08:45  09:00

opening  Frank Jülicher, director of the MPIPKS and the scientific coordinators

09:00  09:40

Plamen Ch. Ivanov
(Boston Univeristy)
The new field of network physiology: mapping the human physiolome
The human organism is an integrated network where complex physiological systems continuously interact to optimize and coordinate their function. Organtoorgan interactions occur at multiple levels and spatiotemporal scales to produce distinct physiologic states. Disrupting organ communications can lead to dysfunction of individual systems or to collapse of the entire organism. Yet, we do not know the nature of interactions among systems and subsystems, and their collective role as a network in maintaining health. The new field of Network Physiology aims to address these fundamental questions.
Through the prism of concepts and approaches from statistical and computational physics and nonlinear dynamics, we will present a new framework to identify and quantify dynamic networks of organ interactions. We will demonstrate how physiologic network topology and systems connectivity lead to integrated global behaviors representative of distinct states and functions.
The presented investigations are initial steps in building a first Atlas of dynamic interactions among organ systems and the Human Physiolome, a new kind of BigData of blueprint reference maps that uniquely represent physiologic states and functions under health and disease.
*We acknowledge support from W M Keck Foundation.

09:45  10:25

Klaus Lehnertz
(Universität Bonn)
Characterizing the dynamics of the human epileptic brain
Epilepsy is a complex malfunction of the brain that affects 50 million people worldwide.
Epileptic seizures are the cardinal symptom of this multifacetted disease and are usually characterized by an overly synchronized firing of neurons. Seizures cannot be controlled by any available therapy in about 25% of individuals, and knowledge about mechanisms underlying generation, spread, and termination of the extreme event seizure in humans is still fragmentary. Over the last decades, an improved characterization of the spatialtemporal dynamics of the epileptic process could be achieved with time series analysis tools from nonlinear dynamics, statistical physics, synchronization and network theory. I will summarize these research findings that already have opened promising directions for the development of new therapeutic possibilities.

10:30  10:50

Elizabeth Bradley
(University of Colorado)
Nonlinear TimeSeries Analysis of a paleoclimate temperature record from antarctica
Until recently, the resolution of icecore records was inadequate for nonlinear timeseries analysis. Advances in laboratory techniques have greatly improved this situation. The isotopic content of the WAIS Divide core, for instancethe longest continuous and highestresolution such record yet recovered from Antarcticawas measured at 0.5 cm intervals. This is an order of magnitude better than older cores from both poles, which lump years or even decades worth of climate information into each data point. These particular isotopic measurementsratios of the heavy to light isotopes of hydrogen and oxygenare considered to be proxies for Earth's temperature. Taking a nonlinear dynamics view of this, we consider these two traces as the outputs of two different measurement functions sampling the dynamics of the paleoclimate and use the method of delays to reconstruct those dynamics over the past 31,000 years. There are a number of unique challenges involved in this analysis. The measurements are spaced unevenly in time because of the progressive downcore thinning of the ice. The relationship between depth and age, and hence the timeline of the data, is uncertain. And the ice itself has undergone tens of thousands of years of unknown natural processes, which can affect both the data values and the timeline. We discuss all of these effects from the standpoint of nonlinear timeseries analysis, including changepoint detection, fractal dimension, and Lyapunov exponents.

10:55  11:25

coffee break

11:25  11:45

Ilya Sysoev
(Kotel'nikov's Institute of RadioEngineering and Electronics)
Reconstruction of complex architecture of couplings in networks of coupled oscillators from time series of stationary dynamics and transient processes
Reconstruction of coupling from time series of oscillatory systems is a problem, having applications in different fields of science, including neurophysiology (and biology in general), climatology, econometrics and radioengineering. There are two main classes of approaches to this problem. The first one declares that a sufficiently good model for each node of the network is hardly to be constructed; therefore, the general (usually, autoregressive) models are used. Different realizations of Granger causality and partial directed coherence follow this idea. The other class declares that a physically/chemically/biologically driven equations can be written for each node, and these equations are simple enough to be fitted to experimental data. The different techniques for reconstruction of ensembles of phase oscillators, stochastic oscillators, timedelayed systems, first order neurooscillators, van der Pol, Rössler and Lorenz systems and some other models were proposed, with these techniques using specifics of the considered type of nodes to increase their efficiency.
Here, we propose some special modifications of previously developed techniques for reconstruction of ensembles of nodes described by ODEs of 1st and 2nd order, targeting problems of:
• Partial effective synchronization of some elements of ensembles (not strict synchronization, but close dynamics during the measurement time interval). We use Fisher criterion to determine the element, driving from which cannot be separated, and then the whole cluster is considered as a source of signal for the network.
• Hidden series of some nodes. We propose to try using the signal of other nodes in case of partial synchronization, and to separate some part of network if the hidden node affects the dynamics of some subnetwork only.
• Transients. We show that using long transients is sometimes as much efficient as using stationary chaotic series. Also we study coupling changes due to short transients between stationary regimes and compare the results with results previously reported for this task using other approaches such as Granger causality.
This study was funded by Russian Science Federation, grant number 191200201.

