Suchergebnis: Katalogdaten im Frühjahrssemester 2012

Rechnergestützte Wissenschaften Master Information
227-0120-00LCommunication NetworksW6 KP4GC. X. Dimitropoulos, K. A. Hummel, S. Neuhaus
KurzbeschreibungThe 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.
LernzielThe 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.
Voraussetzungen / BesonderesPrerequisites: 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 KP2V + 1UF. Bufler, A. Schenk
KurzbeschreibungZum einen wird die Halbleitertransporttheorie einschliesslich der dafür notwendigen Quantenmechanik behandelt. Zum anderen wird die Boltzmann-Gleichung mit den stochastischen Methoden der Monte Carlo
Simulation gelöst. Die Uebungen betreffen u.a. TCAD-Simulationen von MOSFETs. Die Thematik umfasst
daher theoretische Physik, Numerik und praktische Anwendungen.
LernzielEinerseits soll der Brückenschlag zwischen der mikroskopischen Physik und deren konkreter Anwendung in der Bauelementsimulation aufgezeigt werden, andererseits steht die Vermittlung der dabei zum Einsatz kommenden numerischen Techniken im Vordergrund.
InhaltQuantentheoretische Grundlagen I (Zustandsvektoren, Schrödinger- und Heisenbergbild). Bandstruktur (Bloch-Theorem, eindimensionales periodisches Potential, Zustandsdichte). Pseudopotentialtheorie (Kristallsymmetrien, reziprokes Gitter, Brillouinzone). Semiklassische Transporttheorie (Boltzmann-Transportgleichung [BTG], Streuprozesse, linearer Transport). Monte Carlo Methode (Monte Carlo Simula- tion als Lösungsmethode der BTG, Algorithmus, Erwartungswerte). Implementationsaspekte des Monte Carlo Algorithmus (Diskretisierung der Brillouinzone. Selbststreu- ung nach Rees, Acceptance-Rejection Methode, etc.). Bulk Monte Carlo Simulation (Geschwindigkeits-Feld-Kurven, Teilchengeneration, Energieverteilungen, Transportparameter). Monte Carlo Bauelementesimulation (ohmsche Randbedingungen, MOSFET-Simulation). Quantentheoretische Grundlagen II. (Grenzen der semiklassischen Transporttheorie, quantenmechanische Ableitung der BTG, Markov-Limes).
252-0211-00LInformation SecurityW8 KP4V + 3UD. Basin, U. Maurer
KurzbeschreibungThis 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.
LernzielMaster fundamental concepts in Information Security and their
application to system building. (See objectives listed below for more details).
Inhalt1. 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 KP2V + 1UJ. M. Buhmann
KurzbeschreibungThe 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.
LernzielThe 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.
Inhalt# 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.
Skriptno script; transparencies of the lectures will be made available.
LiteraturDuda, 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
Voraussetzungen / BesonderesRequirements:

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
Im Masterstudium können zusätzlich zu den Vertiefungsübergreifenden Fächern nur max. 10 Kreditpunkte über Laboratorien erarbeitet werden. Weitere Laboratorien werden auf dem Beiblatt aufgeführt.
W10 KP9PB. Sumner
KurzbeschreibungDas Ziel dieses Kurses ist ein vertieftes Verständnis der Technologie und der Programmierung von Computer-Spielen. Die Studierenden entwerfen und entwickeln in kleinen Gruppen ein Computer-Spiel und machen sich so vertraut mit der Kunst des Spiel-Programmierens.
LernzielDas Ziel dieses neuen Kurses ist es, die Studenten mit der Technologie und der Kunst des Programmierens von modernen dreidimensionalen Computerspielen vertraut zu machen.
InhaltDies ist ein neuer Kurs, der auf die Technologie von modernen dreidimensionalen Computerspielen eingeht. Während des Kurses werden die Studenten in kleinen Gruppen ein Computerspiel entwerfen und entwickeln. Der Schwerpunkt des Kurses wird auf technischen Aspekten der Spielentwicklung wie Rendering, Kinematographie, Interaktion, Physik, Animation und KI liegen. Zusätzlich werden wir aber auch Wert auf kreative Ideen für fortgeschrittenes Gameplay und visuelle Effekte legen.

