text:
\section{Introduction}\label{sec:Intro}

It is often desirable to obtain estimates of population parameters in small spatial areas that are not sampled or are under-sampled in surveys. In such cases, small area estimation (SAE) is facilitated by the introduction of covariates that inform the population parameters and thus reduce estimation variance.  In its basic form, the Fay-Herriot (FH) model \citep{fay1979estimates} is a two-level hierarchical model in which the direct survey estimates are conditioned on a latent population parameter of interest (or survey ``superpopulation mean") and a survey variance, and the latent parameter is ``regressed'' on relevant covariates. Specifically, the FH model can be expressed as
\begin{eqnarray}
\label{eq:fhcore}
Y_{i}=\theta_{i}+\epsilon_i , \\
\label{eq:fhaux}
\theta_i =\mbf{x}_i' \mbv{\beta} +u_i,
\end{eqnarray}
where $Y_i$ denotes a design-unbiased estimate of $\theta_i$, the parameter of interest at location $i=1,\ldots,n$. In general, the error term $\epsilon_i$ in (\ref{eq:fhcore}) is assumed to be independent, normally distributed with mean zero and variance $\sigma_{i}^{2}$, with $\sigma_{i}^{2}$ representing the sampling variance at location $i$. This survey variance is often assumed known (provided by the official statistical agency) and the normality assumption may be relaxed \citep[e.g.,][]{you2002small}. In the second model stage (\ref{eq:fhaux}), auxiliary information, through the covariates $\mbf{x}_i$, can be utilized to provide reduction of the total mean squared error (MSE). The term $u_i$ denotes a spatially indexed random effect and, in the traditional model, is assumed to follow an independent normal distribution with unknown variance $\sigma_{u}^{2}$. Importantly, by modeling $\theta_i$ through equation (\ref{eq:fhaux}), the model effectively uses the auxiliary covariate information at location $i$
to draw strength across locations.  Such synthetic estimators make use of this auxiliary information in order to reduce the variance of the estimate of the small area parameter of interest, $\theta_i$, but at the expense of a potential introduction of bias \citep{rao2003small} -- the usual variance/bias tradeoff that is common in statistical inference.

In addition to using covariates to facilitate SAE in the classic FH model, one can also borrow strength across the small areas themselves, making use of the spatial dependence to improve estimates as is commonly done in spatial statistics \citep[e.g., see][]{cressie93, cressiewikle2011}. That is, one considers spatial dependence in $\{u_i\}$, which correspond to geographical areas.
The use of spatial dependence structures in SAE is not new, with models utilizing conditional autoregressive (CAR) spatial structure that is prevalent in the disease mapping literature  \citep[e.g.,][]{leroux1999estimation, macnab2003hierarchical}, which builds upon the classic work of \cite{clayton1987empirical}, \cite{cressie1989spatial}, \cite{mollie1991empirical}, \cite{clayton1992bayesian}, among others. An overview of the theory and application of CAR models can be found in \cite{rue2005gaussian}.  Such models have also been used in the FH context, with spatial structures given by CAR, intrinsic CAR (ICAR) and simultaneous autoregressive (SAR) models \citep[e.g.,][]{cressie1990small, pratesi2008small, gomez2010bayesian, you2011hierarchical}.  The majority of spatial FH models in the literature that utilize the CAR or ICAR structure consider are univariate.

In principle, one can also improve SAE by making use of other survey outcomes that are related to the primary outcome of interest.  Indeed, such multivariate FH models have been developed to account for correlation between the survey estimates of several parameters \citep{fay1987application}. Typically, one can attempt to account for the multivariate dependence either through the sampling error term (i.e., $\{\epsilon_i\}$ in (\ref{eq:fhcore})) or through the latent error term (i.e., $\{u_i\}$ in (\ref{eq:fhaux})). Most of the multivariate models in the literature have been concerned with modeling within-location dependence in the sampling errors \citep[e.g.,][]{fay1987application,huang2004empirical, gonzalez2008analytic,fabrizi2011hierarchical}. In some cases, this sampling error dependence is assumed known {\it a priori} \citep[e.g.,][]{fay1987application,huang2004empirical, gonzalez2008analytic} but this can be estimated in a hierarchical Bayesian framework with priors (e.g., inverse Wishart (IW) priors) on the within-location sampling dependence. More generally, \cite{datta1998multivariate} and  \cite{kubokawa2011parametric}  consider the possibility of dependence at both the sampling and latent error levels.  However, these formulations tend to over-generalize the modeling of the dependence in the latent structure, so that explicit spatial dependence is difficult to estimate due to potential confounding with the dependence in the sampling errors.  Finally, \cite{torabi2011hierarchical} considers a univariate outcome that varies with space and time.  That is, the model includes a separable spatio-temporal dependence structure with a  univariate CAR model on the spatial locations along with temporal dependence that is then necessarily assumed to be the same for all spatial locations.

Given that spatial dependence and multivariate dependence have been shown to improve estimation in FH SAE implementations, it follows that allowing for multivariate spatially dependent error structures in this framework could borrow strength across responses and through residual spatial dependence, thus providing improved estimators in the sense of reduction in MSE.  Further, because the FH model utilizes data on an irregular lattice, a sensible way of constructing dependence within the latent random effects for the multivariate FH model would be to extend the CAR structure that is sometimes used in the univariate FH model to the multivariate case.

The first multivariate CAR model was due to \cite{mardia1988multi}, but this model is very general and can be difficult to implement in practice. Other useful models followed, including \cite{kim2001bivariate}, \cite{gelfand2003proper}, \cite{jin2005generalized}, and \cite{sain2011spatial}. We propose two ways of handling the extension of the CAR structure to the multivariate FH model.  In the first, we consider a simple separable covariance structure that uses a single CAR model and builds multivariate dependence though a Kronecker product with an unstructured within-area covariance matrix (that is assumed to have an inverse Wishart (IW) prior in a Bayesian implementation). In the second, we use a fully multivariate CAR structure.   We note that the model of \cite{sain2011spatial} is nonseparable. However, the restrictive parameterization of the variances in this model makes it undesirable for the current application. Instead, we consider the GMCAR model of \cite{jin2005generalized} to jointly model the multivariate spatial dependence within the latent random effects. Importantly, this GMCAR model contains many multivariate CAR models as special cases, giving it the flexibility to account for a wide variety of spatial correlation structures in a nonseparable model and it is practical to include within a hierarchical latent effect framework.  Thus, this model provides an important extension of the recent interest in CAR and ICAR priors and multivariate dependence in the FH framework by providing natural extensions to FH spatial structure in higher dimensions.  Utilizing the GMCAR and separable spatial priors, we demonstrate, by way of two data analyses, that multivariate spatial priors can be effectively used to reduce both the posterior variance and the MSE of FH model estimates as compared to the traditional multivariate FH methodology.

We begin in Section~ \ref{sec:MCARFH} with a discussion of the proposed multivariate spatial FH methodology.  We provide two simulated examples in Section~ \ref{sec:sim}. Then, to compare to a situation in which we have census values, and consider these values as ``truth,'' we provide a state level analysis.  Although this is not strictly dealing with ``small areas,'' it does illustrate the methodology in a situation where we actually have a proxy for the truth and at a level of geography of great interest by practitioners.  This is followed in Section~ \ref{sec:data} by a county-level SAE application.  We conclude with a brief discussion in Section~ \ref{sec:disc}.

\section{Multivariate Spatial Fay-Herriot Models}\label{sec:MCARFH}

Before defining the multivariate spatial FH models, we introduce here notation for spatial CAR models as used in the spatial statistics literature. Specifically, the aforementioned CAR models are defined by a set of full conditional distributions, as developed in \cite{besag1974spatial} \citep[see also][for a recent overview]{rue2005gaussian}:
\begin{eqnarray}
\label{eq:CAR}
u_i|u_j \sim Gau \left(\sum_{i \sim j} \rho w_{ij} u_j , \tau_i^2 \right),
\end{eqnarray}
where  $Gau(a,b)$ denotes a Gaussian random process that follows a normal distribution with mean $a$ and variance $b$, as is common in spatial statistics.  Further, the notation $i \sim j$ indicates that locations $i$ and $j$ are neighbors (typically, that they share a border), $\rho$ is a spatial dependency parameter, and $w_{ij}$ is an adjacency weight.  For our purposes, we set $w_{ij}=1/w_{i+}$ if locations $i$ and $j$ are neighbors and $0$ otherwise, where $w_{i+}$ is the sum of the neighbors of location $i$. When this parameterization is utilized, $\tau_i^2$ is defined as $\tau^2/w_{i+}$, which guarantees the self-consistency of $\mbf{u} \equiv (u_1,\ldots,u_n)'$, and ensures that a symmetric, nonnegative definite precision matrix results from the conditional specification. The spatial dependency parameter $\rho$ has support on (-1,1) in order to guarantee that the precision matrix is positive definite, resulting in a proper joint distribution of the form
\begin{eqnarray}
\mbf{u} \sim Gau \left(\mbf{0},\tau^{2} (\mbf{D}-\rho \mbf{W})^{-1} \right),
\end{eqnarray}
where we define ${\mbf W}$ to be a matrix with element $(i,j)$ taking the value $1$ if locations $i$ and $j$ are neighbors and $0$ otherwise, and ${\mbf D}$ to be a diagonal matrix with element $(i,i)$ being $w_{i+}$.

\subsection{Multivariate FH Models}

The univariate FH model is extended to the multivariate case by assuming $Y_{ij}$ is a direct survey estimator for the $j$th outcome ($j=1,\ldots,m$) at location $i=1,\ldots,n$. Then, a natural multivariate extension of (\ref{eq:fhcore}) and (\ref{eq:fhaux}) is given by
\begin{eqnarray}
\label{eq:mvfhcore}
Y_{ij}&=&\theta_{ij}+\epsilon_{ij}, \\
\label{eq:mvfhaux}
\theta_{ij} &=&\mbf{x}_{ij}' \mbv{\beta}_j +u_{ij},
\end{eqnarray}
where the parameters are defined as above, but are now indexed by the outcome, $j$.  Recall that the structure of the FH model in (\ref{eq:fhcore}) typically assumes a known sampling variance $\sigma_i^2$ at location $i$. Generalizing to the multivariate case, we could analogously assume a known sampling variance-covariance matrix  $\mbox{cov}({\mbv \epsilon}_i) \equiv {\mbf \Sigma}_i$ for location $i$, where ${\mbv \epsilon}_i = (\epsilon_{i1},\ldots,\epsilon_{im})'$ . It is typically assumed that there is independence in the sampling errors between locations, and so $\mbv{\epsilon}\equiv(\mbv{\epsilon}'_1,\ldots, \mbv{\epsilon}'_n)' \sim N(\mbf{0}, \mbf{\Sigma})$, where $\mbf{\Sigma} = \hbox{diag}(\mbv{\Sigma}_1,\ldots,\mbv{\Sigma}_n)$.  As mentioned in Section \ref{sec:Intro}, one could add dependence between locations in the sampling errors so that this covariance structure would not be block diagonal, but information surrounding the dependence in sampling errors between regions is typically not available. For this reason, we prefer to model such dependence in the latent error structure.

