Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives | programme

Conference Programme

Cover of the abstracts booklet.

Wednesday, March 15th

Thursday, March 16th

Friday, March 17th

Wednesday, March 15th


13:00–13:10	Opening
13:10–13:40	Celso Grebogi	Recent achievements in studying ecological networks
		Long-term predictions constitute a fundamental challenge in ecology, epidemiology and climate science. Reliable forecasting is difficult because of sensitive dependence on initial conditions, noise, and incomplete data. Another obstacle to reliable prediction of ecosystems is a phenomenon known as “regime shift”, where any conclusions or estimates based on the observations made before the regime shift become irrelevant after the shift. The timing of the regime shift is difficult to predict and the problem of identifying early warning signals remains largely open. Sudden regimes shift often results in a population collapse, extinction of species and biodiversity loss, making it an important issue for nature conservation and ecosystem management. Focusing on the regime shift or the tipping-point dynamics in ecological mutualistic networks of pollinators and plants constructed from empirical data, I will examine the phenomena of noise-induced collapse and noise-induced recovery, aiming at understanding the interplay between transients and stochasticity. I will discuss control strategies that delay the extinction and advances the recovery by controlling the decay rate of pollinators in a stochastic mutualistic complex network, whose control strategies are affected by Gaussian environmental and state-dependent demographic noises. Since in recent years, the concept of multilayer networks has also been adopted in ecology, I will also look at the influence of the topological structure on the control effect due to multiplexity. This is a basic notion in complex multilayer networks, where a subset of nodes belongs simultaneously to different network layers. I will argue that multiplexity also arises in multilayer ecological networks supported by mutualism and, more importantly, it has the fundamental benefits to sustaining the whole networked system and keeping it in a healthy state by delaying, often significantly, the occurrence of a catastrophic tipping point that would otherwise lead to extinction on a massive scale. References Y. Meng and C. Grebogi, Control of tipping points in stochastic mutualistic complex networks, Chaos 31, 023118(1-9) (2021) C. Grebogi, Sudden regime shifts after apparent stasis: Comment on long transients in ecology, Physics of Life Reviews 32, 41 (2020) Y. Meng, Y.-C. Lai, and C. Grebogi, Tipping point and noise-induced transients in ecological networks, J. Royal Soc. Interface 17, 20200645 (2020) Y. Meng, Y.-C. Lai, and C. Grebogi, The fundamental benefits of multiplexity in ecological networks, J. R. Soc. Interface 19, 20220438 (2022)
13:40–14:10	Ginestra Bianconi	The dynamics of higher-order networks: The effect of topology and triadic interactions
		Higher-order networks capture the interactions among two or more nodes and they are raising increasing interest in the study of brain networks. Here we show that higher-order interactions are responsible for new dynamical processes that cannot be observed in pairwise networks. In this talk we will cover how topology is key to define synchronization of topological signals, i.e., dynamical signal defined not only on nodes but also on links, triangles and higher-dimensional simplices in simplicial complexes. Interesting topological synchronization dictated by the Dirac operator can lead to the spontaneous emergence of a rhythmic phase where the synchronization order parameter displays low frequency oscillations which might shed light on possible topological mechanisms for the emergence of brain rhythms. We will also reveal how triadic interactions can turn percolation into a fully-fledged dynamical process in which nodes can turn on and off intermittently in a periodic fashion or even chaotically leading to period doubling and a route to chaos of the percolation order parameter.
14:10–14:40	Jean-Pierre Eckmann	The predictive power of theoretical biology: An example
		I will argue, supported by an experiment, that theoretical biology moves (very slowly) in a direction where predictions (as in theoretical physics) become possible. We start with a simple, theoretical, mechanical-genetic model of protein. Using the interpration of its spectral properties, one can formulate some predictions on the possible effects when the protein is mutated. The results suggest that only mutations at specific positions in the gene sequence can have a relevant effect on the function of the protein. These predictions have then been checked in a delicate experiment with actual mutations in the protein Guanylate kinase. A clear signal confirms the theoretical prediction.
14:40–15:00	Coffee break
15:00–15:30	Veronika Stolbova	Complex networks in financial systems
