text:
\section{Introduction}

Newsvendor model is a popular inventory management model. This model depends on two simple quantities, the purchase price of a single unit of a product $c$ and the its price when it is sold, $p$. The overall profit is fully defined by the critical fractile $(=(p-c)/p)$. If $F$ is the distribution of the random demand, $D$, then the optimal amount of product to order is $Q = F^{-1}\left((p-c)/p\right)$, where $F^{-1}$ is an inverse of $F$. This solution secures the highest expected profit.

The distribution of the random variable $D$ is often estimated using historic data. Hayes \cite{Hayes1969} considered exponential and Gaussian models to minimize Expected Total Operating Cost in the newsvendor problem. A Bayesian approach was used to improve the estimation. Similarly, Bayesian methodology was used to solve inventory problems in \cite{Scarf1959} and \cite{Karlin1960}. In more recent literature Bayesian frameworks is also very popular.

Liyanagea and Shanthikumar \cite{Liyanagea2005} suggested to use direct profit maximization which simultaneously incorporates both parameter estimation and expected profit maximization.

Quantile estimation methods range from maximum likelihood estimators to more robust methods minimizing specific risk functions: Koenker's quantile regression \cite{Koenker2005} minimizes the sum of absolute deviations of residuals; sum of signs of residuals minimization is suggested in \cite{Tarassenko2014}. All of these methods directly applicable to solving the newsvendor problem as well.

In a situation, when a family of probability distributions of the demand is known, a maximum likelihood estimation can be applied to quantile estimation as maximum likelihood estimators (MLEs) are asymptotically efficient under certain regularity assumptions. Then, asymptotically, MLEs reach the Cramer-Rao lower bound for variance, and no other estimator has asymptotically smaller variance. Can a quantile estimator with a smaller variance than the Cramer-Rao lower bound be found? If a relevant additional information is available then the answer is yes.

Many of the above mentioned statistical methods to solving the newsvender problem lead to estimators regular enough to have two finite moments.
If the two moments exist, then additional information can be combined together with external information (for example, an averaged sales from another store with similar characteristics) known with a degree of uncertainty (for example, a standard error of this average is known as well) \cite{Tarima2006}. This approach assumed that the additional information is unbiased, meaning that averaged sales for both stores are about the same. A similar assumption was made in \cite{Tarima2007}. It is possible that additional information can be biased, then minimum mean squared error (MSE) can be considered instead \cite{Tarima2009, Tarima2013}. The use of additional information known up to a few distinct values is considered in \cite{Dmitriev2014,Dmitriev2015, Dmitriev2017, Dmitriev2017_2}; the minimum MSE criterion was also used in these papers. Zenkova and Krainova \cite{Zenkova2017} considered the use of a known quantile for estimating expectations. The net premium using a known quantile for voluntary health insurance was used as an illustrative application.

This manuscript considers minimum variance and minimum MSE estimation for incorporating additional information. Section \ref{Methodology} presents methodology for combining empirical data (historical sales data directly available for data analysis) and external information available in form of means and standard errors. Sections \ref{Illustrative_Example1} and \ref{Illustrative_Example2} illustrate the use of this new statistical approach to the newsvendor problem for quantile estimation.

\section{Illustrative Example}\label{Illustrative_Example1}
Table \ref{tab:1} reports an artificial dataset with $36$ weeks sales data. Product A is sold at $860$ dollars per unit, Product  B  is  sold  at  $490$ dollars  per  unit.  The  retailer  pays $660$ dollars/unit for product A and $370$ dollars/unit for product B.

\begin{table}[ht]
    \centering
    \begin{tabular}{c|c|cccccc}
        Product A &  &  &  &  &  & \\
       \hline
         6576 & 4263 & 5340 & 3697 & 3535 & 2651\\
         2541 & 2351 & 3611 & 3867 & 4257 & 6204\\
         6666 & 4364 & 5441 & 3727 & 3495 & 2755\\
         2399 & 2452 & 3621 & 3961 & 4291 & 6264\\
         6600 & 4333 & 5391 & 3732 & 3662 & 2498\\
         2576 & 2402 & 3588 & 3900 & 4220 & 6214\\
       \hline
        Product B &  &  &  &  &  & \\
       \hline
        215 & 142 & 155 & 97 & 101 & 83\\
        104 & 96 & 102 & 101 & 130 & 215\\
        223 & 134 & 157 & 99 & 99 & 87\\
        100 & 97 & 98 & 104 & 131 & 202\\
        211 & 139 & 150 & 100 & 105 & 82\\
        103 & 98 & 100 & 102 & 127 & 219
    \end{tabular}
    \caption{thirty six week sales history (in numbers of units sold) for Products A and B}
    \label{tab:1}
\end{table}
The retailer is mainly interested in Product A as it is associated with high sales and is highly  important for the retailer's success. Then, the critical fractile ratio for Product A is $23.26\%(=(860-660)/860)$. The solution to the newsvendor problem is $Q=F^{-1}(0.2326)$. Relying on previous experience the retailer is confident that market demand for the two products, A and B, can be described by normal distributions, and the demands are likely to be correlated. Seasonal variation is so small that historic weekly data can be assumed to be independent. The only complication is that there exists a difficult to predict clustering, see Figure \ref{fig1}, but this problme is not in the focus of this manuscript. Normal distributions depend on two unknown parameters: $\mu$ and $\sigma^2$. Further, we will use subscripts $A$ and $B$ to differentiate between $\mu$ and $\sigma^2$ of Products A and B when needed.

Using Table \ref{tab:1}, the MLEs of the unknown parameters of the normal model are $\hat\mu_A = 4095.694$ (sample mean) and $\hat\sigma^2_A = 1791703$ (sample variance). Note, the sample variance is slightly different from the MLE of $\sigma_A^2$, but the sample variance is an unbiased estimator of $\sigma_A^2$ and will be used instead.

Then, using the $0.2326$-level normal quantile, $Q = 3118.14$ (in Product A units). This is approximately the MLE of optimal inventory levels for Product A. It is possible that another estimating procedure can be chosen to evaluate $Q$. For example, a direct quantile estimation without any assumptions on the underlying parametric family will lead to another estimate = $2859.34$. For illustrative purposes, we will focus on the approximate MLE and assume that the estimate is approximately unbiased. Without loss of generality the approach on the use of additional information, considered in this paper, applies to all unbiased or approximately unbiased estimators with two finite moments.

Given the importance of Product A, it is very difficult to obtain historic sales data from similar retailers. At the same time, additional data on Product B is much simpler to get from other retailers. Since the information on Product B is viewed as less important by other retailers, they freely share their sales data over a cup of coffee.

Consider the following additional information. An owner of a similar retailer store bragged that his store sold $30$ thousand units of Product B in past five years (additional information $1$), whereas an owner of another similar store said that his sales of Product B are higher than $100$ units every other week within the same five year period (additional information $2$). Can we use these two pieces of seemingly irrelevant information to improve estimation accuracy of the optimal inventory levels for Product A? The answer is yes, and we will return to this illustrative example in Section \ref{Illustrative_Example2}.

\section{Methodology}\label{Methodology}
Let $\theta$ be the parameter of interest, $\theta = F^{-1}((p-c)/p)$ for the newsvendor problem. The estimator of $\theta$ based on historical data, $\hat\theta$, is assumed to be an unbiased estimator of $\theta$, so that $E(\hat\theta) = \theta$. The $\hat\theta$ is a normal quantile estimated on historical sales data in Section \ref{Illustrative_Example1} ($\hat\theta = 3118.14$). In addition to $\hat\theta$, another estimator $\tilde\eta$ is available as additional information. This quantity estimates $\eta$ not $\theta$, and $\eta$ is a different and possibly multi-dimensional parameter. Specifically, in Section \ref{Illustrative_Example1}, $\eta=\left(\eta_{1},\eta_{2}\right)$, where $\eta_1$ is the mean weakly sales of Product B and $\eta_2$ is the median weakly sales of Product B. The additional information described in Section \ref{Illustrative_Example1} can be converted into a two-dimensional estimate $\left(\tilde\eta = (115.3846,100)\right)$. The number $115.3846$ is obtained as a ratio $30,000/260$, because there are $260$ weeks within a five year period. The first additional information sets the mean weakly sales of Product B at $115.3846$ units, and the second additional information sets the median sales at $100$ units/month.

Further, we use ``hat'' to denote estimators based on empirical (historical) data and ``tilde'' for the quantities determined by additional information.
Using the data in Table \ref{tab:1}, the mean weakly sales = $128$ ($\hat\eta_1 = 128$) and weakly median sales = $103.2$ ($\hat\eta_2$).

To combine additional information with empirical data, we consider a class of linear combinations
\begin{equation}
\theta^{\Lambda} = \hat\theta + \Lambda\left(\hat\eta - \tilde\eta\right)
\end{equation}
In the above equation, $\hat\eta$ refers to an estimate of $\eta$ based on empirical data. It is clear that $E(\hat\eta) = \eta$ by a property of the sample mean and median of normal data, but $E(\tilde\eta) = \eta + \delta$, where $\delta$ is a possible bias (a vector-column of biases) associated with additional information. In Section \ref{Illustrative_Example1}, the bias has two components and
$$\hat\delta = \hat\eta - \tilde\eta = (12.6154, 3.5).$$

Following \cite{Tarima2009}, the smallest MSE in the class $\theta^{\Lambda}$ is secured with
\begin{equation}
\label{optest_MMSE_mult}
\theta^{0}(\delta) = \hat\theta - cov\left(\hat\theta, \hat\delta\right)E^{-1}\left(\hat\delta\hat\delta^T\right) \hat\delta^T
\end{equation}
and
\begin{eqnarray}
\label{MSEoptest_MMSE_mult}
MSE\left(\theta^{0}\right) = cov\left(\hat\theta\right) -
cov\left(\hat\theta, \hat\delta\right)E^{-1}\left(\hat\delta\hat\delta^T\right)cov\left(\hat\delta, \hat\theta\right),
\notag
\end{eqnarray}
where $E\left(\hat\delta\hat\delta^T\right) = cov\left(\hat\eta\right) + cov\left(\tilde\eta\right) + \delta\delta^T$.

The special case of $\delta = 0$ makes $\theta^{\Lambda}$ unbiased for all choices of $\Lambda$. Then,
\begin{equation}
\label{optest_MVAR_mult}
\theta^{0}(0) = \hat\theta - cov\left(\hat\theta, \hat\delta\right)cov^{-1}\left(\hat\delta\right) \hat\delta^T
\end{equation}
has the smallest variance among all $\theta^{\Lambda}$, see \cite{Tarima2006}, and
\begin{eqnarray}
\label{MSEoptest_MVAR_mult}
cov\left(\theta^{0}(0)\right) = cov\left(\hat\theta\right) -
cov\left(\hat\theta, \hat\delta\right)cov^{-1}\left(\hat\delta\right)cov\left(\hat\delta, \hat\theta\right).
\notag \end{eqnarray}
For one-dimensional $\theta$, the quadratic form on the right hand side of Equation \ref{MSEoptest_MMSE_mult}
$$M = cov\left(\hat\theta, \hat\delta\right)cov^{-1}\left(\hat\delta\right)cov\left(\hat\delta, \hat\theta\right)\ge 0.$$
Two extreme scenarios, associated with $M$, describe how relevant additional information is for estimating $\theta$:
\begin{itemize}
\item If $\hat\theta$ and $\hat\delta$ are uncorrelated, then $M=0$ and $\theta^{0}(\delta) = \hat\theta$ for all $\tilde\eta$.
\item If $cov\left(\hat\theta, \hat\delta\right)=cov\left(\hat\theta\right)$ (the case of exact knowledge $\tilde\eta = \theta$) then
$M=cov\left(\hat\theta\right)$, and $\theta^{0}(0) = \theta$ and $cov(\theta^{0}(0))=0$.
\end{itemize}

The $\theta^{0}(\delta)$ is not directly applicable in practice as covariances are unknown. In addition, the unknown $\delta$ is also present in its structure. Dmitriev and his colleagues \cite{Dmitriev2014} explored the same class of estimators. In contrast to our settings, they hypothesized that  $\tilde\eta=\eta+\delta$ is known to belong to a distinct set of pre-determined values.

We estimate unknown covariances on empirical data to obtain an approximation to the optimal $\theta^0(\delta)$:
\begin{equation}
\label{hat_MMSE_mult2}
\hat\theta^{0}(\delta) = \hat\theta - \widehat{cov}\left(\hat\theta, \hat\delta\right)
\left(\widehat{cov}\left(\hat\eta\right) + \widetilde{cov}\left(\tilde\eta\right) + \delta\delta^T\right)^{-1}
\hat\delta^T
\end{equation}
The useful property of $\hat\theta^{0}(\delta)$ is that it is easy to show
that under some regularity conditions
\begin{equation}
\sqrt{n}\left(\hat\theta^{0}(\delta)-\theta^{0}(\delta)\right) = o_p(1).\label{convergence0}
\end{equation}
Another interesting asymptotic result is that $\forall\delta \ne 0$,
\begin{equation}\label{conv1}\sqrt{n}\left(\theta^{0}(\delta) - \theta\right) = o_p(1)\end{equation} and
\begin{equation}\label{conv2}\sqrt{n}\left(\hat\theta^{0}(\delta) - \theta\right) = o_p(1).\end{equation}
From (\ref{conv1}) and (\ref{conv2})
\begin{equation}\label{conv3}\sqrt{n}\left(\hat\theta^{0}(\delta) - \theta^{0}(\delta)\right) = o_p(1).\end{equation}

Estimator $\hat\theta^{0}(\delta)$, however, still includes an unknown $\delta$. If we plug in $\hat\delta$
instead, we get another approximation:
\begin{equation}
\label{hat_MMSE_mult3}
\hat\theta^{0}(\hat\delta) = \hat\theta - \widehat{cov}\left(\hat\theta, \hat\delta\right)
\left(\widehat{cov}\left(\hat\eta\right) + \widetilde{cov}\left(\tilde\eta\right) + \hat\delta\hat\delta^T\right)^{-1}
\hat\delta^T.
\end{equation}

The use of $\hat\delta$ in (\ref{hat_MMSE_mult2}) creates certain difficulties for (\ref{convergence0}) to hold.
Specifically, if $\delta=0$ then $\sqrt{n}\left(\hat\theta^{0}(\hat\delta) - \theta^{0}(0)\right) = O_p(1)$, meaning that $\sqrt{n}\left(\hat\theta^{0}(\hat\delta) - \theta^{0}(0)\right)$ does not converge to zero, in probability, as $n\to\infty$; even asymptotically it continues to be a non-degenerate random variable.

Overall, if $\delta=0$ can be surely assumed, minimum variance estimator $\hat\theta^{0}(0)$ is to be used, and if some protection against possible bias (disinformation) is needed minimum MSE estimation with $\hat\theta^{0}(\hat\delta)$ is a better choice with the understanding that $\hat\theta^{0}(\hat\delta)$ is inferior to $\hat\theta^{0}(0)$ under $\delta=0$. The estimator $\hat\theta^{0}(\delta)$ can be used to evaluate the impact of bias on the estimating procedure.

\section{Illustrative Example (continuation)}
\label{Illustrative_Example2}
As it was shown in Section \ref{Methodology} a minimum variance estimator $\hat\theta^{0}(0)$ and a minimum MSE estimator $\hat\theta^{0}(\hat\delta)$  are the estimators to use in practice. This section shows how both estimators can be calculated using R package ``AddInf'' available at {\begin{verbatim}https://github.com/starima74/AddInf\end{verbatim}}

\begin{figure}
    \centering
    \includegraphics[scale=0.44]{sales.pdf}
    \caption{Scatter plot of sales of Products A and B; Pearson correlation is 93.6\%.}
    \label{fig1}
\end{figure}
To use ``AddInf'' R package one need to install ``devtools'' library use its ``install\_github'' command to install ``AddInf'' package
\begin{verbatim}
install.packages("devtools")
library(devtools)
install_github("starima74/AddInf",
        force=TRUE)
library(AddInf)
\end{verbatim}

The following part of R code creates weekly sales data for products A and B.
\begin{verbatim}
A <- c(6576,	4263,	5340,	3697,	3535,	2651,
       2541,	2351,	3611,	3867,	4257,	6204,
       6666,	4364,	5441,	3727,	3495,	2755,
       2399,	2452,	3621,	3961,	4291,	6264,
       6600,	4333,	5391,	3732,	3662,	2498,
       2576,	2402,	3588,	3900,	4220,	6214)

B <- c(215, 142, 155,	97,  101, 83,
       104, 96,  102,	101, 130, 215,
       223, 134, 157,	99,  99, 87,
       100, 97,  98,	104, 131, 202,
       211, 139, 150,	100,  105, 82,
       103, 98,  100,	102, 127, 219)
dd <- data.frame(A = A, B = B)

plot(dd, ylab="Product B",
     xlab="Product A",
     main="Weekly sales history")

cor(dd)
## corr = 0.936
\end{verbatim}
First of all, distributions of sales of Products A and B need to be explored, see Figure \ref{fig1}. One can easily conclude that the association between the sales of Products A and B is linear and strong, which is supported by the Pearson correlation of $93.6\% (p<0.0001)$.

The R function below estimates optimal inventory levels at the critical fractile equal to 0.2326. The data in the argument is assumed to follow a normal distribution.
\begin{verbatim}
theta.f <- function(d) {
   qnorm(0.2326, mean = mean(d$A),
   sd = sd(d$A))
}
\end{verbatim}

\subsection{Minimum Variance Estimation}
Additional information is aggregated into a data frame in form of means ($\tilde\eta$) and covariances ($cov(\tilde\eta)$). It is important to be able to estimate $\eta$ on the empirical data. This is why the function implementing estimation of $\eta$ needs to be defined. Here, functions are statistical procedures to calculate $\hat\eta$ using empirical data. We will discuss how to incorporate possible biases in Section \ref{Biases}
\begin{verbatim}
### (Empty Lists) to save
### additional Information
Add.Info.Means <- list()
Add.Info.Vars <- list()
Add.Info.Functions <- list()
Add.Info.Biases <- list()
\end{verbatim}

The first additional data source declares weekly sales of Product B at $115.3846$ units. Since $var(\tilde\eta_1)$ is not available as additional information, but it is stated that additional information comes from a similar store. We can realistically assume that variance is similar as well, $var(\tilde\eta_1)=var(\hat\eta_1)$. Sample variance based on $36$ observations for Product B is $1912.8$. Then, $var(\tilde\eta_1)$ is approximated by $1912.8/260$. Since additional information is given by an averaged value, the function is simply the sample average.

\begin{verbatim}
Add.Info.Means[[1]] <- 115.3846
Add.Info.Vars[[1]] <- 1912.8/260
Add.Info.Functions[[1]] <-
  function(d) mean(d$B,na.rm = TRUE)
\end{verbatim}

Information from the second data source is summarized into lists in a similar manner. The second source reported median = $100$. To estimate its variance,  the sample on Product B is bootstrapped as follows.
\begin{verbatim}
### variance of MEDIAN
### (bootstrapping)
set.seed(123)
res <- 1:10000
for(i in 1:10000)
  res[i] <-
  median(B[sample(1:36,replace=TRUE)])
var(res)*36
### 3227.319
\end{verbatim}
Then, $3227.319$ is used to estimate variance of $\tilde\eta_2$ with $3227.319/260$. Further,
\begin{verbatim}
Add.Info.Means[[2]] <- 100
Add.Info.Vars[[2]] <- 3227.319/260
Add.Info.Functions[[2]] <-
  function(d) median(d$B, na.rm = TRUE)
\end{verbatim}
Note, that in the above R code $\eta_2$ is defined as the median. The lists with additional information (means, variances and functions) are aggregated into a single data frame
\begin{verbatim}
Add.Info <- data.frame(
     Means = rep(NA,2),
     Vars = rep(NA,2),
     Functions = rep(NA,2),
     Biases = rep(NA,2))
Add.Info$Means = Add.Info.Means
Add.Info$Vars = Add.Info.Vars
Add.Info$Functions = Add.Info.Functions
\end{verbatim}

Finally, we run ``MVAR'' function where minimum variance with additional information is implemented. This function internally uses non-parametric bootstrap to estimate unknown covariances needed for $\hat\theta^0(0)$. In addition to the first three arguments described above, the function also  uses number of bootstrap resamples (nboot) and a cutoff on the proportion of eigenvalues, which is a convenient way to deal with weakly definite covariance matrices.
\begin{verbatim}
res <- MVAR(dd, theta.f, Add.Info,
   nboots = 5000, eig.cutoff = 1)
\end{verbatim}
The result consists of $\hat\theta^0(0)$ and its variance, and $\hat\theta$ and its variance.
\begin{verbatim}
res
### $`Theta.Est`
###         [,1]
### [1,] 3072.728
###
### $Theta.Est.Var
###         [,1]
### [1,] 904.6197
###
### $Theta.Hat
### [1] 3118.14
###
### $Theta.Hat.Var
### [1] 1060.981
\end{verbatim}
From these results we can estimate the standard deviation of $\hat\theta^0(0)$ which is approximately equal to $30.0769 (=\sqrt{904.6197})$, and the standard deviation of $\hat\theta$, which is $32.5727 (=\sqrt{1060.981})$. Thus, the asymptotic confidence interval becomes 8\% shorter with the use of additional information. Taking into account that the covariances are estimated with bootstrap resampling, the results may slightly differ from one run to another. To avoid this randomness, the ``set.seed'' function can be used:
\begin{verbatim}
set.seed(123)
\end{verbatim}
The above improvement in standard deviations may seem marginal, but for other choices of additional information the changes can be more visual. For example, what if we assume that the variance of the first additional information is much smaller (for example, the 5 year sales of $30,000$ units of Product B is an averaged value across 10 different stores, which corresponds to $2600$ weeks of follow-up):
\begin{verbatim}
Add.Info.Vars[[1]] <- 1912.8/2600
Add.Info$Vars = Add.Info.Vars
\end{verbatim}
After running the MVAR function
\begin{verbatim}
res <- MVAR(dd, theta.f1, Add.Info,
   nboots = 5000, eig.cutoff = 1)
\end{verbatim}
the result is
\begin{verbatim}
res
### $`Theta.Est`
###          [,1]
### [1,] 2962.054
###
### $Theta.Est.Var
###          [,1]
### [1,] 629.5974
###
### $Theta.Hat
### [1] 3118.14
###
### $Theta.Hat.Var
### [1] 998.8053
\end{verbatim}
From the above, the standard deviation of $\hat\theta^0(0)$
is $25.09178$ and the SD of $\hat\theta$ is $31.60388$ leading to a $21\%$ reduction in the width of the asymptotic confidence interval.

