On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Fast, High-Precision Readout Circuit for Detector Arrays

The GEO-CAPE mission described in NASA's Earth Science and Applications Decadal Survey requires high spatial, temporal, and spectral resolution measurements to monitor and characterize the rapidly changing chemistry of the troposphere over North and South Americas. High-frame-rate focal plane arrays (FPAs) with many pixels are needed to enable such measurements. A high-throughput digital detector readout integrated circuit (ROIC) that meets the GEO-CAPE FPA needs has been developed, fabricated, and tested. The ROIC is based on an innovative charge integrating, fast, high-precision analog-to-digital circuit that is built into each pixel. The 128128-pixel ROIC digitizes all 16,384 pixels simultaneously at frame rates up to 16 kHz to provide a completely digital output on a single integrated circuit at an unprecedented rate of 262 million pixels per second. The approach eliminates the need for off focal plane electronics, greatly reducing volume, mass, and power compared to conventional FPA implementations. A focal plane based on this ROIC will require less than 2 W of power on a 11-cm integrated circuit. The ROIC is fabricated of silicon using CMOS technology. It is designed to be indium bump bonded to a variety of detector materials including silicon PIN diodes, indium antimonide (InSb), indium gallium arsenide (In- GaAs), and mercury cadmium telluride (HgCdTe) detector arrays to provide coverage over a broad spectral range in the infrared, visible, and ultraviolet spectral ranges

Assessment of genotype imputation methods

Several methods have been proposed to impute genotypes at untyped markers using observed genotypes and genetic data from a reference panel. We used the Genetic Analysis Workshop 16 rheumatoid arthritis case-control dataset to compare the performance of four of these imputation methods: IMPUTE, MACH, PLINK, and fastPHASE. We compared the methods' imputation error rates and performance of association tests using the imputed data, in the context of imputing completely untyped markers as well as imputing missing genotypes to combine two datasets genotyped at different sets of markers. As expected, all methods performed better for single-nucleotide polymorphisms (SNPs) in high linkage disequilibrium with genotyped SNPs. However, MACH and IMPUTE generated lower imputation error rates than fastPHASE and PLINK. Association tests based on allele "dosage" from MACH and tests based on the posterior probabilities from IMPUTE provided results closest to those based on complete data. However, in both situations, none of the imputation-based tests provide the same level of evidence of association as the complete data at SNPs strongly associated with disease

Risk of Ovarian Cancer and Inherited Variants in Relapse-Associated Genes

Background: We previously identified a panel of genes associated with outcome of ovarian cancer. The purpose of the current study was to assess whether variants in these genes correlated with ovarian cancer risk. Methods and Findings: Women with and without invasive ovarian cancer (749 cases, 1,041 controls) were genotyped at 136 single nucleotide polymorphisms (SNPs) within 13 candidate genes. Risk was estimated for each SNP and for overall variation within each gene. At the gene-level, variation within MSL1 (male-specific lethal-1 homolog) was associated with risk of serous cancer (p = 0.03); haplotypes within PRPF31 (PRP31 pre-mRNA processing factor 31 homolog) were associated with risk of invasive disease (p = 0.03). MSL1 rs7211770 was associated with decreased risk of serous disease (OR 0.81, 95 % CI 0.66–0.98; p = 0.03). SNPs in MFSD7, BTN3A3, ZNF200, PTPRS, and CCND1A were inversely associated with risk (p,0.05), and there was increased risk at HEXIM1 rs1053578 (p = 0.04, OR 1.40, 95 % CI 1.02–1.91). Conclusions: Tumor studies can reveal novel genes worthy of follow-up for cancer susceptibility. Here, we found that inherited markers in the gene encoding MSL1, part of a complex that modifies the histone H4, may decrease risk of invasiv

Low-density star cluster formation: Discovery of a young faint fuzzy on the outskirts of the low-mass spiral galaxy NGC 247

The classical globular clusters found in all galaxy types have half-light radii of rh ~2-4 pc, which have been tied to formation in the dense cores of giant molecular clouds. Some old star clusters have larger sizes, and it is unclear if these represent a fundamentally different mode of low-density star cluster formation. We report the discovery of a rare, young \u27faint fuzzy\u27 star cluster, NGC 247-SC1, on the outskirts of the low-mass spiral galaxy NGC 247 in the nearby Sculptor group, and measure its radial velocity using Keck spectroscopy. We use Hubble Space Telescope imaging to measure the cluster half-light radius of rh ≃ 12 pc and a luminosity of LV ≃ 4 × 105Lθ. We produce a colour-magnitude diagram of cluster stars and compare to theoretical isochrones, finding an age of ≃300 Myr, a metallicity of [Z/H] ~-0.6 and an inferred mass of M∗ ≃ 9 × 104Mθ. The narrow width of blue-loop star magnitudes implies an age spread of ≲50 Myr, while no old red-giant branch stars are found, so SC1 is consistent with hosting a single stellar population, modulo several unexplained bright \u27red straggler\u27 stars. SC1 appears to be surrounded by tidal debris, at the end of an ∼2 kpc long stellar filament that also hosts two low-mass, low-density clusters of a similar age. We explore a link between the formation of these unusual clusters and an external perturbation of their host galaxy, illuminating a possible channel by which some clusters are born with large sizes

Development of the InTelligence And Machine LEarning (TAME) Toolkit for Introductory Data Science, Chemical-Biological Analyses, Predictive Modeling, and Database Mining for Environmental Health Research