11:50  12:10

Günter Radons
(Technische Universität Chemnitz)
Hidden markov dynamics of chaotically diffusing solitons
We investigate the chaotic diffusion of dissipative solitons in the onedimensional CubicQuintic Complex GinzburgLandau Equation, a prototypical system from nonlinear optics. It turns out that the incremental process of the soliton motion is governed for a wide range of parameters by Hidden Markov Processes with continuous output. We show that a 4state Hidden Markov Modell with Gaussian output density functions approximates very well the observed soliton dynamics with respect to correlation functions, certain waiting time distributions and the distribution of jump widths. In limiting cases of the parameters the dynamics reduces to an AntiPersistent Random Walk with fluctuating jump widths.

12:15  12:40

Mikhail Prokhorov
(Institute of Radio Engineering and Electronics of Russian Academy of Sciences)
Reconstruction of timedelayed feedback systems with hidden variables
We propose a method for the reconstruction of dynamical systems with timedelayed feedback, having several hidden variables, including a hidden variable with a time delay. The method is based on the original approach, which allows one to significantly reduce the number of starting guesses for a hidden variable with a delay. The main idea is to assign only a small number of starting guesses on the delay time interval and find the remaining initial conditions for the hidden variable by interpolating the trajectory with a cubic spline. As the objective function of the method, we use the sum of squares of the distances between the points of the observed variable and its reconstruction. By minimizing the objective function, we obtain an estimation of the unknown parameters and recover the time series of hidden variables.
The method is applied to the reconstruction of the model system of LangKobayashi equations, which describes the dynamics of a singlemode semiconductor laser with timedelayed feedback, from periodic and chaotic time series. The dependence of the quality of the system reconstruction on the accuracy of the assignment of starting guesses for unknown parameters and hidden variables is investigated. It is shown that for periodic regimes, the region of starting guesses, which provides high quality of reconstruction, is greater than for chaotic regimes.
This work was supported by the Russian Foundation for Basic Research, Grant No. 190200071.

12:45  13:45

lunch

13:45  14:30

discussions

14:30  15:10

Celso Grebogi
(University of Aberdeen)
Compressive sensing based prediction of dynamical systems and complex networks
In the fields of complex dynamics and complex networks, the reverse engineering, systems identification, or inverse problem is generally regarded as hard and extremely challenging mathematically as complex dynamical systems and networks consists of a large number of interacting units. However, our ideas based on compressive sensing, in combination with innovative approaches, generates a new paradigm that offers the possibility to address the fundamental inverse problem in complex dynamics and networks. In particular, in this talk, I will argue that evolutionary games model a common type of interactions in a variety of complex, networked, natural systems and social systems. Given such a system, uncovering the interacting structure of the underlying network is key to understanding its collective dynamics. Based on compressive sensing, we develop an efficient approach to reconstructing complex networks under gamebased interactions from small amounts of data. The method is validated by using a variety of model networks and by conducting an actual experiment to reconstruct a social network. While most existing methods in this area assume oscillator networks that generate continuoustime data, our work successfully demonstrates that the extremely challenging problem of reverse engineering of complex networks can also be addressed even when the underlying dynamical processes are governed by realistic, evolutionarygame type of interactions in discrete time. I will also touch on the issue of detecting hidden nodes, on how to ascertain its existence and its location in the network, this being highly relevant to metabolic networks.

