Suchergebnis: Katalogdaten im Herbstsemester 2018
|Rechnergestützte Wissenschaften Master|
Von den angebotenen Wahlfächern müssen mindestens zwei Lerneinheiten erfolgreich abgeschlossen werden.
|401-4623-00L||Time Series Analysis||W||6 KP||3G||N. Meinshausen|
|Kurzbeschreibung||Statistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations,|
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
|Lernziel||Understanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.|
|Inhalt||This course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations.|
Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
|Literatur||A list of references will be distributed during the course.|
|Voraussetzungen / Besonderes||Basic knowledge in probability and statistics|
|401-3901-00L||Mathematical Optimization||W||11 KP||4V + 2U||R. Weismantel|
|Kurzbeschreibung||Mathematical treatment of diverse optimization techniques.|
|Lernziel||Advanced optimization theory and algorithms.|
|Inhalt||1) Linear optimization: The geometry of linear programming, the simplex method for solving linear programming problems, Farkas' Lemma and infeasibility certificates, duality theory of linear programming.|
2) Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization.
3) Integer optimization: Ties between linear and integer optimization, total unimodularity, complexity theory, cutting plane theory.
4) Combinatorial optimization: Network flow problems, structural results and algorithms for matroids, matchings, and, more generally, independence systems.
|Literatur||1) D. Bertsimas & R. Weismantel, "Optimization over Integers". Dynamic Ideas, 2005.|
2) A. Schrijver, "Theory of Linear and Integer Programming". John Wiley, 1986.
3) D. Bertsimas & J.N. Tsitsiklis, "Introduction to Linear Optimization". Athena Scientific, 1997.
4) Y. Nesterov, "Introductory Lectures on Convex Optimization: a Basic Course". Kluwer Academic Publishers, 2003.
5) C.H. Papadimitriou, "Combinatorial Optimization". Prentice-Hall Inc., 1982.
|Voraussetzungen / Besonderes||Linear algebra.|
|227-1033-00L||Neuromorphic Engineering I |
Registration in this class requires the permission of the instructors. Class size will be limited to available lab spots.
Preference is given to students that require this class as part of their major.
|W||6 KP||2V + 3U||T. Delbrück, G. Indiveri, S.‑C. Liu|
|Kurzbeschreibung||This course covers analog circuits with emphasis on neuromorphic engineering: MOS transistors in CMOS technology, static circuits, dynamic circuits, systems (silicon neuron, silicon retina, silicon cochlea) with an introduction to multi-chip systems. The lectures are accompanied by weekly laboratory sessions.|
|Lernziel||Understanding of the characteristics of neuromorphic circuit elements.|
|Inhalt||Neuromorphic circuits are inspired by the organizing principles of biological neural circuits. Their computational primitives are based on physics of semiconductor devices. Neuromorphic architectures often rely on collective computation in parallel networks. Adaptation, learning and memory are implemented locally within the individual computational elements. Transistors are often operated in weak inversion (below threshold), where they exhibit exponential I-V characteristics and low currents. These properties lead to the feasibility of high-density, low-power implementations of functions that are computationally intensive in other paradigms. Application domains of neuromorphic circuits include silicon retinas and cochleas for machine vision and audition, real-time emulations of networks of biological neurons, and the development of autonomous robotic systems. This course covers devices in CMOS technology (MOS transistor below and above threshold, floating-gate MOS transistor, phototransducers), static circuits (differential pair, current mirror, transconductance amplifiers, etc.), dynamic circuits (linear and nonlinear filters, adaptive circuits), systems (silicon neuron, silicon retina and cochlea) and an introduction to multi-chip systems that communicate events analogous to spikes. The lectures are accompanied by weekly laboratory sessions on the characterization of neuromorphic circuits, from elementary devices to systems.|
|Literatur||S.-C. Liu et al.: Analog VLSI Circuits and Principles; various publications.|
|Voraussetzungen / Besonderes||Particular: The course is highly recommended for those who intend to take the spring semester course 'Neuromorphic Engineering II', that teaches the conception, simulation, and physical layout of such circuits with chip design tools. |
Prerequisites: Background in basics of semiconductor physics helpful, but not required.
