text:
\section{Introduction}

\IEEEPARstart{L}{earning} convolutional operators from large datasets is a growing trend in signal/image processing, computer vision, machine learning, and artificial intelligence.
The \emph{convolutional} approach resolves the large memory demands of patch-based operator learning and enables unsupervised operator learning from \dquotes{big data,} i.e., many high-dimensional signals.
See \cite{Chun&Fessler:18arXiv, Chun&Fessler:18TIP} and references therein.
Examples include \emph{convolutional dictionary learning} \cite{Chun&Fessler:18TIP, Chun&Fessler:17SAMPTA} and \emph{convolutional analysis operator learning} (CAOL) \cite{Chun&Fessler:18arXiv, Chun&Fessler:18Asilomar}.
CAOL trains an autoencoding convolutional neural network (CNN) in an unsupervised manner, and is useful for training multi-layer CNNs \cite{Chun&Fessler:18arXiv} and iterative CNNs \cite{Chun&etal:18arXiv:momnet, Chun&Fessler:18IVMSP, Chun&etal:18Allerton} from many training images.
In particular, the block proximal extrapolated gradient method using a majorizer \cite{Chun&Fessler:18TIP, Chun&Fessler:18arXiv} leads to rapidly converging and memory-efficient CAOL \cite{Chun&Fessler:18arXiv}.
However, a theoretical understanding of the impact of using many training images in CAOL has remained an open question.

This paper presents new insights on this topic.
Our first main result provides a {\em deterministic} bound on filter estimation error, and is followed by a bound on the {\em expected} error when ``model mismatch'' has zero mean.
(See Theorem~\ref{t:det} and Corollary \ref{c:det:randNoise}, respectively.)
The expected error bound depends on the training data, and we provide empirical evidence of its decrease with an increase in training samples.
Our second main result provides a {\em high probability} bound that explicitly decreases with increasingly many i.i.d. training samples. The bound improves when model mismatch and samples are uncorrelated.
(See Theorem~\ref{t:conc}.)
Additional empirical findings provide evidence that the correlation can indeed be small in practice.
Put together, our findings provide new insight into how using many  samples can improve CAOL,
underscoring the benefits of the low memory usage of CAOL.

\section{Backgrounds and Preliminaries}

\subsection{CAOL with orthogonality constraints} \label{sec:model}

CAOL seeks a set of filters that \dquotes{best} sparsify a set of training images $\{ x_l \in \bbC^{N} : l = 1,\ldots,L \}$ by solving the optimization problem \cite[\S\Romnum{2}-A]{Chun&Fessler:18arXiv} (see Appendix for notation):
\begingroup
\setlength{\thinmuskip}{1.5mu}
\setlength{\medmuskip}{2mu plus 1mu minus 2mu}
\setlength{\thickmuskip}{2.5mu plus 2.5mu}
\fontsize{9.5pt}{11.4pt}\selectfont
\ea{
\label{sys:CAOL:orth}
\argmin_{D = [d_1, \ldots, d_K]} \min_{\{ z_{l,k} \}} &~ F(D, \{ z_{l,k} \}), \quad \mbox{subj.~to}~ D D^H = \frac{1}{R} \cdot I, \tag{P0}
\\
F(D, \{ z_{l,k} \}) & :=  \sum_{l=1}^L \sum_{k=1}^K  \left\| d_k \circledast x_l - z_{l,k} \right\|_2^2 + \alpha \| z_{l,k} \|_0, \nn
}
\endgroup
where $\circledast$ denotes convolution, $\{ d_k \in \bbC^{R} : k = 1,\ldots,K\}$ is a set of $K \geq R$ convolutional kernels, $\{ z_{l,k} \in \bbC^{N} : l = 1,\ldots,L, k = 1,\ldots,K \}$ is a set of sparse codes,
$\alpha \!>\! 0$ is a regularization parameter controlling the sparsity of features $\{  z_{l,k} \}$,
and $\nm{\cdot}_{0}$ denotes the $\ell^0$-quasi-norm.
We group the $K$ filters into a matrix:
\be{
\label{eq:D}
D := \left[ \arraycolsep=2pt \begin{array}{ccc} d_1 & \cdots & d_K \end{array} \right]
\in \bbC^{R \times K}
.
}
The orthogonality condition $D D^H = \frac{1}{R} I$ in \R{sys:CAOL:orth} enforces \emph{1)} a tight-frame condition on the filters, i.e., $\sum_{k=1}^K \nm{ d_k \circledast x }_2^2 = \nm{ x }_2^2$, $\forall x$ \cite[Prop.~2.1]{Chun&Fessler:18arXiv};
and \emph{2)} filter diversity when $R=K$, since $D D^H = \frac{1}{R} I$ implies $D^H D = \frac{1}{K} I$ and each pair of filters is incoherent, i.e., $| \ip{d_k}{d_{k'}} |^2 = 0$, $\forall k \neq k'$.
One often solves \R{sys:CAOL:orth} iteratively, by alternating between optimizing $D$ (filter update) and optimizing $\{ z_{l,k} : \forall l, k \}$ (sparse code update) \cite{Chun&Fessler:18arXiv}, i.e., at the $i$ iteration, the current iterates are updated as
$\{ z_{l,k}^{(i+1)} \} = \argmin_{\{ z_{l,k} \}} F(D^{(i)}, \{ z_{l,k} \})$ and $D^{(i+1)} = \argmin_{D D^H = \frac{1}{R} \cdot I} F(D, \{ z_{l,k}^{(i+1)} \})$.

\subsection{Filter update in a matrix form}

The key to our analysis lies in rewriting the filter update for \R{sys:CAOL:orth} in matrix form, to which we apply matrix perturbation and concentration inequalities.
Observe first that
\be{
\label{eq:Psi_l}
d_k \circledast x_l
=
\underbrace{
  [\Pi^0 x_l, \dots, \Pi^{R-1} x_l]
}_{\mbox{$=:\Psi_l \in \bbC^{N \times R}$}}
d_k
= \Psi_l d_k
,
\quad l = 1,\ldots,L,
}
where $\Pi := \left[
\begin{smallmatrix}
0 & I_{N-1} \\ 1 & 0
\end{smallmatrix} \right]
\in \bbC^{N \times N}
$
is the circular shift operator and
$(\cdot)^n$ denotes the matrix product of its $n$ copies.
We consider a circular boundary condition to simplify the presentation of $\{ \Psi_l \}$ in \R{eq:Psi_l}, but our entire analysis holds for a general boundary condition with only minor modifications of $\{ \Psi_l \}$ as done in \cite[\S\Romnum{4}-A]{Chun&Fessler:18arXiv}.
Using \R{eq:Psi_l}, the filter update of \R{sys:CAOL:orth} is rewritten as
\be{
\label{opt:filter:orth}
D^\star = \argmin_{D} \sum_{l=1}^L \left\| \Psi_l D - Z_l \right\|_F^2,  \quad \mbox{subj.~to} ~ D D^H = \frac{1}{R} \cdot I,
\tag{P1}
}
where $Z_l := [ z_{l,1}, \ldots, z_{l,K} ] \in \bbC^{{N} \times K}$ contains all the current sparse code estimates for the $l$th sample, and we drop iteration superscript indices $(\cdot)^{(i)}$ throughout.
The next section uses this form to characterize the filter update solution $D^\star$.

\section{Main Results: \\ Dependence of CAOL on Training Data}
\label{sec:caol:data}

The main results in this section illustrate how training with many samples can reduce errors in the filter $D^\star$ from \R{opt:filter:orth} and characterize the reduction in terms of properties of the training data.
Throughout we model the current sparse codes estimates as
\be{
\label{sys:filter}
Z_l
=
\underbrace{ \Psi_l D_{\textnormal{true}} }_{\mbox{$=: \Zt{l}$}} + E_l,
\quad l = 1,\dots,L
}
where $D_{\textnormal{true}}$ is formed from optimal (orthogonal) filters analogously to \R{eq:D},
and $E_l \in \bbC^{N \times K}$ captures model mismatch in the current sparse codes,
e.g., due to the current iterate being far from convergence or being trapped in local minima.

The following theorem provides a {\em deterministic} characterization.

\thm{
\label{t:det}
Suppose that both matrices
\be{
\label{t:det:bound:rowrank}
\sum_{l=1}^L \Psi_l^H \Z{l}  \in \bbC^{R \times K}
\quad\mbox{and}\quad
\sum_{l=1}^L \Psi_l^H \Zt{l} \in \bbC^{R \times K}
}
are full row rank, where $\{ \Psi_l, \Z{l}, \Zt{l} : l=1,\ldots,L \}$
are defined in \R{eq:Psi_l}--\R{sys:filter}.
Then, the solution $D^\star$ to \R{opt:filter:orth} has error with respect to $D_{\textnormal{true}}$ bounded as
\be{
\label{t:det:bound:new}
\| D^\star - D_{\textnormal{true}} \|_F^2
\leq 5
\frac{ \| \sum_{l=1}^L \Psi_l^H E_l \|_F^2 }
  { \eig{\textnormal{min}}^2( \sum_{l=1}^L \Psi_l^H \Psi_l ) },
}
where $\eig{\textnormal{min}}(\cdot)$ denotes the smallest eigenvalue of its argument.
}

The full row rank condition on \R{t:det:bound:rowrank} ensures that the estimated filters $D^\star$ and the true filters $D_{\textnormal{true}}$ are unique, and it further guarantees that the denominator of \R{t:det:bound:new} is strictly positive.
When the model mismatches $E_1,\dots,E_L$ are independent and mean zero, we obtain the following expected error bound:
\cor{
\label{c:det:randNoise}
Under the construction of Theorem~\ref{t:det}, suppose that $E_l$ is a zero-mean random matrix for $l=1,\ldots,L$, and is independent over $l$.
Then,
\be{
\label{c:det:randNoise:bound}
\bbE \| D^\star - D_{\textnormal{true}} \|_F^2
\leq
5 \bar{\sigma}^2 \rho^2,
}
where $\bbE(\cdot)$ denotes the expectation,
\ea{
\label{c:det:randNoise:rho2}
\bar{\sigma}^2 &:= \max_{l=1,\ldots,L} \eig{\textnormal{max}}(\bbE\{ E_l E_l^H\}),
\nn \\
\rho^2 &:=
\frac{ \tr (\sum_{l=1}^L\Psi_l^H\Psi_l) }
  { \eig{\textnormal{min}}^2 (\sum_{l=1}^L \Psi_l^H \Psi_l) }
,
}
$\eig{\textnormal{max}}(\cdot)$ denotes the largest eigenvalue of its argument,
and the expectation is taken over the model mismatch.
}

Given fixed $K$ and $R$,
it is natural to expect that $\bar{\sigma}^2$ is bounded by some constant independent of $L$,
and so the expected error bound in \R{c:det:randNoise:bound} largely depends on $\rho^2$ in \R{c:det:randNoise:rho2}.
When training samples are i.i.d., one may further expect $(1/L) \sum_{l=1}^L \Psi_l^H \Psi_l$ to concentrate around its expectation, roughly resulting in $\rho^2 \propto 1/L$,
with a proportionality constant that depends on $R$
and the statistics of the training data.
Fig.~\ref{fig:CAOL:data} illustrates $\rho^2$ for various image datasets, providing empirical evidence of this decrease in real data.

\begin{figure}[!tp]
\centering

\begin{tabular}{c}
\includegraphics[scale=0.525, trim=0 0 0em 0em, clip]{./Fig/CAOLanal_data,cev2.eps}
\end{tabular}

