Optimierung mechanischer Strukturen: Grundlagen und industrielle Anwendungen (German Edition)

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Home Optimierung mechanischer Strukturen: A good knowledge of Matlab is required to participate in the tutorials and for the mini-project. Algebra and Error Correcting Codes. The course is an introduction to error correcting codes covering both classical algebraic codes and modern iterative decoding. The course includes a self-contained introduction of the pertinent basics of "abstract" algebra.

This course builds on Information Theory I. It introduces additional topics in single-user communication, connections between Information Theory and Statistics, and Network Information Theory. The course has two objectives: Differential entropy, maximum entropy, the Gaussian channel and water filling, the entropy-power inequality, Sanov's Theorem, Fisher information, the broadcast channel, the multiple-access channel, Slepian-Wolf coding, and the Gelfand-Pinsker problem. Thomas, Elements of Information Theory, second edition, Wiley The class focuses on fundamental mathematical aspects of data sciences: Information theory lossless and lossy compression , sampling theory, compressed sensing, dimensionality reduction Johnson-Lindenstrauss Lemma , randomized algorithms for large-scale numerical linear algebra, approximation theory, neural networks as function approximators, mathematical foundations of deep learning.

After attending this lecture, participating in the exercise sessions, and working on the homework problem sets, students will have acquired a working knowledge of the most commonly used mathematical theories in data science. Students will also have to carry out a research project, either individually or in groups, with presentations at the end of the semester.

ETH Zürich - Vorlesungsverzeichnis

Entropy, mutual information, lossy compression, rate-distortion theory, lossless compression, arithmetic coding, Lempel-Ziv compression 2. Frames in finite-dimensional spaces, frames in Hilbert spaces, wavelets, Gabor expansions 3. The sampling theorem as a frame expansion, irregular sampling, multi-band sampling, density theorems, spectrum-blind sampling 4.

Sparsity and compressed sensing: Uncertainty principles, recovery algorithms, Lasso, matching pursuits, compressed sensing, non-linear approximation, best k-term approximation, super-resolution 5. High-dimensional data and dimensionality reduction: Random projections, the Johnson-Lindenstrauss Lemma, sketching 6. Randomized algorithms for large-scale numerical linear algebra: Large-scale matrix computations, randomized algorithms for approximate matrix factorizations, matrix sketching, fast algorithms for large-scale FFTs 7. Mathematics of deep neural networks: Universal function approximation with single-and multi-layer networks, fundamental limits on compressibility of signal classes, Kolmogorov epsilon-entropy of signal classes, geometry of decision surfaces, convolutional neural networks, scattering networks.

This course is aimed at students with a background in basic linear algebra, analysis, and probability.

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We will, however, review required mathematical basics throughout the semester in the exercise sessions. Communication and Detection Theory. This course teaches the foundations of modern digital communications and detection theory. Topics include the geometry of the space of energy-limited signals; the baseband representation of passband signals, spectral efficiency and the Nyquist Criterion; the power and power spectral density of PAM and QAM; hypothesis testing; Gaussian stochastic processes; and detection in white Gaussian noise.

This is an introductory class to the field of wired and wireless communication.

It offers a glimpse at classical analog modulation AM, FM , but mainly focuses on aspects of modern digital communication, including modulation schemes, spectral efficiency, power budget analysis, block and convolu- tional codes, receiver design, and multi- accessing schemes such as TDMA, FDMA and Spread Spectrum. The 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. 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.

Lecture notes and material for the course will be available before each course on: A layered model of communication systems represented by the OSI Reference Model has previously been introduced.

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The 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. Thus the topics include theoretical physics, numerics and practical applications. On 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.

Quantum 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. Bulk Monte Carlo simulation velocity-field characteristics, particle generation, energy distributions, transport parameters. Quantum Transport at the Nanoscale.

This class offers an introduction into quantum transport theory, a rigorous approach to electron transport at the nanoscale. It covers different topics such as bandstructure, Wave Function and Non-equilibrium Green's Function formalisms, and electron interactions with their environment. Matlab exercises accompany the lectures where students learn how to develop their own transport simulator. The continuous scaling of electronic devices has given rise to structures whose dimensions do not exceed a few atomic layers.

At this size, electrons do not behave as particle any more, but as propagating waves and the classical representation of electron transport as the sum of drift-diffusion processes fails.

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The purpose of this class is to explore and understand the displacement of electrons through nanoscale device structures based on state-of-the-art quantum transport methods and to get familiar with the underlying equations by developing his own nanoelectronic device simulator. The following topics will be addressed: