text:
\section{Submission of conference papers to ICLR 2020}

ICLR requires electronic submissions, processed by
\url{https://openreview.net/}. See ICLR's website for more instructions.

If your paper is ultimately accepted, the statement {\tt
  {\textbackslash}iclrfinalcopy} should be inserted to adjust the
format to the camera ready requirements.

The format for the submissions is a variant of the NIPS format.
Please read carefully the instructions below, and follow them
faithfully.

\subsection{Style}

Papers to be submitted to ICLR 2020 must be prepared according to the
instructions presented here.

Authors are required to use the ICLR \LaTeX{} style files obtainable at the
ICLR website. Please make sure you use the current files and
not previous versions. Tweaking the style files may be grounds for rejection.

\subsection{Retrieval of style files}

The style files for ICLR and other conference information are available online at:
\begin{center}
   \url{http://www.iclr.cc/}
\end{center}
The file \verb+iclr2020_conference.pdf+ contains these
instructions and illustrates the
various formatting requirements your ICLR paper must satisfy.
Submissions must be made using \LaTeX{} and the style files
\verb+iclr2020_conference.sty+ and \verb+iclr2020_conference.bst+ (to be used with \LaTeX{}2e). The file
\verb+iclr2020_conference.tex+ may be used as a ``shell'' for writing your paper. All you
have to do is replace the author, title, abstract, and text of the paper with
your own.

The formatting instructions contained in these style files are summarized in
sections \ref{gen_inst}, \ref{headings}, and \ref{others} below.

\section{General formatting instructions}
\label{gen_inst}

The text must be confined within a rectangle 5.5~inches (33~picas) wide and
9~inches (54~picas) long. The left margin is 1.5~inch (9~picas).
Use 10~point type with a vertical spacing of 11~points. Times New Roman is the
preferred typeface throughout. Paragraphs are separated by 1/2~line space,
with no indentation.

Paper title is 17~point, in small caps and left-aligned.
All pages should start at 1~inch (6~picas) from the top of the page.

Authors' names are
set in boldface, and each name is placed above its corresponding
address. The lead author's name is to be listed first, and
the co-authors' names are set to follow. Authors sharing the
same address can be on the same line.

Please pay special attention to the instructions in section \ref{others}
regarding figures, tables, acknowledgments, and references.

The recommended paper length is 8 pages, with unlimited additional pages for
citations.  There will be a strict upper limit of 10 pages for the main text.
Reviewers will be instructed to apply a higher standard to papers in excess of 8
pages.  Authors may use as many pages of appendices (after the bibliography) as
they wish, but reviewers are not required to read these.

\section{Headings: first level}
\label{headings}

First level headings are in small caps,
flush left and in point size 12. One line space before the first level
heading and 1/2~line space after the first level heading.

\subsection{Headings: second level}

Second level headings are in small caps,
flush left and in point size 10. One line space before the second level
heading and 1/2~line space after the second level heading.

\subsubsection{Headings: third level}

Third level headings are in small caps,
flush left and in point size 10. One line space before the third level
heading and 1/2~line space after the third level heading.

\section{Citations, figures, tables, references}
\label{others}

These instructions apply to everyone, regardless of the formatter being used.

\subsection{Citations within the text}

Citations within the text should be based on the \texttt{natbib} package
and include the authors' last names and year (with the ``et~al.'' construct
for more than two authors). When the authors or the publication are
included in the sentence, the citation should not be in parenthesis using \verb|\citet{}| (as
in ``See \citet{Hinton06} for more information.''). Otherwise, the citation
should be in parenthesis using \verb|\citep{}| (as in ``Deep learning shows promise to make progress
towards AI~\citep{Bengio+chapter2007}.'').

The corresponding references are to be listed in alphabetical order of
authors, in the \textsc{References} section. As to the format of the
references themselves, any style is acceptable as long as it is used
consistently.

\subsection{Footnotes}

Indicate footnotes with a number\footnote{Sample of the first footnote} in the
text. Place the footnotes at the bottom of the page on which they appear.
Precede the footnote with a horizontal rule of 2~inches
(12~picas).\footnote{Sample of the second footnote}

\subsection{Figures}

All artwork must be neat, clean, and legible. Lines should be dark
enough for purposes of reproduction; art work should not be
hand-drawn. The figure number and caption always appear after the
figure. Place one line space before the figure caption, and one line
space after the figure. The figure caption is lower case (except for
first word and proper nouns); figures are numbered consecutively.

Make sure the figure caption does not get separated from the figure.
Leave sufficient space to avoid splitting the figure and figure caption.

You may use color figures.
However, it is best for the
figure captions and the paper body to make sense if the paper is printed
either in black/white or in color.
\begin{figure}[h]
\begin{center}
\fbox{\rule[-.5cm]{0cm}{4cm} \rule[-.5cm]{4cm}{0cm}}
\end{center}
\caption{Sample figure caption.}
\end{figure}

\subsection{Tables}

All tables must be centered, neat, clean and legible. Do not use hand-drawn
tables. The table number and title always appear before the table. See
Table~\ref{sample-table}.

Place one line space before the table title, one line space after the table
title, and one line space after the table. The table title must be lower case
(except for first word and proper nouns); tables are numbered consecutively.

\begin{table}[t]
\caption{Sample table title}
\label{sample-table}
\begin{center}
\begin{tabular}{ll}
\multicolumn{1}{c}{\bf PART}  &\multicolumn{1}{c}{\bf DESCRIPTION}
\\ \hline \\
Dendrite         &Input terminal \\
Axon             &Output terminal \\
Soma             &Cell body (contains cell nucleus) \\
\end{tabular}
\end{center}
\end{table}

\section{Default Notation}

In an attempt to encourage standardized notation, we have included the
notation file from the textbook, \textit{Deep Learning}
\cite{goodfellow2016deep} available at
\url{https://github.com/goodfeli/dlbook_notation/}.  Use of this style
is not required and can be disabled by commenting out
\texttt{math\_commands.tex}.

\centerline{\bf Numbers and Arrays}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1in}p{3.25in}}
$\displaystyle a$ & A scalar (integer or real)\\
$\displaystyle \va$ & A vector\\
$\displaystyle \mA$ & A matrix\\
$\displaystyle \tA$ & A tensor\\
$\displaystyle \mI_n$ & Identity matrix with $n$ rows and $n$ columns\\
$\displaystyle \mI$ & Identity matrix with dimensionality implied by context\\
$\displaystyle \ve^{(i)}$ & Standard basis vector $[0,\dots,0,1,0,\dots,0]$ with a 1 at position $i$\\
$\displaystyle \text{diag}(\va)$ & A square, diagonal matrix with diagonal entries given by $\va$\\
$\displaystyle \ra$ & A scalar random variable\\
$\displaystyle \rva$ & A vector-valued random variable\\
$\displaystyle \rmA$ & A matrix-valued random variable\\
\end{tabular}
\egroup
\vspace{0.25cm}

\centerline{\bf Sets and Graphs}
\bgroup
\def1.5{1.5}

\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle \sA$ & A set\\
$\displaystyle \R$ & The set of real numbers \\
$\displaystyle \{0, 1\}$ & The set containing 0 and 1 \\
$\displaystyle \{0, 1, \dots, n \}$ & The set of all integers between $0$ and $n$\\
$\displaystyle [a, b]$ & The real interval including $a$ and $b$\\
$\displaystyle (a, b]$ & The real interval excluding $a$ but including $b$\\
$\displaystyle \sA \backslash \sB$ & Set subtraction, i.e., the set containing the elements of $\sA$ that are not in $\sB$\\
$\displaystyle \gG$ & A graph\\
$\displaystyle \parents_\gG(\ervx_i)$ & The parents of $\ervx_i$ in $\gG$
\end{tabular}
\vspace{0.25cm}

\centerline{\bf Indexing}
\bgroup
\def1.5{1.5}

\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle \eva_i$ & Element $i$ of vector $\va$, with indexing starting at 1 \\
$\displaystyle \eva_{-i}$ & All elements of vector $\va$ except for element $i$ \\
$\displaystyle \emA_{i,j}$ & Element $i, j$ of matrix $\mA$ \\
$\displaystyle \mA_{i, :}$ & Row $i$ of matrix $\mA$ \\
$\displaystyle \mA_{:, i}$ & Column $i$ of matrix $\mA$ \\
$\displaystyle \etA_{i, j, k}$ & Element $(i, j, k)$ of a 3-D tensor $\tA$\\
$\displaystyle \tA_{:, :, i}$ & 2-D slice of a 3-D tensor\\
$\displaystyle \erva_i$ & Element $i$ of the random vector $\rva$ \\
\end{tabular}
\egroup
\vspace{0.25cm}

\centerline{\bf Calculus}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle\frac{d y} {d x}$ & Derivative of $y$ with respect to $x$\\ [2ex]
$\displaystyle \frac{\partial y} {\partial x} $ & Partial derivative of $y$ with respect to $x$ \\
$\displaystyle \nabla_\vx y $ & Gradient of $y$ with respect to $\vx$ \\
$\displaystyle \nabla_\mX y $ & Matrix derivatives of $y$ with respect to $\mX$ \\
$\displaystyle \nabla_\tX y $ & Tensor containing derivatives of $y$ with respect to $\tX$ \\
$\displaystyle \frac{\partial f}{\partial \vx} $ & Jacobian matrix $\mJ \in \R^{m\times n}$ of $f: \R^n \rightarrow \R^m$\\
$\displaystyle \nabla_\vx^2 f(\vx)\text{ or }\mH( f)(\vx)$ & The Hessian matrix of $f$ at input point $\vx$\\
$\displaystyle \int f(\vx) d\vx $ & Definite integral over the entire domain of $\vx$ \\
$\displaystyle \int_\sS f(\vx) d\vx$ & Definite integral with respect to $\vx$ over the set $\sS$ \\
\end{tabular}
\egroup
\vspace{0.25cm}

\centerline{\bf Probability and Information Theory}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle P(\ra)$ & A probability distribution over a discrete variable\\
$\displaystyle p(\ra)$ & A probability distribution over a continuous variable, or over
a variable whose type has not been specified\\
$\displaystyle \ra \sim P$ & Random variable $\ra$ has distribution $P$\\% so thing on left of \sim should always be a random variable, with name beginning with \r
$\displaystyle  \E_{\rx\sim P} [ f(x) ]\text{ or } \E f(x)$ & Expectation of $f(x)$ with respect to $P(\rx)$ \\
$\displaystyle \Var(f(x)) $ &  Variance of $f(x)$ under $P(\rx)$ \\
$\displaystyle \Cov(f(x),g(x)) $ & Covariance of $f(x)$ and $g(x)$ under $P(\rx)$\\
$\displaystyle H(\rx) $ & Shannon entropy of the random variable $\rx$\\
$\displaystyle \KL ( P \Vert Q ) $ & Kullback-Leibler divergence of P and Q \\
$\displaystyle \mathcal{N} ( \vx ; \vmu , \mSigma)$ & Gaussian distribution %
over $\vx$ with mean $\vmu$ and covariance $\mSigma$ \\
\end{tabular}
\egroup
\vspace{0.25cm}

\centerline{\bf Functions}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle f: \sA \rightarrow \sB$ & The function $f$ with domain $\sA$ and range $\sB$\\
$\displaystyle f \circ g $ & Composition of the functions $f$ and $g$ \\
  $\displaystyle f(\vx ; \vtheta) $ & A function of $\vx$ parametrized by $\vtheta$.
  (Sometimes we write $f(\vx)$ and omit the argument $\vtheta$ to lighten notation) \\
$\displaystyle \log x$ & Natural logarithm of $x$ \\
$\displaystyle \sigma(x)$ & Logistic sigmoid, $\displaystyle \frac{1} {1 + \exp(-x)}$ \\
$\displaystyle \zeta(x)$ & Softplus, $\log(1 + \exp(x))$ \\
$\displaystyle || \vx ||_p $ & $\normlp$ norm of $\vx$ \\
$\displaystyle || \vx || $ & $\normltwo$ norm of $\vx$ \\
$\displaystyle x^+$ & Positive part of $x$, i.e., $\max(0,x)$\\
$\displaystyle \1_\mathrm{condition}$ & is 1 if the condition is true, 0 otherwise\\
\end{tabular}
\egroup
\vspace{0.25cm}

\section{Final instructions}
Do not change any aspects of the formatting parameters in the style files.
In particular, do not modify the width or length of the rectangle the text
should fit into, and do not change font sizes (except perhaps in the
\textsc{References} section; see below). Please note that pages should be
numbered.

\section{Preparing PostScript or PDF files}

Please prepare PostScript or PDF files with paper size ``US Letter'', and
not, for example, ``A4''. The -t
letter option on dvips will produce US Letter files.

Consider directly generating PDF files using \verb+pdflatex+
(especially if you are a MiKTeX user).
PDF figures must be substituted for EPS figures, however.

Otherwise, please generate your PostScript and PDF files with the following commands:
\begin{verbatim}
dvips mypaper.dvi -t letter -Ppdf -G0 -o mypaper.ps
ps2pdf mypaper.ps mypaper.pdf
\end{verbatim}

\subsection{Margins in LaTeX}

Most of the margin problems come from figures positioned by hand using
\verb+\special+ or other commands. We suggest using the command
\verb+\includegraphics+
from the graphicx package. Always specify the figure width as a multiple of
the line width as in the example below using .eps graphics
\begin{verbatim}
   \usepackage[dvips]{graphicx} ...
   \includegraphics[width=0.8\linewidth]{myfile.eps}
\end{verbatim}
or
\begin{verbatim}
   \usepackage[pdftex]{graphicx} ...
   \includegraphics[width=0.8\linewidth]{myfile.pdf}
\end{verbatim}
for .pdf graphics.
See section~4.4 in the graphics bundle documentation (\url{http://www.ctan.org/tex-archive/macros/latex/required/graphics/grfguide.ps})

A number of width problems arise when LaTeX cannot properly hyphenate a
line. Please give LaTeX hyphenation hints using the \verb+\-+ command.

\subsubsection*{Author Contributions}
If you'd like to, you may include  a section for author contributions as is done
in many journals. This is optional and at the discretion of the authors.

\subsubsection*{Acknowledgments}
Use unnumbered third level headings for the acknowledgments. All
acknowledgments, including those to funding agencies, go at the end of the paper.

\section{Introduction}
Bits back coding \citep{wallace,hinton} is a method for performing lossless compression using a latent variable model. In an ideal implementation, the method can achieve an expected message length equal to the variational free energy, often referred to as the negative evidence lower bound (ELBO) of the model. Bits back was first introduced to form a theoretical argument for using the ELBO as an objective function for machine learning \citep{hinton}.

The first implementation of bits back coding \citep{frey, fec} made use of first-in-first-out (FIFO) arithmetic coding (AC) \citep{ac}. However, the implementation did not achieve optimal compression, due to an incompatibility between a FIFO coder and bits back coding, and its use was only demonstrated on a small dataset of 8$\times$8 binary images.

Recently, zero-overhead bits back compression with a significantly simpler implementation has been developed by \cite{bb-ans}. This implementation makes use of asymmetric numeral systems (ANS), a last-in-first-out (LIFO) entropy coding scheme \citep{ans}. The method, known as `Bits Back with Asymmetric Numeral Systems' (BB-ANS) was demonstrated by compressing the MNIST test set using a variational auto-encoder (VAE) model \citep{vae,dlgm}, achieving a compression rate within $1\%$ of the model ELBO.

More recently, \cite{integer-flows} and \cite{local-flows} have proposed flow-based methods for lossless compression, and  \cite{Bit-Swap} have presented `Bit-Swap', extending BB-ANS to hierarchical models. In this work we present an alternative method for extending to hierarchical VAEs. This entails the following novel techniques:
\begin{enumerate}
    \item Direct coding of arbitrary sized images using a fully convolutional model.
    \item A vectorized ANS implementation supporting dynamic shape.
    \item Dynamic discretization to avoid having to calibrate a static discretization.
    \item Initializing the bits back chain using a different codec.
\end{enumerate}
We discuss each of these contributions in detail in Section \ref{sec:contributions}. We call the combination of BB-ANS using a hierarchical latent variable model and the above techniques: `Hierarchical Latent Lossless Compression' (HiLLoC). In our experiments (Section \ref{sec:experiments}), we demonstrate that HiLLoC can be used to compress color images from the ImageNet test set at rates close to the ELBO, outperforming all of the other codecs which we benchmark. We also demonstrate the speedup, of nearly three orders of magnitude, resulting from vectorization.  We release an open source implementation based on `Craystack', a Python package which we have written for general prototyping of lossless compression with ANS.

\begin{figure}[t]
    \centering
    \includegraphics[width=\textwidth]{fig1.eps}
    \caption{A selection of images from the ImageNet dataset and the compression rates achieved on the dataset by PNG, WebP, FLIF, Bit-Swap and the HiLLoC codec (with ResNet VAE) presented in this work.}
    \label{fig:test_images}
\end{figure}

\section{Background}
In this section we briefly describe the BB-ANS algorithm first introduced by \cite{bb-ans}. We begin by giving a high-level description of the ANS LIFO entropy coder \citep{ans}, along with a new notation for describing the basic ANS operations. Throughout the rest of the paper we use $\log$ to mean the base two logarithm, usually denoted $\log_2$, and we measure message lengths in bits.

\subsection{Asymmetric numeral systems}
As an entropy coder, ANS was designed for compressing sequences of discretely distributed symbols. It achieves a compressed message length equal to the negative log-probability (information content) of the sequence plus an implementation dependent constant, which is usually less than 32 bits. For long sequences, the constant overhead has a negligible contribution to the overall compression rate. Thus, by Shannon's source coding theorem \citep{shannon}, ANS coding is guaranteed to be near-optimal for long sequences.

There are two basic operations defined by ANS, which we will refer to as `push' and `pop'. Push \emph{encodes} a symbol by adding it to an existing message. It has the signature
\begin{equation}
    \mathrm{push}: (\mathrm{message}, \mathrm{symbol}) \mapsto \mathrm{message}'.
\end{equation}
Pop is the inverse of push, and may be used to \emph{decode} a symbol and recover a message identical to that before pushing.
\begin{equation}
    \mathrm{pop}: \mathrm{message}' \mapsto (\mathrm{message}, \mathrm{symbol}).
\end{equation}
When multiple symbols are pushed in sequence, they must be popped using the precise inverse procedure, which means popping the symbols in the opposite order. Hence why ANS is referred to as a last-in-first-out coder, or a \textit{stack}.

The push and pop operations require access to a probabilistic model of symbols, summarized by a probability mass function $p$ over the alphabet of possible symbols. The way that symbols are encoded depends on the model, and pushing a symbol $s$ according to $p$ results in an increase in message length of $\smash{\log\frac{1}{p(s)}}$. Popping $s$ results in an equal reduction in message length. For details on how the ANS operations are implemented, see \cite{ans}.

Note that any model/mass function can be used for the pop operation, i.e.\ there's no hard restriction to use the distribution that was used to encode the message. In this way, rather than decoding the same data that was encoded, pop can actually be used to \emph{sample} a symbol from a different distribution. The pop method itself is deterministic, so the source of randomness for the sample comes from the data contained within the message. This sampling operation, which can be inverted by pushing the sample back onto the stack, is essential for bits back coding.

For convenience, we introduce the shorthand notation $s\rightarrow p(\cdot)$ for encoding (pushing) a symbol $s$ according to $p$, and $s\leftarrow p(\cdot)$ for decoding (popping).

\subsection{Bits back with ANS}\label{sec:bb-ans}
Suppose we have a model for data $x$ which involves a \emph{latent variable} $z$. A sender and receiver wish to communicate a sample $x$. They have access to a prior on $z$, denoted $p(z)$, a likelihood $p(x\given z)$ and a (possibly approximate) posterior $q(z\given x)$, but not the marginal distribution $p(x)$. Without access to $p(x)$, sender and receiver cannot directly code $x$ using ANS. However, BB-ANS specifies an indirect way to push and pop $x$. It does not require access to the marginal $p(x)$, but rather uses the prior, conditional, and posterior from the latent variable model.

Table \ref{tab:bb-ans}(a) shows, in order from the top, the three steps of the BB-ANS pushing procedure which the sender can perform to encode $x$. The `Variables' column shows the variables known to the sender before each step. \ref{tab:bb-ans}(b) shows the inverse steps which the receiver can use to pop $x$, with the `Variables' column showing what is known to the receiver \emph{after} each step. After decoding $x$, the third step of popping, $z\rightarrow q(\cdot\given x)$, is necessary to ensure that BB-ANS pop is a precise inverse of push.
\begin{table}[h]
      \caption{Indirectly pushing and popping $x$ using BB-ANS. $\rightarrow$ and $\leftarrow$ denote pushing and popping respectively. $\Delta L$ denotes the change in message length resulting from each operation. The three steps to push/pop are ordered, starting at the top of the table and descending.}\label{tab:bb-ans}
  \begin{subtable}{0.49\columnwidth}
    \centering
    \caption{Pushing $x$}
  \begin{tabular}{lll}
Variables &Operation                       &$\Delta L$                    \\\midrule
$x$       &$z\leftarrow  q(\cdot\given x)$ &$-\log\frac{1}{q(z\given x)}$ \\\addlinespace
$x, z$    &$x\rightarrow p(\cdot\given z)$ &$+\log\frac{1}{p(x\given z)}$ \\\addlinespace
$z$       &$z\rightarrow p(\cdot)$         &$+\log\frac{1}{p(z)}$         \\
  \end{tabular}
  \end{subtable}
  \begin{subtable}{0.49\columnwidth}
    \centering
    \caption{Popping $x$}
  \begin{tabular}{lll}
Operation                       &Variables &$\Delta L$                    \\\midrule
$z\leftarrow  p(\cdot)$         &$z$       &$-\log\frac{1}{p(z)}$         \\\addlinespace
$x\leftarrow  p(\cdot\given z)$ &$x, z$    &$-\log\frac{1}{p(x\given z)}$ \\\addlinespace
$z\rightarrow q(\cdot\given x)$ &$x$       &$+\log\frac{1}{q(z\given x)}$ \\
  \end{tabular}
  \end{subtable}
\end{table}

The change in message length from BB-ANS can easily be derived by adding up the quantities in the $\Delta L$ column of \autoref{tab:bb-ans}. For encoding we get
\begin{align}
    \Delta L_\mathrm{BB-ANS} &= -\log\frac{1}{q(z\given x)} + \log\frac{1}{p(x\given z)} + \log\frac{1}{p(z)}\\
    &= -\log\frac{p(x, z)}{q(z\given x)}.
\end{align}
Taking the expectation over $z$ gives the expected message length for a datum $x$
\begin{equation}
    \mathcal{L}(x) = -\mathbb{E}_{q(z\given x)}\left[\log\frac{p(x, z)}{q(z\given x)}\right]
\end{equation}
which is the negative evidence lower bound (ELBO), also known as the free energy. This is a commonly used training objective for latent variable models. The above equation implies that latent variable models trained using the ELBO are implicitly being trained to minimize the expected message length of lossless compression using BB-ANS.