\vspace{-0.5em}
\caption{
Empirical values of $\rho^2$ in \R{c:det:randNoise:rho2} show a decrease with $L$ for different datasets and filter dimensions. (The fruit and city datasets with $L \!=\! 10$ and $N \!=\! 10^4$ were preprocessed with contrast enhancement and mean subtraction; see details of datasets and experiments in \cite{Chun&Fessler:18arXiv, Chun&Fessler:18TIP} and references therein. For $L < 10$, the results are averaged over $50$ datasets randomly selected from the full datasets.)
Under the assumptions of Corollary \ref{c:det:randNoise}, the decrease in this quantity leads to a better expected error bound in \R{t:det:bound:new}.
Without preprocessing, the quantity $\rho^2$ increases by a factor of around $10^3$.
}
\label{fig:CAOL:data}
\end{figure}

\begin{figure}[!tp]
\centering

\begin{tabular}{c}
\includegraphics[scale=0.525, trim=0 0 0 0, clip]{./Fig/PhitE,ce_reg1e-3_paperv2.eps}
\end{tabular}

\vspace{-0.5em}
\caption{
Empirical estimate of $\bar{\chi}$ in \R{eq:conc:terms} across iterations in the alternating optimization algorithm \cite{Chun&Fessler:18arXiv} that solves CAOL~\R{sys:CAOL:orth} with $\alpha \!=\! 10^{-3}$. (The fruit and city datasets with $L \!=\! 10$ and $N \!=\! 10^4$ were preprocessed with contrast enhancement and mean subtraction; see details of datasets and experiments in \cite{Chun&Fessler:18arXiv, Chun&Fessler:18TIP} and references therein.
The model mismatches $\{ E_l^{(i)} : \forall l \}$ at the $i$th iteration were calculated every $50$ iterations based on \R{sys:filter}, where we use the converged filters for $D_{\textnormal{true}}$.)
Observe that $\bar{\chi}^{(i)}$ generally decreases over iterations; when $\bar{\chi}$ is small, the high probability error bound \R{t:det:bound:prob} in Theorem \ref{t:conc} depends primarily on $\bar{\rho}$ defined in \R{eq:conc:terms}.
}
\label{fig:CAOL:anal}
\end{figure}

Our second theorem provides a {\em probabilistic} error bound via concentration inequalities,
given i.i.d. training sample and model mismatch pairs
$(x_1, E_1), \dots, (x_L, E_L)$.\footnote{
We follow the natural convention in sample size analyses of assuming that $\{ x_l \!:\! \forall l \}$ are i.i.d. samples from an underlying training distribution;
see the references cited in Section~\ref{sec:rel} and \cite{Hastie&Tibshirani&Friedman:book, Mohri&Rostamizadeh&Talwalkar:book}
for other examples.
Model mismatches $\{ E_l \!:\! \forall l \}$ also become i.i.d. across samples at all iterations of CAOL, if \dquotes{fresh} training samples are used for each update, e.g., as can be done when solving \eqref{opt:filter:orth} via mini-batch stochastic optimization.
}
It removes the zero-mean assumption for the model mismatches $\{ E_l : \forall l \}$ in Corollary~\ref{c:det:randNoise} that
might be strong, e.g., if training data are not preprocessed to have zero mean.

\thm{
\label{t:conc}
Suppose that training sample and model mismatch pairs
$(x_1, E_1), \dots, (x_L, E_L) \overset{iid}{\sim} (x,E)$,
where $x$ and $E$ are almost surely bounded, i.e.,
\be{
\label{eq:conc:asbound}
\|x\|_2 \leq \gamma \quad\mbox{and}\quad \|E\|_F \leq \sigma,
}
and the matrices in \R{t:det:bound:rowrank} are almost surely full row rank.
Then, for any $0 < \delta < \eig{\textnormal{min}}(\bar{\Lambda})/(2R\gamma^2)$, the solution $D^\star$ to \R{opt:filter:orth} has error with respect to $D_{\textnormal{true}}$ bounded as
\begingroup
\setlength{\thinmuskip}{1.5mu}
\setlength{\medmuskip}{2mu plus 1mu minus 2mu}
\setlength{\thickmuskip}{2.5mu plus 2.5mu}
\ea{
\label{t:det:bound:prob}
&~\| D^\star - D_{\textnormal{true}} \|_F^2
\nn \\
&\leq 5
\bigg\{
\frac{
  \sigma\sqrt{\tr(\bar{\Lambda})/L}
  +
  \| \bbE(\Psi^H E) \|_F
  +
  2 \sigma \gamma \sqrt{R} \delta
}{
  \eig{\textnormal{min}}(\bar{\Lambda}) - 2\gamma^2R \delta
}
\bigg\}^{\!\!2}
,
}
\endgroup
with probability at least
\be{
\label{t:det:prob}
1 - 3 R \exp\left(-L\frac{\delta^2/2}{3+\delta/3}\right)
,
}
where $\bar{\Lambda} := \bbE (\Psi^H \Psi)$ and $\Psi$ is constructed from $x$ as in \R{eq:Psi_l}.
}

Taking $\delta$ sufficiently small, the high probability error bound \R{t:det:bound:prob} is primarily driven by
\be{
\label{eq:conc:terms}
\bar{\rho} := \frac{\sqrt{\tr(\bar{\Lambda})/L}}{\eig{\textnormal{min}}(\bar{\Lambda})}
\quad \text{and} \quad
\bar{\chi} := \frac{\| \bbE(\Psi^H E) \|_F}{\eig{\textnormal{min}}(\bar{\Lambda})},
}
where $\bar{\rho}$ is analogous to $\rho$ in \R{c:det:randNoise:rho2},
and $\bar{\chi}$ captures how correlated the model mismatch is to the training samples.
As the number $L$ of training samples increases, $\bar{\rho}$ decreases as $1/\sqrt{L}$. On the other hand, $\bar{\chi}$ is constant with respect to $L$ and provides a floor for the bound.
Fig.~\ref{fig:CAOL:anal} illustrates $\bar{\chi}$ for CAOL iterates from different image datasets, and provides empirical evidence that this term can indeed be small in real data.
If the model mismatch is sufficiently uncorrelated with the training samples,
i.e., $\bar{\chi}$ is practically zero, then
only the $\bar{\rho}$ term remains and this term decreases with $L$. Namely, if model mismatch is entirely uncorrelated with the training samples, then using many samples decreases the error bound to (effectively) zero.

\section{Related Works} \label{sec:rel}

Sample complexity \cite{Bajwa&etal:bookCh} and synthesis error \cite{Singh&Poczos&Ma:18PMLR} have been studied in the context of synthesis operator learning (e.g., dictionary learning \cite{Aharon&Elad&Bruckstein:06TSP});
see the cited papers and references therein.
A similar understanding for (C)AOL has however remained largely open; existing works focus primarily on establishing (C)AOL models and their algorithmic challenges \cite{Yaghoobi&etal:13TSP, Hawe&Kleinsteuber&Diepold:13TIP, Cai&etal:14ACHA, Ravishankar&Bressler:15TSP, Chun&Fessler:18arXiv}.
The authors in \cite{Seibert&etal:16TSP} studied sample complexity for a patch-based AOL method, but the form of their model differs from that of ours \R{sys:CAOL:orth}. Specifically, they consider the following AOL problem:
$\min_{D} \sum_l f(D^T \hat{x}_l) + g(D)$,
where $f(\cdot)$ is a sparsity promoting function (e.g., a smooth approximation of the $\ell^0$-quasi-norm \cite{Seibert&etal:16TSP}),
$g(\cdot)$ is a regularizer or constraint for the filter matrix $D$,
and $\{ \hat{x}_l : l = 1,\ldots,L \}$ is a set of training {\em patches} (not images).

\section{Proof of Theorem~\ref{t:det}}

Rewriting \R{opt:filter:orth} yields that
$D^\star$ is a solution of the (scaled)
orthogonal Procrustes problem~\cite[\S S.\Romnum{7}]{Chun&Fessler:18arXiv}:
\be{
\label{opt:filter:orth:procrustes}
\argmin_{D} \| \widetilde{\Psi} D - \widetilde{Z} \|_F^2,
\quad \mbox{subj.~to} ~ D D^H = \frac{1}{R} \cdot I,
}
where $\widetilde{\Psi} \in \bbC^{L N \times R}$
arises by stacking $\Psi_1,\dots,\Psi_L$ vertically
and $\widetilde{Z} \in \bbC^{L N \times K}$
arises likewise from $\Z{1},\dots,\Z{L}$.
Similarly, since $\Psi_l D_{\textnormal{true}} = \Zt{l}$ as in \R{sys:filter},
$D_{\textnormal{true}}$ is a solution of the analogous (scaled)
orthogonal Procrustes problem
\be{
\label{opt:filter:orth:procrustes:true}
\argmin_{D} \| \widetilde{\Psi} D - \widetilde{Z}_{\textnormal{true}} \|_F^2,
\quad \mbox{subj.~to} ~ D D^H = \frac{1}{R} \cdot I,
}
where $\widetilde{Z}_{\textnormal{true}} \in \bbC^{L N \times K}$
arises by stacking $\Zt{1},\dots,\Zt{L}$ vertically.

By assumption, both $\widetilde{\Psi}^H \widetilde{Z}$ and $\widetilde{\Psi}^H \widetilde{Z}_{\textnormal{true}}$ are full row rank
and so~\R{opt:filter:orth:procrustes} and~\R{opt:filter:orth:procrustes:true}
have unique solutions given by the unique (scaled) polar factors
\ea{
D^\star &= \frac{1}{\sqrt{R}} \mbox{Q}(\widetilde{Z}^H  \widetilde{\Psi})^H &
D_{\textnormal{true}} &= \frac{1}{\sqrt{R}} \mbox{Q}(\widetilde{Z}_{\textnormal{true}}^H \widetilde{\Psi})^H
}
where $\mbox{Q}(\cdot)$ denotes the polar factor of its argument,
and can be computed as $\mbox{Q}(A) = W V^H$
from the (thin) singular value decomposition $A = W \Sigma V^H$.

Thus we have
\ea{
\label{eq1:t:det:prf}
&~\| D^\star - D_{\textnormal{true}} \|_F^2
\nn \\
&= \frac{1}{R} \| \mbox{Q}(\widetilde{Z}_{\textnormal{true}}^H \widetilde{\Psi}) - \mbox{Q}(\widetilde{Z}^H  \widetilde{\Psi}) \|_F^2
\nn \\
&\leq
  \frac{1}{R} \| \widetilde{E}^H \widetilde{\Psi} \|_F^2
  \Bigg\{
    \bigg[
      \frac{2}{\svd{R}(\widetilde{Z}_{\textnormal{true}}^H \widetilde{\Psi}) + \svd{R}(\widetilde{Z}^H \widetilde{\Psi})}
    \bigg]^2
    \nn \\
    &\qquad\qquad\qquad\quad
    +
    \bigg[
      \frac{1}{\max\{\svd{R}(\widetilde{Z}_{\textnormal{true}}^H \widetilde{\Psi}),\svd{R}(\widetilde{Z}^H \widetilde{\Psi} )\}}
    \bigg]^2
  \Bigg\}
\nn \\
&\leq
\frac{1}{R} \| \widetilde{E}^H \widetilde{\Psi} \|_F^2 \Bigg\{
  \bigg[ \frac{2}{\svd{R}(\widetilde{Z}_{\textnormal{true}}^H \widetilde{\Psi})} \bigg]^2
  +
  \bigg[ \frac{1}{\svd{R}(\widetilde{Z}_{\textnormal{true}}^H \widetilde{\Psi})} \bigg]^2
\Bigg\}
\nn \\
&= \frac{5}{R} \frac{\| \widetilde{\Psi}^H \widetilde{E} \|_F^2}{\svd{R}^2(\widetilde{\Psi}^H \widetilde{Z}_{\textnormal{true}})}
= \frac{5}{R}
  \frac{\| \sum_{l=1}^L \Psi_l^H E_l \|_F^2}
    {\svd{R}^2(\sum_{l=1}^L \Psi_l^H \Zt{l})}
}
where $\widetilde{E} = \widetilde{Z} - \widetilde{Z}_{\textnormal{true}}$ is exactly $E_1,\dots,E_L$ stacked vertically,
and $\svd{r}(\cdot)$ denotes the $r$th largest singular value of its argument.
The first inequality holds by the perturbation bound in \cite[Thm.~3]{Li:95SIAM:JMAA},
and the second holds since $\svd{R}(\widetilde{Z}^H \widetilde{\Psi}) \geq 0$.
Recalling that $\Zt{l} = \Psi_l D_{\textnormal{true}}$,
we rewrite the denominator of \R{eq1:t:det:prf} as
\ea{
\label{eq2:t:det:prf}
&~\svd{R}^2\Big( \sum_{l=1}^L \Psi_l^H \Zt{l} \Big)
= \svd{R}^2\Big( \sum_{l=1}^L \Psi_l^H \Psi_l D_{\textnormal{true}} \Big)
\nn \\
&= \frac{1}{R} \svd{R}^2\Big( \sum_{l=1}^L \Psi_l^H \Psi_l \Big)
= \frac{1}{R} \eig{\textnormal{min}}^2\Big( \sum_{l=1}^L \Psi_l^H \Psi_l \Big)
,
}
where the second equality holds because $D_{\textnormal{true}} D_{\textnormal{true}}^H = (1/R)I$.
Substituting \R{eq2:t:det:prf} into \R{eq1:t:det:prf}
yields \R{t:det:bound:new}.

