Inverse Network Dynamics - Network structure and function from nonlinear dynamics and time series data

Approved poster contributions will only be presented on-site.

For each poster contribution there will be one poster wall (width: 97 cm, height: 250 cm) available. Please do not feel obliged to fill the whole space. Posters can be put up for the full duration of the event.

Network data analysis of sepsis patients

Alkofer, Moritz

Moritz Alkofer, Fenja Drauschke, Rico Berner, Jakub Sawicki, Thomas Löser, and Eckehard Schöll Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany and Institut LOESER, Wettiner Straße 6, 04105 Leipzig, Germany Within a dynamical systems perspective on the modeling of sepsis and its organ-damaging consequences, we present a statistical analysis of medical data of sepsis patients from hospital intense care units. We process the data and group them according to several features. To do so we apply vector autoregression to time series patient data and establish granger causalities. The results are compared with computer simulations within a functional two-layer network model for sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the coevolutionary dynamics of parenchymal, immune cells, and cytokines. By means of the simple paradigmatic model of phase oscillators with adaptive coupling weights in a two-layer system, we analyze the emergence of organ threatening interactions between the dysregulated immune system and the parenchyma. We demonstrate that the complex cellular cooperation between parenchyma and stroma (immune layer) either in the physiological or in the pathological case can be related to dynamical patterns of the network. In this way we explain sepsis by the dysregulation of the healthy homeostatic state (frequency synchronized) leading to a pathological state (desynchronized or multifrequency cluster) in the parenchyma. We provide insight into the complex stabilizing and destabilizing interplay of parenchyma and stroma by determining critical parameters of the model from the real patients' data.

Network reconstruction of chaotic synchronized networks via information theory

Canlı Usta, Özge

When chaotic systems are coupled to each other through state variables, synchronization can happen. Here, we present an analytical study for the reconstruction of chaotic synchronized networks based on average integrated causation entropies. We show that if we inject the random information via impulsive perturbations into the individual systems to destroy the synchronization briefly, that can lead to the prediction of the network structure en route to re-synchronization. An algorithm based on theoretical results is developed to reconstruct the adjacency matrix of the network. The results indicate that the proposed algorithm can be used to reconstruct the network en route to re-synchronization.

Reconstruction of Brain Network Flexibility using FitzHughNagumo Oscillators Located on the Nodes of Diffusion Tensor Imaging Structural Matrix

Chinichian, Narges

In our study, computer simulations of a simple dynamical model of the brain are presented. The model uses an empirical network structure obtained from Diffusion Tensor Imaging (DTI) data and generic dynamics on each node of the network. The model is employed to simulate brain flexibility patterns in order to have a way to assess the mechanism behind the flexibility measure [chinichian et al 2022]. We show that the brain connection structure and the collection of nodes that are being stimulated play crucial roles in the brain-like pattern observed.

A Data-driven Approach to Cattle Epidemic Modelling under Uncertainty

Farokhnejad, Sima

Cattle movement is an intrinsic part of animal husbandry (i.e., breeding, maintenance, slaughter of livestock). There are an estimated 1 billion cattle heads in the world used for the production of meat, milk, leather, among other products, which are consumed by billions of people. The pressures of efficiently delivering animal products to individuals, lead to a stress in the system both in the number of heads kept and traded, and in the number of possible contacts between these heads. Under these conditions, contact tracing and avoidance is an essential part of modern agriculture because highly contagious diseases such as brucellosis and foot-and-mouth disease can spread through contact, leading to heavy economic costs. Many countries track their cattle with electronic tags (e.g. Australia, Canada) which leads to a highly-precise monitoring capability. Unfortunately, several of the largest producers in the world (e.g. Brazil, Mexico, USA), do not mandate such use, and some do not even mandate the tracking of animal movement (e.g. Mexico, USA). Added to this, the lack of tracking capabilities enable people to take advantage of the system by engaging in unregulated cattle trade. The consequence is that official movement data may contain uncertainty in the number of cattle movements as well as the number of actual trades. This work focuses on understanding uncertainty in cattle movement networks and its relation to epidemic modelling.

