Partial Covering Arrays: Algorithms and Asymptotics

A covering array $\mathsf{CA}(N;t,k,v)$ is an $N\times k$ array with entries in $\{1, 2, \ldots , v\}$, for which every $N\times t$ subarray contains each $t$-tuple of $\{1, 2, \ldots , v\}^t$ among its rows. Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems. A central question is to determine or bound $\mathsf{CAN}(t,k,v)$, the minimum number $N$ of rows of a $\mathsf{CA}(N;t,k,v)$. The well known bound $\mathsf{CAN}(t,k,v)=O((t-1)v^t\log k)$ is not too far from being asymptotically optimal. Sensible relaxations of the covering requirement arise when (1) the set $\{1, 2, \ldots , v\}^t$ need only be contained among the rows of at least $(1-\epsilon)\binom{k}{t}$ of the $N\times t$ subarrays and (2) the rows of every $N\times t$ subarray need only contain a (large) subset of $\{1, 2, \ldots , v\}^t$. In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two. In each case, a randomized algorithm constructs such arrays in expected polynomial time

k is the Magic Number -- Inferring the Number of Clusters Through Nonparametric Concentration Inequalities

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically unfounded, such as searching for an elbow in the curve of a given cost measure. In contrast, statistically founded methods often make strict assumptions over the data distribution or come with their own optimization scheme for the clustering objective. This limits either the set of applicable datasets or clustering algorithms. In this paper, we strive to determine the number of clusters by answering a simple question: given two clusters, is it likely that they jointly stem from a single distribution? To this end, we propose a bound on the probability that two clusters originate from the distribution of the unified cluster, specified only by the sample mean and variance. Our method is applicable as a simple wrapper to the result of any clustering method minimizing the objective of $k$-means, which includes Gaussian mixtures and Spectral Clustering. We focus in our experimental evaluation on an application for nonconvex clustering and demonstrate the suitability of our theoretical results. Our \textsc{SpecialK} clustering algorithm automatically determines the appropriate value for $k$, without requiring any data transformation or projection, and without assumptions on the data distribution. Additionally, it is capable to decide that the data consists of only a single cluster, which many existing algorithms cannot

2019 update of the EULAR recommendations for the management of systemic lupus erythematosus

© Author(s) (or their employer(s)) 2019. No commercial re-use. See rights and permissions. Published by BMJ. Our objective was to update the EULAR recommendations for the management of systemic lupus erythematosus (SLE), based on emerging new evidence. We performed a systematic literature review (01/2007-12/2017), followed by modified Delphi method, to form questions, elicit expert opinions and reach consensus. Treatment in SLE aims at remission or low disease activity and prevention of flares. Hydroxychloroquine is recommended in all patients with lupus, at a dose not exceeding 5 mg/kg real body weight. During chronic maintenance treatment, glucocorticoids (GC) should be minimised to less than 7.5 mg/day (prednisone equivalent) and, when possible, withdrawn. Appropriate initiation of immunomodulatory agents (methotrexate, azathioprine, mycophenolate) can expedite the tapering/discontinuation of GC. In persistently active or flaring extrarenal disease, add-on belimumab should be considered; rituximab (RTX) may be considered in organ-threatening, refractory disease. Updated specific recommendations are also provided for cutaneous, neuropsychiatric, haematological and renal disease. Patients with SLE should be assessed for their antiphospholipid antibody status, infectious and cardiovascular diseases risk profile and preventative strategies be tailored accordingly. The updated recommendations provide physicians and patients with updated consensus guidance on the management of SLE, combining evidence-base and expert-opinion

Estimates of array and pool-construction variance for planning efficient DNA-pooling genome wide association studies

<p>Abstract</p> <p>Background</p> <p>Until recently, genome-wide association studies (GWAS) have been restricted to research groups with the budget necessary to genotype hundreds, if not thousands, of samples. Replacing individual genotyping with genotyping of DNA pools in Phase I of a GWAS has proven successful, and dramatically altered the financial feasibility of this approach. When conducting a pool-based GWAS, how well SNP allele frequency is estimated from a DNA pool will influence a study's power to detect associations. Here we address how to control the variance in allele frequency estimation when DNAs are pooled, and how to plan and conduct the most efficient well-powered pool-based GWAS.</p> <p>Methods</p> <p>By examining the variation in allele frequency estimation on SNP arrays between and within DNA pools we determine how array variance [var(e_array)] and pool-construction variance [var(e_construction)] contribute to the total variance of allele frequency estimation. This information is useful in deciding whether replicate arrays or replicate pools are most useful in reducing variance. Our analysis is based on 27 DNA pools ranging in size from 74 to 446 individual samples, genotyped on a collective total of 128 Illumina beadarrays: 24 1M-Single, 32 1M-Duo, and 72 660-Quad.</p> <p>Results</p> <p>For all three Illumina SNP array types our estimates of var(e_array) were similar, between 3-4 × 10^-4for normalized data. Var(e_construction) accounted for between 20-40% of pooling variance across 27 pools in normalized data.</p> <p>Conclusions</p> <p>We conclude that relative to var(e_array), var(e_construction) is of less importance in reducing the variance in allele frequency estimation from DNA pools; however, our data suggests that on average it may be more important than previously thought. We have prepared a simple online tool, PoolingPlanner (available at <url>http://www.kchew.ca/PoolingPlanner/</url>), which calculates the effective sample size (ESS) of a DNA pool given a range of replicate array values. ESS can be used in a power calculator to perform pool-adjusted calculations. This allows one to quickly calculate the loss of power associated with a pooling experiment to make an informed decision on whether a pool-based GWAS is worth pursuing.</p