Note that, as \autoref{tab:bb-ans} shows, the first step of encoding a data point, $x$, using BB-ANS is to, counter-intuitively, \textit{decode} (and thereby sample) a latent $z \leftarrow q(\cdot \given x)$. This requires that there is already a buffer of random data pushed to the ANS coder, which can be popped. This data used to start the encoding process is recovered after the final stage of decoding, hence the name `bits back'.

If we have multiple samples to compress, then we can use `chaining', which is essentially repeated application of the procedure in Table \ref{tab:bb-ans} \citep{bb-ans}. In Section \ref{sec:starting} we describe how we build up an initial buffer of compressed data by using a different codec to code the first images in a sequence.

\section{Scaling up bits back with ANS}\label{sec:contributions}
We now discuss the techniques we introduce to scale up BB-ANS.

\subsection{Fully convolutional models}
When all of the layers in the generative and recognition networks of a VAE are either convolutional or elementwise functions (i.e. the VAE has no densely connected layers), then it is possible to evaluate the recognition network on images of any height and width, and similarly to pass latents of any height and width through the generative network to generate an image. Thus, such a VAE can be used as a (probabilistic) model for images of any size.

We exploit this fact, and show empirically in Section \ref{sec:experiments} that, surprisingly, a fully convolutional VAE trained on 32 $\times$ 32 images can perform well (in the sense of having a high ELBO) as a model for 64 $\times$ 64 images as well as far larger images. This in turn corresponds to a good compression rate, and we implement lossless compression of arbitrary sized images by using a VAE in this way.

\subsection{Vectorized lossless compression}\label{sec:vec}
\begin{figure}[t]
\begin{tikzpicture}
    \pic at (0,0) {scuboid={width=0, height=0, depth=0}};

    \node at (2.85, -1.15) {$x \rightarrow p(\cdot \given z)$};

    \node at (8.5, -1.15) {$z \rightarrow p(\cdot)$};

    \pic [fill=gray!20] at (5.1, -3) {scuboid={width=33, height=5, depth=32}};
    \pic [fill=gray!20] at (11.5, -3) {scuboid={width=50, height=5, depth=32}};

     \draw [-{Latex[length=1.5mm,width=2mm]}] (4,0) -- (4,-2.5);
    \draw [-{Latex[length=1.5mm,width=2mm]}] (9.5,0) -- (9.5,-2.5);

    \node[inner sep=0pt] at (4.05,0)
    {\includegraphics[width=.325\textwidth]{flower_st2.png}};

    \node[inner sep=0pt] at (9.575,0)
    {\includegraphics[width=.45\textwidth]{noise_st3.png}};

    \draw [decorate,decoration={brace,amplitude=10pt,mirror}] (1.25,-1.8) -- (1.25,-4.5);
    \node[text width=1.5cm,align=center] at (0,-3.15) {Vectorized ANS coder};

    \node (xbelow) at (4,-3.375) {};
    \node (zbelow) at (9.5,-3.375) {};
    \node (ztemp) at (8,-4.0) {};
    \node (ztemp2) at (8.25,-4.0) {};
    \node (ztemp3) at (6.65,-4.) {};
    \node (tailleft) at (5.8,-4.5) {};
    \node (tailleft2) at (5.8,-4.45) {};

    \draw [-{Latex[length=1.5mm,width=2mm]}] (xbelow) to [out=-90,in=180] (tailleft2);
    \draw (zbelow) to [out=-90,in=0] (ztemp);
    \draw (ztemp2) -- (6.5, -4);
    \draw [-{Latex[length=1.5mm,width=2mm]}] (ztemp3) to [out=180, in=135] (tailleft);

    \draw[fill=black!75] (5.75,-4.5) rectangle ++(0.25,0.25);
    \draw[fill=black!75] (6,-4.5) rectangle ++(0.25,0.25);
    \draw[] (6.25,-4.5) rectangle ++(0.25,0.25);
    \draw[fill=black!75] (6.5,-4.5) rectangle ++(0.25,0.25);
    \draw[] (6.75,-4.5) rectangle ++(0.25,0.25);
    \draw[] (7,-4.5) rectangle ++(0.25,0.25);
    \draw[] (7.25,-4.5) rectangle ++(0.25,0.25);
    \draw[] (7.5,-4.5) rectangle ++(0.25,0.25);
    \draw[fill=black!75] (7.75,-4.5) rectangle ++(0.25,0.25);
    \draw[fill=black!75] (8,-4.5) rectangle ++(0.25,0.25);
    \draw[] (8.25,-4.5) rectangle ++(0.25,0.25);
    \draw[fill=black!75] (8.5,-4.5) rectangle ++(0.25,0.25);
    \draw[] (8.75,-4.5) rectangle ++(0.25,0.25);
    \draw[fill=black!75] (9,-4.5) rectangle ++(0.25,0.25);
    \draw[fill=black!75] (9.25,-4.5) rectangle ++(0.25,0.25);
    \draw[] (9.5,-4.5) rectangle ++(0.25,0.25);

    \draw (9.75,-4.5) -- (10, -4.5);
    \draw (9.75,-4.25) -- (10, -4.25);

    \node at (10.25, -4.375) {...};

\end{tikzpicture}
\caption{Visualizing the process of pushing images and latents from a VAE to the vectorized ANS stack with Craystack. The ANS stack head is shaped such that images and latents can be pushed and popped in parallel, without reshaping. Beneath the shaped top of the stack is the flat message stream output by ANS.}
\label{fig:vrans_stack}
\end{figure}

The primary computational bottlenecks in the original BB-ANS implementation \citep{bb-ans} were loops over data and latent variables occurring in the Python interpreter. We have been able to vectorize these, achieving an implementation which can scale to large ImageNet images. The effect of vectorization on runtime is shown in Figure \ref{fig:timings}.

A vectorized implementation of ANS was described in \cite{ryg} using SIMD instructions. This works by expanding the size of the ANS stack head, from a scalar to a vector, and interleaving the output/input bit stream. We implement this in our lossless compression library, Craystack, using Numpy. Please refer to the Craystack code and to \cite{ryg} for more detail. We ensure that the compression rate overhead to vectorization is low by using the BitKnit technique described in \cite{bit-knit}, see \autoref{app:vec-overheads} for more detail. Having vectorized, we found that most of the compute time for our compression was spent in neural net inference, whether running on CPU or GPU, which we know to already be reasonably well optimized.

In Craystack, we further generalize the ANS coder using Numpy's n-dimensional array view interface, allowing the stack head to be `shaped' like an n-dimensional array, or a nested Python data-structure containing arrays. We can then use a shape which fits that of the data that we wish to encode or decode. When coding data according to a VAE we use an ANS stack head shaped into a pair of arrays, matching the shapes of the observation $x$ and the latent $z$. This allows for a straightforward implementation and clarifies the lack of data dependence between certain operations, such as the $x\rightarrow p(\cdot\given z)$ and $z\rightarrow p(\cdot)$ during encoding, which can theoretically be performed concurrently. This vectorized encoding process is visualized in \autoref{fig:vrans_stack}.

\subsection{Discretization}\label{sec:discretization}
It is standard for state of the art latent variable models to use continuous latent variables. Since ANS operates over \emph{discrete} probability distributions, if we wish to use BB-ANS with such models it is necessary to discretize the latent space so that latent samples can be communicated. \cite{bb-ans} described a \emph{static} discretization scheme for the latents in a simple VAE with a single layer of continuous latent variables, and showed that this discretization has a negligible impact on compression rate. The addition of multiple layers of stochastic variables to a VAE has been shown to improve performance \citep{Bit-Swap, iaf, biva, ladder-vae}. Motivated by this, we propose a discretization scheme for hierarchical VAEs with multiple layers of latent variables.

The discretization described in \cite{bb-ans} is formed by dividing the latent space into intervals of equal mass under the prior $p(z)$. For a hierarchical model, the prior on each layer depends on the previous layers:
\begin{equation}
    p(z_{1:L}) = p(z_L)\prod_{l=1}^{L-1}p(z_l\given z_{l+1:L}).
\end{equation}
It isn't immediately possible to use the simple static scheme from \cite{bb-ans}, since the marginals $p(z_1),\ldots,p(z_{L-1})$ are not known. \cite{Bit-Swap} estimate these marginals by sampling, and create static bins based on the estimates. They demonstrate that this approach can work well. We propose an alternative approach, allowing the discretization to vary with the context of the latents we are trying to code. We refer to our approach as \textit{dynamic discretization}.

In dynamic discretization, instead of discretizing with respect to the marginals of the prior, we discretize according to the \textit{conditionals} in the prior, $p(z_l \given z_{l+1:L})$. Specifically, for each latent layer $l$, we partition each dimension into intervals which have equal probability mass under the conditional $p(z_l\given z_{l+1:L})$. This directly generalizes the scheme used in BB-ANS \citep{bb-ans}.

Dynamic discretization is more straightforward to implement because it doesn't require callibrating the discretization to samples. However it imposes a restriction on model structure, in particular it requires that posterior inference is done \emph{top-down}. This precludes the use of Bit-Swap. In Section \ref{post_restrictions} we contrast the model restriction from dynamic discretization with the bottom-up, Markov restriction imposed by Bit-Swap itself.