		Policymakers, investors, and firms recognize the need to assess the financial impact of climate change and climate policy on the real economy and the financial system. It is debated, that the introduction of climate policies might lead to a reevaluation of a large portion of financial assets with implications for financial stability. However, currently, there are no consistent bottom-up monetary estimates of climate change-related financial gains and losses of the economy as well as of the current exposure of the economy's financial assets to climate change. To fill this gap, we develop a framework for the assessment of climate change-related financial gains and losses building on recent developments in climate policy assessment, climate stress-testing, and risk analysis. We apply this framework to macro-level and micro-level data of financial contracts (equity holdings, bonds, and loans) between firms worldwide, estimate climate policy risks for the Euro Area, and assess implications for financial stability. We find that direct exposure of the Euro Area through financial assets to fossil-fuel, utility and energy-intensive sectors is relatively small in monetary terms across equity holdings, bonds, and loans. However, financial interconnectedness at the macro-level plays a crucial role in the assessment of climate change-related gains and losses, with noticeable consequences for insurance and pension funds sector of the Euro Area.
15:30–16:00	Kira Rehfeld	Climate variability from the last Glacial to the Anthropocene: Knowns, Unknowns and Future Challenges
		Substantial temperature and precipitation variability with large amplitudes occurred over the last 130,000 years, from the last Interglacial, through the last Glacial up to the last pre-anthropogenic global warming that led to the Holocene Interglacial more than 10 000 years ago. With the industrialization, human influence has overprinted natural variability of the Earth system, and the Holocene has given way to a continued warming now officially recognized as the era of the Anthropocene. Early evidence of large changes in climate variability between cold and warm Earth system states were recognized from Greenland ice core data since the late 20th century. With advances in palaeoclimate data compilation, analysis and proxy modelling we gained a spatio-temporal perspective on the evolution of the climate system over the last 130 000 years. Systematic comparison to state-of-the-art global circulation models (as used in the IPCC projections) shows shortcomings in these model systems beyond the centennial timescale. The newly emerging coupled models out of the PalMod project (www.palmod.de) including dynamic ice sheets and solid Earth components show more promise in representing levels of variability consistent with palaeoclimate evidence. Data-model integration therefore improved our understanding of the longterm predictability of the climate system. Large unknowns in all compartments (Atmosphere, Ocean, Biosphere, Cryosphere, Anthroposphere) remain, each with significant influence on the future trajectory of the Earth system.
16:00–16:30	Matjaž Perc	Nonlinear data analysis and the visual arts
		The 20th century is often referred to as the century of physics. From x-rays to the semiconductor industry, human societies today would indeed be very different were it not for the progress made in physics laboratories around the world [1,2]. What the past 100 years have been for science, the past millennium has been for the arts. From the late Byzantine and Islamic art to Renaissance, Realism and Pop art, the past 1000 years are packed with the most productive periods of our creative existence. The availability of digitized artworks allows us to perform large-scale nonlinear data analysis of the history of visual arts. We have analyzed almost 140,000 visual artworks [3], the majority of which were paintings, by more than 2,300 artists created between the years 1031 and 2016. Based on the complexity and entropy of spatial patterns in the artworks, we were able to hierarchically categorize the artworks on a scale of order-disorder and simplicity-complexity, revealing a temporal evolution of the artworks that coincides with the main historical periods of art. We also outline possibilities for similar research in other forms of art [4]. References [1] M. Perc, Self-organization of progress across the century of physics, Sci. Rep. 3, 1720 (2013) [2] T. Kuhn, M. Perc, and D. Helbing, Inheritance patterns in citation networks reveal scientific memes, Phys. Rev. X 4, 041036 (2014) [3] H. Y. D. Sigaki, M. Perc, and H. V. Ribeiro, History of art paintings through the lens of entropy and complexity, Proc. Natl. Acad. Sci. U.S.A. 115, E8585-E8594 (2018) [4] M. Perc, Beauty in artistic expressions through the eyes of networks and physics, J. R. Soc. Interface 17, 20190686 (2020)
16:30–16:50	Coffee break
16:50–18:20	Minisymposium 1/I (auditorium)	Concepts from complex systems – Networks, synchronisation, recurrence I
	Minisymposium 2 (lecture room 1)	Analysis and modeling of infrastructure networks
18:20–21:00	Poster session I and icebreaker