Der Kurs wird als „Labor“ durchgeführt. Anstelle von traditionellen Vorträgen und Übungen wird der Kurs in einen praktischen, hands-on Ansatz durchgeführt. Wir treffen uns einmal wöchentlich um technische Aspekte zu besprechen und den Fortschritt der Entwicklung zu verfolgen. Wir planen das XNA Game Studio Express von Microsoft zu verwenden, eine Ansammlung von Bibliotheken und Werkzeugen um die Spieleentwicklung zu erleichtern. Die Entwicklung wird zunächst auf dem PC stattfinden, das Spiel wird dann im weiteren Verlauf auf der Xbox 360 Konsole eingesetzt.

Am Ende des Kurses werden die Resultate öffentlich präsentiert.
SkriptOnline XNA Dokumentation.
Voraussetzungen / BesonderesDie Anzahl der Teilnehmer wird begrenzt sein.

Voraussetzung für die Teilnahme sind:

- Gute Programmierkenntnisse (Java, C++, C#, o.ä.)

- Erfahrung in Computergrafik: Teilnehmer sollten mindestens die Vorlesung Visual Computing besucht haben. Wir empfehlen auch noch die weiterführenden Kurse Introduction to Computer Graphics, Surface Representations and Geometric Modeling, und Physically-based Simulation in Computer Graphics.
252-0504-00LNumerical Methods for Solving Large Scale Eigenvalue ProblemsW4 KP3GP. Arbenz
KurzbeschreibungDie Vorlesung behandelt Algorithmen zur Lösung von Eigenwertproblemen
mit grossen, schwach besetzten Matrizen. Die z.T. erst in den letzten Jahren
entwickelten Verfahren werden theoretisch und praktisch mit MATLAB
LernzielKenntnisse der modernen Eigenlöser, ihres numerischen Verhaltens, ihrer Einsatzmöglichkeiten und Grenzen.
InhaltDie Vorlesung beginnt mit verschiedenartigen Beispielen für Anwendungen
in denen Eigenwertprobleme eine wichtige Rolle spielen. Nach einer
Einführung in die Lineare Algebra der Eigenwertprobleme wird ein
Überblick über Verfahren (QR-Algorithmus u.ä.) zur Behandlung kleiner
und mittelgrosser Eigenwertprobleme gegeben.

Danach werden die heute wichtigsten Löser für grosse, typischerweise
schwach-besetzte Matrixeigenwertprobleme vorgestellt und analysiert.
Dabei wird eine Auswahl der folgenden Themen behandelt:

* Vektor- und Teilraumiteration
* Spurminimierungsalgorithmus
* Arnoldi- und Lanczos-Algorithmus (inkl. Varianten mit Neustart)
* Davidson- und Jacobi-Davidson-Algorithmus
* vorkonditionierte inverse Iteration und LOBPCG
* Verfahren für nichtlineaere Eigenwertprobleme

