentences, paragraphs, chapters and texts focusing not only on a quantitative index but also on other elements and mathematical tools that allow, among other things, to analyze similarities and dissimilarities in texts.
I2	Jonas Wassmer, Bruno Merz, Norbert Marwan	Resilience of emergency infrastructure networks after flooding events
		Extreme weather events can drastically influence the dynamics and stability of networked infrastructure systems like transportation networks or power grids. Climate change is increasing the frequency of such events, making their impact on human society and ecosystems increasingly relevant. Prominent examples include damage of critical infrastructure caused by heavy rainfalls and landslides. The devastating floods that struck Germany’s Ahr valley in 2021 are yet another reminder of the threat posed by such extreme events. Due to washed-out roads and further severe infrastructure damages, critical bottlenecks effectively cut off a substantial share of the population from assistance, hampering or even impeding their rescue. In this study, we investigate the impact of flood events on transportation networks where stability is particularly important in order to ensure the accessibility of emergency services. Local changes in the underlying network dynamics can affect the whole road network and, in the worst case, cause a total collapse of the system through cascading failures. Because of the severe consequences of cascading events, we aim to recognise such spreading processes at an early stage and, in a further step, be able to prevent them. To this end, we set up a gravity model of travel to simulate the changes of the traffic load after flooding events to identify vulnerabilities in the system. We further analyse how the accessibility of emergency services is affected and if the population can be effectively reached in time.
I3	Henrik M. Bette, Thomas Guhr	Sensitivity of principal components to changes in the presence of non-stationarity
			Non-stationarity affects the sensitivity of change detection in correlated systems described by sets of measurable variables. We study this by projecting onto different principal components. Non-stationarity is modeled as multiple normal states that exist in the system even before a change occurs. The studied changes occur in mean values, standard deviations or correlations of the variables. Monte Carlo simulations are performed to test the sensitivity for change detection with and without knowledge about the non-stationarity for different system dimensions and numbers of normal states. A comparison clearly shows that the knowledge about the non-stationarity of the system greatly improves change detection sensitivity for all principal components. This improvement is largest for those components that already provide the greatest possibility for change detection in the stationary case
I4	Michael Lindner, Christian Nauck	Graph neural networks beat network science at predicting dynamic stability of sustainable power grids
		A large body of work in network science studies the interplay of network topology with observables of interest. For example, several centrality measures quantify a network's vulnerability to attacks at specific nodes. Recently, Graph Neural Networks have shown great potential for network prediction tasks. They do not rely on explicitly defined network measures but implicitly learn node embeddings from the topology. We compare different predictive models of the highly nonlinear observables single node basin stability (SNBS) and survivability (SURV) in networks of inertial Kuramoto oscillator, which are paradigmatic models of power grids. We explicitly compute a large number of network measures that might be related to SNBS and SURV and provide them as inputs for a linear regression and a multi-layer perceptron. Their performance is then compared to Graph Neural Networks that only receive the network topology and the distribution of sources and sinks as inputs. We study networks of varying size as well as machine learning models with different numbers of trainable parameters and find a remarkable performance of Graph Neural Networks as compared to the more established approaches. While our methods have been developed in the context of power grids, they only rely on general features of complex networks, and may thus be applied to related nonlinear phenomena in other domains as well.
I5	Timo Haselhoff, Tobias Braun, Norbert Marwan, Susanne Moebus	Complex networks for the urban acoustic environment
		The urban acoustic environment (AE) plays an underestimated role in the daily life of residents inhabiting metropolitan regions. The urban AE contains valuable information on complex sub-systems of urban areas, such as traffic, infrastructure and biodiversity. Associations between noise exposure and the mental or physical health of urban residents are an important subject of ongoing research. Despite the extensive information that is recorded by modern acoustic sensors, few approaches are designed to capture the rich complexity embedded in the time-frequency domain of the urban AE. The decreasing costs of acoustic sensors and rapid growth of storage space and computational power have led to an increase of acoustical data to be processed. Quantitative methods need to account for this complexity, while effectively reducing the high dimensionality of terabytes of audio data. We take this as an opportunity to introduce complex networks to the field of urban acoustics. We use one of the world's most extensive longitudinal audio datasets from the SALVE study to systematically characterize the urban AE. SALVE is an ongoing study since 2019, in which 3-min acoustic recordings are made twice per hour at 23 locations in Bochum, Germany. The recorded acoustic samples exhibit a clear diel cycle and reveal site-dependent communities of interlinked frequencies. We demonstrate the utility of frequency-correlation matrices (FCMs) to effectively capture these communities. Based on these results, we construct (functional) networks of day time-specific 3-min audio recordings from 05.2019 to 03.2020 (n = 319,385 = 665 days). We show that the average shortest path length of an acoustic frequency network informs on site- and time-specific distinctiveness of frequency dynamics in the urban AE. To validate our findings, we use the land use mix around each site as a proxy for the AE, as the acoustic environment is heavily impacted by the built environment. The proposed method enables us to clearly identify 4-5 clusters of distinct urban AEs based on hourly variations in the distinctiveness of frequency dynamics. Our results indicate that complex networks represent a promising approach to analyse large-scale audio data and help to understand the time-frequency domain of the urban acoustic environment.
I6	Yunfei Li, Deniz Ural, Caner Aydin, Celine Rozenblat, Jan W. Kantelhardt, Diego Rybski	Indication of long-range city size correlation analysis based on city networks of European countries
			City systems are characterized by the functional organization of cities on a regional or country scale. While there is a relatively good empirical and theoretical understanding of city size distributions, insights about their spatial organization remain on a conceptual level. Here we empirically analyze the correlations between the sizes of cities (in terms of area) across long distances. Therefore, we (i) define city clusters, (ii) obtain the neighbourhood network from Voronoi cells, and (iii) apply a fluctuation analysis along all shortest paths. We find that most European countries exhibit long-range correlations but in several cases these are anti-correlations. In an analogous way we study a model inspired by Central Places Theory and find that depending on the level of disorder, both positive and negative long-range correlations can be simulated. We conclude that the interactions between cities of different sizes extend over distances reaching the country scale.
I7	Patrycja Jaros, Roman Levchenko, Tomasz Kapitaniak, Jürgen Kurths, Yuriy Maistrenko	Asymmetry induces critical desynchronization of power grids
			Dynamical stability of the synchronous regime remains a challenging problem for secure functioning of power grids. Based on the symmetric circular model [Nature Communication 11, 592 (2020)], we demonstrate that the grid stability can be destroyed by elementary violations (motifs) of the network architecture such as cutting a connection between any two nodes or removing a generator or a consumer. We describe the mechanism for the cascading failure in each of the damaging case and show that the desynchronization starts with the frequency deviation of the neighbouring grid elements followed by the cascading splitting of the others, distant elements and ending eventually in the bi-modal or a partially desynchronized state. Our findings reveal that symmetric topology underlines stability of the power grids, while local damaging can cause a fatal blackout.

Group P: Causation and prediction of weather and climate extremes and Nonlinear dynamics in economics


