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High-Dimensional Interactions Detection with Sparse Principal Hessian Matrix

In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to combinatorial complexity and limited data information. We consider detecting interactions by exploring their connections with the principal Hessian matrix. Specifically, we propose a one-step synthetic approach for estimating the principal Hessian matrix by a penalized M-estimator. An alternating direction method of multipliers (ADMM) is proposed to efficiently solve the encountered regularized optimization problem. Based on the sparse estimator, we detect the interactions by identifying its nonzero components. Our method directly targets at the interactions, and it requires no structural assumption on the hierarchy of the interactions effects. We show that our estimator is theoretically valid, computationally efficient, and practically useful for detecting the interactions in a broad spectrum of scenarios.




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Optimal Bipartite Network Clustering

We study bipartite community detection in networks, or more generally the network biclustering problem. We present a fast two-stage procedure based on spectral initialization followed by the application of a pseudo-likelihood classifier twice. Under mild regularity conditions, we establish the weak consistency of the procedure (i.e., the convergence of the misclassification rate to zero) under a general bipartite stochastic block model. We show that the procedure is optimal in the sense that it achieves the optimal convergence rate that is achievable by a biclustering oracle, adaptively over the whole class, up to constants. This is further formalized by deriving a minimax lower bound over a class of biclustering problems. The optimal rate we obtain sharpens some of the existing results and generalizes others to a wide regime of average degree growth, from sparse networks with average degrees growing arbitrarily slowly to fairly dense networks with average degrees of order $sqrt{n}$. As a special case, we recover the known exact recovery threshold in the $log n$ regime of sparsity. To obtain the consistency result, as part of the provable version of the algorithm, we introduce a sub-block partitioning scheme that is also computationally attractive, allowing for distributed implementation of the algorithm without sacrificing optimality. The provable algorithm is derived from a general class of pseudo-likelihood biclustering algorithms that employ simple EM type updates. We show the effectiveness of this general class by numerical simulations.




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Exact Guarantees on the Absence of Spurious Local Minima for Non-negative Rank-1 Robust Principal Component Analysis

This work is concerned with the non-negative rank-1 robust principal component analysis (RPCA), where the goal is to recover the dominant non-negative principal components of a data matrix precisely, where a number of measurements could be grossly corrupted with sparse and arbitrary large noise. Most of the known techniques for solving the RPCA rely on convex relaxation methods by lifting the problem to a higher dimension, which significantly increase the number of variables. As an alternative, the well-known Burer-Monteiro approach can be used to cast the RPCA as a non-convex and non-smooth $ell_1$ optimization problem with a significantly smaller number of variables. In this work, we show that the low-dimensional formulation of the symmetric and asymmetric positive rank-1 RPCA based on the Burer-Monteiro approach has benign landscape, i.e., 1) it does not have any spurious local solution, 2) has a unique global solution, and 3) its unique global solution coincides with the true components. An implication of this result is that simple local search algorithms are guaranteed to achieve a zero global optimality gap when directly applied to the low-dimensional formulation. Furthermore, we provide strong deterministic and probabilistic guarantees for the exact recovery of the true principal components. In particular, it is shown that a constant fraction of the measurements could be grossly corrupted and yet they would not create any spurious local solution.




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Multiparameter Persistence Landscapes

An important problem in the field of Topological Data Analysis is defining topological summaries which can be combined with traditional data analytic tools. In recent work Bubenik introduced the persistence landscape, a stable representation of persistence diagrams amenable to statistical analysis and machine learning tools. In this paper we generalise the persistence landscape to multiparameter persistence modules providing a stable representation of the rank invariant. We show that multiparameter landscapes are stable with respect to the interleaving distance and persistence weighted Wasserstein distance, and that the collection of multiparameter landscapes faithfully represents the rank invariant. Finally we provide example calculations and statistical tests to demonstrate a range of potential applications and how one can interpret the landscapes associated to a multiparameter module.




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Effects of gene–environment and gene–gene interactions in case-control studies: A novel Bayesian semiparametric approach

Durba Bhattacharya, Sourabh Bhattacharya.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 71--89.

