Search result: Catalogue data in Spring Semester 2012

Computational Science and Engineering Master Information
227-0120-00LCommunication NetworksW6 credits4GC. X. Dimitropoulos, K. A. Hummel, S. Neuhaus
AbstractThe students will understand the fundamental concepts of communication networks, with a focus on computer networking. They will learn to identify relevant mechanisms that are used in networks, and will see a reasonable set of examples implementing such mechanisms, both as seen from an abstract perspective and with hands-on, practical experience.
ObjectiveThe students will understand the fundamental concepts of communication networks, with a focus on computer networking. They will learn to identify relevant mechanisms that are used to networks work, and will see a reasonable set of examples implementing such mechanisms, both as seen from an abstract perspective and with hands-on, practical experience.
Prerequisites / NoticePrerequisites: A layered model of communication systems (represented by the OSI Reference Model) has previously been introduced.
227-0158-00LSemiconductor Transport Theory and Monte Carlo Device Simulation Information W4 credits2V + 1UF. Bufler, A. Schenk
AbstractThe first part deals with semiconductor transport theory including the necessary quantum mechanics.
In the second part, the Boltzmann equation is solved with the stochastic methods of Monte Carlo simulation.
The exercises address also TCAD simulations of MOSFETs. Thus the topics include theoretical physics,
numerics and practical applications.
ObjectiveOn the one hand, the link between microscopic physics and its concrete application in device simulation is established; on the other hand, emphasis is also laid on the presentation of the numerical techniques involved.
ContentQuantum theoretical foundations I (state vectors, Schroedinger and Heisenberg picture). Band structure (Bloch theorem, one dimensional periodic potential, density of states). Pseudopotential theory (crystal symmetries, reciprocal lattice, Brillouin zone).
Semiclassical transport theory (Boltzmann transport equation (BTE), scattering processes, linear transport).<br>
Monte Carlo method (Monte Carlo simulation as solution method of the BTE, algorithm, expectation values).<br>
Implementational aspects of the Monte Carlo algorithm (discretization of the Brillouin zone, self-scattering according to Rees, acceptance- rejection method etc.). Bulk Monte Carlo simulation (velocity-field characteristics, particle generation, energy distributions, transport parameters). Monte Carlo device simulation (ohmic boundary conditions, MOSFET simulation).
Quantum theoretical foundations II (limits of semiclassical transport theory, quantum mechanical derivation of the BTE, Markov-Limes).
Lecture notesLecture notes (in German)
252-0211-00LInformation SecurityW8 credits4V + 3UD. Basin, U. Maurer
AbstractThis course provides an introduction to Information Security. The focus
is on fundamental concepts and models, basic cryptography, protocols and system security, and privacy and data protection. While the emphasis is on foundations, case studies will be given that examine different realizations of these ideas in practice.
ObjectiveMaster fundamental concepts in Information Security and their
application to system building. (See objectives listed below for more details).
Content1. Introduction and Motivation (OBJECTIVE: Broad conceptual overview of information security) Motivation: implications of IT on society/economy, Classical security problems, Approaches to
defining security and security goals, Abstractions, assumptions, and trust, Risk management and the human factor, Course verview. 2. Foundations of Cryptography (OBJECTIVE: Understand basic
cryptographic mechanisms and applications) Introduction, Basic concepts in cryptography: Overview, Types of Security, computational hardness, Abstraction of channel security properties, Symmetric
encryption, Hash functions, Message authentication codes, Public-key distribution, Public-key cryptosystems, Digital signatures, Application case studies, Comparison of encryption at different layers, VPN, SSL, Digital payment systems, blind signatures, e-cash, Time stamping 3. Key Management and Public-key Infrastructures (OBJECTIVE: Understand the basic mechanisms relevant in an Internet context) Key management in distributed systems, Exact characterization of requirements, the role of trust, Public-key Certificates, Public-key Infrastructures, Digital evidence and non-repudiation, Application case studies, Kerberos, X.509, PGP. 4. Security Protocols (OBJECTIVE: Understand network-oriented security, i.e.. how to employ building blocks to secure applications in (open) networks) Introduction, Requirements/properties, Establishing shared secrets, Principal and message origin authentication, Environmental assumptions, Dolev-Yao intruder model and
variants, Illustrative examples, Formal models and reasoning, Trace-based interleaving semantics, Inductive verification, or model-checking for falsification, Techniques for protocol design,
Application case study 1: from Needham-Schroeder Shared-Key to Kerberos, Application case study 2: from DH to IKE. 5. Access Control and Security Policies (OBJECTIVES: Study system-oriented security, i.e., policies, models, and mechanisms) Motivation (relationship to CIA, relationship to Crypto) and examples Concepts: policies versus models versus mechanisms, DAC and MAC, Modeling formalism, Access Control Matrix Model, Roll Based Access Control, Bell-LaPadula, Harrison-Ruzzo-Ullmann, Information flow, Chinese Wall, Biba, Clark-Wilson, System mechanisms: Operating Systems, Hardware Security Features, Reference Monitors, File-system protection, Application case studies 6. Anonymity and Privacy (OBJECTIVE: examine protection goals beyond standard CIA and corresponding mechanisms) Motivation and Definitions, Privacy, policies and policy languages, mechanisms, problems, Anonymity: simple mechanisms (pseudonyms, proxies), Application case studies: mix networks and crowds. 7. Larger application case study: GSM, mobility
252-0526-00LStatistical Learning TheoryW4 credits2V + 1UJ. M. Buhmann
AbstractThe course covers advanced methods of statistical learning :
PAC learning and statistical learning theory;variational methods and optimization, e.g., maximum entropy techniques, information bottleneck, deterministic and simulated annealing; clustering for vectorial, histogram and relational data; model selection; graphical models.
ObjectiveThe course surveys recent methods of statistical learning. The fundamentals of machine learning as presented in the course "Introduction to Machine Learning" are expanded and in particular, the theory of statistical learning is discussed.
Content# Boosting: A state-of-the-art classification approach that is sometimes used as an alternative to SVMs in non-linear classification.
# Theory of estimators: How can we measure the quality of a statistical estimator? We already discussed bias and variance of estimators very briefly, but the interesting part is yet to come.
# Statistical learning theory: How can we measure the quality of a classifier? Can we give any guarantees for the prediction error?
# Variational methods and optimization: We consider optimization approaches for problems where the optimizer is a probability distribution. Concepts we will discuss in this context include:

* Maximum Entropy
* Information Bottleneck
* Deterministic Annealing

# Clustering: The problem of sorting data into groups without using training samples. This requires a definition of ``similarity'' between data points and adequate optimization procedures.
# Model selection: We have already discussed how to fit a model to a data set in ML I, which usually involved adjusting model parameters for a given type of model. Model selection refers to the question of how complex the chosen model should be. As we already know, simple and complex models both have advantages and drawbacks alike.
# Reinforcement learning: The problem of learning through interaction with an environment which changes. To achieve optimal behavior, we have to base decisions not only on the current state of the environment, but also on how we expect it to develop in the future.
Lecture notesno script; transparencies of the lectures will be made available.
LiteratureDuda, Hart, Stork: Pattern Classification, Wiley Interscience, 2000.

Hastie, Tibshirani, Friedman: The Elements of Statistical Learning, Springer, 2001.

L. Devroye, L. Gyorfi, and G. Lugosi: A probabilistic theory of pattern recognition. Springer, New York, 1996
Prerequisites / NoticeRequirements:

basic knowledge of statistics, interest in statistical methods.

It is recommended that Introduction to Machine Learning (ML I) is taken first; but with a little extra effort Statistical Learning Theory can be followed without the introductory course.
252-0570-00LGame Programming Laboratory
In the Master Programme max. 10 credits can be accounted by Labs
on top of the Interfocus Courses. Additional Labs will be listed on the Addendum.
W10 credits9PB. Sumner
AbstractThe goal of this course is the in-depth understanding of the technology and programming underlying computer games. Students gradually design and develop a computer game in small groups and get acquainted with the art of game programming.
ObjectiveThe goal of this new course is to acquaint students with the
technology and art of programming modern three-dimensional computer
ContentThis is a new course that addresses modern three-dimensional computer
game technology. During the course, small groups of students will
design and develop a computer game. Focus will be put on technical
aspects of game development, such as rendering, cinematography,
interaction, physics, animation, and AI. In addition, we will
cultivate creative thinking for advanced gameplay and visual effects.

The "laboratory" format involves a practical, hands-on approach with
neither traditional lectures nor exercises. Instead, we will meet
once a week to discuss technical issues and to track progress. We
plan to utilize Microsoft's XNA Game Studio Express, which is a
collection libraries and tools that facilitate game development.
While development will take place on PCs, we will ultimately deploy
our games on the XBox 360 console.