\section{Proof of Corollary~\ref{c:det:randNoise}}

Taking the expectation of \R{t:det:bound:new} over the model mismatch amounts to taking the expectation of the numerator of the upper bound in \R{t:det:bound:new}:
\ea{
\label{c:orth:pert:randNoise:prof1}
&~ \bbE \Big\| \sum_{l=1}^L \Psi_l^H E_l \Big\|_F^2
\nn \\
&= \sum_{l=1}^L \bbE \big\| \Psi_l^H E_l \big\|_F^2
= \sum_{l=1}^L \tr\Big(\Psi_l^H \bbE\{ E_l E_l^H\} \Psi_l\Big)
\nn \\
&\leq \sum_{l=1}^L \lambda_{\textnormal{max}}(\bbE\{ E_l E_l^H\}) \cdot \|\Psi_l\|_F^2
\leq \bar{\sigma}^2 \cdot \sum_{l=1}^L \|\Psi_l\|_F^2,
}
where the first equality holds by using the assumption that $E_l$ is zero-mean and independent over $l$,
the second equality follows by expanding the Frobenius norm then applying linearity of the trace and expectation,
the first inequality holds since $v^H M v \leq \lambda_{\textnormal{max}}(M) \cdot \|v\|_2^2$ for any vector $v$ and Hermitian matrix $M$,
and the last inequality follows from the definition of $\bar{\sigma}^2$.
Rewriting \R{c:orth:pert:randNoise:prof1} using the identity
$
\sum_{l=1}^L \|\Psi_l\|_F^2
= \sum_{l=1}^L \tr(\Psi_l^H\Psi_l)
= \tr ( \sum_{l=1}^L\Psi_l^H\Psi_l )
$
yields the result \R{c:det:randNoise:bound}.

\section{Proof of Theorem \ref{t:conc}}
\label{p:conc}

We derive two high probability bounds,
one each for the numerator and denominator of \R{t:det:bound:new}.
Then, the bound \R{t:det:bound:prob} with probability \R{t:det:prob}
follows by combining the two via a union bound.
Before we begin, note that \R{eq:conc:asbound}
implies that $\|\Psi\|_2 \leq \|\Psi\|_F \leq \gamma \sqrt{R}$
almost surely; our proofs use this inequality multiple times.

\subsection{Upper bound for numerator}

Observe first that
\ea{
\Big\| \sum_{l=1}^L \Psi_l^H E_l \Big\| _F
&=
\Big\|
  L \bbE(\Psi_l^H E_l)
  +
  \sum_{l=1}^L \{\Psi_l^H E_l-\bbE(\Psi_l^H E_l)\}
\Big\|_F
\nn \\
\label{conc:numer:decomp}
&\leq
L \| \bbE(\Psi_l^H E_l) \|_F
+
\Big\| \sum_{l=1}^L \xi_l \Big\|_2
,
}
where $\xi_l := \operatorname{vec}\{\Psi_l^H E_l-\bbE(\Psi_l^H E_l)\} \in \bbC^{RK}$ for $l = 1,\dots,L$.
We next bound $\| \sum_{l=1}^L \xi_l \|_2$ via the vector Bernstein inequality~\cite[Cor.~8.44]{Foucart&Rauhut:book}.
Note that $\xi_1,\dots,\xi_L$ are i.i.d.
with $\bbE \xi_l = 0$ (by construction).
Furthermore, $\xi_l$ is almost surely bounded as
\eas{
\|\xi_l\|_2 &= \|\Psi_l^H E_l-\bbE(\Psi_l^H E_l)\|_F \\
&\leq \|\Psi_l^H E_l\|_F + \|\bbE(\Psi_l^H E_l)\|_F
&&\text{(Triangle ineq.)} \\
&\leq \|\Psi_l^H E_l\|_F + \bbE\|\Psi_l^H E_l\|_F
&&\text{(Jensen's ineq.)} \\
&\leq \|\Psi_l\|_F\|E_l\|_F + \bbE\|\Psi_l\|_F\|E_l\|_F
& \\
&\leq 2\sigma\gamma\sqrt{R}
.
&
}
Thus the vector Bernstein inequality~\cite[Cor.~8.44]{Foucart&Rauhut:book}
yields that for any $t > 0$,
\be{
\label{conc:vector:bernstein:bound}
  \Big\| \sum_{l=1}^L \xi_l \Big\|_2
  \leq \sigma \sqrt{L} \sqrt{\tr(\bar{\Lambda})} + t
,
}
with probability at least
\be{
\label{conc:vector:bernstein:prob}
1
-
\exp\bigg\{
  \frac{-t^2/2}{3L(2\sigma\gamma\sqrt{R})^2+t(2\sigma\gamma\sqrt{R})/3}
\bigg\}.
}
We obtained \R{conc:vector:bernstein:bound} by the following simplification:
\begingroup
\allowdisplaybreaks
\eas{
\bbE \Big\| \sum_{l=1}^L \xi_l \Big\|_2
&\leq \sqrt{\bbE \Big\| \sum_{l=1}^L \xi_l \Big\|_2^2}
= \sqrt{L\bbE \|\xi_l\|_2^2} \\
&= \sqrt{L\bbE \|\Psi_l^H E_l - \bbE(\Psi_l^H E_l)\|_F^2} \\
&=
\sqrt{L\{\bbE \|\Psi_l^H E_l\|_F^2 - \|\bbE(\Psi_l^H E_l)\|_F^2\}} \\
&\leq \sqrt{L\bbE \|\Psi_l^H E_l\|_F^2}
\leq \sqrt{L\bbE (\| \Psi_l \|_F^2 \| E_l \|_F^2)} \\
&\leq \sqrt{L \sigma^2 \bbE \| \Psi_l \|_F^2}
= \sigma\sqrt{L}\sqrt{\tr(\bar{\Lambda})}
,
}
\endgroup
where the third equality holds by $\bbE \| A - \bbE A \|_F^2 = \sum_{i,j} \bbE ( A_{i,j} - \bbE A_{i,j} )^2 = \sum_{i,j} \bbE A_{i,j}^2 - ( \bbE A_{i,j} )^2 = \bbE \| A \|_F^2 - \| \bbE A \|_F^2$.
We obtained \R{conc:vector:bernstein:prob} by the following simplifications:
\begin{gather*}
\sup_{\|x\|_2 \leq 1} \bbE |x^H\xi_l|^2
\leq \bbE \|\xi_l\|_2^2 \leq (2\sigma\gamma\sqrt{R})^2
, \\
\bbE \Big\| \sum_{l=1}^L \xi_l \Big\|_2
\leq
\bbE \sum_{l=1}^L \|\xi_l\|_2
\leq L \bbE \|\xi_l\|_2
\leq L(2\sigma\gamma\sqrt{R})
.
\end{gather*}
Applying \R{conc:vector:bernstein:bound}
and \R{conc:vector:bernstein:prob}
with $t = 2 \sigma \gamma \sqrt{R} L\delta$
to the square of \R{conc:numer:decomp}
yields
\begingroup
\setlength{\thinmuskip}{1.5mu}
\setlength{\medmuskip}{2mu plus 1mu minus 2mu}
\setlength{\thickmuskip}{2.5mu plus 2.5mu}
\fontsize{9.5pt}{11.4pt}\selectfont
\be{
\label{conc:numer:bound}
\Big\| \sum_{l=1}^L \Psi_l^H E_l \Big\|_F^2 \\
\leq
L^2\Big\{
  \sigma\sqrt{\tr(\bar{\Lambda})/L}
  +
  \| \bbE(\Psi_l^H E_l) \|_F
  +
  2 \sigma \gamma \sqrt{R} \delta
\Big\}^{\!\!2}
,
}
\endgroup
with probability at least $1 - \exp( -L \frac{\delta^2/2}{3+\delta/3} )$.

\subsection{Lower bound for denominator}

Observe that
$
\sum_{l=1}^L \Psi_l^H \Psi_l
= L \bar{\Lambda} + \sum_{l=1}^L \Lambda_l
$,
where $\Lambda_l := \Psi_l^H \Psi_l - \bar{\Lambda}$,
so Weyl's inequality \cite{Weyl:1912MA} yields
\be{
\label{eq:Cound:denom}
\eig{\textnormal{min}} \Big( \sum_{l=1}^L \Psi_l^H \Psi_l \Big)
\geq
\eig{\textnormal{min}} (L\bar{\Lambda})
-
\Big\| \sum_{l=1}^L \Lambda_l \Big\|_2
,
}
and it remains to bound $\| \sum_{l=1}^L \Lambda_l \|_2$.
We do so by using
the Matrix Bernstein inequality~\cite[Cor.~8.15]{Foucart&Rauhut:book}.

Note that $\Lambda_1,\dots,\Lambda_L$
are i.i.d. (since $x_1,\dots,x_L$ are i.i.d.)
and $\bbE \Lambda_l = 0$.
Furthermore, $\Lambda_l$ is almost surely bounded as
\eas{
\|\Lambda_l\|_2
&= \|\Psi_l^H \Psi_l - \bbE(\Psi_l^H \Psi_l)\|_2
\\
&\leq \|\Psi_l^H \Psi_l\|_2 + \|\bbE(\Psi_l^H \Psi_l)\|_2
&&\text{(Triangle ineq.)}
\\
&\leq \|\Psi_l^H \Psi_l\|_2 + \bbE \|\Psi_l^H \Psi_l\|_2
&&\text{(Jensen's ineq.)}
\\
&= \|\Psi_l\|_2^2 + \bbE \|\Psi_l\|_2^2
\leq 2\gamma^2R.
}
Thus, the Matrix Bernstein inequality~\cite[Cor.~8.15]{Foucart&Rauhut:book}
yields that for any $t > 0$,
\be{
\label{conc:bernstein}
\bbP \Big\{ \Big\| \sum_{l=1}^L \Lambda_l \Big\|_2 \geq t \Big\}
\leq 2 R \exp\Big\{\frac{-t^2/2}{L (2\gamma^2R)^2+2\gamma^2Rt/3}\Big\},
}
where we use the following simplification:
\bes{
\Big\| \sum_{l=1}^L \bbE \Lambda_l^2 \Big\|_2
= L \big\| \bbE \Lambda_l^2 \big\|_2
\leq L \bbE \|\Lambda_l\|_2^2
\leq L (2\gamma^2R)^2
.
}
Applying \R{conc:bernstein} with $t = 2\gamma^2RL\delta$
to the square of \R{eq:Cound:denom}
yields
\be{
\label{conc:eigenmin}
\eig{\textnormal{min}}^2\Big( \sum_{l=1}^L \Psi_l^H \Psi_l \Big)
\geq L^2 \{\eig{\textnormal{min}}(\bar{\Lambda}) - 2\gamma^2R \delta\}^2
,
}
with probability at least $1-2 R \exp (-L\frac{\delta^2/2}{1+\delta/3} )$.

