text:
# Directory tex-archive/macros/latex/contrib/gatech-thesis

This is the README file for the GATECH-THESIS class for LaTeX.
It corresponds to version 1.5 of the GATECH-THESIS class
(17 August 2002)

GATECH-THESIS may be obtained from any of the following locations:

this is where the official version, approved by the Georgia
Tech Office of Graduate Studies, may be found.  Do NOT
attempt to use the old, out-of-date, LaTeX2.09 style file
(gtthesis.sty) that is STILL on cyberbuzz.

http://www.neuro.gatech.edu/users/cwilson/gatech-thesis/
will always be here.

http://www.ctan.org/tex-archive/macros/latex/contrib/supported/gatech-thesis/
and of course, CTAN.

This class file can be used with the LaTeX typesetting system
to produce dissertations that adhere to Georgia Tech's guidelines
for publishing.

There are a number of files within this archive.  The important
ones are

gatech-thesis.cls
gatech-thesis.bst
gatech-thesis-gloss.sty
gatech-thesis-losa.sty
gatech-thesis-losa.bst
gatech-thesis-index.sty
gatech-thesis-index.ist

Everything else is fluff: examples, licensing, documentation...

=============================
Using the GATECH-THESIS class
=============================

INSTALL.  Take a peek a NEWS, and then (maybe) CHANGES.
Then you can worry about the examples...

Sample File
-----------

example-thesis.tex + example-thesis.bib

There is a sample dissertation (by the fictitious, but very
irritating, Perry H Disdainful) in the file example-thesis.tex.  It
also uses example-thesis.bib as its bibliography database (though
the contents of the database are not important).  Mostly this is
useful as an example of how to produce the front matter.  If you
don't understand LaTeX at all, this file might help you get started,
but, since you're going to be writing a 100+ page document, you
should invest in a copy of the LaTeX manual (by Leslie Lamport, the
original author of LaTeX). This has recently been updated for
LaTeX2e (1, below).

The LaTeX Companion, by Goossens, Mittelbach, and Samarin (who have been
involved in developing and supporting LaTeX2e) is also quite good.  It
gives a lot of useful information if you are going to be writing or
modifying classes, and gives a lot of additional information on commonly
available style packages (2, below).

Helpful books (in no particular order):
(1) "LaTeX: A Document Preparation System" by Leslie Lamport
(2) "The LaTeX Companion" by Goossens, Mittelbach, and Samarin
(3) "A Guide to LaTeX" by Helmut Kopka and Patrick Daly
(4) "LaTeX: Line by Line" by Antoni Diller
(5) "The LaTeX Graphics Companion"
(6) "The TeXbook" by Donald Knuth

Larger Sample
-------------

julesverne/basic/*

This is a slightly more complicated, multi-file example.  The text
is taken from the first five chapters of the Project Gutenberg edition
of Jules Verne's 20,000 Leagues Under the Sea'' and is freely
redistributable as long as the complete text, 2000010.txt, accompanies
the other excerpts. The original document is also available here:
http://promo.net/pg/
ftp://ibiblio.org/pub/docs/books/gutenberg/etext94/2000010.txt
This example can be built with either latex (to generate a .dvi file) or
with pdflatex (to generate a .pdf file).

Gory, all-the-bells-and-whistles example:
------------

julesverne/bellswhistles/*

This directory contains a reworked version of the jules-verne
example "thesis".  However, all of the bells and whistles
provided by the gatech-thesis.cls class and associated styles
are exercised, along with some suggestions for thesis document
structuring.

Features:
*)  segregating preamble code into a document-specific style
*)  How to easily generate OGS format complant documents
and prettier, "personal" copies.
*)  Support for using hyperref (clickable links in the TOC,
when making a .pdf)
*)  Using postscript versions of fonts other than Computer Modern,
like Times, Courier, etc.  See extensive comments in
jules-verne.sty.
*)  Using the listings package for including program code
in appendices
*)  Using the add-on style gatech-thesis-gloss.sty for
generating a glossary
*)  Using the add-on style gatech-thesis-losa.sty for
generating a "List of Symbols or Abbreviations"
*)  Using the add-on style gatech-thesis-index.sty for
generating an index.  Typically a GT thesis doesn't
have one of these, but the style is provided just in case.
*)  Demonstrate the multivolume support, for those theses that
are over 2.5" thick (according to OGS Guidelines).
*)  Using \include instead of \input to incorporate subsidiary
files into the main document.  This lets you use \includeonly
to speed development of your document.

