Applied problems in frame theory

This thesis is a study of two applied problems in frame theory: phase retrieval and quantum detection. These problems are inspired by engineering applications in signal processing and information theory. ... The goal of the injectivity problem is to classify frames which are injective with respect to self-adjoint Hilbert-Schmidt operators. By associating vectors x [is an element of]H[superscript n] with vectors [median]x in a larger space, we are able to use standard linear algebra and functional analysis techniques to provide characterizations for the injectivity problem in complex and real Hilbert spaces, as well as construct solutions. Given an injective frame, the goal of the state estimation problem is to construct a self-adjoint trace one operator T such that the vector with coordinates is equal to a predetermined measurement vector. We give equivalent conditions for solvability of the state estimation problem and provide best approximate solutions when no exact solution is possible. We also show results about density of both problems.Includes bibliographical reference

Phase retrieval by hyperplanes

We show that a scalable frame does phase retrieval if and only if the hyperplanes of its orthogonal complements do phase retrieval. We then show this result fails in general by giving an example of a frame for $\mathbb R^3$ which does phase retrieval but its induced hyperplanes fail phase retrieval. Moreover, we show that such frames always exist in $\mathbb R^d$ for any dimension $d$. We also give an example of a frame in $\mathbb R^3$ which fails phase retrieval but its perps do phase retrieval. We will also see that a family of hyperplanes doing phase retrieval in $\mathbb R^d$ must contain at least $2d-2$ hyperplanes. Finally, we provide an example of six hyperplanes in $\mathbb R^4$ which do phase retrieval

A Research Agenda for Helminth Diseases of Humans: Basic Research and Enabling Technologies to Support Control and Elimination of Helminthiases

Successful and sustainable intervention against human helminthiases depends on optimal utilisation of available control measures and development of new tools and strategies, as well as an understanding of the evolutionary implications of prolonged intervention on parasite populations and those of their hosts and vectors. This will depend largely on updated knowledge of relevant and fundamental parasite biology. There is a need, therefore, to exploit and apply new knowledge and techniques in order to make significant and novel gains in combating helminthiases and supporting the sustainability of current and successful mass drug administration (MDA) programmes. Among the fields of basic research that are likely to yield improved control tools, the Disease Reference Group on Helminth Infections (DRG4) has identified four broad areas that stand out as central to the development of the next generation of helminth control measures: 1) parasite genetics, genomics, and functional genomics; 2) parasite immunology; 3) (vertebrate) host–parasite interactions and immunopathology; and 4) (invertebrate) host–parasite interactions and transmission biology. The DRG4 was established in 2009 by the Special Programme for Research and Training in Tropical Diseases (TDR). The Group was given the mandate to undertake a comprehensive review of recent advances in helminthiases research in order to identify notable gaps and highlight priority areas. This paper summarises recent advances and discusses challenges in the investigation of the fundamental biology of those helminth parasites under the DRG4 Group's remit according to the identified priorities, and presents a research and development agenda for basic parasite research and enabling technologies that will help support control and elimination efforts against human helminthiases

Characterisation of microbial attack on archaeological bone

As part of an EU funded project to investigate the factors influencing bone preservation in the archaeological record, more than 250 bones from 41 archaeological sites in five countries spanning four climatic regions were studied for diagenetic alteration. Sites were selected to cover a range of environmental conditions and archaeological contexts. Microscopic and physical (mercury intrusion porosimetry) analyses of these bones revealed that the majority (68%) had suffered microbial attack. Furthermore, significant differences were found between animal and human bone in both the state of preservation and the type of microbial attack present. These differences in preservation might result from differences in early taphonomy of the bones. © 2003 Elsevier Science Ltd. All rights reserved

NEOTROPICAL XENARTHRANS: a data set of occurrence of xenarthran species in the Neotropics

Xenarthrans—anteaters, sloths, and armadillos—have essential functions for ecosystem maintenance, such as insect control and nutrient cycling, playing key roles as ecosystem engineers. Because of habitat loss and fragmentation, hunting pressure, and conflicts with domestic dogs, these species have been threatened locally, regionally, or even across their full distribution ranges. The Neotropics harbor 21 species of armadillos, 10 anteaters, and 6 sloths. Our data set includes the families Chlamyphoridae (13), Dasypodidae (7), Myrmecophagidae (3), Bradypodidae (4), and Megalonychidae (2). We have no occurrence data on Dasypus pilosus (Dasypodidae). Regarding Cyclopedidae, until recently, only one species was recognized, but new genetic studies have revealed that the group is represented by seven species. In this data paper, we compiled a total of 42,528 records of 31 species, represented by occurrence and quantitative data, totaling 24,847 unique georeferenced records. The geographic range is from the southern United States, Mexico, and Caribbean countries at the northern portion of the Neotropics, to the austral distribution in Argentina, Paraguay, Chile, and Uruguay. Regarding anteaters, Myrmecophaga tridactyla has the most records (n = 5,941), and Cyclopes sp. have the fewest (n = 240). The armadillo species with the most data is Dasypus novemcinctus (n = 11,588), and the fewest data are recorded for Calyptophractus retusus (n = 33). With regard to sloth species, Bradypus variegatus has the most records (n = 962), and Bradypus pygmaeus has the fewest (n = 12). Our main objective with Neotropical Xenarthrans is to make occurrence and quantitative data available to facilitate more ecological research, particularly if we integrate the xenarthran data with other data sets of Neotropical Series that will become available very soon (i.e., Neotropical Carnivores, Neotropical Invasive Mammals, and Neotropical Hunters and Dogs). Therefore, studies on trophic cascades, hunting pressure, habitat loss, fragmentation effects, species invasion, and climate change effects will be possible with the Neotropical Xenarthrans data set. Please cite this data paper when using its data in publications. We also request that researchers and teachers inform us of how they are using these data