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Suchergebnis: Katalogdaten im Herbstsemester 2017

Informatik Master Information
Vertiefungsfächer
Vertiefung in Computational Science
Wahlfächer der Vertiefung in Computational Science
NummerTitelTypECTSUmfangDozierende
252-0543-01LComputer Graphics Information W6 KP3V + 2UM. Gross, J. Novak
KurzbeschreibungThis course covers some of the fundamental concepts of computer graphics, namely 3D object representations and generation of photorealistic images from digital representations of 3D scenes.
LernzielAt the end of the course the students will be able to build a rendering system. The students will study the basic principles of rendering and image synthesis. In addition, the course is intended to stimulate the students' curiosity to explore the field of computer graphics in subsequent courses or on their own.
InhaltThis course covers fundamental concepts of modern computer graphics. Students will learn about 3D object representations and the details of how to generate photorealistic images from digital representations of 3D scenes. Starting with an introduction to 3D shape modeling and representation, texture mapping and ray-tracing, we will move on to acceleration structures, the physics of light transport, appearance modeling and global illumination principles and algorithms. We will end with an overview of modern image-based image synthesis techniques, covering topics such as lightfields and depth-image based rendering.
Skriptno
Voraussetzungen / BesonderesPrerequisites:
Fundamentals of calculus and linear algebra, basic concepts of algorithms and data structures, programming skills in C++, Visual Computing course recommended.
The programming assignments will be in C++. This will not be taught in the class.
263-5001-00LIntroduction to Finite Elements and Sparse Linear System Solving Information W4 KP2V + 1UP. Arbenz
KurzbeschreibungThe finite element (FE) method is the method of choice for (approximately) solving partial differential equations on complicated domains. In the first third of the lecture, we give an introduction to the method. The rest of the lecture will be devoted to methods for solving the large sparse linear systems of equation that a typical for the FE method. We will consider direct and iterative methods.
LernzielStudents will know the most important direct and iterative solvers for sparse linear systems. They will be able to determine which solver to choose in particular situations.
InhaltI. THE FINITE ELEMENT METHOD

(1) Introduction, model problems.

(2) 1D problems. Piecewise polynomials in 1D.

(3) 2D problems. Triangulations. Piecewise polynomials in 2D.

(4) Variational formulations. Galerkin finite element method.

(5) Implementation aspects.


II. DIRECT SOLUTION METHODS

(6) LU and Cholesky decomposition.

(7) Sparse matrices.

(8) Fill-reducing orderings.


III. ITERATIVE SOLUTION METHODS

(9) Stationary iterative methods, preconditioning.

(10) Preconditioned conjugate gradient method (PCG).

(11) Incomplete factorization preconditioning.

(12) Multigrid preconditioning.

(13) Nonsymmetric problems (GMRES, BiCGstab).

(14) Indefinite problems (SYMMLQ, MINRES).
Literatur[1] M. G. Larson, F. Bengzon: The Finite Element Method: Theory, Implementation, and Applications. Springer, Heidelberg, 2013.

[2] H. Elman, D. Sylvester, A. Wathen: Finite elements and fast iterative solvers. OUP, Oxford, 2005.

[3] Y. Saad: Iterative methods for sparse linear systems (2nd ed.). SIAM, Philadelphia, 2003.

[4] T. Davis: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia, 2006.

[5] H.R. Schwarz: Die Methode der finiten Elemente (3rd ed.). Teubner, Stuttgart, 1991.
Voraussetzungen / BesonderesPrerequisites: Linear Algebra, Analysis, Computational Science.
The exercises are made with Matlab.
636-0017-00LComputational Biology Information W6 KP3G + 2AC. Magnus, T. Stadler, T. Vaughan
KurzbeschreibungThe aim of the course is to provide up-to-date knowledge on how we can study biological processes using genetic sequencing data. Computational algorithms extracting biological information from genetic sequence data are discussed, and statistical tools to understand this information in detail are introduced.
LernzielAttendees will learn which information is contained in genetic sequencing data and how to extract information from this data using computational tools. The main concepts introduced are:
* stochastic models in molecular evolution
* phylogenetic & phylodynamic inference
* maximum likelihood and Bayesian statistics
Attendees will apply these concepts to a number of applications yielding biological insight into:
* epidemiology
* pathogen evolution
* macroevolution of species
InhaltThe course consists of four parts. We first introduce modern genetic sequencing technology, and algorithms to obtain sequence alignments from the output of the sequencers. We then present methods for direct alignment analysis using approaches such as BLAST and GWAS. Second, we introduce mechanisms and concepts of molecular evolution, i.e. we discuss how genetic sequences change over time. Third, we employ evolutionary concepts to infer ancestral relationships between organisms based on their genetic sequences, i.e. we discuss methods to infer genealogies and phylogenies. Lastly, we introduce the field of phylodynamics. The aim of phylodynamics is to understand and quantify the population dynamic processes (such as transmission in epidemiology or speciation & extinction in macroevolution) based on a phylogeny. Throughout the class, the models and methods are illustrated on different datasets giving insight into the epidemiology and evolution of a range of infectious diseases (e.g. HIV, HCV, influenza, Ebola). Applications of the methods to the field of macroevolution provide insight into the evolution and ecology of different species clades. Students will be trained in the algorithms and their application both on paper and in silico as part of the exercises.
SkriptLecture slides will be available on moodle.
LiteraturThe course is not based on any of the textbooks below, but they are excellent choices as accompanying material:
* Yang, Z. 2006. Computational Molecular Evolution.
* Felsenstein, J. 2004. Inferring Phylogenies.
* Semple, C. & Steel, M. 2003. Phylogenetics.
* Drummond, A. & Bouckaert, R. 2015. Bayesian evolutionary analysis with BEAST.
Voraussetzungen / BesonderesBasic knowledge in linear algebra, analysis, and statistics will be helpful. Programming in R will be required for the "Central Element". We provide an R tutorial and help sessions during the first two weeks of class to learn the required skills.
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