P1	Akash Singh Raghuvanshi, Ankit Agarwal	Linking Anomalous High Moisture Transport to Extreme Precipitation
		Integrated water vapor transport (IVT) is evaluated to assess anomalous high moisture transports (AHMT) over the Indian Subcontinent, the Arabian Sea, and the Bay of Bengal during the 2013 Uttarakhand and 2015 Tamil Nadu flood events. Using a high-resolution daily gridded rainfall data set, an attempt has been made through analysing the spatiotemporal characteristics of whether anomalous high moisture transports (AHMT) are responsible for the occurrence of heavy precipitation events during the same periods. The spatiotemporal characteristics of specific rainfall events associated with the occurrence of AHMT show the existence of a strong relationship between the presence of AHMT and extreme precipitation events for the northwestern region where AHMT penetrates inland (over Uttarakhand in 2013) and for the east coast region where AHMT make landfalls (over Tamil Nadu in 2015). Further analysis suggests that extreme precipitation events are predominantly influenced by the strong moisture convergence associated with the low-level pressure systems, wind speed, and direction developed in the vicinity of affected regions.
P2	Rubens Sautter, Reinaldo Rosa, Pablo Medina, Juan Valdivia	Characterizing Extreme Patterns from Time Series
		The characterization of extreme events (X-events) from time series has witnessed an increase of interest due to the great observational occurrence found in several fields, such as space and environmental physics. Motivated by this challenge, we propose a new parameter space (namely, chi-space) composed of two attributes that identify different classes of extreme fluctuations in a time series. Based on reformulated measures for statistical quantiles and singularity spectra, the distance from the origin of chi-space characterizes the escape from Gaussianity and monofractality that occurs when extreme fluctuations are present in a time series. To generate time series with different patterns of extreme fluctuations, two canonical systems were carefully chosen as illustrative examples: the so-called p-model for multifractal extreme dissipation and the Lorenz chaotic model within an appropriate parameterization scheme where nonlinear noise-like dynamics is considered. The results show that the investigate attributes are able to compose a two-dimensional space in which the patterns of extreme endogenous and exogenous fluctuations can be distinguished with great precision. A third class of extreme fluctuation pattern based on multifractal diffusion is also discussed. The characterization of some observed fluctuation patterns, from space and environmental physics, are presented as a case of practical application.
P3	Tobias Braun, Sara M. Vallejo-Bernal, Dominik Traxl, Norbert Marwan, Jürgen Kurths	A spatio-temporal analysis of global atmospheric rivers
			Atmospheric rivers (ARs) are narrow, transient corridors of extensive water vapor transport in the lower troposphere. The role ARs play in the global water cycle can be regarded as a double-edged sword: while low-intensity ARs provide vital supply of freshwater and are rarely associated with heavy precipitation events (HPEs), high-level ARs can cause detrimental impacts when they land-fall. Detection of ARs is based on localizing anomalous atmospheric transport of moisture. Many approaches define a threshold to identify local anomalies in integrated vapor transport (IVT) in order to obtain catalogues of ARs, effectively assuming stationary atmospheric moisture levels and often excluding low-level ARs. Here, we employ an AR-detection framework (`ARtracks') based on global ERA5 reanalysis data that utilizes image processing techniques (using the IPART algorithm). Our approach allows us to study the spatio-temporal variability of globally distributed AR tracks and potential changes due to increasing atmospheric moisture levels on a warming planet. We implement a scale that characterizes ARs based on their strength and persistence, distinguishing between ARs with potentially beneficial and detrimental impacts. A recent study has demonstrated the scope of this categorized AR catalogue for the analysis of synchronization of ARs and HPEs in North America. We analyse the robustness of our results for distinct parameter choices in the definition of AR tracks. A novel power spectral measure for the analysis of event-like time series enables us to identify significant cycles in AR occurrence. Finally, we discuss the role of land-falling ARs as a trigger of HPEs on a global scale.
P4	Sara M. Vallejo-Bernal, Tobias Braun, Norbert Marwan, Jürgen Kurths	Synchronized heavy rainfall events in Europe: the role of atmospheric rivers
		Atmospheric rivers (ARs) are channels of enhanced water vapor transport in the lower troposphere. They play a crucial role in the fresh water supply of Europe, contributing to up to 30% of the rainfall budget in some regions along the western coast. However, very intense and persistent ARs are important triggers of heavy rainfall events and have been associated with natural and economical damage. Here, we investigate the large-scale spatio-temporal synchronization patterns between heavy rainfall events and landfalling ARs over Europe, during the period from 1979 to 2019. For that, we employ ARtracks, a novel global catalog of ARs, and select the AR events whose footprint intercept Europe. Then, we use an AR-intensity scale to rank the ARs in terms of strength and persistence. Based on ERA5 daily precipitation estimates, we obtain binary time series indicating the absence or presence of heavy rainfall by thresholding the daily precipitation intensity at the 95th percentile. Subsequently, we utilize event synchronization incorporating varying delays to reveal the temporal evolution of spatial patterns of heavy rainfall events in the aftermath of land-falling ARs. Finally, using composites of integrated water vapor transport, geopotential height, upper-level meridional wind, and rainfall, we attribute the formation of the synchronization patterns to well-known atmospheric circulation configurations, depending on the intensity level of the ARs. Our results reveal the role of ARs in the distribution of heavy rainfall events over Europe and advance the understanding of inland heavy precipitation by revealing the characteristic circulation patterns and the main climatic drivers associated to the synchronization patterns.
P5	Shraddha Gupta, Zhen Su, Abhirup Banerjee, Niklas Boers, Norbert Marwan, Linus Magnusson, Cristobal Lopez, Emilio Hernandez-Garcia, Florian Pappenberger and Jürgen Kurths	Spatial synchronization patterns of extreme rainfall and convection in the Asian Summer Monsoon region
		A deeper knowledge about the spatially coherent patterns of extreme rainfall events in the South and East Asian regions is of utmost importance for substantially improving the forecasts of extreme rainfall as their agro-based economies predominantly rely on the monsoon. In our work, we use a combination of a nonlinear synchronization measure and complex networks to investigate the spatial characteristics of extreme rainfall synchronicity in the Asian Summer Monsoon (ASM) region and gain a comprehensive understanding of the intricate relationship between its Indian and East Asian counterparts. We identify two modes of synchronization between the Indian Summer Monsoon (ISM) and the East Asian Summer Monsoon (EASM) – a southern mode between the Arabian Sea and south-eastern China in June which relates the onset of monsoon in the two locations, and a northern mode between the core ISM zone and northern China which occurs in July. Thereafter, we determine the specific times of high extreme rainfall synchronization, and identify the distinctively different large-scale atmospheric circulation, convection and moisture transport patterns associated with each mode. Furthermore, we discover that the intraseasonal variability of the ISM-EASM interconnection may be influenced by the different modes of the tropical intraseasonal oscillation (ISO). Our findings show that certain phases of the Madden-Julian oscillation and the boreal summer ISO favour the synchronization of extreme rainfall events in the June-July-August season between ISM and EASM. The impact of El Nino-Southern Oscillation on the convective sources of the two monsoon subsystems, and thus their interannual variability is investigated.
P6	Giuseppe Orlando, Giovanna Zimatore	Is deterministic chaos present in business cycles?
		The scientific question explored is whether deterministic chaos appears in business cycles and which model between a purely deterministic one like Kaldor-Kalecki or a stochastic process like Ornstein-Uhlenbeck can best simulate reality. When statistical analyses are unable to distinguish between simulations and real-world data, the model can be assumed to be capable of reproducing reality. The methodological approach, statistical tests and a summary of the best results of recent research are briefly described with the aim of laying the foundations for a common comparison and hypothesizing and sharing new investigation strategies.
P7	Haochun Ma, Alexander Haluszczynski, Davide Prosperino, Christoph Räth	Causalities and their drivers in financial data
		Identifying and describing the dynamics of complex systems is a central challenge in various areas of science, such as physics, finance, or climatology. Here, we analyze the causal structure of chaotic systems using Fourier transform surrogates that enables us to identify the different (linear and nonlinear) causality drivers. We further show that a simple rationale and calibration algorithm are sufficient to extract the governing equations directly from the causal structure of the data. We demonstrate the applicability of the framework to real-world dynamical systems using financial data (stock indices from Europe, United States, China, Emerging Markets, Japan and Pacific excluding Japan) before and after the COVID-19 outbreak. It turns out that the pandemic triggered a fundamental rupture in the world economy, which is reflected in the causal structure and the resulting equations. Specifically, nonlinear causal relations have significantly increased in the global financial market after the COVID-19 outbreak [1]. Further differential analyses revealed that that the stock indices in Germany and the U.S. exhibit a significant degree of nonlinear causality and that correlation, while a very good proxy for linear causality, underestimates causality itself [2]. The presented framework enables the measurement of nonlinear causality and motivates methods for inferring market signals, quantifying portfolio risk, and constructing less risky portfolios. Our model suggests that nonlinear causality can be used as an early warning indicator of abnormal market behavior, allowing for more accurate risk management and better portfolio construction. References [1] H. Ma, A. Haluszczynski, D. Prosperino & C. Räth, Identifying causality drivers and deriving governing equations of nonlinear complex systems, Chaos, 32, 103128 (2022) [2] H. Ma, D. Prosperino, A. Haluszczynski & C. Räth, Linear and nonlinear causality in financial markets, Journal of Physics: Complexity (submitted)
P8	Sijmen Duineveld	Projection methods made easy
		We have developed a toolbox to solve Dynamic Stochastic General Equilibrium models with projection methods. Projection methods are especially useful for highly non-linear models, such as those with inequality constraints, attracting limit cycles, or rare disasters. The Promes toolbox (see Matlab file exchange) can greatly reduce coding time to solve such models with projection methods. The toolbox only requires the user to write a model file, define the boundaries of the grid, supply an initial guess for the policy function, and choose an algorithm. The toolbox will then solve for the policy function. The toolbox can approximate a policy function with cubic splines, complete Chebyshev polynomials, or Smolyak-Chebyshev polynomials as basis functions. For near-linear small scale models Chebyshev polynomials in combination with Galerkin's method perform best. For slightly more complex or less linear models splines perform better. For models with a large number of state variables a Smolyak grid is faster than the other methods, due to the sparsity of the grid. In this paper we evaluate the performance of several algorithms in terms of speed and accuracy for three DSGE models. The first model is a standard RBC model, which can be solved in less than 0.05 seconds with all three basis functions, and a maximum error of less than 1e-6. The second model is an RBC model with habits in consumption and investment adjustment costs, which has four state variables. This model can be solved with a maximum error of 1e-5 in about 5 seconds. The third model is a highly non-linear model featuring an attracting limit cycle, which is best solved with a spline.

