Projection Robust Wasserstein Distance and Riemannian Optimization

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in particular when comparing probability measures in high-dimensions. However, it is ruled out for practical application because the optimization model is essentially non-convex and non-smooth which makes the computation intractable. Our contribution in this paper is to revisit the original motivation behind WPP/PRW, but take the hard route of showing that, despite its non-convexity and lack of nonsmoothness, and even despite some hardness results proved by~\citet{Niles-2019-Estimation} in a minimax sense, the original formulation for PRW/WPP \textit{can} be efficiently computed in practice using Riemannian optimization, yielding in relevant cases better behavior than its convex relaxation. More specifically, we provide three simple algorithms with solid theoretical guarantee on their complexity bound (one in the appendix), and demonstrate their effectiveness and efficiency by conducing extensive experiments on synthetic and real data. This paper provides a first step into a computational theory of the PRW distance and provides the links between optimal transport and Riemannian optimization.Comment: Accepted by NeurIPS 2020; The first two authors contributed equally; fix the confusing parts in the proof and refine the algorithms and complexity bound

Metabolic Signatures of Lung Cancer in Biofluids: NMR-Based Metabonomics of Blood Plasma

In this work, the variations in the metabolic profile of blood plasma from lung cancer patients and healthy controls were investigated through NMR-based metabonomics, to assess the potential of this approach for lung cancer screening and diagnosis. PLS-DA modeling of CPMG spectra from plasma, subjected to Monte Carlo Cross Validation, allowed cancer patients to be discriminated from controls with sensitivity and specificity levels of about 90%. Relatively lower HDL and higher VLDL + LDL in the patients' plasma, together with increased lactate and pyruvate and decreased levels of glucose, citrate, formate, acetate, several amino acids (alanine, glutamine, histidine, tyrosine, valine), and methanol, could be detected. These changes were found to be present at initial disease stages and could be related to known cancer biochemical hallmarks, such as enhanced glycolysis, glutaminolysis, and gluconeogenesis, together with suppressed Krebs cycle and reduced lipid catabolism, thus supporting the hypothesis of a systemic metabolic signature for lung cancer. Despite the possible confounding influence of age, smoking habits, and other uncontrolled factors, these results indicate that NMR-based metabonomics of blood plasma can be useful as a screening tool to identify suspicious cases for subsequent, more specific radiological tests, thus contributing to improved disease management.ERDF - Competitive Factors Thematic Operational ProgrammeFCT/PTDC/ QUI/68017/2006FCOMP-01-0124-FEDER-007439SFRH/BD/ 63430/2009National UNESCO Committee - L'Oréal Medals of Honor for Women in Science 200Portuguese National NMR Network - RNRM

Galaxy Zoo: the dependence of morphology and colour on environment

We analyse the relationships between galaxy morphology, colour, environment and stellar mass using data for over 100,000 objects from Galaxy Zoo, the largest sample of visually classified morphologies yet compiled. We conclusively show that colour and morphology fractions are very different functions of environment. Both are sensitive to stellar mass; however, at fixed stellar mass, while colour is also highly sensitive to environment, morphology displays much weaker environmental trends. Only a small part of both relations can be attributed to variation in the stellar mass function with environment. Galaxies with high stellar masses are mostly red, in all environments and irrespective of their morphology. Low stellar-mass galaxies are mostly blue in low-density environments, but mostly red in high-density environments, again irrespective of their morphology. The colour-density relation is primarily driven by variations in colour fractions at fixed morphology, in particular the fraction of spiral galaxies that have red colours, and especially at low stellar masses. We demonstrate that our red spirals primarily include galaxies with true spiral morphology. We clearly show there is an environmental dependence for colour beyond that for morphology. Before using the Galaxy Zoo morphologies to produce the above results, we first quantify a luminosity-, size- and redshift-dependent classification bias that affects this dataset, and probably most other studies of galaxy population morphology. A correction for this bias is derived and applied to produce a sample of galaxies with reliable morphological type likelihoods, on which we base our analysis.Comment: 25 pages, 20 figures (+ 6 pages, 11 figures in appendices); moderately revised following referee's comments; accepted by MNRA

Global variations and time trends in the prevalence of childhood myopia, a systematic review and quantitative meta-analysis: implications for aetiology and early prevention.