At the end of the course we will present our results to the public.
Lecture notesOnline XNA documentation.
Prerequisites / NoticeThe number of participants is limited.

Prerequisites include:

- good programming skills (Java, C++, C#, etc.)

- CG experience: Students should have taken, at a minimum, Visual
Computing. Higher level courses are recommended, such as Introduction
to Computer Graphics, Surface Representations and Geometric Modeling,
and Physically-based Simulation in Computer Graphics.
252-0504-00LNumerical Methods for Solving Large Scale Eigenvalue ProblemsW4 credits3GP. Arbenz
AbstractIn this lecture algorithms are investigated for solving eigenvalue problems
with large sparse matrices. Some of these eigensolvers have been developed
only in the last few years. They will be analyzed in theory and practice (by means
of MATLAB exercises).
ObjectiveKnowing the modern algorithms for solving large scale eigenvalue problems, their numerical behavior, their strengths and weaknesses.
ContentThe lecture starts with providing examples for applications in which
eigenvalue problems play an important role. After an introduction
into the linear algebra of eigenvalue problems, an overview of
methods (such as the classical QR algorithm) for solving small to
medium-sized eigenvalue problems is given.

Afterwards, the most important algorithms for solving large scale,
typically sparse matrix eigenvalue problems are introduced and
analyzed. The lecture will cover a choice of the following topics:

* vector and subspace iteration
* trace minimization algorithm
* Arnoldi and Lanczos algorithms (including restarting variants)
* Davidson and Jacobi-Davidson Algorithm
* preconditioned inverse iteration and LOBPCG
* methods for nonlinear eigenvalue problems

In the exercises, these algorithm will be implemented (in simplified forms)
and analysed in MATLAB.
Lecture notesLecture notes,
Copies of slides
LiteratureZ. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM, Philadelphia, 2000.

Y. Saad: Numerical Methods for Large Eigenvalue Problems. Manchester University Press, Manchester, 1994.

G. H. Golub and Ch. van Loan: Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore 1996.
Prerequisites / NoticePrerequisite: linear agebra
252-5101-00LNumerical Simulation of Dynamic SystemsW4 credits2V + 1UF. E. Cellier
AbstractNumerical Simulation of Dynamic Systems teaches the numerical solution to differential equation (ODE, PDE, DAE) system descriptions as they result from modeling physical and engineering systems.
ObjectiveThe students learn a broad spectrum of algorithms for the numerical solution of implicitly formulated differential and algebraic equation (DAE) systems, as they commonly result from the derivation of mathematical descriptions of physical and engineering systems. Although the techniques taught in this class are techniques of applied mathematics, the emphasis of the class is one of engineering systems design. The students learn how to simulate across discontinuities, as these are present in most models of engineering systems, such as in power electronics. The students are being taught how to deal with higher index DAE models, as they are derived frequently, e.g. from mechanical multi-body systems. The students learn further how to synchronize the simulation clock with physical time for the purpose of real-time simulations of systems, possibly with hardware in the loop. Finally, they are taught how to distribute simulations over multiple processors, while minimizing the inter-processor communication overhead.
ContentThe class Numerical Simulation of Dynamic Systems (NSDS) teaches the students how to compute the trajectory behavior of implicitly formulated differential and algebraic equation (DAE) systems, as they commonly result from the derivation of mathematical descriptions of physical and engineering systems. NSDS is the sister class of the class Mathematical Modeling of Physical Systems (MMPS), in which the students learn how to derive mathematical descriptions of physical systems. MMPS is offered annually in the fall semester.
Lecture notesPresentations of all lectures will be published on the web.
LiteratureCellier, F.E. and E. Kofman (2006), Continuous System Simulation, Springer-Verlag, New York, ISBN 0-387-26102-8, 643p.
252-1426-00LApproximation Algorithms and Semidefinite Programming Information W7 credits3V + 2U + 1AB. Gärtner, J. Matousek
AbstractOver the last fifteen years, semidefinite programming has become an important tool for approximate solutions of hard combinatorial problems. In this lecture, we introduce the foundations of semidefinite programming, we present some of its applications in (but not only in) approximation algorithms, and we show how semidefinite programs can efficiently be solved.
ObjectiveStudents should understand that semidefinite programs form a well-understood class of optimization problems that can (approximately) be solved in polynomial time and yet are powerful enough to yield good approximate solutions for hard combinatorial problems.
ContentThe Goemans-Williamson MAXCUT algorithm. semidefinite programming, The Lovasz theta function, cone programming and duality, algorithms for semidefinite programming, advanced applications of semidefinite programming in approximation algorithms
Lecture notesThe lecture will follow (parts of) the book "Approximation Algorithms and Semidefinite Programming" by the lecturers (see literature).
LiteratureBernd Gärtner and Jiri Matousek: Approximation Algorithms and Semidefinite Programming, Springer, 2012