\subsection{Combined bound}
Combining the bounds \R{conc:numer:bound} and \R{conc:eigenmin}
via a union bound yields \R{t:det:bound:prob}
with probability at least
\ea{
1
- \exp\bigg( -L\frac{\delta^2/2}{3+\delta/3} \bigg)
- 2 R \exp\bigg(-L\frac{\delta^2/2}{1+\delta/3}\bigg)
,
}
which is greater than or equal to \R{t:det:prob}.

\bibliographystyle{IEEEtran}
\balance

redpajama_set_name: RedPajamaArXiv


This Wiki is a collaborative encyclopedia about the supernatural crime films and TV series that anyone including you can edit.
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Apps often need to display data in similarly styled containers. These containers are often used in lists to hold each item's information. The system provides the CardView API as an easy way for you show information inside cards that have a consistent look across the platform. These cards have a default elevation above their containing view group, so the system draws shadows below them. Cards provide an easy way to contain a group of views while providing a consistent style for the container.
In order to use the CardView you need to add it to your layout file. Use it as a view group to contain other views. In this example, the CardView contains a single TextView to display some information to the user.
The cards are drawn to the screen with a default elevation, which causes the system to draw a shadow underneath them. You can provide a custom elevation for a card with the card_view:cardElevation attribute. This will draw a more pronounced shadow with a larger elevation, and a lower elevation will result in a lighter shadow. CardView uses real elevation and dynamic shadows on Android 5.0 (API level 21) and above and falls back to a programmatic shadow implementation on earlier versions.
To set the corner radius in your layouts, use the card_view:cardCornerRadius attribute.
To set the corner radius in your code, use the CardView.setRadius method.
To set the background color of a card, use the card_view:cardBackgroundColor attribute.
For more information, see the API reference for CardView.


text:
Why I spend my free time telling Ukraine's story (and you should too)
Maidan Nezalezhnosti, Kyiv. Source: SRF
2015/03/07 - 12:01 • More, Op-ed
Article by: Andrew Kinder
The exceptional affection many non-Ukrainians feel for Ukraine was on full display at the September 2014 Yalta European Strategy meetings, held that year in Kyiv, where several US diplomats had returned for panel discussions to share their thoughts on the country's situation. Each of these men, who had no serious connection to Ukraine before serving there, tried to express how they are always drawn back to the country, despite its seemingly never-ending cycle of problems, crises, and disappointments.
Ploshcha Rynok, Lviv, June 2009.
Listening to these Americans attempt to find the right words to explain why they cared about Ukraine struck a chord, and I asked myself, "why do I care about what happens to Ukraine?" Like many of Ukraine's non-Ukrainian supporters, I have a personal connection; for several years I dated a woman whose family had emigrated from Lviv in 1990s. With her I experienced many of the things that can endear Ukraine to a foreigner – hospitality, adventure, hearty food, and relaxed summer days in Lviv. Also apparent were some of the less appealing sides – bribes at the border, bribes at city hall, the pitiful social safety net, horse-drawn carts in the western Ukrainian countryside and Bentleys in front of parliament in Kyiv. After our relationship ended, I still felt a strong urge to go back to Ukraine and returned to Lviv for the Euro 2012 soccer championships (I even brought my parents along). The city was a charming host, and despite the obvious problems in the country, experiencing Ukraine at that moment almost forced a bit of optimism.
The Ukrainian elite suffers during the financial crisis, Kyiv, May 2009.
As for anyone with a connection to Ukraine, Maidan was a captivating experience, and the post-Maidan emergence of civil society and political engagement has offered a beautiful contrast to my home countries: the US, where many can't be bothered to take a couple of hours, once a year, to vote in free and fair elections, and Germany, where high-minded complaining is a national sport, despite a highly-functioning political system (and even more highly-functioning economy). Across from this stand the Ukrainians, who camped out in the freezing cold with EU flags, charged forward against sharpshooters, and later have gone to serve on the front lines, all because they wish to live in a "normal" country, a privilege many in the West don't even recognize that they enjoy. As if Ukraine's challenges were not great enough on their own, the country has been subjected to unprecedented, cynical wars instigated by Russia, for which Western institutions and media have been completely unprepared.
US Deputy Asst. Secretary of State Thomas Melia speaks at YES, September 2014.
Even if you don't have a personal relationship of some kind to Ukraine, it is nearly impossible to read one of the many stories coming of out the country – volunteers who have more or less prevented the collapse of the army and the social safety net, Nadiya Savchenko's unbreakable will in the face of gross injustice, young journalists holding their new government accountable, civilians who volunteered or were drafted into the army holding the line against a blatant Russian invasion – and not feel compelled to do something about the situation, even if that something is only editing an article or translating a leaflet. These stories are real, and they reflect exactly why those US diplomats sat in Kyiv and – almost in disbelief at themselves – said that they couldn't turn their backs on Ukraine, even if at times good sense might have suggested doing just that. Most of us are not ambassadors, decision makers, or front-line soldiers, but we also have a role in not turning our collective backs on Ukraine. What does this mean? Simple: It means that we have an obligation to tell Ukraine's story, even if it's only a personal anecdote or a small fact (How many Americans or western Europeans know that Ukrainian is its own language? How many mistakenly think fascists have taken over Kyiv? How many know that Lviv looks – and acts somewhat – like a smaller Vienna?). This is a task too important to leave to Kremlin propagandists, plodding Western governments, or news organizations that are unable or unwilling to accurately inform the world about Ukraine.
Tags: Op-ed
Andrew Kinder
Andrew Kinder is a contributor and editor at Euromaidan Press. He is currently a business student (M.Sc.) and research assistant at the University of Cologne (Germany) and has formerly worked as an anti-corruption investigator and corporate governance analyst.
» More, Op-ed » Why I spend my free time...
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redpajama_set_name: RedPajamaCommonCrawl


text:
Letters From the Hellbox
Tschichold, Nazis and Allen Lane: The Modernist Politics of Type
by Martin McClellan
"Good typography can never be humorous. It is precisely the opposite of adventure." — Jan Tschichold.
One belief rampaged through the early 20th century: to change culture, you must impose order. This is true of the left and right wing, played out in fascist and communist governments alike. From order, so the thinking went, people will realize the truth of your beliefs (or at least succumb to them). But in order to get them to experience those righteous feelings, one needs a framework to teach those who haven't seen the light yet (or at least keep the non-believers in line).
In 1914 when Jan Tschichold was twelve, a poorly laid-out book with terrible typography so upset his sensibilities that he took scissors to it. He cut it up and redrew the title pages, re-assembling a book more aesthetically tuned to his impeccable standards. That Tschichold has an origin story—usually reserved for patriots, presidents, saints and other super heroes—should tell you what an esteemed place he holds in the annals of twentieth century typography. That the story is true should tell you something about the man himself. In the building of taste, Tschichold would hold the door for us if we wanted to join him at the top of the stairs, but he certainly wouldn't waste time in our pedestrian basement.
In 1928 Tschichold published a book audaciously titled Die neue Typographie, or "The New Typography." He advocated for systems of typographic layout and printing that would align with the new thinking brought to culture through the Dada, Bauhaus, De Stijl, and Futurist movements. The belief was that society was on the verge of a primal step of evolution, born of the machine age. An optimism and excitement parallel to that some seventy years later at the dawn of the Internet. Everyday objects—the train, the automobile, the light bulb—were fetishes signifying the great cultural movements that would liberalize society and free everyday people from the shackles of oppression and individual statehood, with its requisite wars and dogmas. "These objects, designed without reference to the aesthetics of the past, have been created by a new kind of man: the engineer!" he wrote.
With this new excitement a new companion method of typographic expression was required and Tschichold drew the map. "None of the typefaces whose basic form some kind of ornament has been added meet our requirements for clarity and purity… Among all of the types that are available, the so-called "Grotesque" (sanserif)… is the only one in spiritual accordance with our time."
Sans-serif type, literally "without serifs", was not new, but before this time it was primarily relegated to signage and advertising. Headlines you might see, but rarely long text passages. That it was relegated to a classification of "Grotesque" by typographers in the 19th century should give you a clue to the general feeling about those type forms.
Serifs evolved from the pen-strokes scribes used when forming a letter. If you were to blow your computer screen up 200% or so and focus on a lower-case 'r', you'd see a small stroke at the top left end of the stem and on either sides of the bottom of the stem, making a modest foot for the letter to stand on. These are serifs. Serifs are generally believed to aid in legibility, but Tschichold wanted to strip all forms down to their base, looking at ornamentation the way that Charles and Ray Eames probably looked at Rococo.
By ending ornamentation and creating a more pure communication, Tschichold thought that cultural differences could be eradicated through typography. The traditional typeface for Germany was Fraktur, a blackletter not dissimilar to the Textura Gutenberg used nearly 500 years before. Tschichold railed against it. "The emphatically national, exclusivist character of Fraktur… contradicts present-day transnational bonds between people and forces their inevitable elimination."
In Germany, Fraktur had been in battle with roman letterforms, generally called Antiqua, since Germany had lost its monopoly on printing towards the end of the 15th century. Fraktur was generally accepted as the common face, and here was this young punk typographer advocating for doing away with tradition during the most violent and oppressive nationalist uprising of the 20th century.
Indeed, the Nazis declared Fraktur the typeface of the party, and, by extension, of Germany, citing tradition and national pride. They printed it on their stationary and used it in their propaganda. The Nazi party had its own ideas about typography, and needless to say, they did not align with our hero's. They did, however, share that one constant: to change culture, you must impose order.
In 1933 Tschichold was living in Munich with his wife Edith. They had been in the city for seven years, having moved so that Jan could take a teaching post at the Meisterschule für Deutschland Buchdrucker (the Master School for German Book Printing) at the bequest of Paul Renner, whose typeface Futura you've no doubt seen in good use—the titles of most Wes Anderson movies, for example.
The Tschicholds were home with their young son one evening early in March when armed Nazis came to the door. They declared that they were doing a house-to-house search and demanded entrance. They found Soviet posters, and arrested Jan and Edith. Edith they released after two days. Jan they kept locked up, accused of "Cultural Bolshevism." Reader, if you feel that perhaps typography is trivial in the history of culture, look no further than this minor incident in Nazi lore as refutation. The Nazis were willing to imprison people not because of their beliefs in religion or politics per se, but because of their beliefs about typography.
Tschichold was released after six weeks, after the Reichstag passed the "Law for Removing the Distress of the People and the Reich," which voted democracy out and dictator Hitler in. Just like in the great novels (or, at least, the Sound of Music) Tschichold secreted his family out of Germany and moved to Switzerland, where he settled near Basel.
Eventually, the Nazis had a break with their beloved Fraktur. In 1941 Martin Borman, on behalf of Hitler, banned it under the mistaken paranoia that it was of Jewish origin. The letterhead on which the decree was typed was printed in Fraktur.
In 1946 Tschichold wrote: "The Third Reich was second to none in pursuing technical "progress" through its preparations for war, which were hypocritically concealed behind the propaganda for medieval forms of society and expression. Deception lay at its root, and that is why it could not abide the honest modernists who were its political opponents." With a note of caution no doubt directed at himself, he continued: "yet they themselves, without knowing it, stood very close to the mania for 'order' that ruled the Third Reich…"
Tschichold mellowed on his beliefs in a brand new typography. "I am the most severe critic of the young Tschichold," he wrote later in his life. He backed away from sans-serif typography as a salvation as he became better educated in the history of type and why older designers made some of the choices that they did.
He continued as a book designer and typographer in Switzerland during the war, and through his work he gained a reputation as one of the finest designers in Europe. A few years after the Allied victory, he received a call from a British gentleman named Allen Lane, who asked him to come to London and help redesign his line of books.
Legend has it (another origin story!) that Lane was standing on the platform at Exeter station after visiting Agatha Christie. He had nothing good to read, and the newsstand carried only popular and tired historic fare. He lamented the lack of good modern literature available cheaply and readily. He imagined great writing being available everywhere, maybe in a vending machine, for about the price of a pack of cigarettes.
He wanted a moniker that was both 'dignified and flippant.' His secretary recommended the penguin as a mascot, and in 1935 Penguin published its first editions, including the work of Hemingway, Maurois and Christie. Their iconic color-coding—fiction was orange, crime was green and biography was blue—and graphic covers made them easy to spot and identify. The books were hugely successful.
The brand became legendarily seated in the hearts of the British when soldiers carried the books during the war, trading them at far points around the world. A small bit of home and solace that slips easily into a soldier's pocket. On the home front, Penguin published popular titles on cooking under rationing, and the bestselling What's That Plane: How to Identify American and Jap Airplanes.
During the war, publishing was difficult. Materials were rationed, and Penguin had to make due with what it could, and schedule its runs around presses which were often used for the war effort. Editions were smaller. But after the war there were newfound riches for the publisher who chose to exploit them. Lane knew that he had an opportunity to redo the Penguin line with higher quality and better standards. He was introduced to Tschichold, and hired the German designer to come to London.
On arrival at Penguin, Tschichold found chaos. There were no rules in place to govern design. No specs for paper and layout of covers, interiors or anything else. Each book, despite their general graphical uniformity, was prone to the quirks of the designer, or worse, the printer, who might dispose of Penguin's brand in trade for easing the production process.
At first, Tschichold's attempts to draw order from the chaos were met with resentment from the individualistic British for his Germanic, orderly approach. Ruari McLean, in his biography of Tschichold, pointed out that when somebody was appreciative of his efforts, Tschichold spoke fluent English. When they were reproachful that he was not doing it the British way, suddenly he had great trouble with the language barrier, asking people to repeat themselves until they simply gave up.
Tschichold spent two years at Penguin writing exacting standards that specified everything from the paragraph indent (1 em—an em being a unit of typographic measurement equal to the width of a letter 'm' of any given typeface size. An em dash, then, is a dash the width of one em.), to the location and size of the Penguin logo on the front book cover, which he redrew multiple times. He wrote explicit composition rules for the printers to follow, unifying all of the plants that printed Penguin books (most presses in England in that day did, to one degree or another), and thus giving them a baseline standard that they applied to other clients as well. It is alleged by more than one biographer that Tschichold was singularly responsible for creating higher printing standards in post-war England.
He also managed to design over 500 books, transforming Penguin from a publishing house beloved for the quality of their writers to one also well respected for their impeccable design quality. He did it through a refined framework, imposing strict order on the work that Penguin produced.
But in all of Tschichold's specs, precise to the millimeter in so many ways, there is one glaring omission: he never spelled out what typeface a designer was to use. That choice, we can imagine, he thought was better left with the designer. It would be one choice that lived best outside of order. One small influence in a job whose greatest reward consists of disappearing.
"To remain nameless and without specific appreciation, yet to have been of service to a valuable work and to the small number of visually sensitive readers—this, as a rule, is the only compensation for the long, and indeed never-ending, indenture of the typographer."
1. Martin Bormann's 1941 decree banning the use of Fraktur: http://german.about.com/library/gallery/blfoto_fraktur06.htm
2. Richard Hollis on Jan Tschichold, in the Guardian: http://www.guardian.co.uk/artanddesign/2008/dec/05/jan-tschichold-typography
3. Linotype's celebration of Tschichold's 100th birthday: http://www.linotype.com/794/inhonorofthe100thbirthdayofjantschichold.html
"Say Hello To Ur Friends": The Baby-Sitters Club — Reloaded
Lord, Denise, These Almonds
I'm Comic Sans, Asshole
by Mike Lacher
The Convergences Contest: Contest Winner #16: A Rousseau/Hirshfield Convergence
by Adam Webb
FLIP: A Column About Skateboarding: Column 10: 900
by Joel Rice
Notes From an Amateur Spectator at Amateur Mixed Martial Arts Fights: Column 8: AX Fighting 30
by Rory Douglas