We give further details about the dynamic discretization implementation we use in \autoref{app:reparam}.
\subsubsection{Model restrictions}\label{post_restrictions}
\begin{figure}[htb]
\centering
\begin{subfigure}{.25\textwidth}
\centering
\begin{tikzpicture}
\tikzstyle{var}=[circle,draw=black,minimum size=7mm]
\tikzstyle{latent3}  =[]
\tikzstyle{latent2}  =[]
\tikzstyle{latent1}  =[]
\tikzstyle{observed}=[fill=gray!50]
    \node[var,latent3]   (l3)               {$z_3$};
    \node[var,latent2]   (l2) [below of=l3] {$z_2$};
    \node[var,latent1]   (l1) [below of=l2] {$z_1$};
    \node[var,observed] (x) [below of=l1]   {$x$};
    \draw [->] (l3) -- (l2);
    \draw [->] (l2) -- (l1);
    \draw [->] (l3) to[out=-135,in=135] (l1);
    \draw [->] (l1) -- (x);
    \draw [->] (l2) to[out=-45,in=45] (x);
    \draw [->] (l3) to[out=-135,in=135] (x);
\end{tikzpicture}
\caption{HiLLoC generative}
\label{subfig:gen}
\end{subfigure}%
\begin{subfigure}{.25\textwidth}
\centering
\begin{tikzpicture}
\tikzstyle{var}=[circle,draw=black,minimum size=7mm]
\tikzstyle{latent3}  =[]
\tikzstyle{latent2}  =[]
\tikzstyle{latent1}  =[]
\tikzstyle{observed}=[fill=gray!50]
    \node[var,latent3]   (l3)               {$z_3$};
    \node[var,latent2]   (l2) [below of=l3] {$z_2$};
    \node[var,latent1]   (l1) [below of=l2] {$z_1$};
    \node[var,observed] (x) [below of=l1]   {$x$};
    \draw [->] (l3) -- (l2);
    \draw [->] (l2) -- (l1);
    \draw [->] (l3) to[out=-135,in=135] (l1);
    \draw [dashed,->] (x) -- (l1);
    \draw [dashed,->] (x) to[out=45,in=-45] (l2);
    \draw [dashed,->] (x) to[out=45,in=-45] (l3);
\end{tikzpicture}
\caption{HiLLoC inference}
\label{subfig:inf}
\end{subfigure}%
\begin{subfigure}{.25\textwidth}
\centering

\begin{tikzpicture}
\tikzstyle{var}=[circle,draw=black,minimum size=7mm]
\tikzstyle{latent3}  =[]
\tikzstyle{latent2}  =[]
\tikzstyle{latent1}  =[]
\tikzstyle{observed}=[fill=gray!50]
    \node[var,latent3]   (l3)               {$z_3$};
    \node[var,latent2]   (l2) [below of=l3] {$z_2$};
    \node[var,latent1]   (l1) [below of=l2] {$z_1$};
    \node[var,observed] (x) [below of=l1]   {$x$};
    \draw [->] (l3) -- (l2);
    \draw [->] (l2) -- (l1);
    \draw [->] (l1) -- (x);
\end{tikzpicture}

\caption{Bit-Swap generative}
\end{subfigure}%
\begin{subfigure}{.25\textwidth}
\centering

\begin{tikzpicture}
\tikzstyle{var}=[circle,draw=black,minimum size=7mm]
\tikzstyle{latent3}  =[]
\tikzstyle{latent2}  =[]
\tikzstyle{latent1}  =[]
\tikzstyle{observed}=[fill=gray!50]
    \node[var,latent3]   (l3)               {$z_3$};
    \node[var,latent2]   (l2) [below of=l3] {$z_2$};
    \node[var,latent1]   (l1) [below of=l2] {$z_1$};
    \node[var,observed] (x) [below of=l1]   {$x$};
    \draw [->] (l2) -- (l3);
    \draw [->] (l1) -- (l2);
    \draw [dashed,->] (x) -- (l1);
\end{tikzpicture}

\caption{Bit-Swap inference}
\end{subfigure}
\caption{Graphical models representing the generative and inference models with HiLLoC and Bit-Swap, both using a 3 layer latent hierarchy. The dashed lines indicate dependence on the fixed observation.}
\label{fig:graphicalmodel}
\end{figure}
The first stage of BB-ANS encoding is to pop from the posterior, $z_{1:L}\leftarrow q(\cdot \given x)$. When using dynamic discretization, popping the layer $z_l$ requires knowledge of the discretization used for $z_l$ and thus of the conditional distribution $p(z_l \given z_{l+1:L})$. This requires the latents $z_{l+1:L}$ to have already been popped. Because of this, latents in general must be popped (sampled) in `top-down' order, i.e. $z_L$ first, then $z_{L-1}$ and so on down to $z_1$.

The most general form of posterior for which top-down sampling is possible is
\begin{equation}
    q(z_{1:L}\given x)=q(z_L\given x)\prod_{l=1}^{L-1}q(z_l\given z_{l+1:L}, x).
\end{equation}
This is illustrated, for a hierarchy of depth 3, in Figure \ref{subfig:inf}. The Bit-Swap technique \citep{Bit-Swap} requires that inference be done bottom up, and that generative and inference models must both be a Markov chain on $z_1, \ldots,z_L$, and thus cannot use skip connections. These constraints are illustrated in Figure 3c,d. Skip connections have been shown to improve model ELBO in very deep models \citep{ladder-vae, biva}. HiLLoC does not have this constraint, and we do utilize skip connections in our experiments.

\subsection{Starting the bits back chain} \label{sec:starting}
As discussed in Section \ref{sec:discretization}, our dynamic discretization method precludes the use of Bit-Swap for reducing the one-time cost of starting a BB-ANS chain. We propose instead to use a significantly simpler method to address the high cost of coding a small number of samples with BB-ANS, namely we code the first samples using a different codec. The purpose of this is to build up a sufficiently large buffer of compressed data to permit the first stage of the BB-ANS algorithm - to pop a latent sample from the posterior. In our experiments we use the `Free Lossless Image Format' (FLIF) \citep{flif} to build up the buffer. We chose this codec because it performed better than other widely used codecs, but in principal any lossless codec could be used.

The amount of previously compressed data required to pop a posterior sample from the ANS stack (and therefore start the BB-ANS chain) is roughly proportional to the size of the image we wish to compress, since in a fully convolutional model the size of the latent space is determined by the image size.

We can exploit this to allow us to obtain a better compression rate than FLIF as quickly as possible. We do so by partitioning the first images we wish to compress with HiLLoC into smaller patches. These patches require a smaller data buffer, and thus we can use the superior HiLLoC coding sooner than if we attempted to compress full images. We find experimentally that, generally, larger patches have a better coding rate than smaller patches. Therefore we increase the size of the image patches being compressed with HiLLoC as more images are compressed and the size of the data buffer grows, until we finally compress full images once the buffer is sufficiently large. For our experiments on compressing full ImageNet images, we compress 32$\times$32 patches, then 64$\times$64, then 128$\times$128 before switching to coding the full size images directly. Note that since our model can compress any shape image, we can compress the edge patches which will have different shape if the patch size does not divide the image dimensions exactly. Using this technique means that our coding rate improves gradually from the FLIF coding rate towards the coding rate achieved by HiLLoC on full images. We compress only 5 ImageNet images using FLIF before we start compressing 32$\times$32 patches using HiLLoC.

\section{Experimental results}\label{sec:experiments}

Using Craystack, we implement HiLLoC with a ResNet VAE (RVAE) \citep{iaf}. This powerful hierarchical latent variable model achieves ELBOs comparable to state of the art autoregressive models\footnote{Unlike autoregressive models, for which decoding time scales with number of pixels, and is in practice extremely slow, both encoding and decoding with RVAEs are fast.}. In all experiments we used an RVAE with 24 stochastic hidden layers. The RVAE utilizes skip connections, which are important to be able to effectively train models with such a deep latent hierarchy. See \autoref{app:rvae_arch} for more details.

We trained the RVAE on the ImageNet 32 training set, then evaluated the RVAE ELBO and HiLLoC compression rate on the ImageNet 32 test set. To test generalization, we also evaluated the ELBO and compression rate on the tests sets of ImageNet64, CIFAR10 and full size ImageNet. For full size ImageNet, we used the partitioning method described in \ref{sec:starting}. The results are shown in Table \ref{tab:results}.

For HiLLoC the compression rates are for the entire test set, except for full ImageNet, where we use 2000 random images from the test set.

\begin{table}[h]
\caption{Compression performance of HiLLoC with RVAE compared to other codecs. Rates measured in bits/dimension (raw data is 8 bits/dimension). For HiLLoC we display compression rate and theoretical performance (ELBO). All HiLLoC results are obtained from the same model, trained on ImageNet 32.}
    \label{tab:results}
    \centering
    \begin{tabular}{llcccc}
                  &                    & ImageNet 32   & ImageNet 64   & Cifar-10      & ImageNet      \\\midrule[\heavyrulewidth]
\emph{Generic}    & PNG                & 6.39          & 5.71          & 5.87          & 4.71          \\
                  & WebP               & 5.29          & 4.64          & 4.61          & 3.66          \\
                  & FLIF               & 4.52          & 4.19          & 4.19          & 3.37          \\
\midrule
\emph{Flow-based} & IDF\tablefootnote{Integer discrete flows, retrieved from \cite{integer-flows}.}
                                       & 4.18          & 3.90          & 3.34          & -             \\
                  & IDF generalized\tablefootnote{Integer discrete flows trained on ImageNet 32.
                  ImageNet 64 images are split into four 32$\times$32 patches. Retrieved from
                  \cite{integer-flows}.}
                                       & 4.18          & 3.94          & 3.60          & -             \\
                  & LBB\tablefootnote{Local bits back, retrieved from \cite{local-flows}.}
                                       & \textbf{3.88} & \textbf{3.70} & \textbf{3.12} & -             \\
\midrule
\emph{VAE-based}  & Bit-Swap           & 4.50          & -             & 3.82          & 3.51\tablefootnote{
For Bit-Swap, full size ImageNet images were cropped so that their side lengths were multiples of 32.} \\
                  & HiLLoC             & 4.20          & 3.90          & 3.56          & \textbf{3.15} \\
                  & HiLLoC (ELBO)      & (4.18)        & (3.89)        & (3.55)        & (3.14)        \\
\end{tabular}
\end{table}

Table \ref{tab:results} shows that HiLLoC achieves competitive compression rates on all benchmarks, and state of the art on full size ImageNet images. The fact that HiLLoC can achieve state of the art compression on ImageNet relative to the baselines, even under a change of distribution, is striking. This provides strong evidence of its efficacy as a general method for lossless compression of natural images. Naively, one might expect a degradation of performance relative to the original test set when changing the test distribution---even more so when the resolution changes. However, in the settings we studied, the \emph{opposite} was true, in that the average per-pixel ELBO (and thus the compressed message length) was \emph{lower} on all other datasets compared to the ImageNet 32 validation set.

In the case of CIFAR, we conjecture that the reason for this is that its images are simpler and contain more redundancy than ImageNet. This theory is backed up by the performance of standard compression algorithms which, as shown in Table \ref{tab:results}, also perform better on CIFAR images than they do on ImageNet 32. We find the compression rate improvement on larger images more surprising. We hypothesize that this is because pixels at the edge of an image are harder to model because they have less context to reduce uncertainty. The ratio of edge pixels to interior pixels is lower for larger images, thus we might expect less uncertainty per pixel in a larger image.
\begin{figure}[ht]
    \centering
        \includegraphics[width=0.45\textwidth]{timings.eps}

        \caption{Runtime of vectorized vs.\ serial ANS implementations. Times were computed on a desktop with 6 CPU cores and a GTX 1060 GPU.}
        \label{fig:timings}
\end{figure}

To demonstrate the effect of vectorization we timed ANS of single images at different, fixed, sizes, using a fully vectorized and a fully serial implementation. The results are shown in Figure \ref{fig:timings}, which clearly shows a speedup of nearly three orders of magnitude for all image sizes. We find that the run times for encoding and decoding are roughly linear in the number of pixels, and the time to compress an average sized ImageNet image of $500\times374$ pixels (with vectorized ANS) is around 29s on a desktop computer with 6 CPU cores and a GTX 1060 GPU.

\section{Discussion}
Our experiments demonstrate HiLLoC as a bridge between large scale latent variable models and compression. To do this we use simple variants of pre-existing VAE models. Having shown that bits back coding is flexible enough to compress well with large, complex models, we see plenty of work still to be done in searching model structures (i.e.\ architecture search), optimizing with a trade-off between compression rate, encode/decode time and memory usage. Particularly pertinent for HiLLoC is latent dimensionality, since compute time and memory usage both scale with this. Since the model must be stored/transmitted to use HiLLoC, weight compression is also highly relevant. This is a well-established research area in machine learning \citep{deepcompression, weightsharing}.

Our experiments also demonstrated that one can achieve good performance on a dataset of large images by training on smaller images. This result is promising, but future work should be done to discover what the best training datasets are for coding generic images. One question in particular is whether results could be improved by training on larger images and/or images of varying size. We leave this to future work. Another related direction for improvement is batch compression of images of different sizes using masking, analogous to how samples of different length may be processed in batches by recurrent neural nets.

Whilst this work has focused on latent variable models, there is also promise in applying state of the art fully observed auto-regressive models to lossless compression. We look forward to future work investigating the performance of models such as WaveNet \citep{wavenet} for lossless audio compression as well as PixelCNN++ \citep{pcnnpp} and the state of the art models in \cite{menick} for images. Sampling speed for these models, and thus decompression, scales with autoregressive sequence length, and can be very slow. This could be a serious limitation, particularly in common applications where encoding is performed once but decoding is performed many times. This effect can be mitigated by using dynamic programming \citep{fast-wavenet,fast-pcnn}, and altering model architecture \citep{pmar}, but on parallel architectures sampling/decompression is still significantly slower than with VAE models.

On the other hand, fully observed models, as well as the flow based models of \cite{integer-flows} and \cite{local-flows}, do not require bits back coding, and therefore do not have to pay the one-off cost of starting a chain. Therefore they may be well suited to situations where one or a few i.i.d. samples are to be communicated. Similar to the way that we use FLIF to code the first images for our experiments, one could initially code images using a fully observed model then switch to a faster latent variable model once a stack of bits has been built up.

\section{Conclusion}
We presented HiLLoC, an extension of BB-ANS to hierarchical latent variable models, and show that HiLLoC can perform well with large models. We open-sourced our implementation, along with the Craystack package for prototyping lossless compression.

We have also explored generalization of large VAE models, and established that fully convolutional VAEs can generalize well to other datasets, including images of very different size to those they were trained on. We have described how to compress images of arbitrary size with HiLLoC, achieving a compression rate superior to the best available codecs on ImageNet images. We look forward to future work reuniting machine learning and lossless compression.

\subsubsection*{Acknowledgments}
We thank Paul Rubenstein for the substantial constructive feedback and advice which he gave us. We also thank the anonymous reviewers for their feedback. This work was supported by the Alan Turing Institute under the EPSRC grant EP/N510129/1.

\newpage
\bibliographystyle{iclr2020_conference}

redpajama_set_name: RedPajamaArXiv


Researchers will soon be able to access the anonymised HAGIS pilot data via the Gateway to Global Aging Data.
Researchers will soon be able to apply to the Public Benefit Privacy Panel for access to anonymised linked HAGIS survey data with health and education records. This requires researchers having full information governance training in handling personal data.
Currently, linkage of the 2017 HAGIS pilot data to NHS Health records and education data is being carried out.


text:
An exploratory analysis of missing data from the Royal Bank of Canada (RBC) Learn to Play – Canadian Assessment of Physical Literacy (CAPL) project
BMC Public Health. 2018;18(S2):1-9 DOI 10.1186/s12889-018-5901-z
Journal Title: BMC Public Health
Publisher: BMC
LCC Subject Category: Medicine: Public aspects of medicine
Country of publisher: United Kingdom
Full-text formats available: PDF, HTML
Christine Delisle Nyström (Healthy Active Living and Obesity (HALO) Research Group, Children's Hospital of Eastern Ontario Research Institute)
Joel D. Barnes (Healthy Active Living and Obesity (HALO) Research Group, Children's Hospital of Eastern Ontario Research Institute)
Mark S. Tremblay (Healthy Active Living and Obesity (HALO) Research Group, Children's Hospital of Eastern Ontario Research Institute)
Abstract Background Physical literacy comprises a range of tests over four domains (Physical Competence, Daily Behaviour, Motivation and Confidence, and Knowledge and Understanding). The patterns of missing data in large field test batteries such as those for physical literacy are largely unknown. Therefore, the aim of this paper was to explore the patterns and possible reasons for missing data in the Royal Bank of Canada Learn to Play–Canadian Assessment of Physical Literacy (RBC Learn to Play–CAPL) project. Methods A total of 10,034 Canadian children aged 8 to 12 years participated in the RBC Learn to Play–CAPL project. A 32-variable subset from the larger CAPL dataset was used for these analyses. Several R packages ("Hmisc", "mice", "VIM") were used to generate matrices and plots of missing data, and to perform multiple imputations. Results Overall, the proportion of missing data for individual measures and domains ranged from 0.0 to 33.8%, with the average proportion of missing data being 4.0%. The largest proportion of missing data in CAPL was the pedometer step counts, followed by the components of the Physical Competence domain and the Children's Self-Perception of Adequacy in and Predilection for Physical Activity subscales. When domain scores were regressed on five imputed subsets with the original subset as the reference, there were small and statistically detectable differences in the Daily Behaviour score (β = − 1.6 to − 1.7, p < 0.001). However, for the other domain scores the differences were negligible and statistically undetectable (β = − 0.01 to − 0.06, p > 0.05). Conclusions This study has implications for other researchers or educators who are creating or using large field-based assessment measures in the areas of physical literacy, physical activity, or physical fitness, as this study demonstrates where problems in data collection can arise and how missing data can be avoided. When large proportions of missing data are present, imputation techniques, correction factors, or other treatment options may be required.

redpajama_set_name: RedPajamaCommonCrawl


Garment Labels – Types of Fabrics Used!
The label used in a garment is much more than a mere piece of fabric. It is your company's introductory speech. The label helps you to communicate with your clients so that you can connect with them. In short, the label describes the product. It draws the attention of the buyer towards the product. The buyer decides whether he will purchase the product or not after checking out the label.
What is The Purpose of Using Labels?
Labels play an integral role in communicating with the buyers about the material used to make the garment. They communicate how to take care of the particular garment and mention everything about the product. You will come to know about the size of the garment, the name of the manufacturer from the label. In short, it mentions in detail all the important must knows about the apparel in question.
To cash in on the advantages offered by the label, manufacturers use their own type of labels so as to create their own unique identity. Customized Garment Labels are trending. More and more manufacturers are using these labels. Attractive labels help to enhance the beauty of the garment. Labels make it easier for the customer to recognize the brand. It helps to create brand awareness.
What are the Different Types of Garment Labels?
Garment Labels can be made out of different types of fabrics in different styles and finishes. In the ultimate analysis, it depends on the manufacturer as to what type of label he will manufacture.
Manufacturers produce labels as individual pieces or as part of a continuous roll. If the production is carried out in the form of a roll, each label is cut out and then attached to the garment.
What are the Different Types of Fabrics Used in Labels?
The fabrics that are commonly used in manufacturing labels include satin, damask, semi-damask and taffeta. In some cases, as per client specifications, canvas, felt and even cotton are used to make the garment label. Satin is the most preferred material while PVC is used in case of bags and even pants.
Which Fabric is The Best?
Satin labels are soft to touch and look quite pretty but they are not the best fabric as they tend to tear easily. They are not durable and are very thin in texture.
Taffeta labels are stiffer in texture and are durable in nature. However, this fabric can irritate the skin because of its stiffness.
Damask and semi-damask are the best variety of labels. They are soft to touch, extremely durable and there is no irritation caused by these labels. Semi-damask is comparatively cheaper than damask.
Now that you have a fair idea about Garment Labels, you can use them in your clothing line. Opt for the one that best fits your requirement and budget. Labels are the best way to promote your garments in the most effective manner without spending too much. What are you waiting for? Contact the service provider today!


Are dual-boot Windows and Android tablets not enough for you? Then you might want to check out the Evolve III Maestro tablet, which lets you choose between three operating systems at boot.
The Maestro can handle Windows 7, Google Android, and MeeGo Linux. The upcoming tablet has an Intel Atom N475 CPU (although a dual core Oak Trail update may be in the works), 2GB of RAM, and a 32GB solid state disk. It has a 10 inch display, WiFi, and 3G and weighs 1.8 pounds.
The MeeGo operating system is particularly interesting, since the company has spent some time tweaking the OS with home screen widgets and a custom, finger-friendly program launcher.
The tablet is due out during Q2, 2011. There's no word on pricing or which version of Android it will run at launch.
You can check out a hands-on video below, courtesy of Geek.com, and a second video looking at the MeeGo UI, thanks to MyNokiaBlog.
Dont wasting your times with this overpriced bobble.


text:
layout: default
title: schedule
id: schedule
tags: page
---

View the Keystone DH 2017 mobile app

redpajama_set_name: RedPajamaGithub


Scaffolding netting and construction safety net made from flame retardant HDPE monofilament UV stabilized yarn, brass or galvanized eyelet every 30cm.
Galvanized or brass eyelet makes the construction safety net easy fixed.
Knotted scaffolding netting flame retardant and strong enough.
construction scaffolding nets fold package.
Size 3 meters × 50 meters.
Packing in plastic bags per roll.
Size: 1.80 m. × 5.10 m.
Yarn density: 1500D × 1500D 1 × 1 14 × 14 mesh/inch.
Material: polyester coated with PVC.
Edging: add 3 cm width supporting sheet and nylon rope around, install brass eyelet every 30 cm.
Green colour net with button holes (weaved holes, not the metal eyelet), knitted weaving.
Size of the rolls: 1.84 × 50m and 2.5 × 50m.
Flame Retardant approved by the loss prevention.
Good impact resistance and thermal cracking resistance.
Tensile strength > Mpa 38.
Size: 2 Meters × 50 Meters.
Manufactured from flame retardant high density polyethylene.


