mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where

The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sam-pling rates is quantization, i.e., higher bit-depths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bit-depths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement

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I hereby declare that I have created this work completely on my own and used no other sources or tools than the ones listed, and that I have marked any citations accordingly. Hiermit versichere ich, dass ich die vorliegende Arbeit selbständig verfasst und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt sowie Zitate kenntlich gemacht habe.

pages 156–175, 2013. [2] Johannes Buchmann, Denise Demirel, and Jeroen van de Graaf. Towards a publicly-verifiable mix-net providing everlasting privacy. In Financial Cryptog-raphy, pages 197–204, 2013. [3] Denise Demirel, Jeroen van de Graaf, and Roberto Araùjo. Improving helios

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Abstract—This paper highlights and characterizes the main obstacle to deploying a robust wireless sensor network testbed: the USB connections that link each of the nodes via ethernet gateways to the central server. Unfortunately, these connections are also the components that, when properly installed, can reduce testbed costs by attaching multiple nodes per gateway. After illustrating how unreliable current solutions can become (regardless of the used sensor nodes, USB cabling, or gateway setup), a set of experiments led to a list of dos and don’ts in testbed deployment. Furthermore, a simple and cost-effective suggestion is presented that allows to bypass current USB backchannel issues, leading to a more robust testbed that avoids manual maintenance of individual nodes. Index Terms—experimentation; testbeds; testbed reliability; sensor node reprogramming; universal serial bus I.

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the receiver and the transmitter. We restrict our attention to a general class of periodic sub-Nyquist samplers, which subsumes as special cases sampling with periodic modulation and filter banks. We evaluate the loss due to channel-independent (universal) sub-Nyquist design through a sampled capacity loss