Transition to hyperchaos and rare large-intensity pulses in Zeeman laser

Kingston, S. Leo

In this presentation, we explore a few distinct types of intermittent large-intensity pulses, namely, Pomeau-Manneville intermittency, quasiperiodic intermittency, and quasiperiodic breakdown to chaos, that originate from periodic, quasiperiodic, and chaotic states, respectively, in Zeeman laser. During the transitions to large-intensity pulses, we observe the origin of hyperchaos. We classify the transitions to hyperchaos as discontinuous against a parameter change, in all the cases, however, from periodic to hyperchaos, it shows hysteresis, but during quasiperiodic and chaotic to hyperchaos transition, no hysteresis is recorded. These features are revealed by plotting the two largest Lyapunov exponents of the laser model against the parameter. The turbulent phases of intermittency always consist of large intensity pulses. The large intensity pulses show characteristic features of extremes, in the sense, that they are larger than a significant height and have a probability of rare occurrence.

Dynamics of networks present during order-disorder transition in a microscopic swarm

Kishore, Vimal

Coordination among individual elements, exhibiting collective behavior, plays a crucial role in achieving. Here, we show a disorder-order transition in an experimental system consisting of hundreds of magnetic micro-rafts, spinning at the air-water interface. We can characterize this transition by studying dynamics of networks, where edges among rafts are identified using Voronoi tessellation. In the process, initially a random network is observed which gets transformed into a regular network.

Ordinal pattern based complexity analysis of high-dimensional chaotic time series

Kottlarz, Inga

The ordinal pattern-based Complexity-Entropy Plane is a popular tool in nonlinear dynamics for distinguishing noise from chaos. While successful attempts to do so have been documented for low-dimensional maps and continuous-time systems, high-dimensional systems have not been investigated as thoroughly. To address the question in which way time series from systems governed by high-dimensional chaos can be characterized by their location in the Complexity-Entropy Plane we analyze data from several high-dimensional systems of different types, including spatially extended systems, dynamical networks and delay systems. We demonstrate the importance of the choice of the length and lag of the patterns, as well as the influence of the available data length and attractor dimension and discuss their impact on surrogate data tests.

Inferring oscillator's phase and amplitude response from a scalar signal exploiting test stimulation

Mau, Erik

The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator's reaction to stimulation at a specific phase and is a primary characteristic of a self-sustained oscillatory unit. Knowledge of this curve yields a phase dynamics description of the oscillator for arbitrary weak forcing. Similar, though much less studied characteristic, is the amplitude response that can be defined either using an ad hoc approach to amplitude estimation or via the isostable variables. Here, we discuss the problem of the phase and amplitude response inference from observations using test stimulation. Although PRC determination for noise-free neuronal-like oscillators perturbed by narrow pulses is a well-known task, the general case remains a challenging problem. Even more challenging is the inference of the amplitude response. This characteristic is crucial, e.g., for controlling the amplitude of the collective mode in a network of interacting units; this task is relevant for neuroscience. Here, we compare the performance of different techniques suitable for inferring the phase and amplitude response, particularly with application to macroscopic oscillators. We suggest improvements to these techniques, e.g., demonstrating how to obtain the PRC in case of stimuli of arbitrary shape. Our main result is a novel technique denoted by IPID-1, based on the direct reconstruction of the Winfree equation and the analogous first-order equation for isostable dynamics. The technique works for signals with or without well-pronounced marker events and pulses of arbitrary shape; in particular, we consider charge-balanced pulses typical in neuroscience applications. Moreover, this technique is superior for noisy and high-dimensional systems. Additionally, we describe an error measure that can be computed solely from data and complements any inference technique.

