Jan Freund
Research Interests
My main concern is the transfer of paradigmatic models and methods from the realm of theoretical physics and complex systems to other scientific fields, e.g. marine biology, ecology or the neuroscience. Aside from the chance to explain observed phenomena in neighbouring fields by fundamental principles or mechanisms there may arise also a practical value from this approach. For instance, the optimization or control of complex process may follow from a quantitative reconstruction of its causal interaction patterns. Quite often, my methods include a stochastic component, be it in a model approach (via stochastic processes), be it in empirical data analysis (via statistical inference).
Current Projects
Marine Biology Across Scales
causality of Non-linear Diffusion Processes
Reconstructing the Network Structure of Brain Areas
Selected Publications
- B. Wahl, U. Feudel, J. Hlinka, M. Wächter, J. Peinke, and J.A. Freund. Granger-causality maps of diffusion processes.
Phys. Rev. E 93, 022213:1-9 (2016).
- M. Arns, A. Cerquera, R.M. Gutiérrez, F. Hasselman, and J.A. Freund. Non-linear EEG analyses predict non-response to rTMS treatment in major depressive disorder.
Clinical Neurophysiology 125, 1392–1399 (2014).
- J.A. Freund, N. Grüner, S. Brüse, and K.H. Wiltshire. Changes in the phytoplankton community at Helgoland, North Sea: lessons from single spot time series analyses.
Marine Biology 159, 2561-2571 (2012).
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N. Grüner, C. Gebühr, M. Boersma, U. Feudel, K.H. Wiltshire, and J.A. Freund. Reconstructing the realized niche of phytoplankton species from environmental data: fitness versus abundance approach.
Limnol. Oceanogr. Methods 9, 432-442 (2011).
Teaching
Winter Term
Statistical Ecology
type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Modelling (M.Sc.)
Contents:
- Basic concepts and introduction
- Random variables and distributions
- Estimation of population size
- Estimation of population densities
- Statistacal descriptions of ecological communities
Stochastic Processes
type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Modelling (M.Sc.)
Contents:
- Basic stochastic concepts
- Characterization of stochastic processes
- Fundamental equations for ensemble description of stochastic processes
- Stochastic differential equations for descriptions and simulation of realizations
- Applications: random walks, stochastic neuron models, stochastic population dynamics
Time Series Analysis & Multivariate Statistics
jointly with Jan Schulz
type: lecture & tutorial
shw: 2 & 2
ECTS: 4
target group: Marine Sensors (M.Sc.)
Contents:
In this course the focus is on working with empirical data recorded by marine sensors (CTD, flow data, etc.).
In the first part of the course standard methods of time series analysis are developed and applied in the context of practical requirements. Programming experience with Matlab or R are desirable.
Sommer Term
Applied Statistics
jointly with Helmut Hillebrand, Cord Peppler-Lisbach, Gerhard Zotz
type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Sciences (B.Sc.) & Biology (B.Sc.)
Contents:
- Why is there a need for statistics?
- Random variable, distribution, location and shape parameters
- Empirical characteristics, estimators, robustness
- Covariance and correlations
- Statistical tests, null-hypothesis, errors of 1. & 2. kind
- t-Test, ANOVA, Kruskal-Wallis
- Post-hoc tests, multiple testing
- Regression
- ANCOVA
- Supplement (pseudo-random numbers, data transformations, resampling techniques)
Lectures are supplemented and knowledge is deepened by practical work with data within the programming environment R. An introduction to R will be given in the first tutorial sessions. Homework problems will be assigned and rated - sufficient credits will be prerequisite to participation in the final exam.
Population Dynamics
jointly with Ulrike Feudel
type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Modelling (M.Sc.)
Contents:
- Growth dynamics of single species in continuous (flow) and discrete (map) time
- Dynamics of interacting populations (competition and predator-prey models, trophic networks)
- Matrix models for age- and stage-structured populations
- Non-linear matrix models and populations in space
- Stochastic population dynamics
Time Series analysis
type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Modelling (M.Sc.)
Contents:
- Time series as realizations of stochastic processes
- Process characteristics and their estimators
- Component models: trends, rhythms and residuals
- Spectral characterization of time series
- Non-stationary processes: Time-frequency methods
- Linear filters and time-discrete linear stochastic processes
- Non-linear processes: state space and attractor
- Embedding theorem, reconstructed attractor and invariants
- Lyapunov exponents
- Generalized dimensions