system, before you can compile it.  See the local documentation,

NOTE: The julesverne directory is not available in the CTAN version of
gatech-thesis. It can be obtained from the Georgia Tech version at

Building the Examples
---------------------

To compile the examples, you must first install the gatech-thesis
files (see the INSTALL document).  Also, the bells-and-whistles
example needs some additional preparation; see its local documentation

However, once you have all of the required items installed, you can
build the simplest example by executing the following commands:

latex example-thesis.tex
bibtex example-thesis
latex example-thesis.tex
latex example-thesis.tex
dvips example-thesis
(generates a postscript file)

To build the other examples, run the DO_* scripts.  For instance,
if you are using a unix or unix-like system, cd to the julesverne/basic
directory and execute:

./DO_postscript.sh

to generate a postscript output (or ./DO_pdf.sh to generate a pdf).
If, on the other hand, you are on a DOS-ish system, the execute

DO_postscript.bat

(or DO_pdf.bat)  To understand what the scripts do (especially the
ones in the julesverne/bellswhistles/ directory) you really ought

Choosing the GATECH-THESIS class
--------------------------------

To use the GATECH-THESIS class, make sure that the gatech-thesis.cls
file is on your TEXINPUTS search path and use the following command
at the start of your input file:

\documentclass{gatech-thesis}

To insure that gatech-thesis.cls is on your TEXINPUTS search path,
you can copy it into your localtexmf tree and then update the file
database; or you can place it into the same directory as your
thesis .tex files themselves.  This is also described in the INSTALL
document.

=================================
What the GATECH-THESIS class does
=================================

The GATECH-THESIS class builds on the the standard LaTeX REPORT class,
and is accepted for use with Georgia Institute of Technology PhD
dissertations and Masters theses.  The available commands are almost
identical to those of the REPORT class, so your best starting point
for documentation is the LaTeX manual written by Leslie Lamport.

The key features of the class are:

1) The primary modification to the REPORT class is the use of
pseudo-double-spacing, since Georgia Tech's rules are still designed
for typewriters.  This is achieved by increasing the \baselinestretch
parameter to 1.33.  The \baselinestretch is returned to a
single-spaced value of 1.00 for elements like tables, captions, and
footnotes and for all displayed text (quote, quotation, and verse
environments).

2) Margins are 1.5" on left, 1" on top, right and bottom (headers &
footers 1/4" from body)

3) Use 11 point by default; you can use the 10pt or 12pt options

4) Page numbers are in the center at the bottom of the page

5) Complete, correct front matter for Georgia Tech dissertations can
be generated.

Options
---------------

There are a number of primary options.  However, if called without
any options, the approved format -- 11pt, letterpaper, oneside,
doublespaced, normalmargins, final -- will be generated.

Any standard option for the LaTeX2e report' class, including
10pt', 11pt', 12pt', oneside', twoside', etc. is valid.

singlespaced', oneandahalfspaced', or doublespaced':
Set the entire document's default line spacing, except for
notes, which are single-spaced by default.

spacednotes':  Let the line spacing of notes be determined
by the line spacing of the main document, instead of being
forced single-spaced.

normalmargins', narrowmargins', widemargins', extrawidemargins'
or oldmargins':  normalmargins is the default and Georgia Tech-
approved format.  Oldmargins is the OLD Georgia Tech format.

draft':  Produce a draft copy (10pt font, double-sided,
double-spaced, normal margins, with the word DRAFT'' printed
at all four corners of every page, and current date printed in

final': style uses the correct pseudo-double-spacing.  This option
is the default and is redundant, but is included for symmetry.

hyperref': Indicates that the document will \usepackage{hyperref}.
This is a kludge, but I didn't want to explicitly *require*
hyperref, so we must indicate to gatech-thesis.cls whether it should
define certain hyperref commands as dummies.  ALWAYS use this
option if you use the hyperref package.  NEVER use this option if
you do not also use the hyperref package.