Group T: Tipping points


T1	Ayanava Basak, Syamal Kumar Dana, Nandadulal Bairagi	Frequency-dependent tipping in driven ecological system
			Ecological systems with time-dependent parameters may tip, and a catastrophic shift to another state may occur due to the drifting of a parameter. The carrying capacity of an ecological system may experience a periodic fluctuation with time-dependent frequency due to anthropogenic reasons, seasonal variation, and global warming. Such a periodic fluctuation is a growing event in aquatic and terrestrial ecosystems caused by human intervention and climate change. Using three paradigmatic population models of different dimensions, we exemplify that the system may tip from its base attractor (stable fixed point, periodic, or chaotic) to another attractor with the extinction of species if the ecosystem's carrying capacity fluctuates periodically with a time-dependent frequency. For such tipping, the drifting frequency function should have the convex property. This frequency-induced tipping (what we call F-tipping) differs from conventional tipping phenomena and is a generic property of ecological systems.
T2	Da Nian, Sebastian Bathiany, Maya Ben-Yami, Lana Blaschke, Marina Hirota, Regina Rodrigues, Niklas Boers	Combined effects of global warming and the collapse of AMOC over South America
			Amazon forest is at risk of dieback from the impact of future climate change on the mean annual precipitation (MAP) and mean annual temperature (MAT). This study assesses the influence on South American vegetation under two possible future climate change scenarios, global warming and global warming combined with an AMOC collapse. The most possible vegetation state can be estimated by the correspondence between the tree cover distribution and MAP through bifurcation theory. This study takes MAT as another control parameter and estimates possible schemes of vegetation state by MAP combined MAT. Comparing vegetation types in current climates to the ones in future scenarios allows the assessment of scheme shifts of vegetation states due to global warming scenario and global warming combined with an AMOC collapse scenario. The results of the scenario shift suggest that AMOC collapse does not contribute to further Amazon rainforest dieback and conversion to Savanna, it even helps to stabilize the Amazon forest and mitigate the system's loss of resilience in the global warming scenario SSP8.5.
T3	Giulio Tirabassi, Cristina Masoller	Entropy-Based Early Detection of Critical Transitions in Spatial Vegetation Fields
			In semi-arid regions, vegetated ecosystems can display abrupt and unexpected changes, i.e., transitions to different states, due to drifting or time-varying parameters, with severe consequences for the ecosystem and the communities depending on it. Despite intensive research, the early identification of an approaching critical point from observations is still an open challenge. Many data analysis techniques have been proposed, but their performance depends on the system and on the characteristics of the observed data (the resolution, the level of noise, the existence of unobserved variables, etc.). Here we propose an entropy-based approach to identify an upcoming transition in spatio-temporal data. We apply this approach to observational vegetation data and simulations from two dynamical models of vegetation dynamics to infer the arrival of an abrupt shift to an arid state. We show that the permutation entropy computed from the probabilities of two-dimensional ordinal patterns may provide an early warning indicator of an approaching tipping point, as it may display a maximum (or minimum) before decreasing (or increasing) as the transition approaches. Like other spatial early-warning indicators, the spatial permutation entropy does not need a time series of the system dynamics, and it is suited for spatially extended systems evolving on long time scales, like vegetation plots. We quantify its performance and show that, depending on the system and data, the performance can be better, similar or worse than the spatial correlation, which is a classic indicator. Hence, we propose the spatial permutation entropy as an additional indicator to try to anticipate regime shifts in vegetated ecosystems.
T4	Jan Swierczek-Jereczek, George Datseris	TransitionIndicators.jl – A high end software to accelerate research and computation of transition indicators
		Tipping phenomena have become increasingly important, and are nowadays routinely studied in diverse fields, such as climate science, ecosystem dynamics and much more. Despite large interest in analyzing tipping points, software implementations have not kept up with the demand. Only a couple of published code bases exist that can help identify tipping, or transitions across states. Unfortunately, they are limited in scope, consider practically only critical slowing down as a transition identification mechanism. Additionally, in a holistic view, including documentation, testing, extend-ability, computational performance, among other factors, we believe that existing software does not reach highest quality possible. We argue that this limits the efficiency with which tipping point research is performed, but also hinters progress in methodological advancements, i.e., developing and implementing new methods that can identify transitions in data. Here we present TransitionIndicators.jl, a pure Julia package that is part of the DynamicalSystems.jl ecosystem and has been developed from scratch following highest quality standards on modern software design. It is easy to use, exceptionally well documented, outperforms existing alternatives, and provides a carefully designed extendable interface for future methodological research.
T5	Reyk Börner, Ryan Deeley, Raphael Römer, Tobias Grafke, Ulrike Feudel, Valerio Lucarini	Limits of large deviation theory in predicting transition paths of tipping events
			Any multistable dynamical system, when driven by noise, will eventually undergo rare but important critical transitions between the competing metastable states. In the weak-noise limit, large deviation theory allows predicting the transition rate and most probable transition path of these tipping events. However, the limit of zero noise is never obtained in reality. In this work we show that, even for weak finite noise, sample transition paths may disagree with the large deviation prediction -- the minimum action path, or instanton -- if multiple timescales are at play. We illustrate this behavior in selected toy models from climate to neuroscience, where the dynamics exhibit a fast-slow characteristic. While the minimum action path generally crosses the basin boundary at a saddle point, we demonstrate cases in which ensembles of sample transition paths cross far away from the saddle. We discuss the conditions for saddle avoidance and relate this to the flatness of the quasipotential, a central object of large deviation theory. Further, we present an alternative approach that correctly determines the most probable transition path in these examples. Our results highlight that methods from large deviation theory must be applied cautiously in multiscale dynamical systems.
T6	Markus Drüke, Boris Sakschewski, Werner von Bloh, Maik Billing, Wolfgang Lucht, Kirsten Thonicke	Fire prevents future Amazon forest recovery after large-scale deforestation
			The Amazon forest is regarded as a tipping element of the Earth system, because of a potential large-scale regime change from tropical forest to woodland savanna and grassland, which could be triggered by anthropogenic land use and climate change. Recent conceptual and data-driven research focused on the hysteresis of such a regime change and found that fire could enhance the irreversibility of large-scale Amazon die-back. However, large-scale feedback analyses which integrate the interplay of fire with climate and land-use change are currently lacking. Here we apply the fire-enabled Earth system model CM2Mc-LPJmL to study such feedback mechanisms in the Amazon. We specifically test the role of fire in Amazon forest recovery under different atmospheric CO2 concentration levels (i.e., the magnitude of climate forcing) after complete deforestation. We find that fire prevents forests from regrowing on an area of 353--515 Mio ha (56--82 % of potential natural forest), depending on atmospheric CO$_2$ concentration. Our simulation results show that fire is a major contributor to the irreversibility of a transition from forest to grassland by locking the Amazon in a stable grassland state. These findings emphasize the urgency of keeping deforestation and atmospheric CO2 concentrations within stable boundaries that would safeguard the Amazon forest.
T7	Taylor Smith, Niklas Boers	Progress on Data Reliability and Processing Best Practices for Resilience Estimation with Satellite Data
			Satellite data is being used in a growing number of studies on ecosystem resilience, and in particular on vegetation resilience. As methods pioneered on model and deep-time studies are increasingly used in new contexts, it is important to take stock of the assumptions surrounding their use, problems particular to satellite data, and how to ensure the reliability of resilience estimation and quantify uncertainties. To address these open questions, we present ongoing work on two key topics: (1) estimating the reliability of resilience estimates from multi-sensor data sets; and (2) examining the role of de-seasoning and de-trending procedures in complex and heterogeneous time series ensembles. Satellite records – particularly at global resolutions and at multi-decade time scales – are highly heterogeneous in both space and time, and require careful consideration of how best to ensure the reliability of resilience estimates. This is particularly true for studies concerned with changing resilience through time, upon which important inferences about the changing state of global ecosystems under climate change are based.