Abstract:
Present day bio-medical research is pointing towards the fact that cognizance of gene–environment interactions along with genetic interactions may help prevent or detain the onset of many complex diseases like cardiovascular disease, cancer, type2 diabetes, autism or asthma by adjustments to lifestyle. In this regard, we propose a Bayesian semiparametric model to detect not only the roles of genes and their interactions, but also the possible influence of environmental variables on the genes in case-control studies. Our model also accounts for the unknown number of genetic sub-populations via finite mixtures composed of Dirichlet processes. An effective parallel computing methodology, developed by us harnesses the power of parallel processing technology to increase the efficiencies of our conditionally independent Gibbs sampling and Transformation based MCMC (TMCMC) methods. Applications of our model and methods to simulation studies with biologically realistic genotype datasets and a real, case-control based genotype dataset on early onset of myocardial infarction (MI) have yielded quite interesting results beside providing some insights into the differential effect of gender on MI.




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Semiparametric Optimal Estimation With Nonignorable Nonresponse Data. (arXiv:1612.09207v3 [stat.ME] UPDATED)

When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have been developed under the model assumptions on the response mechanism. In this paper, a new statistical test is proposed to guarantee model identifiability without using any instrumental variable. Furthermore, we develop optimal semiparametric estimation for parameters such as the population mean. Specifically, we propose two semiparametric optimal estimators that do not require any model assumptions other than the response mechanism. Asymptotic properties of the proposed estimators are discussed. An extensive simulation study is presented to compare with some existing methods. We present an application of our method using Korean Labor and Income Panel Survey data.




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Efficient estimation of linear functionals of principal components

Vladimir Koltchinskii, Matthias Löffler, Richard Nickl.

Source: The Annals of Statistics, Volume 48, Number 1, 464--490.

Abstract:
We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_{1},dots,X_{n}$ in a separable Hilbert space $mathbb{H}$ with unknown covariance operator $Sigma $. The complexity of the problem is characterized by its effective rank $mathbf{r}(Sigma):=frac{operatorname{tr}(Sigma)}{|Sigma |}$, where $mathrm{tr}(Sigma)$ denotes the trace of $Sigma $ and $|Sigma|$ denotes its operator norm. We develop a method of bias reduction in the problem of estimation of linear functionals of eigenvectors of $Sigma $. Under the assumption that $mathbf{r}(Sigma)=o(n)$, we establish the asymptotic normality and asymptotic properties of the risk of the resulting estimators and prove matching minimax lower bounds, showing their semiparametric optimality.




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Testing for principal component directions under weak identifiability

Davy Paindaveine, Julien Remy, Thomas Verdebout.

Source: The Annals of Statistics, Volume 48, Number 1, 324--345.

Abstract:
We consider the problem of testing, on the basis of a $p$-variate Gaussian random sample, the null hypothesis $mathcal{H}_{0}:oldsymbol{ heta}_{1}=oldsymbol{ heta}_{1}^{0}$ against the alternative $mathcal{H}_{1}:oldsymbol{ heta}_{1} eq oldsymbol{ heta}_{1}^{0}$, where $oldsymbol{ heta}_{1}$ is the “first” eigenvector of the underlying covariance matrix and $oldsymbol{ heta}_{1}^{0}$ is a fixed unit $p$-vector. In the classical setup where eigenvalues $lambda_{1}>lambda_{2}geq cdots geq lambda_{p}$ are fixed, the Anderson ( Ann. Math. Stat. 34 (1963) 122–148) likelihood ratio test (LRT) and the Hallin, Paindaveine and Verdebout ( Ann. Statist. 38 (2010) 3245–3299) Le Cam optimal test for this problem are asymptotically equivalent under the null hypothesis, hence also under sequences of contiguous alternatives. We show that this equivalence does not survive asymptotic scenarios where $lambda_{n1}/lambda_{n2}=1+O(r_{n})$ with $r_{n}=O(1/sqrt{n})$. For such scenarios, the Le Cam optimal test still asymptotically meets the nominal level constraint, whereas the LRT severely overrejects the null hypothesis. Consequently, the former test should be favored over the latter one whenever the two largest sample eigenvalues are close to each other. By relying on the Le Cam’s asymptotic theory of statistical experiments, we study the non-null and optimality properties of the Le Cam optimal test in the aforementioned asymptotic scenarios and show that the null robustness of this test is not obtained at the expense of power. Our asymptotic investigation is extensive in the sense that it allows $r_{n}$ to converge to zero at an arbitrary rate. While we restrict to single-spiked spectra of the form $lambda_{n1}>lambda_{n2}=cdots =lambda_{np}$ to make our results as striking as possible, we extend our results to the more general elliptical case. Finally, we present an illustrative real data example.