David P. Williamson and David B. Shmoys: The Design of Approximation Algorithms, Cambridge University Press, 2011
Prerequisites / NoticeBasic knowledge in linear algebra and analysis; the ability to fill in routine details in proofs;
252-0564-00LScientific VisualizationW4 credits2V + 1UR. Peikert
AbstractScientific visualization is the application of computer graphics to the visual analysis and interactive exploration of scientific data which have typically spatial or spatio-temporal domain. Such datasets arise in engineering, natural and medical sciences, and are generated by simulation, measurement or imaging techniques.
ObjectiveBecoming familiar with the fundamental methods and some advanced techniques of scientific visualization. Being able to apply visualization to measurement or simulation data and to correctly interpret visualization results.
ContentThis course covers advanced topics in Scientific Visualization, including: contouring and isosurfaces, direct volume rendering, visualization of flow and vector fields, texture advection, feature extraction, topological methods, information visualization, visualization software, and hot topics of current research.
252-0538-00LShape Modeling and Geometry ProcessingW4 credits2V + 1UO. Sorkine Hornung
AbstractThis course covers some of the latest developments in geometric modeling and digital geometry processing. Topics include surface modeling based on triangle meshes, mesh generation, surface reconstruction, subdivision schemes, mesh fairing and simplification, discrete differential geometry and interactive shape editing.
ObjectiveThe students will learn how to design, program and analyze algorithms and systems for interactive 3D shape modeling and digital geometry processing.
ContentRecent advances in 3D digital geometry processing have created a plenitude of novel concepts for the mathematical representation and interactive manipulation of geometric models. This course covers some of the latest developments in geometric modeling and digital geometry processing. Topics include surface modeling based on triangle meshes, mesh generation, surface reconstruction, subdivision schemes, mesh fairing and simplification, discrete differential geometry and interactive shape editing.
Lecture notesSlides and course notes
Prerequisites / NoticePrerequisites:
Introduction to Computer Graphics, experience with C++ programming. Some background in geometry or computational geometry is helpful, but not necessary.
252-0579-00L3D PhotographyW4 credits3GM. Pollefeys, K. Köser
AbstractThe goal of this course is to provide students with a good understanding of how 3D object shape and appearance can be estimated from images and videos. The main concepts and techniques will be studied in depth and practical algorithms and approaches will be discussed and explored through the exercises and a course project.
ObjectiveAfter attending this course students should:
1. Understand the concepts that allow recovering 3D shape from images.
2. Have a good overview of the state of the art in 3D photography
3. Be able to critically analyze and asses current research in the area
4. Implement components of a 3D photography system.
ContentThe course will cover the following topics a.o. camera model and calibration, single-view metrology, triangulation, epipolar and multi-view geometry, two-view and multi-view stereo, structured-light, feature tracking and matching, structure-from-motion, shape-from-silhouettes and 3D modeling and applications.
252-0312-00LUbiquitous ComputingW3 credits2VF. Mattern
AbstractUbiquitous computing integrates tiny wirelessly connected computers and sensors into the environment and everyday objects. Main topics: The vision of ubiquitous computing, trends in technology, smart cards, RFID, Bluetooth, sensor networks, location awareness, application areas and business issues, privacy.
ObjectiveThe vision of ubiquitous computing, trends in technology, smart cards, RFID, Bluetooth, sensor networks, location awareness, application areas and business issues, privacy.
Lecture notesCopies of slides will be made available
LiteratureWill be provided in the lecture. To put you in the mood:
Mark Weiser: The Computer for the 21st Century. Scientific American, September 1991, pp. 94-104
263-2300-00LHow To Write Fast Numerical CodeW6 credits3V + 2UM. Püschel
AbstractThis course introduces the student to the foundations and state-of-the-art techniques in developing high performance software for numerical functionality such as linear algebra and others. The focus is on optimizing for the memory hierarchy and for special instruction sets. Finally, the course will introduce the recent field of automatic performance tuning.
ObjectiveSoftware performance (i.e., runtime) arises through the interaction of algorithm, its implementation, and the microarchitecture the program is run on. The first goal of the course is to provide the student with an understanding of this interaction, and hence software performance, focusing on numerical or mathematical functionality. The second goal is to teach a general systematic strategy how to use this knowledge to write fast software for numerical problems. This strategy will be trained in a few homeworks and semester-long group projects.
ContentThe fast evolution and increasing complexity of computing platforms pose a major challenge for developers of high performance software for engineering, science, and consumer applications: it becomes increasingly harder to harness the available computing power. Straightforward implementations may lose as much as one or two orders of magnitude in performance. On the other hand, creating optimal implementations requires the developer to have an understanding of algorithms, capabilities and limitations of compilers, and the target platform's architecture and microarchitecture.