text:
Q: How to set bold in ComboBox only in presentation line, not in whole drop down list (WPF)? I have in my DataGrid ComboBox implementation. Also I have a IsColorCalibFolderBold property by this property ComboBox know when it should represent data in bold style and when no.
So, my property
        public bool IsColorCalibFolderBold
        {
            get { return _IsColorCalibFolderBold; }
            set
            {
                _IsColorCalibFolderBold = value;
                OnPropertyChanged();
            }
        }

and my .xalm
...

              <DataGridTemplateColumn.CellTemplate>
                                        <DataTemplate>
                                            <ComboBox
                                                x:Name="Cb_color_calibration"
                                                SelectionChanged="Cb_color_calibration_SelectionChanged"
                                                ItemsSource="{Binding Path=ColorCalibrationFolders}"
                                                      SelectedItem="{Binding Path=SelectedColorCalibrationFolder}">
                                                <ComboBox.ItemTemplate>
                                                    <DataTemplate>
                                                        <TextBlock Text="{Binding Path=UIRepresentation}" />
                                                    </DataTemplate>
                                                </ComboBox.ItemTemplate>

                                                <ComboBox.Style>
                                                    <Style TargetType="ComboBox">
                                                        <Style.Triggers>
                                                            <DataTrigger Binding="{Binding IsColorCalibFolderBold}"
                                                                         Value="True">
                                                                <Setter Property="FontWeight" Value="Bold"/>
                                                            </DataTrigger>
                                                        </Style.Triggers>
                                                    </Style>
                                                </ComboBox.Style>
                                            </ComboBox>
                                        </DataTemplate>
                                    </DataGridTemplateColumn.CellTemplate>

...

And all is works fine here

Text is really bold when property set true and otherwise when false, but problem is here

When I open drop down list, so all items also bold... I need that only representation is bold, but dropdown list itself not.
How to make it?

A: I believe you need to set the ComboBox.ItemContainerStyle, so as part of the ComboBox definition:
<ComboBox.ItemContainerStyle>
  <Style TargetType="ComboBoxItem">
    <Setter Property="FontWeight" Value="Normal"/>
  </Style>
</ComboBox.ItemContainerStyle>

redpajama_set_name: RedPajamaStackExchange


text:
Léon (1994)
Posted on July 3, 2016 by badblokebob
He moves without sound.
Kills without emotion.
Disappears without trace.
Also Known As: The Professional (USA) *shudder*
Runtime: 110 minutes | 132 minutes (version intégrale)
BBFC: 18 | 15 (version intégrale)
MPAA: R
Original Release: 14th September 1994 (France)
US Release: 18th November 1994
UK Release: 3rd February 1995
First Seen: VHS, c.1999
Jean Reno (Les visiteurs, Ronin)
Natalie Portman (Star Wars – Episode I: The Phantom Menace, Black Swan)
Gary Oldman (Bram Stoker's Dracula, Tinker Tailor Soldier Spy)
Luc Besson (Nikita, The Fifth Element)
Luc Besson (The Transporter, Taken)
When her family are murdered by a corrupt police officer, 12-year-old Mathilda runs to hide with her quiet, reclusive neighbour, Léon. Turns out he's a hitman, and she begins to train with him so she can exact her revenge…
As the title character, Jean Reno's child-like hired killer is likeable, sympathetic, and quite sweet — traits one wouldn't typically associate with his profession. As his young ward, Mathilda, Natalie Portman is compelling, playing a hardened, emotionally bruised kid in desperate need of support and guidance, more so than she needs vengeance.
Gary Oldman brings pure entertainment value to the film in one of his most iconic performances: Stansfield, the crazy copper with a penchant for both drugs and quotable dialogue.
There's not much room for anyone else to stand out around the three lead performances, but Danny Aiello comes closest as Léon's kindly mafioso handler, Tony.
Stansfield: "Bring me everyone."
Benny: "What do you mean 'everyone'?"
Stansfield: "EV-RY-ONE."
As Mathilda returns home from buying groceries, she sees the door to her family's apartment open and a man standing suspiciously outside. As she nears, she catches a glimpse inside — her father sprawled on the floor in a pool of blood. She keeps walking, pretending not to have seen, and approaches Léon's door — where he's been watching through his peephole. Trying to hold back tears, she rings his bell. Behind the door, Léon fidgets, not answering — he doesn't want to get involved. She pleads under her breath. She rings again. The man at her door watches, suspicious. She rings again, desperate. Léon is torn… OK, you know all along what he's going to do, but Besson's direction and the performances from Portman and Reno ring every second of tension out of the sequence.
Letting the Side Down
Some people find the relationship between Léon and Mathilda problematic, and that gets in the way of their enjoyment of the movie. I've never seen it that way. Mathilda tries to inappropriately push herself on Léon, but he never takes her up on it. He's a child himself in many ways and that side of life doesn't seem to engage him at all, never mind in an unacceptable fashion.
The film's second shot (still in the credits) is a tracking shot that travels along a New York road without stopping. It was only possible after studying the pattern of the traffic lights along the route to make sure the camera truck didn't encounter any red lights.
The film was inspired by Jean Reno's role in Besson's previous film, Nikita (aka La Femme Nikita), in which he turns up in the third act as "Victor the Cleaner", dressed in an outfit similar to Léon's, to deal with Nikita's botched mission.
Besson wrote a script for a sequel focusing on a grown-up Mathilda. While they waited for Portman to age into the role, Besson left Gaumont to start his own studio, EuropaCorp. Unhappy at his departure, Gaumont have apparently refused to let him have the necessary rights. According to Olivier Megaton (the director of Besson projects like Transporter 3 and both Taken sequels) it will now likely never happen. Reportedly the script was recycled into Colombiana, which I am now 100% more interested in seeing.
7 César nominations (Film, Actor (Jean Reno), Director, Music, Cinematography, Editing, Sound)
"For Luc Besson, [Léon] is a poetic brute, a man without humanity who has lived so close to darkness for so long that he has lost all connection to the light. The universe around him, too, is a symbolic construction, an interweaving of opera, film noir and existentialism, where the larger-than-life forces of innocence and corruption explode in blood and violence. […] Reno plays it minimally; Oldman splatters his performance all over the screen. Oldman is the least inhibited actor of his generation, and as this deranged detective, he keeps absolutely nothing in reserve. When the camera gets close to him, you feel as if you want to back away. […] Stansfield's signature is his passion for music. He thinks of everything, even his blood orgies, in terms of rhythm and color. You want Beethoven? he asks, picking up a shotgun. I'll play you some Beethoven. Fortunately, Besson structures his film in much the same way. Not only does music play an important role in giving texture to his material, his scenes — especially the violent ones — are presented as arias, chamber pieces, symphonies." — Hal Hinson, The Washington Post
Worst Spurious Connection in a Supposedly Professional Review
"A favorite of IMDb fanboys (who have absurdly — but predictably — ranked it the 27th best movie of all time!) and reportedly of pedophiles as well" — Matt Brunson, Creative Loafing (You're right about one thing, though, Matt: 27th is ridiculous — Léon is top ten material.)
Counterpoint to Mr Brunson
"[It] would go on to become one of his most highly-regarded films among audiences. Sadly it was not thought of nearly as well by critics, merely receiving somewhat average reviews, giving us another sad oversight [and] proving that there are those times where the general audience can have more perception into a film than those that analyze them for a living." — Jeff Beck, examiner.com
"In spite of ranking on the top ten lists of many, many movie fans since its release, my love for [Léon] was not immediate. As a matter of fact I pretty much disliked it on the first and second outings because I couldn't quite grasp what Luc Besson was going for with this film. It's not an action movie, it's more of a love story set to the tone of bloodshed and corruption, a subtle poetic masterpiece that relies on characterization and artistic strokes of pure raw emotion than some shoot em up gangster flick. […] I've come to truly appreciate what a pure piece of brilliant filmmaking this is and the loose allusions this has toward another Besson masterpiece La Femme Nikita. Everything about this film from the performances right down to the set pieces are like pieces of moving art, and Besson is the artist with the brush. […] Besson's incomparable film is almost impossible to beat and there's yet to be a director who could match his magnum opus. Even after almost twenty years, [Léon] stands as the superlative masterpiece of action filmmaking and has yet to be matched or toppled by any director in the business." — Felix Vasquez, Cinema Crazed
IMDb Top 250 #27
Elsewhere on 100 Films…
I reviewed the extended "version intégrale" cut of the film in 2008, asserting that "I prefer this version. Not because there's anything wrong with the original — far from it — but because this one has more. […] I love the film and the characters, I could happily take more of them, and I very much enjoyed all of the added material. […] Léon (in either cut) is unquestionably essential."
Léon delivers the kind of tense sequences of action you'd imagine of a dramatic action-thriller (i.e. not highly-choreographed punch-ups every five minutes, but the action scenes that do appear are suspenseful), but the film's real joy lies in its characters, who are expertly performed and wonderful to spend time with (in a movie context — in real life, I wouldn't be so sure…) As a whole, Besson brews the grittily realistic with something far more fantastical to create a film that is, perhaps, a little too unique for some to get a handle on (I'm thinking of the handful of low-rated critics reviews on Rotten Tomatoes, which fly in the face of the consensus opinion). For the majority, however, Léon is a gripping, characterful, rewatchable masterpiece.
#52 just can't wait… to be king.
This entry was posted in "100 Films", 100 Favourites, 1990s, 5 stars, Crime, Drama, Thriller, world cinema and tagged Gary Oldman, Jean Reno, Léon, Leon: The Professional, Luc Besson, Natalie Portman, The Professional by badblokebob. Bookmark the permalink.
3 thoughts on "Léon (1994)"
vinnieh on July 18, 2016 at 10:55 am said:
I like how different this movie is, it doesn't really conform to the genres instead marching to the beat of it's own drum.
badblokebob on July 19, 2016 at 12:12 am said:
That's a really good way of putting it. There are genres it can be 'forced' into just because of what it's about, but it's actually not like anything else.
vinnieh on July 19, 2016 at 8:00 am said:
Gotta love a film that doesn't play by any expected rules and forges its own path.