'Tis the season—Football season that is. If your game day is anything like ours, there will be plenty of snacks and the drinks flowing. Getting your game face on is definitely easier when there's wine involved, so grab a glass and a few goodies that will get the party started.
These little charms really add the perfect little touch, don't they? Cute and clever, these guys help distinguish whose glass is whose, while adding and extra dose of football. And since they aren't team specific you won't have guests clamoring over which one represents them best. Available for $19.50 on Amazon.
Ready, set, halftime! Pop one of these babies into your bottle while you make a run to the snack table-- before everyone else nabs the jalapeno poppers. Available for $8.75 at The Royal Standard.
Nothing says spirit like a toast to your team's latest touchdown. Be a fashionable fan and raise your team-themed glass to fall's greatest game. Sets of 2 are available for $59.95 at The Bradford Exchange.
This t-shirt exists to help remind everyone what your priorities on Sunday are, just in case they forgot. The best part about this tee is that you can get it in several different shades (might we suggest your team colors?) or just wear a different one every Sunday of the season. Available for $19.49 at Original James Tee.
If you're going to be game day ready, you're going to need your wine as pumped up as you are. Luckily you can have someone protecting your bottle during all the key plays with this football player-shaped holder. Made of recycled steel, you know he's not going to fumbling anytime soon. Available for $79.95 at the Gifted Grape.


At artrepublic, we stock a vast range of printsand art posters byLaura Kikauka -and the artisthas become increasinglypopular with us here at artrepublic. We aim to make buying art fun and affordable, stocking art from well known names, along with new talented artists. This page showcases all works by Laura Kikauka we currentlyhave in stock, but if there's something else you're interested in by Laura Kikauka do get in touch and we will do our best to source it for you, however if your perfect Laura Kikauka print is listed, buying it couldn't be simpler. Simply select your chosen Laura Kikauka print and select 'add to basket' - your print will then be automatically be added to your account and all you have to do is select your chosenframing options, should you require them and thencheckout. Remember - at artrepublic, we stockthousands of prints -including many limited editions and rare posters by some of today's most collectable artists. Search our artiststo view more.


SINGAPORE - A 32-year-old man was charged on Wednesday (April 18) with voluntarily causing hurt to Jurong GRC MP Tan Wu Meng during a Meet-the-People Session in Clementi.
Mohammad Ameen Mohamed Maideen is also accused of criminal trespass.
The court heard that on Monday, at around 10.10pm, Ameen entered a first floor unit at Block 334 Clementi Avenue 2.
Court documents stated that he grabbed Dr Tan forcefully around the neck, slammed him backwards against the wall, and punched him multiple times on his body.
Ameen is now remanded at the Institute of Mental Health, and will be back in court on May 2.
Dr Tan had given an account of the incident in a Facebook post on Tuesday. He wrote that a young man had rushed into the interview area during the MPS and started hitting him.
"I was with another resident, and suddenly found myself being hit and fell to the ground," he wrote, adding that the attacker was quickly restrained by residents and volunteers.
Dr Tan suffered bruises on his arm and abrasions on his neck as a result.
After a check-up at the National University Hospital, Dr Tan said he returned to the MPS to continue writing appeal letters for residents - including his alleged attacker.
If convicted of voluntarily causing hurt, Ameen may be jailed for up to two years, fined up to $5,000, or both. If convicted of criminal trespass, he can be jailed for up to three months, fined up to $1,500 or both.


text:
ROC President statements
International Olympic movement news
Russian Olympic movement news
Russian sports Federations news
Events with ROC support
Congratulations and awards
PyeongChang-2018 news
Buenos Aires-2018 news
ROC projects
About Buenos Aires 2018
Olympic Charter
Public commissions
ROC strategy
Honourable presidents
Honourable vice-presidents
Summer Olympic sports
Winter Olympic sports
Russian Olympic Committee Executive Board
Executive committee bureau
General director
President office
General Directorate for Participation in the Olympic Sporting Events
Event Marketing and Communications Department
Marketing and partner service Department
Department of Finance and Economics
Control Department
Department of programs in mass sports
Organizational Department
Sport for All Commission
Media Relations Commission (Press Commission)
International Activities Commission
Fair Play Committee
Commission on Awards
Commission on the implementation of the projects "Olympic Channel" and "Olympic Museum"
Membership Commission
Control Review Committee
Athletes' commission
Olympic Education Commission
Vinogradova O.L. – Doctor of Biological Sciences, Professor, Head of the Russian Federation State Research Center Institute of Biomedical Problems RAS (IBMP) laboratory.
Vice-Chairman
Grushin A.A. – Candidate of Pedagogical Sciences, Professor, Honored Coach of the USSR and Russian Federation, Deputy Head of the Main Directorate for Ensuring Participation in Olympic Sports Events of Russian Olympic Committee.
Sedykh E.E.– Head of the composite-analytical sector of the Main Directorate for ensuring participation in Olympic sports events at ROC.
Abalyan A.G. – Chief Expert of the Sports and Methodological Support expert section, Candidate of Pedagogical Sciences.
Berzin I.A. – Doctor of Medical Sciences, Professor, Head of the Department of Science and Innovative Technologies in Sports Medicine, FMBA Russia.
Buziashvili Y.I. – Head of the Health and Biomedical Support Expert Department, Academician of the Russian Academy of Sciences, Deputy Director of the Bakulev Scientific Center for Cardiovascular Surgery, Chief Cardiologist of Moscow.
Vasin V.A. – Adviser to the President of ROC on the implementation of the ″Sport for All″ program.
Golovachyov A.I. – Candidate of Pedagogical Sciences, Head of the Olympic Cyclic Sports Center FSBI Federal Science Center for Physical Culture and Sport.
Zholinsky A.V.– Candidate of Medical Sciences, Director of Sport Medicine Center of FMBA of Russia.
Leonov B.I. – Doctor of Technical Sciences, Professor, President of the Medical-Technical Academy of the Russian Federation, Director General of the All-Russian Scientific Research Institute of Medical Equipment.
Loginova V.V. – Head of the anti-doping support department and interdepartmental cooperation of the Ministry of Sport of the Russian Federation.
Lysenko E.A.– Candidate of Biological Sciences, acting Lead Researcher, Laboratory of Physiology of Muscular Activity at the State Scientific Center of the Russian Federation – Institute of Biomedical Problems of the Russian Academy of Sciences.
Myakinchenko E.B. – Doctor of Pedagogical Sciences, Head of the Federal Training Sport Center of the Representative Teams of Russia analytical center.
Ostroumov A.V. – Head of the Scientific and Technical Support expert department, Candidate of Physical and Mathematical Sciences, l Moscow University Institute of Mechanics leading programmer.
Parastaev S.A.– Professor, Doctor of Medical Sciences, Professor of the Department of Rehabilitation, Sports Medicine and Physical Education of the Pirogov Russian National Research Medical University.
Pendzyukh I.N. – Candidate of Technical Sciences, Research Institute of the Ministry of Defense of Russia, Senior Researcher of the Research Information Department, Specialist in Probability Theory, Mathematical Statistics and Mathematical Modeling of Technical Systems.
Polyaev B.A.– Professor, Doctor of Medical Sciences, Head of the Department of Rehabilitation, Sports Medicine and Physical Education of the Pirogov Russian National Research Medical University (RNRMU).
Pushkina T.A.– Deputy Head of the Department of Sports Medicine and Rehabilitation of the Federal Medical and Biological Agency of Russia.
Sonkin V.D.– Professor, Doctor of Biological Sciences, Head of the Department of Physiology at Russian State University of Physical Education, Sport, Youth and Tourism.
Tambovskiy A.N.– Doctor of Pedagogical Sciences, Professor, Pro-rector on scientific work at the Moscow State Academy of Physical Education.
Fomichenko T.G.– Doctor of Pedagogical Sciences, Director of the Department of Science and Education of the Ministry of Sports of the Russian Federation.
Cherkashin V.P. – Doctor of Pedagogical Sciences, Professor, Head of the Scientific and Methodological Department of the ROC Olympic Preparation Supporting Department.
Shakhnazarov A.A. – Candidate of Physical and Mathematical Sciences, Head of the Laboratory of Biomechanics, Institute of Mechanics at Moscow State University.


text:
Il femminismo in Corea del Sud nacque durante gli anni del colonialismo giapponese (1910-45). Nonostante le diverse lotte sociali sostenute dai movimenti al suo interno, le donne entrarono ufficialmente a far parte della società nel 1948, quando il suffragio femminile venne incluso nell'articolo undici della Costituzione nazionale. La Costituzione diceva "Tutti i cittadini sono uguali davanti alla legge, non vi devono essere discriminazioni politiche, economiche, sociali o culturali riguardanti il sesso, la religione o lo status di una persona".

Il femminismo riuscì ad emergere nonostante i drastici cambiamenti economici, implementati grazie alla industrializzazione economica e alla globalizzazione; i valori culturali sudcoreani invece subirono pochi cambiamenti.

Storia
Mentre oggi in Corea del Sud sono presenti alcuni movimenti femministi fondati prima della seconda guerra mondiale e dopo il 1945, molti di questi gruppi non erano focalizzati solo sui diritti delle donne fino alla metà del 1980. Il femminismo contemporaneo, presente in Corea, può ricollegarsi al movimento Minjung Feminism, nato durante la colonizzazione ovvero tra il 1910 e il 1945. L'inizio di questo movimento è caratterizzato da un aspetto molto importante: le lotte delle lavoratrici per i sindacati democratici. Esso è inoltre sezionabile in quanto esistono diversi aspetti del femminismo; quello teorico, pratico e organizzativo.
Il Minjung Feminism esercitava una maggiore influenza sulle intellettuali e organizzatrici femministe. Tra le più importanti troviamo Choi Soon Young e Hang Mi Young che vinsero la posizione di legislatori regionali.
Questa corrente di pensiero nel 1970 venne brevemente influenzata dai movimenti femministi occidentali, in particolar modo da quello statunitense. Tuttavia, nel 1980, organizzazioni di donne radicali cominciarono a resistere all'influenza del femminismo americano concentrandosi soprattutto su questioni come diritti umani e sulla riunificazione piuttosto che uguaglianza di genere. Sotto l'oppressiva occupazione nipponica che occupò la Corea del Sud dal 1910 al 1945, le donne coreane aderirono attivamente alla lotta nazionalista e formarono organizzazioni segrete sotterranee, di cui le più importanti la Songjuk-Hoe (1913) e la Kun'u-Hoe (1927).  Quest'ultima ha annunciato in una conferenza del 1928 l'indipendenza nazionale come obiettivo primario dell'organizzazione.

Le studentesse femministe concordarono sul fatto che queste organizzazioni segnalarono l'inaugurazione di un movimento coreano organizzato da donne, come il movimento Minjung anch'esso iniziato come risposta al colonialismo giapponese, si ripropose successivamente tra il 1961 e il 1992. Questo movimento ha combattuto per la liberazione dall'oppressione del lavoro forzato e ad esso contribuirono studenti, provinciali, lavoratori e intellettuali. Durante gli anni tra il 1961 e il 1979, sotto il regime del generale Park Chung Hee, il lavoro femminile (o Yo'Kong) era svolto da ragazze provenienti per lo più dalle provincie che furono costrette a lavorare in fabbriche di tessuti, elettronica, indumenti, materie plastiche e alimentari. Queste donne soffrivano date le difficili condizioni lavorative infatti i loro dormitori erano costituiti da materassi condivisi e situati all'interno della fabbrica, venivano pagate con bassi salari e spesso venivano molestate sessualmente.