This interdisciplinary course introduces the student to the foundations and state-of-the-art techniques in high performance software development using important functionality such as linear algebra functionality, transforms, filters, and others as examples. The course will explain how to optimize for the memory hierarchy, take advantage of special instruction sets, and, if time permits, how to write multithreaded code for multicore platforms. Much of the material is based on state-of-the-art research.

Further, a general strategy for performance analysis and optimization is introduced that the students will apply in group projects that accompany the course. Finally, the course will introduce the students to the recent field of automatic performance tuning.
401-3901-00LMathematical OptimizationW6 credits2V + 1UR. Weismantel
AbstractMathematical treatment of diverse optimization techniques.
ObjectiveAdvanced optimization theory and algorithms.
Content1. Mixed integer optimization models: Geometry and basic examples.

2. Discrete optimization technique: 0/1-lift and project, cutting plane theory and proximity of integer and continuous points.

3. Combinatorial optimization: Basic concepts of complexity theory (notions of P, NP and NP-complete), optimization problems in graphs, polynomial combinatorial algorithms, integrality of polyhedra.

4. Nonlinear optimization: Basic concepts and algorithms for unconstrained optimization (descent methods, conjugate gradient and (Quasi-) Newton method) with convergence analysis for the convex case, Lagrange and Kuhn-Tucker theory
Prerequisites / NoticeThis course assumes the basic knowledge of linear programming, which is taught in courses such as "Introduction to Optimization" (401-2903-00L).
401-3908-09LPolyhedral ComputationW6 credits2V + 1UK. Fukuda
AbstractPolyhedral computation deals with various computational problems associated with convex polyhedra in general dimension. Typical problems include the representation conversion problem (between halfspace and generator representations), the polytope volume computation, the construction of hyperplane arrangements and zonotopes, the Minkowski addition of convex polytopes.
ContentIn this lecture, we study basic and advanced techniques for polyhedral computation in general dimension. We review some classical results on convexity and convex polyhedra such as polyhedral duality, Euler's relation, shellability, McMullen's upper bound theorem, the Minkowski-Weyl theorem, face counting formulas for arrangements, Shannon's theorem on simplicial cells. Our main goal is to investigate fundamental problems in polyhedral computation from both the complexity theory and the viewpoint of algorithmic design. Optimization methods, in particular, linear programming algorithms, will be used as essential building blocks of advanced algorithms in polyhedral computation. Various research problems, both theoretical and algorithmic, in polyhedral computation will be presented.

We also study applications of polyhedral computation in combinatorial optimization, integer programming, game theory, parametric linear and quadratic programming.
Lecture notesLecture notes will be posted as pdf file.
Prerequisites / NoticeThis course assumes the basic knowledge of linear programming, which is taught in courses such as "Mathematical Optimization" (401-3901-00L) and "Introduction to Optimization" (401-2903-00L).
401-3904-00LConvex Optimization Information W6 credits2V + 1UM. Baes
AbstractThe course "Convex optimization" encompasses in a balanced manner theory (convex analysis, duality theory, optimality conditions), applications, and algorithms for convex optimization.
ObjectiveThe aim of this course is to give to mathematicians and practitioners an overview of useful concepts and techniques in convex optimization. A particular attention is given to convex modeling and to algorithms for solving convex optimization problems. Some exercise sessions are devoted to an initiation to a convex optimization solver.