In den Übungen werden diese Algorithmen (in vereinfachter Form) in
MATLAB implementiert und numerisch untersucht.
SkriptLecture notes (Englisch),
Kopien der Folien
LiteraturZ. 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.
Voraussetzungen / BesonderesVoraussetzung: Lineare Algebra
252-5101-00LNumerical Simulation of Dynamic SystemsW4 KP2V + 1UF. E. Cellier
KurzbeschreibungNumerical 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.
LernzielThe 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.
InhaltThe 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.
SkriptPresentations of all lectures will be published on the web.
LiteraturCellier, 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 KP3V + 2U + 1AB. Gärtner, J. Matousek
KurzbeschreibungOver 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.
LernzielStudents 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.
InhaltThe 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
SkriptThe lecture will follow (parts of) the book "Approximation Algorithms and Semidefinite Programming" by the lecturers (see literature).
LiteraturBernd 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
Voraussetzungen / BesonderesBasic knowledge in linear algebra and analysis; the ability to fill in routine details in proofs;
252-0564-00LScientific VisualizationW4 KP2V + 1UR. Peikert
KurzbeschreibungScientific 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.
LernzielBecoming 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.
InhaltThis 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 KP2V + 1UO. Sorkine Hornung
KurzbeschreibungThis 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.
LernzielThe students will learn how to design, program and analyze algorithms and systems for interactive 3D shape modeling and digital geometry processing.
InhaltRecent 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.
SkriptSlides and course notes
Voraussetzungen / BesonderesPrerequisites:
Introduction to Computer Graphics, experience with C++ programming. Some background in geometry or computational geometry is helpful, but not necessary.
252-0579-00L3D PhotographyW4 KP3GM. Pollefeys, K. Köser
KurzbeschreibungThe 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.
LernzielAfter 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.
InhaltThe 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 KP2VF. Mattern
KurzbeschreibungUbiquitous 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.
LernzielThe vision of ubiquitous computing, trends in technology, smart cards, RFID, Bluetooth, sensor networks, location awareness, application areas and business issues, privacy.
SkriptCopies of slides will be made available
LiteraturWill 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 KP3V + 2UM. Püschel
KurzbeschreibungThis 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.
LernzielSoftware 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.
InhaltThe 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 KP2V + 1UR. Weismantel
KurzbeschreibungMathematical treatment of diverse optimization techniques.
LernzielAdvanced optimization theory and algorithms.
Inhalt1. 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
Voraussetzungen / BesonderesThis 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 KP2V + 1UK. Fukuda
KurzbeschreibungPolyhedral 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.
InhaltIn 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.
SkriptLecture notes will be posted as pdf file.
Voraussetzungen / BesonderesThis 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 KP2V + 1UM. Baes
KurzbeschreibungThe course "Convex optimization" encompasses in a balanced manner theory (convex analysis, duality theory, optimality conditions), applications, and algorithms for convex optimization.
LernzielThe 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.
InhaltConvexity 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.
SkriptThe 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.
Literatur* 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 KP4GA. Barth, A. Lang
KurzbeschreibungMathematical 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
LernzielThe mathematical formulation of stochastic and random partial
differential equations and the main discretization methods.
Inhalt1 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
SkriptNo lecture notes but handouts on selected topics will be provided.
Literatur1. 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)
Voraussetzungen / BesonderesFunctional analysis, numerical solution of elliptic and parabolic PDEs, probability theory, stochastic processes
402-0577-00LQuantum Systems for Information TechnologyW8 KP2V + 2US. Filipp
KurzbeschreibungIntroduction 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.
LernzielIn 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.
InhaltA syllabus will be provided on the class web server at the beginning of the term (see section 'Besonderes'/'Notice').
SkriptElectronically available lecture notes will be published on the class web server (see section 'Besonderes'/'Notice').
LiteraturQuantum 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').
Voraussetzungen / BesonderesThe 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
Findet dieses Semester nicht statt.
W8 KP3V + 1UA. Imamoglu
KurzbeschreibungDescription 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.
LernzielThis 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.
InhaltDescription 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.
SkriptY. Yamamoto and A. Imamoglu, "Mesoscopic Quantum Optics," (Wiley, 1999).
402-0804-00LNeuromorphic Engineering II Information W6 KP5GT. Delbrück, G. Indiveri, S.‑C. Liu
KurzbeschreibungDiese Vorlesung lehrt die Basis des analogen Chip-Design und Chip-Layout mit Betonung auf Neuromorphe Schaltungen, welche im Herbstsemester in der Vorlesung "Neuromorphic Engineering I" eingeführt werden.
LernzielDiese Vorlesung mit Übungen ermöglicht den Teilnehmern, selbst neuromorphe Schaltungen zu entwerfen und herstellen zu lassen.
InhaltEs werden verschiedene Computerprogramme vorgestellt und benutzt, die zur Simulation, zum Entwurf und zur Entwurfsverifikation von neuromorphen Schaltungen geeignet sind. Anhand von Beispielen wird aufgezeigt, worauf beim Schaltungsentwurf zu achten ist. Nützliche und notwendige Schaltungen werden erklärt und zur Verfügung gestellt. Es werden verschiedenen CMOS-Prozesse erläutert und gezeigt, wie man sie benutzen kann. Gegen Ende des Semesters kann jeder Student eine eigene Schaltung konzipieren und herstellen lassen.
LiteraturS.-C. Liu et al.: Analog VLSI Circuits and Principles; Software-Dokumentation.
Voraussetzungen / BesonderesVoraussetzungen: dass die Studenten bereits über die Grundkenntnisse der neuromorphen Schaltungstechnik verfügen, die sie sich am besten in der Vorlesung "Neuromorphic Engineering I" im vorangehenden Herbstsemester erwerben.
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