text:
\section{Introduction}
Recently, the theory of optimal design has been exploited to draw a subsample from huge datasets, containing the most information for the inferential goal; see for instance, \cite{drovandi2017, wang2019, wang2018, deldossi2020} among others.
Unfortunately, Big Data sets usually are the result of passive observations, so some high leverage values in the covariates and/or outliers in the response variable (denoted by Y) may be present.
The most commonly applied criterion is the D-optimality. It is well known that D-optimal designs tend to lie on the boundary of the design region thus in presence of high leverage values, all of them would be selected. Since this circumstance could have a severe influence on the estimated linear model (leverage points with high influence), in this study we propose an "exchange" procedure to select a "nearly" D-optimal subset which does not include the high leverage values.
Avoiding high leverage points, however, does not guard from all the outliers in Y. Therefore, we also modify the previous method  to exploit the information about the responses and avoid the selection of the abnormal Y-values.
The first proposal is an unsupervised  procedure, as it is not based on the response observations, while the latter is a supervised exchange method.
Finally, both these exchange algorithms are extended to the I-criterion, which aims at providing accurate predictions in a set of covariate-values.

After introducing methodology and notation in Section~\ref{sec:notation}, in Section~\ref{sec:modified_exchange} we introduce the novel modified exchange algorithm to obtain both a noninformative and an informative D-optimal sample without outliers. Moreover an approach for the initialization of the above algorithms is proposed.  In Section~\ref{sec:I_optimal_sample} we adapt our proposal to the I-optimal criterion with the goal of selecting a subsample to get accurate predictions. Finally in Section~\ref{sec:simulations}  we perform some simulations which serve as motivation for the problem presented in this paper.

\section{Notation and motivation of the work}
	\label{sec:notation}

	Assume that $N$ independent responses have been generated by a super-population model
	$$
	Y_i = \bm{x}^\top_i \boldsymbol{\beta} + \varepsilon_i, \quad i=1,\ldots, N,
	$$
	where  $^\top$ denotes transposition, $\boldsymbol{\beta}=(\beta_0,\beta_1,\ldots,\beta_k)^\top$ is  a vector of unknown coefficients, $\bm{x}_i^\top=(1,\tilde{\bm{x}}_i^\top)$ where
	$\tilde{\bm{x}}_i=({x}_{i1},\ldots,x_{ik})^\top$, for $i=1,\ldots, N$, are $N$  iid repetitions of a $k$-variate explanatory variable, and $\varepsilon_i$ are iid random errors with zero mean and equal variance $\sigma^2$. \\
	$\bm{D}=\{(\tilde{\bm{x}}_1^\top, Y_1),\ldots,(\tilde{\bm{x}}_N^\top, Y_N)\}$ indicates the available dataset, which is assumed to be a tall dataset, i.e. with $k << N$.
	\\
	The population under study is denoted by $U=\{1,\ldots,N\}$ and $s_n \subseteq U$ denotes a sample without replications of size $n$ from $U$ (i.e. a collection of $n$ different indices from $U$).
	Herein we describe a new sampling method from a given dataset $\bm{D}$ with the goal of selecting $n$ observations ($k < n << N$) which produce an efficient estimate of the model coefficients even in the presence of outliers.

	Given a sample $s_n=\{i_1,\ldots,i_n \}$, let $\bm{X}$ to be the $n \times (k+1)$ matrix whose rows are $\bm{x}_i^\top$, for $i \in s_n$, and let $\bm{Y} = (Y_{i_1}, \ldots, Y_{i_n})^\top$ be the $n \times 1$ vector of the sampled responses.
	We consider the  OLS estimator of the coefficients of the linear model based on the sample $s_n$:
	\begin{eqnarray*}
		\hat{\boldsymbol{\beta}}
		& = &
		\hat{\boldsymbol{\beta}}(s_n) = (\bm{X}^\top  \bm{X})^{-1} \bm{X}^\top  \bm{Y} \\
		& = &
		\left(\sum_{i=1}^{N} \bm{x}_i \bm{x}_i^T I_l\right)^{-1} \sum_{i=1}^{N} \bm{x}_i \, Y_i\, I_i,
	\end{eqnarray*}
	where
	\begin{equation*}
	I_i = \begin{cases}
	1 & \mbox{if } i \in s_n\\
	0 & \mbox{otherwise}
	\end{cases} \, , \qquad \text{with } i = 1, \ldots, N
	\end{equation*}
	denotes the sample inclusion indicator.

	To improve the precision of  $\hat{\boldsymbol{\beta}}$, we suggest to select the sample $s_n$ according to $D$-optimality. We denote the $D$-optimum sample as
	\begin{equation*}
	s_n^* = \underset{s_n = \left\{ I_1, \ldots,I_N \right\} }{\operatorname{arg\,sup}}  \left| \sum_{i = 1}^{N} \bm{x}_i \bm{x}_i^\top I_i \right| \,.
	\end{equation*}

	Since the D-optimal support points usually lie in the boundary of the experimental region, when  the dataset $\bm{D}$ contains  high leverage points, $s_n^*$ includes them and if they are associated to abnormal responses then they may produce a non-reliable estimate.  Example~\ref{example_doptimal_outliers} shows how the outliers are selected by the $\bm{D}$-optimal sample.
	\begin{expl}
		\label{example_doptimal_outliers}
		An artificial dataset $\bm{D}$ with $N=10000$ observations has been generated from a simple linear model,
		\begin{equation*}
		Y_{i} = \beta_0 + \beta_1 x_i + \varepsilon_i, \quad i = 1, \ldots, N,
		\end{equation*}
		in the following way:\\
		for $i = 1, \ldots, 9990$, $\boldsymbol{\beta} = (1.5, 2.7)^\top$,
		$x_i \sim \mathcal{N}(3, 4)$, $\varepsilon_i \sim \mathcal{N}(0, 9^2)$;\\
		for $i = 9991, \ldots,10000$, $\boldsymbol{\beta} = (1.5, -2.7)^\top$
		$x_i \sim \mathcal{N}(3, 20)$, $\varepsilon_i \sim \mathcal{N}(0, 20^2)$.\\
		 The left-hand side of Figure~\ref{fig:example_doptimal_outliers} displays these last 10 observations in red, while the majority of the data, generated from the first distribution,  are displayed in black.
		The right-hand side of Figure~\ref{fig:example_doptimal_outliers} emphasises the D-optimal subsample  of size $n =100$, $s_n^*$, displaying its support points in blue.
		As expected, all the abnormal values in $X$ are included in $s_n^*$ because they maximize the determinant of the information matrix ($s_n^*$ has been obtained by applying the  function \texttt{od\_KL} of the \texttt{R} package \texttt{OptimalDesign}~\cite{harman2019optimaldesign}).

		\begin{figure}
			\centering
			\includegraphics[width=0.9\textwidth]{figure1.png}
			\caption{Outliers (in red) and the $D$-optimal sample (in blue). \label{fig:example_doptimal_outliers}}
		\end{figure}
	\end{expl}
	To avoid the outliers when applying  D-optimal subsampling, we propose  a modification of the well known exchange algorithm.
	Before describing our proposal, we recall that an observation  $\bm{x}_i$ with $i=1, \cdots, n$ is called an \textit{high leverage point} when its leverage value
$h_{ii} =\bm{x}^\top_i (\bm{X}^\top  \bm{X})^{-1} \bm{x}_i $ is greater than a threshold, i.e. $$h_{ii} >\nu_1\,\frac{k+1}{n} $$
where $\nu_1$ is a tuning parameter usually set equal to 2 ~\cite{hoaglin1978}.\\
 A high leverage point can be either \textit{good} or \textit{bad}:  if its  associated response is \lq\lq abnormal'', it is bad  because,  in this case, it might alter the  model fitted by the bulk of the data; otherwise, if the response is not an outlier, the high leverage point is good because it would reduce the variance of the parameters' estimates.
    \section{Modified Exchange Algorithms}
    \label{sec:modified_exchange}
    The common structure of the $t$-th iteration of an exchange algorithm consists in adding a point $\bm{x}_{j_a}$ (chosen from a list of candidate points ${\cal C}^{(t)}$) to the available sample $s_n^{(t-1)}$ and then delete a point from it. The choice of the augmented and deleted points is based on the achievement of some optimality criterion. For D-optimality, the augmented observation $\bm{x}_{j_a}$ is the $x$-value of the unit with the largest prediction variance,
    $$
    j_a=\arg\max_{j\in {\cal C}^{(t)}}\bm{x}^\top_j (\bm{X}^\top  \bm{X})^{-1} \bm{x}_j,
    $$
    and is chosen from the experimental domain, if replications are admitted, or from  the complementary space of $s_n^{(t-1)}$, if it is not.
    The deleted point is that with the smallest prediction variance, i.e. with the smallest leverage value $h_{ii}$, $i=1,\ldots,n+1$ (see Chp. 12 in \cite{atkinson2007}).
    Our main idea is to modify the algorithm in such a way that points with high leverage scores are not proposed for the exchange, avoiding  the dangerous combination of high leverage scores and abnormal responses. This goal is reached:
        a) by  switching the augmentation and deletion steps; b) by changing the set ${\cal C}^{(t)}$ where the observation to be added is searched.

    In step b), if the information about the responses is not used to identify the set  ${\cal C}^{(t)}$, then
     the modified D-optimal sample
     is non-informative for the parameters of interest.  This unsupervised procedure is described in detail in Subsection \ref{sec:sampling_strategy}.

      Avoiding high leverage points, however, does not guard from all the outliers in $Y$;  points may be present which are in the core of the data wrt the auxiliary variables but are abnormal wrt the response variable.
      In Subsection \ref{informative sample} we propose a supervised version of the algorithm, where in step b) we exploit the response values to remove the outliers in $Y$. Let us note that the obtained optimal sample becomes informative because it depends on the responses.
	\subsection{Noninformative D-optimal samples without high leverage points}
	\label{sec:sampling_strategy}
	Let $s_n^{(0)}$ be an initial sample of size $n$, which does not include high leverage points. At the end of this section we describe a method for getting such an initial sample.

	Let $ {\cal C}^{(t)}$ be a set of candidate points for the exchange at the current iteration and let  ${\bm{X}}_t$ be the design matrix associated to the sample $s_n^{(t)}$.
	To update  $s_n^{(t)}$, firstly  we remove from it the unit $i_{m}$  with the smallest prediction variance, i.e.
	$$
	i_{m} = \underset{i \in s_n^{(t)}}{\arg \min} ~ h_{ii};
	$$
	let ${\bm{X}}_t^{\!-}$ denote the design matrix obtained by omitting the row  $\bm{x}_{i_m}$ from $\bm{X}_t$.
	Subsequently, we add the unit $j_a \in {\cal C}^{(t)} $  which presents the largest prediction variance
	${\bm{x}}_{j_a}^\top ({{\bm{X}}_t^{\!-}}^\top  {\bm{X}}_t^{\!-})^{-1} \bm{x}_{j_a}$, where
	\begin{equation}
	\label{candidate_p}
	{\cal C}^{(t)}= \left\{j:\;\;
	h_{i_{m} i_{m}}< h_{i_m i_m}(\bm{x}_j) < \nu_1 \,\frac{k+1}{n},
	\right\}
	\end{equation}
	and
	$h_{i_m i_m}(\bm{x}_j)$
	is the leverage score obtained exchanging $\bm{x}_{i_m}$ with $\bm{x}_j$ for $j\in \{U-s_n^{(t)}\}$. For computational purposes, let us note that from Saerle (1982, p.153)
 \begin{equation}
 \label{inv_X-}
 ({\bm{X}_t^{\!-}}^\top  \bm{X}_t^{\!-})^{-1}=(\bm{X}_t^\top  \bm{X}_t)^{-1}
+(\bm{X}_t^\top  \bm{X}_t)^{-1}  \frac{\bm{x}_{i_m} \bm{x}_{i_m}^T}{1- \bm{x}_{i_m}^T (\bm{X}_t^\top  \bm{X}_t)^{-1} \bm{x}_{i_m}} (\bm{X}_t^\top  \bm{X}_t)^{-1}
\end{equation}
 in addition,
	the next theorem provides an analytical expression for $h_{i_m i_m}(\bm{x}_j)$.
\begin{theorem}
	Let  $\widetilde{\bm{X}}_t$ be the design matrix obtained from $\bm{X}_t$ exchanging $\bm{x}_{i_m}$ with $\bm{x}_j$,
  then
	\begin{eqnarray}
	\label{h_xj}
	h_{i_m i_m}(\bm{x}_j)= \bm{x}^\top_j \left(\widetilde{\bm{X}}_t^\top  \widetilde{\bm{X}}_t\right)^{-1} \bm{x}_j
	\end{eqnarray}
	where
	\begin{equation}
	\label{Inv_s}
	\left(\widetilde{\bm{X}}_t^\top  \widetilde{\bm{X}}_t\right)^{-1}=
	(\bm{X}_t^\top  \bm{X}_t)^{-1}-(\bm{X}_t^\top  \bm{X}_t)^{-1} \,\frac{\bm{A}}{d}\, (\bm{X}_t^\top  \bm{X}_t)^{-1},
	\end{equation}
	with
	\begin{eqnarray*}
		\bm{A}&=& \bm{x}_{i_m}^\top
		(\bm{X}_t^\top \bm{X}_t)^{-1}
		\bm{x}_{j} \,
		(\bm{x}_{j} \bm{x}_{i_m}^\top+\bm{x}_{i_m} \bm{x}_{j}^\top)
		+ [1-\bm{x}_{i_m}^\top (\bm{X}_t^\top \bm{X}_t)^{-1} \bm{x}_{i_m}]\,\bm{x}_{j}\bm{x}_{j}^\top\red{+}\\
		&-&
		[1+\bm{x}_{j}^\top (\bm{X}_t^\top \bm{X}_t)^{-1} \bm{x}_{j}]\,\bm{x}_{i_m}\bm{x}_{i_m}^\top;\\[.2cm]
		d &=&
		[1-\bm{x}_{i_m}^\top (\bm{X}_t^\top \bm{X}_t)^{-1} \bm{x}_{i_m}]\,[1+\bm{x}_{j}^\top (\bm{X}_t^\top \bm{X}_t)^{-1} \bm{x}_{j}]+[\bm{x}_{i_m}^\top
		(\bm{X}_t^\top \bm{X}_t)^{-1}
		\bm{x}_{j} ]^2.
	\end{eqnarray*}
\end{theorem}
\begin{proof}
	Expression (\ref{Inv_s}) can be obtained from Lemma 3.3.1 in Fedorov (1972) after some cumbersome algebra.
\end{proof}

	In force of the upper bound in (\ref{candidate_p}), our proposal is to consider as candidates for the exchange only observations in $\{U-s_n^{(t)}\}$ which  are not high leverage points.
	In addition, to speed up the algorithm we reduce the number of exchanges by imposing the lower bound in (\ref{candidate_p}). Without this lower bound, whenever $h_{i_m i_m}(\bm{x}_j) \leq h_{i_{m} i_{m}}$, the new observation $j$ would be immediately removed at the subsequent step of the algorithm.

	Algorithm 1  describes in detail all the steps to select a D-optimal sample without high leverage points; instead Algorithm 2 illustrates how to select an initial sample $s_n^{(0)}$ to start Algorithm 1.
	\begin{algorithm}[!h]
		{
			\caption{Non-informative D-optimal sample without high leverage points}
			\label{Algorithm 1}
			\SetAlgoLined
			\vspace{0.1cm}
			\KwInput{Dataset $\bm{D}$, sample size $n$, initial sample $s_n^{(0)}$, $\nu_1$}
			\KwOutput{D-optimal sample without high leverage points}
			Set $t=0$\;
			\While{$t<t_{max}$}
			{Compute the leverage scores for the current sample $h_{ii}={\bm{x}}_{i}^\top (\bm{X}_{t}^\top                {\bm{X}_{t}})^{-1} {\bm{x}_i},$
				where $\bm{X}_{t}$ is the $n \times k$ matrix whose rows are $\bm{x}_i^T$ with $i \in s_n^{(t)}$\;
				Identify unit
				$i_{m} = \underset{i \in s_n^{(t)}}{\arg \min} ~ h_{ii}$\;
					Compute
				$
				(\bm{X}_{t}^{\!-\top} \bm{X}_{t}^{\!-})^{-1}=(\bm{X}_{t}^\top  \bm{X}_{t})^{-1}
				+(\bm{X}_{t}^\top  \bm{X}_{t})^{-1}  \frac{\bm{x}_{i_m} \bm{x}_{i_m}^T}{1- \bm{x}_{i_m}^T (\bm{X}_{t}^\top  \bm{X}_{t})^{-1} \bm{x}_{i_m}} (\bm{X}_{t}^\top  \bm{X}_{t})^{-1}
				$\;
				Select randomly $\tilde N \leq N-n$ units from $\Big\{ U-s_n^{(t)} \Big\}$. Let $\bm{x}_j$, with $j = 1, \ldots, \tilde{N}$, the observations for these units\;
				From (\ref{Inv_s}), compute $(\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1}$ and determine
				the leverage scores $h_{i_m i_m}(\bm{x}_j)=\bm{x}_j^\top (\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1} \bm{x}_j$\;
				Identify the set of candidate points for the exchange with $i_{m}$:
				${\cal C}^{(t)}=\left\{j:\;\;
				h_{i_{m} i_{m}}< h_{i_m i_m}(\bm{x}_j) < \nu_1 \,\frac{k+1}{n}
				\right\}$\;
				Select from ${\cal C}^{(t)}$ the observation $j_a = \underset{j \in {\cal C}^{(t)}}{\operatorname{arg\,max}} ~
				\bm{x}_j^\top (\bm{X}_{t}^{\!-\top} \bm{X}_{t}^{\!-})^{-1} \bm{x}_j$\;
				Update $s_n^{(t)}$ by replacing unit $i_m$ with $j_a$, to form  $s_n^{(t+1)}$\;
				Set $t=t+1$\;
			}
		}
\vspace{0.1cm}
	\begin{remark}
		In step \textit{6} it is reasonable to consider  $\tilde{N}=N-n$ whenever $N$ is not too large.
	\end{remark}
	\end{algorithm}

	\begin{algorithm}[!h]
		{
			\caption{Initialization step for Algorithm 1}
			\label{Algorithm 2}
			\SetAlgoLined
			\vspace{0.1cm}
			\KwInput{Dataset $\bm{D}$, sample size $n$, $\nu_2$}
			\KwOutput{$s_n^{(0)}$: initial sample  without high leverage points}
			From $U$ select without replacement a simple random sample of size $n$,  $r_n^{(0)}$ and set $t=0$\;
			\While{$t<t_{max}$}
			{Compute the leverage scores for the current sample $h_{ii}={\bm{x}}_{i}^\top (\bm{X}_{t}^\top {\bm{X}_{t}})^{-1} {\bm{x}_i},$
				where $\bm{X}_{t}$ is the $n \times k$ matrix whose rows are $\bm{x}_i^T$ with $i \in r_n^{(t)}$\;
				Identify unit
				$i_{m} = \underset{i \in s_n^{(t-1)}}{\arg \max} ~ h_{ii}$ \;
				{\eIf{$h_{i_{m} i_{m}}<  \nu_2 \,\frac{k+1}{n}$ } {set $s_n^{(0)}=r_n^{(t)}$ and stop the iterative procedure} {
				Select randomly $\tilde N \leq N-n$ units from $\Big\{ U-r_n^{(t)} \Big\}$. Let $\bm{x}_j$, with $j = 1, \ldots, \tilde{N}$, the observations for these units. From (\ref{h_xj}), compute  $h_{i_m i_m}(\bm{x}_j)$ and identify the set of  points candidate for the exchange with $i_{m}$:
				${\cal C}^{(t)}=\left\{j:\;\;
				 h_{i_m i_m}(\bm{x}_j) < \nu_2 \,\frac{k+1}{n}
				\right\}$\;
				Select at random a unit $j_a$ from  ${\cal C}^{(t)}$ \;
				Determine  $r_n^{(t+1)}$ by replacing unit $i_m$ with $j_a$ in $r_n^{(t)}$ \;
				Compute $(\bm{X}_{t+1}^\top {\bm{X}_{t+1}})^{-1}$ by applying (\ref{Inv_s}) which is based on $(\bm{X}_{t}^\top {\bm{X}_{t}})^{-1}$\;
				Set $t=t+1$\;
			}
		}
			}
		}
		\vspace{0.1cm}
		\begin{remark}
			In step \textit{8} it is reasonable to consider  $\tilde{N}=N-n$ whenever $N$ is not too large.
		\end{remark}
	\end{algorithm}
	\subsection{Informative D-optimal sample without outliers}
	\label{informative sample}
	The previous exchange algorithm can be applied whenever
	the response values are not observed (for instance, if it is expensive to measure $Y$); this selection procedure protects against potential outliers in $Y$ that are associated with the high leverage points in the factor-space. However, if  the response values are available, then this information can be exploited by the exchange algorithm to avoid all the outliers in $Y$, obtaining an informative D-optimal subsample.

	According  to \cite{Chatterjee1986influential} an influential data point is an observation that strongly influences the fitted values. To identify these influential data points, Cook's distance may be applied. In fact, Cook's distance  for the $i$-th observation, $C_i$, measures how much all of the fitted values in the model change when the $i$-th data point is deleted:
	\begin{eqnarray}
		C_i&=&\dfrac{(\hat{\bm{Y}}-\hat{\bm{Y}}_{(i)})^\top (\hat{\bm{Y}}-\hat{\bm{Y}}_{(i)})}{(k+1)\hat\sigma^2},
		\nonumber
		\\
		&=&
		\frac{(Y_i-\hat{Y}_i)^2}{(k+1) \hat\sigma^2} \cdot \frac{h_{ii}}{(1-h_{ii})^2},
		\quad
		i=1,\ldots,n,
		\label{Cook_distance}
	\end{eqnarray}
	where $\hat{\bm{Y}}= \bm{X} \hat{\boldsymbol{\beta}}^\top$, $\hat\sigma^2$ is the residual mean square estimate of $\sigma^2$ and $\hat{\bm{Y}}_{(i)}= \bm{X} \hat{\boldsymbol{\beta}}_{(i)}^\top$  is the vector of predicted values when the $i$-th unit is removed from the data set $\bm{D}$.

	 A general practical rule is that any observation with a Cook's distance larger than $4/n$ may be considered an influential point.

	 When the response values are available, Algorithm 1 can be improved by removing the influential points from the  set ${\cal C}^{(t)}$ of the data candidate for the exchange, as illustrated in Algorithm 3 (for the computation of Cook's distance, expression  (\ref{Cook_distance}) is used to reduce the computational burden).

\begin{algorithm}[!h]{
		\caption{Informative D-optimal sample without outiliers: additional steps to be included between 9 and 10 in Algorithm 1 }
		\label{Algorithm 3}
		\SetAlgoLined
		\setcounter{AlgoLine}{0}
		\vspace{0.1cm}
		\KwInput{Dataset $\bm{D}$, sample size $n$}
		\KwOutput{Informative D-optimal sample without outliers}
		Compute Cook's distance for unit $j_a$,  $C_{j_a}$, from (\ref{Cook_distance})\;
		{\eIf{$C_{j_a} < 4/n$
		} {accept the exchange and go to step {\bf 10} of Algorithm 1}  {reject the exchange; remove unit $j_a$ from ${\cal C}^{(t)}$ and go back to step {\bf 9} of Algorithm 1}
		}
	}
\end{algorithm}

\section{Optimal subsampling to get accurate predictions}
	\label{sec:I_optimal_sample}
In the previous section we aim at selecting a subsample with the goal of getting a precise estimation of the parameters. Differently, if we are interested in obtaining accurate predictions on a set of values ${\cal X}_0=\{ \bm{x}_{01},\ldots,\bm{x}_{0N_0}\}$, then we should 	select the observations minimizing the overall prediction variance.
Let $\hat{Y}_{0i}= \hat{\boldsymbol{\beta}}^\top \bm{x}_{0i}$ be the prediction of $\mu_{0i}=E(Y_{0i}|\bm{x}_{0i})$ at $\bm{x}_{0i}$, $i=1,\ldots,N_0$.
 The prediction variance at $\bm{x}_{0i}$, also known as \lq\lq mean squared prediction error'' is
	$${\rm MSPE}(\hat{Y}_{0i}|\bm{x}_{0i},\bm{X})={\rm E}[(\hat{Y}_{0i}-\mu_{0i})^2|\bm{x}_{0i},\bm{X}].$$
If ${\bm{X}}_0$ is the $N_0\times k$ matrix whose $i$-th row is $\bm{x}_{0i}^\top$, then a measure of the overall mean squared prediction error is the sum of the prediction variances in ${\cal X}_0$:
\begin{eqnarray}
&\sum_{i=1}^{N_0} &  \!\!
{\rm MSPE}(\hat{Y}_{0i}|\bm{x}_{0i},\bm{X})
\,=\,
 \sigma^2 \,
{\rm trace} [{\bm{X}}_0 ({\bm{X}}^\top {\bm{X}})^{-1} {\bm{X}}_0^\top]\!
 \nonumber\\
&=&\!\!\!
\sigma^2  \,\operatorname{trace} \!\left[\left( \sum_{i = 1}^{N} \bm{x}_i \bm{x}_i^\top I_i\right)^{-1}  \!
		 {\bm{X}}_0^\top {\bm{X}}_0  \right]\!,
		\quad
		I_i = \begin{cases}
			1 & \mbox{if } i \in s_n\\
			0 & \mbox{otherwise}
		\end{cases}
\label{MSPE}
\end{eqnarray}
with $l = 1, \ldots, N$.
In this context, the I-optimal sample should be selected, which minimizes the  overall prediction variance (\ref{MSPE}):
$$
		s_n^{I}
		=
		\underset{s_n = \left\{ I_1, \ldots,I_N \right\} }{\operatorname{arg\,inf}} \operatorname{trace} \left[\left( \sum_{i = 1}^{N} \bm{x}_i \, \bm{x}_i^\top I_i\right)^{-1}  \!
		 {\bm{X}}_0^\top {\bm{X}}_0  \right].
$$

	If we also aim at preventing outliers, then we have to modify the deletion and augmentation steps of the exchange algorithm described in Section \ref{sec:sampling_strategy} accordingly to the $I$-criterion. By taking into account the results given in Appendix A of Meyer and Nachtsheim (1995),  the current sample $s_n^{(t)}$ should be updated by removing the unit $i_{m}$
		which minimises
		$$\tilde{h}_{ii}=\frac{  \bm{x}_i^\top \,({\bm{X}}_t^\top {\bm{X}_t})^{-1}

			\;{\bm{X}}_0^\top {\bm{X}}_0\;
			({\bm{X}}_t^\top {\bm{X}_t})^{-1}\,
			\bm{x}_i }
		{1- \bm{x}_i^T ({\bm{X}}_t^\top {\bm{X}}_t)^{-1} \bm{x}_i },
		$$
		where $\bm{X}_t$ is the $n \times k$ matrix whose rows are $\bm{x}_i^T$ with $i \in s_n^{(t)}$.

		Subsequently, from a set ${\cal C}^{(t)}$ of candidate points,  we should add the unit
		$$
		j_a=\arg\max_{j\in {\cal C}^{(t)}}\frac{{  \bm{x}_j^\top \,({\bm{X}}_t^{\!-\top} {\bm{X}}_t^{\!-})^{-1}

				\;{\bm{X}}_0^\top {\bm{X}}_0\;
				({\bm{X}}_t^{\!-\top} {\bm{X}}_t^{\!-})^{-1}\,
				\bm{x}_j }}
		{1+ \bm{x}_j^T ({\bm{X}}_t^{\!-\top} {\bm{X}}_t^{\!-})^{-1} \bm{x}_j },
		$$
		where ${\bm{X}}_t^{\!-}$
		is the design matrix obtained by removing the row  $\bm{x}_{i_m}$ from $\bm{X}_t$ and $({\bm{X}}_t^{\!-\top} {\bm{X}}_t^{\!-})^{-1}$
		can be computed from (\ref{inv_X-}).
		The set of candidate points should be formed by units that are not immediately removed in the subsequent step of the procedure and also are not high leverage points; therefore, ${\cal C}^{(t)}$ is
		$$
		{\cal C}^{(t)}=\left\{j:\;\;
		\tilde{h}_{i_m i_m}(\bm{x}_j) >\tilde{h}_{i_{m} i_{m}}\, \cap \,
		{h}_{i_m i_m}(\bm{x}_j)< \nu_1 \,\frac{k+1}{n}
		\right\}
		$$
		where
		$$
		\tilde{h}_{i_m i_m}(\bm{x}_j)=
		\frac{  \bm{x}_j^T \,(\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1}

		\;{\bm{X}}_0^\top {\bm{X}}_0\;
			(\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1}\,
			\bm{x}_j }
		{1- \bm{x}_j^T (\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1} \bm{x}_j },
		$$
		$$
		{h}_{i_m i_m}(\bm{x}_j)=\bm{x}_j^T (\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1} \bm{x}_j,
		$$
		$\widetilde{\bm{X}}_t$ is the matrix obtained from $\bm{X}_t$ by exchanging $\bm{x}_{i_m}$ with $\bm{x}_j$ and $(\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1}$ can be computed from (\ref{Inv_s}).

		\begin{algorithm}[]
		{
			\caption{Non-informative I-optimal sample without high leverage points}
			\label{Algorithm 4}
			\SetAlgoLined
			\vspace{0.1cm}
			\KwInput{Dataset $\bm{D}$, sample size $n$, initial sample $s_n^{(0)}$, prediction-set ${\cal X}_0=\{ \bm{x}_{01},\ldots,\bm{x}_{0N_0}\}$, $\nu_1$}
			\KwOutput{I-optimal sample without high leverage points}
			Set $t=0$\;
			\While{$t<t_{max}$}
			{For the current sample, compute
			$\tilde{h}_{ii}=\dfrac{  \bm{x}_i^\top \,({\bm{X}}_t^\top {\bm{X}_t})^{-1}

			\;{\bm{X}}_0^\top {\bm{X}}_0\;
			({\bm{X}}_t^\top {\bm{X}_t})^{-1}\,
			\bm{x}_i }
		{1- \bm{x}_i^T ({\bm{X}}_t^\top {\bm{X}}_t)^{-1} \bm{x}_i },$
				where $\bm{X}_{t}$ is the $n \times k$ matrix whose rows are $\bm{x}_i^T$ with $i \in s_n^{(t)}$ and
				${\bm{X}}_0$ is the $N_0\times k$ matrix whose rows are the elements of ${\cal X}_0$
				\;
				Identify unit
				$i_{m} = \underset{i \in s_n^{(t)}}{\arg \min} ~ \tilde{h}_{ii}$\;
				Compute
				$
				(\bm{X}_{t}^{\!-\top} \bm{X}_{t}^{\!-})^{-1}\!=\!(\bm{X}_{t}^\top  \bm{X}_{t})^{-1}
				\!+\!  \dfrac{(\bm{X}_{t}^\top  \bm{X}_{t})^{-1}\,
				\bm{x}_{i_m} \bm{x}_{i_m}^T \,
				(\bm{X}_{t}^\top  \bm{X}_{t})^{-1}}
				{1- \bm{x}_{i_m}^T (\bm{X}_{t}^\top  \bm{X}_{t})^{-1} \bm{x}_{i_m}}
				$
				\;
				Select randomly $\tilde N \leq N-n$ units from $\Big\{ U-s_n^{(t)} \Big\}$. Let $\bm{x}_j$, with $j = 1, \ldots, \tilde{N}$, the observations for these units\;
				From (\ref{Inv_s}) compute $(\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1}$ and  determine the leverage scores
				$h_{i_m i_m}(\bm{x}_j)=\bm{x}_j^\top (\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1} \bm{x}_j $ and
				$
		\tilde{h}_{i_m i_m}(\bm{x}_j)=
		\dfrac{  \bm{x}_j^T \,(\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1}

			\,{\bm{X}}_0^\top {\bm{X}}_0\,
			(\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1}\,
			\bm{x}_j }
		{1- \bm{x}_j^T (\widetilde{\bm{X}}_t^\top \widetilde{\bm{X}}_t)^{-1} \bm{x}_j }
		$
		\;
		Identify the set of candidate points for the exchange with $i_{m}$:
		$
		{\cal C}^{(t)}=\left\{j:\;\;
		\tilde{h}_{i_m i_m}(\bm{x}_j) >\tilde{h}_{i_{m} i_{m}}\, \cap \,
		{h}_{i_m i_m}(\bm{x}_j)< \nu_1 \,\frac{k+1}{n}
		\right\}
		$\;
		Select from ${\cal C}^{(t)}$ the observation $
		j_a=\arg\max_{j\in {\cal C}^{(t)}}\dfrac{{  \bm{x}_j^\top \,({\bm{X}}_t^{\!-\top} {\bm{X}}_t^{\!-})^{-1}

				\;{\bm{X}}_0^\top {\bm{X}}_0\;
				({\bm{X}}_t^{\!-\top} {\bm{X}}_t^{\!-})^{-1}\,
				\bm{x}_j }}
		{1+ \bm{x}_j^T ({\bm{X}}_t^{\!-\top} {\bm{X}}_t^{\!-})^{-1} \bm{x}_j }
		$\;
				Update $s_n^{(t)}$ by replacing unit $i_m$ with $j_a$, to form  $s_n^{(t+1)}$\;
				Set $t=t+1$\;
			}
		}
\vspace{0.1cm}
	\end{algorithm}
\section{Numerical studies}
	\label{sec:simulations}

\subsection{Simulation results}

In this section, we evaluate the performance of our proposals through a simulation study.
We start from the random generation of $H=30$ datasets of size $N=10^6$, each one including $N_2=500$ high leverage points/outliers. The computation of some metrics will illustrate the validity of our procedure in selecting a D- or I-optimal subsample without outliers.

Precisely, for $h=1, \ldots, H$,  $N$  iid repetitions of a $10$-variate explanatory variable
	$_h\tilde{\bm{x}}_i=({x}_{i1},\ldots,x_{i10})^\top$ are generated as follows:
\begin{enumerate}
   \item
 for $j=1,\ldots,3$, $x_{ij}$ are independently distributed as $U(0,5)$;
 \item
 for $j=4,\ldots,7$, $x_{ij}$  are distributed as a multivariate normal r.v. with zero mean and:\\
 2.a) for $  i=1, \ldots, (N-N_2)$, covariance matrix $
\bm{\Sigma}_1=\left[\begin{array}{cc}
9 & -1 \\
-1 & 9\\
\end{array}  \right]$ \\
2.b)  for $i=(N-N_2)+1, \ldots, N$, covariance matrix $
\bm{\Sigma}_{1.out}=\left[\begin{array}{cc}
25& 1 \\
1 & 25\\
\end{array}  \right]$;
\item
 for $j=8,9$,  $x_{ij}$ are distributed as a multivariate  t-distribution with $3$ degrees of freedom and scale matrix
$
\bm{\Sigma}_2=\left[\begin{array}{cc}
1 & 0.5 \\
0.5 & 1\\
\end{array}  \right]
$;
\item
for $j=10$, $x_{ij}$ is distributed as a Poisson distribution ${\cal P}(5)$.
\end{enumerate}
For each $N\times (k+1)$ factor-matrix $_h\bm{X}$, whose $i$-th raw is $_h{\bm{x}}^\top_i=(1,  _h{\tilde{\bm{x}}}^\top_i)$ ($i=1,\ldots,N$), we have generated  $S=50$ independent $N\times 1$ response vectors
$_h{\!\bm{Y}\!}_{s}$ (with $s=1,\ldots, S$), whose $i$-th item is
$$
_h{Y}_{s,i} = _h\!\bm{x}^\top_i \boldsymbol{\beta} + \varepsilon_{si}, \quad i=1,\ldots, N,
$$
with
\begin{itemize}
    \item[i)]
     $\bm{\beta}=(1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1)$ and $\sigma=3$ for $i=1, \ldots, N-N_2$
    \item[ii)]
	 $\bm{\beta}\!=\!(1, 1, 1, 1, -2, -2, -2, -2, 1, -1, -1)$, $\sigma\!=\!20$  for $i\!=\!N\!-\!N_2\!\ +1, \ldots, N$.
\end{itemize}
At each simulation step $(h,s)$, with $h=1,\ldots,H$ and $s=1,\ldots,S$,
we have applied the following Algorithms:
\begin{enumerate}
    \item Non-informative I (Algorithm 4)
    \item Non-informative D (Algorithm 1)
    \item  Informative I (Algorithm 4 and Algorithm 3)
    \item Informative D (Algorithm 1 and Algorithm 3)
    \item Simple random sampling (SRS): passive learning selection
\end{enumerate}
to draw a different subsample from the simulated dataset:
$$_h\bm{D}_{s}=\{(_h{\bm{x}}_1^\top,\, _{h}{y}_{s,1}),\ldots,(_h{\bm{x}}_N^\top,\, _{h}{y}_{s,N})\},\quad h=1, \ldots,H,\; s=1,\ldots,S.
$$

To check the validity of the inferential results obtained from the distinct subsamples, we have generated a test set of size $N_T=500$:  $$\bm{D}_{T}=\{(\bm{x}_{T1},y_{T1}),\ldots, (\bm{x}_{TN_{T}},y_{TN_{T}}) \},$$ without high leverage points and outliers (i.e. with $N_2=0$).

Finally, to implement the I-optimality procedure, we have generated a prediction region ${\cal X}_0$
	without high leverage points; in addition, to compare the behaviour of the distinct subsamples in ${\cal X}_0$, we have generated also the corresponding responses (without outliers). Let
	$$\bm{D}_{0}=\{(\bm{x}_{01},y_{01}),\ldots, (\bm{x}_{0N_{0}},y_{0N_{0}}) \}$$
	be the prediction set, where $N_0=500$.
\\[.2cm]
Let us denote by $s_{n}^{(h,s)}$ a subsample selected from the dataset $_h\bm{D}_{s}$ generated at the $(h,s)$-th simulation step, for $h=1,\ldots,H$ and $s=1,\ldots,S$, and
let
  $$
  I_{i}^{(h,s)}\! = \begin{cases}
			1 & \mbox{if } i \in s_n^{(h,s)}\\
			0 & \mbox{otherwise}
		\end{cases}, \quad i=1,\ldots,N,
$$
be the corresponding sampling indicator variable.\\
At each simulation step $(h,s)$,
to evaluate the performance of the subsampling techniques, we have computed:
\begin{itemize}
    \item
   The average mean squared prediction error in ${\cal X}_0$ (from (\ref{MSPE})):
$$
  {\rm MSPE}_{{\cal X}_0}^{(h,s)}=
\sigma^2  \dfrac{\operatorname{trace} \!\left[\!\left( \sum_{i = 1}^{N} {_h\bm{x}}_i\, {_h\bm{x}}_i^\top I_{i}^{(h,s)}\right)^{\!-1}  \!
		 \bm{X}_0^\top \bm{X}_0  \right]}{N_0};
$$
   \item
    The logarithm of the determinant of the information matrix:
$$
	{\rm Log(det)}^{(h,s)} =  \log \left| \sum_{i = 1}^{N} {_h\bm{x}}_{i}\, {_h\bm{x}}_{i}^\top I_{i}^{(h,s)} \right|;
$$
    \item
    The average squared prediction error in ${\cal X}_0$ and in ${\cal X}_{T}=\{\bm{x}_{T1},\ldots,\bm{x}_{TN_{T}}\}$:
    $$
{\rm SPE}_{{\cal X}_{0}}^{(h,s)}=  \dfrac{\sum_{i=1}^{N_{0}} (
\hat{y}_{0i}^{(h,s)}- \mu_{0i})^2}{N_{0}}
\;\; {\rm and} \;\;
{\rm SPE}_{{\cal X}_{T}}^{(h,s)} =  \dfrac{\sum_{i=1}^{N_{T}} (
\hat y_{Ti}^{(h,s)}- \mu_{Ti})^2}{N_{T}},
    $$
    where $\hat{y}_{0i}^{(h,s)}={_h\hat{\bm{\beta}}_s\!\!}^\top \bm{x}_{0i}$,
    $\hat{y}_{Ti}^{(h,s)}={_h\hat{\bm{\beta}}_s\!\!}^\top \bm{x}_{Ti}$, $\mu_{0i}=\bm{\beta}^\top \bm{x}_{0i}$,
$\mu_{Ti}=\bm{\beta}^\top \bm{x}_{Ti}$ and $_h\hat{\bm{\beta}}_s$ is the OLS estimate of ${\bm{\beta}}$ based on the subsample $s_{n}^{(h,s)}$;
\item
    The  standard error in the prediction set ${\bm{D}_0}$ and   in the test set  ${\bm{D}_T}$:
    $$
    {\rm SE}_{\bm{D}_0}^{(h,s)} =\dfrac{\sum_{i=1}^{N_{0}} \big( \hat y_{0i}^{(h,s)} - y_{0i}\big)^2}{N_{0}}
     \;\; {\rm and} \;\;
     {\rm SE}_{\bm{D}_T}^{(h,s)}=\dfrac{\sum_{i=1}^{N_{T}} \big( \hat y_{Ti}^{(h,s)} - y_{Ti}\big)^2}{N_{T}}
    .
    $$
\end{itemize}

\noindent
Table 1 displays the Monte Carlo averages,
$$
{\rm MSPE}_{{\cal X}_0}=\dfrac{\sum_{h=1}^H \sum_{s=1}^S  {\rm MSPE}_{{\cal X}_0}^{(h,s)}}{HS} \;\; {\rm and} \;\;
{\rm Log(det)}=\dfrac{\sum_{h=1}^H \sum_{s=1}^S {\rm Log(det)}^{(h,s)}}{HS},
$$
for the different sampling strategies: non-inf. I, non-inf. D, inf. I, inf. D and SRS, respectively.
The results are obtained  having setted $n=500$, $\tilde{N}=2 \cdot n$, $\nu_1=2$ and $\nu_2=3$.
\begin{table}[ht]
\centering
\begin{tabular}{rcc}
  \hline
 Algorithm &  ${\rm MSPE}_{{\cal X}_0}$ &  Log(det) \\
  \hline
non-inf. I & {\bf 0.0857}  & 93.4269 \\
non-inf. D & 0.0947  & {\bf 94.3877} \\
inf. I & 0.0938  & 92.0869 \\
inf. D & 0.1030  & 92.7748 \\
SRS & 0.2056  & 82.5234 \\
   \hline
\end{tabular}
\caption{{\footnotesize Monte Carlo averages ${\rm MSPE}_{{\cal X}_0}$ and Log(det) for the subsamples of size $n=500$ obtained from the different Algorithms
}}
\end{table}

Accordingly to the definitions of I- and D-optimality, the minimum value of the ${\rm MSPE}_{{\cal X}_0}$ is associated to the noninformative I-Algorithm, while the maximum value of the Log(Det) corresponds to the noninformative D-subsample. Therefore, Algorithms 1 and 4 provide samples that do not include high leverage points and are \lq\lq nearly" D- and I-optimal (they are not exactly D- and I-optimal because of the exclusion of these high values).

Table 2 lists the following Monte Carlo averages: \\[.2cm]
${\rm SPE}_{{\cal X}_{0}}=\sum_{h=1}^H \sum_{s=1}^S {\rm SPE}_{{\cal X}_{0}}^{(h,s)}/HS\;$,
$\;\;{\rm SPE}_{{\cal X}_{T}}=\sum_{h=1}^H \sum_{s=1}^S {\rm SPE}_{{\cal X}_{T}}^{(h,s)}/HS$, \\[.2cm]
${\rm SE}_{\boldmath{D}_0}=\sum_{h=1}^H \sum_{s=1}^S {\rm SE}_{\boldmath{D}_0}^{(h,s)}/HS\;$
and
$\;{\rm SE}_{\boldmath{D}_T}= \sum_{h=1}^H \sum_{s=1}^S {\rm SE}_{\boldmath{D}_T}^{(h,s)}/HS$,\\[.2cm]
for the different subsamples. These Monte Carlo averages represent an empirical version of MSPE and MSE on ${\cal X}_{0}$ and ${\cal X}_{T}$, respectively.
From these results, we can appreciate the prominent role of the informative procedures in selecting subsamples without outliers. In fact, when the database includes outliers in $Y$ which are not associated with high leverage points (as in this simulation study), then  only the informative procedure enables us to exclude these abnormal values from the subsample.

\begin{table}[ht]
\centering
\begin{tabular}{rccccc}
  \hline
 Algorithm & ${\rm SPE}_{{\cal X}_{0}}$ & ${\rm SPE}_{{\cal X}_{T}}$ & ${\rm SE}_{\boldmath{D}_0}$ & ${\rm SE}_{\boldmath{D}_T}$ \\
  \hline
 non-inf. I & 6.5104 & 6.8020 & 16.0792 & 16.3538 \\
 non-inf. D & 6.1011 & 6.2945 & 15.5982 & 15.7969 \\
 inf. I & {\bf 0.1464} & {\bf 0.1494} & {\bf 9.4445} & {\bf 9.5337} \\
 inf. D & 0.1594 & 0.1601 & 9.4564 & 9.5448 \\
 SRS & 0.2629 & 0.2671 & 9.5683 & 9.6594 \\
   \hline
\end{tabular}
\caption{{\footnotesize Monte Carlo averages ${\rm SPE}_{{\cal X}_{0}}$, ${\rm SPE}_{{\cal X}_{T}}$, ${\rm SE}_{\boldmath{D}_0}$ and ${\rm SE}_{\boldmath{D}_T}$ for the subsamples of size $n=500$ obtained from the different Algorithms
}}
\end{table}

\noindent
{\bf Remark.}
Actually, to take into consideration the randomness of the SRS technique, we have drawn $N_{SRS}=50$ different independent SRSs from each dataset  $_h\bm{D}_{s}$, for $h=1, \ldots,H$ and $s=1,\ldots,S$; the Monte Carlo averages for SRS are based also on these additional observations.

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text:
01 — Intro. And Radio Derb is on the air. This is your flamboyantly genial host John Derbyshire, with our round-up of the week's news.
All is quiet here at Buckley Towers, I am glad to report. The spot of bother we had last week with demonstrators in the street outside was most ingeniously solved by Jonah. He diverted the water pumps that supply the grotto to discharge their contents out of the 96th floor windows, to the great discomfort of the protestors, who soon dispersed. Never let it be said that we are without resources to defend our bastion of conservatism! My own original suggestion was for boiling oil, but I regret to report that this was vetoed by the National Review suits. There is just no respect for creative thinking nowadays.
OK, on with the show. What have we got? A debate, of course. How did this one go?
02 — GOP Bloomberg debate 1. Yes: another week, another GOP candidates debate. What did we learn from the Bloomberg-sponsored event on Tuesday?
Nothing certain, of course. It's still early days, and there aren't any certainties yet. The fun of the game here is to see how the probabilities change.
There is pretty universal agreement — and you can include me in it — that the probability of Mitt Romney being at the head of next year's GOP ticket went up a few notches. I'd guess it at around 80 percent right now.
There's a Chinese idiom that comes to mind every time I see Mitt: 八面玲瓏. The literal meaning is "smooth and finished on all eight sides," with repeated "jade" elements in the written characters. So I guess it refers to a finely-worked piece of jade — an octahedron, presumably. When it's used of a person it means "deft, slick, and smooth in all kinds of social exchanges." That's how Mitt strikes me: 八面玲瓏.
And of course that's how he wants to appear: as a polished professional act, with no rough edges. He's playing to his strengths; and Mitt's undoubted strengths are as a capable, calm, effective manager. If he tried to come on as a charismatic uplifter, he'd just make a fool of himself, and he knows that. After running for president all these years, Mitt's the one in the room who best has it down to an art, and it's not the least bit surprising that this is so. That's most of his polling numbers right there: The capable, experienced executive who, even though he may not make anyone swoon, at least won't screw things up, and might even un-screw a few.
Herman Cain comes into clearer focus each time we see him on stage. Cain's positives have been generally noted, including by me: that sunny unflappable disposition, pretty good across-the-board conservatism, radical simplification of taxes. A few mild negatives have been registered: his odd position on Second Amendment rights — he seems to believe that Congress can't impose gun control but states can, which is constitutional nonsense, and there's a lack of clarity on immigration.
I've picked up a broader Cain negative — not by any means a deal-breaker, but slightly off-putting. I haven't got it into really good focus yet, but it's something like narrowness. I'm just getting the impression this is not an imaginative guy, perhaps even not a guy much interested in anything outside his own direct experience. This has come up before, in his obvious vagueness towards foreign policy. It showed again on Tuesday when he was asked to name the Fed chairman he most admired. That's a no-brainer for any conservative: you just say "Volcker."
Cain named Alan Greenspan. Asked why, he replied as follows, quote: "Because that's when I served on the board of the Federal Reserve in the early 1990s. And the way Alan Greenspan oversaw the Fed and the way he coordinated with all of the Federal Reserve banks, I think that it worked fine back in the early 1990s." End quote.
Now, maybe I'm reading too much into this, and to be sure there is some kind of a case to be made for Alan Greenspan, but it was Cain's appeal to his own experience that snagged my attention.
Sure, our own personal experiences loom especially large to all of us; but wisdom comes from getting outside your own skin and taking a wider view. The way to do that is, first, by constant reading, and second, by seeking out people who've had experiences widely different from your own, and listening attentively to what they say. I'm getting the beginning of a hint of an impression that Herman Cain hasn't done a whole lot of that.
Well, I'm told there are 13 more debates scheduled, so things will get clearer, faster. Quite possibly I'm wrong about Cain; and even if I'm not, there is some downside to every one of these candidates. Mr Flawlessly Perfect unfortunately did not register as a Republican presidential candidate; neither did Mrs Flawlessly Perfect. We'll go with what we've got.
And one thing I found myself thinking while watching Tuesday's debate is that we've got a lot. The exchanges were intelligent and civilized. You have to have lived in a nation that doesn't have open political debate to understand what a miracle this is. We'll get a presidential candidate out of this, and a vice-presidential one too, and send Barack Obama and his cronies back to Chicago.
03 — GOP Bloomberg debate 2. Tuesday's debate was restricted to economic issues. That idea is a little fuzzy around the edges, though. Everything the federal government does is an economic issue to some degree in that it either costs or raises public money. But OK, let's rule out gay marriage, Supreme Court nominations, space exploration, and the Middle East peace process as being only very indirectly related to the national economy. That still leaves a fringe of issues you could plausibly argue in.
Immigration, for example, both legal and illegal. It's annoying, but seems to be necessary, to add those words "both legal and illegal" every time I say "immigration," because the word "immigration" seems to have become wellnigh a synonym for "illegal immigration," leaving us no way to discuss the large and important topic of legal immigration. Indeed, on the political left it's even worse than that. Over there, the word "immigration" is a synonym for "illegal immigration of Spanish-speaking people from south of our southern border."
OK, immigration. It's as close to an economic issue as an issue can be without being one. For example, there's the question I've been asking for the last few months, but which hasn't yet come up in any of the debates. To quote from myself, posting on The Corner June 6th, quote: "Why, with unemployment stuck at close to ten percent, are we bringing in well over a million foreigners a year for settlement, around 80 percent of them of working age? Why do you not send to Congress a request for a moratorium on further immigration until the unemployment rate drops below five percent?" End quote.
OK, that's actually two questions. They're two good questions, though, and pretty intimately related to economic issues. So why didn't we hear them, or anything like them, on Tuesday? Especially with Rick Perry on stage — Rick Perry who, you'll no doubt remember, suffered the most serious wound so far inflicted in these debates on this very topic, back on September 22nd.
So why didn't the topic come up? A pretty good guess would be that Tuesday's debate was sponsored by Michael Bloomberg's organization. Bloomberg is an open-borders fanatic. He's even something more extreme than that: an open-borders hysteric, really. He flushes and sputters if anyone suggests any kind of restriction on people settling in the U.S.A. In his mind, making a foreigner apply for a visa to enter our country is tantamount to tattooing a number on the foreigner's arm and throwing him in a cattle wagon. I'll bet some kind of word went down that immigration was totally off the table for Tuesday's debate.
If so, it cost Michele Bachmann a good debating point. Mitt Romney asked Mrs Bachmann, quote: "You've got young people coming out of college, maybe not here at Dartmouth, but a lot of colleges across the country wondering where they can get a job. What would you do — beyond the tax policies you describe — to get people back to work?" End Mitt quote.
Now back in August, in the presidential debate in Ames, Iowa, Mitt Romney said this, quote: "If someone comes here and gets a Ph.D in — in physics, that's the person I'd like to staple a green card to their — to their diploma, rather than saying to them to go home." End August Mitt quote.
So: according to October Mitt, we have young people coming out of college wondering where they can get a job. According to August Mitt, we should staple green cards — that's permanent residency — to the diplomas of foreign physics graduates. Michele should have jumped all over that. But I guess if she had, a flushed, crazed, sputtering Michael Bloomberg would have barged into the power closet and thrown all the circuit breakers.
04 — Religions and cults. Rick Perry made a speech last Friday to Christian conservatives in Washington, D.C. He was introduced by the Reverend Robert Jeffress, who is the senior minister at First Baptist Church in Dallas. Perry's not himself a Baptist. He was raised a Methodist, but lately he's been attending a nondenominational megachurch in Austin. Pastor Jeffress is a big Perry supporter, though, and that's why he was in D.C. introducing Perry.
Perry's speech was basic campaign stuff, with some extra family-values affirmations added to make the speech apt to the occasion — it was actually the Values Voter Summit. It wasn't the substance of Perry's speech that got everyone's attention, though. What got our attention was Pastor Jeffress' remarks before and after the speech.
Introducing Perry, the pastor said, referring to the struggle for poll numbers between Mitt Romney and Rick Perry, the pastor told the audience that they would be able to choose between, quote, "a conservative out of convenience" and a candidate of true conviction. Talking to reporters later, Pastor Jeffress amplified his opinions, calling Mitt Romney's Mormon church a "cult." He did allow that Romney had some good qualities, quote: "He's a fine family person. But being a fine person with a great family and great values does not get you to heaven." End quote.
Undoubtedly there's a politically significant issue here. Polls regularly show a big lump of the electorate unwilling to vote for Romney just because he's a Mormon; though what doesn't get mentioned often enough is that some large portion of that lump is religion-hating leftists who wouldn't vote for a Republican anyway.
Then there's the whole issue of Evangelicals and conservatism, which has more wrinkles in it than Joan Rivers' neck. Like many other conservatives, I regard Evangelicals as fair-weather friends. I remember how hot they were for Jimmy Carter in '76; and Evangelical superstar pastor Rick Warren back in '08 seemed to me to be smiling on Barack Obama a tad more benignly than the requirements of simple patriotic non-partisanship required.
To me, an unbeliever, an ex-Christian who 'fessed up to myself rather late in life that I don't have a religious bone in my body, these issues are all a bit abstract and remote. As my colleague Jonah remarked in a column last week, to an unbeliever it looks like cults all the way down. Religion is about supernatural agents, and we get off the bus right there. (And if you think Theravada Buddhism is an exception, I refer you to Chapter 4 of Jason Slone's fine book Theological Incorrectness. Whatever your hippie pal over in Sausalito told you, nearly all the world's practicing Buddhists regard Lord Buddha as a supernatural agent. California Buddhism is the Unitarian version.)
So from the unbeliever's point of view there's an element of preposterosity in all religion. Since the great majority of human beings claim some religious belief, we heathens just have to come to terms with the fact that perfectly healthy, useful, admirable, happy, socially-responsible, and often brilliant people believe preposterous things in one corner of their minds.
It even sometimes seems that the more preposterous the belief, the better socialized are the believers. I've met a lot of Mormons, and they all seemed to me exceptionally well-adjusted. The statistics of Mormons in the U.S.A. are very good: High levels of education, health, family cohesion and social involvement, low levels of crime, divorce, illegitimacy, and lifestyle diseases. Yet this is a religion based on stuff a farmer in upstate New York claims to have read off golden tablets given to him by an angel, using magic spectacles the angel — who apparently had training as an optometrist — gave him for the purpose. Mark Twain described the Book of Mormon as, quote, "chloroform in print," and having looked into that scripture, I wouldn't disagree. So go figure: wacky beliefs, great social outcomes.
In Romney's case, I'll go with those great social outcomes. He's not my candidate — right just now I'm pondering a Cain-Bachmann ticket, with Ron Paul as Treasury Secretary — but I can't see any downside to his being a Mormon. Conservatism, in Pastor Jeffress' mind, is inseparable from mainstream Christian belief. Conservatism, in my mind, is about diminishing the power of the state, maximizing the liberty of the individual, looking skeptically at social revolutions (including demographic ones), respecting accumulated wisdom, and safeguarding national sovereignty. You can wish for those things and work for those things with almost any religious belief, or none at all.
05 — Iranian plot? Or not? I really don't know what to make of this Iranian terror plot story.
The key figure here is Manssor Arbabsiar, 56 years old, born in Iran, a naturalized U.S. citizen, been living for 25 years in and around Corpus Christi, Texas. Arbabsiar is a businessman, though a mighty unimpressive one. He's run convenience stores, kebab houses, and used-car lots; never seems to have made much money, has a record of not paying bills or keeping proper accounts. He has a string of petty misdemeanors: drug possession, driving with a suspended license, suspicion of theft, that sort of thing.
Lately this rather seedy loser has been spending time in Tehran. Now the story is that he offered a million and a half dollars, presumably supplied by Iran, to a Mexican drug gang to assassinate the Saudi ambassador. The "Mexicans" were in fact American G-men, and the whole thing was a sting.
It's not implausible, but there's a funny smell about the whole business. Not a real knock-out open-sewer-type smell; more like last week's Kung Pao chicken doggie bag your wife left at the back of the fridge and forgot about.
First, an operation of this significance, if it was an Iranian government operation, would have been given to the Quds Force, an elite arm of Iran's Revolutionary Guards charged with overseas operations. And in fact the Department of Justice claims that Gholam Shakuri, Arbabsiar's partner in the plot, is a Quds operative. Yet the Quds force is experienced, professional, swift, and lethal. If Quds wants you dead, you're dead before anyone knows anything about it, you're dead before you can finish saying the word "dead." These guys are the Mossad of the Moslem world. They wouldn't touch a bumbling loser like Arbabsiar with a ten-foot pole.
And then there's the timing of the announcement. Arbabsiar was arrested September 29th, and is said to have confessed immediately, even waiving his Miranda rights. The announcement from the Department of Justice came on Tuesday, which was October 11. That's twelve days; not an unreasonable gap, but you'd actually expect something longer, with so much digging to do, and especially with Gholam Shakuri, Arbabsiar's co-conspirator, still at large. Ah, but the announcement came just one day before another announcement: House Oversight Committee Chairman Darrell Issa declaring on Wednesday that he has subpoenaed Attorney General Eric Holder on the "Fast and Furious" gun-running fiasco.
All of that is circumstantial, of course, but if I were POTUS at this point, I'd be deeply hesitant to take any major action based on what we so far know.
The whole Middle East in in a highly unstable condition right now. The Saudis and the Iranians are playing chess for regional hegemony. Iran is struggling to shore up its Syrian client state and keep the lid on its Lebanon client state. The Saudis have their own clients in Yemen and Bahrain to support. Egypt, a natural ally of the Saudis, is a total mess, headed towards no-one knows where. With the world financial system stuck in permanent crisis, nobody wants to risk an oil price spike.
Iran itself has major internal problems. Li'l Squinty Ahmedinejad seems not to be on speaking terms with Supreme Leader Ayatollah Khamenei, and the position of the Revolutionary Guard, who run the Quds force, is unclear in the dispute. The urban population is unhappy over stagnant living standards and unemployment. There are endless possibilities for ethnic unrest: a third of the population is not Persian.
In these circumstances, restraint is the only thing that makes sense. Some angry talk is appropriate, and swipes like the one we've just taken against the Iranian airline, but for once I have to agree with the Pentagon spokesman: this should be handled as a judicial and diplomatic issue. I see John Bolton and Bill Kristol are lacing up their combat boots, but the administration would be fools to follow them. There are plenty of fools in this administration, but none are such big fools as that.
06 — Hispanic Heritage Month. We are in the closing days of Hispanic Heritage Month, which runs September 15 to October 15. It was originally Hispanic Heritage Week, proclaimed by President Lyndon Johnson in 1968; then Ronald Reagan extended it to a whole month twenty years later.
I'm not going to beat about the bush here: I'm against the whole thing. If private citizens want to hold private celebrations of their ancestry, I'm fine with it, so long as government doesn't interfere. I'm totally against state and federal governments getting into the ethnicity business, though. It sows discord and division, and creates lobbies for ethnic favoritism.
I'm especially against government recognition of a Hispanic identity. I believe, in fact, that Hispanic identity is an utterly bogus concept. Florida Cubans, California Mexicans, and New York Puerto Ricans have nothing in common, other than their grandmothers all spoke Spanish. And all three of those groups have as much in common with Lithuanians and Lapps as they have with Spaniards from Spain.
When Sonia Sotomayor was picked for the Supreme Court, the administration seems to have thought that Hispanics nationwide would cheer. Professional activists of course did cheer; that's probably all that this administration, made up as it is largely of professional ethnic activists, noticed. The average Mexican or Guatemalan immigrant, however, couldn't see what it had to do with him. Sotomayor's people were Puerto Rican. To a Mexican in Escondido or a Salvadorean in East Hampton, Puerto Rico might as well be one of the moons of Uranus.
And what is up with affirmative action for Hispanics? When did the U.S.A. ever enslave Hispanics? In fact, since the only unifying feature of Hispanics is that they or their ancestors spoke Spanish, which is to say the language of the Conquistadors, we are giving affirmative action to people on the grounds they speak the language of colonizers and ethnic cleansers. Now, you could of course argue for separating out by race the aborigines whose enslaved ancestors had Spanish forced on them, from the white-European descendants of the enslavers … But somehow I don't think you'd get very far with that.
In terms of social outcomes, too, Hispanics are all over the place. Cuban immigrants do very well in the U.S.A., as do immigrants from Spain, like Charlie Sheen's grandad. Mexicans, though of course there are some success stories, overall do badly, and Puerto Ricans and Central Americans even worse. So even a simple question like, "Is mass Hispanic immigration good for the U.S.A.?" can't be answered until you specify which Hispanics you're talking about.
In short: I say it's spinach, and I say the hell with it. "Hispanic" is a bogus and meaningless ethnic category; but even if it were as precise as "Amish" or "Norwegian," the federal government would have no business telling us to celebrate it, or awarding it preferences and favoritism. Hispanic Heritage Month? Bah, humbug.
07 — Miscellany. And now, ladies and gentlemen, our closing miscellany of brief items.
Item: A listener emailed in last week to wonder why I hadn't given a mention to Steve Jobs. I didn't give him a very coherent answer, so I'll have another go at it here.
The death last weekend of Dennis Ritchie, who devised the C programming language and was instrumental in developing the UNIX operating system, that clarified things for me a bit. I spent much of my working life in corporate IT. From that perspective, Dennis Ritchie and others like him were the boys in the backroom, building the weapon systems that we corporate IT grunts could use in our daily battles to deliver projects on time and in budget.
To us — and it's very unfair, and I mean no disrespect to the dead, I'm just trying to paint a picture for you here — to us, Steve Jobs was a guy who made pretty, stylish toys for depilated metrosexual yuppie types to play with while sipping their Chai Crême Frappuccinos through designer straws.
As I said, it's unfair: Jobs was a great entrepreneur, and we can never have enough of those. Furthermore, as Kevin Drum explained on the Mother Jones website last week, the triumph of PCs in the corporate world was to some degree a matter of luck.
And of course, as I'm sure you're thinking right now, this attitude of mine is a case of over-privileging my own experience — the very thing that a few minutes ago I was chiding Herman Cain for. I mention it only to explain what is, to judge from commentary I've been seeing, quite a widespread attitude among veterans of corporate IT.
I shall now strive to broaden my horizons. I'll go to the Apple store and buy something. A USB cable, perhaps, or maybe an adapter plug …
Item: What can one say about these Occupy Wall Street protestors? Can't we lease some South Korean riot squads?
New York Police Commissioner Ray Kelly raised my hopes Thursday when he ordered the lefties to vacate a park they'd occupied so it could be cleaned up. I should think that with power hoses and dumps of ammonia or carbolic acid from helicopters, the job could be done with the protestors in situ, but Kelly said he wanted them out. The fun confrontation has been postponed somehow, though. Pity.
Meanwhile, George Will extracted the main political point. The last time middle-class lefties were out demonstrating on this scale, Will pointed out, was in the run-up to the 1968 election. Result of that election: Richard Nixon took 32 states and George Wallace another five: the Democrat got 13. The GOP picked up five seats in the Senate and five in the House. So … go to it, kids.
Item: Listeners are constantly clamoring for more news from Turkmenistan. How are things going over there, under the wise, benign rule of our good friend President Gurbanguly Berdymukhamedov?
Things are going so well that there is in fact no news to report. However, Turkmenistan's neighbor to the north, Uzbekistan, did get a passing mention this week.
GOP presidential contender Herman Cain was asked by an interviewer on the Christian Broadcasting Network whether he could name the president of Uzbekistan. Cain came back with an endearingly — well, it endeared him to me — politically incorrect response: [Clip of Cain: "… when they ask me who is the president of Ubeki-beki-beki-beki-stan-stan I'm going to say, you know, I don't know. Do you know?"]
I guess Herb lost the Uzbek-American vote right there. It was the right response, though. We're electing a president here, not the Columbia Desk Encyclopedia. Cain's response was directly in the spirit of Winston Churchill, who once said, quote, "I have lived 78 years without hearing of bloody places like Cambodia."
A chief executive needs to clear his mind of irrelevant junk and concentrate on what's significant. In foreign policy, that means fixing your attention on big, important nations, like China, Russia, India, Germany, and Turkmenistan. [Clip: Turkmenistan national anthem.]
Item: And speaking of utterly insignificant nations, here is I believe Radio Derb's first ever news item from Bhutan, a teeny little kingdom up there in the Himalayas somewhere.
Bhutan's current monarch rejoices in the name Jigme Khesar Namgyel Wangchuck, age 31. Well, King Wangchuck got married Thursday. In the Dzong. That's the monastery where they got married, the Dzong. In Bhutan.
All joy to the happy couple, King Wangchuck and his bride Queen Jetsun (Jetson?) Pema.
If it's not an act of lèse majesté on my part — and I very much hope it's not, I don't want the Bhutanese equivalent of the Quds force showing up in my driveway — if it's not disrespectful, I must say, looking at pictures of the wedding, Queen Jetsun is a fox.
(Note to self: Have staffers look at possibility of RD franchises in Bhutan …)
08 — Signoff. There you have it, listeners: another week of sliding down History's razor blade. Things look bad all over; but are we downhearted? Well, some of us are. Not Gracie, though.
[Music clip: Gracie Fields "Sing As We Go"]


Patrick Novecosky, editor of this blog, is an occasional correspondent for the National Catholic Register. In the following article, published in the April 6 issue, he writes about Florida's regional major seminary and the Sunshine State's vocations boom.
Julio De Jesus was only 16 when he came to the United States with his family from the Dominican Republic. As a teen in a new country, he struggled with leaving behind his friends, his language and his culture, but he knew he would not have to leave his faith behind.
In his effort to discern his vocation, De Jesus said that Pope John Paul II was his anchor.


Coming soon to Floreana Island will be the foremost and leading eco-luxury hotel to be seen in all of Ecuador and the Galapagos Islands. Renewable energy will be the main source of power and the infrastructure will be made of only sustainable material, blending in with the natural surroundings of this extraordinary island.
Welcome to the Ecuador Eco-Luxury Group. We are the country's foremost sustainable tour operators promoting a luxury experience, while committing to maximizing human development and environmental quality to unique destinations like the Galapagos Islands and Amazon Rainforest.
© 2018 Eco Luxury Group Ecuador | Haugan Cruises.


text:
<?php

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

use Login\Entity\Pessoa;
use Zend\Test\PHPUnit\Controller\AbstractHttpControllerTestCase;

/**
 * Description of IndexControllerTest
 *
 * @author leonardo
 */
class LoginControllerTest extends AbstractHttpControllerTestCase {

    protected $traceError = true;

    public function setUp() {
        $this->setApplicationConfig(
                include '/var/www/html/circuitodavisaoZF2/config/application.config.php'
        );
        parent::setUp();
    }

    public function testLoginActionCanBeAccessed() {
        $this->dispatch('/');
        $this->assertResponseStatusCode(200);

        $this->assertModuleName('Login');
        $this->assertControllerName('Login\Controller\Login');
        $this->assertControllerClass('LoginController');
        $this->assertMatchedRouteName('login');
    }

//    public function testLogarActionRedirectsAfterValidPost() {
//
//        $authService = $this->getMockBuilder('Zend\Authentication\AuthenticationService')
//                ->disableOriginalConstructor()
//                ->getMock();
//        $entityManager = $this->getMockBuilder('Doctrine\ORM\EntityManager')
//                ->disableOriginalConstructor()
//                ->getMock();
//
//        $serviceManager = $this->getApplicationServiceLocator();
//
//        $serviceManager->setAllowOverride(true);
//
//        $serviceManager->setService(
//                'Zend\Authentication\AuthenticationService', $authService
//        );
//
//        $serviceManager->setService(
//                'Doctrine\ORM\EntityManager', $entityManager
//        );
//
//        $postData = array(
//            'email' => 'falecomleonardopereira@gmail.com',
//            'senha' => '123',
//        );
//        $this->dispatch('/logar', 'POST', $postData);
//        $this->assertResponseStatusCode(200);
//
//        $this->assertRedirectTo('/acesso');
//    }

//    protected function mockLogin() {
//        $userSessionModel = new Pessoa();
//        $userSessionModel->setId(1);
//        $userSessionModel->setNome('Tester');
//
//        $authService = $this->getMock('Zend\Authentication\AuthenticationService');
//        $authService->expects($this->any())
//                ->method('getIdentity')
//                ->will($this->returnValue($userSessionModel));
//
//        $authService->expects($this->any())
//                ->method('hasIdentity')
//                ->will($this->returnValue(true));
//
//        $this->getApplicationServiceLocator()->setAllowOverride(true);
//        $this->getApplicationServiceLocator()->setService('Zend\Authentication\AuthenticationService', $authService);
//    }
}

redpajama_set_name: RedPajamaGithub


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text:
Q: awk / gawk asorti() problem I've got following problem with gawk's asorti function:
gawk 'BEGIN{ \

  a[1]=6; \

  a[2]=7; \

  a[3]=8; \

  a[21]=9; \

  a[123]=10; \

  t=asorti(a, o); \

  for (i=1; i<=t; i++) { \

    print i,o[i]; \

  } \

}'

The result is:
1 1

2 123

3 2

4 21

5 3

So it's pretty clear awk, sorted indices in lexicographical order, but awk's doc says (asort(s[, d])):

"The contents of s are sorted using gawk's normal rules for comparing values..."

However, when I copy indices itself into temp array, and sort that new array using asort(),
it seems ok (using something like):
j=1; for(e in a) { temp[j++] = e; }

Am I DOIN-IT-WRONG, or is it problem with gawk's asorti() ?

A: According to the gawk manual: "An important aspect about arrays to remember is that array subscripts are always strings."

A: I know there were limitations on gawk 3, but on gawk 4 (at least on 4.1.1) it's trivial:
t=asorti(a, o, "@ind_num_asc");

A: As a workaround you could use something like this (you may need to adjust the padding):
gawk 'BEGIN {
  a[1] = 6; a[2] = 7; a[3] = 8; a[21] = 9; a[123] = 10;
  for (i in a) io[sprintf("%15s", i)] = a[i]
  t = asorti(io, o)
  for (i = 0; ++i <= t;) print i, o[i] + 0
    }'

With Gnu awk you can even preserve the original keys/indexes:
WHINY_USERS=oops gawk 'BEGIN {
  a[1]=6; a[2]=7; a[3]=8; a[21]=9; a[123]=10;
  for (i in a) o[sprintf("%15s", i)] = a[i]
  for (i in o) print i + 0, o[i]
    }'

redpajama_set_name: RedPajamaStackExchange


text:
Великий ікосаедр — 45-я зірчаста форма ікосаедра, одне з тіл Кеплера — Пуансо. Його символ Шлефлі — . Це означає, що у нього 5 трикутників з чергуванням вершин сходяться в кожній вершині (див. малюнок нижче). Двоїстий багатогранник до нього — .

Як кирпатий багатогранник

Великий ікосаедр можна визначити як ретрокирпатий тетраедр. Якщо початковий багатогранник (або паркет) має символ Шлефлі {p, q}, то ретрокирпатий багатогранник (або паркет) буде мати конфігурацію вершини (3.3.p.3.q)/2 (тобто як звичайний кирпатий багатогранник, але з чергуванням вершин).

Як зірчаста форма ікосаедра
Його грані складені з 11 і 12 відсіків (див. нижче). Зірчасті форми ікосаедра з 42 по 57 дуже схожі на великий ікосаедр, але в багатьох з них розірвані грані. Наприклад, у 44-ї форми відсутній 12-й відсік, але є 10-й. Але всі з них мають 11-й відсік.

Примітки

Література

 Александров П. С., Маркушевич А. И., Хинчин А. Я. Энциклопедия элементарной математики. — ГИФМЛ, 1963. — Т. IV.

Посилання

 Однорідні багатогранники та двоїсті до них

Багатогранники Кеплера — Пуансо

redpajama_set_name: RedPajamaWikipedia


text:
e-clinics bring healthcare to rural areas in Pakistan
Home Innovation Digest e-clinics bring healthcare to rural areas in Pakistan
Using technology to reimagine how health care is delivered to the most vulnerable people in Pakistan is an initiative by 24 year old Muhammad Sarim Raza.
With almost 70% of the Pakistani population living in underserved rural areas, where there is lack of medical personnel, sparse healthcare facilities, and high cost of treatments.
Muhammad Sarim Raza, the founder of a social enterprise called Riayat, and also coordinates the Youth Action Hub Pakistan, an UNCTAD youth network of young change makers running innovative programmes to improve the lives of local people; has partnered with Idara al Khair, a local nonprofit organization, to improve healthcare coverage for rural dwellers.
Using telehealth to provide healthcare services via electronic information and telecommunication technologies, they offer virtual medical consultations to patients in remote locations, and in the comfort of their homes. 'Many people cannot afford to physically go to a doctor. Our e-health initiative makes consultations affordable and available to low-income communities', Mr. Raza said.
At the peak of the COVID-19 outbreak in the country, his team created an e-health platform and mobilised local teachers to conduct door-to-door visits to introduce residents to it, offering general medical check-ups free of charge. They also established an e-clinic at a local school and organized a virtual workshop to train the teachers on how to register patients on the platform and book appointments with doctors. A psychologist trained the teachers on how to identify mental health problems such as stress, anxiety and depression.
The team visited 90 families comprising about 540 people and registered them on the platform. They found that many people did not know the benefits of good mental health. 'They believed that if physical needs were met, mental health did not matter', Mr. Raza said.
Today, the e-clinic has evolved into a subsidised medical centre with doctors, nurses and technicians. With specialised care and emergency treatments now available to the local community, the number of patients is steadily growing. Mr. Raza is committed to using technology for good – expanding access to health care, education and employment opportunities for all.
His enterprise's first project involved distributing food supplies to more than 300 low-income households around Karachi, Lahore and Multan cities in Pakistan to tackle hunger, while creating awareness on how to curb the spread of COVID-19. During the project, he identified weak internet connectivity and the lack of digital literacy as key barriers for many people. He then mobilised Youth Action Hub Pakistan to launch the 'Right to Technology' initiative to advocate for digital inclusion.
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5Qs with Jane Shi, Character Designer and Illustrator
Our 5Qs series is a chance for the SGN members to know more about folks in the community, where we pose 5 questions to exciting individuals to find out more about what they do.
By SGN | 22 Apr 2022
Meet Jane, a talented LA-based Character Designer and learn about her unconventional route to the US in order to pursue her dreams of being an artist. Keep a look-out for an upcoming show that she worked on with Warner Bros Animation!
Tell us a bit about yourself – what brought you to the U.S.?
I was born and brought up in Singapore to parents that immigrated from Shanghai in their 20s. I attended the Singapore education system all the way until Junior College, studying sciences and mathematics, even though that was not where my interests lie. After flunking my A Levels, I think my parents realized that I am neither going to be happy nor do well in the science field, and gave me the green light to pursue art. I spent 2-3 years figuring out what I wanted to do, applied to 10 art schools around the world, and eventually decided on Art Center College of Design in Pasadena, LA due to the proximity to the entertainment industry, and here I am!
Jane (left) at the historic El Capitan Theatre, LA
Tell us more about why you chose to be a character designer
I've been drawing since I could remember. I was always that kid that was doodling on everything. Exam papers, worksheets, notebooks etc. I think deep down, I've always known that I wanted to study art and design, but it was difficult to realise that dream with the stress of the Singapore education system and traditional chinese parenting. I think around the first year of Junior College, I started drawing a lot of portraits, and was deeply fascinated by them. I realized that the way someone posed in photographs, or even the photographs someone chooses to represent themselves, says tons about their personality. I started trying to include these subtleties I see in my portraits. And when I started taking art seriously, my fascination in portraits naturally progressed into a fascination in character design.
One of my first self-portraits that I ended up really liking!
A fun illustration I did to commemorate a Disney world trip I took with some friends!
Share with us about some of your favourite designs and the story behind it
This lineup of characters remains one of my favourite designs I have done. They are reimagined designs of characters from the musical "Rock of Ages", which I was absolutely obsessed with at the time. I had so much fun with their shapes and personalities, and I am very happy with how this project turned out.
These are sketches of a selfish, self absorbed kind that I played with that I ended up really liking just because he ended up being such a melodramatic, funny character.
This was a quick gesture sketch that I fleshed out a little more, but I also ended up really liking the dramatic lighting on her and her attitude.
I am currently working on an animated show with Warner Bros Animation. I can't say anything yet, but keep an eye out, it's going to be really cool!
I am one of those people that have way more hobbies than I probably should. For the most part, I love crocheting amigurumi and designing and sewing my own clothes. I also recently started a small business with my boyfriend selling our own handmade ceramics. Feel free to give it a follow on instagram @seajamstudios!
First batch of mugs that Jane and her boyfriend, Nick, made for their small business
How do you stay connected to Singapore?
Aside from the pandemic years, I go back to Singapore at least once a year. I also have frequent video calls with my friends, and they sometimes send me sauces and condiments from home. I am also constantly trying out Southeast Asian restaurants that pop up in LA! So far, my favourite is Ipoh Kopitiam in Alhambra. Their prata + curry chicken, kaya toast, and kopi makes me feel, for a minute, that I am back home again.
Karyan (left), Nick (top), Jane (top right), Weng Siang (right) enjoying dinner at Newton Food Court
Connect with Jane Shi
I am always open for illustration and/or design opportunities! Feel free to check out more of my work on my instagram:
Instagram: @janershee
Website: https://www.janeshi.studio/


Rural-urban migration patterns can be either voluntary or involuntary. Involuntary in-migration is often the result of populations being pushed out of their communities to make room for development and infrastructure; voluntary resettlement occurs in response to the pull of economic opportunity, such as employment. Though the populations in both categories are at risk for unemployment homelessness, food insecurity, education loss, and social isolation, the forms these risks can take are varied.
Rural-urban migrants face intensified impoverishment risks of landlessness, homelessness, and increased morbidity as compared to urban-urban and rural-rural relocation, as migrants can be less familiar with the challenges of life in an urban setting. Lack of adequate education or training can prevent access to the social, educational, and economic opportunities that attracted migrants to cities, resulting in low-paying and unstable employment.


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Q: System boots to a black screen after upgrade to 11.04 I was a similar situation to this user: Dual Boot 10.10 and 11.04 can't boot into 10.10 after an update
Only many more GRUB entres.
Natty still worked - and I could still access the natty partition, until I ran sudo apt-get dist-upgrade to install a kernel update.  Now trying to boot natty gives me a black screen.  Booting into the same kernel in 'recovery mode' gets me a little further: Plymouth appears and pressing any key shows me that it's stuck at 'CUPS printing... OK'.

A: For Maverick users who have NVIDIA and/or ATI graphics together with activation of graphics drivers in the Additional Hardware Window are likely to suffer from the issue as described in the question.  These drivers (especially nvidia) create a file called /etc/X11/xorg.conf.  This file gives details about resolutions and describes the actual driver in use.
However, during the upgrade to Natty, the file remains in place - but the proprietary driver from NVIDIA is replaced by an open-source driver called nouveau.  Since the file is still in place, the underlying graphics system called "X" still tries to invoke the old NVIDIA driver because its relying on the instructions in the xorg.conf file - the NVIDIA driver is not there resulting in black-screens etc.
For these users, the suggested route is to remove this file BEFORE upgrading.
However, this can be overcome by booting from a Live CD - the desktop CD.
Start a terminal and type
gksudo nautilus

then navigate to the folder /etc/X11/xorg.conf on your local hard-drive and either rename it or remove it.


Things were pretty slow throughout the morning and afternoon… And THEN, we enjoyed some amorous grizzlies in the early evening.
My sister, Stacy, and I started Memorial Day with a run through the Northern Range. The only critters of note were a mama mallard and her brood of ducklings.


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our toes numbed by Florida grass at a February midnight.
as we must have been.
they found our daughter and loved her well.
and hence the son and second daughter.
We are still children who cannot keep our hands to ourselves.
keeping one another at arm's length always.


Consulting an ENT allergist is a wise choice. You want a physician that has a broad background of knowledge to treat your problems. A medical evaluation and onsite allergy testing are the first steps to finding out what can help you. Our office offers allergy shots and sublingual drops as a treatment option.
Drops taken at home. Only the first dose of each new build-up bottle must be taken at the office (every 21 days for 4 build-up bottles). First five injections at physician's office then may be taken at home.
No time away from work or school except during build-up phase. A 20 minutes wait is required after taking drops (once every 21 days). Time to get injections plus a 15 minute wait after receiving injections (only during initial 5 injections).
Very small chance of mild reactions. Small needles used for injections.
Small chance of mild reactions.
Maintenance dose achieved in 84 days. May have fewer allergy-related symptoms in 2-3 months. Maintenance dose achieved in 1-2 years. May have fewer allergy-related symptoms in 6-8 months.
Not covered by insurance; requires payment by cash, credit card or check. May be able to use flexible spending account.
$75.00 each for the 4 build-up bottles (One bottle every 21 days).
Approximately $900.00 per year. Partially or completely covered by most insurance after deductible is met, if applicable.
Extracts FDA approved but delivery method not approved. Insurance will not cover extracts because of delivery method. Extracts and delivery method approved by FDA.
Patient responsible for correct dose and staying on daily schedule. Patient responsible for staying on schedule, but nurse responsible for correct dose.
Patient required to have liquid Benadryl & EpiPen on hand when drops are taken. Patient required to have liquid Benadryl & EpiPen on hand for home injections.