Harmonic analysis of finite lamplighter random walks

Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular when the underlying graph is the infinite path $\mathbb{Z}$. In the present paper, we develop a spectral analysis for lamplighter random walks on finite graphs. In the general case, we use the $C_2$-symmetry to reduce the spectral computations to a series of eigenvalue problems on the underlying graph. In the case the graph has a transitive isometry group $G$, we also describe the spectral analysis in terms of the representation theory of the wreath product $C_2\wr G$. We apply our theory to the lamplighter random walks on the complete graph and on the discrete circle. These examples were already studied by Haggstrom and Jonasson by probabilistic methods.Comment: 29 page

Harmonic analysis on a finite homogeneous space

In this paper, we study harmonic analysis on finite homogeneous spaces whose associated permutation representation decomposes with multiplicity. After a careful look at Frobenius reciprocity and transitivity of induction, and the introduction of three types of spherical functions, we develop a theory of Gelfand Tsetlin bases for permutation representations. Then we study several concrete examples on the symmetric groups, generalizing the Gelfand pair of the Johnson scheme; we also consider statistical and probabilistic applications. After that, we consider the composition of two permutation representations, giving a non commutative generalization of the Gelfand pair associated to the ultrametric space; actually, we study the more general notion of crested product. Finally, we consider the exponentiation action, generalizing the decomposition of the Gelfand pair of the Hamming scheme; actually, we study a more general construction that we call wreath product of permutation representations, suggested by the study of finite lamplighter random walks. We give several examples of concrete decompositions of permutation representations and several explicit 'rules' of decomposition.Comment: 69 page

The impact of the changing nature of work and employment on non-profit organisation management in the field of sport in Estonia and the United Kingdom

http://www.ester.ee/record=b5145898*es

Identity and dynamics of the microbial community responsible for carbon monoxide oxidation in marine environments

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2003As colored dissolved organic matter in seawater absorbs UV solar radiation, a variety of simple chemical species are produced, including carbon monoxide (CO). The ocean surface water is saturated with respect to CO, and is thus a source of CO to the atmosphere. CO reacts with and removes free-radical compounds, and may itself contribute to the 'greenhouse' gas content of the atmosphere. An important sink for CO in seawater is the biological oxidation of CO to CO2 by marine microorganisms. The objectives of this study are to identify component members of the microbial community responsible for the oxidation of CO in coastal marine environments through a combination of recent microbiological and molecular approaches, and to estimate their contributions to total in situ CO bio-oxidation. We utilize an enrichment method that involves cultivation of bacteria on membrane filters, subsequent incubation with radiolabeled CO, and the use of autoradiography to screen colonies with the desired phenotype. Cell-specific CO-oxidation activity is determined for selected purified strains with a time-series 14CO-oxidation method. Molecular phylogeny based on 16S-rDNA gene sequence information within the context of the large and growing 168 database determines the phylogenetic relatedness and identity of marine CO-oxidizing bacteria that result from our cultivation program. The CO oxidizing organisms isolated in this study with greatest activity are closely related to the Roseobacter and Paracoccus genera of the alpha-proteobacteria, collectively known as the "marine alpha group". Other microorganisms found to oxidize CO at environmentally relevant rates are members of beta- and gamma-proteobacteria, and one in the Cytophaga-Flavobacterium-Bacteroides group. A collective CO-oxidation activity was calculated from physiological measurements of purified isolates and abundance estimates of CO-oxidizing marine alpha group organisms. Relative proportions of CO-oxidizing Roseobacter and Paracoccus cells were resolved microscopically by microautoradiography in combination with DAPI and fluorescent-labeled oligonucleotide probes (Substrate Tracking AutoRadiography - Fluorescent In Situ Hybridization (STAR-FISH)). Marine alpha group organisms were a major component of total cell numbers (45.7%) at the time of sampling (March 2003), and CO-oxidizing members of the marine alpha group contributed up to 40.7% of total CO oxidation occurring in coastal waters.Financial support was provided by the WHOI Education office and the wonderful people who work there, NSF grant #OCE-0136876, and the Coastal Ocean Institute and Rinehart Coastal Research Center grant #BI10918