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Two-step semiparametric empirical likelihood inference

Francesco Bravo, Juan Carlos Escanciano, Ingrid Van Keilegom.

Source: The Annals of Statistics, Volume 48, Number 1, 1--26.

Abstract:
In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks’ theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks’ theorem breaks down. This article suggests a general approach to restore Wilks’ phenomenon in two-step semiparametric empirical likelihood inferences. The main insight consists in using as the moment function in the estimating equation the influence function of the plug-in sample moment. The proposed method is general; it leads to a chi-squared limiting distribution with known degrees of freedom; it is efficient; it does not require undersmoothing; and it is less sensitive to the first-step than alternative methods, which is particularly appealing for high-dimensional settings. Several examples and simulation studies illustrate the general applicability of the procedure and its excellent finite sample performance relative to competing methods.




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Distributed estimation of principal eigenspaces

Jianqing Fan, Dong Wang, Kaizheng Wang, Ziwei Zhu.

Source: The Annals of Statistics, Volume 47, Number 6, 3009--3031.

Abstract:
Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication cost can prohibit the computation of PCA in a central location and distributed algorithms for PCA are thus needed. This paper proposes and studies a distributed PCA algorithm: each node machine computes the top $K$ eigenvectors and transmits them to the central server; the central server then aggregates the information from all the node machines and conducts a PCA based on the aggregated information. We investigate the bias and variance for the resulting distributed estimator of the top $K$ eigenvectors. In particular, we show that for distributions with symmetric innovation, the empirical top eigenspaces are unbiased, and hence the distributed PCA is “unbiased.” We derive the rate of convergence for distributed PCA estimators, which depends explicitly on the effective rank of covariance, eigengap, and the number of machines. We show that when the number of machines is not unreasonably large, the distributed PCA performs as well as the whole sample PCA, even without full access of whole data. The theoretical results are verified by an extensive simulation study. We also extend our analysis to the heterogeneous case where the population covariance matrices are different across local machines but share similar top eigenstructures.




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Semiparametrically point-optimal hybrid rank tests for unit roots

Bo Zhou, Ramon van den Akker, Bas J. M. Werker.

Source: The Annals of Statistics, Volume 47, Number 5, 2601--2638.

Abstract:
We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, that is, have the correct (asymptotic) size, irrespective of the true innovation density. For a correctly specified reference density, our test is point-optimal and nearly efficient. For arbitrary reference densities, we establish a Chernoff–Savage-type result, that is, our test performs as well as commonly used tests under Gaussian innovations but has improved power under other, for example, fat-tailed or skewed, innovation distributions. To avoid nonparametric estimation, we propose a simplified version of our test that exhibits the same asymptotic properties, except for the Chernoff–Savage result that we are only able to demonstrate by means of simulations.




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A comparison of principal component methods between multiple phenotype regression and multiple SNP regression in genetic association studies

Zhonghua Liu, Ian Barnett, Xihong Lin.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 433--451.

