Summer Semester 2021

Theoretical concepts to deal with stochastic, correlation and memory effects in nanoscale- and bio-physics systems (liquids, proteins, organisms) will be introduced and discussed.  These concepts will be applied to experiments that probe the motion of particles or organisms, the structure and spectroscopic properties of liquids and chemical or conformational transitions. Concepts will be explained in the lectures, detailed theoretical derivations will be presented in handouts that will be discussed in the tutorial. Analytical theory will be compared with numerical approaches and simulations. The exam will take place in terms of a homework that can be chosen from the different topics covered in class.

- Brownian motion in liquids and complex systems
       classical Brownian theory
       stochastic theory for financial and meteorological time series data
       motion of living organisms
       environmental memory effects, aging
       normal and anomalous diffusion

- Central limit theorem, equipartition theorem, deviations from Gaussian distributions on the nanoscale

- Correlations in interacting liquids
       Ornstein-Zernike theory, classical density functional theory, scattering functions

- Rare events, non-linear effects
       barrier crossing events
       chemical reaction kinetics in liquids
       protein folding

- Spectroscopy
       harmonic damped oscillator
       anharmonic effects
       homogeneous versus inhomogeneous line broadening
       spectral life times

- Non-equilibrium systems
       approach to equilibrium
      stationary non-equilibrium systems

 

Statistics is a must-needed set of tools in experimental sciences. In almost every study, methods from statistics are necessary and their justification is required for a good level publication. Despite the availability of a number of powerful and sophisticated software, it is not always obvious what analysis approach is needed in any particular case if one does not have an introductory level background in the matter. This compact course will cover a few of the fundamentals in statistics.

 

The course will start with a summary of probability theory. In a second part we will move on to cover methods for estimating means and proportions by defining and computing confidence intervals. In a third part we will discuss methods for hypothesis testing for means and proportions using rejection region, p-value and confidence interval approaches. The tools discussed in the class will be the most used ones in everyday work with experimental data (including z-test, t-test). The course won't refer to any particular software but people used to work with any given software are welcome to use it in order to solve the exercises.

 

Everyone interested is welcome to join. This course will be available online only and will be delivered live in a compact form, for three days in the row, five hours per day around end of April. Registration to attend this course is compulsory at this side:

https://statistics.mpikg.mpg.de/

 

 

 

Statistics is a must-needed set of tools in experimental sciences. In almost every study, methods from statistics are necessary and their justification is required for a good level publication. Despite the availability of a number of powerful and sophisticated software, it is not always obvious what analysis approach is needed in any particular case if one does not have an introductory level background in the matter.

 

This course builds on the previous course (Part I) but people with some knowledge of statistics can still take this course without having attended Part I.

 

This course will start with a summary of probability theory for bivariate distributions. We will explore maximum likelihood methods. Move on into simple linear regression, ANOVA and tests for contingency tables. If time will allow it, we will explore a few numerical approaches like permutation tests and bootstrapping.

 

The course won't refer to any particular software but people used to work with any given software are welcome to use it in order to solve the exercises. Most exercises and solutions provided with this course are written in python and will be available as well together with the lecture notes.

 

Everyone interested is welcome to join.

This course will be delivered live, online only.

The first lecture will take place on May 5, 2021.

Each lecture will be 1.5hrs with little breaks.