Analogous to the sampling errors, we define the latent error variance-covariance matrix $\mbox{cov}({\mbf u}_i) \equiv {\mbf \Sigma}_{u,i}$ for location $i$, where ${\mbf u}_i = (u_{i1},\ldots,u_{im})'$. In this case, we do not necessarily assume independence between spatial areas, and so we seek to model the joint $(m \times n)$-dimensional variance-covariance matrix of ${\mbf u} = ({\mbf u}'_1,\ldots,{\mbf u}'_n)'$, which we denote ${\mbf \Sigma}_u$.  For realistic sizes of $m$ and $n$, we will be unable to estimate an unstructured ${\mbf \Sigma}_u$ and thus, must find reasonable parameterizations.  \cite{datta1998multivariate} consider a useful, but fairly simple, structure given by ${\mbf \Sigma}_u = \mbf{I}_{n} \otimes \mbv{\Sigma}_{IW}$, where $\otimes$ denotes a Kronecker product and ${\mbf \Sigma}_{IW}$ is an $m$-dimensional unstructured covariance matrix between outcomes that is given an inverse-Wishart (IW) prior in their Bayesian implementation.  We consider this to be the ``state-of-the-art" latent dependence structure for multivariate FH models and refer to it as the ``IW-FH'' model.

Most multivariate FH models developed subsequent to \cite{datta1998multivariate} use a similar structure, accounting for within location correlation, but ignoring an explicit formulation for spatial structure that may be present in the latent spatially-referenced vector, $\mbf{u}$.  We propose to model the latent spatial structure in $\mbf{u}$ explicitly, in order to achieve a reduction in MSE for small area estimates. We describe two such structures below.

\subsection{Separable Multivariate Spatial FH Model}\label{sec:sepFHmod}

The simplest potentially realistic dependence structure in multivariate spatial models is a separable model that is a fairly simple extension of the IW-FH model described above. In the FH context of interest here, this implies considering a common spatial dependence structure that is appropriate for all outcomes, but where such outcomes share a common dependence within each spatial region. That is, we consider
$${\mbf u} \sim Gau({\mbf 0}, {\mbf \Sigma}_s \otimes {\mbf \Sigma}_o),$$
where ${\mbf \Sigma}_s$ denotes an  $n$-dimensional spatial covariance matrix and ${\mbf \Sigma}_o$ denotes an $m$-dimensional outcome covariance matrix. We refer to this as the ``Separable-FH'' model.  Even in this simplified separable framework, there are typically too many parameters to estimate an unstructured form for ${\mbf \Sigma}_s$, but for most applications, $m$ is fairly small and so it may be possible to estimate an unstructured ${\mbf \Sigma}_o$.  We thus propose a fairly simple, but potentially useful, structure in which ${\mbf \Sigma}_s$ is parameterized by the aforementioned CAR spatial dependence structure and ${\mbf \Sigma}_o$ is given an IW prior (in a Bayesian implementation). In this case, the latent random effects vector has distribution
\[\mbf{u} \sim N({\mbf 0},(\mbf{I}-\rho \mbf{W})^{-1} \otimes \mbv{\Sigma}_{IW}),\]
where ${\mbf \Sigma}_{IW}$ is given an IW prior and we would also assign a prior to $\rho$  (see below). Note, the parameter $\tau^2$ is not included in the CAR structure in this model due to identifiability issues. That is, because each element of $\mbv{\Sigma}_{IW}$ is estimated, $\tau^2$ becomes a multiplicative constant in the covariance matrix, and thus, it cannot be uniquely estimated.  In the case where all the off-diagonal elements of ${\mbf \Sigma}_{IW}$ are zero, the model reverts to the case of independent CAR models that share a common spatial dependence parameter.

Despite the seemingly limited nature of such a separable model, this model is actually quite flexible.  The IW structure allows a different conditional variance to be used for the spatial structure of each outcome, but this structure assumes that all areas have a common spatial dependency parameter, $\rho$.  This assumption would be reasonable if one had survey outcomes that are demographically related, but may not be realistic when the outcome measures are quite different. In the ICAR framework, $\rho$ is fixed at a value of 1, and in that case, there is no limitation in this aspect of the specification.  Perhaps the primary advantage of this separable formulation is that the model scales up to $m>2$ quite naturally by increasing the dimensionailty of $\mbv{\Sigma}_{IW}$ without increasing the number of parameters in the spatial dependence covariance matrix.

\subsection{The GMCAR-FH Model}\label{sec:GMCARFHmod}
Although the separable model described in Section \ref{sec:sepFHmod} can be quite useful, there may be situations for which sampling outcomes have a more complex multivariate spatial structure. In particular, we may require that the spatial structure be different for different outcomes, and that there should be more complicated cross-dependence between spatial location and outcome variable. This more complicated structure can be accommodated fairly easily in the latent effects structure. As summarized in \cite{cressiewikle2011}, there are several approaches to modeling multivariate spatial structure, but the one that has gained the most favor in recent years is the conditional approach first detailed in a hierarchical framework by \cite{royle1999hierarchical}.  The GMCAR of \cite{jin2005generalized} extends this concept of conditioning to the CAR model framework.

To reduce the notational complexity, we present the GMCAR formulation in terms of the bivariate spatial processes $\mbf{u}_1$ and $\mbf{u}_2$, as defined previously, and assume that
\[\mbf{u}_1|\mbf{u}_2 \sim N(\mbf{A} \mbf{u}_2, \tau_1^2 (\mbf{D}- \rho_1 \mbf{W})^{-1}),\]
 and
\[\mbf{u}_2  \sim N(\mbf{0}, \tau_2^2(\mbf{D}-\rho_2 \mbf{W})^{-1}),\]
where the matrix ${\mbf A}$ is parameterized in terms of two parameters, $\eta_0$ and $\eta_1$, such that $\mbf{A}=\eta_0 \mbf{I} +\eta_1 \mbf{W}$.  Thus, the conditional distribution of ${\mbf u}_1$ given ${\mbf u}_2$ is a CAR structure with mean given by ${\mbf A}{\mbf u}_2$, and the marginal distribution of ${\mbf u}_2$ is also a CAR model, but with zero mean.  Both of these distributions have unique spatial dependence parameters given by $\rho_1$ and  $\rho_2$. One can easily show that the joint distribution of ${\mbf u} = ({\mbf u}'_1, {\mbf u}'_2)'$ then follows a multivariate Gaussian process with mean ${\mbf 0}$ and covariance matrix
\[  {\mbf \Sigma}_u =  \left( \begin{array}{cc}
\tau_1^2 (\mbf{D}-\rho_1 \mbf{W})^{-1}+ \mbf{A}' \tau_2^2 (\mbf{D}-\rho_2 \mbf{W})^{-1} \mbf{A} & \mbf{A}' \tau_2^2 (\mbf{D}-\rho_2 \mbf{W})^{-1} \\
 \tau_2^2 (\mbf{D}-\rho_2 \mbf{W})^{-1} \mbf{A} & \tau_2^2 (\mbf{D}-\rho_2 \mbf{W})^{-1} \\
 \end{array} \right). \]
The advantage of this conditional approach to multivariate spatial modeling is that one is guaranteed a valid joint covariance structure so long as the conditional and marginal models are valid.  In this case, they are valid given that the CAR models are formulated as stated in the introduction of Section \ref{sec:MCARFH}.  We refer to this model as the ``GMCAR-FH'' model.

It is important to note that the GMCAR formulation directly incorporates two sources of correlation into the latent spatial effects. First, there is the direct consideration of the spatial structure in the lattice for each of $\mbf{u}_1$ and $\mbf{u}_2$ due to the CAR models. Second, the model allows correlation between the spatial random effects for each outcome through the ${\mbf A}$ matrix.  Specifically, the parameter $\eta_0$ allows for cross-correlation between the latent effects within the same areal unit, and $\eta_1$ allows for cross-correlation depending on the adjacent areas.

We note that the GMCAR structure contains many multivariate CAR models as special cases, {including the models of \cite{kim2001bivariate}, \cite{gelfand2003proper}, and two independent CAR models}, as outlined in \cite{jin2005generalized}. In particular, with $\eta_0=\eta_1=0$, the model reverts to the independent CAR model case.  This is often a case worth considering for the FH model, and it is ideal to have the flexibility for this specification, depending on the estimates one obtains from $\eta_0$ and $\eta_1$ (which, clearly would be near zero if the independent CAR models were more appropriate).  Finally, although the description of the GMCAR model presented here considers only two processes, it is possible to extend the model to $m > 2$ with added notational and computational overhead.

\section{Simulated Examples}\label{sec:sim}

To gain insight into the GMCAR-FH and Separable-FH model performance relative to the IW-FH model, we consider two simulated examples. Both simulations are designed from the perspective of the data analysis provided in Section~ \ref{sec:data}.

\subsection{Simulated Example One}
In order to assess model performance at small geographies where the true underlying values are known, we provide a simulated example using the Missouri county lattice structure (see Figure~ \ref{Fi:VAR}). We consider a bivariate outcome, generated from a GMCAR-FH structure, where the survey variances are the same as those from the data analysis in Section~ \ref{sec:data}. We utilize median household income (divided by 1000) as reported by the ACS as auxiliary information for both outcomes.

The bivariate outcome is generated according to the GMCAR-FH model of Section~\ref{sec:data}, with all parameters used for generating data set to the median values of the GMCAR-FH posterior distributions in that analysis.  Total survey variances, assumed known, are also set to be equivalent to those in the data analysis of Section~\ref{sec:data}.  Of particular interest in this analysis are the values of $\eta_0$ and $\eta_1$, which determine the cross-correlation structure. For the simulated data generation, $\eta_0$ is set to 0.26, and $\eta_1$ is set to -0.04. This results in a strong within-unit correlation and a relatively weak non-separable structure.