Abstract:
Principal component analysis (PCA) is a popular method for dimension reduction in unsupervised multivariate analysis. However, existing ad hoc uses of PCA in both multivariate regression (multiple outcomes) and multiple regression (multiple predictors) lack theoretical justification. The differences in the statistical properties of PCAs in these two regression settings are not well understood. In this paper we provide theoretical results on the power of PCA in genetic association testings in both multiple phenotype and SNP-set settings. The multiple phenotype setting refers to the case when one is interested in studying the association between a single SNP and multiple phenotypes as outcomes. The SNP-set setting refers to the case when one is interested in studying the association between multiple SNPs in a SNP set and a single phenotype as the outcome. We demonstrate analytically that the properties of the PC-based analysis in these two regression settings are substantially different. We show that the lower order PCs, that is, PCs with large eigenvalues, are generally preferred and lead to a higher power in the SNP-set setting, while the higher-order PCs, that is, PCs with small eigenvalues, are generally preferred in the multiple phenotype setting. We also investigate the power of three other popular statistical methods, the Wald test, the variance component test and the minimum $p$-value test, in both multiple phenotype and SNP-set settings. We use theoretical power, simulation studies, and two real data analyses to validate our findings.




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Estimating the health effects of environmental mixtures using Bayesian semiparametric regression and sparsity inducing priors

Joseph Antonelli, Maitreyi Mazumdar, David Bellinger, David Christiani, Robert Wright, Brent Coull.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 257--275.

Abstract:
Humans are routinely exposed to mixtures of chemical and other environmental factors, making the quantification of health effects associated with environmental mixtures a critical goal for establishing environmental policy sufficiently protective of human health. The quantification of the effects of exposure to an environmental mixture poses several statistical challenges. It is often the case that exposure to multiple pollutants interact with each other to affect an outcome. Further, the exposure-response relationship between an outcome and some exposures, such as some metals, can exhibit complex, nonlinear forms, since some exposures can be beneficial and detrimental at different ranges of exposure. To estimate the health effects of complex mixtures, we propose a flexible Bayesian approach that allows exposures to interact with each other and have nonlinear relationships with the outcome. We induce sparsity using multivariate spike and slab priors to determine which exposures are associated with the outcome and which exposures interact with each other. The proposed approach is interpretable, as we can use the posterior probabilities of inclusion into the model to identify pollutants that interact with each other. We utilize our approach to study the impact of exposure to metals on child neurodevelopment in Bangladesh and find a nonlinear, interactive relationship between arsenic and manganese.




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Principal nested shape space analysis of molecular dynamics data

Ian L. Dryden, Kwang-Rae Kim, Charles A. Laughton, Huiling Le.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2213--2234.

Abstract:
Molecular dynamics simulations produce huge datasets of temporal sequences of molecules. It is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA [ Biometrika 99 (2012) 551–568]. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D subshape spaces and provide some practical fitting algorithms. The methodology is applied to cluster analysis of peptides, where different states of the molecules can be identified. Also, the temporal transitions between cluster states are explored.




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A semiparametric modeling approach using Bayesian Additive Regression Trees with an application to evaluate heterogeneous treatment effects

Bret Zeldow, Vincent Lo Re III, Jason Roy.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1989--2010.

Abstract:
Bayesian Additive Regression Trees (BART) is a flexible machine learning algorithm capable of capturing nonlinearities between an outcome and covariates and interactions among covariates. We extend BART to a semiparametric regression framework in which the conditional expectation of an outcome is a function of treatment, its effect modifiers, and confounders. The confounders are allowed to have unspecified functional form, while treatment and effect modifiers that are directly related to the research question are given a linear form. The result is a Bayesian semiparametric linear regression model where the posterior distribution of the parameters of the linear part can be interpreted as in parametric Bayesian regression. This is useful in situations where a subset of the variables are of substantive interest and the others are nuisance variables that we would like to control for. An example of this occurs in causal modeling with the structural mean model (SMM). Under certain causal assumptions, our method can be used as a Bayesian SMM. Our methods are demonstrated with simulation studies and an application to dataset involving adults with HIV/Hepatitis C coinfection who newly initiate antiretroviral therapy. The methods are available in an R package called semibart.




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Bayesian methods for multiple mediators: Relating principal stratification and causal mediation in the analysis of power plant emission controls

Chanmin Kim, Michael J. Daniels, Joseph W. Hogan, Christine Choirat, Corwin M. Zigler.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1927--1956.

