Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations in Sciences and

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

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 group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond to integer n-sequences and the nodes in the path generate all n! permutations. The extra node has a more complicated action, adding a certain quantity to some of the numbers.

Commutative, idempotent groupoids and the

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

First, I would like to thank to Dimka Karastoyanova and Mariano Cilia for all the fruitful discussions, their guidance and support through the course of this project. Thanks also to Prof. Alejandro Buchmann who sponsored my stay at Technische Universität Darmstadt during the spring of 2004. The special thanks go to my advisor, Mariano Cilia, who has made all this possible. Finally, I’d like to thank to my family for all these years of support.

Caractérisation des problèmes conjoints de détection et d'estimation

quantified by isotopic non

belowground functioning of tropical biomes

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