Articles

Computational Biology 1 FFR110

(7.5 credit units)

Kristian Gustavsson (lectures, examiner)
Bernhard Mehlig (lectures)
Johan Fries (examples classes)

New: link to Kristian Gustavsson's  course home page for this course (including links to examples sheets)

Schedule

The course starts Friday January 22 at 15:15 in MA. Map.
Schedule.

Plan

1. Introduction
2. Population dynamics
3. Interacting species and reaction kinetics
4. Pattern formation
5. Disease dynamics
6. Synchronisation

Literature

Lecture notes.

Further literature

1. J. D. Murray, Mathematical Biology, Springer, Berlin (1993) - Matematikbiblioteket
A. Okubo, Diffusion and Ecological Problems: Mathematical Models, Springer, Berlin (1980)

2. E. S. Lander and M. S. Waterman, eds., Calculating the secrets of life, National Academic Press, Washington (1995), On-line version of this book.

3. J. Maynard Smith and Eörs Szathmary, The major transitions in evolution, Oxford University Press, Oxford (1995)

4. J. Keener and J. Sneyd, Mathematical Physiology, Springer, New York (1998)

5. G. Nicolis, Introduction to nonlinear science, Cambridge University Press

6. W. Hirsch and S. Smale, Differential equations, dynamical systems, and linear algebra, Academic Press, New York (1974)

Examination

Credits for this course are obtained by solving the homework set (solutions of examples and programming projects).

Link to examples sheets and further information on examination and grading.

Further Resources

D. Barkley's homepage with a link to the code for simulating spiral waves.

Computational Biology 2 FFR115

(7.5 credit units)
Bernhard Mehlig (lectures, examiner) Office: S3050
Marina Rafajlovic (examples classes)

Schedule

Schedule in TimeEdit can be found here.

Lectures by A. Blomberg and S. Sagitov in week 7

DNA sequencing - the past, the present, and the future  (A. Blomberg, University of Gothenburg) Mon Feb. 10 10-12 in EC Salen. Map. Lecture notes: pdf.
Statistical inference  (S. Sagitov, Chalmers) Wed Feb. 12 10-12 in EC Salen. Map. Lecture notes: link.

Plan

Molecular Biology aims at explaining the chemical structures and processes determining life. Due to new measurement techniques information on structure and function of biological macromolecules has increased significantly in recent years. The amount of data is so huge that it has become necessary to use computational and statistical methods to analyse the data. Further, new experimental data allow statistically significant testing of models for genetic evolution. This has led to a renewed interest in evolution models on the genetic and molecular level. New numerical algorithms and mathematical models have been developed describing population genetics. It is the aim of this course to introduce the mathematical models and computational methods used in the analysis and modelling of genetical data and their evolution.

1. Introduction to the course (course content, basic concepts)
2. Models of proteins: structure and dynamics
3. Genetic maps: sequencing, the double digest problem
4. Markov-chain Monte-Carlo techniques
5. Evolution of genes: Mendelian inheritance, Wright Fisher dynamics, genetic drift
6. Analysing patterns of genetic variation (mutations (single-nucleotide popymorphisms, microsatellites),
   coalescent)
7. Effective population size, the molecular clock
8. Population structure: population expansions, founder events, bottlenecks,
9. Geographic structure
10. Bayesian methods
11. Multi-locus data: the coalescent with recombination
12. Selection          

Literature

W. J. Ewens, Mathematical population genetics, Springer (1979)
E. S. Lander and M. S. Waterman, eds., Calculating the secrets of life, National Academic Press, Washington (1995). An on-line version of this book is available.
A. Okubo, Diffusion and ecological problems: mathematical models, Springer (1980)
J. D. Murray, Mathematical Biology, Springer (1989)
M. S. Waterman, Introduction to Bioinformatics, Chapman and Hall (1995); Errata
W. Ewens and G. Grant, Bioinformatics, to be published in May 2001
M. T. Madigan, J. M. Martinko and J. Parker, Biology of microorganisms, Prentice Hall (2000)
N. G. van Kampen, Stochastic processes in physics and chemistry, North-Holland (1981)

Examination and examples sheets

Details on the examination of this course and the compulsory examples sheets can be found here.

Dynamical Systems FFR130

(7.5 credit units)
Bernhard Mehlig (lectures, examiner) Office: S3050

Schedule

Schedule in TimeEdit can be found here.

Plan

This course provides and introduction to the subject of chaos in dynamical systems.

  1. Introduction
  2. Some definitions and more examples
  3. One-dimensional maps
  4. Chaotic attractors and fractal dimension
  5. Dynamical properties of chaotic systems
  6. Chaos in Hamiltonian systems
  7. Chaotic scattering
  8. Mixing in fluids
  9. Chaos in microlasers
  10. Advection of small particles in turbulent flows

Literature

1. Chaos in dynamical systems, E. Ott, Cambridge University Press, Cambridge 1993 (reprinted with corrections 1993, 1997).
2. Classical and quantum chaos: a cyclist treatise, P. Cvitanovic et al. See in particular chapter 17 Fixed points and how to get them.
3. A. Einstein, Ann. Phys. 17 (1905) 549 [pdf]
4. R. Brown, Phil. Mag. 4 (1828) 161 [pdf]
5. H. A. Kramers, Physica 7 (1040) 284 [pdf]

Examination

Credits for this course are obtained by solving the homework set (solutions of examples and programming projects). There will be five sets of homework which are graded.