|227-1037-00L||Introduction to Neuroinformatics||W||6 KP||2V + 1U||V. Mante, M. Cook, B. Grewe, G. Indiveri, D. Kiper, W. von der Behrens|
|Kurzbeschreibung||The course provides an introduction to the functional properties of neurons. Particularly the description of membrane electrical properties (action potentials, channels), neuronal anatomy, synaptic structures, and neuronal networks. Simple models of computation, learning, and behavior will be explained. Some artificial systems (robot, chip) are presented.|
|Lernziel||Understanding computation by neurons and neuronal circuits is one of the great challenges of science. Many different disciplines can contribute their tools and concepts to solving mysteries of neural computation. The goal of this introductory course is to introduce the monocultures of physics, maths, computer science, engineering, biology, psychology, and even philosophy and history, to discover the enchantments and challenges that we all face in taking on this major 21st century problem and how each discipline can contribute to discovering solutions.|
|Inhalt||This course considers the structure and function of biological neural networks at different levels. The function of neural networks lies fundamentally in their wiring and in the electro-chemical properties of nerve cell membranes. Thus, the biological structure of the nerve cell needs to be understood if biologically-realistic models are to be constructed. These simpler models are used to estimate the electrical current flow through dendritic cables and explore how a more complex geometry of neurons influences this current flow. The active properties of nerves are studied to understand both sensory transduction and the generation and transmission of nerve impulses along axons. The concept of local neuronal circuits arises in the context of the rules governing the formation of nerve connections and topographic projections within the nervous system. Communication between neurons in the network can be thought of as information flow across synapses, which can be modified by experience. We need an understanding of the action of inhibitory and excitatory neurotransmitters and neuromodulators, so that the dynamics and logic of synapses can be interpreted. Finally, the neural architectures of feedforward and recurrent networks will be discussed in the context of co-ordination, control, and integration of sensory and motor information in neural networks.|
|327-1201-00L||Transport Phenomena I||W||5 KP||4G||H. C. Öttinger|
|Kurzbeschreibung||Phenomenological approach to "Transport Phenomena" based on balance equations supplemented by thermodynamic considerations to formulate the undetermined fluxes in the local species mass, momentum, and energy balance equations; fundamentals, applications, and simulations|
|Lernziel||The teaching goals of this course are on five different levels:|
(1) Deep understanding of fundamentals: local balance equations, constitutive equations for fluxes, entropy balance, interfaces, idea of dimensionless numbers, ...
(2) Ability to use the fundamental concepts in applications
(3) Insight into the role of boundary conditions
(4) Knowledge of a number of applications
(5) Flavor of numerical techniques: finite elements, finite differences, lattice Boltzmann, Brownian dynamics, ...
|Inhalt||Approach to Transport Phenomena|
Refreshing Topics in Equilibrium Thermodynamics
Forces and Fluxes
Measuring Transport Coefficients
|Skript||The course is based on the book D. C. Venerus and H. C. Öttinger, A Modern Course in Transport Phenomena (Cambridge University Press, 2018)|
|Literatur||1. D. C. Venerus and H. C. Öttinger, A Modern Course in Transport Phenomena (Cambridge University Press, 2018)|
2. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd Ed. (Wiley, 2001)
3. S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, 2nd Ed. (Dover, 1984)
4. W. M. Deen, Analysis of Transport Phenomena (Oxford University Press, 1998)
5. R. B. Bird, Five Decades of Transport Phenomena (Review Article), AIChE J. 50 (2004) 273-287
|Voraussetzungen / Besonderes||Complex numbers. Vector analysis (integrability; Gauss' divergence theorem). Laplace and Fourier transforms. Ordinary differential equations (basic ideas). Linear algebra (matrices; functions of matrices; eigenvectors and eigenvalues; eigenfunctions). Probability theory (Gaussian distributions; Poisson distributions; averages; moments; variances; random variables). Numerical mathematics (integration). Equilibrium thermodynamics (Gibbs' fundamental equation; thermodynamic potentials; Legendre transforms). Maxwell equations. Programming and simulation techniques (Matlab, Monte Carlo simulations).|
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