The options are selected on the \documentclass line, e.g.:

\documentclass[10pt,hyperref,draft]{gatech-thesis}

Thus, the default options:
\documentclass[11pt,letterpaper,oneside,
doublespaced,normalmargins,final]{gatech-thesis}
will generate a document that conforms to the graduate studies office
and is identical to setting no options at all
\documentclass{gatech-thesis}

------------

If you want to use page headers or footers other than the default
ones, you should try using fancyheadings.sty''.  It is easy to use,
widely distributed, and well documented.  However, the default headers
and footers are the Georgia Tech-approved ones.  There are also
some interesting variations defined within the gatech-thesis.cls
itself (tcplain, gtthesis), but those should ONLY be used for personal
copies, and NOT for your official version.  See the
julesverne/bellswhistles example.

============
Front matter
============

The other key service provided by this class is that it generates
correct front matter (title page, approval page, dedication, etc.) with
a fairly simple set of commands.  The format of the front matter is
specified quite explicitly in the document Manual for Graduate Theses:
Georgia Institute of Technology'' distributed by Office of Graduate
Studies.

A complete example of the use of the front matter commands can be
found in any of the examples distributed with the class
(example-thesis.tex or julesverne/basic or julesversion/bellswhistles).

Declarations
------------

To use the front matter macros and environments, you must first
declare a number of text strings within the preamble of your document
(that is, these must be declared BEFORE the \begin{document} command.)

\title{...}         Dissertation title

\author{...}        Your name as registered with Georgia Tech

\department{...}    Specify the name of the graduate department.
\dept{...}    synonym

\degree{...}        Title of your degree (e.g. Doctor of Philosophy'')

commands may be ommitted -- but your signature page will look a little
silly if you don't include SOME names.

\committeechair{...}   Name of your committee chairperson

\firstreader{...}   Name of other committee member
\secondreader{...}  Name of other committee member
\thirdreader{...}   Name of other committee member
\fourthreader{...}  Name of other committee member
\fifthreader{...}   Name of other committee member
\sixthreader{...}   Name of other committee member

\bibfiles{...}      List of files to use when generating a bibliography

\submitdate{...}    Specify the month year'' in which dissertation
submitted

\linespacing{...}   Use this to override the default double-spacing.
NOT recommended; the default is approved by the
Graduate Studies Office.  For draft/personal copies,
use the draft'' or singlespace'' options in your
\spacing{...}       compatibility synonym

Switches
------------

Also, there are a number of true/false'' flags that can be used to
control the frontmatter generation.  However, the defaults will result
in the approved Georgia Tech format.  These flags, if specified, should
also be in the document preamble (BEFORE the \begin{document} command).

\titlepagetrue or \titlepagefalse
- produce or don't produce a title page (TRUE by default)

\signaturepagetrue or \signaturepagefalse
- produce or don't produce a signature page (TRUE by default)

- place or don't place a copyright notice on the title page
(FALSE by default)

\figurespagetrue or \figurespagefalse
- produce or don't produce a List of Figures page (TRUE by default)

\tablespagetrue or \tablespagefalse
- produce or don't produce a List of Tables page (TRUE by default)

\contentspagetrue or \contentspagefalse
(TRUE by default)

\bibpagetrue or \bibpagefalse
- produce or don't produce a Bibliography page (TRUE by default)

\thesisproposaltrue or \thesisproposalfalse
- indicate Thesis Proposal'' or Thesis'' on the title page
(FALSE by default -- e.g. default is to say Thesis'')

- display DEDICATION'' heading on the dedication page
(FALSE by default)

\strictmarginstrue or \strictmarginsfalse
- if true, then obey the margin rules EVEN on the title and
signature page. Default TRUE and REQUIRED by Graduate Studies
Office, but not very appealing.  (under oldmargins'' an extra
50p spacing is added so that the title page looks like the
chapter headings.  In any case, \strictmarginsfalse looks better
for personal copies but \strictmarginstrue is necessary for
official ones.

\multivolumetrue or \multivolumefalse
- if true, indicates that the thesis will span multiple volumes.
triggers automatic generation of the first volume title page
(in addition to the entire work'' title page), but it''s up
to you to place the part{}'' commands in the appropriate
locations for volume 2, volume 3, etc.