Every student must hand in her/his own solution on paper. Same rules as for written exams apply: it is not allowed to copy any material from anywhere unless appropriate reference is given. All figures must have axis labels and captions giving all information necessary to reproduce the figure. Describe your results in words. Always compare with theory. Summarise problems, discuss possible reasons. Program code must be appended. Each of the five examples sheet gives 5 points. In order to pass the course at least 14 points are required. The examples sheets will be processed by URKUND. Your solutions should be submitted before the deadline as PDF files electronically to This email address is being protected from spambots. You need JavaScript enabled to view it. , and as hardcopies into the letter box on floor 3 of Soliden/Physics.

Examples

Sheet 1 [pdf]
Sheet 2 [pdf]
Sheet 3 [pdf]
Sheet 4 [pdf]
Sheet 4 [pdf]
 

Learning: models, algorithms, and applications

Supervised learning: simple perceptrons and layered networks (pp. 85 to 132)

  1. Formulation of the problem: correlated patterns
  2. Feed-forward networks
  3. Simple perceptron with threshold units
  4. A simple learning algorithm
  5. Simple perceptron with linear units: gradient-descent learning
  6. Multilayer perceptron
  7. Backpropagation
  8. Examples
  9. Alternative cost functions
  10. Momentum
  11. Steepest descent and conjugate gradient methods
  12. Local minima
  13. Example: parity problem
  14. Summary

Performance of multilayer perceptrons (pp. )

  1. Introduction
  2. Necessary number of hidden units
  3. Transformation of input data
  4. Pruning and weight decay

Unsupervised learning

  1. Introduction
  2. Unsupervised Hebbian learning with one linear unit
  3. Oja's rule
  4. Simple competitive learning
  5. Vector quantisation
  6. Feature mapping
  7. Kohonen's algorithm

Reinforcement learning

  1. Introduction
  2. Associative reward/penalty algorithm 

 

Chance and chaos FFR150

(4.5 credit units)
Bernhard Mehlig (lectures, examiner) Office: S3050

Schedule

The course consists of seven 2h lectures introducing the mathematical methods and computational tools.
Schedule in TimeEdit can be found here.

Plan

Stochastic dynamics in Physics, Chemistry, and Biology.  The course provides an introduction to stochastic models of complex systems. What are complex systems? Many systems observed in the world around us exhibit apparently irregular fluctuations. Examples are the density variations of inertial particles moving in random flows (Fig. 1), cross-section fluctuations in the photodissociation of large molecules, but also the apparently random patterns of genetic variation in the human genome (Fig. 2). The cause of the apparently random fluctuations is the same in all cases: irregular dynamics. It may be a consequence of disorder (due to randomly distributed impurities for example), it may arise dynamically (as in chaotic motion in highly excited molecules), it may be due to the interaction of a large (but finite) number of individuals (as in the evolution of the human genome), or may be a consequence of the interaction of many constituents (gas molecules forming a turbulent fluid). These examples have in common that the number of degrees of freedom exceeds the number of conservation laws. This makes the corresponding systems complex, and requires stochastic methods to describe the empirically observed fluctuations.

Literature

1. B. Mehlig, Chaos and Disorder: Dynamics of Complex Systems, Lecture notes, Freiburg (1999)
2. N. G. van Kampen, Stochastic processes in physics and chemistry, 2nd edition, North-Holland (1992)
3. O. Bohigas, Random matrices and chaotic dynamics, in: Chaos and Quantum Physics, eds: G. J. Giannoni, A. Voros and J. Zinn-Justin, North-Holland (1991)
4. Lecture notes for this course

Examination

Credits for this course are obtained by solving the homework set (solutions of examples and programming projects). There are two sets of homework which are graded.

Every student must hand in her/his own solution on paper. Same rules as for written exams apply: it is not allowed to copy any material from anywhere unless appropriate reference is given. All figures must have axis labels and captions giving all information necessary to reproduce the figure. Describe your results in words. Always compare with theory. Summarise problems, discuss possible reasons. Program code must be appended. Each of the five examples sheet gives 5 points. In order to pass the course at least 14 points are required. The examples sheets will be processed by URKUND. Your solutions should be submitted before the deadline as PDF files electronically to This email address is being protected from spambots. You need JavaScript enabled to view it. , and as hardcopies to Marina Rafajlovic: letter box on floor 3 of Soliden/Physics.

Examples

Sheet 1 [pdf]
Sheet 2 [pdf]

Fig. 1: Distribution of inertial particles suspended in a randomly moving gas. Blue corresponds to low, yellow to high particle density. The figure illustrates a striking similarity with optical patterns that can be seen at the bottom of a swimming pool on a sunny day [M. Berry, Nature 267, 34-36 (1977)].

 
Fig. 2: a In DNA, genetic information is encoded by the sequence of the four nucleic acids adenine (A), thymine (T), guanine (G), and cytosine (C). In a sample of three individuals, three polymorphic sites are shown. b The most common variation is a difference at a single position (single-nucleotide polymorphism or SNP), caused by a mutation at one position. The three mutations in panel a are shown as filled circles in a genealogy of the three individuals (blue). Mutation 4 does not cause a polymorphism in the sample, since all individuals in the sample inherit the mutation from the common ancestor. c In recombination, one of the two copies of a chromosome is inherited from one parent and the rest from the other parent. A sample gene history with one recombination event is shown, for two loci (a and b).