Recurrence analysis and Hurst exponents
Recurrence analysis is a modern method for non-linear time series analysis. New developments combine non-linear approaches with those from fractal geometry. In this Master's thesis, the properties of the method are compared with alternative approaches such as "Detrended Fluctuation Analysis" and "Hurst Exponent".
Improving phase sync measure using τ-recurrence rate
τ-recurrence rate can be used to study phase synchronisation. Comparing τ-recurrence rates of different systems was originally introduced by Pearson correlation coefficient, but other measures seem better suited. τ-recurrence rate is actually a probability of recurrence, therefore, measures to compare probabilities should be tested and compared.
Recurrence analysis of past Indian monsoon variability
Coupled land-ocean-atmosphere interactions play a crucial role in climate variability on all time scales. Among these interactions, monsoons are one of the most important phenomena in low latitudes. The Indian monsoon rainfall has a direct effect on the livelihoods of two billion people in the Indian-subcontinent and is an important component of tipping elements in climate. However, short-time scale monsoon dynamics and their forcing mechanisms are still not fully elucidated. In paleoclimate studies to date, the major focus has been on the role of millennial and multicentennial climate variability of the Indian monsoon intensity, but its evolution on sub-decadal to sub-centennial scales is poorly constrained. As paleoclimate records with the appropriate resolution to study subdecadal to multidecadal monsoon dynamics are extremely scarce, decadal Indian monsoon reconstruction has been essentially limited to the most recent past, where climate variability is recorded with instrumental data. To address this, we applied mass spectrometry imaging (MSI) to generate biomarker-based sea surface temperature (SST) reconstruction from the finely laminated northeastern Arabian Sea sediment deposited during the large part of the Holocene (from 1,500 to 10,500 years before preset), which represent a great archive to study high resolution past Indian monsoon variability. MSI on sediments is recently introduced technique in paleoclimatology and allows for the detection and visualization of biomarkers on intact sediment core sections at micrometre-scale resolution allowing for unprecedented resolution. We are seeking for a student that will perform recurrence network analysis on this highly resolved SST time series for detecting episodes with pronounced non-linear changes in Indian monsoon intensity.
Design and implemenation of algorithms to assess the role of nodes in spreading processes on networks
Master project together with DLR: In this thesis, you will delve into the challenging problem of identifying vital nodes in complex, temporal networks. Vital nodes are those with the most influence on the network, which is critical in various scenarios, such as the spread of viruses, misinformation, and radicalization. Our focus is on epidemic preparedness and controlling virus spread. However, the methods you develop could be adapted to other fields as well. Your task will be to design and implement a novel algorithm that combines message-passing principles with machine learning techniques in temporal networks. The unique aspect of this work is the use of privacy-preserving methodologies that do not require direct access to the entire network. Instead, you will work with indirectly propagated information to estimate a node's vitality. More information and official application form at https://dlr.concludis.de/prj/shw/c281d780ae00740bafb97fea5389bbc9_0/.
Development of Sonification Framework for Palaeoclimate Data
Are you interested in exploring how data can be transformed into sound? This project involves developing a framework to convert palaeoclimate data, such as Milankovitch cycles and various proxy records (e.g., ice cores, sediment layers, tree rings), into an auditory experience. By sonifying complex data patterns, the aim is to create an intuitive way to understand long-term climate changes and enhance the interpretation of cyclical phenomena like orbital forcing. This project combines climate science, data analysis, and digital audio processing, offering a unique opportunity to bridge scientific research and creative technology. Ideal for students with a background in environmental science, data science, or digital media.
Einfluß der Quasi-biennial Oscillation auf die Europäischen Winter-Temperaturen
Oszillationen sind in der Natur allgegenwärtig und nehmen auch im Klimawandel eine Schlüsselrolle ein. Die Quasi-biennial Oscillation (QBO) ist eine zeitliche Veränderung der Richtung des zonalen Windes in der äquatorialen unteren Stratosphäre mit Perioden von etwas mehr als zwei Jahren (28 Monate). Diese Richtungsänderungen haben signifikanten Einfluss auf die vertikale Ausbreitung Planetarer Wellen in den mittleren Breiten der Winterhemisphäre und auf den Temperaturverlauf über Europa. Jedoch sind die Mechanismen nur unzureichend verstanden was die Abschätzung des Einflusses der globalen Erwärmung auf die QBO und die Wintertemperaturen erschwert. Um den Mechanismus dieses Zusammenhanges besser zu verstehen soll in einem Master-Projekt ein konzeptionelles Modell für dieses gekoppelte System entwickelt und damit Synchronisationsphänomene studiert werden. Anhand instrumenteller Beobachtungsdaten sollen die Kopplungsrichtungen und -stärken zwischen den atmosphärischen Teilsystemen mit modernen Verfahren (z. B. Tigramite) untersucht und quantifiziert werden.
Übersicht chaotische Systeme (Bachelor-/ Praktikumsprojekt)
Systematische Zusammenstellung charakteristischer Maße (Lyapunov-Exponent, Dimension, Recurrence-Maße) für verschiedene chaotische Systeme.
[not available] Recurrence analysis of tipping points
Tipping points are important features in dynamical systems. Their detection and the definition of early warning indicators is of high interest in the light of the climate crisis. In this Master's project, an alternative approach for their detection and potential early warnings will be tested, based on recurrence analysis. Recurrence analysis is a novel approach, combining the fields of nonlinear dynamics, fractal geometry, and complex systems. A focus will be tipping models with multiple time scales. Further, data from different applications will be considered, such as palaeoclimate data from speleothems.
[not available] New metrics for event recurrence analysis
New extensions in the recurrence plot framework allow their direct application on event data (highly discrete data). In this project, alternative metrics for recurrence analysis will be implemented and investigated with respect of their usability.
[not available] New metrics for spectral analysis of event data
Recent developments introduced the concept of spectral analysis for event data. In this project, alternative metrics for this analysis will be implemented and investigated with respect of their usability.
If you are interested, contact Norbert Marwan.