Abstract:
Emission control technologies installed on power plants are a key feature of many air pollution regulations in the US. While such regulations are predicated on the presumed relationships between emissions, ambient air pollution and human health, many of these relationships have never been empirically verified. The goal of this paper is to develop new statistical methods to quantify these relationships. We frame this problem as one of mediation analysis to evaluate the extent to which the effect of a particular control technology on ambient pollution is mediated through causal effects on power plant emissions. Since power plants emit various compounds that contribute to ambient pollution, we develop new methods for multiple intermediate variables that are measured contemporaneously, may interact with one another, and may exhibit joint mediating effects. Specifically, we propose new methods leveraging two related frameworks for causal inference in the presence of mediating variables: principal stratification and causal mediation analysis. We define principal effects based on multiple mediators, and also introduce a new decomposition of the total effect of an intervention on ambient pollution into the natural direct effect and natural indirect effects for all combinations of mediators. Both approaches are anchored to the same observed-data models, which we specify with Bayesian nonparametric techniques. We provide assumptions for estimating principal causal effects, then augment these with an additional assumption required for causal mediation analysis. The two analyses, interpreted in tandem, provide the first empirical investigation of the presumed causal pathways that motivate important air quality regulatory policies.




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Consistent semiparametric estimators for recurrent event times models with application to virtual age models

Eric Beutner, Laurent Bordes, Laurent Doyen.

Source: Bernoulli, Volume 26, Number 1, 557--586.

Abstract:
Virtual age models are very useful to analyse recurrent events. Among the strengths of these models is their ability to account for treatment (or intervention) effects after an event occurrence. Despite their flexibility for modeling recurrent events, the number of applications is limited. This seems to be a result of the fact that in the semiparametric setting all the existing results assume the virtual age function that describes the treatment (or intervention) effects to be known. This shortcoming can be overcome by considering semiparametric virtual age models with parametrically specified virtual age functions. Yet, fitting such a model is a difficult task. Indeed, it has recently been shown that for these models the standard profile likelihood method fails to lead to consistent estimators. Here we show that consistent estimators can be constructed by smoothing the profile log-likelihood function appropriately. We show that our general result can be applied to most of the relevant virtual age models of the literature. Our approach shows that empirical process techniques may be a worthwhile alternative to martingale methods for studying asymptotic properties of these inference methods. A simulation study is provided to illustrate our consistency results together with an application to real data.




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Sydney in 1848 : illustrated by copper-plate engravings of its principal streets, public buildings, churches, chapels, etc. / from drawings by Joseph Fowles.




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Learning Semiparametric Regression with Missing Covariates Using Gaussian Process Models

Abhishek Bishoyi, Xiaojing Wang, Dipak K. Dey.

Source: Bayesian Analysis, Volume 15, Number 1, 215--239.

Abstract:
Missing data often appear as a practical problem while applying classical models in the statistical analysis. In this paper, we consider a semiparametric regression model in the presence of missing covariates for nonparametric components under a Bayesian framework. As it is known that Gaussian processes are a popular tool in nonparametric regression because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. However, in the absence of covariates, the most frequently used covariance functions of a Gaussian process will not be well defined. We propose an imputation method to solve this issue and perform our analysis using Bayesian inference, where we specify the objective priors on the parameters of Gaussian process models. Several simulations are conducted to illustrate effectiveness of our proposed method and further, our method is exemplified via two real datasets, one through Langmuir equation, commonly used in pharmacokinetic models, and another through Auto-mpg data taken from the StatLib library.




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Semiparametric Multivariate and Multiple Change-Point Modeling

Stefano Peluso, Siddhartha Chib, Antonietta Mira.

Source: Bayesian Analysis, Volume 14, Number 3, 727--751.

Abstract:
We develop a general Bayesian semiparametric change-point model in which separate groups of structural parameters (for example, location and dispersion parameters) can each follow a separate multiple change-point process, driven by time-dependent transition matrices among the latent regimes. The distribution of the observations within regimes is unknown and given by a Dirichlet process mixture prior. The properties of the proposed model are studied theoretically through the analysis of inter-arrival times and of the number of change-points in a given time interval. The prior-posterior analysis by Markov chain Monte Carlo techniques is developed on a forward-backward algorithm for sampling the various regime indicators. Analysis with simulated data under various scenarios and an application to short-term interest rates are used to show the generality and usefulness of the proposed model.