Thursday, March 16th


9:00–10:30	Minisymposium 3 (lecture room 3)	Adaptive and multistable networks
	Minisymposium 4 (auditorium)	World-earth system analysis
	Minisymposium 5 (lecture room 1)	Cardiovascular dynamics and sleep disorders
10:30–10:45	Coffee break
10:45–12:15	Poster session II
12:15–12:45	Ying-Cheng Lai	Deficiency of deterministic modeling and data-based causal analysis of complex dynamical systems
		This talk will focus on my joint papers with Jürgen in the past as well as some recent effort in climatic dynamics stimulated by Jürgen’s pioneering works in this field. First, I will argue that in complex dynamical systems, there are situations such as unstable dimension variability in which deterministic modeling fails, rendering necessary to develop completely data-driven approaches. I will then discuss the challenging problem of detecting direct causation by eliminating indirect causal influences in situations where the variables of the underlying dynamical system are non-separable and are weakly coupled. I will present a model-free and completely data-driven method of partial cross mapping based on a synthesis of three known methods from nonlinear dynamics and statistics: phase-space reconstruction, mutual cross mapping, and partial correlation, and provide support from a number of real-world systems. Finally, I will discuss a recent work on detecting and quantifying the causal influence among different climate regions in the contiguous U.S. in response to temperature perturbations using the long-term (1901–2018) record of near surface air temperature. The directed causal network constructed by the convergent cross-mapping algorithm enables us to distinguish the causal links from spurious ones rendered by statistical correlation and to identify the Ohio Valley region as an atmospheric convergent zone that acts as the regional gateway and mediator to the long-term thermal environments in the contiguous U.S. References [1] Y.-C. Lai, C. Grebogi, and J. Kurths, “Modeling of deterministic chaotic systems,” Physical Review E 59, 2907-2910 (1999). [2] H.-F. Ma, S.-Y. Leng, C.-Y. Tao, X. Ying, J. Kurths, Y.-C. Lai, and W. Lin, “Detection of time delays and directional interactions based on time series from complex dynamical systems,” Physical Review E 96, 012221, 1-8 (2017). [3] S.-Y Leng, H.-F. Ma, J. Kurths, Y.-C. Lai, W. Lin, K. Aihara, and L.-N. Chen, “Partial cross mapping eliminates indirect causal influences,” Nature Communications 11, 2632, 1-9 (2020). [4] X.-L. Yang, Z.-H.Wang, C.-H.Wang, and Y.-C. Lai, “Detecting the causal influence of thermal environments among climate regions in the United States,” Journal of Environmental Management 322, 116001, 1-9 (2022).
12:45–13:15	Elizabeth M. Cherry, Shahrokh Shahi	Machine-learning approaches for predicting cardiac voltage dynamics