text:
Q: Creating a SQL query that performs math with variables from multiple tables Here's an example of what I've attempted thus far:
A mockup of what the tables look like:
Inventory
ID  |  lowrange  |  highrange
-------------------------------
1   |  15        |  20
2   |  21        |  30

Audit (not used in this query asides from the join)
MissingOrVoid
ID  |  Item  |  Missing  |  Void
---------------------------------
1   |  17    |   1       |  0
1   |  19    |   1       |  0

The most recent query I've attempted to use:
SELECT    I.*,
          SUM(
              (I.HIGHRANGE - I.LOWRANGE + 1)
              - (Count(M.Missing) from M where M.ID = I.ID)
              - (Count(M.Void) from M where M.ID = I.ID)) AS Item_Quantity

FROM Inventory I
    JOIN Audit A
        ON A.ID = I.ID
    JOIN MissingOrVoid M
        ON M.ID = I.ID

The result should be:
ID  |  lowrange  |  highrange  |  Item_Quantity
-----------------------------------------------
1   |  15        |  20         |  4
2   |  21        |  30         |  10

I can't remember exactly where I've made changes, but in a previous attempt the error message received prior was "Cannot perform an aggregate function on an expression containing an aggregate or a subquery." Currently the error is incorrect syntax near "from" (the one beside M.Missing but in my minimal knowledge of SQL, it appears that these syntax issues cause an outright failure and there may be underlying issues with the query that aren't visible until all of the syntax problems are fixed).
The part where I'm really bombing on is obviously the SUM() section. I am far from a database architect so could someone explain how to correctly perform this and possibly point me in the direction of a resource to learn about this type of function?
Thanks

A: You almost had it right. I am guessing missing/void are BIT types, which you cannot SUM directly.
SELECT I.*,
    (I.HIGHRANGE - I.LOWRANGE + 1)
    - (select Count(nullif(M.Missing,0)) from MissingOrVoid M where M.ID = I.ID)
    - (select Count(nullif(M.Void,0)) from MissingOrVoid M where M.ID = I.ID)
    AS Item_Quantity
FROM Inventory I

If an item cannot both be missing and void, then
SELECT I.*,
       I.HIGHRANGE - I.LOWRANGE + 1
           - (select Count(case when M.Missing=1 or M.Void=1 then 1 end)
              from MissingOrVoid M where M.ID = I.ID)
           AS Item_Quantity
FROM Inventory I

In fact, if it is only present in MissingOrVoid when it is missing or void, then the CASE in the above query will always be true, so this simplifies to
SELECT I.*,
       I.HIGHRANGE - I.LOWRANGE + 1
           - (select Count(*) from MissingOrVoid M where M.ID = I.ID)
           AS Item_Quantity
FROM Inventory I

A: Initially I have a question as to whether you need to sum those values. If your inventory table has one row per item, that shouldn't be necessary. I'll assume that your table can have multiple rows for a given item, though, and proceed from there.
I think the issue is just a problem with the construction of the subquery. I haven't tested this, but I think it should look more like:
select I.ID,
    I.Item,
    SUM(I.HighRange - I.LowRange + 1)
    - (
        select SUM(M.Missing + M.Void)
        from dbo.Audit A
        where A.ID = I.ID
      )
from Inventory I
group by I.ID, I.Item

A: Is this what you're trying to do? I'm not sure what the numbers in the missing and void columns are unless they're just flags...
SELECT    I.*,
          ((I.highrange - I.lowrange + 1)
              - SUM(M.Missing)
              - SUM(M.Void)) AS Item_Quantity

FROM Inventory I
    JOIN MissingOrVoid M
        ON M.ID = I.ID

A: The following query works. This assumes there is only one highrange and lowrange for each id.
CREATE TABLE #Inventory (ID INT,Lowrange INT,highrange INT)
CREATE TABLE #MissingOrVoid (Id INT,item INT, missing INT, void INT)

INSERT #Inventory
        ( ID, Lowrange, highrange )
VALUES  ( 1, -- ID - int
          15, -- Lowrange - int
          20  -- highrange - int
          )
INSERT #Inventory
        ( ID, Lowrange, highrange )
VALUES  ( 2, -- ID - int
          21, -- Lowrange - int
          30  -- highrange - int
          )
INSERT #MissingOrVoid
        ( Id, item, missing, void )
VALUES  ( 1, -- Id - int
          17, -- item - int
          1, -- missing - int
          0  -- void - int
          )
INSERT #MissingOrVoid
        ( Id, item, missing, void )
VALUES  ( 1, -- Id - int
          19, -- item - int
          1, -- missing - int
          0  -- void - int
          )

SELECT #Inventory.ID,
       #Inventory.highrange,
       #Inventory.Lowrange,
       highrange-Lowrange+1
           -SUM(ISNULL(missing,0))
           -SUM(ISNULL(void,0)) AS ITEM_QUANTITY
FROM #Inventory
left JOIN  #MissingOrVoid ON #Inventory.ID = #MissingOrVoid.Id
GROUP BY #Inventory.ID,#Inventory.highrange,#Inventory.Lowrange

DROP TABLE #Inventory
DROP TABLE #MissingOrVoid

A: I'd say this would work :
SELECT  I.ID,I.Lowrange as Lowrange,
        I.highrange as Highrange,
        Highrange-Lowrange+1-COUNT(J.missing)-COUNT(J.void) AS ITEM_QUANTITY
FROM Inventory I
left JOIN  ( select missing as missing, void as void, id from MissingOrVoid
            ) J
    ON I.ID = J.Id
JOIN Audit A
    ON A.ID = I.ID
GROUP BY I.ID,Highrange,Lowrange

But it looks like what RemoteSojourner suggested a lot (and his one is also more esthetic).

A: I'm going to give the derived table approach as it could  be faster than a correlated subquery (which run row by row)
SELECT I.*,
I.HIGHRANGE - I.LOWRANGE + 1 -  MissingVoidCount AS Item_Quantity
FROM Inventory I
JOIN
    (SELECT ID,Count(*) AS MissingVoidCount FROM MissingOrVoid GROUP BY ID) M
        on M.ID = I.ID

Of course in real life, I would never use select *. You also could use a CTE approach.
    ;WITH  MissingVoid(ID, MissingVoidCount) AS
    (
        SELECT ID, Count(*)  FROM MissingOrVoid GROUP BY ID
    )
    SELECT
        I.*,
        I.HIGHRANGE - I.LOWRANGE + 1 -  MissingVoidCount AS Item_Quantity
    FROM Inventory I
    JOIN MissingVoid M
        on M.ID = I.ID


Sambucus ebulus subsp. africanus (Engl.) Bolli, Revis. Genus Sambucus (Diss. Bot., 223): 144. 1994.
Sambucus ebulus var. africanus Engl., Ann. Bot. (Oxford) 18(72): 537. 1904.
Sambucus africana Standl., Smithsonian Misc. Collect. 68(5): 19. 1917.
Sambucus adnata var. puberula Schwer.
African Flowering Plants Database. Conservatoire et Jardin botaniques de la Villle de Genève and South African National Biodiversity Institute, Pretoria. 2009 Jul 10. .


A wonderful message board post about the Lougheed Family. Very good story all round. Lin is an author and teacher. Wish I hadn't lost the author's information.
"The Irish word for lake is Lough. The name was originally Scottish. The clan was originally Macdonald, some of them moved to the head of the Lake and they were known as the Locheed Macdonalds. Loch being the Scots spelling of Lake. When part of the Clan was transplanted to Ireland the Irish spelling of Lake was used making it Lougheed. The transition from Scotland was in 1688 following the Battle of the Boyne from which King William the III (King William of Orange) emerged victorious and cemented his position by transplanting English but chiefly Scots to Ireland, we being among those transplanted. That is also why Orange day is celebrated and why so many Lougheeds are Williams.
from a Lougheed in Australia.
and they were known as the Locheed Macdonalds.
celebrated and why so many Lougheeds are Williams.
their non-business name is Lougheed.
give the date as 1800".
born in Ballymote not far from Sligo.
receive. I have written to A. Lougheed.


Oil and fuel absorbents - what are they and why do we use them?
We talk about oil and fuel absorbents all the time – how amazing they are and the difference they make to cleaning up spills.
But why? What's so great about them and what's this magic behind why they work the way they do?
Oil and fuel absorbents are unique – they have been designed to absorb only a select range of liquids, namely anything that's hydrocarbon based.
This is important, as hydrocarbons (think oil, fuel, diesel, oil-based paints etc) are extremely harmful to the environment, and some are dangerous due to their highly flammable nature.
Often when hydrocarbons are spilled, water or other liquids are present. This is not ideal when you're cleaning up a spill in the rain or if the oil has spilled into a sump or waterway. You really need to be capturing the damaging hydrocarbons instead of any water that's present.
Oil and fuel absorbents have been designed to repel water, eliminating the aforementioned problem. They are known as hydrophobic…i.e. they hate water. The fibres of poly oil and fuel absorbents are woven in such a way that they will easily capture any hydrocarbons, but won't allow any water in. Very, very clever.
Poly oil and fuel absorbents have been developed in a variety of different form factors to suit different applications. Pads are the most popular – these are single-use squares of absorbent material which are available in either standard or heavy duty thickness. They are similar to a cloth, however more rigid so as to be able to hold up to 20 times their own weight in liquid. This material is also available on a large roll which can then be cut off to size depending on how it's to be used or as a mat, which is pre-cut but quite a bit larger than just a pad.
These poly oil and fuel absorbents are also made into booms (think of a draught excluder/stopper that you use against a door) which are excellent to contain a spill which is creeping, or into pillows which are your number one tool to absorb any pooled liquids.
Larger, brightly coloured oil and fuel absorbent marine booms are also available, to help out with larger spills on inland water (ponds, sumps, lakes, rivers, creeks etc) but they're a whole other topic best kept for another day.
Peat is also an outstandingly clever oil and fuel absorbent floorsweep which is used alongside poly absorbents. Naturally derived, it's a highly absorbent and bio-active solution for hydrocarbon spills in wet areas. But again, that's a fascinating topic for another day!
So there you have it folks, hopefully we've shed some light on why we think oil and fuel absorbents are amazing and that you now understand why they might fit in to your workplace.