Model 1 uses an IW prior (see Section \ref{sec:Intro}). All the priors selected were deliberately chosen to be vague and, thus, impart little impact on our analysis. These priors are vague enough to be suitable across a wide range of analyses, and are used for all analyses presented here. We recommend $\mbox{Unif}(0,1)$ priors on the spatial parameters rather than $\mbox{Unif}(-1,1)$ priors due to the work of \cite{wall2004close}, which demonstrates that CAR models possess a variety of undesirable properties for spatial datasets with negative spatial autocorrelation. The specific prior utilized is $\mbox{IW}({\mbf I}_2,2)$, which is a vague independence prior. Model 2 is the proposed Separable-FH model, where we assume an $\mbox{IW}({\mbf I}_2,2)$ prior or ${\mbf \Sigma}_{IW}$ and a $\mbox{Unif}(0,1)$ prior for $\rho$.  Model 3 is the proposed GMCAR-FH prior, where we place relatively vague $\mbox{Unif}(0.001,100)$ priors on $\tau_1$ and $\tau_2$, $\mbox{Unif}(0,1)$ priors on $\rho_1$ and $\rho_2$, and $N(0,10^2)$ priors on $\eta_0$ and $\eta_1$.

Model comparisons are then based on posterior MSE, specifically in terms of $\mbv{\theta}_1$ and $\mbv{\theta}_2$.  These results are summarized in Table~\ref{TA:Sim1}. In this example, both the GMCAR-FH and the Separable-FH spatial models perform better than the IW-FH model in terms of MSE. The GMCAR-FH outperforms the Separable model in terms of MSE for outcome one, with both models performing similarly for outcome two. By location, the GMCAR-FH outperforms the IW-FH in terms of MSE in 70\% of locations for outcome one and 62\% of locations for outcome two, with the Separable-FH outperfoming the IW-FH model in 69\% and 65\% of locations, respectively. Additionally, the GMCAR-FH model outperforms the Separable-FH model in 52\% of locations for outcome one and the Separable-FH model outperforms the GMCAR-FH model in 51\% of locations for outcome two.

The GMCAR-FH recovers the parameters well. However, in this dataset, the true value of $\eta_1$ is -0.04, which is near enough to zero that it does not generate much non-separable structure in the model. This leads to similar performance between the GMCAR-FH and Separable-FH models in terms of MSE.

\bigskip

\begin{table}[h]
\centering
\begin{tabular}{|c|c|c|c|c|} \hline
Model & MSE1 & MSE2 \\ \hline \hline
Model 1: IW  & 0.07595 & 0.05640\\ \hline
Model 2: Separable &  0.06822& \textbf{0.05227}\\ \hline
Model 3: GMCAR & \textbf{0.06801} & 0.05230\\ \hline
\end{tabular}
\parbox{5.0in}{
\caption{The posterior MSEs for $\mbv{\theta}_1$ and $\mbv{\theta}_2$ for the IW-FH, GMCAR-FH and Separable-FH models for the Missouri county lattice simulated data described in Section 3.1. Note that MSE1 corresponds to outcome one and MSE2 corresponds to outcome two.}
\label{TA:Sim1}}
\end{table}

\subsection{Simulated Example Two}\label{sec:sim2}
In this simulated example, we utilize the exact same data generation structure as in the first simulated example, but we increase the cross correlation parameter $\eta_1$ to 0.21 in order to investigate the effects of strong cross correlation on our model. All three models were run on this new simulated data with the same prior specifications as the previous simulation.

\bigskip

\begin{table}[h]
\centering
\begin{tabular}{|c|c|c|c|c|} \hline
Model & MSE1 & MSE2 \\ \hline \hline
Model 1: IW & 0.0822 & 0.0437\\ \hline
Model 2: Separable &  0.0756 & 0.0405\\ \hline
Model 3: GMCAR &  \textbf{0.0734} & \textbf{0.0402}\\ \hline
\end{tabular}
\parbox{5.0in}{
\caption{The posterior MSEs for $\mbv{\theta}_1$ and $\mbv{\theta}_2$ for the IW-FH, GMCAR-FH and Separable-FH models for the Missouri county lattice simulated data described in Section 3.2. Note MSE1 corresponds to outcome one and MSE2 corresponds to outcome two.}
\label{TA:Sim2}}
\end{table}

The results from this simulation, summarized in Table~\ref{TA:Sim2}, clearly demonstrate an improvement in terms of MSE of the Separable-FH and GMCAR-FH models over the IW-FH model, with the GMCAR-FH providing lower MSE for the estimates of both outcomes.  The GMCAR-FH and Separable-FH models both outperform the IW-FH model in 70\% of locations in terms of MSE for both outcomes. The GMCAR-FH model additionally outperforms the Separable-FH model in 59\% of locations in terms of MSE for outcome one and 48\% of locations for outcome two. However, as is clear from Table \ref{TA:Sim2}, it performs better in terms of overall MSE.

\section{Example: State Level Estimation for Validation}\label{sec:state}

We consider the model on U.S. state-level data for which decennial census data are available. We work at the state level as these data typically exhibit spatial dependence and provide  a way to test various multivariate FH models relative to a ``known'' quantity (e.g., census data).  In particular, we predict the percentage of vacant residences and the percent of renter-occupied units in each of the contiguous 48 states and in Washington D.C. for 2010 based on American Community Survey (ACS) one-year estimates.  The 2010 decennial Census values for the same question differ in terms of residency rules (i.e., see www.census.gov).   However, we do not expect that the variables of interest here will be greatly affected by these residency rule differences and so we consider the census value as ``true" when analyzing the MSE of the IW-FH, Separable-FH, and GMCAR-FH models.  Areas with increased numbers of vacant locations are thought to be associated with economic recessions, as are areas with large percentages of renter occupied units.  Thus, we consider median household income as an auxiliary variable for both response outcomes.

In order to satisfy the normality constraint of the models considered here, the percentage of vacant properties is transformed by multiplying by 100 and then applying a log transform.  Due to the requirement in these models that the sampling errors, $\epsilon_i$, follow a normal distribution, we use the Delta method and ACS-reported margins of error (MOEs) to obtain the survey variance of the transformed variables.  We assume the errors are uncorrelated at the survey level when conditioned on the latent process as described previously.

Exploratory data analysis, in the form of linear regression, demonstrates that the auxiliary information is positively associated with the respective outcomes  ($\mbox{$p$-value} <0.05$). Further, the residuals have latent spatial structure based on a Moran's I test with a first order weight matrix ( $\mbox{$p$-value} <0.01$ for both regressions). The residuals are strongly correlated  (a test that the population correlation coefficient is non-zero yielded a $\mbox{$p$-value} =0.07$), which suggests that these are data that many researchers would find suitable for the IW-FH model. However, it is also the case that the spatial pattern in the residuals is strong, and thus, should be accounted for when modeling these data.

We perform a leave-one-out experiment where each of the 49 locations is left out of the model one at a time, and a Markov chain Monte Carlo (MCMC) algorithm is run for 15,000 iterations for each. We discard the first 1,000 iterations from each location as burn-in. Convergence of the MCMC algorithm was assessed through visual inspection of the sample chains, with no evidence of nonconvergence detected.

The mean squared error (MSE) for both outcomes at each location is then computed assuming the 2010 decennial census values to be the truth; these results are shown in Table \ref{TA:census}. In this example, the GMCAR-FH outperforms both Model 1 and Model 2, with the GMCAR-FH yielding a 35\% reduction in posterior predictive MSE for the percentage of vacant houses in the state and a 75\% reduction in posterior predictive MSE for the percentage of renter occupied residences relative to the standard IW-FH model.   As expected, the Separable-FH model performed better than the IW-FH model but not as well as the GMCAR-FH. The added spatial structure is clearly important, but the separable structure does not offer the flexibility of the GMCAR-FH model for this dataset.

\begin{table}[h]
\centering
\begin{tabular}{|c|c|c|} \hline
Model & MSE1 & MSE2 \\ \hline \hline
Model 1: IW & 0.1280 & 0.0218 \\ \hline
Model 2: Separable & 0.0974 & 0.0123 \\ \hline
Model 3: GMCAR & \textbf{0.0883} & \textbf{0.0055} \\ \hline
\end{tabular}
\parbox{5.0in}{
\caption{The posterior MSEs for the three FH Models applied to the state-level data. MSE1 is the posterior predictive MSE for the transformed percentage of vacant units, and MSE2 is the posterior predictive MSE for the transformed percentage of families below the poverty level.}}
\label{TA:census}
\end{table}

Additionally, the relative improvement of the posterior predictive MSE of the GMCAR-FH model over the baseline IW-FH model is plotted as a function of location in Figure \ref{Fi:MSE}. The actual proportions are computed using the relative MSE formula given by
\begin{equation}
\nonumber \frac{\mbox{MSE}_{\mbox{\tiny{IW}}}(i)-\mbox{MSE}_{\mbox{\tiny{GMCAR}}}(i)}{\frac{1}{2}\mbox{MSE}_{\mbox{\tiny{IW}}}(i)
+\frac{1}{2}\mbox{MSE}_{\mbox{\tiny{GMCAR}}}(i)},
\end{equation}
where we define $\mbox{MSE}_{\mbox{\tiny{GMCAR}}}(i)$ to be the MSE for the GMCAR-FH model $i$ and $\mbox{MSE}_{\mbox{\tiny{IW}}}(i)$ similarly for the IW-FH model.
We see that the GMCAR-FH outperforms the IW-FH in all but four locations with respect to the prediction of vacant houses, and outperforms the IW-FH in every location with respect to the prediction of renter occupied residences.

\section{Example: County-Level Small Area Estimation}\label{sec:data}
To examine the model at smaller levels of geography, we consider county-level data in the state of Missouri.  We use ACS five year period estimates of the percentage of families below the poverty level as well as the percentage of unemployed individuals in each county between the years of 2006 and 2010.  Log transforms were used to obtain normally distributed outcomes, and the Delta method was used to compute the transformed survey variances, which are computed based on the MOEs reported by the ACS and assumed uncorrelated.  We consider the ACS variable median household income as auxiliary information for both outcomes.

