Recovering piecewise smooth functions from nonuniform Fourier measurements

In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the reconstruction space and the bandwidth of the nonuniform samples, and show that it is linear for splines and piecewise polynomials of fixed degree, and quadratic for piecewise polynomials of varying degree

The circulatory effects produced in a patient with pneumopericardium by artificially varying the intrapericardial pressure

1. 1. Observations on changes in pulse rate, respiratory rate, arterial pressure, venous pressure, and circulation time were made with artificially produced changes in intrapericardial pressure in a patient with pneumopericardium. These relationships have been illustrated graphically.2. 2. The intrapericardial pressure fluctuated with respiration, and, as higher pressures were reached, these fluctuations decreased.3. 3. The intrapericardial pressure fluctuated with systole and diastole. Kymographic tracings were made of the fluctuations in intrapericardial pressure caused by respiration and the heartbeat. With the higher intrapericardial pressures, the changes in pressure produced by systole and diastole were less marked.4. 4. Significant changes in pulse rate, arterial pressure, venous pressure, and circulation time did not occur until the intrapericardial pressure was elevated to, or above, 145 mm. of water.5. 5. In order to maintain the circulation, it was necessary that venous pressure exceed intrapericardial pressure by at least 35 to 40 mm. of water.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32599/1/0000739.pd

Decision and function problems based on boson sampling

Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and the possible usefulness of boson-sampling devices is mainly limited to the proof of quantum supremacy. The purpose of this work is to investigate whether boson sampling can be used as a resource of decision and function problems that are computationally hard, and may thus have cryptographic applications. After the definition of a rather general theoretical framework for the design of such problems, we discuss their solution by means of a brute-force numerical approach, as well as by means of non-boson samplers. Moreover, we estimate the sample sizes required for their solution by passive linear interferometers, and it is shown that they are independent of the size of the Hilbert space.Comment: Close to the version published in PR

A transcriptome-driven analysis of epithelial brushings and bronchial biopsies to define asthma phenotypes in U-BIOPRED

RATIONALE AND OBJECTIVES: Asthma is a heterogeneous disease driven by diverse immunologic and inflammatory mechanisms. We used transcriptomic profiling of airway tissues to help define asthma phenotypes. METHODS: The transcriptome from bronchial biopsies and epithelial brushings of 107 moderate-to-severe asthmatics were annotated by gene-set variation analysis (GSVA) using 42 gene-signatures relevant to asthma, inflammation and immune function. Topological data analysis (TDA) of clinical and histological data was used to derive clusters and the nearest shrunken centroid algorithm used for signature refinement. RESULTS: 9 GSVA signatures expressed in bronchial biopsies and airway epithelial brushings distinguished two distinct asthma subtypes associated with high expression of T-helper type 2 (Th-2) cytokines and lack of corticosteroid response (Group 1 and Group 3). Group 1 had the highest submucosal eosinophils, high exhaled nitric oxide (FeNO) levels, exacerbation rates and oral corticosteroid (OCS) use whilst Group 3 patients showed the highest levels of sputum eosinophils and had a high BMI. In contrast, Group 2 and Group 4 patients had an 86% and 64% probability of having non-eosinophilic inflammation. Using machine-learning tools, we describe an inference scheme using the currently-available inflammatory biomarkers sputum eosinophilia and exhaled nitric oxide levels along with OCS use that could predict the subtypes of gene expression within bronchial biopsies and epithelial cells with good sensitivity and specificity. CONCLUSION: This analysis demonstrates the usefulness of a transcriptomic-driven approach to phenotyping that segments patients who may benefit the most from specific agents that target Th2-mediated inflammation and/or corticosteroid insensitivity

DNA methylation testing with S5 for triage of high-risk HPV positive women

Methylation of host and viral genes is promising for triage of women with high‐risk human papillomavirus infections (hrHPV). Using a population‐based sample of hrHPV positive women with cervical biopsies within 12 months after cervical screening, the clinical value of the S5 methylation classifier (S5), HPV genotyping and cytology were compared as potential triage tests, for outcomes of cervical intraepithelial neoplasia (CIN) grade 3 or greater (CIN3+), CIN2+ and CIN2, and the area under the curve (AUC) calculated. S5 scores increased with histopathology severity (P (trend) < .001). For CIN3+, the AUC was 0.780 suggesting S5 provides good discrimination between <CIN3 and CIN3+. AUCs were significant for all pairwise comparisons of <CIN2, CIN2 and CIN3+ (P < .001). The positive predictive value (PPV) of HPV16/18 genotyping for women with any abnormal cytology was greater than S5 (25.36% vs 20.87%, P = .005) for CIN3+, while sensitivity was substantially greater for S5 (83.33% vs 59.28%, P < .001). Restricting to women with abnormal cytology, but excluding those with high‐grade cytology, both S5 and HPV16/18 provided CIN3+ PPVs high enough to recommend colposcopy. Triage with S5 also appeared useful for hrHPV positive women negative for HPV16/18 (CIN3+ PPV: 7.33%, sensitivity: 57.52%). S5 provided increased sensitivity for CIN3+ compared to HPV16/18 genotyping for hrHPV positive women, overall and when restricted to women with abnormal cytology, suggesting S5 may improve colposcopy referral. S5 also has the ability to distinguish between <CIN2, CIN2 and CIN3+, a finding of importance for managing CIN2, given the complexity and uncertainty associated with this diagnosis

