495 research outputs found

    Slepian functions and their use in signal estimation and spectral analysis

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    It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

    Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

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    It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

    HIV Disease Impact on Mothers: What They Miss During Their Children’s Developmental Years

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    Adjusting to chronic illness is very complicated for families with children, as they are already faced with the challenge of development and childrearing. In this study, qualitative interviews were conducted with HIV positive mothers on a number of issues related to being an HIV positive mother raising young children. One topic of the interview was whether or not they felt that HIV had caused them to miss activities with their children while the children were growing up, what types of activities they had missed, the age of the child for each example, and how HIV had led to missing these activities. Interviews were conducted in 2008 with a random sample of 57 mothers being followed in a longitudinal assessment study. All study participants were English or Spanish speaking. Mean age was 44.1 (SD = 5.6) years; 47% were Latina; 35% African American; 11% White; and 7% other race. About 60% of the mothers disclosed that their HIV status had caused them to miss out on activities with their children while their children were growing up, ranging from daily care activities to major school and extra-curricular activities. Some mothers missed significant amounts of time with their children due to hospitalizations. In some cases mothers felt forced into a choice between mothering ability and their own health, including adherence to medications. Implications for the mothers and the children are discussed

    BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory

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    We present a field theoretical proof of the conjectured KLT relation which states that the full tree-level scattering amplitude of gluons can be written as a product of color-ordered amplitude of gluons and color-ordered amplitude of scalars with only cubic vertex. To give a proof we establish the KK relation and BCJ relation of color-ordered scalar amplitude using BCFW recursion relation with nonzero boundary contributions. As a byproduct, an off-shell version of fundamental BCJ relation is proved, which plays an important role in our work.Comment: 26 pages, 9 figure

    Flux balance analysis of primary metabolism in Chlamydomonas reinhardtii

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    Background Photosynthetic organisms convert atmospheric carbon dioxide into numerous metabolites along the pathways to make new biomass. Aquatic photosynthetic organisms, which fix almost half of global inorganic carbon, have great potential: as a carbon dioxide fixation method, for the economical production of chemicals, or as a source for lipids and starch which can then be converted to biofuels. To harness this potential through metabolic engineering and to maximize production, a more thorough understanding of photosynthetic metabolism must first be achieved. A model algal species, C. reinhardtii, was chosen and the metabolic network reconstructed. Intracellular fluxes were then calculated using flux balance analysis (FBA). Results The metabolic network of primary metabolism for a green alga, C. reinhardtii, was reconstructed using genomic and biochemical information. The reconstructed network accounts for the intracellular localization of enzymes to three compartments and includes 484 metabolic reactions and 458 intracellular metabolites. Based on BLAST searches, one newly annotated enzyme (fructose-1,6-bisphosphatase) was added to the Chlamydomonas reinhardtii database. FBA was used to predict metabolic fluxes under three growth conditions, autotrophic, heterotrophic and mixotrophic growth. Biomass yields ranged from 28.9 g per mole C for autotrophic growth to 15 g per mole C for heterotrophic growth. Conclusion The flux balance analysis model of central and intermediary metabolism in C. reinhardtii is the first such model for algae and the first model to include three metabolically active compartments. In addition to providing estimates of intracellular fluxes, metabolic reconstruction and modelling efforts also provide a comprehensive method for annotation of genome databases. As a result of our reconstruction, one new enzyme was annotated in the database and several others were found to be missing; implying new pathways or non-conserved enzymes. The use of FBA to estimate intracellular fluxes also provides flux values that can be used as a starting point for rational engineering of C. reinhardtii. From these initial estimates, it is clear that aerobic heterotrophic growth on acetate has a low yield on carbon, while mixotrophically and autotrophically grown cells are significantly more carbon efficient

    Origins of domestic dog in Southern East Asia is supported by analysis of Y-chromosome DNA

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    Global mitochondrial DNA (mtDNA) data indicates that the dog originates from domestication of wolf in Asia South of Yangtze River (ASY), with minor genetic contributions from dog–wolf hybridisation elsewhere. Archaeological data and autosomal single nucleotide polymorphism data have instead suggested that dogs originate from Europe and/or South West Asia but, because these datasets lack data from ASY, evidence pointing to ASY may have been overlooked. Analyses of additional markers for global datasets, including ASY, are therefore necessary to test if mtDNA phylogeography reflects the actual dog history and not merely stochastic events or selection. Here, we analyse 14 437 bp of Y-chromosome DNA sequence in 151 dogs sampled worldwide. We found 28 haplotypes distributed in five haplogroups. Two haplogroups were universally shared and included three haplotypes carried by 46% of all dogs, but two other haplogroups were primarily restricted to East Asia. Highest genetic diversity and virtually complete phylogenetic coverage was found within ASY. The 151 dogs were estimated to originate from 13–24 wolf founders, but there was no indication of post-domestication dog–wolf hybridisations. Thus, Y-chromosome and mtDNA data give strikingly similar pictures of dog phylogeography, most importantly that roughly 50% of the gene pools are shared universally but only ASY has nearly the full range of genetic diversity, such that the gene pools in all other regions may derive from ASY. This corroborates that ASY was the principal, and possibly sole region of wolf domestication, that a large number of wolves were domesticated, and that subsequent dog–wolf hybridisation contributed modestly to the dog gene pool

    Effect of cellular and extracellular pathology assessed by T1 mapping on regional contractile function in hypertrophic cardiomyopathy

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    Background Regional contractile dysfunction is a frequent finding in hypertrophic cardiomyopathy (HCM). We aimed to investigate the contribution of different tissue characteristics in HCM to regional contractile dysfunction. Methods We prospectively recruited 50 patients with HCM who underwent cardiovascular magnetic resonance (CMR) studies at 3.0 T including cine imaging, T1 mapping and late gadolinium enhancement (LGE) imaging. For each segment of the American Heart Association model segment thickness, native T1, extracellular volume (ECV), presence of LGE and regional strain (by feature tracking and tissue tagging) were assessed. The relationship of segmental function, hypertrophy and tissue characteristics were determined using a mixed effects model, with random intercept for each patient. Results Individually segment thickness, native T1, ECV and the presence of LGE all had significant associations with regional strain. The first multivariable model (segment thickness, LGE and ECV) demonstrated that all strain parameters were associated with segment thickness (P < 0.001 for all) but not ECV. LGE (Beta 2.603, P = 0.024) had a significant association with circumferential strain measured by tissue tagging. In a second multivariable model (segment thickness, LGE and native T1) all strain parameters were associated with both segment thickness (P < 0.001 for all) and native T1 (P < 0.001 for all) but not LGE. Conclusion Impairment of contractile function in HCM is predominantly associated with the degree of hypertrophy and native T1 but not markers of extracellular fibrosis (ECV or LGE). These findings suggest that impairment of contractility in HCM is mediated by mechanisms other than extracellular expansion that include cellular changes in structure and function. The cellular mechanisms leading to increased native T1 and its prognostic significance remain to be established
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