We develop a new algorithm to compute the eigenvalues and eigenfunctions of the gravitational Schrödinger equation. The nonlinear two-point boundary problem is solved by an inner–outer iteration and the resulting method is fast, readily parallelizable, and, unlike shooting methods, is able to compute eigenfunctions with a very large number (>50) of nodes. The theory and implementation of the method are discussed and it is applied to compute the s-wave spectrum of a gravitational Bose–Einstein condensate.
<p>Supplementary Methods, Table S1, Figures S1-7. Methods for quantitative multiplex proteomics imaging (QMPI) Clinical studies: Statistical plan Table S1. Clinical Validation Study. Comparison of Predictive Value of the 8-Biomarker Assay for Favorable Pathology with D'Amico Risk Categories. Figure S1. Outline of all four quantitative multiplex immunofluorescence triplex assay formats Figure S2. Clinical validation study, full cohort (N=276): performance for "GS 6" pathology (surgical Gleason =3+3 and localized {less than or equal to}T3a). A) Sensitivity (P[risk score> threshold| "non-GS 6" pathology]) of the assay, as a function of medical decision level. Figure S3. Clinical validation study, full cohort (N=274): performance for prediction of favorable pathology (surgical Gleason {less than or equal to}3+4 and organ-confined {less than or equal to}T2). Figure S4. Clinical validation study, Subset of validation cohort that contained sufficient annotation for National Comprehensive Cancer Network (NCCN) and D'Amico categorization (N=256) Figure S5. Clinical validation study: performance for prediction of favorable pathology. Figure S6. Net Reclassification Index analysis illustrates how biomarker assay categories of favorable (risk score {less than or equal to}0·33) and non-favorable (risk score >0·8) may supplement NCCN Figure S7. Decision Curve Analysis provides another method for characterizing performance of different risk systems and at different cut points.</p>
Genetic testing for disease risk is an increasingly important component of medical care. However, testing can be expensive, which can lead to patients and physicians having limited access to the genetic information needed for medical decisions. To simplify DNA sample preparation and lower costs, we have developed a system in which any gene can be captured and sequenced directly from human genomic DNA without amplification, using no proteins or enzymes prior to sequencing. Extracted whole-genome DNA is acoustically sheared and loaded in a flow cell channel for single-molecule sequencing. Gene isolation, amplification, or ligation is not necessary. Accurate and low-cost detection of DNA sequence variants is demonstrated for the BRCA1 gene. Disease-causing mutations as well as common variants from well-characterized samples are identified. Single-molecule sequencing generates very reproducible coverage patterns, and these can be used to detect any size insertion or deletion directly, unlike PCR-based methods, which require additional assays. Because no gene isolation or amplification is required for sequencing, the exceptionally low costs of sample preparation and analysis could make genetic tests more accessible to those who wish to know their own disease susceptibility. Additionally, this approach has applications for sequencing integration sites for gene therapy vectors, transposons, retroviruses, and other mobile DNA elements in a more facile manner than possible with other methods.
In part I (Guven et al 2007 Inverse Problems 23 1115–33), we analysed the error in the reconstructed optical absorption images resulting from the discretization of the forward and inverse problems. Our analysis led to two new error estimates, which present the relationship between the optical absorption imaging accuracy and the discretization error in the solutions of the forward and inverse problems. In this work, based on the analysis presented in part I, we develop new adaptive discretization schemes for the forward and inverse problems in order to reduce the error in the reconstructed images resulting from discretization. The proposed discretization schemes lead to adaptively refined composite meshes that yield the desired level of imaging accuracy while reducing the size of the discretized forward and inverse problems. We present numerical experiments to validate the error estimates developed in part I and show the improvement in the accuracy of the reconstructed optical images with the new adaptive mesh generation algorithms.
In diffuse optical tomography (DOT), the discretization error in the numerical solutions of the forward and inverse problems results in error in the reconstructed optical images. In this work, based on the analysis presented by Guven, M et al., we present two theorems that constitute the basis for adaptive mesh generation for the forward and inverse DOT problems. The proposed discretization schemes lead to adaptively refined composite meshes that yield the desired level of imaging accuracy while reducing the size of the discretized forward and inverse problems. Our numerical experiments validate the error estimates developed by Guven, M et al. and show that the new adaptive mesh generation algorithms improve the accuracy of the reconstructed optical images
Key challenges of biopsy-based determination of prostate cancer aggressiveness include tumour heterogeneity, biopsy-sampling error, and variations in biopsy interpretation. The resulting uncertainty in risk assessment leads to significant overtreatment, with associated costs and morbidity. We developed a performance-based strategy to identify protein biomarkers predictive of prostate cancer aggressiveness and lethality regardless of biopsy-sampling variation. Prostatectomy samples from a large patient cohort with long follow-up were blindly assessed by expert pathologists who identified the tissue regions with the highest and lowest Gleason grade from each patient. To simulate biopsy-sampling error, a core from a high- and a low-Gleason area from each patient sample was used to generate a 'high' and a 'low' tumour microarray, respectively. Using a quantitative proteomics approach, we identified from 160 candidates 12 biomarkers that predicted prostate cancer aggressiveness (surgical Gleason and TNM stage) and lethal outcome robustly in both high- and low-Gleason areas. Conversely, a previously reported lethal outcome-predictive marker signature for prostatectomy tissue was unable to perform under circumstances of maximal sampling error. Our results have important implications for cancer biomarker discovery in general and development of a sampling error-resistant clinical biopsy test for prediction of prostate cancer aggressiveness.