The aim of this review was to quantify the global variation in childhood myopia prevalence over time taking account of demographic and study design factors. A systematic review identified population-based surveys with estimates of childhood myopia prevalence published by February 2015. Multilevel binomial logistic regression of log odds of myopia was used to examine the association with age, gender, urban versus rural setting and survey year, among populations of different ethnic origins, adjusting for study design factors. 143 published articles (42 countries, 374 349 subjects aged 1-18 years, 74 847 myopia cases) were included. Increase in myopia prevalence with age varied by ethnicity. East Asians showed the highest prevalence, reaching 69% (95% credible intervals (CrI) 61% to 77%) at 15 years of age (86% among Singaporean-Chinese). Blacks in Africa had the lowest prevalence; 5.5% at 15 years (95% CrI 3% to 9%). Time trends in myopia prevalence over the last decade were small in whites, increased by 23% in East Asians, with a weaker increase among South Asians. Children from urban environments have 2.6 times the odds of myopia compared with those from rural environments. In whites and East Asians sex differences emerge at about 9 years of age; by late adolescence girls are twice as likely as boys to be myopic. Marked ethnic differences in age-specific prevalence of myopia exist. Rapid increases in myopia prevalence over time, particularly in East Asians, combined with a universally higher risk of myopia in urban settings, suggest that environmental factors play an important role in myopia development, which may offer scope for prevention

The Eighth Data Release of the Sloan Digital Sky Survey: First Data from SDSS-III

The Sloan Digital Sky Survey (SDSS) started a new phase in August 2008, with new instrumentation and new surveys focused on Galactic structure and chemical evolution, measurements of the baryon oscillation feature in the clustering of galaxies and the quasar Ly alpha forest, and a radial velocity search for planets around ~8000 stars. This paper describes the first data release of SDSS-III (and the eighth counting from the beginning of the SDSS). The release includes five-band imaging of roughly 5200 deg^2 in the Southern Galactic Cap, bringing the total footprint of the SDSS imaging to 14,555 deg^2, or over a third of the Celestial Sphere. All the imaging data have been reprocessed with an improved sky-subtraction algorithm and a final, self-consistent photometric recalibration and flat-field determination. This release also includes all data from the second phase of the Sloan Extension for Galactic Understanding and Evolution (SEGUE-2), consisting of spectroscopy of approximately 118,000 stars at both high and low Galactic latitudes. All the more than half a million stellar spectra obtained with the SDSS spectrograph have been reprocessed through an improved stellar parameters pipeline, which has better determination of metallicity for high metallicity stars.Comment: Astrophysical Journal Supplements, in press (minor updates from submitted version

Depletion of Human Histone H1 Variants Uncovers Specific Roles in Gene Expression and Cell Growth

At least six histone H1 variants exist in somatic mammalian cells that bind to the linker DNA and stabilize the nucleosome particle contributing to higher order chromatin compaction. In addition, H1 seems to be actively involved in the regulation of gene expression. However, it is not well known whether the different variants have distinct roles or if they regulate specific promoters. We have explored this by inducible shRNA-mediated knock-down of each of the H1 variants in a human breast cancer cell line. Rapid inhibition of each H1 variant was not compensated for by changes of expression of other variants. Microarray experiments have shown a different subset of genes to be altered in each H1 knock-down. Interestingly, H1.2 depletion caused specific effects such as a cell cycle G1-phase arrest, the repressed expression of a number of cell cycle genes, and decreased global nucleosome spacing. On its side, H1.4 depletion caused cell death in T47D cells, providing the first evidence of the essential role of an H1 variant for survival in a human cell type. Thus, specific phenotypes are observed in breast cancer cells depleted of individual histone H1 variants, supporting the theory that distinct roles exist for the linker histone variants

The Fifth Data Release of the Sloan Digital Sky Survey

This paper describes the Fifth Data Release (DR5) of the Sloan Digital Sky Survey (SDSS). DR5 includes all survey quality data taken through June 2005 and represents the completion of the SDSS-I project (whose successor, SDSS-II will continue through mid-2008). It includes five-band photometric data for 217 million objects selected over 8000 square degrees, and 1,048,960 spectra of galaxies, quasars, and stars selected from 5713 square degrees of that imaging data. These numbers represent a roughly 20% increment over those of the Fourth Data Release; all the data from previous data releases are included in the present release. In addition to "standard" SDSS observations, DR5 includes repeat scans of the southern equatorial stripe, imaging scans across M31 and the core of the Perseus cluster of galaxies, and the first spectroscopic data from SEGUE, a survey to explore the kinematics and chemical evolution of the Galaxy. The catalog database incorporates several new features, including photometric redshifts of galaxies, tables of matched objects in overlap regions of the imaging survey, and tools that allow precise computations of survey geometry for statistical investigations.Comment: ApJ Supp, in press, October 2007. This paper describes DR5. The SDSS Sixth Data Release (DR6) is now public, available from http://www.sdss.or

