Wavelet methods for inverting the Radon transform with noisy data

Because the Radon transform is a smoothing transform, any noise in the Radon data becomes magnified when the inverse Radon transform is applied. Among the methods used to deal with this problem is the wavelet-vaguelette decomposition (WVD) coupled with wavelet shrinkage, as introduced by Donoho (1995). We extend several results of Donoho and others here. First, we introduce a new sufficient condition on wavelets to generate a WVD. For a general homogeneous operator, whose class includes the Radon transform, we show that a variant of Donoho's method for solving inverse problems can be derived as the exact minimizer of a variational problem that uses a Besov norm as the smoothing functional. We give a new proof of the rate of convergence of wavelet shrinkage that allows us to estimate rather sharply the best shrinkage parameter needed to recover an image from noise-corrupted data. We conduct tomographic reconstruction computations that support the hypothesis that near-optimal shrinkage parameters can be derived if one can estimate only two Besov-space parameters about an image f. Both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than Kolaczyk's (1996) variant of Donoho's method and the classical filtered backprojection method.     

Induction of mortality and malformation in Xenopus laevis embryos by water sources associated with field frog deformities

Water samples from several ponds in Minnesota were evaluated for their capacity to induce malformations in embryos of Xenopus laevis. The FETAX assay was used to assess the occurrence of malformations following a 96-hr period of exposure to water samples. These studies were conducted following reports of high incidences of malformation in natural populations of frogs in Minnesota wetlands. The purpose of these studies was to determine if a biologically active agent(s) was present in the waters and could be detected using the FETAX assay. Water samples from ponds with high incidences of frog malformations (affected sites), along with water samples from ponds with unaffected frog populations (reference sites), were studied. Initial experiments clearly showed that water from affected sites induced mortality and malformation in Xenopus embryos, while water from reference sites had little or no effect. Induction of malformation was dose dependent and highly reproducible, both with stored samples and with samples taken at different times throughout the summer. The biological activity of the samples was reduced or eliminated when samples were passed through activated carbon. Limited evidence from these samples indicates that the causal factor(s) is not an infectious organism nor are ion concentrations or metals responsible for the effects observed. Results do indicate that the water matrix has a significant effect on the severity of toxicity. Based on the FETAX results and the occurrence of frog malformations observed in the field, these studies suggest that water in the affected sites contains one or more unknown agents that induce developmental abnormalities in Xenopus. These same factors may contribute to the increased incidence of malformation in native species.     

The Lowry test: A simple status-free measure of intellectual ability.

The validity of an intelligence test is discussed. "The Lowry Reasoning Test Combination has been found to be relatively free of social status bias and to measure intellectual function. It is easily administered and simply scored and does not depend upon a high level of verbal ability. Variance in concept difficulty is obtained by altering combinations of constructs while keeping the verbal material on a uniformly simple level. Whereever such a discriminative and effective selection device is needed the present writers would recommend that the Lowry test be tried." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Receptor mechanisms and dose-response models for the effects of dioxins

There is increasing evidence that receptor-mediated events impact one or more stages responsible for tumor development in experimental animals and humans. Although many chemicals and endogenous hormones require receptor interactions as a necessary event in their carcinogenic activity, 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and its structural analogs are the most visible examples of receptor-mediated carcinogens. TCDD, or dioxin as it is frequently called, interacts with the Ah receptor (AhR), which functions in a manner analogous to receptors for steroids. TCDD produces a wide spectrum of biochemical and toxic responses in in vitro and in vivo systems, and the Ah receptor is generally considered necessary for most if not all of these responses. Risk assessments for dioxin made by the United States and other countries throughout the world have been based on its carcinogenecity in experimental animals. Recently, epidemiology studies have indicated that TCDD is a human carcinogen at high doses. Because TCDD appears to be acting like a potent and persistent hormone agonist, it appears reasonable to incorporate mechanistic information on receptor-mediated events in risk assessments for TCDD. This information may be obtained from steroid receptor action and from molecular data on the Ah receptor. In this paper, we evaluate the scientific foundation on which mechanistic models for estimating dioxin's risks should be based. These models need to recognize the mechanisms possible for the diversity of biological responses that are initiated by a single receptor interacting with a single ligand. The U.S. EPA is currently reevaluating dioxin's risks by examining the possibility of developing biologically based models.(ABSTRACT TRUNCATED AT 250 WORDS)     

Average-case analysis of QuickSort and Binary Insertion Tree height using incompressibility

We study the Kolmogorov complexity of a Binary Insertion Tree, and present a succinct encoding scheme for Binary Insertion Trees produced from incompressible permutations. Based on the encoding scheme, we obtain a simple incompressibility argument that yields an asymptotic analysis of the average height of a Binary Insertion Tree. This argument further implies that the QuickSort algorithm sorts a permutation of n elements in Θ(nlgn) comparisons on average.     

Multiple sites of V lambda diversification in cattle

Ig repertoire diversification in cattle was studied in the ileal Peyer's patch (IPP) follicles of young calves and in the spleens of late first-trimester bovine fetuses. To investigate follicular diversification, individual IPP follicles were isolated by microdissection; VA diversity was examined by RT-PCR and subsequent cloning and sequencing. When 52 intrafollicular sequences from a 4-wk-old calf were determined and compared, two major groups, one of 23 members and the other of 25, could be delineated. An examination of these groups revealed clear genealogic relationships that implicated in situ diversification of V lambda sequences within the confines of an IPP follicle. V lambda expression was also examined in early (95 and 110 gestational day) fetal bovine spleens. Although earlier studies in cattle and sheep implicated the IPP as a likely site of Ab diversification, a close investigation of V lambda sequences in late first-trimester fetal calves revealed that diversity appears in the early fetal spleen before the establishment of a diverse repertoire in the ileum. When the sequences for the fetal spleen were compared with an existing pool of germline sequences, we found evidence of possible gene conversion events and possible untemplated point mutations occurring in sequences recovered from fetal spleens. We conclude that IPP is not the sole site of VA diversification in cattle. Also, as suggested for rabbits, cattle may use both gene conversion and untemplated somatic point mutation to diversify their primary VA repertoire.     

Effect of wavelet bases on compressing digital mammograms

The purposes of this paper are four-fold: (a) develop a variety of wavelet methods, including standard, hyperbolic, and adaptive wavelet bases, for the compression of high-resolution digital mammograms, (b) apply different levels of compression to the images and determine the dependence of the information loss on the compression ratio, (c) determine qualitatively the types of artifacts and errors introduced to the compressed reconstructed images by the various wavelets and make a relative comparison, and (d) discriminate among the various wavelet bases and select those worthy of further analysis and study