Dear all, This is a reminder for the upcoming Cologne Summer School on non-linear analysis methods for master's degree and PhD students. Deadline for applications is 10th of July, 2015. ------------------------------------------------------------------- Cologne Summer School 2015: *Non-Linear Methods for Complex Systems Analysis* Date: Mon-Fri 28.09-02.10.2015 Location: *University of Cologne*, Germany ------------------------------------------------------------------- This one-week summer school brings together *master's degree and PhD students from international universities* for an interdisciplinary hands-on learning experience. The workshop will introduce non-linear analysis methods using the Python toolbox pyunicorn. With the techniques presented in the summer school, such as complex networks and phase space concepts, the students will be able to characterize highly complex systems. Such systems are frequently encountered, e.g., in *biology, chemistry, economics, geoscience, neuroscience, and physics*. Lectures and computer labs will be led by Dr. Reik Donner and Marc Wiedermann from the Potsdam Institute for Climate Impact Research. For the complete program visit *complexsystems.uni-koeln.de/summerschool.html*. The application deadline is 10.07.2015. The summer school is organized by the Competence Area 3: Quantitative Modeling of Complex Systems of the University of Cologne. Contact: Dr. Michael von Papen (/vonpapen@geo.uni-koeln.de/) ------------------------------------------------------------------- *Information* The Competence Area 3: Quantitative Modeling of Complex Systems of the University of Cologne hosts a summer school to introduce novel and groundbreaking methods for the analysis of scientific data. For this matter, we bring together master's degree and PhD students from the University of Cologne and from international universities for an interdisciplinary learning experience. The aim of the summer school is not only to teach new analysis methods, but also to foster scientific collaboration and discussion between students of different fields of study. This year, the summer school of the Competence Area 3 will introduce non-linear analysis methods to study highly complex systems, which cannot be sufficiently characterized with linear methods. Such systems are frequently encountered, e.g., in biology, chemistry, economics, geoscience, neuroscience, and physics. The one-week summer school will take place from Monday to Friday, September 28 - October 2, at the University of Cologne, Germany. The strongly interdisciplinary hands-on course consists of lectures and computer labs and will provide the students with novel analysis techniques and concepts. Amongst others, the workshop will cover topics such as detrended fluctuation analysis, complex networks, scaling analysis, synchronization, transfer entropy, and causality, which help to characterize systems that are governed by non-linear processes. The summer school is led by *Dr. Reik Donner and Marc Wiedermann* from the *Potsdam Institute of Climate Impact Research* based on their lectures at the Humboldt University, Berlin, and their popular short-courses at the European Geosciences Union General Assembly. They will introduce the Python toolbox /pyunicorn/ for non-linear analysis along with prominent examples of modern analysis frameworks highlighting the methodological variety of complex systems based data analysis (see program below). The techniques that are taught in the summer school will be illustrated by applications to real-world data from different fields of study. The course materials will be made available to the participants after the course, including example codes for the platform-independent open-source software Python and the toolbox pyunicorn. The course will be held in English. For questions, please contact Mitch von Papen (vonpapen@geo.uni-koeln.de). *Program* The summer school consists of approximately the same amount of lectures and computer labs. During the lectures, the basics of the analysis methods are explained. Subsequently, these methods are applied to synthetic and real-world data in computer labs. The students work on a project in small groups and present and discuss their results at the end of the workshop. The students are introduced to the concepts of several non-linear analysis methods and will gain experience in applying the toolbox pyunicorn as well as in interpreting the results. Ideally, the summer school will enable the students to use the learned techniques on their own scientific data after the summer school. The approximate schedule for the summer school is given below. Note however, that changes may occur due to group dynamics. /Monday, September 28th/ 09:00 a.m. | Lecture 1: Introduction - linear vs. non-linear methods, Stationarity, uni- and multivariate correlation analysis, classical early warning methods, non-linearity tests and surrogate data 11:00 a.m. | Lecture 2: Long-range dependence and scaling analysis, Persistence and anti-persistence, power spectrum, Hurst exponent, detrended fluctuation analysis 02:00 p.m. | Tutorial 1: Introduction to Python, Why Python in science?, important packages for scientific computing, common data types, structure of pyunicorn 04:00 p.m. | Tutorial 2: Assignment of group projects, (6 groups a 5 persons) 07:00 p.m. | Social get-together at local brewery /Tuesday, September 29th/ 09:00 a.m. | Lecture 3: Introduction to complex networks, Mathematical representation of networks, structural network characteristics, basic network models, identification of power-laws, interconnected and multi-layer networks 11:00 a.m. | Lecture 4: Inferring networks from data, Functional network analysis (correlation networks, examples from climatology, neurophysiology and economics), visibility graphs 02:00 p.m. | Tutorial 3: tbd 04:00 p.m. | Tutorial 4: tbd /Wednesday, September 30th/ 09:00 a.m. | Lecture 5: Information theory and entropy, Basic concepts, Shannon-, Renyi- and Tsallis-entropies as statistical quantifiers, Kolmogorov-Sinai (source) entropy and estimation via block entropies, order patterns and permutation entropy, mutual information, transfer entropy and causality, independent component analysis 11:00 a.m. | Lecture 6: Synchronization, Definition and types of synchronization, phase synchronization: order parameters and phase dynamics from data, generalized synchronization 02:00 p.m. | Tutorial 5: tbd 04:00 p.m. | Tutorial 6: tbd /Thursday, October 1st/ 09:00 a.m. | Lecture 7: Phase space concepts, Phase space of dynamical systems, embedding, fractal dimensions, correlation integral and relation with entropies, entropy estimates from embedded data 11:00 a.m. | Lecture 8: Recurrence analysis, Recurrence in phase space; recurrence plots, quantification analysis and networks; multivariate generalizations; applications: synchronization analysis, coupling direction 02:00 p.m. | Tutorial 7: tbd 04:00 p.m. | Tutorial 8: tbd /Friday, October 2nd/ 09:00 a.m. | Presentation and discussion of projects 1-3 from the tutorials 11:00 a.m. | Presentation and discussion of projects 4-6 from the tutorials 02:00 p.m. | Open discussion: Outlook on contemporary developments in the field 03:30 p.m. | End of day 5: Farewell -- ------------------------------------------ UNIVERSITY OF COLOGNE Institute of Geophysics & Meteorology Coordinator of Competence Area III: Quantitative Modeling of Complex Systems Dr. Michael von Papen Pohligstr. 3 (R 3.224) 50969 Cologne Tel.: +49 (0)221 470-2841 Email: vonpapen@geo.uni-koeln.de http://complexsystems.uni-koeln.de