Session 2: Thursday, March 16th, 10:45–12:15

Group M: Methods


M1	Alistair White, Niklas Boers	Stabilized Universal Differential Equations for Hybrid Machine Learning of Conservative Dynamical Systems
			Universal Differential Equations (UDEs) provide a powerful framework for combining dynamical systems with machine learning. In particular, they allow unknown parts of a differential equation model to be parameterized by a universal function approximator, such as a neural network. The result is a hybrid model, containing both process-based and data-driven components. However, the flexibility of the data-driven part of the differential equation comes at the expense of potentially violating known physical constraints, such as conservation laws. This problem is especially critical in applications requiring very long simulations, such as climate modeling, where long-term numerical stability remains one of the main barriers to adoption of hybrid models. In addition, it is hoped that enforcing physical constraints will aid generalization to out-of-sample conditions unseen during training. We introduce Stabilized Universal Differential Equations, which augment a UDE model with compensating terms that ensure physical constraints are approximately satisfied during numerical simulations. Numerical solution of the stabilized system does not require specialized numerical methods, meaning that existing efficient solvers can be used without modification. We apply Stabilized UDEs to the double pendulum and Henon-Heiles systems, both of which are conservative, chaotic dynamical systems with a time-independent Hamiltonian. We show that Stabilized UDE models, unlike their unstabilized counterparts, conserve energy even during very long simulations. In addition, we show that Stabilized UDE models remain numerically stable for significantly longer and reproduce the underlying dynamics of the target system with far higher accuracy than non-energy conserving models. In addition to providing a new and lightweight method for combining physical constraints with UDEs, our results provide new evidence for the impact of physical constraints on the long-term numerical stability and dynamical fidelity of hybrid models.
M2	Gábor Drótos, Emilio Hernández-García, Cristóbal Lopez	Local characterization of transient chaos on finite times in open systems
			To characterize local finite-time properties associated with transient chaos in open dynamical systems, we introduce an escape rate and fractal dimensions suitable for this purpose in a coarse-grained description. We numerically illustrate that these quantifiers have a considerable spread across the domain of the dynamics, but their spatial variation, especially on long but non-asymptotic integration times, is approximately consistent with the relationship that was recognized by Kantz and Grassberger for temporally asymptotic quantifiers. In particular, deviations from this relationship are smaller than differences between various locations, which confirms the existence of such a dynamical law and the suitability of our quantifiers to represent underlying dynamical properties in the non-asymptotic regime. We also show that some other attempts to define the quantifiers in question perform worse in the mentioned respect. As an outlook, we sketch an application to the escape of particles from the atmosphere across the globe.
M3	Zhen Su, Jürgen Kurths, Henning Meyerhenke	Network Sparsification via Degree- and Subgraph-based Edge Sampling
			Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with filtering-based edge sampling being the most typical one, heavily relies on an appropriate definition of edge importance. Instead, we propose a different perspective with a generalized local-property-based sampling method, which preserves (scaled) local node characteristics. Apart from degrees, these local node characteristics we use are the expected (scaled) number of wedges and triangles a node belongs to. Through such a preservation, main complex structural properties are preserved implicitly. We adapt a game-theoretic framework from uncertain graph sampling by including a threshold for faster convergence (at least 4 times faster empirically) to approximate solutions. Extensive experimental studies on functional climate networks show the effectiveness of this method in preserving macroscopic to mesoscopic and microscopic network structural properties.
M4	Inga Kottlarz, Ulrich Parlitz	Ordinal pattern based complexity analysis of high-dimensional chaotic time series
			The ordinal pattern-based complexity-entropy plane is a popular tool in nonlinear dynamics for distinguishing stochastic signals (noise) from chaos. While successful attempts to do so have been documented for low-dimensional maps and continuous-time systems, high-dimensional systems have been somewhat neglected so far. To fill this gap, we present an analysis in the complexity-entropy plane of time series representing high-dimensional dynamics of the Lorenz-96 system, the generalized H'enon map, the Mackey-Glass equation and the Kuramoto-Sivashinsky equation. We find that time series from these systems often cannot be visually distinguished from their surrogates in the complexity-entropy plane, although a surrogate data test yields significant results in most cases. Based on these findings, we develop a guide on how to best proceed with an analysis of systems of unknown attractor dimension using the complexity-entropy approach.
M5	Matheus R. Sales, Michele Mugnaine, Ricardo L. Viana, Iberê L. Caldas, José D. Szezech Jr.	Uncertainty boundaries in Hamiltonian Systems
			The boundaries between regular and chaotic motion in two-dimensional Hamiltonian systems are not smooth, in fact they can be very complicated with distinct levels in the hierarchy. Our main objective is to characterize the topology of these boundaries using a paradigmatic model, more specifically the standard map. We apply a recent test introduced to determine whether an orbit is regular or chaotic called the Birkhoff weighted average method. Through these results we use the uncertainty fraction method to calculate the fractal dimension. Our results point out that the initial condition in phase space plays a crucial role in uncertainty. Also, for inner levels on islands implies larger dimensions due a persistent dynamical traps.
M6	Maximilian Gelbrecht, K. Hauke Krämer, Norbert Marwan	TreeEmbedding: Optimal state space reconstruction via Monte Carlo decision tree search
			TreeEmbedding is a novel method for an optimal time delay state space reconstruction from uni- and multivariate time series. The embedding process is considered as a decision tree, in which each leaf corresponds to an embedding cycle and is subject to an evaluation through an objective function. By using a Monte Carlo ansatz, the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path that minimises the objective function. The Monte Carlo approach aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way: Practitioners can choose suitable statistics for delay-preselection and the objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. To showcase the method, we demonstrate its improvements over the classical time delay embedding methods on various application examples. We compare recurrence plot-based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. The method is ready to use in the form of an accompanying Julia package TreeEmbedding.jl.
M7	Sergio Iglesias, Regino Criado	Combining multiplex networks, time series and machine learning: A methodology for reducing the dimensionality of data representation and making effective predictions
			The processing of large amounts of information is a great challenge for which the latest big data techniques provide some solutions. In this poster we present a methodology based on time series algorithms and multiplex networks. This methodology allows to process a large amount of information and to obtain a more effective and useful way of grouping the information, allowing to solve problems with a large number of temporal variables in an efficient way. The methodology presented to combine all this information is based both on the original use of some unsupervised machine learning techniques and on the use of certain attributes of the time series and their representation as a complex multiplexed network, achieving a very significant reduction in the dimensionality of the resulting data representation. The poster includes as an application a practical example of the evolution of housing prices in New York City based on cab trips between different areas of the city.
M8	Tushar Mitra, Md. Kamrul Hassan	Infinitely many conserved quantities in a weighted planar stochastic lattice and their connection to Noether's theorem
			In this talk, I shall discuss a class of weighted planar stochastic lattice (WPSL1) created by random sequential nucleation of seed from which a crack is grown parallel to one of the sides of the chosen block and ceases to grow upon hitting another crack. It results in the random partitioning of the square into contiguous and non-overlapping blocks. Interestingly, we find that the dynamics of WPSL1 is governed by infinitely many conservation laws and each of the conserved quantities, except the trivial conservation of total mass or area, is a multifractal measure. On the other hand, Noether's theorem suggests that whenever there exist a continuous conserved quantity there must exist symmetry. Earlier, we have shown that area distribution exhibits dynamic scaling. In this talk we show that the distribution of every non-trivial conserved quantity too exhibits dynamic scaling. It means that the distribution of every conserved quantity at different times are similar which we show using the idea of data collapse. On the other hand, since the same system at different times are similar we call the exhibits self-similarity which is also a kind of symmetry. Besides, I will show that the dual of the lattice is a scale-free network as its degree distribution exhibits a power-law. The network is also a small-world network as we find that (i) the total clustering coefficient C is high and independent of the network size and (ii) the mean geodesic path length grows logarithmically with N.
M9	Yang Liu, Xiaoqi Wang, Xi Wang, Zhen Wang, Jürgen Kurths	Percolation-based Evolutionary Framework for the diffusion-source-localization problem in large networks
			We assume that the state of a number of nodes in a network could be investigated if necessary, and study what configuration of those nodes could facilitate a better solution for the diffusion-source-localization (DSL) problem. In particular, we formulate a candidate set which contains the diffusion source for sure, and propose the method, Percolation-based Evolutionary Framework (PrEF), to minimize such set. Hence one could further conduct more intensive investigation on only a few nodes to target the source. To achieve that, we first demonstrate that there are some similarities between the DSL problem and the network immunization problem. We find that the minimization of the candidate set is equivalent to the minimization of the order parameter if we view the observer set as the removal node set. Hence, PrEF is developed based on the network percolation and evolutionary algorithm. The effectiveness of the proposed method is validated on both model and empirical networks in regard to varied circumstances. Our results show that the developed approach could achieve a much smaller candidate set compared to the state of the art in almost all cases. Meanwhile, our approach is also more stable, i.e., it has similar performance irrespective of varied infection probabilities, diffusion models, and outbreak ranges. More importantly, our approach might provide a new framework to tackle the DSL problem in extreme large networks.

