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

Abstract — We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing kernel Hilbert spaces (RKHS). After a characterization of the RKHS associated with the SLGM, we derive a lower bound on the minimum variance achievable by estimators with a prescribed bias function, including the important special case of unbiased estimation. This bound is obtained via an orthogonal projection of the prescribed mean function onto a subspace of the RKHS associated with the SLGM. It provides an approximation to the minimum achievable variance (Barankin bound) that is tighter than any known bound. Our bound holds for an arbitrary system matrix, including the overdetermined and underdetermined cases. We specialize

Responses of soil biological processes to elevated atmospheric [CO2] and nitrogen addition in a poplar plantation

We analyze the consumption-portfolio selection problem of an investor facing both Brownian and jump risks. By adopting a factor structure for the asset returns and decomposing the two types of risks on a well chosen basis, we provide a new methodology for determining the optimal solution up to an implicitly defined constant, which in some cases can be reduced to a fully explicit closed form, irrespectively of the number of assets available to the investor. We show that the optimal policy is for the investor to focus on controlling his exposure to the jump risk, while exploiting differences in the asset returns diffusive characteristics in the orthogonal space. We also examine the solution to the portfolio problem as the number of assets increases and the impact of the jumps on the diversification of the optimal portfolio.

de nationalité suisse et originaire de Zurich (ZH) et Lucerne (LU) acceptée sur proposition du jury:

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We explore two fundamental questions at the intersection of sampling theory and information theory: how is channel capacity affected by sampling below the channel’s Nyquist rate, and what sub-Nyquist sampling strategy should be employed to maximize capacity. In particular, we first derive the capacity of sampled analog channels for two prevalent sampling mechanisms: filtering followed by sampling and sampling following filter banks. Connections between sampling and MIMO Gaussian channels are illuminated based on this analysis. Optimal prefilters that maximize capacity are identified for both cases, as well as several kinds of channels for which these sampling mechanisms are optimal to maximize capacity at sub-Nyquist rates. We also highlight connections between sampled analog channel capacity and minimum mean squared error estimation from sampled data. In particular, it is shown that for both filtering and filter-bank sampling strategies, the filters maximizing capacity and minimizing mean squared error are equivalent. We also investigate a more general sampling strategy by adding modulation banks to filter-bank sampling. This general sampling method subsumes most nonuniform sampling techniques applied in both theory and practice. We also show a connection between this general sampling method and MIMO Gaussian channels. We then identify the optimal sampling strategy for piece-wise flat sampled

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