Frontmatter Environments
------------------------
GATECH-THESIS provides a number of specialized environments for the
various frontmatter sections.  Of course, you don't have to use them
all.  The provided environments include

dedication:        \begin{dedication}
text here
\end{dedication}

preface:           \begin{preface}
text here
\end{preface}

acknowledgements:  \begin{acknowledgements}
text here
\end{acknowledgements}

abstract:          \begin{abstract}
text here
\end{abstract}

summary:           \begin{summary}
text here
\end{summary}

And if that isn't enough for you, you can add your own:
\prefacesection{other-title}{...text...}
Note that these add-a-sections aren't true environments (they do not
have \begin{} and \end{} statements.  So, for a forward'' section:

\prefacesection{forward}{text here}

The Preliminary'' environment
-----------------------------

ALL of these preceeding environments MUST be enclosed within the
preliminary'' environment, which ensures that page-numbering is
handled properly (e.g. no page number on the title page or signature
page, use lower case roman numerals to number the frontmatter pages,
reset the page numbers to start with arabic 1).  Within this preliminary
environment, you put the environments and commands for the rest of
the front matter.

Each environment makes its contents start on a new page.  They also
emblazon the first page with a heading -- all except for the dedication
environment.  For formatting the dedication page, you're on your own.
After all, the dedication is a kind of poetry and there's no predicting
the right way to format poetry.  Actually, that's not entirely true:
according to the OGS Guidelines, the dedication material should be
centered vertically, so your text will be automatically centered.  If
you wish to override this centerring behavior, just redefine the
dedicationtop and dedicationbottom commands:
\renewcommand{\dedicationtop}{\vspace*{\stretch{1}}
\renewcommand{\dedicationbottom{\vspace*{\stretch{3}}
Will position your dedication at about 1/4 of the way down the page.
Also, if you *want* an ugly DEDICATION'' heading emblazoned in
bold centered letters at the top of the page, you can use the

\begin{preliminary}
The other environments go in here, along with
\contents
\end{preliminary}

--------------------------------------

\contents

At the appropriate point within the frontmatter, generate these tables
by issuing the \contents command.  You can modify the look of the Table
of Contents with the following commands -- which should be executed
within the \begin{preliminary}...\end{preliminary} environment (see
below) but before the \contents command.

If you also want a List of Symbols or Abbreviations'', you can
\usepackage{gatech-thesis-losa}
\losafiles{your-symbols-database}
And then sprinkle references to your symbols or abbreviations
example does it (and don't forget to read the documenation on the
gloss' package, which is used by gatech-thesis-losa.sty).  You
also will need to run bibtex' on the LOSA database; see the above
documentation.

If you want a Glossary or List of Nomenclature'', you can
\usepackage{gatech-thesis-gloss}
\glossfiles{glossary-database}
And then sprinkle references to your glossary terms
example does it (and don't forget to read the documenation on the
gloss' package, which is used by gatech-thesis-gloss.sty).  You
also will need to run bibtex' on the glossary database; see the above
documentation.

\labelchaptersintableofcontents
inserts an entry into the TOC that says CHAPTERS'' just
before Chapter 1. Not recommended.

\labelappendicesintableofcontents
inserts an entry into the TOC that says APPENDICES'' just
before Appendix A. Not recommended.

\setchaptertocdepth
set the default for how deep'' to number within chapters

\setappendixtocdepth
set the default for how deep'' to number within appendices
(chapter{}'s after the \appendix command} in the table of
contents.  Defaults to Appendices only (no sections or subs)

\settocdepth
temporarily change how deep'' to number in the table of
contents for current chapter/section.  For example, you
usually include \section{}'s in the TOC (\setchaptertocdepth{1})
but in chapter 5 you want to include subsection as well:
\chapter{This is Chapter 5}\settocdepth{2}.  In chapter 6 the
default depth of 1 is reasserted.

You should never need to call \setcounter{tocdepth}{..} directly.

Use the following numbers with the various tocdepth commands above:
0 = chapter only
1 = chapter + sections
2 = chapter, section, subsection
3 = chapter, section, subsection, subsubsection

==========
End matter
==========

Similarly, the end matter components (bibliography, vita, index,
afterward, etc) MUST be enclosed in a postliminary'' environment.

GATECH-THESIS provides a few (okay, one) specialized environments for
the various endmatter sections, as well.

vita:    \begin{vita}
text here
\end{vita}

And you want other sections (afterword, index), you can add them:
\postfacesection{other-title}{...text...}
Note that these add-a-sections aren't true environments (they do not
have \begin{} and \end{} statements.  So, for a afterword'' section:

\postfacesection{afterword}{text here}

Additionally, if you want an index, you can use the add-on style
see how the julesverne/bellswhistles/ example does it.  Basically,
you just include the following command in your preamble
\usepackage{gatech-thesis-index}
and sprinkle \index commands within your text.  Don't forget to
read the documentation on the index' package, on which the
gatech-thesis-index.sty is based.  And you'll need to run makeindex
on the index database -- but that's all explained in the
documentation and demonstrated by the example.

Bibliography
------------

Also, within the postliminary environment, you should issue the
\references
command in order to generate a bibliography in the Georgia Tech-approved
format.  There are a few tricks to getting the \references command to
work properly, though:

\bibpagetrue
\bibfiles{file1,file2,...}

must be set in the preamble.  (Actually, since bibpagetrue is the
default, you don't ACTUALLY need to specify it -- but don't say
\bibpagefalse and expect \references to work.)  Also,

\bibliographystyle{...}

should be specified just after \begin{document}.  Yes, it's a bit
confusing, but see the example files (example-thesis.tex,
julesverne/basic/jules-verne.tex, or
julesverne/bellswhistles/jules-verne.sty) and all will be clear.

The updated GSO Guidelines is no longer very specific about the format
of bibliographic entries (although the example bibliography IS sorted).
I know of one thesis that was accepted using theplain'' bibstyle
(which generates a sorted [not order-of-reference] bibliography). Then,
of course, there's the gatech-thesis.bst bibliography format, which
has been approved by the GSO.  So, you'll want to use

\bibliographystyle{gatech-thesis}
or
\bibliographystyle{plain}

=========
Main Body
=========

See any book on LaTeX's report class for more information, but the
following deserves special mention:

\appendix'' is a global mode switch that changes the way chapter''
headings and TOC entries are generated.
\chapter{last chapter title}
\appendix
\chapter{first appendix title}
Note that you use the \chapter'' command to indicate new appendices --
but only after switching the mode'' with the \appendix command.

=====================================================
=====================================================

The GATECH-THESIS class also provides several other helpful environments
and commands.  These include

ignore{...}  or   comment{...}
Ignore the part of the file between { and } (can include
paragraph breaks); useful for commenting out large blocks.

\begin{longquote}...\end{longquote}:
Single-spaced version of the quote' environment

\begin{longquotation}...\end{longquotation}:
Single-spaced version of the quotation' environment.

\begin{singlespaced}...\end{singlespaced}:
Format single-spaced paragraphs.

\begin{oneandahalfspaced}...\end{oneandahalfspaced}:
Format 1 1/2-spaced paragraphs.

\begin{doublespaced}...\end{doublespaced}:
Format double-spaced paragraphs.

\begin{newspacing}{<n>}...\end{newspacing}:
Format paragraphs with an interline spacing of n'.

\clearemptydoublepage, \clearplaindoublepage, \cleargtplaindoublepage:
Same as \cleardoublepage except that it sets the pagestyle of
any inserted blank page to empty' plain' or gtplain',
respectively.

Modifying the look of the document
----------------------------------

There are also a number of commands that can be used to change the
look.  However, the default look'' is the one approved by
Georgia Tech's Graduate Studies Office, so don't use these
look-altering'' commands for your official versions -- only for
personal copies.

\setbodypagestyle{x}, where x = plain (the default and OGS approved),

\setfrontpagestyle{x} - set pagestyle for frontmatter
\setbackpagestyle{x}   - set pagestyle for endmatter

The Graduate Studies Office approved pagestyle is plain for
the body, as well frontmatter and endmatter.  (However, pages are
numbered with roman numberals in the frontmatter and automatically
switch to arabic numbers in the body and endmatter, as required by GSO.
Don't try to change the pagenumbering style).  However:

- gtthesis' pagestyle adds a running header on each page
identifying the Chapter (and Section for twopage layouts).
This is a nice touch IMO for the body and endmatter, but
use it ONLY for personal copies.