Group B: Dynamics of complex biological systems


B1	Cedric Hameni Nkwayep, Samuel Bowong	Modelling, parameter and state estimation, and optimal control of COVID-19 pandemic: A study case of Cameroon
			In this paper, we formulate and analyze a compartmental model of COVID-19 in order to predict and control the outbreak in Cameroon. We first formulate a comprehensive mathematical model based on ordinary differential equations for the dynamical transmission of COVID-19 in Cameroon. We provide the theoretical analysis of the model. After, assuming continuous measurement of the weekly number of newly COVID-19 detected cases, newly deceased indivijduals and newly recovered individuals, the Ensemble of Kalman filter (EnKf ) approach is used to estimate the unmeasured variables and unknown parameters which are assumed to be time-dependent using real data of COVID-19 in Cameroon. We present the forecasts of the current pandemic in Cameroon using the estimated parameter values and the estimated variables as initial conditions. Our findings suggest that at November 2022, the basic reproduction number is approximately 1.86 in Cameroon meaning that the disease will not die out without any control measures. Also, the number of undetected cases remains high, which could be the source of new vagues of COVID-19 pandemic. Further, we found that there is a necessity to increase timely the surveillance by using awareness programs, detection process and the eradication of the pandemic is highly dependent on the control measures taken by the government. Based on this continuous model, the COVID-19 control is formulated and solved as an optimal control theory problem, indicating how control terms based on the awareness programs, detection process and vaccination should be introduced to reduce the number of COVID-19 infected individuals in Cameroon. Results provide a framework for designing the cost-effective strategies for COVID-19 with these three intervention strategies.
B2	Daniel Koch	Nonlinearity in biochemical networks resulting from protein homo-oligomerisation
			Reversible protein homo-oligomerisation, i.e., the formation of larger protein complexes out of identical subunits, is observed for 30-50% of all vertebrate proteins. Despite being a ubiquitous phenomenon, the specific function of protein homo-oligomerisation remains poorly understood. Based on simple mass-action and Miachelis-Menten models, I show that homo-oligomerisation could be a versatile mechanism for a range of nonlinear phenomena including homeostasis, ultrasensitivity and bistability via pseudo-multisite modification. Applying these findings to a real biological example, I will present the first dynamical systems model of phospholamban (PLN), a crucial mediator protein of the physiological 'fight-or-flight' response triggered by beta-adrenergic signaling and a key regulator of calcium cycling in heart muscle cells. Importantly, PLN forms homo-pentamers whose function remained elusive for decades. Simulations and model analyses demonstrate that pentamers enable bistable phosphorylation and further constitute substrate competition based low-pass filters for phosphorylation of monomeric PLN. Both predictions of the model were confirmed experimentally by demonstrating substrate competition in vitro and and by demonstrating hysteresis of pentamer phosphorylation in cardiomyocytes. These non-linear phenomena may ensure consistent monomer phosphorylation and calcium cycling despite noisy signaling activity in the upstream network and may be impaired by perturbations (e.g., via genetic mutations or in the context of underlying heart disease) which cause cardiac arrhythmias. These studies show that homo-oligomerisation can play unanticipated and potentially disease relevant roles in biochemical signaling networks.
B3	Elena Adomaitienė, Skaidra Bumelienė, Arūnas Tamaševičius	Stabilizing equilibrium in an array of the neuronal oscillators by injecting electrical current proportional to inverted mean membrane potential

B4	Karin Mora, Jana Wäldchen, Michael Rzanny, Guido Kraemer, Ingolf Kühn, Patrick Mäder, Miguel D. Mahecha	Dynamics of collective flora behaviour from crowd-sourced data
			Monitoring changes in phenology, i.e., changes in flora states, is key to understanding the impact of climate change on ecosystems and biodiversity. Crowd-sourced data from smartphone applications are gaining in popularity in many ecological applications and are especially relevant for automated species recognition. However, the potential of crowd-sourced data for studying phenology at macroecological scales has not been deeply explored. We aim to quantify the collective phenological cycle of plant co-ocurrences based on citizen science data. We analyse crowd-sourced German plant observation data collected with the smartphone application Flora Incognita, which identifies plant species native to Central Europe from images in real time using deep learning. We propose that the dynamics of collective flora behaviour is embedded in the temporal co-occurrence observations. To extract this collective phenological dynamics we propose the manifold learning method isometric feature mapping. As this approach is data driven no a priori assumptions are made about how to define collective behaviour. We propose a complexity measure to characterise the dynamics across large spatial scales. Our results demonstrate that the phenology of macroecological patterns can be effectively detected from crowd-sourced plant observation data. The strong collective flowering in spring and summer allows us to clearly characterise phenological transitions, specifically the faster changes in spring compared to autumn. The emerging complexity measure of collective behaviour is an indicator for linear and nonlinear temporal changes in macroecological patterns in the summer and the rest of the year, respectively. Despite biases and uncertainties associated with opportunistically collected crowd-sourced data it is possible to derive meaningful indicators for monitoring plant phenology. In the near future multi-year records of such data will be available to explore phenological shifts and how they are impacted by climate change in near real time.
B5	Michele Mugnaine, Enrique C. Gabrick, Paulo R. Protachevicz, Kelly C. Iarosz, Silvio L. T. de Souza, Alexandre C. L. Almeida, Antonio M. Batista, Iberê L. Caldas, José D. Szezech Jr., Ricardo L. Viana	Control attenuation and second wave scenario in a cellular automata SEIR epidemic model
			Mathematical models are applied to study the consequences and to estimate the future of a disease spread in a population. They are an important tool to analyze impacts and plan to mitigate epidemics in communities. In order to estimate the impact of control measures and a possible second wave of infections, we analyze the SEIR epidemic model based on cellular automata. The control measure is based on the restriction of individual mobility in space. From our mathematical simulations, we observe that the implementation of control measures decreases the amplitude of the curve of infected individuals and increases the duration of the spread. For a control with more than 70% of the possible paths of contact blocked, the decrease in the total number of infected individuals is greater than 15% , throughout the epidemic. Analyzing the possibility of a second wave of infections in our CA based model, our numerical results show that the total attenuation of control measures in the system can lead to a second wave scenario, and it happens for greater values of the control parameter.
B6	Yu Meng, Ying-Cheng Lai, Celso Grebogi	The fundamental benefits of multiplexity in ecological networks
			a tipping point presents perhaps the single most significant threat to an ecological system as it can lead to abrupt species extinction on a massive scale. climate changes leading to the species decay parameter drifts can drive various ecological systems towards a tipping point. we investigate the tipping point dynamics in multilayer ecological networks supported by mutualism. we unveil a natural mechanism by which the occurrence of tipping points can be delayed by multiplexity that broadly describes the diversity of the species abundances, the complexity of the interspecific relationships, and the topology of linkages in ecological networks. for a double layer system of pollinators and plants, coupling between the network layers occurs when there is dispersal of pollinator species. multiplexity emerges as the dispersing species establish their presence in the destination layer and have a simultaneous presence in both. we demonstrate that the new mutualistic links induced by the dispersing species with the residence species have fundamental benefits to the wellbeing of the ecosystem in delaying the tipping point and facilitating species recovery. articulating and implementing control mechanisms to induce multiplexity can thus help sustain certain types of ecosystems that are in danger of extinction as the result of environmental changes.
B7	Nikita Frolov, Liliana Piñeros, Bartosz Prokop, Lendert Gelens	Scaling relationship between nuclear density and cell cycle duration in frog egg extracts
			The cell cycle is a highly regulated spatio-temporal process controlled by a large and complex network of proteins. Precise coordination of its timing during early embryogenesis guarantees the healthy development of the organism. Conversely, abnormalities of the cell cycle duration might critically affect later development. Previous studies recognized the size of the nucleus as one of the determinants of the cell cycle period. However, the exact relationship between these quantities is not yet fully understood. In this work, we use extensive data analysis to reveal such a relationship in cell-free extracts of the Xenopus laevis frog, a suitable biological model in which one can manipulate biochemical conditions and nuclear density. We identify that the cell cycle period scales under the variation of nuclear density. More strikingly, we reveal a mapping of nuclear density from cycle to cycle, based on which we can to predict the idealized trajectory of cell division progression during early embryogenesis.
B8	Philipp Hövel, Sebastian Jenderny, Karlheinz Ochs, Jorge Ruiz, Thomas Maertens	Simulating the locomotion of C. Elegans via an extended Hindmarsh-Rose model
			We investigate how locomotory behavior is generated in the brain focusing on the paradigmatic connectome of nematode Caenorhabditis elegans (C. Elegans), which includes different layers describing connections via electrical gap junctions and various chemical synapses. We study neuronal and muscular activity patterns that control forward locomotion. Combining Hindmarsh-Rose equations for neuronal activity with a leaky integrator model for muscular activity, we model the dynamics within the multi-layer network and predict the forward locomotion of the worm using a harmonic wave model. Finally, we present a power-flow-based simplification of the model, which is inspired by electronic circuit synthesis and allows the emulation of neuronal behavior on larger networks by means of analog circuits.
B9	Sabrina Hempel, Huyen Vu, Moustapha Doumbia, Qianying Yi, David Janke, Thomas Amon	Livestock-environment-interaction in naturally ventilated housing on the example of ammonia
			Contemporary livestock husbandry is far from being sustainable. One the one hand, livestock is in principle capable to provide essential micronutrients from food that is not digestible by humans and thus could recycle otherwise unused nutrients. On the other hand, there are issues of animal welfare, the competition between food and feed and the pollutant emissions of gases and particles, which are negatively affecting the climate system, environment and health. One crucial substance in this context is ammonia, where nearly half of all global emissions are associated with livestock husbandry (particularly cattle and pig farming). However, there are large differences in the emission rate between individual farms, which are not well understood so far. One of the reasons is the complex interaction between outdoor climate, indoor microclimate and the emission source strength and gas dilution. We use fluid dynamics and reaction-kinetics modelling to better understand these interactions, predict emission values, optimize monitoring systems, and identify and evaluate emission mitigation potentials. Simulations of a naturally ventilated dairy cattle building, as it is common in many parts of Europe and the US, showed that annual average ammonia emission strongly depends on the relation between pH and temperature in urine puddles and liquid manure, while variations at the daily and subdaily time scale are dominated by changes in the local airflow patterns. The latter emerge from a complex interplay of building characteristics, inflow conditions and buoyancy effects, which renders smart ventilation control challenging. At the same time, the typical air flow patterns are associated with large differences in air quality in different locations with regards to temperature and pollutant concentration. Without adapting the husbandry systems (e.g., using targeted cooling / heating, feed and/or manure additives, fast separation of urine and faeces and smart ventilation control) several thousand tons of ammonia will be additionally released from livestock husbandry as a consequence of climate change.
B10	Shaoxuan Cui, Fangzhou Liu, Hildeberto Jardón Kojakhmetov, Ming Cao	Modelling and analysis of the mean-field SIWS epidemic model with higher-oder interactions
			Recently, a simplicial model of social contagion has been proposed. Such a model captures not only the pairwise interactions but also the multi-body interactions, which makes the model more realistic. However, the model only takes human-to-human interaction into account and does not consider the possibility of spreading via media. By further coupling the system with a pathogen-like dynamics, we propose a new mean-field simplicial epidemic model (SIWS-type, where W stands for the media compartment). Our model captures the indirect spreading through media like Tiktok or Twitter. We provide analytical results showing that our model may present bistability. We further give a number of sufficient conditions for the stability of the healthy-state and the endemic equilibrium.
B11	Sourav Roy, Sayantan Nag Chowdhury, Prakash Chandra Mali, Matjaz Perc, Dibakar Ghosh	Eco-evolutionary dynamics with multi-games under mutation
			Major section of practical scenarios impart significant favor to defection over cooperation due to natural selection, depicting the instinct of persistence and survivability of the strongest living creature in nature at the very tail end of each dilemma. Be that as it may, the emergence of cooperation is omnipresent in most of the biological, social, and economic systems, proving out to be sufficiently contrary to the well-cherished Darwinian theory of evolution. Many researches have been devoted to understand and establish in a better manner how and why cooperation is being preserved among self-interested individuals even in their competition for limited resources. In our work, we go further beyond one single social dilemma, since individuals usually encounter various social challenges in various complex chains of scenario day by day. In particular, we implement a mathematical model with analytical and numerical studies, which incorporates both the prisoner’s dilemma and the snowdrift game, to be taking place with complementary possibilities of occurrence with each other. We further extend this model by consideration of ecological signatures like mutation and selfless one-sided contribution of altruist free space. The nonlinear evolutionary dynamics that results out from these upgrades offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection with the increasing chain of iteration. With the help of analytical and numerical calculations, our theoretical model sheds light on the mechanisms that maintain biodiversity, and it helps to explain the evolution of social order in human societies.

