A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Knowledge-based IMRT treatment planning for prostate cancer.

PURPOSE: To demonstrate the feasibility of using a knowledge base of prior treatment plans to generate new prostate intensity modulated radiation therapy (IMRT) plans. Each new case would be matched against others in the knowledge base. Once the best match is identified, that clinically approved plan is used to generate the new plan. METHODS: A database of 100 prostate IMRT treatment plans was assembled into an information-theoretic system. An algorithm based on mutual information was implemented to identify similar patient cases by matching 2D beam's eye view projections of contours. Ten randomly selected query cases were each matched with the most similar case from the database of prior clinically approved plans. Treatment parameters from the matched case were used to develop new treatment plans. A comparison of the differences in the dose-volume histograms between the new and the original treatment plans were analyzed. RESULTS: On average, the new knowledge-based plan is capable of achieving very comparable planning target volume coverage as the original plan, to within 2% as evaluated for D98, D95, and D1. Similarly, the dose to the rectum and dose to the bladder are also comparable to the original plan. For the rectum, the mean and standard deviation of the dose percentage differences for D20, D30, and D50 are 1.8% +/- 8.5%, -2.5% +/- 13.9%, and -13.9% +/- 23.6%, respectively. For the bladder, the mean and standard deviation of the dose percentage differences for D20, D30, and D50 are -5.9% +/- 10.8%, -12.2% +/- 14.6%, and -24.9% +/- 21.2%, respectively. A negative percentage difference indicates that the new plan has greater dose sparing as compared to the original plan. CONCLUSIONS: The authors demonstrate a knowledge-based approach of using prior clinically approved treatment plans to generate clinically acceptable treatment plans of high quality. This semiautomated approach has the potential to improve the efficiency of the treatment planning process while ensuring that high quality plans are developed.

Newly resolved relationships in an early land plant lineage: Bryophyta class Sphagnopsida (peat mosses).

UNLABELLED: PREMISE OF THE STUDY: The Sphagnopsida, an early-diverging lineage of mosses (phylum Bryophyta), are morphologically and ecologically unique and have profound impacts on global climate. The Sphagnopsida are currently classified in two genera, Sphagnum (peat mosses) with some 350-500 species and Ambuchanania with one species. An analysis of phylogenetic relationships among species and genera in the Sphagnopsida were conducted to resolve major lineages and relationships among species within the Sphagnopsida. • METHODS: Phylogenetic analyses of nucleotide sequences from the nuclear, plastid, and mitochondrial genomes (11 704 nucleotides total) were conducted and analyzed using maximum likelihood and Bayesian inference employing seven different substitution models of varying complexity. • KEY RESULTS: Phylogenetic analyses resolved three lineages within the Sphagnopsida: (1) Sphagnum sericeum, (2) S. inretortum plus Ambuchanania leucobryoides, and (3) all remaining species of Sphagnum. Sister group relationships among these three clades could not be resolved, but the phylogenetic results indicate that the highly divergent morphology of A. leucobryoides is derived within the Sphagnopsida rather than plesiomorphic. A new classification is proposed for class Sphagnopsida, with one order (Sphagnales), three families, and four genera. • CONCLUSIONS: The Sphagnopsida are an old lineage within the phylum Bryophyta, but the extant species of Sphagnum represent a relatively recent radiation. It is likely that additional species critical to understanding the evolution of peat mosses await discovery, especially in the southern hemisphere.

Atmospheric neutrino oscillation analysis with subleading effects in Super-Kamiokande I, II, and III

We present a search for nonzero θ13 and deviations of sin2θ23 from 0.5 in the oscillations of atmospheric neutrino data from Super-Kamiokande I, II, and III. No distortions of the neutrino flux consistent with nonzero θ13 are found and both neutrino mass hierarchy hypotheses are in agreement with the data. The data are best fit at Δm2=2.1×10-3eV2, sin2θ13=0.0, and sin2θ23=0.5. In the normal (inverted) hierarchy θ13 and Δm2 are constrained at the one-dimensional 90% C.L. to sin2θ13<0.04(0.09) and 1.9(1.7)×10 -3<Δm2<2.6(2.7)×10-3eV2. The atmospheric mixing angle is within 0.407≤sin2θ23≤0.583 at 90% C.L. © 2010 The American Physical Society.