\subsection{Minimum Mean Square Estimation}\label{Biases}
It is not impossible that the additional information came from a biased source. For example, what if the additional information said that 5 year sales were equal to $100,000$ units of Product B, not $30,000$? This leads to a very different estimated weekly sales of $384.6154$ units of Product B ($=100,000/260$).
\begin{verbatim}
Add.Info.Means[[1]] <- 100000/260
Add.Info$Means = Add.Info.Means
\end{verbatim}
If this information is incorrect, it will lead to a very different and misleading optimal inventory levels for product A:
\begin{verbatim}
### $`Theta.Est`
###        [,1]
### [1,] 6238.16
###
### $Theta.Est.Var
###         [,1]
### [1,] 635.5988
###
### $Theta.Hat
### [1] 3118.14
###
### $Theta.Hat.Var
### [1] 1002.272
\end{verbatim}
This, incorrect or deliberately altered additional information may lead to serious biases and, thus, have to be approaches with extreme caution. On the other hand, if such additional information is actually correct, it can fix optimal inventory assessment based on low quality empirical data.

If, however, the empirical data is of good quality, the minimum MSE approach can be used, which provides robustness to undue influence of additional information. In this case, an indicator of possible bias needs to be added to the ``Add.Info'' data structure:
\begin{verbatim}
Add.Info.Biases[[1]] <- 1
Add.Info.Biases[[2]] <- 0
Add.Info$Biases = Add.Info.Biases
\end{verbatim}
The above R code defines that the first source of additional information may be unreliable, whereas the second source is reporting unbiased additional information. In this situation,  $\hat\theta^0(\hat\delta)$ should be applied instead
\begin{verbatim}
res <- MMSE(dd, theta.f, Add.Info,
   nboots = 5000, eig.cutoff = 1)
res
###  $`Theta.Est`
###          [,1]
### [1,] 3110.567
###
### $Theta.Est.Var
###         [,1]
### [1,] 976.0103
###
### $Theta.Hat
### [1] 3118.14
###
### $Theta.Hat.Var
### [1] 1045.683
\end{verbatim}
Now, the $\hat\theta^0(\hat\delta)=3110.567$ and is very close to
$\hat\theta=3118.14$. The unreliable additional information is automatically suppressed, as its serious bias is easily detected, whereas the second source still contributed to a smaller asymptotic variance $976.0103$ of $\hat\theta^0(\hat\delta)$ versus $1045.683$ of $\hat\theta$.

If the bias is small, for example ($\tilde\eta_1 = 130$ and $\hat\eta_1 = 128$)
\begin{verbatim}
Add.Info.Means[[1]] <- 130
Add.Info$Means = Add.Info.Means
\end{verbatim}
then
\begin{verbatim}
res <- MMSE(dd, theta.f, Add.Info,
    nboots = 5000, eig.cutoff = 1)
res
### $`Theta.Est`
###         [,1]
### [1,] 3114.023
###
### $Theta.Est.Var
###         [,1]
### [1,] 647.4465
###
### $Theta.Hat
### [1] 3118.14
###
### $Theta.Hat.Var
### [1] 1002.441
\end{verbatim}
Thus, when additional information is consistent with empirical data, MMSE and minimum variance approaches show similar improvement of asymptotic variance.

\section{Summary}\label{Summary}

Additional information in form of known statistical quantities and their standard errors can be helpful in estimating many statistical quantities including optimal inventory levels in the newsvendor models. This manuscript shows how to incorporate such additional information into statistical estimation. An illustrative example on estimating optimal inventory levels with additional information is analyzed with the R package ``AddInf''.

The illustrative example shows how information from multiple additional sources can be used. If the additional information is not correct or deliberately altered (disinformation) the minimum variance estimation may be inappropriate. At the same time minimum mean squared estimation detects that such additional information is inconsistent with the empirical data and its impact is automatically suppressed. On the other hand if the additional information is consistent with the empirical data, the benefits of using minimum variance and minimum MSE approach are comparable.

Thus, with the use of additional information, more accurate assessment of optimal inventory  levels is obtained, which maximizes expected profit.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


text:
Pacific News, Papua New Guinea » Seven Network defends PNG corruption story
Seven Network defends PNG corruption story
Posted by Staff Reporter on Thursday, August 29, 2013 in Pacific News, Papua New Guinea | 0 comments
THE Seven Network has defended a story which linked Australian aid to corruption in Papua New Guinea, after Prime Minister Peter O'Neill called for the network to apologise and a reporter to be sacked.
In a statement, Seven said it did not not allege $A1.7 billion in Australian aid money had been stolen in PNG in a story aired on current affairs program Today Tonight on Monday.
"Rather, the story stated that about half of PNG's total budget - $1.7 billion - is lost to corruption every year, and that some of this stolen money is laundered in Australia by corrupt officials," the network said in a statement on Thursday.
"The allegations were based on interviews with the head of PNG's Anti-Corruption Task Force, Mr Sam Koim - who was appointed by Prime Minister O'Neill himself - and Professor Jason Sharman from Griffith University, one the world's foremost experts on corruption and money laundering."
Prime Minister O'Neill on Wednesday night issued a statement calling for an apology from Seven, and said journalist James Thomas should be sacked.
"I can say without fear or favour that the Channel 7 TV report alleging $A1.7 billion of Australian aid money being stolen from PNG's budget annually is the Australian media's most ill-researched, mischievous and misinformed piece of journalism coverage on PNG affairs," Mr O'Neill said.
"No one has stolen Australian taxpayers' precious $A1.7 billion because that amount of Australian money has never featured in any of our national budgets to date."
Mr Koim told Radio Australia the next day that PNG loses about 40 per cent of its national budget annually to corruption, waste and mismanagement.
In the report, Prof Sharman suggested the amount of money being stolen from PNG could cause the country to collapse, sparking a refugee crisis with direct implications for Australia.
Tags: Pacific News, Papua New Guinea

redpajama_set_name: RedPajamaCommonCrawl


Northfield's Public Library was born of the private collection of the Northfield Lyceum Society, organized in 1856 by John North as "an association for the purpose of establishing a Reading Room, Circulating Library, and Debating Society…" The Lyceum's book collection was transferred to the City of Northfield in 1878.
Northfield shared the nation's economic prosperity over the next three decades. In his "Evolution of a Community", Clifford Clark cites the Northfield News' summary of the progress of this time. The population had grown to 3,600, not including the 501 students at Carleton and the 601 students at St. Olaf. Besides the educational institutions, the town's other major employers were two creameries, a knitting factory, a factory that produced sheet metal road culverts, a seed and nursery company, two printing presses and the Ames flour mill. The town also had nine churches, a Carnegie Library, an Odd Fellow Home for the elderly and orphans, three banks, and service by four railroads, with freight delivery and twenty-six passenger trains daily.
It is notable that in the dozen or so things mentioned by the News as signs of progress, the Carnegie Library is prominently included. Few other developments represented the availability of free learning opportunities and the continuance of culture in a community more than the Carnegie Library.
Northfield's Carnegie Library was built in 1910. It was designed by architects Bell, Tyrie and Chapman. It's location on a steep slope rising from Division Street reflected it's prominence in the community. The Carnegie Library was part of a golden age of construction of prominent buildings in Northfield including Odd Fellows Home (1900), Northfield HIgh (Old Middle) School (1910), Ytterboe Hall (1901), St. John's Lutheran Church (1913), and St. Dominic's Catholic Church (1914).
The Carnegie Library was renovated and enlarged in 1984. The project included an 8,000 square foot expansion and retrofitting accessibility. The architect was Steve Edwins of SMSQ. In a Northfield News article of the time, the project architect assured the community that all work would be in keeping with the Carnegie building's "Prairie Style" architecture. The 1984 project successfully expanded the library's space while preserving the building's architecture.
In less than four years, Northfield's Carnegie Library will celebrate its Centennial. Let's make sure that the upcoming library expansion project follows the path of the 1984 project by preparing for the future while respecting the past. It only seems right to celebrate the hundred years of service to the community in the Carnegie Library.


Next week I have four library reading groups, and, while I've read all the books in question, I like to go through each again to prepare for the discussions.
So right now I'm part way through Le Soleil des Scorta by Laurent Gaudé (Outremont), with Gabrielle Roy's Bonheur d'occasion (Kirkland) cued up right behind. The English books are Jane Eyre by Charlotte Brontë (Atwater) and Nemesis by Philip Roth (Pierrefonds.) Quite an eclectic collections. All good reading too... but back to work.
When Lee was a boy, buying local meant buying produce from the Central Valley. That's where his family lived, and he has many stories of going to farm stands for produce and of lucious fruit off his father's half dozen back yard trees.
I don't buy much from the Valley these days: Sunmaid Raisins are the only consistent purchase. Anything grown in California has to be trucked--or, even worse, flown--thousands of kilometers to Montreal. Better to eat locally as mch as possible, I figure. If root vegetables are about all local suppliers have in the winter, well, that'st the way it has to be.
The New York Times today has a story about how the Central Valley is being badly treated, It is a cautionary tale, as troubling as the E.coli cases linked to the XL plant in Alberta that apparently processed 35 per cent of Canada's beef.
The real message may be to buy locally--for everything.
Trying to Make Sense of the World: Why Did the Straw Break the Camel's Back?
The New York Times has a very interesting story about catatraophe theory, and the way things can jog along forever and then suddenly change.
We are recovering from one of the best holiday of the year. For some time now, we've been having a Canadian Thanksgiving buffet for family and friends. This year the final count was 38 adults and 14 children, with the age range from 85 to 4 weeks. Lots of delicious food--and much turkey left over--plus the company of some very dear people.
Several things of note this year: visiting parents of friends of the kids came along too, which suggests that people really enjoy the occasion, Grandpapa Marc (Sophie's Dad) carved the turkey most skillfully, pitching in because Emmanuel was off in Williamsburg VA playing Lafayette's interpretor in a historical re-enactment, and Jeanne who spent the night here with Elin, woke up about 5 a.m. shouting "Je veux la fête" or "I want the party."
Little Thomas, who was passed from welcoming arms to welcoming arms, almost smiled at all the attention. Pretty good for not quite a month!
And now that things are cleaned up (we rented the dishes and cutlery, but, my, there were a lot of pots and pans) I have no energy for another sort of post!
This weekend--Thanksgiving in Canada, Columbus Day in the US--always marks the end of summer in my books. The weather, even in these days of climate change, is cooling, and the opportunity to sit outside is becoming rare.
So here are two tributes to the pleasures of a small garden in the middle of the city. Both of these pictures were taken one block over about a week ago. They are on the sunny side of the street, so the owners should be able to eke out a few more pleasant afternoons in the next couple of weeks.
They're probably inside today though: we're getting rain which is much needed after a summre when I'm sure these little oases got a lot of use.
What do you do in the middle of the night when your toddler starts vomiting and won't stop? Probably it's just a messy nothing, but you never know. A lot of serious diseases start that way.
Jeanne had that problem last night, and after a half dozen episodes of throwing up, in between which she kept asking for water, toward morning her mother called 811, Quebec's free 24/7 health hot line, InfoSanté. Christian, the nurse on call, walked Elin through the necessary steps. Did Jeanne have a fever? How high? Could she move her head without complaiing? Did she have a headache? And so on.
Then he gave some excellent advice. In effect he said, I see you live a few blocks away from a drugstore that will be open in half an hour. Go there, get some pediatric rehydrating fluid and give it to her by the teaspoon every five minutes. If she stops vomiting, wait an hour and then give her a cup. If she continues to vomit or if her fever goes about 38.5 C (slightly more than 101 F) take her to an emergency room.
Glad to say that Jeanne quit vomiting by 8 a.m., and seemed to be her usual self by mid-day, if quite ready to take a nap.
This is great front line health service. Bravo!
I woke up this morning to a delightful story about the city of Montreal planting trees. It's not particularly new news: the city announced last summer that it was planning on putting in 300,000 trees over the next 10 years. The aim is increase the urban canopy of leaves in order to cut down on hot spots in the city.
If I had any doubt that trees do make things cooler, I would have had them allayed this summer. The picture at the right was taken in a nearby park about 7:30 a.m. on a day when it was frightfully hot and humid. Yet in the shade of the trees it was delightful, and this couple had escaped their hot apartment to have breakfast on the grass. As it happened I spent quite a bit of time in this park this summer later in the day when I'd take Jeanne over a for a swing, and I can vouch for the fact that, while it was hot there, it was much less hot than it was a few streets over where there were smaller trees.
More new cases of E.coli infections in Alberta and Sasketchwan and Stephen Harper insists that Canadians are better protected than ever ! Talk about double talk!
If you let an industry regulate itself, you're not going to have real regulation. Disaster in the Making, a report from the Canadian Centre for Policy Alternatives, outlined what was in store 18 months ago. This short but trenchant report is free for downloading and is an excellent backgrounder for anyone concerned about what is happening to our food, water and environment.
Justinn Trudeau is supposed to announce his candidacy for the leadership of the Liberal Party of Canada today. This is bad news for the Libs, and good news for the NDP, I think. The young man is personable, goodlooking and what the French call a bon parleur. But that's about all he is. The following video from a Quebec TV show has him talking about how he likes to shake things up at a party by doing a prat fall. It starts with shots of his father, the famous Pierre, doing a couple of his light-hearted turns and ends with Justin falling down stairs on purpose. What Justin does not mention is that his father had a solid initellectual base, and his hijinks were there to show a human side, the 1960s equivalent of having a beer with the boys. Justin does not have that, he is all attention-getting silliness and very little substance. It's highly likely he'll be elected on a wave of hype. Can you imagine how Tom Mulcair--who's pretty good with the quip--will run circles around The Boy in a debate, to say nothing about in the House of Commons? that One last thing: to day would have been Justin's brother Michel's 37th birthday. I know that because our Elin was born the same day. Michel, of course, was killed in an avalanche in his 20s. Their father, it is said, never recovered from the loss. It will be interesting to see whether Justin mentions this, or rather if he lets it pass as just a private family memory, a quiet wink toweard whereever Pierre and Michel now rest.
I was glad to see that most of the news outlets and newspapers are making a big thing out of the return to Canada of Omar Khadr, the child soldier. The way the Harper government announced the decision on a Saturday morning suggested that they really hoped nobody would notice.
That's the way this government does things: when it might get bad press and stir up things, it just plays it low. But when it wants to send a message, you can be sure that all the flags will be out waving. Take the closing of Canada's embassy to Iran and the expelling of Iranian diplomats here earlier this month. That was done very early on a Friday morning (the announcement was made when Foreign Affairs Minister James Baird was in Russia at a conference that was well covered by foreign and Canadian media. The lead time allowed comments on Friday here, and analysis in the weekend newspapers.


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"Eat, Pray, Love" – Padang Padang's endless supply of perfect waves, and a paradisiac vibe is all you need for an ideal vacation! Our Bali surf camp Padang Padang is a great place to hang out and relax. The resort offers spacious dorms, luxurious villas or private bungalows, surrounded by beautiful Balinese gardens. The rooms and facilities provide you with everything you need during your stay. In the common areas, you can challenge your surf buddies to a game of pool, or you can just enjoy the smooth side of life and take a dip in our stunning swimming pool.
Padang Padang has been kept somewhat secretive to be enjoyed by the surf community only. You can still surf the renowned waves all year round, in peace and surrounded by untouched nature. Depending on your level you can choose between Padang Padang famous left or its more mellow cousin Padang Padang Right. You can also rent a scooter and visit another surf spot or explore Bali's breathtaking scenery.
Visit one of the most uncrowded beaches of Bali: Green Bowl. With white sand beaches and just a few meters away from the grassy cliff village of Ungasan, this small coastal gem is just one hour away from Nusa Dua. It's an authentic paradise of gorgeous sandy beaches and breath-taking temples. Our surf break, with world-class waves, is only 150m away from camp. Our Bali surf camp, elegantly built into the cliffside, features a delightful mix of Western and Javanese architecture. You can choose to stay in our shared dorms or treat yourself to a private suite. Relax on our terrace equipped with sofas and loungers. Enjoy the perfect after-surf chill session or take a dip in the infinity pool – the jewel of this location, overlooking both the rainforest and the Indian ocean.
Bali is one of the most surfed destinations around the world, for both pros and beginners. It offers a wide variety of waves 365 days a year, making our surf camp an advantage point for surfers. Famous surf spots like Uluwatu, Balangan and more are easily accessible from our surf camp. We offer surf lessons for beginners as well as surf guiding for intermediate surfers. Our surf school features qualified and experienced surf instructors. If you feel like some post-surf relaxation, you can participate in yoga sessions held daily or book yourself a massage.


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HomeBooksFiction & Literature
A Summer Fling
by Milly Johnson
When five women become friends, it's one for all, and all for one! A heartwarming and hilarious novel from the bestselling author of Afternoon Tea at the Sunflower Cafe and The Queen of Wishful Thinking.
When dynamic, power-dressing Christie blows in like a warm wind to take over their department, five very different women find themselves thrown together at work. But none of them could have predicted the fierce bond of friendship that her leadership would inspire ...
Anna, 39, is reeling from the loss of her fiancé, who ran off with a much younger woman. Her pride in tatters, these days Anna finds it difficult to leave the house. So when a handsome, mysterious stranger takes an interest in her, she's not sure whether she can learn to trust again? Then there's Grace, in her fifties, trapped in a loveless marriage with a man she married because, unable to have children of her own, she fell in love with his motherless brood. Grace worries that Dawn is about to make the same mistake: orphaned as a child, engaged to love-rat Calum, is Dawn more interested in the security that comes with his tight-knit, boisterous family? When a sexy, footloose rock singer catches her eye, will Dawn have the courage to follow her heart?
At 28, Raychel is the youngest member of their little gang. And with a loving husband, Ben, and a cosy little nest for two, she would seem to be the happiest. But what dark secrets are lurking behind this perfect facade, that make sweet, pretty Raychel so guarded and unwilling to open up?
Publisher: Simon & Schuster UKReleased: Apr 29, 2010ISBN: 9781849831024Format: book
Read More From Milly Johnson
Afternoon Tea at the Sunflower Café
The Yorkshire Pudding Club
The Birds and the Bees
Here Come the Girls
It's Raining Men
The Teashop on the Corner
A Winter Flame
Sunshine Over Wildflower Cottage
The Mother of All Christmases
The Wedding Dress (short stories)
An Autumn Crush
The Barn on Half Moon Hill
A Spring Affair
Ladies Who Launch
Here Come the Boys (short story)
The Perfectly Imperfect Woman
Restoring Grace: A Novel
The Cherry Tree Cafe: Cupcakes, crafting and love - the perfect summer read for fans of Bake Off
Heidi Swain
Staying at Daisy's
An Offer You Can't Refuse
The Accidental Life of Jessie Jefferson
Paige Toon
Rules for Dating a Romantic Hero
Harriet Evans
Summer at the Comfort Food Cafe
The Love of Her Life
A Hopeless Romantic
The Vintage Cinema Club
Jane Linfoot
Confetti at the Cornish Café (The Cornish Café Series, Book 3)
Second Thyme Around: A Novel
It Started at Sunset Cottage
A Summer Fling - Milly Johnson
Milly Johnson is a half-Scots, half-Sassenach author who lives in Barnsley, South Yorkshire with her two sons, a squadron of cats and Teddy, her German Eurasier pup.
Her hobbies include salivating over handsome vampires, watching Nicolas Cage films, taking warm holidays on big ships and learning Italian.
She is also a very proud Patron of Haworthcatrescue.org and promoter of their £2 million appeal to build a cat re-homing centre. All donations gratefully received.
A Summer Fling is Milly's fourth novel.
Also by Milly Johnson
First published in Great Britain by Pocket Books, 2010
An imprint of Simon & Schuster UK Ltd
A CBS COMPANY
Copyright © Milly Johnson, 2010
This book is copyright under the Berne Convention.
® and © 1997 Simon & Schuster Inc. All rights reserved.
Pocket Books & Design is a registered trademark of
Simon & Schuster, Inc.
The right of Milly Johnson to be identified as author of this work has been asserted by her in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act, 1988.
Simon & Schuster UK Ltd
222 Gray's Inn Road
London WC1X 8HB
www.simonandschuster.co.uk
Simon & Schuster Australia
A CIP catalogue record for this book is available
from the British Library
ISBN-13: 978-1-84739-283-1
eBook ISBN: 978-1-84983-102-4
This book is a work of fiction. Names, characters, places and incidents are either a product of the author's imagination or are used fictitiously.
Typeset in Bembo by M Rules
Printed by CPI Cox & Wyman, Reading, Berkshire RG1 8EX
This book is dedicated to six fabulous women who inspired this book.
To Nancy Scrimshaw, Sheila Isherwood and Mary Sutcliffe, who taught me that age is no barrier to friendship, laughter or fun, especially when eating illegal mince pies in front of a Yorkshire range.
And to my SUN Sisters: Pam Oliver, Helen Clapham and Karen Baker. Life would not be the same if we didn't share our stories about work, men – and what some of us have done on a mountain.
'To love and be loved is to feel the Sun from both sides.'
DAVID VISCOTT
The Queen of Wishful Thinking Excerpt
After only three words of Malcolm's speech, Dawn tuned out. She didn't want to listen to his monotonous voice. Nor did she want to think about old people retiring from Bakery departments. Her head was too full of confetti and honeymoons and she was counting down the hours until tomorrow morning, when she would finally be choosing her wedding dress.
While Malcolm was still droning on about being at the end of an era and raising his thick polystyrene cup full of cheap white wine in Retiring-Brian's direction, she was calculating how long it was to her big day. Eighty-four days, eighteen hours, eleven minutes and forty-three seconds, forty-two seconds, forty-one seconds. Every tick of the clock brought her one tiny step closer to being Mrs Calum Crooke.
People were clapping now, so Dawn joined in to make it appear that she was part of the celebrations. Malcolm was smiling, she noticed. Crikey. Fourteen million more of those and he'd have a wrinkle. Probably wind, thought Dawn, watching Malcolm's face return to its normal 'pissed off with the world' cast. Mind you, he was very pissed off with the world at the moment. He had presumed, as Deputy Head of Bakery, that he would jump straight into the top slot when Brian retired. He wasn't best pleased to find out he was being shunted over to Cheese and the new Head of Bakery was going to be an unknown outsider that the MD, Mr McAskill, was bringing in.
That he was going to be 'Cheese Head' and no longer a deputy, didn't do much to take the edge off his disappointment. Bakery was growing and secure, Cheese was sinking. Rumour had it that Mr McAskill was in the process of phasing it out totally. And Cheese was an entirely male department, unlike Bakery, which would now be all female. There would be far less opportunity to look down blouses or sidle up closer to his co-workers than he should do by the photocopying machines. Dawn shuddered as she remembered feeling his hand on her bum on her first day in the department. He'd said 'whoops' and left it at that, but she'd known it was deliberate. She had kept herself out of his way as much as possible after that.
Raychel stood alone, swilling the awful wine around in her cup. She was a natural wallflower, most comfortable against the sidelines. She felt awkward in social situations like this, but also she felt obliged to stay behind after work with the others and wave Brian off. He was an affable enough man, and talking about spending the summer in a caravan with his wife, a new microwave and his Cairn Terrier, Lady, was probably the most animated she had seen him since she joined the department late last year.
When she heard that Brian was leaving, she'd presumed that Malcolm would take over as boss, seeing as he had been acting more or less as Head anyway. She had started looking at the noticeboard for any up-and-coming jobs within other departments then. She didn't like Malcolm one bit. He was too touchy-feely for her liking, using any excuse to have skin-to-skin contact and Raychel hated to be touched by anyone – except her husband Ben. She hadn't told Ben about Malcolm and his inability to understand the concept of 'personal space' because he would have been down at the office like a shot to sort the little squirt out. So she was delighted and as surprised as the other three women in the department to hear that Malcolm was being moved to Cheese, and that Grace – the oldest lady in the department – was being made Deputy. The big boss, James McAskill, was bringing in a woman from outside as Head of Bakery, which had got the tongues wagging.
Not that Raychel had discussed any of this with her co-workers. They had all been in the same department for ages now and hadn't progressed beyond the 'morning, nice day' or 'have a good weekend' stage – give or take a bit of work talk. They were nice enough women, all different ages though. And now there was going to be another woman amongst them. Raychel wondered how all these changes would affect the dynamics of the department, but it didn't really matter that much. Work was a place to get her head down and earn a crust, nothing else.
Anna gave Brian a big kiss on the cheek. As bosses went, he was a nice man who just couldn't be arsed any more, if the truth be told. His retirement had been long in his sights and he had let Malcolm take over most of the running of the department. Thank goodness that creep was leaving as well. He hadn't been at all happy about his move to Cheese though, that was obvious. Actually he was a miserable sod at the best of times. It was as if he had a row with his wife every morning and was intent on polluting the office air with a bad mood. He was always so rude to his underlings. 'Please' and 'Thank you's didn't feature in his vocabulary and he would bark 'tea' at any of them when he wanted a drink. Plus she hated the way his eyes flicked to her breasts when he was talking to her. She wondered what sort of woman found him attractive enough to marry him. But apparently he could sustain a relationship: he had been married for over fifteen years, which is more than she could say for herself.
Anna listened to Brian getting all excited about spending the summer in a caravan on the coast and she envied him that enthusiasm for something. She had not one single thing to look forward to this weekend or after. She couldn't get interested in the storylines of Coronation Street, didn't fancy anything particular to eat, had lost the ability to lose herself in a book and knock out the image of her fiancé bonking the nineteen-yearold hired help in his barber's shop. Life stretched before Anna – longer, greyer and wetter than the entire British coastline in February.
Grace picked up Malcolm's retirement present to look at it – a carriage clock which had a very loud tock. She could almost hear it saying 'slow death, slow death, slow death' to the beat.
'You next, with any luck!' said Brian in her ear hole.
'Wha . . . at?' said Grace, before quickly recovering. 'Oh yes, maybe.' God forbid. The thought of standing where Brian was now, admiring her own clock, being toasted in warm plonk, brought on a cold, clammy sweat at the back of her neck. She came over ever-so-slightly faint.
Slow death, slow death, slow death.
'I just can't understand why you'd want to up the ante when you'd got the chance to leave this place and live a life of leisure. Could have been your retirement do as well,' said Brian with a smile.
'Oh well, you know me, I like a challenge,' said Grace. She had worked with Brian for just over three years now and liked his merry ways, even though he was a man who was born old and was just happily growing into himself. He would so enjoy not having to set his alarm clock any more and spending his days pottering around busily doing nothing. Apart from his cheery disposition, he reminded her so much of her husband Gordon – too much for comfort, as he prattled on about the joys of retirement.
Grace's thoughts drifted off. Did Brian ever think when he was seventeen and in the dance halls that he would one day be standing here, getting excited about taking a new microwave to Skegness? Was that the zenith of his ambition? Or was Grace not normal in being the same age as him and panicking every time the word 'caravan' entered a conversation? She'd done the caravan thing when her three children were small and they had enjoyed it, even though she herself had found it far from relaxing as a choice of holiday. The children were adults now but she was still very close to them and didn't want to spend weeks and weeks away from them and her grandchildren with only Gordon for company.
She had always said that she would leave him when the children grew up. She wondered how many other women had resolved to do the same and were still there years after the kids had moved out because they simply weren't brave enough to go. Her son and two daughters had left a huge, gaping hole in her home when they left, as if they had taken its heart along with them.
Her eyes caught Malcolm refilling his cup with wine. He wasn't a happy man by any stretch. She could easily believe the rumours he was being moved to the much less prestigious department of Cheese because he wasn't efficient enough to handle the growing Bakery department. Malcolm Spatchcock was neither liked nor respected, although his ego was so big that he was oblivious to that fact.
Grace only hoped that she wouldn't be wishing Malcolm back after meeting her new boss. Still, Mrs Christie Somers would have to be really bad to knock Malcolm off the unpopularity stakes, ghastly little gnome. She had worked under his inefficient management for too long.
The wine and crisps were gone now and people were starting to pack up and drift off. Grace's weekend stretched out long and stark in front of her. Same old, same old. Babysitting her granddaughter tonight while Gordon went to the Legion and her daughter and son-in-law went out for some posh meal. Shopping, washing and cleaning tomorrow, then on Sunday morning she would make the lunch, clear up, iron and then sit down in front of Heartbeat – or really break out and watch Frost – before a hot bath and bed, ready for the week ahead.
She looked at the office youngsters from other departments filing out of the door, full of Friday night beans. She hadn't done that whole donning lippy and going out with friends thing for well over twenty-five years. She said goodnight to Brian and her three co-workers. They all seemed nice women, although they didn't really mix much. Still, the atmosphere at work was so much lighter than it was at home. Gordon's hair had gone grey in his thirties, but when did he get so grey in his head? Life would have been so much easier for Grace had she done the same.
Calum was virtually sitting on the telephone but it would have rung forever had Dawn not come in from the kitchen and picked it up. She mouthed 'Idle beggar' at him, but he was too lazy even to look up.
'Hello, love,' said the cheery voice down the line.
'Hi, Muriel,' said Dawn. Calum exhaled loudly and waved his hands like an irate air-traffic controller. The message was clearly I'm not here if she asks.
'So, what time are you picking me up tomorrow, pet?' asked her future mother-in-law brightly.
'Half-past ten all right for you, Mu?'
'Well, I'll make sure I'm up, seeing as it's a special occasion,' said Muriel.
'I'm so excited, I bet I don't sleep much.'
'Knock yourself out with a few lagers. That's what I do when I can't sleep, lass!'
Dawn laughed. Muriel was ever so funny sometimes. She had laughed with Mu from the first time they met, over two years ago, in the miserable hairdressing salon where Dawn used to work. Dawn had given her a perm and Muriel had chattered on for two solid hours. She had been an absolute tonic that day with her rough, bawdy sense of humour. She had exploded into Dawn's life when she badly needed some laughs.
'Is our Calum back?'
'Yes, but you've just missed him.'
Calum stuck up a satisfied thumb.
'Aw well!' said Muriel with a deep sigh. 'Mind you, it is Friday and a bloke deserves a pint after a hard week at work.'
Dawn didn't know about the hard week. All he seemed to do was faff about on a fork-lift truck and have fag breaks.
'Anyway, when you see him, tell him Killer's brought him a box of DVDs.'
'I will.'
'See you tomorrow then, pet.'
'See you, Mu.'
Dawn clicked the phone off and Calum stood up and stretched like a lean, scraggy street cat.
'Killer has brought you some DVDs apparently,' Dawn delivered the message.
'Oh, cheers.'
'Not pirates, are they?' she asked suspiciously.
'Don't be daft, they're from house clearances.'
'And what do you do with them?'
'Questions, questions,' he sighed. 'Sell them on for him down the pub – for a cut.'
'OK,' said Dawn, temporarily satisfied by his answer. 'So, what do you want for your tea?' she asked.
'Thought we were having a Chinese?' he said.
'And I thought we were cutting back. I've got a wedding dress to buy tomorrow.'
Calum scratched his head, leaving his hair all sexily mussed up.
'We've got to live, Dawn! We've both been working all week. We need a bit of a treat.'
'OK then,' she reluctantly agreed. He could always talk her round. 'I'm hungry now; shall I ring up and order? I'll have chicken and mushroom with fried rice and won tons. Are we sharing? If we are, don't get that black bean thing.' She went to the drawer for the Chinese menu. It was at the top of a stack of takeaway menus all clipped neatly together. Her fastidious organizational skills were something Calum teased her about on a regular basis.
'I'll share if you want. But I thought I'd go out for a couple and then pick it up on the way back.'
'Aw! Don't go out!' Dawn tutted, disappointed.
Calum yawned. 'Just for a couple. Won't be any more than that, 'cos I'm shattered.'
'Now, where have I heard that before?'
Calum grinned his cheeky schoolboy smile that had got him into and out of all sorts of trouble ever since he was old enough to use it to its full advantage. It disarmed Dawn, as usual.
'I promise this time,' he said. 'No later than ten past nine. You have the plates warmed up for us.'
'Oh, anything else I should do?' asked Dawn with her hands on her hips.
'Funny you should ask. You couldn't lend me twenty quid, could you?'
Dawn opened her purse and handed over the money with a sigh, hating herself for being unable to say no. Especially as she knew that at ten o'clock she would, most likely, have given up waiting for Calum to come home early. She would go and make herself a cheese toastie. Calum would roll in after midnight, having forgotten the Chinese. She hoped one day he would break the pattern and surprise her, but so far he hadn't.
'Oh bloody hell, I've burned the garlic bread!' said Ben as the smoke alarm went off.
Raychel followed his mad dash into the kitchen and laughed.
'It's not funny, Ray, I was really looking forward to that,' said Ben, looking like a little kid who had just watched his ice-cream drop off his cornet and get eaten by a lucky passing mongrel.
Raychel grabbed the broom handle and poked up at the smoke alarm, but she was too small to reach it.
'Shift yourself, shorty,' said Ben, pushing her gently out of the way. He stretched up his long, muscular arm to depress the button with his big thumb. 'God, that's better; it was deafening me!'
'Look, it's not that bad, Ben,' said Raychel, inspecting the damage. 'It's only the top bit that's burned. I can cut it off.'
'Can you really do that? For me?' He sank to the floor and pretended to thank God.
Raychel slapped him playfully. 'You're so easily pleased.'
He grabbed her around the legs and pulled her to him as she squealed. He was almost as tall as her full height on his knees.
'I'm not actually. I'd say I was rather fussy myself.'
Raychel looked down into his lovely, sweet, smiling face. The stubble was growing back even though he'd had a good shave that morning. Dark and manly, his arms were tight around her. His body was hard with muscle and solid against her. She loved him so much.
'I'll get the pasta dished up then, shall I?'
'In a minute,' he said, savouring the feel of her, curling strands of her long, black hair around his finger, taking in her long-faded perfume. He could have breathed her in for hours.
'Am I enough for you?' she said, eventually. It was a question he had heard so many times and he answered it as always.
'Ray, you're all I could ever want.'
Grace got up the next morning at five-thirty and watched the Teletubbies, Bob the Builder and Thomas the Tank Engine for a brain-numbing two and a half hours with four-year-old Sable. The combination of a young child's energy and an early morning following a restless night made her feel far older than her fifty-five years. Gordon was, of course, in bed. It was women's work getting up and seeing to the children. Or, at least, that was the regime she had always been used to – first at home with Mum and Dad, then when she married the widower with the four dependants: Laura aged six, Paul aged five, Sarah aged three and Rose aged fifty-four. It was funny to think she was older than her mother-in-law was when she died. Rose had seemed like an old, old woman.
Sarah arrived at eleven with her customary 'Sorry I'm late. Thanks for letting her stay the night. I know it was last minute.'
'It's all right, love,' said Gordon, up and dressed now in his gardening clothes, his thick, steel-grey hair still wet from a leisurely shower.
'Any chance you could look after her for another hour?' asked Sarah in her best wheedling little girl tone. 'Just so I can go to the supermarket?'
' 'Course she can stay here,' said Gordon, his voice drowning out anything Grace might have had to say on the subject. He chucked Sable under the chin. 'She can come out and watch her grandad plant some seeds.'
'It's far too chilly for her to be outside,' said Sarah, wrapping her fur-trimmed maternity coat a little further around herself at the mere thought of it.
'Well, she can stay inside with her grandma then,' said Gordon. Grandma. The word grated on Grace's nerves like a fingernail scraping down a blackboard. She preferred Nana and Gordon knew that. It was as if he was using the word on purpose – a Chinese water torture slow drip, drip: 'you will be old'.
'I promise I won't be longer than two hours,' beamed Sarah, happy at having an extension to her freedom. 'Three at the most.'
She tried to ignore how tired her mother looked and concentrated on her father's expression of bonhomie instead. Gordon disappeared out to his allotment. Grace wrestled with trying to get the washing done, the beds stripped and entertaining a hyper Sable. She needed to go out shopping herself but she was exhausted. Gordon was so generous with other people's time.
Sarah came back after lunch, just as Sable had drifted off to sleep. And just as the postman arrived with two catalogues for caravan sites in Blegthorpe-on-Sea.
Calum's loud beer-snoring awoke Dawn. She went downstairs to try and sleep on the sofa but what she gained in peace levels, she lost in comfort. The sofa was old and past it; they really could do with another one but every spare penny was being put aside for the wedding. Well, every spare penny of hers, that was. At least Calum had a job at the moment, and one he was sticking at – not that it brought in mega-bucks. But where she was saving everything she could, Calum contributed what was left out of his 'social fund'. She would have to get a loan out at this rate for the honeymoon, but she was going to have the fairytale. If it took her the rest of her life to pay off her wedding day, she would have the frock, the flowers and the fancy cake. She knew it was the start to a marriage that her mum and dad would have wanted for her. Then, when the wedding debt had been paid off, they could start looking at something a bit better than Calum's dump of a house. Dawn had moved into it eight months ago and not managed to persuade Calum to do anything to it. There were still wires hanging down from the ceiling, bare plaster walls, furniture that looked as if it had been dragged out of a skip. He was five years younger than her. Dawn rationalized that as some sort of excuse for his student-like existence.
Calum was still in bed when she pulled up in front of her future mother-in-law's council house semi at the other end of town. She beeped the horn of her antique, but thankfully reliable Fiesta, and a minute later Muriel wobbled down the path in tired leggings, a grubby-looking fleece and flip-flops. Not that Dawn would ever have been ashamed to be seen with her. Muriel was Muriel, and Dawn loved her to bits, just as she was.
'Morning, lovely,' said Muriel with an excited little half-toothless grin. The Crookes were a rough family, but they had taken Dawn to their bosom. This was especially important to Dawn since her own parents had died in a car crash sixteen years ago and left a gaping hole in her heart. She missed them so much. She wished it was her mum sitting in the car beside her now, helping to pick out her wedding clothes. But Muriel Crooke was the next best thing.
Their first stop was 'Everything but the Bride' on the out-skirts of town by the new Tesco. The tired display in the window was awful and was a perfect indication of what lay inside. A cracked, headless mannequin with no bust was wearing a white dress that was the colour of old greying knickers and would have better befitted a toilet roll doll of the 1970s. The accompanying bridesmaid mannequin did have a head, and a face that had been painted on by someone with a very shaky hand and no artistic talent: she wore the pained expression of a kid being given a wedgie. She looked uncomfortable in her lilac satin dress that had long faded in the sun. Yellowing confetti was sprinkled around their feet, resembling bird poo.
Dawn went in but knew instantly that she wouldn't find her dress in here. The buyer wanted a slap. There wasn't a lot of choice because the owner was obviously phasing the wedding dresses out and prom dresses in. Each one seemed the same as the rest but in a different colour. It was as if there was only one standard pattern for all the frocks – big wide skirt and puffy sleeves – with slight variations of neckline or ribbon/sequin detail. They weren't harassed by the sales assistant whose ear was stuck on the phone.
'. . . it can't be too short, you were there when we measured you. I asked you if that length felt comfortable and you said yes. Well, maybe you should have had on the shoes you'd be wearing for your wedding. If you come in here in flats to be measured up and you're wearing heels on the day, how can that be our fault?'
Dawn reckoned the gold stars for customer service might be thin on the ground in this place.
Muriel pulled a face at her, making Dawn chuckle. They slid out of the shop and Dawn took a big gulp of air.
'If that were me on the other end of that phone, I'd have slammed it down, got a taxi over here and smashed her cocky bleeding face in,' said Muriel.
Dawn was laughing so hard it took her four attempts to open her car door. She knew Muriel would tell the others how the day went, adding her funny embellishments. She hoped she would save it until Dawn was present to hear it.
They drove through Penistone and to stop number two, 'Love and Marriage', a far superior site on the Holmfirth Road. The window display was gorgeous: an ivory dress around a wire frame that represented an exaggerated hourglass figure. It was surrounded by handbags and shoes with expensive designer names. This was a pendulum swing to the other end of the market. A frighteningly big one if those names were anything to go by: Choo, Prada, Chloe, Louboutin . . .
They had barely stepped foot in the shop when an assistant bore down on them offering help.
'Just looking, thanks,' said Dawn.
'Are you searching for anything in particular?' pressed the assistant, giving Muriel a sneaky look up and down, which Muriel saw and her lip instinctively curled back over her teeth.
'I don't know,' said Dawn, wishing she could just wander around for a bit, unharassed.
'This is nice, Dawn,' said Muriel, picking out a long, cream dress. 'Can't find the price tag though.'
'Nine thousand,' said snotty assistant woman.
'Pounds?' gasped Muriel. 'You're having a laugh?'
'No, it's a Vladimir Darq. The reason it's so cheap is that it's second-hand.'
Muriel's jaw dropped. Cheap was the last word that came to her mind. She was speechless with amazement that someone would pay that amount of money for a frock.
'He's a famous designer,' said the assistant. 'You have heard of him, presumably?'
'Can't be that famous if I've never heard of him!' sniffed Muriel, enjoying that she was rankling the snotty cow.
'I have,' nodded Dawn. 'I didn't realize he was a wedding dress designer though.'
'He doesn't make bridal gowns any more,' said the assistant. 'This dress was from his very last collection of them – very much sought after.'
'Aye, by people with more money than sense.' Muriel clicked her tongue loudly.
'I'm not looking for anything that . . . fancy,' said Dawn. Of course the assistant knew she meant 'expensive' by 'fancy'. She'd taken one look at the pair of them and knew they'd be leaving empty-handed. The mother, she presumed, would have thought a Vera Wang was something that came with fried rice and prawn crackers.
'Our range starts at five thousand for this one,' said the assistant, presenting a plain white satin dress in a thick polythene cover.
'Oh,' said Dawn. She cooed over the dress to be polite, but all parties knew this was a no-go sale opportunity. Dawn made noises of 'maybe having to go home and look at some magazines first,' in order to leave the shop with some dignity intact. Two minutes later, she let loose a long breath of relief as she stepped outside.
'She thinks she's in Paris not bloody Barnsley!' Muriel laughed loudly on the doorstep. 'Twenty-two quid for a pair of tights? A pair of tights, did you see?'
It was as they were coming back to Barnsley, via the small, pretty village of Maltstone, that Dawn braked hard opposite the church, nearly sending Muriel through the windscreen.
'Didn't know there was a bridal shop here, did you, Mu?'
'I wouldn't know,' said Muriel with a sniff. 'I've no reason to come to Maltstone. There's nothing around here for me.' She wasn't a woman for garden centres and rural tea-shops.
Dawn reversed into a parking spot in front of a shop with a bay-window full of the prettiest display of bridalwear. Above the door hung a sign in romantic, swirly text, saying simply 'White Wedding'.
The doorbell tinkled daintily as Dawn and Muriel entered.
' 'King hell, it's a Tardis!' said Muriel over-loudly as the narrow shop seemed to go on forever in length. Racks of dresses lined the walls, and showcases of tiaras and shoes ran floor to the cottage-low ceiling. Dawn's mouth opened in a round O of delight. This is more like it!
A very slim and smart assistant greeted them with a big smile. On her plain, black fitted dress she wore the name badge 'Freya'. She was probably the same age as Muriel, thought Dawn, although with her coiffeured hair and unchewed nails, she looked fifteen years younger.
'Can I help you?' Freya asked Dawn politely.
'I'm getting married and I er . . . need a dress,' replied Dawn shyly.
'Well, do feel free to wander,' said Freya. 'I will say though, don't judge the dress until you have tried it on. You'd be surprised how many brides go out looking for one particular style only to find it doesn't suit them at all.'
'Thank you,' said Dawn, feeling very much at ease in this shop. She and Muriel had a look around but Dawn realized she might need some expert help after all.
'I don't know where to start, there's just so many,' she said. She wanted to get it right because what if she found a dress, bought it, then spotted another one that was nicer? That thought had tortured her a few times.
'Well, let's start with colour,' said the assistant. She studied Dawn's pale, heavily freckled skin and her shoulder-length copper hair. 'May I recommend ivory rather than white? White isn't always flattering, especially to people with pale skin like yourself. Size 10, at a guess?'
'Spot on,' returned Dawn. Freya went to the rack of 10s as Muriel was pulling size 24s off the hangers and holding them up against herself.
'And are we going to be a summer bride or a winter one?' asked Freya.
'June,' said Dawn.
'I might try on one myself,' said Muriel. 'Get Ronnie to renew his vows, seeing as I'm a lot thinner than the first time we went down the aisle.'
Freya's face never twitched, even though Muriel was twenty-five stone plus now.
'We'll have a joint do,' laughed Dawn.
Freya pulled out a long, tapering gown, shaking out the creases.
'This is silk, ivory as you see, a bow on the back, beaded detail on the front bodice. Very flattering for the smaller-busted woman.'
'Not do me any good then,' snorted Muriel and laughed so hard that her enormous and flimsily restrained breasts jiggled like two giant blancmanges. The bra hadn't been built that could hold them in place without industrial strength scaffolding.
'It's lovely,' said Dawn, but she was shaking her head. 'It's not leaping out at me, though.'
'OK,' said Freya, and flicked the plastic protective case swiftly back over it. 'What about this?' She presented something swimming with ruffles.
'Oooh,' squealed Muriel.
'Too fancy,' said Dawn quietly. 'Sorry, it's not me at all!'
'Oh, don't apologize,' said Freya. 'Finding out what you don't want is the most effective way to lead us to what you do want. So, less frills . . . let me see.'
She pulled out a very unfussy number in satin.
'Ah, it's too plain. Heck, I'm not easy to please, am I?' Dawn half-expected Freya to sigh in that annoyed way that Calum's sister Demi was always doing.
'Don't worry,' said Freya, though. 'I've seen would-be brides come in here and reject forty dresses!'
'How much is this?' called Muriel, holding up a white satin gown. There was enough material in it to make a sail for a billionaire's yacht.
'That particular one is three thousand pounds,' said Freya.
'Chuffing hell, they aren't cheap, are they?' said Muriel and slid it back on the rail, none too straight either, although Freya didn't give a hint of disapproval.
'This one, perhaps?'
'Neck's too high.' Dawn shook her head. 'That's gorgeous though.' She pointed to a rather full-skirted confection in white. Freya didn't look convinced that Dawn and the frock were a good match, but hung it up in the changing room for her all the same. A couple of minutes later, Dawn emerged to show herself off.
'Bleeding hell, where's your sheep, Bo Peep?' asked Muriel with a snort.
The dress drowned Dawn and, true enough, the white material made her skin look like the colour of uncooked pastry. Freya nodded in an 'I told you so', but kindly, way. She was holding up a gown that made Dawn's eyes shine.
'It's from our vintage collection,' explained Freya. 'It's a very special dress.'
Long and flowing, it had a beautiful scooped neck with peach rosebud detail, a full skirt, three-quarter sleeves and was made of smooth, smooth ivory silk. Dawn's hands reached greedily for the hanger. She closed the dressing room curtain and when she opened it again and emerged in that dress, both Muriel and Freya gasped with delight.
'Gorgeous,' said Freya. The dress suited the tall, slim woman to a T. The ivory lent her pale skin some colour, her neck looked extended by inches and the fitted bodice gave the illusion of curves where there were few.
'Oh. My. God. This is the one, I just know it,' said Dawn. She was almost in tears imagining the skirt trailing behind her, brushing the aisle floor. 'Do you know anything about the original owner? Was she happy?' She didn't want a dress with negative vibes stored in the threads.
'Very,' Freya said, adding, 'Eventually.'
'Well, you would say that,' parried Muriel. But Dawn wanted to believe Freya anyway. She was hooked.
'It is lovely, mind,' said Muriel. 'How much is it though?'
'It's fifteen hundred pounds. Any alterations are free and you will most likely need them despite it being a near-perfect fit now. Most brides lose some weight and have to have their dresses nipped in nearer the date.'
'Fifteen hundred quid – for a second-hand frock!' Muriel gave a mirthless little laugh.
'It's very special,' said Freya again, smiling. 'It looks meant for you.'
Dawn gulped. It was over her budget, but she knew anything else would be second-best. She could cut back on something else, but not the dress. She would pray for a miracle pay rise or a big win. She would start putting an extra line on the lottery, starting this week.
'I don't care – I'll take it,' she heard herself say.
An hour later, Dawn had spent another two hundred and fifty pounds on shoes, a medium-length ivory veil, a tiara and some matching earrings. She hid the purchases on her Visa card and tried not to let worries about the expense spoil the excitement.
'Look at this one,' said Gordon. 'It's an eight berth.'
Grace dutifully left the sink, peered over his shoulder at the catalogue and then returned to scrubbing the Sunday dinner pans, which were infinitely more interesting.
'Plenty of room for our Sarah and Hugo and Sable and the baby when it arrives, and our Laura and Joe.'
And Paul too, Grace added to herself, but there wouldn't have been much point saying it aloud. Gordon was a master at ignoring what he didn't want to hear. Paul was as good as dead to his father.
'It's got central heating and a built-in washing machine and dishwasher.' He looked at Grace standing with the tea-towel. 'It's got more than we've got here, in fact. It would be just ideal for us when you retire. You're over ready for a long rest.'
'I'm only fifty-five, Gordon.'
'Only?' he snorted. 'You're getting older every day. You've got to be in the next batch of early retirements. I can't understand why you haven't been asked already. They've retired loads at your place!'
Grace shrugged, but didn't say any more. If Gordon had a magic wand, she was sure he would use it to age her and see her in a bathchair wrapped in a nice shawl.
'I don't know, anyone else at your age would be looking forward to winding down. Can't you imagine, long summers and walks by the sea? According to the brochure, there's even a social club on site and Skegness, Mablethorpe and Ingoldmells are only a short drive away.'
'Gordon, wouldn't you prefer to go on lots of fortnights abroad in the sun? Italy, Spain, France?'
'Oh, I can't do with all that travelling.'
'It's only two hours to Spain. It would take us not much less than that to get to Blegthorpe in the car.'
Gordon changed tack then. 'Oh, I can't be doing with all that heat.'
'We don't have to go in August!'
'Anyway, we couldn't take the grandkiddies abroad. Our Sarah wouldn't agree to that.'
Grace doubted that. Sarah was greedy as far as babysitting duties were concerned. It wasn't that Grace minded helping her daughter out, Sable was her granddaughter after all and she loved her dearly, but Sarah presumed that if her mother wasn't at work, she should be on hand 24/7 for her convenience. Grace also knew that Sarah was another one who was pressurizing her to retire early so she could take over as permanent child-minder and Sarah could escape back to work.
'We should go for a weekend and take a look at some of these in the flesh,' suggested Gordon, flicking through the pages of the 'Clark's Caravans' brochure.
'Gordon, we've talked about this before and I don't really want to,' said Grace, standing her corner for once. She couldn't remember how many times they'd had this interchange and as usual Gordon did not acknowledge her point of view.
'You don't know what you'd like until you try it,' he said, which was ironic seeing as he would have spontaneously combusted had he ever tried anything out of his very small comfort zone. 'It'll be lovely having our own caravan instead of renting someone else's, just you wait and see,' he said, because Gordon Beamish always knew best.
Christie Somers studied herself in the huge hall mirror, smoothed the red suit down over her hips and then whisked around with a flourish.
'Niki, will I do? What do you think? Is this too bright?'
'When do you not dress in primary colours?' her brother said, shaking his head in mock exasperation. 'Don't tell me you're nervous and want to hide yourself inside a black suit?'
'I have no black clothes, so it's just as well that's a ridiculous observation,' said Christie with a good-humoured sniff. 'You know I don't do nerves.'
'Yes I do, and I also know that you must be the only woman in the world without black clothes.' Niki grinned at his little sister.
'Possibly,' said Christie. 'But my new department is full of women and I don't want to frighten them into thinking I'm a power-suited ogre.'
'Just because you always dress so beautifully it doesn't mean you're an ogre. Even though you are,' said Niki, bending to give her a kiss on the head. She was a totally different body shape to him, hourglass-figured and short, where he was tall and rangy, but their wide smiles, serious cheekbones and bright blue eyes made them instantly recognizable as siblings.
'It will be funny going back to work after so long a break,'
said Christie, looking in the mirror again. Maybe scarlet was too aggressive a colour for a first meet.
'James knows what he's doing,' said Niki. 'He wouldn't have offered you this job had he thought you couldn't do it. He's a businessman first, soft touch second. You're up to speed, you'll be fine and it will do you good. You've been a long time in hibernation away from the world. I have every confidence in you and, more to the point, James has every confidence in you.'
'Thank you, Niki,' said Christie with a fond look at him.
'Pleasure, Sis,' said Niki, saluting her as he left by the front door.
'OK,' said Christie to her own reflection. She clapped her hands together and grabbed her minx-red handbag. 'Let's start as we mean to go on.'
Grace arrived first into the department after the weekend. She found that the Maintenance fairies had been at work. A thick new carpet had been laid and a huge executive mahogany desk replaced the standard issue ones that Malcolm and Brian had been working from. There was a whiteboard now on the wall and boxes of stationery and what looked like promotional gift examples piled up in the corner. A rather arty iron coat-andumbrella stand had arrived too. Mr McAskill wasn't a man renowned for splashing his cash on fripperies so the gossip machine would be well cranked up by this expenditure.
No sooner had Grace sat down and switched on her PC than Dawn came in.
'Hiya,' she said breezily. 'Car park's a bit full this morning, isn't it?'
'Yes it is,' said Grace. They were still at that polite nicey-nicey stage, having the sort of lightweight interchanges with each other that they'd have with a hairdresser. Had a nice weekend? Lovely weather we're having!
'This carpet


text:
Bullets Fired Into Ferguson Home Kill 9-Year-Old Girl
"I kept holding and holding her. I still have her blood on my hands."
By Andy Campbell
KMOV.com
A 9-year-old girl in Ferguson, Missouri, was killed as she lay in bed Tuesday night when someone fired several rounds into her home.
Police say Jamyla Bolden was still alive when officers responded at about 9:30 p.m. to the gunshots. A city press release says that "two officers tried desperately to keep the little girl alive," but she later died at the hospital, the St. Louis Post-Dispatch reports.
Jamyla's grandmother said she ran downstairs to help the girl when bullets started flying.
"I was holding her the whole time," she said of the child. "I kept holding and holding her. I still have her blood on my hands. She was still breathing. I was telling her to just breathe."
Jamyla's mother, 34, was also shot in the leg, and was treated and released from the hospital, according to KMOV.
A shooting motive isn't clear, and police refused to comment on the shooting except to say that they "do everything possible to find the person responsible," WSMV reports.
The Post-Dispatch reports:
"She was very sweet, kind and soft spoken," said Melanie Powell-Robinson, spokeswoman for Riverview Gardens schools. "We're trying to figure out why in the world did this happen. We just can't make sense of this."
The home where Jamyla was killed is not far from the location on Canfield Drive where Michael Brown Jr. was fatally shot by police last year.
Ferguson Protests 2015
Senior Reporter, HuffPost
Ferguson Black Lives Matter Jamyla Bolden
FERGUSON, MO - AUGUST 09: Demonstrators, marking the one-year anniversary of the shooting of Michael Brown, march along West Florrisant Street in a driving rain on August 9, 2015 in Ferguson, Missouri. There are reports that two people were shot when gun fire broke out during protests later in the evening. Brown was shot and killed by a Ferguson police officer on August 9, 2014. His death sparked months of sometimes violent protests in Ferguson and drew nationwide focus on police treatment of black offenders. (Photo by Scott Olson/Getty Images)
Scott Olson via Getty Images


Alabama Today's publisher, Apryl Marie Fogel, wrote an op-ed published Wednesday over on AL.com in her role as executive director and founder of Conservatives for Better Leadership (CBL), which seeks to hold elected officials accountable to the promises they've made on the campaign trail and to ensure transparency within state government. In the piece, she shines a light on the glaring problems with the state's open records laws.
Fogel's frustrations with the law stem from first-hand experiences in both her role with CBL, and her role at Alabama Today. Here, we've faced on-going issues with the Alabama Department of Transportation (ALDOT) dating back to May.
May 18: We first reached out to Tony Harris, spokesman for ALDOT, with questions about the flyover bridge project in Baldwin County. He called back that afternoon and promised a response the following week.
May 25: We had yet to hear anything back from Harris, so we reached out again and he said they were working on it.
June 12: Again, crickets from Harris and ALDOT, so we reached back out and more empty promises were made.
Aug. 24: after previously asking Alabama Today to avoid submitting an official public records request, Harris tells us that is what we have to do if we want the information. That there are issues being held up in the courts (by the way, they've all been resolved) and he's unable to answer otherwise.
Jan. 4:We ask Daniel Sparkman, Press Secretary for Ivey, for a list of top agency heads the Governor has replaced from the Bentley administration by department and date for a simple story we're working on for her appointments. This was to bring back a series we regularly published when Robert Bentley was governor. Sparkman tells us it's going to take a while to put together the list, despite the fact it typically took Bentley's team less than 24 hrs.
Jan 29: We check back in for the information, it's still not available.
Feb. 26: Fogel now reaches out to Sparkman in hopes of moving this simple request forward more quickly.
Feb. 27: Fogel provides Sparkman with the information and process timeline we used to get from the Bentley administration.
March 5: Fogel follows-up on still unfulfilled records request.
March 6: We are sent an unsorted, unorganized list of all the appointments made since Ivey first took office. We publish our first segment of the list.
April 19: We requested all of the appointments from March 6 – current.
April 26: Another follow-up is made, no response.
May 9: Another follow-up is made, which now includes Ivey's Chief of Staff Steve Pelham and Josh Pendergrass, her Communications Director. No response.
May 21: The three are emailed yet again, no response.
It's now Sept. and we've yet to have the Governor's office respond to our request.
It's no wonder Fogel wrote, "No longer should the governor, her staff, and her cabinet members be able to do business in complete secrecy. No longer should they be able to skirt and mock transparency laws with a level of nonchalance that says to the public we are peasants in their kingdom who have to just take what they dish out if and when they provide anything at all.," in her AL.com op-ed.