Group S: Cardiovascular dynamics and sleep disorders


S1	Alondra Albarado-Ibañez, Martha Ita-Amador, Julian Torres-Jacome	Dimorphism sexual and frequency cardiac: Non-linear method analyses
			The heart rate variability time series is a novel approach for prognostic and diagnostic development of disease that produces lethal arrhythmias. Until, the data shown were on the male sex, due to the data of female sex have influence hormonal period and other rhythms. However, in this study, the time series shows the existence of a delicate difference between them independently of the hormonal period. We obtained the RR intervals of ECG of college students, 134 females and 68 males. Disclosed the heart rate in female 74 bpm is minor than 77 bpm in male, the principal characteristic in analysis of FFT were that highest wave on the lower frequencies in male while in female highest frequencies. The analyses suggest an ability to differentiate the rhythm cardiac according to gender.
S2	Chiara Barà, Yuri Antonacci, Luca Faes	Estimating the decomposition of the mutual information rate in short-term cardiovascular variability time series: Comparison between different discretization strategies

S3	Daniel Suth, Thomas Lilienkamp	From 2D to 3D: Comparing the performance of different GPU based algorithms to simulate cardiac excitation wave dynamics
			In the field of cardiac dynamics, numerical simulations play an important role in understanding fundamental mechanisms and features of the dynamics within the myocardium. Of special interest are chaotic processes of cardiac dynamics, such as ventricular fibrillation, and methods for their treatment. Electrical activity in the myocardium can be modelled as a set of coupled partial differential equations (PDE). These equations can, for instance, be solved using Runge-Kutta methods. The use of the rapidly developing capabilities of graphics processing units (GPU) allows a significant acceleration of computation times, compared to CPU-based computations, for the numerical solution of the given PDEs. However, writing the necessary source code to exploit the full potential of GPUs is often a major challenge. Nowadays, there are various possibilities and software packages to realize this. We present a comparison of different possibilities to perform GPU calculations in order to investigate their performance in different situations and to highlight the advantages and disadvantages over CPU-based calculations. The objective of this study is to investigate the possibilities of current programming languages and their respective libraries that enable the usage of GPUs (and thus a significant acceleration of computing time). Of particular interest are comparisons in terms of performance (in computing time) and code complexity. We therefore implemented four different cardiac cell models for the simulation of electrical activity in the myocardium in both CPU- and in GPU-capable code. All models were simulated on two-dimensional and on three-dimensional spatial domains. Furthermore, all models were simulated on a realistic three-dimensional geometry of a cardiac muscle in order to introduce a benchmark for further studies. Time measurements were performed to investigate the speedup in computational time due to the utilization of GPUs.
S4	Mateusz Ozimek, Karolina Rams, Jan Zebrowski, Teodor Buchner	Information dynamics of heart rhythm, repolarization and amplitudes time series in Long QT Syndrome
			The human organism is considered complex and consists of many interacting subsystems. These interactions are nonlinear, and such systems are characterized by a high degree of complexity, which is closely related to health condition and age. Interactions between subsystems can be considered in terms of physiological networks. In our work, we examined a fragment of such a network that governs the cardiac cycle. We focus on the relations between heart rhythm and repolarization. For this, the framework of information dynamics was used. Our goal is to find metrics, which can be useful for risk stratification of LQTS based on noninvasive 24-hour Holter ECG. We have estimated entropy measures for as well univariate as multivariate time series. The conditional entropies were calculated for simultaneous RR, QT and diastolic intervals (DI). Moreover, we also consider time series of amplitude values of QRS and T wave. We study the asymmetry of information flow. The data were extracted from the ECG recordings in two of the THEW databases: E-HOL-03-0202-003 (202 ECG of healthy individuals) and E-HOL-03-0480-013 (480 ECGs for patients with the LQTS). We study a subset of this data, for which automatic detection of QT intervals and T wave amplitude could be applied. The results show differences between healthy and LQTS patients in case of directionality of information flow. The asymmetry is present for information flow between heart rate and the time series of QT intervals and T-wave amplitudes. Estimated values of information dynamics show promising result in differentiating the complex dynamics of repolarization and hearth rhythm between healthy and LQTS patients. Machine learning tools can be used to build a model with high accuracy, specificity and sensitivity, however, bigger datasets are required.
S5	Richa Tripathi, Rammah Abohtyra, Bruce J. Gluckman	Mechanistic Neural Masses for modeling seizures and spreading depolarization
			Seizures and spreading depolarization events occur apparently spontaneously in epileptic brains. Why epileptic brains aren't seizing all the time is a fundamentally unanswered question. Brain rhythms emerge from the activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities – termed neural masses – to understand in particular the origins of evoked potentials, intrinsic patterns of brain activity, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Such elements activities cannot be linked directly back to the activities of single neurons, the details of their function, genetics mutations, or linked to tissue level parameters such as extracellular potassium that are known to contribute to seizures and spreading depolarization. We defined a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type models) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium and related volume-conducted features - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance. Analysis of such models already provide experimentally predictable insights into why the basin of stability against seizures for epileptic brain may be smaller. Additionally, by introducing the change in function in sodium channels associated with genetic mutations associated with specific epilepsies, we similarly obtain networks that are more seizure-susceptible.
S6	Sayedeh Hussaini, Johannes Schroeder-Schetelig, Aidai M. Kyzy, Sarah L. Lädke, Laura Diaz, Raul Q. Uribe, Vishalini Venkatesan, Claudia Richter, Annette Witt, Vadim Biktashev, Rupamanjari Majumder, Valentin Krinski, Stefan Luther	Efficient Termination of Cardiac Arrhythmias using Optogenetic Resonant Feedback Pacing
			Over the past decade, optogenetics has been explored from basic to translational research, particularly in the area of control of cardiac arrhythmia, i.e., abnormal electrical activity of the heart. Caridac optogenetics is a technique which allows normal light-insensitive cardiac tissue to become senstitive to light stimuli by genetic modification. A better mechanistic understanding of the onset, progression, and control of cardiac arrhythmias benefits the development of alternative methods to conventional treatments, which are often associated with significant side effects for patients. To this end, optogenetics is a promising tool for these fundamental research. We study the control of arrhythmias in N=5 intact Langendorff-perfused alphaMHC-ChR2 mouse hearts using two protocols: (i) a single global light pulse (duration10 and 100 ms, wavelength 470 nm) and (ii) resonant feedback stimulation with a sequence of global light pulses (duration 20 ms, wavelength 470 nm). The termination success rate is determined as a function of light intensity for both protocols. ECG recording and potentiometric optical mapping (dye Di-4-ANBDQPQ) are used to measure cardiac activation before, during, and after optical control. Corresponding numerical simulations of cardiac tissue are performed using the Bondarenko model in conjunction with a channelrhodopsin-2 model in a 2D domain $25 \times 25$ mm$^2$. Resonant feedback pacing supersedes single pulse in termination efficacy in Langendorff-perfused alphaMHC-ChR2 mouse hearts [reduced by two orders of magnitude with respect to $I_{50}$ = intensity for 50% termination success]. We observe efficient termination of arrhythmias using resonant feedback pacing even at subthreshold light intensities, i.e., below the minimum light intensity required to evoke an action potential. Numerical simulations show a dose-response consistent with the experimental findings. At subthreshold light intensities, simulations suggest that resonant feedback pacing results in resonant drift of the spiral wave core and subsequent arrhythmia termination.
S7	Stefan Luther	Spatial-temporal organisation of cardiac fibrillation: From principles to patients
			Cardiac fibrillation is an electro-mechanic dysfunction of the heart that is driven by complex three-dimensional electrical excitation waves, resulting in incoherent mechanical contraction, loss of pumping function, and risk of sudden cardiac death. The nonlinear dynamics of vortex-like rotating waves play an essential role in the spatial-temporal organisation of fibrillation. However, the visualisation of these rotors, their interaction with each other and with the three-dimensional heterogeneous and anisotropic anatomical substrate remains a significant scientific challenge. In our talk, we will discuss the nonlinear dynamics of electrical and mechanical rotors during ventricular fibrillation. We will also address the application of rotor mapping using high-resolution 4D ultrasound for novel diagnostic and therapeutic approaches.