Welcome to our Puppies page! Here you can see pictures of all the dogs that the Contra Costa East Guide Dog Raisers have raised, or are currently raising.
Some pictures may appear to be stretched out, just click on the small version to see a larger full size picture of that dog. Every dogs picture can be made full size just by clicking on it.
Some dogs have an individual page with extra pictures or information regarding that dog. These are denoted by the dogs name being bold.
We hope you enjoy looking at our puppies!
All of these puppies are currently in training with their volunteer puppy raisers.
These are dogs that have finished their puppy training with their puppy raisers. They are now in formal guidework training at the GDB campus with the licensed instructors.
These are dogs that have successfully completed their formal training with the licensed instructors and have graduated from the GDB campus. They are now working guide dogs with their blind or visually impaired partner.
"Only those dogs who have met the highest physical and temperamental standards are considered for the Guide Dogs breeding program by a team of training, veterinary and breeding experts." - Guide Dogs for the Blind, Inc.
These are dogs that have not successfully passed either their training with the puppy raiser or their formal training in guidework at the GDB campus. Common reasons for a dog to be career changed include medical (conditions such as skin allergies or chronic ear infections) and behavioral (such as inability to stay focused on guidework or excessive ground sniffing). Many of the career changed dogs are successful in other types of service work. GDB has partnered with the San Francisco SPCA Hearing Dog Program and the California Highway Patrol. Many GDB career changed dogs have successfully graduated as a dog for a person with a hearing impairment or as a narcotic or bomb detection dog with the CHP. Those career changed dogs who have not graduated as another type of service dog become loving pets adopted out to the general public. Many of them become pet therapy dogs. We are extremely proud of all of our dogs and their chosen careers.


Marigold 'Himalayan Stone Cottages' are a unique and specialized exhibit of 'Shimla Architecture'. It is recall of the localized stone techniques, which have developed over past centuries, to counter the natural cold elements of the hills.
The cottages at 'Holiday Cottages' are designed for the needs of today's modern traveler. Each one is spacious, luxurious, and comfortable – and is built to provide you and your family with an experience you will long cherish. The adventurous trekking, water rafting & picnic spots around Shimla including the Manali kinnaur backpack trek are worth unearthing. Besides, the elegant conference facility enables official meetings at our venue.


text:
Australia's Beston to manufacture plant-based products for Soulfresh Group
Australia-based Beston Global Food Co. (BFC) has signed a manufacturing contract with a local plant-based food business.
By Leonie Barrie
Australia-based Beston Global Food Co. (BFC) has signed a manufacturing contract with local plant-based food business Soulfresh Group.
The Eaty and Wildly Good-branded products it will make have already won listings with major supermarket groups in the country including Coles and, most recently, Woolworths.
Beston, also a dairy and meat business, said annualised production forecasts for the products amount to AUD6m (US$4.1m).
Financial details of the manufacturing contract have not been disclosed.
Beston will produce the plant-based meat alternative and vegetarian products for Victoria-based Soulfresh through its Provincial Food Group (PFG) arm.
Beston CEO Jonathan Hicks said: "The partnership between BFC and Soulfresh came about as a result of Soulfresh recognising the breadth of our capabilities and cutting-edge food technology which has been developed at PFG since BFC took 100% control of this business in August 2018.
"With Australia projected to continue as the third-fastest-growing vegan market in the world, both companies have an aligned vision."
He added: "Combining the synergies of vision, purpose, agility and innovation, at Soulfresh with the production capabilities of BFC has produced a winning partnership for the supply of alternative meat products into a rapidly growing food category."
Soulfresh CEO Didi Lo, an entrepreneur and former chef who founded his business 15 years ago, said: "The Eaty range of vegan recipes have the same amount of protein as meat equivalents, which will no doubt be very appealing to the large number of Australians, not only vegans and vegetarians but also people who opt to go meat-free at least one day a week.
"Both BFC and Soulfresh are taking their beliefs and purpose forward to create a better future for all, not just a few."
Triad Magnetics
Transformers, Inductors and Power Supplies for Food Processing Equipment
DIOSNA
Dough Mixing and Kneading Machines
Topics in this article: Allergen-free, Beston Global Food Co.
Leonie Barrie


text:
Celtic Nations Magazine > Recent Posts > Celtic Nations Magazine Blogs > Celtic Nations Magazine Author Blogs > Arian Niwl > May Day Celebration in Wales
May Day Celebration in Wales
In Wales the celebration of May Day derived from traditions that most people are familiar with as Beltane on the other side of the Irish Sea, but has roots in its own Celtic culture stretching back into olden times. In Wales this is the celebration of Calan Mai or sometimes called Calan Haf. Calan means the first of something like the beginning of a year or a month. Mai is Welsh for May and Haf means summer. These customs and celebrations as mentioned stretch back before the establishment of the Christian church in Wales and though frowned upon for centuries like Fairy Faith, the Church could not stamp them out and eventually just allowed them to go on. In Wales and the rest of Insular Celtic culture the year was approximately divided into half. That being summer and then on the opposite end Calan Gaeaf or the first of winter occurring on approximately November 1st.
Broadly, the celebration as with Beltane is a celebration of fertility and new growth and a time when the herds of cattle and the flocks of sheep would be turned out into fields now greening from the sleep of winter.
In Celtic times, bonfires would be lit and the herds and flocks driven between them for purification. People would leap the bonfires for the same reason and couples would hand in hand leap the fires to show their faith in each other. If there was disease in the herd or the flocks a calf or lamb would be thrown to the flames to ward off disease spreading to the rest of the herd or flock.
Now specifically in Wales the night before called Nos Galan or May Day's Eve was a very important event. It was considered one of the great three ysbrydnos or spirit nights of the year. It was thought that on these special nights that the veil between this world and the Otherworld was very thin. Spirits and especially the Y Tylwyth Teg (literally the Fair Family) or the fairies would be about and the later especially would in rades (procession) move from their winter spots to their summer spots. People would then put Draenen Wen (White Thorn) what is known as Hawthorn or Hawthorn flowers in front of their homes to ward off the fairies or show that they meant friendship with the fairies and not be cursed with ill fortune for the herds, flocks and harvest. It was considered to be extremely bad luck to bring a Hawthorn into the house especially on this day as Hawthorn is sacred to the fairies and bringing in anything of Hawthorn was considered to be stealing from them.
The fairies though were known to steal cattle, sheep, spoil the milk and blight the harvest if upset. Thus, the driving of the cattle and flocks through the smoke was to ward off the fairies and in some cases the flocks and cattle were sprinkled with salt which was thought to help ward the fairies off.
Some traditions the lighting of the May bonfires would be done by nine men who would turn their pockets inside out and make sure there was no metal of any kind on them and then go to the woods to gather the wood. Again, this speaks back to Fairy Faith, as it was thought that turning one's pockets out, or wearing one's clothing inside out confused the fairies. Ensuring there was no metal ensured that there was no iron. The former would help hide the men and the later would hurt the fairies and going into the woods to take wood was going into their territory and stealing or hurting them would invite their curse and wrath bringing about sickness and failed harvest.
On the morning of Calan Mai, young men usually would then go about singing songs and going from house to house asking for favours and giving blessings and usually with a verse dedicated to the family of each house visited. These were called the Carolau Mai (May Carrols), Carolau Haf (Summer Carrols) or just Canu Haf (Summer Singing). In northern part of the Wales these songs would be carried out by twenty young men dressed all in white with ribbons attached to them. Except for two of the young men. One would be dressed garishly and would be the Fool. His job was to be the orator, the buffoon making jokes and bringing merriment to the households visited. The other was the Caid. Now the Cadi'r Haf (Caddy of Summer) would dress in a man's surcoat and a woman's petticoat, to represent that this was a transitional time of year. The Cadi would carry (but sometimes the Fool) the Cangen Haf (Summer Branch) usually of birch and decorated with silver watches, spoons and vessels that were donated by the village.
An example of a poem or carol from the 12th century goes:
The beginning of summer, fairest season;
Noisy are the birds, green the woods,
The ploughs are in the furrow, the ox at work,
Green the sea, the lands are many-coloured.
When the cuckoos sing in the tops of the fair trees
My despondency becomes greater;
The smoke is smarting, it is plain I cannot sleep.
Since my friends have passed away,
In hill, in vale, in islands of the sea,
In every way one goes,
There is no seclusion from the blessed Christ.
An echo from older times that is found in the Red Book of Hergest and collected in the Mabinogion is the fight between Gwyn ap Nudd who is a king of the Otherworld or the realm of the fairies and a member of one of King Arthur's retinue Gwythyr fad Greidawl over a woman.
The rivalry was so intense that King Arthur made peace by decreeing that the two would meet every first day of May and fight for the hand of the woman until judgement day. A custom then mostly in the north of Wales would be the gware gwr gwylt (playing straw man) or sometimes called the crogi gwr gwellt (hanging straw man). A man that had lost his sweetheart to another man would make a man out of straw and put it someplace near where the girl lived. The straw man represented the new sweetheart and usually had a note pinned to it with the name of the rival and that one's not so desirable qualities. This led to fights between the two at the May Fair in many cases. I some places two men would have a mock fight in which one would then use a shield decorated with sheep's wool representing winter and the other with a shield decorated with greenery representing summer to show that summer was overcoming winter.
It was also on May Day that the custom of the Twmpath Chwarae or the village green was officially opened so that dances and sports in the evening could now take place including the Dawnsio Haf (Summer Dancing) which was usually quite lively.
So put out a bit of butter, or cream or honey for the fairies to show friendship on eve before May Day and sing lively on the morning. Summer has just begun!
Arian Niwl
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An Afghan woman's triumphant journey!
By all accounts and appearances, Saweeta Durrani, a microfinance client of First Microfinance Bank Afghanistan (FMFB-A), has become a highly successful, young businesswoman, privileged to enjoy the best of both worlds.
Professionally, the 26-year old Economics graduate from Herat University leveraged her academic achievement to turn her passion for jewelry design into a thriving business. Personally, she fulfills her role as wife to her husband; mother to her 10-year old son and five-year old daughter; and caretaker of her extended family.
Saweeta has come a long way since she started her business four years ago, with only AFN50, 000 (nearly $1,000). Today, Saweeta owns and runs her jewelry manufacturing company specializing in gemstones and now has three stores across Herat province. Her firm is also a supplier to jewelry chains in other major cities in the country, including Kabul.
Saweeta's current capital is AFN 400,000 (about US$ 8,000) and her monthly net income exceeds AFN 50,000 (approximately US$1,000). She employs 12 women and has trained many others. She is also able to send her two children to good schools, with her son attending a private school.
Her success would not have been possible without the loan from FMFB-A, which accepted her application backed by two women guarantors, based on her track record and business expansion plan. She used the loan to purchase her own polishing machines for gemstones, which significantly enhanced her production capacity and the quality of gemstones her company sells in the market, while reducing her overhead costs.
Before acquiring such machines, Saweeta, like many others in the same business, had to purchase Afghan gemstones at marked up prices because they were shipped to either India or Pakistan for polishing. As a result, the final product costs higher, which impacts sale and profit. By investing in her own machines, Saweeta was able to maximize her profit without passing own additional costs to potential clients.
Her struggle to access credit as a woman is also experienced by a majority of Afghans, men and women across the country, who are unbanked and do not have the credentials to access financial services from formal institutions.
This is what the MISFA is trying to address by promoting financial inclusion by on-lending funds and technical supports to microfinance institutions, including Saweeta's lender FMFB-A.


Their numbers increased and in September 1948, the group officially formed the reform Coral Gables Jewish Center. Soon thereafter, in 1950, a full-time rabbi and cantor were hired, followed by construction of a temple in the commercial business district of downtown Coral Gables near Miracle Mile.
In 1956, the Coral Gables Jewish Center changed its name to Temple Judea.


April 2011 ROTM Nomination Thread!
How does the weather go from a high of 50F with rain... to 80F/sunny.... back to 50F/rain in 1 day?
I suppose I should be happy it's not snowing like last week, but still. lol.
And for all of you with good riding weather all year round... I still don't want to hear about it.
Anyway.... lets get to some nominations.
The 5 nominated bikes will then be voted on by the masses later in April.
also agnyte, i think shes hot, the bike i mean.
Last edited by scorpionvmu; 04-04-2011 at 09:59 PM.
Those pics our quite outdated (looks even better now), I will get some updated pics up when the rain clears out of here.
Last edited by kazspeed; 04-05-2011 at 07:32 AM.
Last edited by __Z__; 04-05-2011 at 08:16 AM.
Quick Reply: April 2011 ROTM Nomination Thread!


