The lectures can be roughly divided into "Fundamentals" (Part I) and "Special Topics" (Part II). That does not exclude, of course, applications to specific research problems in Part I, whereas some of the methods introduced in Part II have a wider scope and may well be regarded as "fundamental". Finally, there are the "Practical Exercises" on special topics from the second week of lectures.

For dates and times, please refer to the Schedule

Part I: Fundamentals

Algorithms and Data Structures I - III

Pekka Orponen, Helsinki University of Technology TKK

We review the basic discrete data structures (sequences, trees, graphs) and discuss their efficient implementations in terms of arrays or objects and pointers. We introduce some core algorithm design paradigms (divide-and-conquer, greedy algorithms, dynamic programming), and illustrate these with fundamental techniques in sorting and searching, spanning trees and shortest paths in graphs, and sequence comparison. We discuss the analysis and significance of the runtime complexity of algorithms, and conclude with some observations about the distinction between efficiently solvable and inherently complex computational problems.

Software Engineering for Scientists

Helmut G. Katzgraber, Texas A&M University and ETH Zürich

Writing complex computer programs to study scientific problems requires careful planning and an in-depth knowledge of programming languages and tools, as well as analysis and visualization programs. In this lecture the importance of using the right tool for the right problem is emphasized. Furthermore, the core concepts needed to work in an Unix environment are presented. Common tools to organize computer programs (cvs and make), as well as to debug (gdb, valgrind) and improve them (gprof, compiler flags) are discussed, followed by simple data reduction strategies and visualization tools. Finally, some scientific libraries such as boost, GSL, LEDA and numerical recipes are outlined.

Statistical Data Analysis I + II

Thomas Kneib, University of Oldenburg

Exploratory data analysis falls in between the two classical branches of statistics which are dealing with the description of observed data without referring to the underlying data generating mechanism (descriptive statistics) or with methods for drawing inferential conclusions about the data generating mechanism (inferential statistics). While the former does not make use of any stochastic assumptions about the data, the latter relies on the formulation of statistical models in terms of suitable probability distributions. Exploratory data analysis, bridges this gap in providing statistical tools that are often based on descriptive statistics but already hint at inferential procedures. In particular, exploratory data analysis is often used to generate hypotheses about features of the data generating mechanism or on relations between variables.
In the first lecture, we will introduce methods for describing the distribution of univariate variables. These will either concentrate on specific features such as the location or the variability or may aim at describing the complete distribution. The second lecture provides us with possibilities to study interrelations between variables. A particular focus will be on graphical methods but we will also sketch certain association measures such as correlation coefficients.

Ordinary differential equations, and a brief introduction to elliptic partial differential equations

Burkhard Kleihaus, University of Oldenburg

These lectures focus on methods to compute numerical solutions of ordinary differential equations and elliptic partial differential equations. First, simple methods and basic properties like convergence and numerical error estimates are introduced. Subsequently, more sophisticated methods like multi-step methods and Runge-Kutta methods are discussed. As example we apply these methods to Black Holes and Black Strings. In the second part of the lectures the basic methods for numerical solutions of elliptic differential equations are introduced.

Monte Carlo Methods in Statistical Physics I + II

Helmut G. Katzgraber, Texas A&M University and ETH Zürich

Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance, critical slowing down, and ergodicity, as well as the Metropolis algorithm are explained. The Monte Carlo method is illustrated by numerically studying the critical behavior of the two-dimensional Ising ferromagnet using finite-size scaling methods.

In the second part of the lecture advanced Monte Carlo methods are described (parallel tempering Monte Carlo) and illustrated with nontrivial models from the physics of glassy systems. Special attention is paid to the equilibration of the simulations, as well as the inclusion of autocorrelation effects.

Random Number Generation

Stephan Mertens, Otto-von-Guericke University Magdeburg

Monte Carlo simulations are an important tool in statistical physics, complex system science, and many other fields. An increasing number of these simulations is run on parallel systems ranging from multicore desktop computers to supercomputers with thousands of CPUs. This raises the issue of generating large amounts of random numbers in a parallel application. In this lecture we will learn just enough of the theory of pseudo random number generation to make wise decisions on how to choose and how to use random number generators when it comes to large scale, parallel simulations.

Optimization I + II

Stephan Mertens, Otto-von-Guericke University Magdeburg

Many computational problems in science, technical and commercial applications are optimization problems. Physicists want to find the ground state of a many particle system, engineers the cheapest way to connect a set of houses to the cable network, and manufacturers the most efficient distribution of tasks among workers. In these lectures we will discuss some fundamental optimization problems and how to solve them or understand why we can't. And of course we will also talk about how to deal with optimization problems that we can't solve.