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An Overview of Semiparametric Extensions of Finite Mixture Models

Sijia Xiang, Weixin Yao, Guangren Yang.

Source: Statistical Science, Volume 34, Number 3, 391--404.

Abstract:
Finite mixture models have offered a very important tool for exploring complex data structures in many scientific areas, such as economics, epidemiology and finance. Semiparametric mixture models, which were introduced into traditional finite mixture models in the past decade, have brought forth exciting developments in their methodologies, theories, and applications. In this article, we not only provide a selective overview of the newly-developed semiparametric mixture models, but also discuss their estimation methodologies, theoretical properties if applicable, and some open questions. Recent developments are also discussed.




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The Comfy Sneakers That Kate Middleton, Kelly Ripa, and More Celebs Love Are on Sale at Amazon

Keep your feet comfy and your wallet fat.




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Seventeen people participate in SHI's moccasin workshop




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This Art Campaign Wants You to Participate in the 2020 Census

Due to COVID-19, Art + Action's "Come to Your Census" project has pivoted from posters and events to social media and online outreach




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Super-Constipated Florida Lizard Breaks Records With Gargantuan Poop

An unfortunate diet of pizza grease and sand clogged her innards, amassing a giant and unpassable lump of feces in her gut




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Municipality of Qikiqtarjuaq faces 5 charges under Nunavut Safety Act

The N.W.T. and Nunavut Workers’ Safety and Compensation Commission says it filed multiple charges in the Nunavut Court of Justice under the Nunavut Safety Act on May 1.



  • News/Canada/North

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Manitoba municipalities to receive most operating funds sooner than normal due to COVID-19

Manitoba municipalities will be receiving most of their operating funding from the province sooner than usual because of the COVID-19 pandemic, the province announced Friday.



  • News/Canada/Manitoba

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Zoey Roy first Indigenous author to participate in NAC's #CanadaPerforms

Last month, the National Arts Centre launched #CanadaPerforms, an initiative that pays musicians and writers to perform from their living rooms. Poet Zoey Roy gave an intimate performance from her living room in Kingston. 




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How some B.C. municipalities are handling the financial impacts of COVID-19

Municipalities across the province are re-evaluating their financial situations as COVID-19 continues to keep municipal facilities closed and has put other revenue streams on hold. 



  • News/Canada/British Columbia

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Hands on: Brydge Pro+ firmware updated improves iPadOS user experience



Brydge on Wednesday launched a new update to improve its Brydge Pro+ keyboard with trackpad that recently starting shipping for iPad Pro. AppleInsider goes hands-on with the latest firmware to see how Brydge's improvements have strengthened the user experience of its flagship product.




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Apple expects iPad, Mac sales to grow in June Q3 despite COVID-19



It's not exactly surprising that with all of the uncertainty in the world, Apple decided that it couldn't provide useful revenue guidance for its fiscal Q3 ending in June. It is unexpected, however, that Apple felt confident in announcing a silver lining to the pandemic -- it expects to sell more Macs and iPads in the summer of 2020 compared to 2019.



  • iPhone/iPad/Apple Watch

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'X-ray teardown' of iPad Pro Magic Keyboard illustrates complex engineering



Repair site iFixit has shared x-ray photographs of the new Magic Keyboard for iPad Pro, and they reveal an accessory more complicated than it might appear from the outside.




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Participants have a plan but rely on God to act

OM Ireland's biggest outreach of the year teaches participants to commit their ways to Him and trust Him to act.




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Participants share about refugee outreach in Austria

Thirteen participants from all over the world spent a week getting to know and supporting the refugee work in Linz. Six share about their experiences.




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The Latest iPad Mini Is Back at Its Lowest Amazon Price Ever

The 2019 iPad mini with Wi-Fi and 256GB of storage normally sells for $549, but is available on Amazon right now for just $519. That's the lowest it's ever been on the site.




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The 2018 Apple iPad Is More Than $200 Off at Walmart

The sixth-generation 9.7-inch iPad with 128GB of storage and cellular connectivity would normally set you back $559, but is currently marked down to just $349.