		Disruptions to the electrical behavior of the heart caused by cardiac arrhythmias can result in complex dynamics, from period-2 rhythms in single cells to spatiotemporally complex spiral and scroll waves of electrical activity, which can inhibit contraction and may be lethal if untreated. Accurate forecasts of cardiac voltage behavior could allow new opportunities for intervention and control, but predicting complex nonlinear time series is a challenging task. In this talk, we discuss our recent work using machine-learning approaches based in reservoir computing to forecast cardiac voltage dynamics. First, we show that a novel method combining an echo state network with automated feature extraction via an autoencoder can successfully and efficiently predict time series of synthetic and experimental datasets of cardiac voltage in one cell 20-30 action potentials in advance. Building on this work, we then demonstrate a novel method for predicting the complex spatiotemporal electrical dynamics of cardiac tissue using an echo state network integrated with a convolutional autoencoder. We show that our approach can forecast complex spiral-wave behavior including breakup several periods in advance for time series ranging from model-derived synthetic datasets to optical-mapping recordings of explanted human hearts.
13:15–14:45	Lunch break
14:45–15:15	Rajarshi Roy	Singular, Dual and Plural: A Tale of Numbers, Networks and Synchrony
		Life is full of examples where one progresses from one, to two and then to many; you can just open the Bible and realize that such thoughts have occupied us from a long time back. We will reflect on the dynamics of systems on their own, and then in twos, and finally in threes and fours and more. While creating many identical replicas is difficult (specially for nonlinear dynamical systems), we will examine situations where diversity is important and useful for networks and for synchrony. Some examples from our laboratory and beyond will illustrate these ideas at different scales of space and time. Light will play a central role in illuminating what is distinguishable and indistinguishable.
15:15–15:45	Sudeshna Sinha	Chaos and Noise in the Aid of Logic
		We discuss how understanding the nature of chaotic dynamics allows us to manipulate these complex systems to obtain versatile pattern generators that can be used for a range of applications. Specifically we will discuss the application of chaos to the design of reconfigurable dynamic logic gates. Further we indicate how one can exploit the interplay of nonlinearity and noise to obtain more consistent and robust logic operations. We also suggest how these concepts may be applied to systems ranging from electronic circuits and synthetic genetic networks, to nanomechanical oscillators.
15:45–16:15	Rene van Westen, Sven Baars, Henk A. Dijkstra	Tipping of the Atlantic Ocean Circulation
		The Atlantic Ocean Circulation, in particular its zonally averaged component called the Atlantic Meridional Overturning Circulation (AMOC), is one of the tipping elements in the climate system. The AMOC is sensitive to freshwater perturbations and may undergo a transition to a climate disrupting state within a few decades under continuing greenhouse gas emissions. The potential climate impacts of such a collapse are enormous and hence reliable estimates of the probability of its occurrence before the year 2100 are crucial information for policy makers. In his talk, an overview will be given of the current state of addressing the AMOC collapse problem and approaches to determine AMOC transition probabilities in a hierarchy of ocean-climate models.
16:15–16:45	Coffee break
16:45–18:45	Special birthday session
18:45–22:00	Reception