A short ad hoc introduction to spectral methods for parabolic PDE
and the Navier-Stokes equations I + II

Hannes Uecker, University of Oldenburg

We provide and explain a simple self-contained octave (Matlab) implementation of a Fourier spectral solver for the 2D Navier-Stokes equations in a periodic box, including a discussion of anti-aliasing and power-spectra. We illustrate the solver with some examples including some (weakly) turbulent flows.

Part II: Special Topics

Principal Component Analysis

Jörn Anemüller, University of Oldenburg

Modern experimental methods in the natural sciences and engineering disciplines routinely measure multidimensional data where each sample is represented by an N-dimensional measurement vector, e.g., derived from multiple sensors. The N dimensions of the measurement are typically redundant to some extent such that knowledge of one sensor's signal provides at least partial information about another sensor. Hence, the measured data can be modeled as largely confined to an M-dimensional subspace of the N-dimensional measurement space (M < N).
Principal Component Analysis (PCA) and a more general variant, Independent Component Analysis (ICA), are derived in the Lecture as methods that extract the appropriate subspace from knowledge of the measurements alone. I.e., the data embedding is derived in a data-driven way that makes use of the statistics of the data. Benefits and limitations, together with applications are discussed.

Computational Fluid Dynamics I - III

Joachim Peinke, University of Oldenburg

An introduction to CFD (Computational Fluid Dynamics) will be given. In particular we discuss the RANS and LES approximation commonly used for applications. Examples will be explained in a tutorial using OpenFOAM. Finally the use of CFD for wind energy research will be presented.

Quantum Chemistry and Quantum Dynamics:
New insight from first principles in Surface Photochemistry

Thorsten Klüner, University of Oldenburg

Photodesorption of small molecules from surfaces is one of the most fundamental processes in surface photochemistry. Despite its apparent simplicity, a microscopic understanding beyond a qualitative picture still poses a true challenge for theory. While the dynamics of nuclear motion can be treated on various levels of sophistication, all approaches suffer from the lack of sufficiently accurate potential energy surfaces, in particular for electronically excited states involved in the desorption scenario.
In the last decade, we have developed a systematic and accurate methodology to reliably calculate accurate ground and excited state potential energy surfaces (PES) for different adsorbate-substrate systems. These potential energy surfaces serve as a prerequisite for subsequent quantum dynamical wave packet calculations, which allow for a direct simulation of experimentally observable quantities such as velocity distributions.
In this contribution, I will focus on recent results obtained for photodesorption of NO and CO from a NiO(100) surface. In contrast to previous studies, we were able to construct highly accurate potential energy surfaces based on correlated quantum chemical calculations (CASPT-2/CCSD(T)). Despite the enormous computational cost, this level of theory turns out to be crucial, since less sophisticated approaches such as density functional theory (DFT) cannot even provide a reliable description of ground state properties, not to mention electronically excited states [1].
These potential energy surfaces were used in subsequent wave packet studies which reveal new desorption mechanisms. In the NO/NiO(100) case, we observed an anti-Antoniewicz scenario in which the wave packet is initially repelled from the surface but eventually reaches a turning point before it is back-scattered from the surface. State resolved desorption velocity distributions have been calculated, and the results are in good agreement with experimental findings [2].
In the CO/NiO(100) system, we observe the formation of a genuine covalent bond upon photoexcitation for the first time. As demonstrated in the current study, this chemical bond formation is the crucial step in the desorption mechanism for this system [3,4]. Again, our results are in good agreement with recent experiments.

References

1. I. Mehdaoui, T. Klüner, J. Phys. Chem. A 111 (2007), 13233: Bonding of CO and NO to NiO(100): A strategy for obtaining accurate adsorption energies.
   
2. I. Mehdaoui, D. Kröner, M. Pykavy, H.-J. Freund, T. Klüner, Phys. Chem. Chem. Phys. 8, 1584 (2006): Photo-induced desorption of NO from NiO(100): Calculation of the four-dimensional potential energy surfaces and systematic wave packet studies.
   
3. I. Mehdaoui, T. Klüner, Phys. Rev. Lett. 98, 037601 (2007): Understanding Surface Photochemistry from First Principles: The Case of CO-NiO(100).
   
4. I. Mehdaoui, T. Klüner, Phys. Chem. Chem. Phys. 10 (2008), 4559: New mechanistic insight into electronically excited CO-NiO(100): A quantum dynamical analysis.