Massachusetts Car Insurance You are required to have car insurance in Massachusetts in order to drive legally. You must apply for car insurance from one of the state's approved auto insurers as well.
Because Massachusetts requires this minimum insurance coverage and expects people driving in Boston and around the state to have auto insurance, the state only allows personal injury car accident lawsuits for injuries costing over $2,000 per person, unless the injured party sustained a fracture or damage to their hearing or sight.
This coverage reimburses you for loss due to theft or damage caused by something other than a collision with another car or object. Comprehensive covers events such as fire, falling objects, missiles, explosion, earthquake, windstorm, hail, flood, vandalism, riot, or.
In the state of Massachusetts, automobiles need to be registered in order to be legally driven on the state's roads and highways and buying minimum insurance coverage is.
Massachusetts mandatory minimum coverage for uninsured motorist bodily injury is $20,000 per individual and $40,000 per accident. Did you know? If car insurance has got you down, consider buying a horse and carriage in Amesbury, Massachusetts, the carriage capital of the world.
Auto insurance is required by law in Massachusetts. Unfortunately, with many insurance providers one little ding, speeding ticket, fender bender or forgotten payment can get you a canceled policy. At A-Affordable Insurance Agency, Inc. we believe there's got to.
MA Auto Insurance Agent Serving Newton, Needham, Wellesley and all of Massachusetts This guide, taken from the Division of Insurance, Consumer Service Department of the Commonwealth of Massachusetts, explains the specialized terminology you'll find in each part of your Massachusetts Auto Insurance policy.
A minimum limit of $5,000 is required for Massachusetts Auto Insurance. With the rising costs of autos and property repair, it makes sense to purchase more than the compulsary $5,000 minimum auto insurance.
Drivers must carry several types of Massachusetts car insurance in order to comply with state law. You can read more about the kind of policy you need in the section below. If you are a resident and in the market for a new policy, this is the place to do your shopping.


held officially during the 68th UN General Assembly.
Innovation and cutting-edge technologies are helping global governments and corporations as they strive for growth, increasing exponentially the creation of new industries and jobs. This interactive discussion will address those innovative industries, investments, policies, consumer demand, up and coming regions, and new game-changing technologies that can transform industries and ignite growth for the world's economies.
Produced with IEA Global Partner CEA. The Consumer Electronics Association (CEA®) is the world's most renowned consumer electronics trade association representing over 2,000 companies. CEA is the producer of the the International CES® - The Global Stage for Innovation.
of the World's Most Successful Businesses.
"GLOBAL IMPACT OF THE SHALE REVOLUTION"
CEO of Halcón Resources. Mr. Wilson grew his last company, Petrohawk Energy, from $60m investment to sale for $15.1 Billion in 7 years.
Dr. Joseph Stanislaw, Independent Senior Advisor for Energy and Sustainability at Deloitte; Co-founder of Cambridge Energy Research Associates (CERA).
Berggruen Holdings, a global investor across a range of companies and continents.
"AMERICA, WHERE DO WE STAND?"
In the lingering wake of the financial crisis and with global economic powers in flux, a question materializes for the world's most powerful nation, "America, Where Do We Stand?" An insiders view and potential answers are offered by Senator Phil Gramm, Senior Partner US Policy Metrics, former Vice Chairman of UBS, and former US Senator from Texas and Chairman of the Senate Banking Committee.
"INNOVATION IN EDUCATION, FOUNDATIONS OF GROWTH"
An educated workforce is critical to growth in all regions. What are the implications of the recent revolution in online education technology for improving outcomes in education, job training, and national economic competitiveness? Steven Kennedy Smith outlines the future of education both nationally and abroad.
the Kennedy family investment office; Serving Member of Kennedy family financial board.
Additional IEA Country Members available for Private Meetings at GIS 2013, September 25th.
Russia has designated their Ambassador to the US to be the non-presenting country delegate who is available for private meetings concerning investment opportunities in Russia.
King Abdullah II of Jordan has designated Deputy Chief of Mission and Economic Advisor to be the non-presenting country delegate who is available for private meetings concerning investment opportunities in Jordan.
*This luncheon is in addition to the September 25th Global Investment Symposium—all registered GIS attendees are welcome to attend this separate event dedicated to investment in Vietnam with complementary seating.
"According to a forecast by PricewaterhouseCoopers, Vietnam may be the fastest growing of emerging economies by 2025. Vietnam's export continues to grow at a high level while import of machines, equipment, and materials improves production at a rapid pace."
11:30 - 11:40 IEA and co-hosts Welcome Speech, Description of the Meeting Format.
12:05 - 12:45 Interactive Lunch Discussions with CEOs, Ministers and other executives.
12:45 - 1:15 Prime Minister's Interactive Q&A and Concluding Remarks.
1:15 - 1:20 IEA and co-hosts Closing Remarks.
IEA Country Members include countries from all regions of the world: Americas, Europe, Asia, Africa and Middle East. The following country Heads of State, Ministers, economic officials or Ambassadors participate in IEA by leading Country Presentations or private meetings. Ambassadors are also part of the IEA Ambassador Alliance. Throughout the year, IEA holds interactive Symposia, TelePresence events and the annual Global Investment Symposium at the Harvard Club during the UN General Assembly.


Tavolàta's ever-popular whole pig Sunday Feast is back! Join chef Brandon Kirksey for dinner on June 3 as he roasts up a couple of pigs and makes some great Italian inspired dishes for guests to enjoy.
Dinner will be served family style at the communal table (tavolàta) where seating is limited to 26 guests. Dinner begins at 6pm and cost is $75 per person.


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Crowdfunding USA Forum Conference - Reg A+ a True Game Changer
CrowdfundBeat was kind enough to invite CrowdDD.com founder Mark Robertson to it's Crowdfunding USA Forum Conference last month at the National Press Club. It was a very exciting conference and we were able to join a panel discussion about the issues facing the real estate crowdfunding industry. The biggest buzz at the conference was the effect on the crowdfunding industry from new Security Exchange Commission (SEC) RegA+ rules.
They are a game changer for raising capital and Crowdfunding USA had a panel devoted to this topic. The moderator was Jonathan Frutkin who is an attorney from Phoenix, Arizona active in the crowdfunding space since 2012. The esteemed guests included Samuel Guzik, Mark Roderick, Stevens Sadler, and Craig Denlinger.
Sam Guzik is a well-known securities attorney from Los Angeles. Mark Roderick is a securities attorney from the firm of Flaster Greenberg in New Jersey. Stevens Sadler is from Allegiancy in Richmond, Virginia. Craig Denlinger is a CPA who used to work for Deloitte, who has now opened his own firm to specialize in providing accounting and auditing services that are necessary for companies wishing to file a registration for a Regulation A+ offering.
Here is what the panel members had to say:
Sam Guzik - Regulation A+ requires filing a registration statement for the securities with the SEC. The offering will receive SEC review and comments, which need answering before approval. The benefit is when the offering completes the SEC process; the company can sell free-trading securities. There are no 144 restrictions on the sale of shares. A company bypasses all of the previous holding period for shares under 144 restrictions and the restriction only to take investments from accredited investors, Under Regulation A+, a company starts raising money as an initial public offering (IPO) immediately. The shares trade publicly without any restrictions as long as a secondary market exists or can be created. The ability to buy and sell shares provides liquidity. Both accredited and non-accredited investors can participate. Once the SEC approves the offering, companies are free to advertise their investment offering any way they want. Regulation A+ only requires a federal review and does not require state review in any state that the securities are sold. This makes the filing of a Regulation A+ offering less expensive.
Mark Roderick - He points out to achieve the pre-emption from filing the offering with the states, the Regulation A+ offering must be a Tier 2 A+ offering under the new law, which goes into place June 19, 2015. Tier 1 is the old regulation A with increased capital raising limits from $5 million to $20 million. Tier 2 is the new Regulations A+ that is the paradigm shift, which has a higher limit of raising $50 million per 12 months. Audited financial statements are required. Non-accredited investors can only invest 10% of annual income or net worth, whichever is higher.
Stevens Sadler - Steve manages real estate portfolios and did a $5 million Regulation "A" offering for accredited investors last year. He now plans to do a $30 to $50 million regulation "A+" filing during June 2015, with SEC approval expected in Fall 2015. He is most excited about the preemption of state approval, which in the past has been problematic.
Craig Denlinger - Craig provides audit services, even for raw start-ups. Investors want this as well, because it provides credibility.
Regulation A+ has challenges in getting SEC approval, but has advantages in that a Regulation A+ creates a public offering of stocks that are tradable and can be advertised to seek investment from anyone. Investors want to have information so the best Regulation A+ offerings are the ones that give investors audited information to increase investor confidence. You can discover, rate, and review crowdfunding investments at CrowdDD.com.
elisa grace
Jun 28,[email protected];18 AM
It have also heard from my friend about this discussion. Since the SEC has approved title III in 2012 relating to Jobs Act, dramatically changes have seen in the way to raise capital for new ventures making it possible for companies to raise up to $1 million annually through equity crowdfunding without having to cut through the red tape of registering those securities with the Securities and Exchange Commission. http://crowdfund.co/real-estate/


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Star Wars Jedi: Fallen Order Optimized for PS5 with Today's Update
Star Wars Jedi: Fallen Order received a new title update today, January 12. Those who are playing the game on PlayStation 4 may be disappointed to find there's no difference to the game for them; the patch's sole purpose was to optimize the game's performance on PS5.
The patch has improved the game's framerate, dynamic resolution range, and post-processing resolution. These are the PlayStation 5 specific patch notes:
Star Wars Jedi: Fallen Order PS5 Update
Framerate has been increased to 60 FPS (up from 45 FPS)
Postprocessing increased to 1440p
Dynamic resolution has been disabled and the game is rendering at 1200p (up from 810-1080p)
Importantly, this is an update to optimize the PS4 version of the game when played via backwards compatibility on the PS5. It is not a native PS5 application.
This is the game's first patch since it was included under the Lucasfilm Games banner, the brand that now represents all Star Wars games. Publisher EA currently holds the video game exclusivity license for the Star Wars brand until 2023, at which point many people expect Disney to begin allowing other developers and publishers to produce games in the franchise.
The Lucasfilm Games brand promises to keep an "eye toward the future", one that will include Jedi: Fallen Order as part of a new franchise as confirmed by EA. Rumors have already been circling that a sequel to the game is in development, and this will largely be due to the first game's success.
Jedi: Fallen Order had sold more than 8 million units this time last year, so that figure will likely have grown since then. Indeed, the publisher had hoped the game would reach 10 million units by March 2020, although they never confirmed whether they hit that target. What we do know is it had registered 10 million unique players across all platforms by the end of fiscal year 2020. That figure will only have increased seeing as the game was introduced to EA Play on PlayStation 4 on November 10. Overall, the title has well and truly managed to exceed EA's expectations.
[Source: EA]
This article was originally published by Playstationlifestyle.net. Read the original article here.
Scott Pilgrim vs. The World: The Game – Complete Edition Arrives on Xbox One and Xbox Series X|S
Scott Pilgrim Vs The World: The Game kicks off its comeback tour
Random: Breath Of The Wild Players Are Trying To Speedrun Bread
Toppo coming to Dragon Ball Xenoverse 2 in its spring update
Super Mario 3D World + Bowser's Fury: Bowsers Fury can be selected from title screen and played anytime


This is one of my favorite pieces. It's simple but cute! Listing includes 2 circle pieces with necklace. You may add additional circles as well as charms, and Swarovski birthstones.
If you need additional circle disks they are available for an extra cost.
It's all made of stainless steel. Will not tarnish nor change color.
-Only the fonts that are provided under the drop down box are available for this specific piece.