Data based identification and prediction of nonlinear and complex dynamical systems, W.X. Wang, Y.C. Lai, and C. Grebogi, Phys. Reports 644, 176 (2016)
Predicting catastrophe in nonlinear dynamical systems by compressive sensing, W.X. Wang, R. Yang, Y.C. Lai, V. Kovanis, and C. Grebogi, Phys. Rev. Lett. 106, 154101 (2011)
Network reconstruction based on evolutionarygame data via compressive sensing, W.X. Wang, Y.C. Lai, C. Grebogi, and J. Ye, Phys. Rev. X 1, 021021 (2011)
Forecasting the future: Is it possible for adiabatically timevarying nonlinear dynamical systems? R. Yang, Y.C. Lai, and C. Grebogi, Chaos 22, 033119 (2012)
Optimizing controllability of complex networks by minimum structural perturbations, W.X. Wang, X. Ni, Y.C. Lai, and C. Grebogi, Phys. Rev. E 85, 026115 (2012)

15:15  15:35

Leonid Rubchinsky
(Indiana University Purdue University Indianapolis and Indiana University School of Medicine)
Modelling experimentally observed properties of intermittent neural synchronization
Synchronization of neural activity in the brain is involved in a variety of brain functions including perception, cognition, memory, and motor behavior. Excessively strong, weak, or otherwise improperly organized patterns of synchronous oscillatory activity may contribute to the generation of symptoms of different neurological and psychiatric diseases. However, synchrony in cortical and subcortical circuits is frequently variable in time and not perfect. Few long intervals of desynchronized dynamics may be functionally different from many short desynchronized intervals although the average synchrony may be the same. Analysis of experimental recordings reveals a rich temporal structure of intermittent neural synchronization. Some of its properties appear to be potentially universal, while some a specific to particular brain states and other conditions. We will discuss the techniques to analyze the temporal patterning of synchronized activity in the experimental data and its implications for neural model building.

15:40  16:00

George Datseris
(MPI for Dynamics and SelfOrganization)
Predicting spatiotemporal timeseries using DimensionReduced local states
Spatiotemporal systems are ubiquitous in nature, ranging from biological systems, active matter, turbulence, electromagnetism and wave propagation, to name a few. It is advantageous to be able to temporally predict the evolution of such systems, in an iterative fashion. Also, it is often necessary to be able to cross estimate one field of a pair of coupled fields, given the complementary one.
What makes this task difficult is that the complex dynamics of spatiotemporal systems typically lead to highdimensional chaos and are thus hard to predict.
An additional difficulty comes from the nature of spatiotemporal data, which when sampled discretely lead to high dimensional data points. This can make some numeric prediction techniques unfeasible, from a computational perspective.
Here we will present a method for both cross estimation and iterated timeseries prediction of spatiotemporal systems based on estimating the local dynamics. Our method works using reconstructed local states, PCA dimension reduction, and nearest neighbour prediction methods. The effectiveness of this approach will be shown for (noisy) data from a cubic Barkley model, the BuenoOrovioCherryFenton model, and the KuramotoSivashinsky model.

16:05  16:30

coffee break

16:30  17:30

dymecs19 colloquium (chair: Holger Kantz, mpipks)
Edward Ott (University of Maryland)
We first review the basic idea of using machine learning in conjunction with a limited duration of time series data to construct a closedloop, autonomous, dynamical system that can predict the future evolution of the state of the unknown system that generated the data [1]. Using the reservoir computing type of machine learning, we then present examples of extensions and applications of this idea. These will include a parallel implementation enabling forecasting of the states of very large spatiotemporally chaotic systems with local interactions [2], a hybrid scheme where an imperfect knowledgebased model component is combined with a limitedsize machine learning component to achieve prediction performance much better than that of either of the components acting alone [3], an architecture combining the parallel and hybrid schemes, and generalization of ensemble Kalman filtering to cyclic prediction using the parallel/hybrid machine learning schemes. As an example of the potential utility of these elements for large complex spatiotemporally chaotic systems, their use in our ongoing project on improving weather forecasting [4] will be outlined.
[1] Jaeger, Haas, Science (2004).
[2] Pathak, Hunt, Girvan, Lu, Ott, Phys Rev Lett (2018).
[3] Pathak, Wikner, Fussell, Chandra, Hunt, Girvan. Ott, CHAOS (2018).
[4] Collaborators on our current weather forecasting project: T. Acomano, M. Girvan, B. Hunt, G. Katz, J. Reggia, I. Szunyogh, C.Y. Wang, A. Wikner.


Using machine learning for prediction of large, complex, spatially extended systems

18:00  19:00

dinner

19:00  20:00

discussions

20:00  22:00

Poster session I (focus on odd poster numbers)