Modeling Auditory Scene Analysis by multidimensional statistical filtering

Volker Hohmann, University of Oldenburg

"Auditory Scene Analysis" (ASA) denotes the ability of the human auditory system to decode information on sound sources from a superposition of sounds in an extremely robust way. ASA is closely related to the 'Cocktail-Party-Effect' (CPE), i.e., the ability of a listener to perceive speech in adverse conditions at low signal-to-noise ratios.
This contribution discusses theoretical and empirical evidence suggesting that robustness of source decoding is partly achieved by exploiting redundancies that are present in the source signals. Redundancies reflect the restricted spectro-temporal dynamics of real source signals, e.g., of speech, and limit the number of possible states of a sound source. In order to exploit them, prior knowledge on the characteristics of a sound source needs to be represented in the decoder/classifier ("expectation-driven processing"). In a proof-of-concept approach, novel multidimensional statistical filtering algorithms have been shown to successfully incorporate prior knowledge on the characteristics of speech and to estimate the dynamics of a speech source from a superposition of speech sounds [1].

1. Nix, J. and Hohmann, V. (2007): "Combined estimation of spectral envelopes and sound source direction of concurrent voices by multidimensional statistical filtering", IEEE Trans. Audio, Speech and Lang. Proc. 15(3): 995-1008.

Hybrid Systems I + II

Martin Fränzle, University of Oldenburg

Embedded digital systems have become ubiquitous in everyday life. Many such systems, including many of the safety-critical ones, operate within or comprise tightly coupled networks of both discrete-state and continuous-state components. The behavior of such hybrid discrete-continuous systems cannot be fully understood without explicitly modeling and analyzing the tight interaction of their discrete switching behavior and their continuous dynamics, as mutual feedback confines fully separate analysis to limited cases. Tools for building such integrated models and for simulating their approximate dynamics are commercially available, e.g. Simulink with the Stateflow extension. Simulation is, however, inherently incomplete and has to be complemented by verification, which amounts to showing that the coupled dynamics of the embedded system and its environment is well-behaved, regardless of the actual disturbance and the influences of the application context, as entering through the open inputs of the system under investigation. Basic notions of being well-behaved demand that the system under investigation may never reach an undesirable state (safety), that it will converge to a certain set of states (stabilization), or that it can be guaranteed to eventually reach a desirable state (progress).
Within this school, we concentrate on automatic verification and analysis of hybrid systems, with a focus on fully symbolic methods manipulating both the discrete and the continuous state components symbolically by means of predicates. We provide an introduction to hybrid discrete-continuous systems, demonstrate the use of predicative encodings for compactly encoding operational high-level models, and continue to a number of methods for automatically analyzing safety, stability, and progress.

Message Passing

Marc Mézard, Université de Paris Sud

A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. It deals with problems which are very important in each of these fields, like spin glasses, error correction, or satisfiability.
All these problems can be formulated within a common framework. An important general method which has been developed independently in each of these fields over the last few decades is the message passing strategy, which has generated very powerful algorithms. The talk will survey this field, putting special emphasis on a unified approach based on message passing.

An introduction to phylogenetic analysis

Olaf R.P. Bininda-Emonds, University of Oldenburg

Biological species do not represent independent units of analysis because of the pattern of descent with modification through evolution. Although this fact has been appreciated since at least Darwin, it is only in the past 15 years that biologists have increasingly appreciated the need to account for evolutionary relatedness in their analyses. However, phylogeny transcends pure biology to play an important role in related fields. For instance, alignment programs like Clustal rely on phylogenetic information in constructing their guide trees. Unfortunately, finding the optimal phylogeny for a given data set, like most other interesting problems in computational biology, is an NP-hard problem because the number of potential solutions ("tree space") grows super-exponentially with the number of taxa in the analysis. With the rapid growth of phylogenomic data and the scope of the analyses, phylogenetic inference has also garnered increasing attention from computer scientists eager to find fast solutions to this difficult problem.
In this talk, I introduce the problem of phylogenetic inference in general and discuss several optimization criteria (parsimony, likelihood, and distance methods) and the strengths and weaknesses of each for building evolutionary trees.

Sediment Dynamics

Jörg-Olaf Wolff, University of Oldenburg

Over the last 8 years, the area-specific hydrodynamics and the suspended particulate matter (SPM) dynamics in the East-Frisian Wadden Sea have been extensively investigated under the umbrella of the DFG Research Group on BioGeoChemistry of Tidal Flats at the University of Oldenburg. High-resolution modelling efforts for this area in combination with high-resolution measurements at the Wadden Sea time series station and novel theoretical approaches have revealed various new and exciting insights into this complex system thus significantly contributing to the current state of research. The available suite of numerical models integrates worldwide experience with innovative concepts in numerical modelling such as state-of-the-art parameterizations of physical processes and novel concepts of suspended particulate matter transport. These models have been widely used for various research applications in the Wadden Sea and the German Bight in different horizontal resolutions. Combined with sophisticated measurements using ADCP and satellite data these models enable a reliable state estimate for hydrodynamics and sediment dynamics. The response of the Wadden Sea system to atmospheric and hydrological impacts (storms and sea-level rise) will be highlighted in this lecture along with the basic underlying physics and model details.