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Latest 11-Inch iPad Pro With Cellular Gets $199 Discount

The latest iPad Pro featuring 1TB of storage and cellular connectivity is on sale at Amazon for just $1,299.99. Models with less storage and just Wi-Fi are also marked down.




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Snag the 2019 Apple iPad Air for Just $459

The 64GB Wi-Fi model is currently on sale for $459 at Walmart (down from $499.99).




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Deals: 10.2-Inch iPad, 65-Inch Vizio 4K TV, Amazon Echo Buds

The 10.2-inch Apple iPad with 128GB of storage is $100 off, a 65-inch Vizio 4K TV is $500 off and includes a $250 Dell gift card, and you can score the first discount on Echo Buds.




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iPad Air (2019), iPad Mini 5 Join Apple's Refurbished Lineup

Grab a refurbished third-generation iPad Air or fifth-generation iPad Mini from Apple to save big while getting nearly the same experience new tablets offer.




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Deal Alert: The Latest Apple iPads Are Up to $150 Off

scrolling through Amazon in the same way has turned up some great deals on iPads. Right now the latest models are available at all-new low prices.




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National Principals' Union Chases More Members

A national union for principals is campaigning to increase its membership, drafting in part off the momentum created by the surge in educator activism over the past two years.




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Obituary: George Forfar, Principal Teacher of English who inspired pupils and colleagues alike

George Forfar: An appreciation




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Harvard Business Review, MBA Lessons Guide Principals' Ed-Tech Leadership

Effective management approaches are not skills principals typically learn through the traditional pathways of education. To fill the gap, they are turning to business programs and publications.




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'Middle School' Movie Is Fun for Students, and a Sticky Situation for Principals

The film is the first from the James Patterson book series about a middle school student dealing with school rules that don't always make sense.




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Principal Running for Congress to Challenge Incumbent in Democratic Primary

While the number of principals running for office has been dwarfed by teachers, school leaders are hoping to change policies in statehouses and in Washington that they say impact their students and families.




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Health Risks of Oregon Eighth-Grade Participants in the "Choking Game": Results From a Population-Based Survey

Estimates of youth participation in strangulation activity, commonly referred to as the "choking game," range from 5% to 11%. Previous studies have documented correlations between youth choking game participation and health risks such as substance use and mental health issues.

Among Oregon eighth-graders surveyed, >6% had ever participated in the choking game. Participation was linked to poor nutrition and gambling among females, exposure to violence among males, and sexual activity and substance use among both genders. (Read the full article)




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An Evaluation of Mother-Centered Anticipatory Guidance to Reduce Obesogenic Infant Feeding Behaviors

Childhood obesity occurs in 20% of children before they enter kindergarten. Treatment is difficult, making prevention desirable, but little is known about effective methods using anticipatory guidance to prevent obesity in pediatric primary care.

This study provides a comparison of 2 approaches versus usual care using anticipatory guidance to improve infant feeding during the first year of life, and demonstrates positive specific feeding behavior differences at 1 year in the intervention groups. (Read the full article)




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Factors Influencing Participation in a Population-based Biorepository for Childhood Heart Disease

Understanding human disease genomics requires large population-based studies. There is lack of standardization, as well as social and ethical concerns surrounding the consent process for pediatric participation in a biorepository.

The study identifies specific barriers to pediatric participation in biorepositories relative to adults, and proposes strategies to improve ethical and responsible participation of pediatric-aged patients in large-scale genomics and biorepository-driven research without significantly increasing research burden for affected families. (Read the full article)




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Associations of Food Stamp Participation With Dietary Quality and Obesity in Children

The Supplemental Nutrition Assistance Program (SNAP) is the largest federal nutrition assistance program. Studies among adults suggest that SNAP participation may be associated with suboptimal diets. Few studies have extensively examined these associations among children.

SNAP participation was not associated with childhood obesity. SNAP children consumed diets poorer in some aspects than nonparticipants, but intake of some micronutrients was higher. The diets of both groups of low-income children were far from meeting dietary guidelines. (Read the full article)