Per la prima volta nella storia della penisola nel 1972 una donna fu eletta come presidente del movimento di unione democratica e lo mantenne in vita per i sei anni successivi, prima che esso venga ufficialmente chiuso dal governo. Nel 1980 sotto il generale Chun Doo Hwan venne sciolto un altro importante movimento, il Chunggye Pibok. A metà degli anni '80 vi fu anche un periodo di turbolenza politica e di riforme: la partecipazione delle donne nei movimenti studenteschi e nei sindacati rafforzò il movimento femminista.  In questo periodo inoltre si assiste alla creazione di un istituto di ricerca femminile fondato dall'Ewha University ovvero la prima università femminile coreana. Nel 1985 vi fu un dibattito nazionale femminista il cui tema era "Il Movimento Femminile in unione con il Movimento Democratico Nazionale Minjung." Successivamente nel 1986, date le torture e gli stupri subiti dalla lavoratrice Kwon In Suk da parte della polizia di Buchon, le donne si unirono e formarono il movimento KWAU (Korean Women's Associations United) che fu creato dall'unione di altre 33 organizzazioni. La partecipazione del Korean Women's Association United in proteste nazionali ha forzato il generale Chun Doo Hwan a dimettersi, ed il suo successore a indire delle elezioni presidenziali dirette.

Dal 1987 le donne costituivano il 55% della forza lavoro, il servizio delle industrie aveva la più alta percentuale femminile di lavoratori se comparato con il settore dei servizi, degli impiegati e quello manifatturiero. Nello stesso anno venne fondata la KWWA (Korean Women Workers Association) in risposta alla discriminazione di genere nella forza lavoro, questa associazione fu essenziale per proseguire la campagna sui diritti delle donne dopo la riforma democratica e politica che avvenne nel paese. Tutt'oggi il KWWA combatte per una giornata lavorativa di otto ore, salari più alti, protezione della maternità, porre fine alla discriminazione sessuale sul posto di lavoro e anche alla violenza sessuale contro le donne in Corea. Le sue sedi sono sparse su tutto il territorio coreano; sono principalmente a Seoul, Pusan, Buchon, Inchon, Changwon, Masan e Kwanju. I movimenti femministi sono stati di vitale importanza per portare alla luce i crimini commessi contro le donne nelle forze armate e hanno fornito supporto per le comfort women. Tra queste donne le superstiti provenivano per lo più dalla Corea e da altri territori occupati dall'Impero giapponese come le Filippine e il Taiwan. Grazie alle comfort women il centro di soccorso coreano contro la violenza sessuale e le Associazioni Femminili Unite riuscirono a presentare una testimonianza alla commissione diritti umani delle Nazioni Unite nel 1993. Tale testimonianza comprendeva anche le loro richieste per porre fine alla violenza subita dalle donne in campo militare e durante la guerra.

Il KWAU
La KWAU o Korean Women's Association United venne fondata nel febbraio del 1987. Era costituita dall'ala femminista sinistra pro-lavoratrice risvegliata dalle accuse di molestie sessuali portate da Kwon In Suk contro il governo coreano. Le donne coinvolte erano un gruppo diverso di operaie, impiegate, casalinghe, studentesse universitarie e donne povere e rurali che abitano in città.

KWAU era collegata al movimento Minjung e anche al Movimento Nazionale Democratico. Inizialmente vi erano 21 associazioni in corea del sud che successivamente si unirono per creare la Korean Women's Association United. Alcune delle organizzazioni originali del KWAU includevano l'Associazione della Democrazia Femminile, la Korea Women's Hot Line, la Women's Newspaper (ora chiamato Women's News), la KWWA, la Korean Catholic Farmers, la Women's Committee e altre. La KWAU era particolare perché al contrario degli altri gruppi femministi, prendeva posizione contro lo stato repressivo di Chun Doo Hwan. Questa associazione aiutò le organizzazioni individuali sotto il suo patrocinio ad ottenere supporti finanziari, condusse riunioni a nome dei gruppi e organizzò corsi di leadership.

 Korean Women's Association United lavorò non solo per portare le donne sullo stesso piano degli uomini, ma anche per trasformare le strutture sociali che le opprimevano. La KWAU aiutò a promuovere il congedo per maternità, la risoluzione dei problemi per la cura dei bambini e la distribuzione di uguali paghe per uguale lavoro. La Korean Women's Association United fu anche attiva come riferimento per gli atti di violenza contro le donne. Nell'aprile del 1992, formò una speciale commissione per la legislazione di una legge speciale per la violenza sessuale. Questo portò all'annuncio del governo di "Sostanziali proposte contro la violenza sessuale includendo la legislazione di una legge speciale".

Questa organizzazione pose l'attenzione anche alla partecipazione delle donne a rappresentazione della politica locale. Entro il 1995, la KWAU portò ad un significativo incremento della partecipazione femminile in politica attraverso il reclutamento e la promozione di candidati di sesso femminile; quattordici su diciassette candidate furono elette quell'anno. Sempre nel 1995, alla KWAU fu garantito lo stato legale da parte del governo.

Il KWWA
La KWWA (Korean Women Workers Association o Han'guk Yosong Nodongjahe) è un'organizzazione in Corea del Sud, dedicata a lavorare sui problemi di uguaglianza e a sostenere le donne sul posto di lavoro. Ha lavorato attivamente per migliorare la condizione delle donne nella società coreana, ed ha fornito un sistema di formazione della leadership.

Questa organizzazione controlla anche gli effetti delle politiche di governo sulle donne nel mondo del lavoro. Prima che cambiasse il suo nome, KWWA era la prima associazione delle lavoratrici in Corea del Sud. È un'organizzazione indipendente, fu uno dei primi gruppi a essere inclusi sotto l'organizzazione ombrello dell'associazione unita delle donne coreane (KWAU). In Corea del Sud, prima delle riforma in campo lavorativo, le donne sposate o che avevano dei bambini erano costrette al ritiro. La KWWA è stata fondata nel 1987, al fine di organizzare la presenza delle donne nei sindacati istituzionali, tale sforzo era indirizzato per lo più a tutti i sindacati maschili che ignoravano le riforme, nonostante molte donne ne avessero già aderito. Inoltre per organizzare i colletti blu, l'organizzazione aiutò coloro che erano disoccupati, trovando per loro dei lavori domestici ed altri lavori informali.

Poco dopo la sua creazione, la KWWA ha giocato un grande ruolo nel sostenere l'atto di eguale passaggio nel 1987. Nel 1989,  ha inscenato una protesta occupando una fabbrica a Masan. Anche nel 1980, questa associazione era responsabile di alcune fabbriche della Nike, decise però di alzare i salari dei lavoratori nelle strutture di loro proprietà. Nel 1990, hanno aiutato a ottenere la legge sulla cura del neonato.  Nel 1993, sul posto di lavoro, ha avuto uno scontro con i centri di guardia in costruzione li vicino. Nel 1996, un ex lavoratrice appartenente al Comitato delle Donne Asiatiche (CAW), Maria Chol-Soon Rhie, divenne il capo dell'organizzazione. KWWA è stato un esempio per altri paesi asiatici che cercavano di migliorare l'uguaglianza sul lavoro. Nel 2007, l'organizzazione KWWA ha celebrato il suo 20º anniversario.

Le Comfort Women
Le Comfort women o donne del comfort erano ragazze costrette a far parte dei corpi di prostitute creati dall'Impero giapponese. I documenti presenti in Corea del Sud affermano che tale organizzazione non fosse volontaria, e dal 1989 diverse donne testimoniarono che furono rapite dai soldati giapponesi.

Il Femminismo moderno

Ci sono generalmente due tipologie di movimenti femminili in Corea, quello radicale e quello riformista. Questi due termini sono diversi nel contesto sudcoreano rispetto al contesto femminista americano o Occidentale. I movimenti femministi della Corea del Sud si concentrano soprattutto sulla modifica del ruolo delle donne nella società. Questi movimenti assomigliano più al femminismo americano, in quanto i loro metodi comprendono attività di lobbying, e l'influenza dei politici e di riforme. Questi gruppi sono i più conosciuti e sono costituiti da donne della classe media che parlano sia coreano che inglese. La maggior parte di essi sono affiliati con il Council of Korean Women's Organization (CKWO); alcuni esempi di organizzazioni conosciute sono: la Young Women Christian Association (YWCA);  stabilitasi in corea nel 1922, il centro coreano per diritto alla famiglia fondato nel 1954; la Business and Professional Women (BPW); la Korean Association of University Women (KAUW); la Korean National Mother's Association (KNMA) fondata nel 1958 e la federazione coreana delle casalinghe (KFHC) fondata nel 1963.

Le ultime due organizzazioni sono le più grandi avendo rispettivamente 40.000-50.000 membri la prima e oltre 180.000 membri la seconda. La KFHC e la KNMA supportano le modifiche della legge familiare e l'Equal Employment Opportunity Act, che è stato approvato nell'aprile del 1988 e comprende l'uguaglianza per le donne nel collocamento, nelle promozioni, nel pensionamento, nella formazione al lavoro e concede l'indennità per il congedo di maternità. I gruppi radicali hanno criticato questa legge affermando che non ha un "meccanismo per implementazione", mentre i riformisti hanno indicato l'atto come un primo passo e un segno di incoraggiamento per le riforme a venire. Gli sforzi dei gruppi riformisti per cambiare la legge famigliare sudcoreana raggiunsero il culmine con il cambiamento del regime di custodia dei bambini nel 1991, ovvero venne cambiata la legge che dopo il divorzio i bambini dovessero andare obbligatoriamente a stabilirsi col padre.

I movimenti radicali femminili in Corea del Sud si concentrano su questioni riguardanti i diritti umani, molti di questi gruppi sono stati formati durante la fine degli anni '80 in contrasto con i più grandi gruppi riformisti. Si tratta per lo più di questioni come la riunificazione con la Corea del Nord e la prevenzione della tortura dei prigionieri. I metodi includono scioperi, marce e manifestazioni pubbliche. Si può affermare che la parola radicale è usata dato il contesto della società coreana che è molto più oppressivo e conservatore rispetto alla società Occidentale. I gruppi radicali sono anche più giovani rispetto ai riformisti e si compongono di solito da donne ben istruite, della classe media che preferiscono parlare solo coreano, esse di solito sono affiliate con il KWAU. Esempi di organizzazioni radicali sono: la Società delle Donne per la Democrazia che venne fondata nel 1987; Women's Hotline fondata nel 1983, Women's Newspaper fondata nel 1986; Korean Women's Worker Association (KWWA); Korean Catholic Farmers e molte altre organizzazioni religiose.

La società delle Donne per la Democrazia ritiene che le questioni dei diritti umani hanno la precedenza su quelle per la parità dei sessi, mentre l'organizzazione delle Women's Hotline in Seoul si concentra soprattutto su problemi di stupro, prostituzione, discriminazione sul lavoro e abusi domestici. Un'altra importante organizzazione che non è affiliata con i gruppi radicali e riformisti sudcoreani è la Korean League of Women Voters, recentemente le sue attività sono aumentate per incoraggiare la partecipazione femminile tra gli elettori.