In summary, we will discuss one of the most challenging research areas of nonlinear optimization for which there are many interesting open questions both in theory and practice.

Here is a brief syllabus of the course.
* Mathematical background (6 lectures)
Introduction, convex sets, Semidefinite cone, separation theorems,
Duality, Farkas Lemma, Optimality conditions, Lagrangian duality,
Subgradients, conjugate functions, KKT conditions and applications.

*Applications, convex modeling (3 lectures)
Conic Optimization and applications,
Applications of Semidefinite Optimization
Applications of Convex Optimization to Data Fitting and Statistical

*Algorithms (5 lectures)
Black-box methods, Self-concordant functions,
Interior-point methods, Primal-dual interior-point methods.
ContentConvexity plays a central role in the design and analysis of modern and highly successful algorithms for solving real-world optimization problems. The lecture (in English) on convex optimization will treat in a balanced manner theory (convex analysis, optimality conditions), modeling issues, and algorithms for convex optimization. Beginning with basic concepts and results about the structure of convex sets, continuity and differentiability of convex functions (including conjugate functions), the lecture will cover separation theorems and their important consequences: the theory of Lagrange multipliers, the duality theory and some min-max theorems.

On the algorithmic part, the course will study some simple first and second-order algorithms, as well as some efficient interior-point methods in the framework of self-concordant functions.
Lecture notesThe slides of the course are available online, on the course website. An important reference book for the lecture is "S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004", available online for free.
Literature* A. Barvinok, A Course in Convexity. American Mathematical Society, 2003.
* A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization - Analysis, Algorithms, and Engineering Applications, MPS-SIAM Series on Optimization, MPS-SIAM.
* D. P. Bertsekas, A. Nedic and A. E. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, 2003.
* D. Bertsimas and J. N. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific, 1997.
* S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
* S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. SIAM, 1994.
* E. de Klerk, Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications, Book Series: APPLIED OPTIMIZATION, Vol. 65. Kluwer Academic Publishers.
* Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Book Series: APPLIED OPTIMIZATION, Vol. 87. Kluwer Academic Publishers,
* R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
* J. Renegar, A Mathematical View of Interior-Point Methods in Convex Optimization, MPS-SIAM Series on Optimization.
* H. Wolkowicz, R. Saigal and L. Vandenberghe, Handbook of Semidefinite Programming: Theory, Algorithms, and Applications, Kluwer Academic Publishers.
* A. Nemirovski and D. Yudin, Problem complexity and method efficiency in optimization, Wiley, 1983.
401-4606-00LNumerical Analysis of Stochastic Partial Differential EquationsW8 credits4GA. Barth, A. Lang
AbstractMathematical formulation of partial differential equations with random inputs,
and numerical analysis of deterministic approximation
methods for them:
Karhunen-Loeve expansion of random fields, measures on Hilbert spaces,
multilevel Finite Element methods, sparse tensor and polynomial chaos type approximation methods
ObjectiveThe mathematical formulation of stochastic and random partial
differential equations and the main discretization methods.
Content1 Preliminaries
1.1 Functional analysis
1.2 Probability theory

2 Stochastic partial diffrential equations
2.1 Gaussian measures
2.2 Wiener processes
2.3 Stochastic integration
2.4 Solutions of stochastic partial differential equations
2.5 Finite Element approximation
2.6 Noise approximation
2.7 (Multilevel) Monte Carlo methods

3 Random partial differential equations
3.1 Distributions on Banach spaces
3.2 Elliptic partial differential equation with stochastic right hand
3.2.1 Existence and uniqueness
3.2.2 Finite Element method
3.2.3 Full and sparse tensor approximations
3.3 Elliptic partial differential equation with stochastic operator
3.3.1 Existence and uniqueness
3.3.2 Finite Element method
3.3.3 (Multilevel) Monte Carlo methods
3.3.4 Stochastic Galerkin methods
Lecture notesNo lecture notes but handouts on selected topics will be provided.
Literature1. Stochastic Equations in Infinite Dimensions
G. Da Prato and J. Zabczyk
Cambridge Univ. Press (1992)