The auxiliary information is apparently an important predictor of both outcomes based on an exploratory linear regression ($\mbox{$p$-value} <0.01$). Further, Moran's I tests with a first order weight matrix demonstrate latent spatial structure in both sets of residuals $(\mbox{$p$-value} <0.01)$ and both sets of residuals are correlated based on a Pearson correlation test $(\mbox{$p$-value} <0.05)$. Shapiro-Wilk tests did not reject the assumption of normality for both sets of residuals $(\mbox{$p$-value} >0.05)$. The three models considered in the county-level analysis were run with the same prior specifications, as given in Section \ref{sec:state}.

We compare the three FH models in terms of a leave-one-out mean squared prediction error (MSPE) experiment, where we compare our model predictions to the observed value at the left-out location.  Each model is run for 11,000 iterations, with the first 1,000 iterations discarded for burn-in. Convergence of the MCMC algorithm is assessed through visual inspection of the trace plots of the sample chains. No evidence of nonconvergence was detected. The results of the experiment can be found in Table \ref{TA:VAR}.

\begin{table}[h]
\centering
\begin{tabular}{|c|c|c|} \hline
Model & MSPE1 & MSPE2 \\ \hline \hline
Model 1: IW & 0.1367 & 0.0804 \\ \hline
Model 2: Separable  & \textbf{0.1197} & 0.0686  \\ \hline
Model 3: GMCAR &  0.1205 & \textbf{0.0684} \\ \hline
\end{tabular}
\parbox{5.0in}{
\caption{The leave-one-out MSPEs for the county level example for the three FH models. MSPE1 is the average posterior MSPE for the transformed transformed percentage of families below the poverty level, and MSPE2 is the average posterior MSPE for the percentage of unemployed individuals in each county.}
\label{TA:VAR}}
\end{table}
The Separable-FH model performs similarly to the GMCAR-FH model for this dataset. As demonstrated in the simulated examples, this is due to the near-zero value of $\eta_1$ in this dataset (i.e., posterior median $= -0.04$) and similar distributions for $\rho_1$ and $\rho_2$, which suggests that there is little nonseparable structure in this particular dataset. However, the results clearly demonstrate the importance of accounting for the multivariate spatial dependence in these data, with both models outperforming the the IW-FH for both outcomes. Figure \ref{Fi:VAR} shows the relative MSPE reduction for the GMCAR-FH model over the IW-FH model by location. We note that the GMCAR-FH model outperforms the IW-FH model in terms of MSPE in 79\% of locations for percentage of families below the poverty level and 80\% of locations for percentage of unemployed individuals, while the Separable-FH model outperforms the IW-FH in 78\% and 79\% of locations respectively.

\section{Discussion}\label{sec:disc}
In addition to MSE reduction via auxiliary covariate information, FH models can be improved by borrowing strength across spatial location as well as by the addition of multivariate relationships between outcomes. In this regard, we present two specifications for latent dependence that can be utilized to effectively incorporate the explicit CAR spatial structure within a multivariate FH framework. We have demonstrated that the proposed GMCAR-FH model shows a substantial reduction in MSE when compared to equivalent decennial census values at the state level.  In addition, for county-level SAE, we demonstrate that both the proposed GMCAR-FH and Separable-FH models show substantial reduction in MSPE over a baseline IW-FH model.  Exploratory analysis for both datasets suggested that there was correlation between both sets of residuals, which suggests that the IW-FH methodology would not be unreasonable. However, in both cases where there was additional spatial structure in the residuals, and thus, it is reasonable that our multivariate CAR structure provides improvement in estimation.

It is important to note that although the GMCAR-FH model is sometimes preferable to the Separable-FH model and the IW-FH model, it comes with increased overhead as the number of outcomes increase beyond two.  In that case, the Separable-FH model provides a more computationally convenient alternative, and the simulation results presented here suggest that it its performance with regards to MSE is typically better than the standard IW-FH model.

Because it is common that the ACS and other surveys exhibit outcomes are that spatially correlated, and it is unlikely that one will have access to all of the necessary auxiliary information to capture all of the underlying spatial structure in the residuals of the FH regressions. As such, this work provides two important classes of models for SAE in the context of federal surveys. The work extends the current thrust of explicitly accounting for spatial correlation in the FH structure to the multivariate case, which can assist in the estimation of multivariate outcomes. Future work will consider realistic spatio-temporal structures for latent effects in both the univariate and multivariate settings.

\section*{Acknowledgments}
This research was partially supported by the U.S. National Science Foundation (NSF) and the U.S. Census Bureau under NSF grant SES-1132031, funded through the NSF-Census Research Network (NCRN) program.

\clearpage\pagebreak\newpage
\bibliographystyle{apa}

redpajama_set_name: RedPajamaArXiv


defense: (sports) the team that is trying to prevent the other team from scoring; "his teams are always good on defense"
defense: an organization of defenders that provides resistance against attack; "he joined the defense against invasion"
refutation: the speech act of answering an attack on your assertions; "his refutation of the charges was short and persuasive"; "in defense he said the other man started it"
defense: the justification for some act or belief; "he offered a persuasive defense of the theory"
Defense (aka Mekelakeya) is an Ethiopian football club, in the city of Addis Abeba. They play in the Ethiopian Premier League, the top level of professional football in Ethiopia.
Within the sport of association football, a defender is an outfield player whose primary role is to prevent the opposition from attacking.
Defense (or defence) has several uses in the sphere of military application.
The Defence was an American Revolutionary War ship that was part of the Penobscot Expedition. The ship burned to the waterline and sank. The location of the wreck was discovered in 1972 by the Maine Maritime Academy and the Massachusetts Institute of Technology. The wreck was studied later.
(Defences) The statement by way of defence lodged by the defender, being the party against whom a civil action is brought. The plural signifies, presumably, that the defender may rely on more legal answers than one.
(Defences) Are the walls around a player's center of power, they help the defender by applying a penalty to the attacker's strength the bigger the walls the bigger the penalty while the more damaged walls are the smaller it is. They also help increasing recruiting if they are manned.
(Defences) a document lodged by the Defender in the Court of Session or the Sheriff Court in response to the Initial Writ or Summons.
The accused person's case and the lawyers who represent them.
Reply to Particulars or Statement of Claim.
A defendant or accused person's reason(s) why a plaintiff or a prosecutor does not have a valid case.
A reply, rebuttal or answer to an action or application. A Respondent's defence may attack a Claimant's claim on the truth of the facts set out by the Claimant, the law applicable to the case, or both.
(1) Arguments put to a court to show that a criminal charge or a civil claim has not been proved. (2) The lawyers who try to persuade the court that an accused person is not guilty or that a civil claim has not been proved.


text:
Q: Cmake is not able to find Python-libraries Getting this error:
sudo: unable to resolve host coderw@ll
-- Could NOT find PythonLibs (missing:  PYTHON_LIBRARIES PYTHON_INCLUDE_DIRS)
CMake Error at /usr/share/cmake-2.8/Modules/FindPackageHandleStandardArgs.cmake:108
(message):
Could NOT find PythonInterp (missing: PYTHON_EXECUTABLE)
Call Stack (most recent call first):
/usr/share/cmake-2.8/Modules/FindPackageHandleStandardArgs.cmake:315
(_FPHSA_FAILURE_MESSAGE)
/usr/share/cmake-2.8/Modules/FindPythonInterp.cmake:139
(FIND_PACKAGE_HANDLE_STANDARD_ARGS)
Code/cmake/Modules/FindNumPy.cmake:10 (find_package)
CMakeLists.txt:114 (find_package)

-- Configuring incomplete, errors occurred!
See also "/home/coderwall/Desktop/rdkit/build/CMakeFiles/CMakeOutput.log".
See also "/home/coderwall/Desktop/rdkit/build/CMakeFiles/CMakeError.log".

I have already installed:

*

*sudo apt-get install python-dev

*Environment variable are already set as follow:
PYTHON_INCLUDE_DIRS=/usr/include/python2.7
PYTHON_LIBRARIES=/usr/lib/python2.7/config/libpython2.7.so

Location of python.h : /usr/lib/include/python2.7/python.h
Location of python libs: /usr/lib/python2.7/
How to solve this?

A: You can fix the errors by appending to the cmake command the -DPYTHON_LIBRARY and -DPYTHON_INCLUDE_DIR flags filled with the respective folders.
Thus, the trick is to fill those parameters with the returned information from the python interpreter, which is the most reliable. This may work independently of your python location/version (also for Anaconda users):
$ cmake .. \
-DPYTHON_INCLUDE_DIR=$(python -c "import sysconfig; print(sysconfig.get_path('include'))")  \
-DPYTHON_LIBRARY=$(python -c "import sysconfig; print(sysconfig.get_config_var('LIBDIR'))")

If the version of python that you want to link against cmake is Python3.X and the default python symlink points to Python2.X, python3 -c ... can be used instead of python -c ....
In case that the error persists, you may need to update the cmake to a higher version as stated by @pdpcosta and repeat the process again.

A: This problem can also happen in Windows. Cmake looks into the registry and sometimes python values are not set. For those with similar problem:
http://ericsilva.org/2012/10/11/restoring-your-python-registry-in-windows/
Just create a .reg file to set the necessary keys and edit accordingly to match your setup.
Windows Registry Editor Version 5.00

[HKEY_CURRENT_USER\Software\Python]

[HKEY_CURRENT_USER\Software\Python\Pythoncore]

[HKEY_CURRENT_USER\Software\Python\Pythoncore\2.6]

[HKEY_CURRENT_USER\Software\Python\Pythoncore\2.6\InstallPath]
@="C:\\python26"

[HKEY_CURRENT_USER\Software\Python\Pythoncore\2.6\PythonPath]
@="C:\\python26;C:\\python26\\Lib\\;C:\\python26\\DLLs\\"

[HKEY_CURRENT_USER\Software\Python\Pythoncore\2.7]

[HKEY_CURRENT_USER\Software\Python\Pythoncore\2.7\InstallPath]
@="C:\\python27"

[HKEY_CURRENT_USER\Software\Python\Pythoncore\2.7\PythonPath]
@="C:\\python27;C:\\python27\\Lib\\;C:\\python27\\DLLs\\"

A: For me this is helpful:
# if using python2
apt-get install python-dev

# if using python3
apt-get install python3-dev

A: I hit the same issue,and discovered the error message gives misleading variable names. Try setting the following (singular instead of plural):
PYTHON_INCLUDE_DIR=/usr/include/python2.7
PYTHON_LIBRARY=/usr/lib/python2.7/config/libpython2.7.so

The (plural) variables you see error messages about are values that the PythonLibs sets up when it is initialised correctly.