text:
Jarrett Adams
The Innocence Project
"Close your eyes and picture something you want, no matter what is in front of it, that you would do anything humanly possible to get to...all you have to do is keep fighting until you figure out a way to get to that other side."
My road in life took a while to figure out.
Born and raised on the South Side of Chicago by a single mother.
When he was 17 years old, he was falsely accused of a rape while attending a college party with some friends.
He couldn't afford to hire a lawyer, so the court appointed him one—the lawyer failed to call some key witnesses or enter a defense, which resulted in him receiving a 28-year prison sentence.
He had served almost 10 years of his sentence before the Innocence Project took his case, got his conviction reversed, and had his record expunged.
He was released in February of 2007 and was back in school by April of that year—says that he knew getting an education was the key to getting himself reacclimated into society.
Started at community college and eventually went on to graduate with his law degree from Loyola University Chicago's School of Law.
His first job out of law school was working as a clerk in the Seventh Circuit Court of Appeals in Chicago—the same court that overturned his conviction.
He now works closely with the Innocence Project, in addition to running his own law office and continuing to act as an advocate for criminal justice reform.
South Suburban College
Criminal Justice/Law Enforcement Administration
Loyola University-Chicago
I am an attorney with the Innocence Project, Co-Founder of Life After Justice, and advocate for criminal justice reform.
I spend most days as an attorney working on a variety of cases including trials, arrests & arraignments, sentencing, and sentence modification. It involves reading and researching the case I am working on, getting to know my client, and then developing a defense or prosecution depending on the case. I also work with the Innocence Project to review potential false imprisonment cases and bring those back to trial to get them overturned.
Going to community college is a great first step to get your foot in the door and help you build the relationships needed to succeed. Getting an AA in something general like Liberal Arts sets you up to study almost anything you want.
From Society in General:
"You have to forgive the people that did you wrong and move on. "
I don't forgive them. I'm still very angry, but I use that anger constructively and use it to motivate me forward. I want to use my experiences to positively effect others and ensure this doesn't happen to anyone else.
Formerly Incarcerated
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text:
Cognitively impaired aged Octodon degus recapitulate major neuropathological features of sporadic Alzheimer's disease.
Contributor: Zhiqun Tan,B Maximiliano Garduño,Pedro Fernández Aburto,Lujia Chen,Nicole Ha,Patricia Cogram,Todd C Holmes,Xiangmin Xu
The long-lived Chilean rodent (Octodon degus) has been reported to show spontaneous age-dependent neuropathology and cognitive impairments similar to those observed in human AD. However, the handful of published papers on degus of differing genetic backgrounds yield inconsistent findings about sporadic AD-like pathological features, with notably differing results between lab in-bred degus versus outbred degus. This motivates more extensive characterization of spontaneously occurring AD-like pathology and behavior in degus. In the present study, we show AD-like neuropathological markers in the form of amyloid deposits and tau abnormalities in a cognitively impaired subset of aged outbred degus. Compared to the aged degus that show normal burrowing behavior, the age-matched degus with burrowing behavior deficits correlatively exhibit detectable human AD-like Aβ deposits and tau neuropathology, along with neuroinflammatory markers that include enhanced microglial activation and higher numbers of reactive astrocytes in the brain. This subset of cognitively impaired aged degus also exhibits cerebral amyloid angiopathy and tauopathy. We find robust neurodegenerative features in behaviorally deficient aged degus, including hippocampal neuronal loss, altered parvalbumin and perineuronal net staining in the cortex, and increased c-Fos neuronal activation in the cortex that is consistent with the neural circuit hyperactivity reported in human AD patients. By focusing on the subset of aged degus that show AD-like behavioral deficits and correlative neuropathology, our findings establish outbred degus as a natural model of sporadic AD and demonstrate the potential importance of wild-type outbred genetic backgrounds for AD pathogenesis.
© 2022. The Author(s).
Zhiqun Tan
Department Anatomy and Neurobiology, School of Medicine, University of California, Irvine, CA, 92697, USA.
Institute for Memory Impairments and Neurological Disorders, University of California, Irvine, CA, 92697, USA.
The Center for Neural Circuit Mapping, University of California, Irvine, CA, 92697, USA.
B Maximiliano Garduño
Pedro Fernández Aburto
Institute of Ecology and Biodiversity, Department of Ecological Sciences, Faculty of Sciences, University of Chile, Santiago, Chile.
Lujia Chen
Nicole Ha
Patricia Cogram
Todd C Holmes
Department Physiology and Biophysics, School of Medicine, University of California, Irvine, CA, 92697, USA.
Xiangmin Xu
Department Anatomy and Neurobiology, School of Medicine, University of California, Irvine, CA, 92697, USA. xiangmix@uci.edu.
Institute for Memory Impairments and Neurological Disorders, University of California, Irvine, CA, 92697, USA. xiangmix@uci.edu.
The Center for Neural Circuit Mapping, University of California, Irvine, CA, 92697, USA. xiangmix@uci.edu.