Friday, March 17th


9:00–9:30	Yong Xu	Early warning and suppression of noise-induced critical transitions
		Noise-induced critical transitions (CTs) from one dynamical state to another contrasting one are widespread in real systems. Once they take place, it is often difficult to restore a system to the previous state, and may cause some catastrophic effects on human living environment, economy and health. Therefore, early warning and suppression of noise-induced CTs have been always the hottest topics in the investigation of nonlinear stochastic dynamics. In this presentation, Gaussian white noise-induced CTs between adjacent states and L\'evy noise-induced CTs between two non-adjacent states are shown, respectively. Correspondingly, a more general early-warning indicator, the parameter dependent basin of the unsafe regime (PDBUR), is proposed. This is a new and efficient tool to quantify the ranges of the parameters where Gaussian white noise or L\'evy noise-induced CTs may occur. Furthermore, by an external linear augmentation method, a new perspective to suppress noise-induced critical transitions away from a desirable state to another contrasting one is presented. All of these results may provide some guidance for managers to take some measures to avoid such catastrophic noise-induced critical transitions in practical applications. This is a joint work with Jinzhong Ma (Shanxi University) and Jürgen Kurths (Humboldt University and PIK)
9:30–10:00	Ulrike Feudel, Lukas Halekotte, Sarah Schoenmakers, Anna Vanselow, Sebastian Wieczorek	Multistability and Tipping: Critical Transitions in Complex Systems
		Many systems in nature are characterized by multistabiliy, i.e., the coexistence of different stable states for a given set of environmental parameters and external forcing. Examples for such behavior can be found in different fields of science ranging from mechanical or chemical systems to ecosystem and climate dynamics. As a consequence of the coexistence of a multitude of stable states, the final state of the system depends strongly on the initial condition. Perturbations, applied to those natural systems can lead to a critical transition from one stable state to another. Such critical transitions are called tipping phenomena in climate science, regime shifts in ecology or phase transitions in physics. Such critical transitions can happen in various ways: (1) due to bifurcations, i.e., changes in the dynamics when external forcing or parameters are varied extremely slow (2) due to fluctuations which are always inevitable in natural systems, (3) due to rate-induced transitions, i.e., when external forcing changes on a characteristic time scale comparable to the time scale of the considered dynamical system and (4) due to shocks or extreme events. We discuss these critical transitions and their characteristics and illustrate them with examples from mechanical and natural systems. Moreover, we discuss the concept of resilience, which has been originally introduced by C.S. Holling in ecology, and reformulate it in terms of dynamical systems theory.
10:00–10:30	Peng Ji	Asymptotic scaling of signal propagation in complex networks
		Many collective phenomena such as epidemic spreading and cascading failures in socioeconomic systems on networks are caused by perturbations of the dynamics. How perturbations propagate through networks, impact and disrupt their functions may depend on the network, the type and location of the perturbation as well as the spreading dynamics. Previous work has analyzed the retardation effects of the nodes along the propagation paths, suggesting a few transient propagation ``scaling'' regimes as a function of the nodes' degree, but regardless of motifs such as triangles. Yet, empirical networks consist of motifs enabling the proper functioning of the system. Here, we show that basic motifs along the propagation path jointly determine the previously proposed scaling regimes of distance-limited propagation and degree-limited propagation, or even cease their existence. Our results suggest a radical departure from these scaling regimes and provide a deeper understanding of the interplay of self-dynamics, interaction dynamics, and topological properties.
10:30–11:00	Coffee break
11:00–12:30	Minisymposium 6 (auditorium)	Dynamics of complex biological systems
	Minisymposium 7 (lecture room 1)	Nonlinear dynamics in economics
	Minisymposium 8 (lecture room 3)	Causation and prediction of weather and climate extremes
12:30–14:00	Lunch break
14:00–15:30	Minisymposium 9 (lecture room 1)	Tipping points
	Minisymposium 1/II (auditorium)	Concepts from complex systems – Networks, synchronisation, recurrence II
15:30–15:50	Coffee break
15:50–16:20	Deniz Eroglu	Recurrences: Fingerprints of dynamics – A journey from low dimensional systems to climate networks
		Climate systems comprise parts (nodes) that interact through an intricate network, and climate events result from these unknown complex interactions. Understanding such complex systems that evolve in time is dependent on measured datasets. However, only data availability does not lead to a better understanding of a system if the interactions governing the evolution of the system’s behavior remain unknown. Data analysis for the behavior characterization of dynamical systems requires sufficiently long time series, which is mostly unavailable for palaeoclimate proxies. In this talk, I will briefly overview recurrence plot based time series analysis using limited data, from characterizing low-dimensional systems to reconstructing paleoclimate networks. In the applications, topological changes in the paleoclimate networks allow the detection of climate regime switches in the past, which are the recursive events that will help to forecast oncoming climate events in large time scales.
16:20–16:50	R. I. Sujith	Complex system approach to investigate and mitigate thermoacoustic instability in turbulent combustors
		The onset of thermoacoustic instability leading to large amplitude self-sustained oscillations is a plaguing problem in the development of modern gas turbine and rocket engines. Thermoacoustic instability occurs as a consequence of the nonlinear interaction between the unsteady flame, the hydrodynamic field and the acoustic field in the combustor. Traditionally, this phenomenon has been modeled using a linear acoustic framework. An alternate perspective in which a thermoacoustic system in a turbulent combustor can be viewed as a complex system and its dynamics be perceived as emergent behaviors of this complex system has emerged recently. This perspective has led to strategies to forewarn and mitigate thermoacoustic instability based on complex systems theory.
16:50–17:05	Closing