Learning in neural nets

Andreas Engel, University of Oldenburg

Networks of artificial neurons can perform various tasks of information processing. A particularly simple architecture called feed-forward networks is well suited for the classification of input data. In many cases these networks are able to implement target classification by learning from examples. In many complex classification problems as arising, e.g., in pattern recognition, supervised learning sessions are an interesting alternative to explicit programming. Starting from a simple example some capabilities and limits of learning from examples in artificial neural nets are discussed.

Analysis of neuronal data

Jutta Kretzberg, University of Oldenburg

Biological neurons communicate with sequences of "action potentials", stereotyped changes in their membrane voltage. These signals are the basis for our perception of the word. E.g., all information about the visual world is transmitted by action potentials of retinal ganglion cells from the eye to the brain. However, it is still a matter of intense scientific debate which features of spike sequences of neuronal populations are most important to encode sensory information. To address this question, the activity of many neurons is recorded simultaneously in electrophysiological experiments. Based on this data, computational methods are applied to reconstruct the stimulus, which was present during the recording.
In this lecture, a short overview of some basic concepts of neuronal data analysis will be given. In particular, I will introduce a Bayesian method of stimulus reconstruction by providing Matlab routines and demonstrating their application to multi-channel recordings from the retina.

Nonlinear Dynamics

Ulrike Feudel, University of Oldenburg

Nonlinear dynamical systems exhibit a variety of different long-term behaviors on invariant sets such as stationary states, periodic, quasiperiodic and chaotic motion for a given set of parameters. These invariant sets are invariant with respect to the flow and with respect to coordinate transformations. Moreover, they can be stable or unstable with respect to small perturbations. Stable sets are called attractors, while unstable sets are in general of saddle type. The long-term dynamics of nonlinear dynamical systems can change suddenly when a parameter crosses a critical threshold value. Such changes are called bifurcations.
The lecture gives a short phenomenological introduction into bifurcation as well as chaos theory, discusses numerical methods how to compute invariant sets and their stability and the most important bifurcations. Furthermore it gives insight into free software tools containing the numerical algorithms. Finally examples from applications are discussed such as the breakdown of the thermohaline ocean circulation and chaotic behavior in population dynamics to illustrate the methods.

Adaptive Networks

Bernd Blasius, University of Oldenburg

The investigation of complex networks has received a rapidly increasing amount of attention in recent years, with many applications in social, biological and technical systems. In particular, most research proceeded in two distinct directions. On the one hand, attention has been paid to the structure of the networks, revealing that simple dynamical rules, such as preferential attachment, can be used to generate complex topologies. Many of these rules are not only a useful tool for the generation of model graphs, but are also believed to shape real-world networks. On the other hand research has focused on large ensembles of dynamical systems, where the interaction between individual units is described by a complex graph. These studies have shown that the network topology can have a strong impact on the dynamics of the nodes, e.g., the absence of epidemic thresholds on scale free networks. This lecture will review recent progress in the field of complex networks. We will introduce adaptive networks which combine topological evolution of the network with dynamics in the network nodes and discuss several applications from biology and epidemiology.

Exercises: Parallel Sessions

Computational Chemistry - Introduction and Practical Exercises

Rainer Koch, University of Oldenburg

This practical session comprises two main parts: first, there will be a brief introduction to theoretical concepts used in computational chemistry [1]; and the second part will be a combined tutorial and practical course on what you can actually do with computational chemistry. You will be guided to running your first calculations and analysing their results.

1. F. Jensen, Introduction to Computational Chemistry, John Wiley & Sons, Chichester, 1999.

Neural Networks

Jutta Kretzberg, Andreas Engel, University of Oldenburg

In the practical session "neural netwoks" we will combine aspects of the lectures "learning in neural nets" and "analysis of neuronal data". Using Matlab programs provided in these lectures, we will apply a simple artifical neural network (perceptron) to experimental data from a network of biological neurons. The goal will be to classify which of the responses from retinal ganglion cells was elicited by which light stimulus. Depending on the prior knowledge and interests of the participants we will give a short introduction to the Matlab proramming environment in the first session of the course and / or compare the classification performance of the perceptron with a Bayesian classification approach in the second session.