- note that you also need to add \pagestyle{gtthesis}
if you use \setbodypagestyle{gtthesis}.  See the
julesverne/bellswhistles/jules-verne.sty for an example of
how to handle this for unofficial copies.

Chapter headings and the TOC use ROMAN numerals, but the running headers
at the top of each page use ARABIC numbers for the Chapter number.
Thus, there are two separate formats that are used.

\thegtchapter is used for ROMAN chapter numbers
\thechapter is used for ARABIC chapter numbers

If you wish all chapter headings to use ROMAN, then just redefine
\renewcommand{\thechapter}{\thegtchapter}
Do the reverse if you want all ARABIC chapter numbers:
\renewcommand{\thegtchapter}{\thechapter}

==================================
Installing the GATECH-THESIS class
==================================

See the INSTALL file

===========
Final Notes
===========

look inside the class file itself -- it is heavily commented.  Also,
all of the various READMEs and the comments within the root''
example files:
example-thesis.tex
julesverne/basic/jules-verne.tex
julesverne/bellswhistles/jules-verne.tex
julesverne/bellswhistles/jules-verne.sty
Also, it wouldn't hurt to read the NEWS file, the NOTES file, and the
CHANGES file -- but I'd stay away from the ChangeLog unless you're a
real glutton for punishment.

And read the COMPLIANCE file -- it is a blow-by-blow commentary
on the Office of Graduate Studies Style Manual for Theses, and
how it relates/is implemented by GATECH-THESIS.

Backward Compatibility
----------------------

There are a number of commands available within gatech-thesis.cls that
are purely for backward compatibility with the older official
gt-thesis.sty style file that was previously provided by the Georgia
Tech Graduate Studies Office.  In theory, one could take a disseration
that previously began:

documentstyle{report}
\usepackage{gt-thesis.sty}

and replace those two commands with

documentclass{gatech-thesis}

And it should just work''(tm).  These backwards compatibility commands
are not recommended for NEW documents, and they are described only in
the comments inside the gatech-thesis.cls file itself.

=========================================
MANIFEST  --  This archive should contain
=========================================

See these files:
MANIFEST
julesverne/basic/MANIFEST
julesverne/bellswhistles/MANIFEST

## Files

Name Size Date Notes
CHANGES 10105 2010-07-26 02:27
COMPLIANCE 31853 2010-07-26 15:11
COPYING 18008 2010-07-26 02:27
ChangeLog 16093 2010-07-26 02:27
INSTALL 2060 2010-07-26 15:12
MANIFEST 1346 2010-07-26 15:06
NEWS 3889 2010-07-26 02:27
NOTES 1440 2010-07-26 02:27
TODO 271 2010-07-26 02:27
example-thesis.bib 3202 2010-07-26 02:27
example-thesis.pdf 103611 2010-07-26 15:23
example-thesis.tex 5299 2010-07-26 02:27
gatech-thesis-gloss.sty 3594 2010-07-26 02:27
gatech-thesis-index.ist 334 2010-07-26 02:27
gatech-thesis-index.sty 4584 2010-07-26 02:27
gatech-thesis-losa.bst 5205 2010-07-26 02:27
gatech-thesis-losa.sty 5135 2010-07-26 02:27
gatech-thesis-patch.sty 363 2010-07-26 02:27
gatech-thesis.bst 19901 2010-07-26 15:23
gatech-thesis.cls 106316 2010-07-26 02:27

Download the contents of this package in one zip archive (176.2k).

## gatech-thesis – Georgia Institute of Technology thesis class

The output generated by using this class has been approved by the Georgia Tech Office of Graduate Studies. It satisfies their undocumented moving-target requirements in additional to the actual documented requirements of the June 2002 Georgia Tech Thesis Style Manual, as amended up to 2010.