Group W: World-earth system analysis


W1	Andrej Spiridonov, Shaun Lovejoy, Lauras Balakauskas	Scaling of tectonics, biogeographical structures, and macroevolution
			The fundamental questions of macroevolution are: what drives origination and extinction of taxa, and what is the long-term expected pattern of global biodiversity change? Here we use the perspective of time scaling and multiplicative multifractal processes in suggesting unified framework connecting multiscale Earth system dynamics, and scale free and time scale dependant features of evolutionary dynamics. Here we tackle a classical problem in evolutionary paleobiology - the causes of demise of the major marine animal phylum Brachiopoda through the Phanerozoic eon. We analyzed the evolution of longitudinal and latitudinal geographic ranges of brachiopod genera and compared their dynamics to the continental fragmentation index dynamics, which reflects the degree of fragmentation or conversely amalgamation of continents and terrains. The Haar fluctuation analyses of geographic ranges and continental indices revealed that there is a direct functional connection between the fragmentation and the shapes and sizes (in longitudinal direction) of brachiopod ranges. Positively scaling tectonics controls the positive scaling of geographical distributions of brachiopods. Since geographic ranges in times other than mass extinctions are the major determinants of survival, this indicates that the stability, and conversely the turnover of marine biota is directly related to the multiscale random dynamics of continental amalgamation. The low of brachiopod geographic ranges and the occurrence of the most isometric shapes of their ranges are coincident to the maximal amalgamation of the supercontinent Pangaea. Therefore, the multiscale perspective in combination with the advanced tools of nonlinear dynamics show significant potential in solving decades-long problems, and building unified theory of coupled Earth-Life dynamics. The study was supported by the project S-MIP-21-9 “The role of spatial structuring in major transitions in macroevolution”.
W2	Françoise Martine Enyegue à Nyam, Collins Djouda Paguem	Modelling the evolution of the volcanic plume height as a function of the eruption time and the seasonal climate
			The forecasting of the volcanic plume height is the topic of many studies in physical volcanology. Therefore, several physical and mathematical models have been used. One of the leading physical models derived from observations is the Woods model since 1988 which includes a gas thrust, buoyancy driven and tracking zones. In the same way, a second physical study was published, showing that the atmospheric boundary is made up of three layers: the surface, the mixing or convective and the free atmosphere layer whose thicknesses vary with the daytime and seasonal climate. By comparing these two models, we find a similarity and we wonder if one can justify the other or if these two models are complementary. In this project we use the Reynolds Averaged Navier Stokes equations separating the turbulent fluctuations from the stationary evolution of the different variables to model and simulate the evolution of the lower atmosphere in terms of the daytime. The results show that the height of the atmospheric boundary layer increases from midnight and reaches its maximum at twelve noon, and decreases thereafter till its minimum at midnight. From the data analysis method, we were able to determine a first pattern in winter. In particular, we find that the volcanic plume height is weakly affected by the wind speed which is known to be a major factor in the forecast of volcanic plume height. We plan to redefine the seasonal climate in order to find other patterns, to identify the seasonal factors that control the dynamics of the volcanic plume height. Our mathematical model based on the Navier Stokes equations has also allowed us to simulate the evolution of plume velocity as a function of height, hence to predict the duration of an eruption, thanks to the known results.
W3	Gaurav Chopra, V. R. Unni, R. I. Sujith	Spatiotemporal dynamics of the ITCZ using complex network analysis of outgoing longwave radiation
			We study the Spatiotemporal dynamics of the Inter-Tropical Convergence Zone (ITCZ) using the complex network analysis of Outgoing Longwave Radiation (OLR). We use the Pearson’s correlation to construct the network. The OLR data for thirty years (1992-2021) with a resolution of three hours is considered. The OLR network brings out the regions in the tropics affected by the ITCZ. The network also captures the significant variation in the characteristics of the ITCZ with geographical location. We use community detection to subdivide the tropics into regions of similar ITCZ characteristics. Communities in the OLR network reveal the seasonal position and structure of the ITCZ. The densely connected communities explicitly represent the mean structure of the ITCZ in the Northern and Southern hemispheres during the respective spring and summer seasons. Across these communities, the ITCZ shows coherent annual migration patterns. These communities also have a significant amount of long-range intra-community connections which is representative of the large-scale structure of the ITCZ. Meanwhile, communities encompassing the equatorial Pacific, Atlantic and Indian oceans have relatively sparse connections due to incoherence in the annual migration pattern and strength of the ITCZ in these regions. Furthermore, most connections within these communities are short-range or local connections, while long-range connections are scarce.
W4	Hannah Prawitz	Towards modelling the Anthropocene: Conception and analysis of potential planetary-scale socio-ecological feedbacks the nexus of climate change, loss of biosphere integrity and human mitigation behaviour
			Ever since we entered the Anthropocene, (some) humans are not only affected by earth system changes but are the most important determinant of environmental alterations like climate change and the sixth mass extinction. This leads to non-linear interactions and complex systems that challenge current predominant modelling approaches. Thus, a new generation of models is needed that integrate coupled human and environmental dynamics endogenously and go well beyond established Integrated Assessment Models. Recently, some studies were published that propose such an integrated understanding and include dynamical social factors like norms and values regarding human emissions behaviour in their analyses and found possible social tipping elements. However, those models almost only regard the planetary boundary dimension of climate change, and there are currently no models that address social actions and social tipping points, which are also critical to effectively mitigate biodiversity loss. This study aims to address aforementioned issues , as it seeks to understand how a combined socio-climate-biodiversity model - that concentrates on human values and behavior - might provide insights into the trajectories of global temperatures and biodiversity loss by focusing on two main feedback loops: 1. Climate-Biosphere Feedback: Climate change and Biosphere Integrity are the two core Planetary Boundaries and there are crucial climate-biosphere interactions that could significantly alter the resilience of the Earth system. However, ecosystem level feedbacks are not routinely included in models and projections. 2. Risk perception – Mitigation Feedback: The human perception of the environmental state and a corresponding risk can trigger pro-environmental behaviors. Extreme events but also gradual change can motivate people to intensify their mitigation efforts. Based on a systematic review, a model that depicts those interactions between the climate system and the biosphere is coupled with a simple model that conceptualises human mitigation behaviour. The coupling is done by using the copan:CORE framework for World-Earth modelling, which allows for capturing all human and natural processes adequately. The resulting non-linear dynamics and interactions, the sensitivity of all included formulas and parameters, as well as possible tipping points are explored using a Monte Carlo Analysis. This allows a wide variation of terms and parameters and an analysis of the importance of interactions and feedbacks in the resulting complex system.
W5	Leonard Schulz, Karin Mora, Jürgen Vollmer, Miguel Mahecha	Inferring dynamical information of the Earth system by dimensionality-reduction
			Understanding dynamics of the Earth system such as the climate is challenging for many reasons. Relevant systematic information can be obtained from observation time series. For variables such as carbon uptake by vegetation, there are only short observation time series and we do not have accurate models. Dimensionality-reduction methods decompose the delay-embedded observations into additive data-adaptive modes. These modes offer an understanding of information about underlying dynamics, such as dominant timescales. The analysis of climate models has been shown to require nonlinear dimensionality-reductions in order to extract such systematic information. The extraction quality of such information is highly impeded by the interactions between modes such as variance compression and degeneracy. Here we show the difference in timescale extraction by Singular Spectral Analysis and Nonlinear Laplacian Spectral Analysis for carbon uptake measurements. The influence of nonlinear inter-annular variability, the role of the seasonal trend, and the role of the delay-embedding are investigated. We showed that dimensionality-reduction methods need to be applied correctly to extract timescale related information, such as the unharmonic seasonal trend. Utilizing the additional feasibility to differentiate quasiperiodic variability accurately from such trends, nonlinear methods offer the reliable extraction of relevant information in observation-data. Besides timescales, the individual modes also enable the investigation systematic information about the the Earth system, such as spatiotemporal coupling dynamics from phase synchronization.