Research in environmental health is becoming increasingly reliant upon data science and computational methods that can more efficiently extract information from complex datasets. Data science and computational methods can be leveraged to better identify relationships between exposures to stressors in the environment and human disease outcomes, representing critical information needed to protect and improve global public health. Still, there remains a critical gap surrounding the training of researchers on these in silico methods. We aimed to address this gap by developing the inTelligence And Machine lEarning (TAME) Toolkit, promoting trainee-driven data generation, management, and analysis methods to “TAME” data in environmental health studies. Training modules were developed to provide applications-driven examples of data organization and analysis methods that can be used to address environmental health questions. Target audiences for these modules include students, post-baccalaureate and post-doctorate trainees, and professionals that are interested in expanding their skillset to include recent advances in data analysis methods relevant to environmental health, toxicology, exposure science, epidemiology, and bioinformatics/cheminformatics. Modules were developed by study coauthors using annotated script and were organized into three chapters within a GitHub Bookdown site. The first chapter of modules focuses on introductory data science, which includes the following topics: setting up R/RStudio and coding in the R environment; data organization basics; finding and visualizing data trends; high-dimensional data visualizations; and Findability, Accessibility, Interoperability, and Reusability (FAIR) data management practices. The second chapter of modules incorporates chemical-biological analyses and predictive modeling, spanning the following methods: dose-response modeling; machine learning and predictive modeling; mixtures analyses; -omics analyses; toxicokinetic modeling; and read-across toxicity predictions. The last chapter of modules was organized to provide examples on environmental health database mining and integration, including chemical exposure, health outcome, and environmental justice indicators. Training modules and associated data are publicly available online (https://uncsrp.github.io/Data-Analysis-Training-Modules/). Together, this resource provides unique opportunities to obtain introductory-level training on current data analysis methods applicable to 21st century science and environmental health

Association between type 2 diabetes and changes in myocardial structure, contractile function, energetics, and blood flow before and after aortic valve replacement in patients with severe aortic stenosis

BACKGROUND: Type 2 diabetes (T2D) is associated with an increased risk of left ventricular dysfunction after aortic valve replacement (AVR) in patients with severe aortic stenosis (AS). Persistent impairments in myocardial energetics and myocardial blood flow (MBF) may underpin this observation. Using phosphorus magnetic resonance spectroscopy and cardiovascular magnetic resonance, this study tested the hypothesis that patients with severe AS and T2D (AS-T2D) would have impaired myocardial energetics as reflected by the phosphocreatine to ATP ratio (PCr/ATP) and vasodilator stress MBF compared with patients with AS without T2D (AS-noT2D), and that these differences would persist after AVR. METHODS: Ninety-five patients with severe AS without coronary artery disease awaiting AVR (30 AS-T2D and 65 AS-noT2D) were recruited (mean, 71 years of age [95% CI, 69, 73]; 34 [37%] women). Thirty demographically matched healthy volunteers (HVs) and 30 patients with T2D without AS (T2D controls) were controls. One month before and 6 months after AVR, cardiac PCr/ATP, adenosine stress MBF, global longitudinal strain, NT-proBNP (N-terminal pro-B-type natriuretic peptide), and 6-minute walk distance were assessed in patients with AS. T2D controls underwent identical assessments at baseline and 6-month follow-up. HVs were assessed once and did not undergo 6-minute walk testing. RESULTS: Compared with HVs, patients with AS (AS-T2D and AS-noT2D combined) showed impairment in PCr/ATP (mean [95% CI]; HVs, 2.15 [1.89, 2.34]; AS, 1.66 [1.56, 1.75]; P<0.0001) and vasodilator stress MBF (HVs, 2.11 mL min g [1.89, 2.34]; AS, 1.54 mL min g [1.41, 1.66]; P<0.0001) before AVR. Before AVR, within the AS group, patients with AS-T2D had worse PCr/ATP (AS-noT2D, 1.74 [1.62, 1.86]; AS-T2D, 1.44 [1.32, 1.56]; P=0.002) and vasodilator stress MBF (AS-noT2D, 1.67 mL min g [1.5, 1.84]; AS-T2D, 1.25 mL min g [1.22, 1.38]; P=0.001) compared with patients with AS-noT2D. Before AVR, patients with AS-T2D also had worse PCr/ATP (AS-T2D, 1.44 [1.30, 1.60]; T2D controls, 1.66 [1.56, 1.75]; P=0.04) and vasodilator stress MBF (AS-T2D, 1.25 mL min g [1.10, 1.41]; T2D controls, 1.54 mL min g [1.41, 1.66]; P=0.001) compared with T2D controls at baseline. After AVR, PCr/ATP normalized in patients with AS-noT2D, whereas patients with AS-T2D showed no improvements (AS-noT2D, 2.11 [1.79, 2.43]; AS-T2D, 1.30 [1.07, 1.53]; P=0.0006). Vasodilator stress MBF improved in both AS groups after AVR, but this remained lower in patients with AS-T2D (AS-noT2D, 1.80 mL min g [1.59, 2.0]; AS-T2D, 1.48 mL min g [1.29, 1.66]; P=0.03). There were no longer differences in PCr/ATP (AS-T2D, 1.44 [1.30, 1.60]; T2D controls, 1.51 [1.34, 1.53]; P=0.12) or vasodilator stress MBF (AS-T2D, 1.48 mL min g [1.29, 1.66]; T2D controls, 1.60 mL min g [1.34, 1.86]; P=0.82) between patients with AS-T2D after AVR and T2D controls at follow-up. Whereas global longitudinal strain, 6-minute walk distance, and NT-proBNP all improved after AVR in patients with AS-noT2D, no improvement in these assessments was observed in patients with AS-T2D. CONCLUSIONS: Among patients with severe AS, those with T2D demonstrate persistent abnormalities in myocardial PCr/ATP, vasodilator stress MBF, and cardiac contractile function after AVR; AVR effectively normalizes myocardial PCr/ATP, vasodilator stress MBF, and cardiac contractile function in patients without T2D