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

Teaching

Winter Term

Statistical Ecology

field data: 3 species in 9 plots

type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Modelling (M.Sc.)

 

Contents:

  1. Basic concepts and introduction
  2. Random variables and distributions
  3. Estimation of population size
  4. Estimation of population densities
  5. Statistacal descriptions of ecological communities

Stochastic Processes

ensemble evolution of the OU process

type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Modelling (M.Sc.)

 

Contents:

  1. Basic stochastic concepts
  2. Characterization of stochastic processes
  3. Fundamental equations for ensemble description of stochastic processes
  4. Stochastic di fferential equations for descriptions and simulation of realizations
  5. Applications: random walks, stochastic neuron models, stochastic population dynamics

Time Series Analysis & Multivariate Statistics

jointly with Jan Schulz

RV OTZUM in front of measurement station

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
Two-factorial ANOVA

 

 

 

 

 

type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Sciences (B.Sc.) & Biology (B.Sc.)


Contents:

  1. Why is there a need for statistics?
  2. Random variable, distribution, location and shape parameters
  3. Empirical characteristics, estimators, robustness
  4. Covariance and correlations
  5. Statistical tests, null-hypothesis, errors of 1. & 2. kind
  6. t-Test, ANOVA, Kruskal-Wallis
  7. Post-hoc tests, multiple testing
  8. Regression
  9. ANCOVA
  10. 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

Tribolium bifurcation diagram

 

 

 

type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Modelling (M.Sc.)

 

Contents:

  1. Growth dynamics of single species in continuous (flow) and discrete (map) time
  2. Dynamics of interacting populations (competition and predator-prey models, trophic networks)
  3. Matrix models for age- and stage-structured populations
  4. Non-linear matrix models and populations in space
  5. Stochastic population dynamics

Time Series analysis

multivariate time series

type: lecture & tutorial
shw: 2 & 2
ECTS: 6
target group: Environmental Modelling (M.Sc.)

 

Contents:

  1. Time series as realizations of stochastic processes
  2. Process characteristics and their estimators
  3. Component models: trends, rhythms and residuals
  4. Spectral characterization of time series
  5. Non-stationary processes: Time-frequency methods
  6. Linear filters and time-discrete linear stochastic processes
  7. Non-linear processes: state space and attractor
  8. Embedding theorem, reconstructed attractor and invariants
  9. Lyapunov exponents
  10. Generalized dimensions
 

Contact

jan.freund[at]uni-oldenburg.de

Tel: +49 441 798 - 3231
Fax: +49 441 798 - 3404

ICBM, Campus Wechloy
Raum: W15 1-101

office hours: Tue 14-16h

postal address:
ICBM, CvO Univ. OL
Carl von Ossietzky Str. 9-11
D-26111 Oldenburg