Debye temperature of disordered bcc-Fe-Cr alloys

Debye temperature, TD, of Fe100-xCrx disordered alloys with 0<x<99.9 was determined from the temperature dependence of the centre shift of 57Fe Mossbauer spectra recorded in the temperature range of 80-300K. Its compositional dependence shows an interesting non-monotonous behaviour. For 0<x<~45 as well as for ~75<x<~95 the Debye temperature is enhanced relative to its value of a metallic iron, and at x=~3 there is a local maximum having a relative height of ~12% compared to a pure iron. For ~45~95 the Debye temperature is smaller than the one for the metallic iron, with a local minimum at x=~55 at which the relative decrease of TD amounts to ~12%. The first maximum coincides quite well with that found for the spin-waves stiffness coefficient, D0, while the pretty steep decrease observed for x>~95 which is indicative of a decoupling of the probe Fe atoms from the underlying chromium matrix is likely related to the spin-density waves which constitute the magnetic structure of chromium in that interval of composition. The harmonic force constant calculated from the Debye temperature of the least Fe-concentrated alloy (x>99.9) amounts to only 23% of the one characteristic of a pure chromium.Comment: 15 pages, 7 figures, 26 reference

X-ray Amorphous and Poorly Crystalline Fe-Containing Phases in Terrestrial Field Environments and Implications for Materials Detected on Mars

Recent analyses of X-ray diffraction (XRD) data from the CheMin instrument using the FULLPAT program have documented the presence of X-ray amorphous materials at multiple sites within Gale Crater, Mars. These materials are believed to be to be iron-rich based on chemical data, and at least some of them are believed to be weathering products based on volatile contents. However, the characteristics of these proposed Fe-rich weathering products remain poorly understood. To better understand these X-ray amorphous materials on Mars, we are 1) examining weathering products formed on Fe-rich parent material in terrestrial soils across a range of climatic conditions, and 2) performing burial experiments of Fe- and Mg- rich olivine in these soils. We describe each of these approaches below

A genome-wide association study implicates the pleiotropic effect of NMUR2 on asthma and COPD

Asthma and chronic obstructive pulmonary disease (COPD) are two distinct diseases that are associated with chronic inflammation. They share common features in terms of their advanced stages and genetic factors. This study aimed to identify novel genes underlying both asthma and COPD using genome-wide association study (GWAS) to differentiate between the two diseases. We performed a GWAS of asthma and COPD in 7828 Koreans from three hospitals. In addition, we investigated genetic correlations. The UK Biobank dataset was used for the replication studies. We found that rs2961757, located near neuromedin U receptor 2 (NMUR2) on chromosome 5, was genome-wide significant ([Formula: see text] = 0.44, P-valueAsthma-COPD = 3.41 × 10-8), and significant results were replicated with the UK Biobank data ([Formula: see text] = 0.04, P-valueAsthma-COPD = 0.0431). A positive genetic correlation was observed between asthma and COPD (39.8% in the Korean dataset and 49.8% in the UK Biobank dataset). In this study, 40-45% of the genetic effects were common to asthma and COPD. Moreover, NMUR2 increases the risk of asthma development and suppresses COPD development. This indicates that NMUR2 allows for better differentiation of both diseases, which can facilitate tailored medical therapy

The persistence landscape and some of its properties

Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine learning. Furthermore, the mapping from persistence diagrams to persistence landscapes is stable and invertible. We introduce a weighted version of the persistence landscape and define a one-parameter family of Poisson-weighted persistence landscape kernels that may be useful for learning. We also demonstrate some additional properties of the persistence landscape. First, the persistence landscape may be viewed as a tropical rational function. Second, in many cases it is possible to exactly reconstruct all of the component persistence diagrams from an average persistence landscape. It follows that the persistence landscape kernel is characteristic for certain generic empirical measures. Finally, the persistence landscape distance may be arbitrarily small compared to the interleaving distance.Comment: 18 pages, to appear in the Proceedings of the 2018 Abel Symposiu