Six Year Refractive Change among White Children and Young Adults: Evidence for Significant Increase in Myopia among White UK Children

OBJECTIVE:To determine six-year spherical refractive error change among white children and young adults in the UK and evaluate differences in refractive profiles between contemporary Australian children and historical UK data. DESIGN:Population-based prospective study. PARTICIPANTS:The Northern Ireland Childhood Errors of Refraction (NICER) study Phase 1 examined 1068 children in two cohorts aged 6-7 years and 12-13 years. Prospective data for six-year follow-up (Phase 3) are available for 212 12-13 year olds and 226 18-20 year olds in each cohort respectively. METHODS:Cycloplegic refractive error was determined using binocular open-field autorefraction (Shin-Nippon NVision-K 5001, cyclopentolate 1%). Participants were defined by spherical equivalent refraction (SER) as myopic SER ≤-0.50D, emmetropic -0.50D<SER<+2.00 or hyperopic SER≥+2.00D. MAIN OUTCOME MEASURES:Proportion and incidence of myopia. RESULTS:The proportion of myopes significantly increased between 6-7 years (1.9%) and 12-13 years (14.6%) (p<0.001) but not between 12-13 and 18-20 years (16.4% to 18.6%, p = 0.51). The estimated annual incidence of myopia was 2.2% and 0.7% for the younger and older cohorts respectively. There were significantly more myopic children in the UK at age 12-13 years in the NICER study (16.4%) than reported in Australia (4.4%) (p<0.001). However by 17 years the proportion of myopia neared equivalence in the two populations (NICER 18.6%, Australia 17.7%, p = 0.75). The proportion of myopic children aged 12-13 years in the present study (2006-2008) was 16.4%, significantly greater than that reported for children aged 10-16 years in the 1960's (7.2%, p = 0.01). The proportion of hyperopes in the younger NICER cohort decreased significantly over the six year period (from 21.7% to 14.2%, p = 0.04). Hyperopes with SER ≥+3.50D in both NICER age cohorts demonstrated persistent hyperopia. CONCLUSIONS:The incidence and proportion of myopia are relatively low in this contemporary white UK population in comparison to other worldwide studies. The proportion of myopes in the UK has more than doubled over the last 50 years in children aged between 10-16 years and children are becoming myopic at a younger age. Differences between the proportion of myopes in the UK and in Australia apparent at 12-13 years were eliminated by 17 years of age

The Seventh Data Release of the Sloan Digital Sky Survey

This paper describes the Seventh Data Release of the Sloan Digital Sky Survey (SDSS), marking the completion of the original goals of the SDSS and the end of the phase known as SDSS-II. It includes 11663 deg^2 of imaging data, with most of the roughly 2000 deg^2 increment over the previous data release lying in regions of low Galactic latitude. The catalog contains five-band photometry for 357 million distinct objects. The survey also includes repeat photometry over 250 deg^2 along the Celestial Equator in the Southern Galactic Cap. A coaddition of these data goes roughly two magnitudes fainter than the main survey. The spectroscopy is now complete over a contiguous area of 7500 deg^2 in the Northern Galactic Cap, closing the gap that was present in previous data releases. There are over 1.6 million spectra in total, including 930,000 galaxies, 120,000 quasars, and 460,000 stars. The data release includes improved stellar photometry at low Galactic latitude. The astrometry has all been recalibrated with the second version of the USNO CCD Astrograph Catalog (UCAC-2), reducing the rms statistical errors at the bright end to 45 milli-arcseconds per coordinate. A systematic error in bright galaxy photometr is less severe than previously reported for the majority of galaxies. Finally, we describe a series of improvements to the spectroscopic reductions, including better flat-fielding and improved wavelength calibration at the blue end, better processing of objects with extremely strong narrow emission lines, and an improved determination of stellar metallicities. (Abridged)Comment: 20 pages, 10 embedded figures. Accepted to ApJS after minor correction