W6	Markus Abel, Thomas Seidler, Markus Quade, Fabian Emmerich	Phase Transitions in Machine Learning
			The methods of statistical mechanics are used in a wide range of applications exceeding the physics domain, such as problems from biology, chemistry, socio-ecology, graph theory, and last, but not least statistical learning theory. The latter is key to many studies in climatetology, e.g., in the context of tipping points. The prediction of critical points motivates us to apply the methods to study phase transitions to statistical learning or methods of artificial intelligence (AI). To this end, we draw the anology between learning in AI and physical systems, like the well-understood Ising model: the development of AI applications has a two-fold nature in that the data used and the AI algorithm belong tightly together via the problem and objective defined. Here, we understand data and algorithm textit{together} as a statistical system. An extremely relevant question concerns the nature of the cognition transition, i.e., the phase transition that characterises the ability of an AI algorithm to recognize objects or fulfill a task successfully. This transition may be classified according to its universaltiy class and consequently this may be a way to obtain fundamental understanding of AI algortihms. In this contribution, we illustrate the concepts by a study of large-scale weather events over europe: we investigate 3 years of ERA data from ECMWF over Europe with clustering algorithms in order to determine structure of large-scale weather over Europe. The results are important, both for the unsupervised classification of weather and for the understanding of the cognition transition in AI.
W7	Max Bechthold	Local resource dynamics and normative spreading of behaviour in a world-earth model
			Analysis of Earth system dynamics in the Anthropocene requires explicitly taking into account the increasing magnitude of processes operating in human societies, their cultures and economies and their growing feedback entanglement with those in the physical, chemical and biological systems of the planet. One major process in the domain of the anthroposphere that is entangled with environmental processes, is the spreading of behaviour in a social norms and groups context. This talk introduces a World-Earth Model that tries to model such norms and groups, their influence on human behaviour and the resulting effects on the dynamics of a renewable resource, which illustrates either a sustainable or unsustainable macro outcome. The models implementation in the copan:CORE framework is explained, which is designed to explicitly model with a focus on feedback interactions between the environmental and the socio-cultural realm. Finally, analyses of the model with tools from statistical physics are laid out and implications of these results on the importance of social norms in the transition to a more sustainable future are discussed.
W8	Moritz Adam, Kira Rehfeld	Artificial trees and sustainable development – Towards coupling decision making on carbon dioxide removal with a comprehensive Earth system modeling framework
			At the current rate of decarbonization, limiting global warming to 2 degree Celsius by 2100 requires large-scale artificial carbon dioxide removal (CDR). CDR approaches involve extensive interventions in the Earth system. As a result, they are likely to conflict with the United Nations' Sustainable Development Goals (SDGs). This raises the dilemma of trade-offs between mitigating global warming and achieving other SDGs, while reduced CO2 concentrations would also positively impact some SDGs. Simulation-based decision support on CDR has so far been limited to quantifying globally driven effects of individual CDR processes in the Earth system. Coupled spatial simulations of land use decisions on CDR and their impacts on sustainable development and ecosystem services do not exist. However, for proactive management, the question of how agents could interact with the Earth system through CDR in space and time and how they could, themselves, respond to CDR side effects is vital. Here, we outline our concept towards interactively simulating CDR land use decisions in a comprehensive Earth system model (ESM). Our setup consists of two main building blocks: an extensively expanded and validated version of the Max Planck Institute-ESM and an agent-based model of coupled CDR decisions that is to be developed. The ESM representation resolves some challenges to represent idealized CDR land cover explicitly in space within coupled Earth system simulations. It parametrizes irradiation-driven CO2 withdrawal and responds interactively to transient negative emission targets derived from socioeconomic scenarios. Incorporating potential trade-offs between CDR technologies and sustainable development, the land use component could simulate idealized decision-making under different configurations of simulated agents, climate, biosphere, and CDR impacts. It will be coupled to the Earth system's state and CDR side effects, driving the CDR land cover within the ESM in turn. Our coupled setup will enable studying idealized interactions between CDR side effects and land use decisions to enrich the debate on the impacts and trade-offs of CDR. It could also open a new way toward comprehensive World-Earth modeling.
W9	Niklas Kitzmann, Jonathan Donges	Assortativity and consensus: A stylized model of frontrunner cities and global sustainability action
		Among the global community of cities, some display higher readiness than others to take action for decarbonization and sustainability. Often, these 'Frontrunner Cities' are far ahead of their local peers and national legislative context. This phenomenon creates the potential to blaze a trail and pull other actors along, but also for increased polarization and division. The formation of Frontrunner Cities is one example of humans tendency for assortative mixing: associating themselves with groups and individuals that they share some characteristics (such as political positions) with. We investigate the effects that such assortative behavior has on a political action consensus under growing pressure. Using several stylized models of social contagion and peer influencing, we show that assortative behavior can lead to faster consensus-forming when influence is drawn from both the local (peer) and global (aggregate) contexts. In the Frontrunner City example, this translates to a faster global response to rising global anthropogenic environmental pressures.
W10	Takahito Mitsui, Metteo Willeit, Niklas Boers	Synchronization theory for Quaternary ice age cycles
			The dominant periodicity of glacial-interglacial cycles changed from 41 thousand years (kyr) to roughly 100 kyr across the Mid-Pleistocene Transition (MPT) around one million years ago. The mechanisms leading to these dominant periodicities and their changes during the MPT remain debated. Here we propose a synchronization theory explaining these features of glacial cycles and confirm it using an Earth system model that reproduces the MPT under gradual changes in volcanic CO2 outgassing rate and regolith cover. We show that the model exhibits self-sustained oscillations without astronomical forcing. Before the MPT, glacial cycles synchronize to the 41-kyr obliquity cycles because the self-sustained oscillations have periodicity relatively close to 41 kyr. After the MPT the time scale of internal oscillations becomes too long to follow every 41-kyr obliquity cycle, and the Earth's climate system synchronizes to the 100-kyr eccentricity cycles that modulate the amplitude of climatic precession. The latter synchronization is only possible with the help of the 41-kyr obliquity forcing through a nonlinear mechanism that we term vibration-enhanced synchronization.
W11	Francesco Martinuzzi, Miguel D. Mahecha, Karin Mora	Learning Biosphere Response to Climate Drivers Using Echo State Observers
			Modeling the vegetation dynamics response to climate drivers represents a crucial component in the understanding of land-atmosphere interactions. Driven by nonlinear behavior, the biosphere state presents long term trends, a strong seasonal component as well as an immediate nonlinear response to weather stimuli. Vegetation memory effects also play a role, affecting its response to external inputs. In addition, while some atmospheric variables are known to have a stronger impact on vegetation dynamics compared to others, their influence is hard to quantify and the full extent of the relationship remains unknown. All of these factors compound, making the vegetation state and its drivers a challenging system to model. We frame the problem of modeling vegetation dynamics from atmospheric drivers as creating a function, called observer, that can infer unmeasured state variables from known components. In this study we show that echo state networks (ESNs), used as observers, can learn the normalized difference vegetation index (NDVI) from climate variables such as temperature and precipitation. This approach is tested for a range of conditions, such as different vegetation covers and locations in various climate zones in the European continent. The quality of the results is examined with multiple measures including those quantifying temporal approximation changes. Challenges and limitations are also discussed. Our results show that ESNs are a powerful AI paradigm for modeling land-atmosphere interactions, able not only to replicate the trend and seasonal components of the vegetation dynamics but also sub-seasonal dynamics.

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	Norbert Marwan, Gorka Zamora Lopez	Juergen Kurths' World of Publications