2. Taylor Approximations for Stochastic Partial Differential Equations
A. Jentzen and P.E. Kloeden
Siam (2011)

3. Numerical Solution of Stochastic Differential Equations
P.E. Kloeden and E. Platen
Springer Verlag (1992)

4. A Concise Course on Stochastic Partial Differential Equations
C. Prévôt and M. Röckner
Springer Verlag (2007)

5. Galerkin Finite Element Methods for Parabolic Problems
V. Thomée
Springer Verlag (2006)
Prerequisites / NoticeFunctional analysis, numerical solution of elliptic and parabolic PDEs, probability theory, stochastic processes
402-0577-00LQuantum Systems for Information TechnologyW8 credits2V + 2US. Filipp
AbstractIntroduction to experimental quantum information processing (QIP). Quantum bits. Coherent Control. Quantum Measurement. Decoherence. Microscopic and macroscopic quantum systems. Nuclear magnetic resonance (NMR) in molecules and solids. Ions and neutral atoms in electromagnetic traps. Charges and spins in quantum dots. Charges and flux quanta in superconducting circuits. Novel hybrid systems.
ObjectiveIn recent years the realm of quantum mechanics has entered the domain of information technology. Enormous progress in the physical sciences and in engineering and technology has allowed us to envisage building novel types of information processors based on the concepts of quantum physics. In these processors information is stored in the quantum state of physical systems forming quantum bits (qubits). The interaction between qubits is controlled and the resulting states are read out on the level of single quanta in order to process information. Realizing such challenging tasks may allow constructing an information processor much more powerful than a classical computer. The aim of this class is to give a thorough introduction to physical implementations pursued in current research for realizing quantum information processors. The field of quantum information science is one of the fastest growing and most active domains of research in modern physics.
ContentA syllabus will be provided on the class web server at the beginning of the term (see section 'Besonderes'/'Notice').
Lecture notesElectronically available lecture notes will be published on the class web server (see section 'Besonderes'/'Notice').
LiteratureQuantum computation and quantum information / Michael A. Nielsen & Isaac L. Chuang. Reprinted. Cambridge : Cambridge University Press ; 2001.. 676 p. : ill.. [004153791].

Additional literature and reading material will be provided on the class web server (see section 'Besonderes'/'Notice').
Prerequisites / NoticeThe class will be taught in English language.

Basic knowledge of quantum mechanics is required, prior knowledge in atomic physics, quantum electronics, and solid state physics is advantageous.

More information on this class can be found on the web site:
402-0472-00LMesoscopic Quantum Optics
Does not take place this semester.
W8 credits3V + 1UA. Imamoglu
AbstractDescription of open quantum systems using quantum trajectories. Cascaded quantum systems. Decoherence and quantum measurements. Elements of single quantum dot spectroscopy: interaction effects. Spin-reservoir coupling.
ObjectiveThis course covers basic concepts in mesoscopic quantum optics and builds up on the material covered in the Quantum Optics course. The specific topics that will be discussed include emitter-field interaction in the electric-dipole limit, spontaneous emission, density operator and the optical Bloch equations, quantum optical phenomena in quantum dots (photon antibunching, cavity-QED) and confined spin dynamics.
ContentDescription of open quantum systems using quantum trajectories. Cascaded quantum systems. Decoherence and quantum measurements. Elements of single quantum dot spectroscopy: interaction effects. Spin-reservoir coupling.
Lecture notesY. Yamamoto and A. Imamoglu, "Mesoscopic Quantum Optics," (Wiley, 1999).
402-0804-00LNeuromorphic Engineering II Information W6 credits5GT. Delbrück, G. Indiveri, S.‑C. Liu
AbstractThis course teaches the basics of analog chip design and layout with an emphasis on neuromorphic circuits, which are introduced in the fall semester course "Neuromorphic Engineering I".
ObjectiveDesign of a neuromorphic circuit for implementation with CMOS technology.
ContentThis course teaches the basics of analog chip design and layout with an emphasis on neuromorphic circuits, which are introduced in the autumn semester course "Neuromorphic Engineering I".

The principles of CMOS processing technology are presented. Using a set of inexpensive software tools for simulation, layout and verification, suitable for neuromorphic circuits, participants learn to simulate circuits on the transistor level and to make their layouts on the mask level. Important issues in the layout of neuromorphic circuits will be explained and illustrated with examples. In the latter part of the semester students simulate and layout a neuromorphic chip. Schematics of basic building blocks will be provided. The layout will then be fabricated and will be tested by students during the following fall semester.
LiteratureS.-C. Liu et al.: Analog VLSI Circuits and Principles; software documentation.
Prerequisites / NoticePrerequisites: Neuromorphic Engineering I strongly recommended
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