A: Note that if you are using cMake version 3.12 or later, variable PythonInterp and PythonLibs has been changed into Python.
So we use:
find_package(Python ${PY_VERSION} REQUIRED)
instead of:
find_package(PythonInterp ${PY_VERSION} REQUIRED)
find_package(PythonLibs ${PY_VERSION} REQUIRED)
see https://cmake.org/cmake/help/v3.12/module/FindPython.html for details.

A: I had upgraded to python3.8 on my system and had an incomplete install. Managed to fix it by installing the rest of the 3.8 packages:
sudo apt-get install python3.8 python3.8-dev python3.8-distutils python3.8-venv

A: Even after adding -DPYTHON_INCLUDE_DIR and -DPYTHON_LIBRARY as suggested above, I was still facing the error Could NOT find PythonInterp. What solved it was adding -DPYTHON_EXECUTABLE:FILEPATH= to cmake as suggested in https://github.com/pybind/pybind11/issues/99#issuecomment-182071479:
cmake .. \
-DPYTHON_INCLUDE_DIR=$(python -c "from distutils.sysconfig import get_python_inc; print(get_python_inc())")  \
-DPYTHON_LIBRARY=$(python -c "import distutils.sysconfig as sysconfig; print(sysconfig.get_config_var('LIBDIR'))") \
-DPYTHON_EXECUTABLE:FILEPATH=`which python`

A: I was facing this problem while trying to compile OpenCV 3 on a Xubuntu 14.04 Thrusty Tahr system.
With all the dev packages of Python installed, the configuration process was always returning the message:
Could NOT found PythonInterp: /usr/bin/python2.7 (found suitable version "2.7.6", minimum required is "2.7")
Could NOT find PythonLibs (missing: PYTHON_INCLUDE_DIRS) (found suitable exact version "2.7.6")
Found PythonInterp: /usr/bin/python3.4 (found suitable version "3.4", minimum required is "3.4")
Could NOT find PythonLibs (missing: PYTHON_LIBRARIES) (Required is exact version "3.4.0")

The CMake version available on Thrusty Tahr repositories is 2.8.
Some posts inspired me to upgrade CMake.
I've added a PPA CMake repository which installs CMake version 3.2.
After the upgrade everything ran smoothly and the compilation was successful.

A: Some last version of Ubuntu installs Python 3.4 by default and the CMake version from Ubuntu (2.8) only searches up to Python 3.3.
Try to add set(Python_ADDITIONAL_VERSIONS 3.4) before the find_package statement.
Remember to clean CMakeCache.txt too.

A: Paste this into your CMakeLists.txt:
# find python
execute_process(COMMAND python-config --prefix OUTPUT_VARIABLE PYTHON_SEARCH_PATH)
string(REGEX REPLACE "\n$" "" PYTHON_SEARCH_PATH "${PYTHON_SEARCH_PATH}")
file(GLOB_RECURSE PYTHON_DY_LIBS ${PYTHON_SEARCH_PATH}/lib/libpython*.dylib ${PYTHON_SEARCH_PATH}/lib/libpython*.so)
if (PYTHON_DY_LIBS)
    list(GET PYTHON_DY_LIBS 0 PYTHON_LIBRARY)
    message("-- Find shared libpython: ${PYTHON_LIBRARY}")
else()
    message(WARNING "Cannot find shared libpython, try find_package")
endif()

find_package(PythonInterp)
find_package(PythonLibs ${PYTHON_VERSION_STRING} EXACT)

A: In case that might help, I found a workaround for a similar problem, looking at the cmake doc :
https://cmake.org/cmake/help/v3.0/module/FindPythonLibs.html
You must set two env vars for cmake to find coherent versions.
Unfortunately this is not a generic solution...
cmake -DPYTHON_LIBRARY=${HOME}/.pyenv/versions/3.8.0/lib/libpython3.8.a -DPYTHON_INCLUDE_DIR=${HOME}/.pyenv/versions/3.8.0/include/python3.8/ cern_root/

A: In Python 3.2 and onward distutils.sysconfig is deprecated in favor of sysconfig.
To get all the variable names in data structure and inspect the situation we can use get_paths function
import sysconfig
sysconfig.get_paths()

which will return us a dict with all the relevant variable names as keys, and corresponding paths as values.
When we know the key we can get the value dynamically,
>>> sysconfig.get_path("include")
'C:\\Program Files\\Python310\\Include'

However, the most convenient feature of sysutils for this situation is that it can list all the variables at once from the command-prompt by invoking python -m sysconfig:
$ python -m sysconfig

Platform: "macosx-10.4-i386"
Python version: "3.2"
Current installation scheme: "posix_prefix"

Paths:
        data = "/usr/local"
        include = "/Users/tarek/Dev/svn.python.org/py3k/Include"
        platinclude = "."
        platlib = "/usr/local/lib/python3.2/site-packages"
        platstdlib = "/usr/local/lib/python3.2"
        purelib = "/usr/local/lib/python3.2/site-packages"
        scripts = "/usr/local/bin"
        stdlib = "/usr/local/lib/python3.2"

Variables:
        AC_APPLE_UNIVERSAL_BUILD = "0"
        AIX_GENUINE_CPLUSPLUS = "0"
        AR = "ar"
        ARFLAGS = "rc"
        ...

A: Maybe below command line works for you if all of above methods didn't work.
sudo apt-get install cython cython3

A: On Ubuntu 20 at least, since Python 2.7 is deprecated, you can:
sudo apt install python2.7-dev

And then PYTHON_INCLUDE_DIR can be set to /usr/include/python2.7

redpajama_set_name: RedPajamaStackExchange


As a DXF file is an unstable file, data compatibility is not perfect.Reading data might be imperfect depending on CAD software you use. The downloaded file is a self-decompressing file. Double-click on it, and the DXF file will be unfolded. Pro-face has confirmed that it's possible to read the DXF file above via the CAD software below.


text:
Cygnus falconeri — вид ископаемых птиц из рода лебедей семейства утиных. Видовое название дано в честь шотландского ботаника, палеонтолога и геолога Хью Фальконера (1808—1865).

Описание
Систематически находится ближе всего к лебедю-шипуну, чем к другим видам лебедей. Обитал в среднем плейстоцене на островах Мальта и Сицилия. Ископаемые остатки известны из раннего плиоцена (занклский ярус), из слоёв возрастом около 5,3 миллиона лет. Подобно сицилийским карликовым слонам (Elephas falconeri) и другим средиземноморским островным эндемикам, этот вид, вероятно, оказался в изоляции на островах, когда уровень Средиземного моря вновь повысился около 5,3 миллиона лет назад.

Изучение окаменелостей позволило выяснить, что размеры этого лебедя превышали размеры современного лебедя-шипуна на одну треть. Таким образом, длина его тела от кончика клюва до хвоста составляла около 190—210 см (у лебедя-шипуна 145—160 см) при массе, превышающей 16 кг. Этот вид лебедей был выше (но не тяжелее), чем сицилийские карликовые слоны, обитавшие одновременно с ним на острове и достигавшие 0,9—1 м в холке.

Из-за своих размера и массы Cygnus falconeri был, скорее всего, плохо летающей или вовсе нелетающей птицей. В отличие от других лебедей, хорошо был приспособлен для передвижения по земле, где, вероятно, и проводил довольно много времени. Вероятно, в пищу употреблял в основном наземные растения.

Вымер в голоцене в результате экстремальных климатических изменений или появления новых хищников и конкурентов в местах своего обитания.

Примечания

†
Вымершие гусеобразные
Птицы плиоцена
Птицы плейстоцена
Ископаемая фауна Евразии
Фоссилии, описанные в 1865 году
Фальконер

redpajama_set_name: RedPajamaWikipedia


text:
UK: Industry efforts to cut salt content appear wasted on consumers
Despite the "considerable efforts" of industry to reduce salt content in food products, a new UK study suggests it is having zero impact on people's salt intake. The Food Standards Agency in Scotland (FSAS) has published research indicating that there has been no significant change in the amount of salt consumed by people in Scotland since 2006.
People in Scotland are eating nearly 9g per day on average, which is 50% higher than the recommended 6g per day. Eating too much salt is a significant risk factor in developing high blood pressure. High blood pressure can significantly increase the risk of heart disease and stroke.
The results of this survey are similar to a previous survey carried out in Scotland in 2006, which suggests no significant change to salt intakes. Results are also similar to the last UK survey in 2008.
Seventy-five per cent of the salt eaten is already in every day foods such as bread, meat products and cereals, and convenience foods like pizza, ready meals, savoury snacks and cakes and pastries, so work carried out by the food industry to reformulate their products to reduce the salt content is very important, says a FSAS report.
In 2006 the Food Standards Agency introduced voluntary salt reductions for industry across 85 categories of food, for achievement by 2010. After consultation with the food industry, the FSA set more challenging targets for 2012. The revised targets reflect the progress made by industry and were set at levels intended to make a further real impact on consumers' intakes.
Bread is a major source of salt in the diet and to assist craft bakers to reduce the salt content of bread, the FSA, in collaboration with stakeholders have produced a new online calculator to help bakers to reduce the amount of salt in bread (see link below).
To date, the food industry in Scotland has made real efforts to reduce the salt levels in many products. For example:
Macphie of Glenbervie use 100 tonnes per year less salt which equates to an 18% reduction
Baxters have reduced the average salt content of their soup by approximately 50% since 2001, equating to 190 tonnes of salt per year
Nairns have made a 56% reduction in the salt content of their oatcakes since 2003
The Scottish Government is also committed to improving the Scottish diet through product reformulation and is collaborating with key partners in Scotland, including the FSA, to support industry to reduce salt, fat and sugar in their products. This includes grant funding for the Scottish Food and Drink Federation (SFDF) to engage an Industry Technical Manager to provide support to reformulate products. In addition, Scottish Enterprise is funding a Food and Health Innovation Service for Scotland that will provide advice to companies on how to reduce salt, fat and sugar.
Given the considerable efforts by industry to reduce the salt content of manufactured food products for home consumption, it is also necessary to address the salt content of foods eaten outside the home.
Consumers could also help lower their salt intakes towards the recommended population average of 6g a day by checking labels, using reduced salt products and adding less salt to their food.
Charles Milne, Director, Food Standards Agency said: 'We are disappointed that salt intakes have remained static, but will continue our efforts to help people reduce the amount of salt in their diets. FSA in Scotland are committed to salt reduction as part of their strategic plan and we will work in partnership with the Scottish Government and the food industry to drive the necessary changes required to help reduce salt intakes.'
The science behind the story
The study involved taking a 24-hour urine collection from participants in a sub-sample of the Scottish Health Survey. The samples were obtained from 941 adults aged 19-64 years, covering all geographical areas across Scotland, and reflecting the population's gender balance and difference levels of income.
A sample of urine collected over 24 hours is the 'gold standard' method for measuring salt intake. This is because salt intake can't be measured precisely either by taking blood samples or by estimating the amount eaten from a food diary. Food diaries are not accurate enough because the salt content of individual foods can be quite variable and when salt is added at the cooking stage and at the table you can't work out how much has been consumed.
Salt is the major source of sodium in the diet, and the key evidence for the association with blood pressure relates to sodium. Therefore, we measure sodium in the urine. The body normally keeps sodium levels steady in the blood and so the sodium excreted in urine reflects the sodium intake from the diet.
Source: Foods Standards Authority
Tags: Preservatives and acidulants, salt and fat reduction, Science & Nutrition, Sugar