How electrical power grid topology influences dangerous solitary states

Niehues, Jakob

The operational stability of electrical power grids is of utmost importance to ensure a reliable supply of energy and prevent damages and blackouts. Conventional control schemes and grid architecture are challenged by the transition to sustainable energy generation as few, large generators with massive rotating turbines in a highly centralized grid are replaced by many distributed, fluctuating sources of varying size, such as solar and wind power. Therefore, identifying robust and cost-efficient grid architecture, as well as weak points to avoid when planning and building power grids, is an ongoing research area. The voltage and frequency dynamics of AC power grids can be modeled as coupled non-linear oscillators on sparse complex networks. In addition to the desired operating state, in which all nodes are synchronized at network frequency, e.g., 50 Hz, there exists a variety of partially synchronized attractor states. Solitary states consist of a large, synchronized cluster and a single oscillator that rotates with a different velocity, i.e., AC frequency. They pose a threat to power grid stability, as they would cause overload damages and can be easily reached through single-node perturbations. Especially vulnerable to such perturbations are dense sprouts, which are degree-1 nodes with distinct topological properties and a well-connected neighbor. Novel solitary states in which the velocity of the dense sprout differs from its natural velocity have recently been discovered in numerical simulations. In this work, we propose a toy model with which we can theoretically explain the presence of the novel solitary states. It can be used to adjust network architecture to prevent their occurrence. In this model, the rest of the synchronized complex network is reduced to its key factor, i.e. the degree of the neighbor. Applying a linearization approach, we obtain an approximate analytical solution close to the full non-linear dynamics. We then derive a self-consistency equation for the velocity of the solitary node. We demonstrate that the toy model resembles highly localized network modes in the linear stability regime around the operating state. The velocity of the dense sprout arises from resonance with this network mode under the constraint of matching the network‘s power flow. We investigate the stability regime of the novel solitary states and its dependence on initial conditions, system parameters, i.e., characteristics of grid components, and topology.

Inferring network connectivity using modified Reservoir Computing

Rojas, Pablo

Inferring directed links in networks of interacting systems is a problem spanning many disciplines. Systems out of equilibrium represent a special case, where samples are not independent but structured as timeseries. In this context, Recurrent Neural Networks (RNN) have attracted recent attention, due to their ability to learn dynamical systems from sequences. We introduce a method to infer connectivity of a network from the timeseries of its nodes, using a RNN based on Reservoir Computing (RC). We show how modifications of the standard RC architecture enable a reliable computation of the existence of links between nodes. While the method does not require information about the underlying mathematical model, its performance is further improved if the selection of hyperparameters is roughly informed by knowledge about the system. The method is illustrated with examples from different complex systems, ranging from networks of chaotic Lorenz attractors to biological neurons. Using simulations of these systems, we demonstrate its power and limitations under a variety of conditions, such as noise levels, delayed interactions, size of the network and hidden variables. *joint work with Marie Kempkes and Martin E. Garcia

Prediction of different dynamics and identification of basins of multi-stable attractor using ESN.

Roy, Mousumi

In the field of complex dynamics, multistable attractors have been gaining a significant attention due to its unpredictability in occurrence and extreme sensitivity to initial conditions. Diverse systems ranging from climate to finance market, ecological system to engineering co-existing attractors arise, but a straight-forward numerical pathway for identifying those attractors is still not available. In this article, we investigate a possible route of identifying multistablity using echo state network (ESN). Initially, we train ESN with the time-series of one of the attractors with the corresponding parameter values. We do not reveal any other information about the system dynamics to ESN. Interestingly, after successful training, ESN becomes dynamically aware about the parameter values and able to predict the dynamics at diverse parameter range only based on the values of the new parameters. In this context, continuing this process, we can perfectly recreate the bifurcation diagram using ESN with the information of only a few time series. Furthermore, we can also make a prediction of different dynamics of a multistable attractor and identify the corresponding basins for different attractors using ESN. We generalize the results with another model as well.

How-to Science Advice – Lessons from UNESCO and the German Parliament

Vogel, Hannes

Science and technology are shaping and changing our society. The challenges of today and tomorrow are increasingly complex and require both societal as well as technological solutions. But how can science purposefully support decision-making processes in politics? What are relevant stakeholder, when and how to reach out to them? How to communicate important information? In this talk, I would like to share my experiences from the European Physical Society, the German Parliament and the German Commission for UNESCO.

Resilience of emergency infrastructure networks after flooding events

Wassmer, Jonas

Extreme weather events with tremendous socio-economic impacts are often caused by a combination of multiple climate drivers and hazards. Such 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 weather-related damage of critical infrastructure caused by heavy rainfalls and landslides. The devastating floods that struck western Germany’s Ahr valley in the summer of 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 modified gravity model of travel to simulate the changes of the traffic load during the event and identify vulnerabilities in the system. We further compute how the time to emergency services like hospitals and fire stations changes during the flood to enhance their accessibility.