Enhanced data Detection for Massive MIMO with 1-Bit ADCs

We present new insightful results on the uplink data detection for massive multiple-input multiple-output systems with 1-bit analog-to-digital converters. The expected values of the soft-estimated symbols (i.e., after the linear combining and prior to the data detection) have been recently characterized for multiple user equipments (UEs) and maximum ratio combining (MRC) receiver at the base station. In this paper, we first provide a numerical evaluation of the expected value of the soft-estimated symbols with zero-forcing (ZF) and minimum mean squared error (MMSE) receivers for a multi-UE setting with correlated Rayleigh fading. Then, we propose a joint data detection (JD) strategy, which exploits the interdependence among the soft-estimated symbols of the interfering UEs, along with its low-complexity variant. These strategies are compared with a naive approach that adapts the maximum-likelihood data detection to the 1-bit quantization. Numerical results show that ZF and MMSE provide considerable gains over MRC in terms of symbol error rate. Moreover, the proposed JD and its low-complexity variant provide a significant boost in comparison with the single-UE data detection.Comment: Presented at the IEEE Asilomar Conference on Signals, Systems, and Computers 2023. arXiv admin note: text overlap with arXiv:2303.1806

Biological CO oxidation in the Sargasso Sea and in Vineyard Sound, Massachusetts

Author Posting. © The Author(s), 2005. This is the author's version of the work. It is posted here by permission of American Society of Limnology and Oceanography for personal use, not for redistribution. The definitive version was published in Limnology and Oceanography 50 (2005): 1205-1212.In situ dissolved carbon monoxide (CO) in oligotrophic waters follows a diel cycle varying from 0.3 to 0.5 nmol L-1 before dawn to 2.5 to 3 nmol L-1 in early afternoon, when photo-production of CO exceeds biological CO oxidation and other sinks. Coastal waters may contain up to 15 nmol L-1 [CO] in the daytime. Assays to measure the rate of CO bio-oxidation typically involve the addition of labeled CO to sealed samples, resulting in CO concentrations that are above ambient levels during incubation (up to 9 nmol L-1 CO). We find that biological oxidation of CO obeys first-order kinetics when incubated with up to 4 nmol L-1 [CO] in coastal water samples and up to between 4 and 10.8 nmol L-1 in oligotrophic waters. At higher [CO], kinetic behavior transitions to zero-order or saturation kinetics. CO–oxidation rate coefficients obtained in dark incubations were not representative of the entire diurnal period, as others have assumed. Biological CO–oxidation rate coefficients kco measured in dark incubations of Sargasso Sea surface water in summer were 0.020 ± 0.002 h-1 (mean ± standard deviation) and an order of magnitude greater than those measured in situ during daylight hours (0.002 ± 0.001 h-1). Dark and in situ rate coefficients in early spring were 0.006 ± 0.004 h-1 and 0.003 ± 0.001 h-1, respectively. In dark incubations of Vineyard Sound water, kco was 0.127 ± 0.038 h-1. The apparent half-saturation constant Kapp for CO ranged from 2.04 to 5.44 nmol L-1 CO in both environments.This research was supported by National Science Foundation grants OCE-98-11208 and OCE-01-36876, and the Reinhard Coastal Research Center and Coastal Ocean Institute grant BI-10918

Discrete Harmonic Analysis. Representations, Number Theory, Expanders and the Fourier Transform

This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science

Trees, wreath products and finite Gelfand pairs

We present a new construction of finite Gelfand pairs by looking at the action of the full automorphism group of a finite spherically homogeneous rooted tree of type r on the variety V(r, s) of all spherically homogeneous subtrees of type s. This generalizes well-known examples as the finite ultrametric space, the Hamming scheme and the Johnson scheme. We also present further generalizations of these classical examples. The first two are based on Harary's notions of composition and exponentiation of group actions. Finally, the generalized Johnson scheme provides the inductive step for the harmonic analysis of our main construction. (C) 2005 Elsevier Inc. All fights reserved