redpajama_set_name: RedPajamaCommonCrawl


Amsterdam is very much a global city with a lot of history and a rich cultural heritage. As such, it is fair to say that whenever you decide to go to, there will be a wide range of events and activities going on. Although these are too numerous to list here, we have put together some of the highlights for you to give you a taste of what you might expect whenever you decide to visit Amsterdam..
Jumping Amsterdam is Amsterdam's premier equestrian show jumping event which draws the world's leading show jumpers as well as large crowds. It takes place at the city's RAI exhibition centre between the 23rd-26th January.
It will be Chinese New Year on February month and there will be celebrations in the Nieuwmarkt and Zeedijk districts within Amsterdam's substantial Chinese community. Expect fireworks as well as other traditional cultural celebrations.
For lovers of techno and electronic music, the 5 Days Off festival takes place at the beginning of every March. From relatively humble beginnings, the festival now takes place across several of Amsterdam's top venues including De Balie, Paradiso and Melkweg.
April 27th sees the King's Day celebrations kick off with Amsterdam turning into a veritable sea of orange. Street parties, food stalls, markets and much more besides make this a fascinating time to be in the city.
The Holland festival is a cutting-edge, innovative festival with many highly regarded and respected theatre performances from around the world.
Sail Amsterdam is an impressive event for lovers of historic tall ships and takes place once every five years. The event returns in 2015 and sees a large flotilla of ships sailing along the River Ij with thousands of onlookers cheering them on.
The Discovery Festival is a science based event which takes place in Amsterdam Noord (Tolhuistuin) in September. The festival includes various scientific experiments, musical events, art and film installations spearheaded by young scientists on a "voyage of discovery".
Amsterdam is well known for its electronic music and the Amsterdam Dance Event brings together many of the leading exponents of dance music with more than 450 events and 2,000 artists at 100 locations across the city.
Late November sees the unpronounceable "Het Hoofdgerecht" food festival to the city with a huge market hall at the Food Center in Amsterdam. The festival is a celebration of food but also features music and even a fun fair.
December sees the Amsterdam Light Festival which makes the city feel particularly festive. A canal cruise called "Water Colours" and a walking tour called the "Illuminade". There are many events taking place throughout the city at this time at museums, theatres, restaurants and shops and it is worth checking out what is on if you are there in December.


text:
Fact Versus Fiction: How 'Bombshell' Tells the Truth About Sexual Assault
Oscar Nominations Are Here and I Have Thoughts
The Pokémon Direct Should Sate Fans for Now
Looking For a New Series? Check Out Netflix's 'Spinning Out'
The Impact of Technology on the Casino World
With films like, "Halloween," "The Nun" and "Slender Man" set to premiere soon, your playlist is about to get a whole lot scarier. (Image via GeekTyrant).
Screens x July 6, 2018
12 Horror Movies Coming Out Later This Year
After watching these movies, you'll be afraid of absolutely everything.
By Alexis Rogers, Temple University
FacebookTwitterGooglePinterestRedditStumbleuponTumblr
This year has been filled with the release of several successful horror movies, such as "A Quiet Place" and "Hereditary," but that's not all of the movies that film directors and producers have in store for avid horror audiences.
The rest of the year promises even more scary movies, and there have even been announcements about some of the horror flciks being released in 2019. It doesn't have to be Halloween to watch scary movies, so check out this list for some upcoming movies to add to your watchlist.
1. The Devil's Doorway
Set in 1960, The Vatican sends two priests are sent to a home for "fallen women" in Ireland, and their investigation leads them to horrifying discoveries. This movie will be released on July 13.
2. Unfriended: Dark Web
This movie ties technology into horror as the film takes place through a video chat with a group of friends.
When one of the friends finds a computer in the lost and found at work, he quickly realizes that it was a bad idea to claim the laptop as his own after the real owner starts stalking him. The computer holds dark secrets, and the owner is willing to do anything in his power to regain possession of the computer. This movie will hit theaters on July 20.
3. Slender Man
Slender Man is a tall, skinny character with long limbs and face without features. The terrifying figure wears a black suit and terrorizes children by stalking and abducting his victims.
When a high school girl goes missing in Massachusetts after trying to summon Slender Man and disprove his existence, the mysterious disappearance can only mean one thing: Slender Man is real. This movie will be released on Aug. 24.
4. Boarding School
After becoming obsessed with his dead grandmother, a young boy is sent to an abnormal boarding school. This movie will premiere on Aug. 31.
5. The Little Stranger
Taking place in 1948, Dr. Faraday receives notice of a patient at Hundred Hall. The house is occupied by a mother and her two children, and the doctor soon learns that something is haunting the house and its inhabitants.
This movie will appear in theaters on Aug. 31.
6. The Nun
After the mysterious suicide of a nun in Romania, a priest and novitiate (a woman who is studying to becoming a nun) must go on a journey to uncover the mystery. Along the way, they encounter paranormal forces. This movie will premiere on Sept. 7.
Michael Myers returns for his victim Laurie Strode, who was a high school student in the 1978 version of the film, but four decades later, Laurie is ready to take revenge on the infamous masked man who almost killed her one Halloween night. This movie will hit theaters on Oct. 19.
'21 Bridges' Attempts Commentary About Police and Justice
8. Suspiria
This upcoming film, which premieres on Nov. 2, is a remake of the original 1977 film.
Audiences will follow the story of a world-renowned dance company in Berlin as they battle supernatural forces and mysterious murders.
9. Glass
This movie connects with "Split," which followed Kevin Wendell Crumb, a man that suffering from multiple personality disorder.
Now, a security guard tries to use his supernatural power to trace Crumb, specifically his personality of "The Beast." Audience members will be introduced to Mr. Glass, who has been imprisoned for committing mass murders. You can meet this new character when this movie premieres on Jan. 18, 2019.
10. It: Chapter Two
"Chapter Two" takes place 27 years after the first film, where viewers first met the group of friends called "The Losers Club."
3 Reasons to Watch 'Sorry for Your Loss' on Facebook Watch
Years later, the friends have moved on with their lives, but one day, they get a phone call that brings the club back together. Has Pennywise returned? Who is his latest victim? All questions will be answered on Sept. 6, 2019.
11. Pet Sematary
Adapted from the Steven King novel, this film follows the Creed family, who recently moved to a new house located near a "Pet Sematary." Let's just say it's a terrifying place. You can see how scary when the film hits theaters on April 5, 2019
12. Polaroid
Don't get your picture taken with this polaroid camera because everyone who does experiences a fatal end to their life. Bird Fitcher is a high school who discovers the camera and all of its terrifying consequences. Although there is no specific release date, this movie is expected to hit theaters sometime in 2019.
So what are you looking forward to seeing? These movies will be sure to have you screaming and throwing your popcorn in the theaters.
'The Messiah' and Its Controversial Christ-Figure
The Nonsense That Wrestling Fans Have To Deal With
How Goat Yoga and Yoga Trends Contribute to Cultural Appropriation
6 Ways to Make Your Spotify Playlists in the New Year
Tea Time: The Wonderfully Weird Story of Kombucha
'The Magicians' New Trailer Promises a Spellbinding Season 5
How Hipsters Saved the World — Before It Was Cool
'John Mulaney and the Sack Lunch Bunch': A Misguided Artistic Feat
Looking at Past Predictions Made About 2020
Elliott Brood Is the Best Canadian Band That You've Never Heard Before
Bong Joon-ho Perfects His Craft With Masterpiece 'Parasite'
We Should Be Preparing for the Age of Zoey Deutch
'Time Trap' and 'In the Shadow of the Moon' Add Fresh Twists to Time Travel
'It Chapter Two': 2019's Best Non-Horror Horror Film
'Blinded by the Light' Is a Far Cry From Springsteen's Success
Why Every Dog Lover Should See 'The Art of Racing in the Rain'
Screens /// Thoughts
Netflix's 'The Politician,' and the Issue of Age and Casting
OnlyFans Is the Only Social Media Site Built Exclusively for Sharing Nudes
The 10 Most Relaxing Songs in the World, According to Science, Ranked
Texas Alcohol Laws: Can't Live With 'Em, Pass the Beer Nuts
Screens, Thoughts
Remember Those Times Paul Walker Dated Teenage Girls?
What's Happening to Lia Marie Johnson?
10 Tips for Having First-Time Sex with a New Partner
Resurrecting Actors: Has CGI Gone Too Far?
'The Mandalorian' Isn't Just for Fans of the 'Star Wars' Universe
'Charlie's Angels' Is a Feminist Action Film, But That's Not Why It Flopped


