Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

Irrigated lands assessment for water management: Technique test

A procedure for estimating irrigated land using full frame LANDSAT imagery was demonstrated. Relatively inexpensive interpretation of multidate LANDSAT photographic enlargements was used to produce a map of irrigated land in California. The LANDSAT and ground maps were then linked by regression equations to enable precise estimation of irrigated land area by county, basin, and statewide. Land irrigated at least once in California in 1979 was estimated to be 9.86 million acres, with an expected error of less than 1.75% at the 99% level of confidence. To achieve the same level of error with a ground-only sample would have required 3 to 5 times as many ground sample units statewide. A procedure for relatively inexpensive computer classification of LANDSAT digital data to irrigated land categories was also developed. This procedure is based on ratios of MSS band 7 and 5, and gave good results for several counties in the Central Valley

Colonization Density of the Upper Respiratory Tract as a Predictor of Pneumonia-Haemophilus influenzae, Moraxella catarrhalis, Staphylococcus aureus, and Pneumocystis jirovecii.

Background. There is limited information on the association between colonization density of upper respiratory tract colonizers and pathogen-specific pneumonia. We assessed this association for Haemophilus influenzae, Moraxella catarrhalis, Staphylococcus aureus, and Pneumocystis jirovecii. Methods. In 7 low- and middle-income countries, nasopharyngeal/oropharyngeal swabs from children with severe pneumonia and age-frequency matched community controls were tested using quantitative polymerase chain reaction (PCR). Differences in median colonization density were evaluated using the Wilcoxon rank-sum test. Density cutoffs were determined using receiver operating characteristic curves. Cases with a pathogen identified from lung aspirate culture or PCR, pleural fluid culture or PCR, blood culture, and immunofluorescence for P. jirovecii defined microbiologically confirmed cases for the given pathogens. Results. Higher densities of H. influenzae were observed in both microbiologically confirmed cases and chest radiograph (CXR)–positive cases compared to controls. Staphylococcus aureus and P. jirovecii had higher densities in CXR-positive cases vs controls. A 5.9 log10 copies/mL density cutoff for H. influenzae yielded 86% sensitivity and 77% specificity for detecting microbiologically confirmed cases; however, densities overlapped between cases and controls and positive predictive values were poor (\u3c3%). Informative density cutoffs were not found for S. aureus and M. catarrhalis, and a lack of confirmed case data limited the cutoff identification for P. jirovecii. Conclusions. There is evidence for an association between H. influenzaecolonization density and H. influenzae–confirmed pneumonia in children; the association may be particularly informative in epidemiologic studies. Colonization densities of M. catarrhalis, S. aureus, and P. jirovecii are unlikely to be of diagnostic value in clinical settings

Harmonic analysis of iterated function systems with overlap

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.Comment: 37 page

Galaxies with unusually high abundances of molecular hydrogen

A sample of 66 galaxies from the catalog of Bettoni et al. (CISM) with anomalously high molecular-to-atomic hydrogen mass ratios (M_{mol}/M_{HI}>2) is considered. The sample galaxies do not differ systematically from other galaxies in the catalog with the same morphological types, in terms of their photometric parameters, rotational velocities, dust contents, or the total mass of gas in comparison with galaxies of similar linear sizes and disk angular momentum. This suggests that the overabundance of $H_2$ is due to transition of HI to H_2. Galaxies with bars and active nuclei are found more frequently among galaxies which have M_{mol} estimates in CISM. In a small fraction of galaxies, high M_{mol}/M_{HI} ratios are caused by the overestimation of M_{mol} due to a low conversion factor for the translation of CO-line intensities into the number of H_2 molecules along the line of sight. It is argued that the "molecularization" of the bulk of the gas mass could be due 1) to the concentration of gas in the inner regions of the galactic disks, resulting to a high gas pressure and 2) to relatively low star-formation rate per unit mass of molecular gas which indeed takes place in galaxies with high M_{mol}/M_{HI} ratios.Comment: 11 pages,7 figures, published in Astronomy Report

Bayesian Estimation of Pneumonia Etiology: Epidemiologic Considerations and Applications to the Pneumonia Etiology Research for Child Health Study.

In pneumonia, specimens are rarely obtained directly from the infection site, the lung, so the pathogen causing infection is determined indirectly from multiple tests on peripheral clinical specimens, which may have imperfect and uncertain sensitivity and specificity, so inference about the cause is complex. Analytic approaches have included expert review of case-only results, case-control logistic regression, latent class analysis, and attributable fraction, but each has serious limitations and none naturally integrate multiple test results. The Pneumonia Etiology Research for Child Health (PERCH) study required an analytic solution appropriate for a case-control design that could incorporate evidence from multiple specimens from cases and controls and that accounted for measurement error. We describe a Bayesian integrated approach we developed that combined and extended elements of attributable fraction and latent class analyses to meet some of these challenges and illustrate the advantage it confers regarding the challenges identified for other methods

Should Controls With Respiratory Symptoms Be Excluded From Case-Control Studies of Pneumonia Etiology? Reflections From the PERCH Study.

Many pneumonia etiology case-control studies exclude controls with respiratory illness from enrollment or analyses. Herein we argue that selecting controls regardless of respiratory symptoms provides the least biased estimates of pneumonia etiology. We review 3 reasons investigators may choose to exclude controls with respiratory symptoms in light of epidemiologic principles of control selection and present data from the Pneumonia Etiology Research for Child Health (PERCH) study where relevant to assess their validity. We conclude that exclusion of controls with respiratory symptoms will result in biased estimates of etiology. Randomly selected community controls, with or without respiratory symptoms, as long as they do not meet the criteria for case-defining pneumonia, are most representative of the general population from which cases arose and the least subject to selection bias

Gravitational stability and dynamical overheating of stellar disks of galaxies

We use the marginal stability condition for galactic disks and the stellar velocity dispersion data published by different authors to place upper limits on the disk local surface density at two radial scalelengths $R=2h$. Extrapolating these estimates, we constrain the total mass of the disks and compare these estimates to those based on the photometry and color of stellar populations. The comparison reveals that the stellar disks of most of spiral galaxies in our sample cannot be substantially overheated and are therefore unlikely to have experienced a significant merging event in their history. The same conclusion applies to some, but not all of the S0 galaxies we consider. However, a substantial part of the early type galaxies do show the stellar velocity dispersion well in excess of the gravitational stability threshold suggesting a major merger event in the past. We find dynamically overheated disks among both seemingly isolated galaxies and those forming pairs. The ratio of the marginal stability disk mass estimate to the total galaxy mass within four radial scalelengths remains within a range of 0.4---0.8. We see no evidence for a noticeable running of this ratio with either the morphological type or color index.Comment: 25 pages, 5 figures, accepted to Astronomy Letter