Azimuthal anisotropy and correlations at large transverse momenta in p+pp+p and Au+Au collisions at sNN\sqrt{s_{_{NN}}}= 200 GeV

Results on high transverse momentum charged particle emission with respect to the reaction plane are presented for Au+Au collisions at $\sqrt{s_{_{NN}}}$= 200 GeV. Two- and four-particle correlations results are presented as well as a comparison of azimuthal correlations in Au+Au collisions to those in $p+p$ at the same energy. Elliptic anisotropy, $v_2$, is found to reach its maximum at $p_t \sim 3$ GeV/c, then decrease slowly and remain significant up to $p_t\approx 7$ -- 10 GeV/c. Stronger suppression is found in the back-to-back high-$p_t$ particle correlations for particles emitted out-of-plane compared to those emitted in-plane. The centrality dependence of $v_2$ at intermediate $p_t$ is compared to simple models based on jet quenching.Comment: 4 figures. Published version as PRL 93, 252301 (2004

Azimuthal anisotropy in Au+Au collisions at sqrtsNN = 200 GeV

The results from the STAR Collaboration on directed flow (v_1), elliptic flow (v_2), and the fourth harmonic (v_4) in the anisotropic azimuthal distribution of particles from Au+Au collisions at sqrtsNN = 200 GeV are summarized and compared with results from other experiments and theoretical models. Results for identified particles are presented and fit with a Blast Wave model. Different anisotropic flow analysis methods are compared and nonflow effects are extracted from the data. For v_2, scaling with the number of constituent quarks and parton coalescence is discussed. For v_4, scaling with v_2^2 and quark coalescence is discussed.Comment: 26 pages. As accepted by Phys. Rev. C. Text rearranged, figures modified, but data the same. However, in Fig. 35 the hydro calculations are corrected in this version. The data tables are available at http://www.star.bnl.gov/central/publications/ by searching for "flow" and then this pape

Problems in obtaining precise and accurate Sr isotope analysis from geological materials using laser ablation MC-ICPMS

This paper reviews the problems encountered in eleven studies of Sr isotope analysis using laser ablation multicollector inductively coupled plasma mass spectrometry (LA-MC-ICPMS) in the period 1995–2006. This technique has been shown to have great potential, but the accuracy and precision are limited by: (1) large instrumental mass discrimination, (2) laser-induced isotopic and elemental fractionations and (3) molecular interferences. The most important isobaric interferences are Kr and Rb, whereas Ca dimer/argides and doubly charged rare earth elements (REE) are limited to sample materials which contain substantial amounts of these elements. With modern laser (193 nm) and MC-ICPMS equipment, minerals with >500 ppm Sr content can be analysed with a precision of better than 100 ppm and a spatial resolution (spot size) of approximately 100 μm. The LA MC-ICPMS analysis of 87Sr/86Sr of both carbonate material and plagioclase is successful in all reported studies, although the higher 84Sr/86Sr ratios do suggest in some cases an influence of Ca dimer and/or argides. High Rb/Sr (>0.01) materials have been successfully analysed by carefully measuring the 85Rb/87Rb in standard material and by applying the standard-sample bracketing method for accurate Rb corrections. However, published LA-MC-ICPMS data on clinopyroxene, apatite and sphene records differences when compared with 87Sr/86Sr measured by thermal ionisation mass spectrometry (TIMS) and solution MC-ICPMS. This suggests that further studies are required to ensure that the most optimal correction methods are applied for all isobaric interferences

Potential impact of infant feeding recommendations on mortality and HIV-infection in children born to HIV-infected mothers in Africa: a simulation

<p>Abstract</p> <p>Background</p> <p>Although breast-feeding accounts for 15–20% of mother-to-child transmission (MTCT) of HIV, it is not prohibited in some developing countries because of the higher mortality associated with not breast-feeding. We assessed the potential impact, on HIV infection and infant mortality, of a recommendation for shorter durations of exclusive breast-feeding (EBF) and poor compliance to these recommendations.</p> <p>Methods</p> <p>We developed a deterministic mathematical model using primarily parameters from published studies conducted in Uganda or Kenya and took into account non-compliance resulting in mixed-feeding practices. Outcomes included the number of children HIV-infected and/or dead (cumulative mortality) at 2 years following each of 6 scenarios of infant-feeding recommendations in children born to HIV-infected women: Exclusive replacement-feeding (ERF) with 100% compliance, EBF for 6 months with 100% compliance, EBF for 4 months with 100% compliance, ERF with 70% compliance, EBF for 6 months with 85% compliance, EBF for 4 months with 85% compliance</p> <p>Results</p> <p>In the base model, reducing the duration of EBF from 6 to 4 months reduced HIV infection by 11.8% while increasing mortality by 0.4%. Mixed-feeding in 15% of the infants increased HIV infection and mortality respectively by 2.1% and 0.5% when EBF for 6 months was recommended; and by 1.7% and 0.3% when EBF for 4 months was recommended. In sensitivity analysis, recommending EBF resulted in the least cumulative mortality when the a) mortality in replacement-fed infants was greater than 50 per 1000 person-years, b) rate of infection in exclusively breast-fed infants was less than 2 per 1000 breast-fed infants per week, c) rate of progression from HIV to AIDS was less than 15 per 1000 infected infants per week, or d) mortality due to HIV/AIDS was less than 200 per 1000 infants with HIV/AIDS per year.</p> <p>Conclusion</p> <p>Recommending shorter durations of breast-feeding in infants born to HIV-infected women in these settings may substantially reduce infant HIV infection but not mortality. When EBF for shorter durations is recommended, lower mortality could be achieved by a simultaneous reduction in the rate of progression from HIV to AIDS and or HIV/AIDS mortality, achievable by the use of HAART in infants.</p