text:
Startups making its presence felt in the Indian Television Ads business
Category Startups
Someone from the internet fraternity defines prime-time as "the time at which a radio or television audience is expected to be at its highest". While the Indian prime-time shows ideally include adrenaline pumped debating sessions and highly dramatic "reality-shows", companies bet on putting the big money to showcase its products to the viewers on such time slots.
Remember the days in the early 2000's when Indian television was all about the regular "saas bahu" serials, the advertising world highlighted the best of consumer products like biscuits, washing powders, motorcycles, bathing soaps, life insurances and body sprays from the renowned companies like P&G, ITC, Nestle and Unilever. But over the years as content on this mass media changed drastically, the advertising space did change as well. Now, it's no more of the computer designed super-natural ads, but is about sensible real life human crafted commercials. This has happened largely due to the success of the new age ideas like that of the Indian startups.
If you are in India and have turned on the TV, it's hard to miss the relentless pounding of ads by the growing number of innovative tech firms. For a country still striving to increase its internet penetration, television continues to remain as one among the most effective digital media. Every second ad seems to be about an e-commerce website or a mobile app. A section of the crowd in the venture capital industry joke that the real winners of the digital boom are the advertising agencies and the television channels. A rough estimate done by a 3rd party agency confirms that as many as 66 mobile and online companies were advertising on mainstream TV channels during mid last year, a significant pie being from the startup community. As of 2015, Indian startups like Flipkart, Snapdeal, PayTm and ShopClues spent between INR 150-500 Crores in ads with TV accounting almost 50% of the overall.
So, let's check out the Indian consumer tech startups advertising on National Television:
Impacting the "desi" way
People staying in advanced countries like US may label this as old fashioned but spending millions of dollars on television ads makes sense in India. A country where "reach" is the answer to most marketing queries, startups looking to grab early advantage and consumer attention are ready to shell out on traditional marketing methods. Specially, in a case where most Indian households enjoy television shows as a part of their shared social experience. This is a society which is driven by traditional values and concepts like e-commerce, taxi apps, mobile wallets and utility apps are still new.
So, what about the numbers?
India's new economy, led from the front by eCommerce companies, startups and internet enabled services, is driving the domestic advertising industry. TAM Adex data reveals that for the first time in 5 years, 2000+ new companies joined India's advertiser base just in the first 9 months of 2015. Another 500 advertisers could have joined during the last quarter of the year. Estimates suggest, the advertiser base must be around 12,748 by the end of 2015 against 10,065 in 2014. This in a nutshell is a rise by 26.65% in 2015. In this context, it is noteworthy to mention that a significant share of the aforementioned data is contributed by the startup community.
With due respect to the larger players, the contribution by Indian tech startups in the domestic advertising world looks significant. Market Research studies backed up by various independent bodies agrees to the fact that this share of the pie is expected to increase further with the Government's "Startup India" campaign. This would soar further prime time costs making startups to increase their marketing and promotional budget.


Can I reorder Register Closure columns?
Why is the COGs line on a register closure the same after updating the average cost of a product?
Can I delete a register closure?
Why does my closing float display as a negative amount?
Can I change the cash movements on a closed register?
Why doesn't the expected cash in my register closure take into account cash movements?
I have voided a sale, why are my register closure totals the same?
Can I split my register closure by date if I have left it open?
Why are there sales from other dates in my register closure summary?
Why do sales appear in the wrong register closure?
Can I reopen or edit a closed register?
What is a Register Closure?


Since I really need to start wrapping up this trip report, I'm going to just post photographs of things, without too much narrative. I hate that this is going to be an incomplete trip report, but I feel like I've dragged this on for too long now.
Along the way, we saw some characters, did some Trick or Treating, and had some Halloween cupcakes.
I managed to just get a picture of the Headless Horseman although, it's still a rubbish pic! I really am going to try and get better photos of Mickey's Not-So-Scary Halloween Party this year – we are going to two parties, so that means 2 chances for the HalloWishes fireworks, and 4 chances for the Boo To You Parade!
After the second roll out of the parade, the party was over, so we made our way out of the park. I bought a Jack Skellington balloon on the way, which floated in our hotel room until we went back home to the UK. I then deflated it and brought it back with me!
Staying at Wilderness Lodge was very handy after the party, as we were able to catch the boat direct back to the resort, without battling the huge lines for the Monorail, Ferryboat, and Buses!
And that is where we end day 9 of my Halloween In The Wilderness 2015 Trip Report, so I'll close out with a few more photographs, including one of some of the candy from our Trick Or Treatin' the next day.


text:
James Francis Gunn Jr.  ()  este un regizor de film american. A început cariera ca scenarist la mijlocul anilor 1990, cu scenarii pentru Tromeo si Juliet (1996), The Specials (2000), Scooby-Doo (2002) si continuarea sa, Scooby-Doo 2: Monsters Unleashed și versiunea din 2004 a filmului Dawn of the Dead. Apoi a început să lucreze ca regizor, începând cu filmul de groază-comedie Slither (2006). Ulterior, el a scris și regizat seria  web James Gunn's PG Porn (2008-09), filmul cu supereoi Super (2010) și filmele Marvel Cinematic Universul Gardienii Galaxiei (2014) și continuarea acestuia, Gardienii Galaxiei Vol. 2 (2017).

Filmografie

Film

Filme scurte

Ca actor

Televiziune

Ca actor

Jocuri video

Premii și nominalizări

Bibliografie

Note de subsol

Referințe

Legături externe

Nașteri în 1966
Romano-catolici americani
Oameni în viață
Americani de origine irlandeză
Regizori de film americani


The More 4 Doors team have been supplying door handle packs to customers across the UK for over a decade. The door handle packs supplied by More 4 Doors have been carefully put together to ensure all items complement each other remarkably. One of the best reasons for purchasing door handle packs is that they enable you to save a great deal of time and money. The packs available feature some of the company's most popular products. Should you have any questions about any of the door handle packs or any other products available from More 4 Doors, you can contact the team at any point.
Packs including door handles on rose and backplate are available, and there are several clearance door handle packs available too. The Door Handles on Rose Pack – Latch – Polished Chrome or Satin Chrome packs are amongst the most popular sets in the More 4 Doors catalogue and provide you with everything that you need to hang your doors. You can easily upgrade to the larger 100mm or 4-inch hinges if you need to. The pack comes complete with instructions, and there is a 10-year mechanical parts guarantee on handles. Also included are 3-inch ball bearing hingers and a tubular latch with face plates.
Currently available at a very special price are Black Nickel Door Handle Packs For Latch, Lock & Bathroom Doors. Packs are available to suit all internal doors and are ideal for installing new doors or replacing the furniture on old doors. Black nickel is an incredibly popular choice thanks to its stylish, sleek appearance as well as its durability. Whether you're hanging new or existing doors, these packs can provide all the quality and support you need.
More 4 Doors is a leading door accessories supplier that has seen many competitors come and go since its launch over a decade ago. Should you have any questions about the door handle packs offered by the team, simply send an e-mail to info@more4doors.com or call 01637 875255.


Name of the Organization : Chennai Petroleum Corporation Ltd.
Advertisement No. : 1of2018 – CPCL/HRD : 03: 056.
No. of Vacancy : 42 Posts.
Education Qualification for CPCL Jobs : Candidates should have done B.E./B.Tech, MBA in relevant Discipline according to desire posts. However, to get more information related to education qualification, candidates should check official notification before apply.
Age Limit for CPCL Vacancy : Upper age limit of the participating candidates is 26 years as on 01.09.2018.
CPCL Selection Process for CPCL Jobs : In this CPCL Recruitment Process the selection of the involving applicants will be based on Written Test and Personal Interview.
Application Fee : GEN/OBC candidates have to pay as Registration Fee of Rs. 500/- through Online Only. The SC/ST/PwBD / Ex-Serviceman candidates are exempted from payment of Application Fee.
Interested and Eligible candidates may apply Online in CPCL Recruitment 2018 go through the CPCL's website i.e. www.cpcl.co.in from 24/09/2018 to 08/10/2018. Afterward Online Apply web link will be disabled.
Starting Date for Submission of CPCL Online Application : 24 September 2018.
Closing Date for Submission of CPCL Online Application : 08 October 2018.
For more information regarding to CPCL Recruitment 2018 or CPCl Bharti 2018, kindly check first official notification or visit official CPCl's Website i.e. www.cpcl.co.in before apply online. Stay connected with us (DivyaJobs.in) to get more relevant updates related to Latest & Upcoming CPCL Vacancy 2018-19 and other Sarkari Naukri alert.


text:
DuTemple Flying Machine - $$4.95
The DuTemple Flying Machine with the first powered flight and the first retractable landing gear, helped to push the exploration of the Earth to higher heights.
Felix du Temple Early flying machine downloadable cardmodel
Felix du Temple Early Flying Machine Monoplane
This original artwork by Derek Roberts is available in much higher quality (suitable for framing), on the Full Collection DVD.
By 1874 the du Temple had constructed a large finely-built monoplane, at Brest, France, with a wing span of some 40 feet and a weight (minus the operator) of only about 160 pounds.
At least one attempt to actually fly the machine was made and it is generally agreed that after gaining speed down an incline, the flying machine lifted off for a short time and then returned to the ground, with both machine and operator uninjured.
The duTemple Monoplane comes in a folder of two sizes plus great instructions. The larger version has a span of 14" !!
What people say...
I love what you guys are doing with these Early Birds. Not only do we get a model but another fascinating lesson in Aviation History..Keep up the good work friends.... Bob G
I built your duTemple monoplane (as I did with all the other Early Flying Machines) and hung them from the ceiling in our bedroom. They're so cute and grounding and fun to watch as I get ready to start my day at NASA.. Robt M
Felix du Temple's Flying Machine
Felix du Temple de la Croix (known almost universally as "Felix du Temple") patented his design for an aerial machine in 1857. The design featured retractable wheeled landing gear, a tractor propeller, an internal engine and a boat-shaped hull (Mons. Du Temple had been a French Naval officer). He believed that a 6 h.p. engine would suffice to lift the machine, which had an estimated weight of about one ton. To pursue his design, Felix du Temple constructed numerous bird-shaped models and deduced that a dihedral angle to the wings would assist in stability, as well as placing most of the weight to the front of the machine. He ultimately worked with his brother, Louis, to build a large-sized version of his design. Finding existing steam engines to not be lightweight and powerful enough, in 1867 the two brothers built and patented an innovative "hot air" steam engine.
By 1874 the du Temples had constructed a large finely-built monoplane, at Brest, France, with a wing span of some 40 feet and a weight (minus the operator) of only about 160 pounds. At least one attempt to actually fly the machine was made and it is generally agreed that after gaining speed down an incline, the flying machine lifted off for a short time and then returned to the ground, with both machine and operator uninjured.
The car was to be shaped like a boat, lightly constructed of wood or iron ribs, and might be covered on the outside with tarred or rubber cloth. Beneath it were to be hinged three hollow legs, which might either be folded up or allowed to hang down. Strong springs inside of them were to carry rods or feet, at the outer end of which were to be wheels to roll over the ground. These legs were to be so adjusted in length that the apparatus should present an angle of incidence of about 20 to the horizon, and upon being put into forward motion, at the rate of about 20 miles per hour, by the screw, it was expected to rise upon the air and to enter upon its flight, the latter being regulated by the horizontal tail and by the vertical rudder.
The motor might be steam, electricity, or some other prime mover, and it was estimated that 6 H.P. would be required for en apparatus; weighing one ton. This was a very great underestimate, for the proposed plan of driving the machine over the ground by means of the aerial screw would largely increase the resistance, and sufficient speed could not be obtained to rise upon the air.
M. Du Temple tried many experiments with models shaped like birds, and his patent indicates that he had carefully considered the question of stability, for he places the majority of the weight toward the front of the car, provides for a dihedral angle during flight, and produces a slight turning up of the rear edge by making it flexible. There was a weak point, however, all the flexibility of the wings and tail caused a need for a shift of center of gravity, however Du Temple did not allow for this.
When he began with the aid of his brother, M. Louis du Temple, to experiment on a large scale, the inadequacy of all motors then known became apparent. They first tried steam at very high pressures, then a hot-air engine, and finally built and patented a very light steam boiler weighing from 39 to 44 lbs to the horse power. It consisted in a series of very thin tubes less than 1/8 in. in internal diameter, through which water circulated very rapidly, and was flashed into steam by the surrounding flame.
This is understood to have been applied to a slightly modified form of the main apparatus, built in 1874 at Brest by M. Du Temple. This was calculated to carry a man, was 40 ft. across from tip to tip, weighed about 160 lbs, and cost upward of $6,000, the workmanship being very fine.