Il femminismo in corea del sud è stato diviso anche tra socialismo e marxismo. Le femministe socialiste si concentrano sugli effetti del patriarcato e problemi di genere mentre le femministe marxiste guardano al divario delle classi, ai diritti della donna, alle oppressioni e si concentrano principalmente sui poveri rurali e urbani. Sia le organizzazioni socialiste che quelle marxiste sono combinate per formare una cultura alternativa e centri di ricerca per gli studi femminili in Corea.

Il diritto della famiglia e il confucianesimo sottolineano i rapporti patriarcali in Corea. Molte donne ancora oggi sono limitate nella loro opportunità di lavoro date le aspettative della penisola, nonostante la forte influenza femminista occidentale nel 1970. Il femminismo coreano ha resistito all'influenza americana con la nascita di gruppi femministi radicali, organizzazioni per i diritti delle donne, che sono divise in due categorie: quelli che combattono per i diritti umani e allo stesso tempo per le questioni di genere e altri che si concentrano su questioni dei diritti specifici femminili e sono pro-governo.

Note

Bibliografia

Altri progetti

Corea del Sud
Corea del Sud

redpajama_set_name: RedPajamaWikipedia


Hohensalzburg Fortress looms over Salzburg's floodlit old town. The home of Mozart and (much) more recently "The Sound of Music", Salzburg is a very interesting stop in Austria.
Date Uploaded: April 12, 2015, 5:22 p.m.


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Евклідова відстань (Евклідова метрика) — формула традиційної відстані між двома точками  та  для Евклідового простору:

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Пов'язана з нею норма називається — Евклідова норма.

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Метрична геометрія


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Category: Bonnie McKee
Home Artists Archive by Category "Bonnie McKee"
Bonnie McKee Debuts Voyeuristic Music Video for "Thorns" Shot Entirely on VHS
September 14, 2017 Nicole GovelArtists, Bonnie McKee, Music, New Video, VIDEOBonnie McKee, music, Music Video, Music Video Promotion, new, New Music, new music video, video
Trendsetter is thrilled to be working with Bonnie McKee again on the sultry, voyeuristic video for "Thorns." Shot entirely on VHS through the POV of an unidentified cameraman (Director Darren Craig), we experience a coy seduction with a playful dash of danger, transporting us back to the grungy aesthetic of 90's cable a la COPS. Watch the…
Bonnie McKee and Trendsetter Together Again!
June 21, 2016 Amanda WilligBonnie McKee, MusicBonnie McKee, I Want It All, Music Video
We are so happy to be working with Bonnie McKee again for her new music video "I Want It All"! Bonnie debuted the video today and we absolutely love it! Watch HERE! More Info: Bonnie McKee began her musical pursuits at an early age. First Inspired by the theme songs she heard on TV. "I was…
Katy Perry's co-writer, Bonnie McKee steps out on her own with "American Girl" video
July 23, 2013 AllieBonnie McKeeadam lambert, american girl, bonnie, epic records, katy perry, kesha, mckee
Trendsetter's newest client, Bonnie McKee recently debuted the new video for "American Girl" on VEVO. The track "American Girl" serves as the debut single off her highly anticipated major label debut album, which will be available later on this year via Epic Records. The video, directed by Justin Francis, follows Bonnie and some friends as they embrace a perfect summer…


Mobile devices have changed the way we interact with each other, but also brands and companies. Smartphones in particular have become ubiquitous in our lives and ever more consumers are using their handhelds in-store to research products and compare prices (63%).
This has enhanced the shopping experience for the consumer, but at the same time opened up opportunities for retailers.
According to a new study by BRP Consulting, 33% of consumers frequently use their mobile devices to make a purchase, whilst 41% are planning to do so over the next 24 months.
When in-store, 34% of respondents said they used their phone to compare prices whilst 28% looked for offers and coupons online.
Interestingly, 44% of consumers would also be interested in shopping with retailers which offer self-scanning apps to check out with minimal assistance. However, just 8% of retailers were offering scan-and-pay (POS) solutions in 2018, up to 22% in 2019.
Retailers however have picked up on the mobile trend and are implementing more information into their mobile services including enhanced product information, mobile coupons, mobile loyalty services, prior purchase visibility and shopping lists.
Three-quarters of retailers also plan to provide mobile solutions to their associates to boost the consumer experience over the next three years.
However, 72% of retailers do not currently have solutions installed that could help identify loyal customers.


Let me first say that I think Job's friend is off base on the thinking that Job had caused his calamity from sin. Does sin sometimes result in consequences ? Yes..but not in this case. We can't label everything so broadly. We live in a fallen world where tragedy strikes the innocent. However not all of what Job's friends say in chapter 5 is wrong. There is some good stuff in there…I especially love "so the poor have hope and injustice shuts its mouth." Did he have bad advice? yes..but he also seems to know something about God and His ways.
Poor Job..You can just feel his pain can't you? The despair..the anguish…the hopelessness. As I read this, I can't help but think of Haiti and how those same feeling must be there. Friends, let's be earnest in our prayers. Let's ask the God of all comfort to be there in Haiti.
As we speak about hope, let me share some pictures of the new Hannah's Hope. The kids are so blessed to be staying at a wonderful place thanks to all of the supporters of Hannah's Hope Ethiopia.
Thanks to Kim Wenzel for sharing her pictures.
If you'd like to learn more about Hannah's Hope you can visit All God's Children and if you'd like to support Hannah's Hope by sending supplies, send me an email at gcknight@verizon.net and I will gladly help you!
I'm always trying to 'be good' in exchange for God's grace - and then kicking myself for thinking this, and then asking God to please... please, please don't give me what I deserve.... it's a cycle with me!


The a la carte restaurant Austria is located on the ground floor right next to the main reception with fountain view, and offers a variety of drinks and delicious dishes of local, international and vegetarian cuisine.
The warm welcome atmosphere and selected wine selection will make you happy.
The Bosna Restaurant is intended for serving meals for hotel guests in a beautiful atmosphere with a rustic interior and park view.
Room service is available with supplement.
Working hours from 07:00 to 23:00.


text:
package org.engine.component;

import java.io.EOFException;

import org.engine.app.GameAble;
import org.engine.core.Interactable;
import org.engine.rendering.RenderingEngine;
import org.engine.utils.Maths;
import org.lwjgl.util.vector.Matrix4f;

import glib.util.IDGenerator;
import glib.util.vector.GMatrix4f;
import glib.util.vector.GVector3f;

public abstract class GameComponent implements Interactable{
	private int			id	= IDGenerator.getId();
	private GVector3f	position;
	private GVector3f	rotation;
	private GVector3f	scale;
	private boolean		dead;
	private boolean		active;
	private boolean		change;
	private GameAble	parent;

	//CONSTRUCTORS

	public GameComponent(GameAble parent) {
		this(parent, new GVector3f(), new GVector3f(), new GVector3f(1));
	}

	public GameComponent(GameAble parent, GVector3f position) {
		this(parent, position, new GVector3f(), new GVector3f(1));
	}

	public GameComponent(GameAble parent, GVector3f position, GVector3f rotation, GVector3f scale) {
		this.position = position;
		this.rotation = rotation;
		this.scale = scale;
		this.parent = parent;
		active = true;
		dead = false;
	}

	//OTHERS

	public void move(GVector3f vec){
		if(vec.isNull())
			return;
		change = true;
		position = position.add(vec);
	}

	public void rotate(GVector3f vec){
		if(vec.isNull())
			return;
		change = true;
		rotation = rotation.add(vec);

	}

	//GETTERS
	public String 	 getData(){return position + " " + rotation + " " + scale;}
	public GVector3f getPosition() {return position;}
	public GVector3f getRotation() {return rotation;}
	public GameAble  getParent(){return parent;}
	public GVector3f getScale() {return scale;}
	public int 		 getId(){return id;}
	public boolean   isDead() {return dead;}
	public boolean   isActive() {return active;}
	public boolean 	 isChange() {return change;}

	public GMatrix4f getTransformationMatrix(){
		Matrix4f trans = Maths.createTransformationMatrix(position, rotation, scale);
		return Maths.MatrixToGMatrix(trans);
	}

//	public GVector3f getForwardVector(){
//		double x = Math.cos(Math.toRadians(360-rotation.getY())) * Math.cos(Math.toRadians(rotation.getX()));
//		double y = Math.sin(Math.toRadians(360-rotation.getY())) * Math.cos(Math.toRadians(rotation.getX()));
//		double z = Math.sin(Math.toRadians(rotation.getX()));
//		return new GVector3f((float)y,(float)z,(float)-x).Normalized();
//	}

	//SETTERS

	public void setPosition(GVector3f position) {this.position = position;}
	public void setRotation(GVector3f rotation) {this.rotation = rotation;}
	public void setActive(boolean active) {this.active = active;}
	public void setChange(boolean change) {this.change = change;}
	public void setScale(GVector3f scale) {this.scale = scale;}
	public void setDead(boolean dead) {this.dead = dead;}

}


text:
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Posted on August 21, 2012 by Regan Zambri Long PLLC
Posted by: Salvatore J. Zambri, founding member and partner
Police have identified two victims who were killed in the CSX train derailment, which occurred in downtown Ellicott City overnight. According to police, Elizabeth Conway Nass and Rose Louese Mayr, both 19, of Ellicott City, were on the tracks when a freight train came off the tracks around midnight.
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I'm with you 100% of the way about punctuality. Why do some people arrange to meet at a time they have no intention of achieving, or are incapable of achieving? Like you, it annoys me when one makes an appointment with a doctor or some other "professional" and have to wait as thought their time is valuable but your's is not.


The course is aimed at teachers with a responsibility for computing. It will be delivered by IBM professionals alongside teachers from the award winning London Connected Learning Centre.
A free introductory session on Artsmark for teachers from all phases.
Tuesday the 23rd May 1pm-4.30 pm. £80.00 instead of the usual fee of £140.00.
Update: This cancelled through unforseen circumstances!
Through practical workshops, this day will provide you with an introduction to Performance-Parkour as a way of generating dance material and developing creativity in a new dance style that is appealing to young people and boys.
Worried about the impact of cuts on your organisation? Not sure how to navigate your way forward? This workshop will help you get started.
Are you looking for creative, affordable, and easy ways to incorporate technology into your own teaching or workshop practice?
Free event for school staff to hear about the new report from the Communications Trust from their Director, Octavia Holland.
Needing some inspiration for your vocal group work and new group singing ideas to incorporate into your practice? This one-day course, led by Pete Churchill, is the singing boost you need!
One day training. Not sure what Arts Award is about? see more on our website.
This professional development opportunity for primary and secondary school teachers is a practical introduction to cross-arts performance making with young people. Delivered by professional artists from Trinity Laban Conservatoire of Music and Dance, the session will explore creative methods of progressing young people through rehearsal to a high-quality music and dance performance.
This professional development day is for education/project managers in arts and cultural organisations, music education hubs and others who are interested in developing new ways to engage with music in schools at Key Stage 3.
What role do the arts and music education play in our work with early years and families in challenging circumstances? What barriers do children in early years and their families face to accessing arts activities?