Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Statistical Analysis and Stochastic Modelling of Complex Systems

Head of group:  Eule, Stephan 

The vast majority of real-world systems is too complex to be described ab initio. Typically, these systems are in state far from equilibrium and governed by complicated non-linear interactions and intricate fluctuations. Almost all biological und socio-economic systems belong to the sphere of complex systems.

To gain quantitative insight into the behavior of complex systems, we follow a two-fold approach. Firstly, we pursue a data driven modelling strategy that employs techniques from computational statistics, machine learning and, in particular, deep learning.  Secondly we develop and analyse stochastic non-linear models that try to capture typical function-defining dynamics of a given complex system.


Statistical Properties of Order Books

In recent years there have been considerable efforts to employ methods from theoretical physics to problems in economics. Our group is interested in the dynamics of the order book, which can be seen as the ultimate microscopic level of description of financial markets.

Dynamics and Control of Infectious Diseases

The sudden appearance and rapid spread of an infectious diseases can pose a serious threat to human or animal populations that calls for immediate actions by national and international health agencies. Their response is guided by epidemiological models whose primary use is to provide means of comparing the effectiveness of different containment strategies. The focus of our group is to quantify, how heterogeneity of the infection process affects the course of an infectious disease. In particular, we are interested in the effect of indiviudal variation in disease transmission on control strategies in the early phase of an epidemic outbreak and the consequences of spatially varying infection rates on travel restrictions.

Automated Cell-Segmentation with Cycle-Consistent Generative Adversarial Networks

A central problem in biomedical imaging is the preparation of images for further quantitative analysis via automated image segmentation. Especially the segmentation of images with lower quality remains challenging. We propose a new semi-supervised image segmentation method based on generative adversarial Networks (GANs) that can be trained even in absence of prepared image - mask pairs. In particular, we use a Cycle-GAN architecture to train on unpaired training data. Our model generalises well to test data differing from the training data and successfully performs image segmentation tasks on samples with substantial defects.

Anomalous Stochastic Processes

If the time-evolution of the mean-squared displacement of some quantity is non-linear, the system is said to exhibit anomalous diffusion. The underlying mechanisms leading to such anomalous diffusion can be multifold. Our group focuses on processes whose anomalous behavior is due to heavy-tailed distributions of either the waiting time distribution between the displacements or of the displacements themselves.

Automated Identification and Facial Expression Recognition of Primates in the Wild

Monitoring the behavior groups of animals is important in many different areas, such as cognitive neuroscience and animal welfare. We are establishing an automated data analysis pipeline that detects the full body of primates as well as their faces on videos recordings, identifies the respective animals and predicts their facial expressions.

People working in this Group:

Name Email Phone
Stephan Eule send email   [+49-(0)551-5176-411
Theo Geisel send email   [+49-(0)551-5176-400
Matthias Häring send email   [+49-(0)551-5176-421
Nicolas Lenner send email   [+49-(0)551-5176-421