text:
Blu-ray & Home Theatre
4K UHD Blu-ray Player 3
3D Blu-ray Player/Hard Drive Recorder 2
Hard Drive Recorder 1
Blu-ray Player 1
DVD Player 1
Read about DVD & Blu-ray Players
Experience Blu Ray
Don't sell yourself short when it comes to your movies and TV shows – enjoy them in real high definition with a Blu ray DVD player, and take it to the next level. A Blu Ray will deliver ultimate quality video so that you receive a cinema-like experience in the comfort of your own home.
Our Blu Ray players include top names in the industry including LG, Sony, and Panasonic – all just a few clicks away. So what is all the fuss about? Blu Ray is a new development by the world's leaders in electronics, transcending ordinary picture experiences. The audio and picture are enhanced to high definition quality so when you watch action packed films, adventure movies, sports or play games you are able to see and hear detailing like never before.
Not only do we provide standard DVD players but we also offer a portable DVD player which work well for travelling. You've also got the option of DVD recorders, which enable you to watch TV programmes in better quality than normal television. There are several possibilities to cater to all needs and tastes. Have a browse on the website to view our collection and watch films and TV shows in style by shopping online today.
Panasonic 3D Blu-ray Player/1TB Hard Drive Recorder
This smart Blu-ray Disc/DVD recorder and player features 4K netwroking with native 4K images from a digital camera or camcorder, plus remote streaming via TV Anytime, internet apps and a Twin HD Tuner. It also offers five times more HD recording with a 1TB HDD and 684 hours (HM Mode) HD recording. There's even a mode that automatically records your favourite content.
Panasonic 4K UHD Blu-ray Player
The Panasonic DP-UB820 4K Ultra HD Blu-ray Player features unique chroma processing technology to maximise the beauty of 4K/HDR content, built-in wi-fi with a full smart networking suite that supports 4K streaming, and a 7.1-channel analogue audio output for lifelike surround sound.
Panasonic 3D Blu-ray Player/500GB Hard Drive Recorder
Experience 4K networking, video playback and archiving with PWT560. You'll never miss your favourite TV programmes with the Series and Keyword Recording functions and there's also a wide range of Internet Apps, including Netflix and Youtube
Panasonic 1TB Hard Drive Recorder
Experience outstanding Full-HD entertainment with HWT260. Featuring 1-TB-HDD and 5-times longer HD recording, you'll never miss your favourite TV programmes with the Series and Keyword recording functions. There's also a wide range of Internet Apps, including Netflix and Youtube
Sony 4K UHD Blu-ray Player
Get the best seat in the house with this 4K Ultra HD Blu-ray™ Player. Advanced surround sound, 4K detail, and vibrant High Dynamic Range images offer a visual experience never before possible, for the ultimate immersion.
The Ultra HD Blu-ray Player UB150 features uncompromising performance in picture quality. Also compatible with HDR10+, it reproduces high quality 4K images.
Panasonic Blu-ray Player
Take your movie experience to another level with the compact and smart BD84 Blu-ray Player. It plays photos from external HDD storage and you can also play a wide range of videos from YouTube, Netflix and more.
Konka DVD Player
Excellent value for money, this DVD player from Konka delivers great picture quality at an affordable price. With a a USB port for media playback from an external hard drive as well as easy to use menu options, it's a great value basic DVD player.


Signal transduction by the TGF-beta superfamily.
Transforming growth factor-beta (TGF-beta) superfamily members regulate a plethora of developmental processes, and disruption of their activity has been implicated in a variety of human diseases ranging from cancer to chondrodysplasias and pulmonary hypertension. Intense investigations have revealed that SMAD proteins constitute the basic components of the core intracellular signaling cascade and that SMADs function by carrying signals from the cell surface directly to the nucleus. Recent insights have revealed how SMAD proteins themselves are regulated and how appropriate subcellular localization of SMADs and TGF-beta transmembrane receptors is controlled. Current research efforts investigating the contribution of SMAD-independent pathways promise to reveal advances to enhance our understanding of the signaling cascade.


text:
module.exports = {
  name: 'type.number',
  init: function(){
    var type = basis.require('basis.type');
    var catchWarnings = basis.require('./helpers/common.js').catchWarnings;

    var nonNumbersExceptNull = [
      '123,45',
      {},
      { foo: 'bar' },
      [],
      [1, 2],
      NaN,
      Infinity,
      undefined
    ];
  },
  test: [
    {
      name: 'accepts native and stringified numbers',
      test: function(){
        assert(type.number(2.718) === 2.718);
        assert(type.number('234.5') === 234.5);
      }
    },
    {
      name: 'is 0 by default',
      test: function(){
        assert(type.number.DEFAULT_VALUE === 0);
      }
    },
    {
      name: 'ignores incorrect objects',
      test: function(){
        nonNumbersExceptNull.forEach(function(incorrectValue){
          var warned = catchWarnings(function(){
            assert(type.number(incorrectValue, 42) === 42);
          });

          assert(warned);
        });

        catchWarnings(function(){
          assert(type.number(null, 42) === 42);
        });
      }
    },
    {
      name: 'ignores previous value if can transform new value',
      test: function(){
        [
          2.3,
          '1234.56'
        ].forEach(function(correctValue){
          assert(type.number(correctValue, 42) === type.number(correctValue));
        });
      }
    },
    {
      name: 'nullable',
      test: [
        {
          name: 'accepts correct values',
          test: function(){
            [
              2.3,
              '1234.56'
            ].forEach(function(correctValue){
              assert(type.number.nullable(correctValue, 23) === type.number(correctValue));
            });
          }
        },
        {
          name: 'accepts null',
          test: function(){
            assert(type.number.nullable(null, 23) === null);
          }
        },
        {
          name: 'is null by default',
          test: function(){
            assert(type.number.nullable.DEFAULT_VALUE === null);
          }
        },
        {
          name: 'ignores incorrect values',
          test: function(){
            nonNumbersExceptNull.forEach(function(incorrectValue){
              var warned = catchWarnings(function(){
                assert(type.number.nullable(incorrectValue, 42) === 42);
              });

              assert(warned);
            });
          }
        },
        {
          name: 'default',
          test: [
            {
              name: 'behaves like nullable version',
              test: function(){
                var transform = type.number.nullable.default(96);

                catchWarnings(function(){
                  nonNumbersExceptNull.concat([
                    null,
                    2.3,
                    '1234.56'
                  ]).forEach(function(value){
                    assert(transform(value, 23) === type.number.nullable(value, 23));
                  });
                });
              }
            },
            {
              name: 'sets default value',
              test: function(){
                assert(type.number.nullable.default(1).DEFAULT_VALUE === 1);
              }
            },
            {
              name: 'accepts stringified defaults',
              test: function(){
                assert(type.number.nullable.default('777').DEFAULT_VALUE === 777);
              }
            },
            {
              name: 'ignores default value if it is incorrect',
              test: function(){
                var transform;
                var warned = catchWarnings(function(){
                  transform = type.number.nullable.default({});
                });

                assert(warned);
                assert(transform.DEFAULT_VALUE === null);
              }
            }
          ]
        }
      ]
    },
    {
      name: 'default',
      test: [
        {
          name: 'behaves like usual version',
          test: function(){
            var transform = type.number.default(96);

            catchWarnings(function(){
              nonNumbersExceptNull.concat([
                null,
                2.3,
                '1234.56'
              ]).forEach(function(value){
                assert(transform(value, 23) === type.number(value, 23));
              });
            });
          }
        },
        {
          name: 'sets default value',
          test: function(){
            assert(type.number.default(1).DEFAULT_VALUE === 1);
          }
        },
        {
          name: 'accepts stringified defaults',
          test: function(){
            assert(type.number.default('123').DEFAULT_VALUE === 123);
          }
        },
        {
          name: 'ignores default value if it is incorrect',
          test: function(){
            nonNumbersExceptNull.concat([null]).forEach(function(incorrectValue){
              var transform;
              var warned = catchWarnings(function(){
                transform = type.number.default(incorrectValue);
              });

              assert(warned);
              assert(transform.DEFAULT_VALUE === 0);
            });
          }
        }
      ]
    }
  ]
};

redpajama_set_name: RedPajamaGithub


Home » Events » Welcome to the Inprint Bookstore!
Welcome to the Inprint Bookstore!
Brazos Bookstore is proud to support and partner with Inprint and the Margarett Root Brown Reading Series. We offer each author's featured titles for sale at the venue, but you can purchase books in advance from this page. Pre-purchased books will be available for pickup before and after the presentation at the Brazos Bookstore table in each venue. Books will be pre-signed whenever possible.
Buy online and pick your book up from the Brazos Bookstore table at the reading.
No need to make change. No need to wait with a credit card. Just bring us your name and/or order number. Your book will be waiting for you.
Buy online and pick your book up from the store.
We'll have your book signed for you and bring it back to the bookstore. Choose Pick-Up In Store as your shipping option.
Buy online and we'll ship your signed book to you.
We'll have your book signed and shipped anywhere in the US. International shipping may be available. Email shipping [at] brazosbookstore.com to inquire.