Homeostatic imbalance of purine catabolism in first-episode neuroleptic-naïve patients with schizophrenia.

BACKGROUND: Purine catabolism may be an unappreciated, but important component of the homeostatic response of mitochondria to oxidant stress. Accumulating evidence suggests a pivotal role of oxidative stress in schizophrenia pathology. METHODOLOGY/PRINCIPAL FINDINGS: Using high-pressure liquid chromatography coupled with a coulometric multi-electrode array system, we compared 6 purine metabolites simultaneously in plasma between first-episode neuroleptic-naïve patients with schizophrenia (FENNS, n = 25) and healthy controls (HC, n = 30), as well as between FENNS at baseline (BL) and 4 weeks (4w) after antipsychotic treatment. Significantly higher levels of xanthosine (Xant) and lower levels of guanine (G) were seen in both patient groups compared to HC subjects. Moreover, the ratios of G/guanosine (Gr), uric acid (UA)/Gr, and UA/Xant were significantly lower, whereas the ratio of Xant/G was significantly higher in FENNS-BL than in HC. Such changes remained in FENNS-4w with exception that the ratio of UA/Gr was normalized. All 3 groups had significant correlations between G and UA, and Xan and hypoxanthine (Hx). By contrast, correlations of UA with each of Xan and Hx, and the correlation of Xan with Gr were all quite significant for the HC but not for the FENNS. Finally, correlations of Gr with each of UA and G were significant for both HC and FENNS-BL but not for the FENNS-4w. CONCLUSIONS/SIGNIFICANCE: During purine catabolism, both conversions of Gr to G and of Xant to Xan are reversible. Decreased ratios of product to precursor suggested a shift favorable to Xant production from Xan, resulting in decreased UA levels in the FENNS. Specifically, the reduced UA/Gr ratio was nearly normalized after 4 weeks of antipsychotic treatment. In addition, there are tightly correlated precursor and product relationships within purine pathways; although some of these correlations persist across disease or medication status, others appear to be lost among FENNS. Taken together, these results suggest that the potential for steady formation of antioxidant UA from purine catabolism is altered early in the course of illness.

Valuing drinking water provision as an ecosystem service in the neuse river basin

The valuation of ecosystem services such as drinking water provision is of growing national and international interest. The cost of drinking water provision is directly linked to the quality of its raw water input, which is itself affected by upstream land use patterns. This analysis employs the benefit transfer method to quantify the economic benefits of water quality improvements for drinking water production in the Neuse River Basin in North Carolina. Two benefit transfer approaches, value transfer and function transfer, are implemented by combining the results of four previously published studies with data collected from eight Neuse Basin water treatment plants. The mean net present value of the cost reduction estimates for the entire Neuse Basin ranged from $2.7 million to $16.6 million for a 30% improvement in water quality over a 30-year period. The value-transfer approach tended to produce larger expected benefits than the function-transfer approach, but both approaches produced similar results despite the differences in their methodologies, time frames, study sites, and assumptions. © 2010 ASCE.

Hybrid error correction and de novo assembly of single-molecule sequencing reads.

Single-molecule sequencing instruments can generate multikilobase sequences with the potential to greatly improve genome and transcriptome assembly. However, the error rates of single-molecule reads are high, which has limited their use thus far to resequencing bacteria. To address this limitation, we introduce a correction algorithm and assembly strategy that uses short, high-fidelity sequences to correct the error in single-molecule sequences. We demonstrate the utility of this approach on reads generated by a PacBio RS instrument from phage, prokaryotic and eukaryotic whole genomes, including the previously unsequenced genome of the parrot Melopsittacus undulatus, as well as for RNA-Seq reads of the corn (Zea mays) transcriptome. Our long-read correction achieves >99.9% base-call accuracy, leading to substantially better assemblies than current sequencing strategies: in the best example, the median contig size was quintupled relative to high-coverage, second-generation assemblies. Greater gains are predicted if read lengths continue to increase, including the prospect of single-contig bacterial chromosome assembly.