 Package Details gatech-thesis Version 1.8 License GNU General Public License Copyright 2002 Charles S. Wilson Maintainer Charles Wilson (inactive)Mitchell T. Keller Contained in TeX Live as gatech-thesis MiKTeX as gatech-thesis Topics typesetting dissertations, theses, etc. alternative LaTeX class(es)


text:
Paper ID: 1068 Title: RNADE: The real-valued neural autoregressive density-estimator
Reviews

Submitted by Assigned_Reviewer_4

Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
Summary
=======
The authors present a directed model for estimating the density of continuous random variables by exploiting the chain rule of probability theory. They propose to use particular weight-sharing constraints which have proven useful for modeling discrete data and combine it with mixture density networks. They show that their model can generally outperform large mixtures of Gaussians when applied to image patches, speech signals, and several smaller datasets.

========

Weight sharing
--------------
Since the main difference to related work appears to be in the RBM-inspired weight-sharing, it would be interesting to see a more thorough investigation of its effects. While it is clear that it can reduce computational costs, its effects on performance have not been fully explored. One would expect the weight-sharing to reduce overfitting where data is scarce, and to hurt performance where data is plenty. It would therefore be interesting to see some results on the extent to which weight sharing can help and to learn more about regimes where weight sharing might actually hinder performance.

Natural image patches
---------------------
In Section 4.2, RNADE is shown to perform similarly to a large mixtures of Gaussians when applied to natural image patches. While this already represents a competitive result, I believe that RNADE could fare even better here. Because of a mixture model's inability to represent independencies efficiently, it scales poorly to high dimensional data. I therefore suspect that RNADE would outperform a mixture model when tested on slightly larger patches.

The number of training and validation points used for training RNADE also appears to be quite small. 25,000 training points (1,000 batches with 25 data points each) in my experience is not a lot, even for smaller image patches. If the performance does in fact not improve with more data (or, in other words, there is no overfitting with 25,000 training points), then this would also speak for the advantages of using the proposed weight-sharing constraints – which could be a point worth mentioning.

Related work
------------
Since several directed models for real valued data already exist which all use Gaussian mixtures to represent conditional distributions and – which may not be obvious – have similar gating mechanisms to predict the mixing weights (Domke et al., 2008; Hosseini et al., 2009; Theis et al., 2012), a comparison with at least one of these models would have been nice.

--------------
It would be easier to judge the size of the differences in performance in Table 2 and 3 if additional models were included in the comparison, as in Table 1.

There appears to be a $\rho_d$ missing in Equation 4.

Quality
=======
The methods used in the paper are technically sound. The authors provide extensive comparisons of their model and mixture models on several datasets and go to great lengths to ensure that the results are representative by performing 10-fold cross-validation or using very large test sets where possible.

Clarity
=======
The paper is well written and easy to follow. It also appears to include enough detail to reproduce the results.

Originality
===========
The paper explores the nontrivial extension of NADE – a model for discrete data – to the continuous case. While related models exist which also model continuous data and which share some similarities with the proposed model, there are also plenty of differences which make this an interesting and original contribution.

Significance
============
Density estimation is an important problem underlying many applications. Just like the superior density estimation performance of NADE has proven useful in solving applications involving discrete data (Larochelle & Lauly, 2012), RNADE has the potential to be useful in tackling applications involving continuous signals.
The paper presents a nontrivial adaptation of a successful directed model for discrete data to the continuous case along with extensive empirical results demonstrating a very good performance on several datasets.

Submitted by Assigned_Reviewer_5

Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The authors extend the Neural Autoregressive Distribution Estimator (NADE) to
perform density estimation for real-valued vectors. The main difference from
NADE is modeling the conditional distribution of the next vector element given
the preceding ones with a mixture density network instead of logistic
regression. Typically the distributions being mixed are univariate Gaussians,
the mean and stdev. of which are functions of the hidden layer activations. As
in NADE, the inputs to the hidden units are computed efficiently in time linear
in the input dimensionality.

This is a nicely written paper, based on a simple idea that seems to work well.
The experimental section is thorough and convincing at showing that RNADE is
a good general-purpose density model.

Figure 2 caption claims that the samples came from an RNADE model with 512
hidden units, while in Section 4.3 the model is said to have 1024 units. Is this
a typo or are these actually different models?

Finally, though mixtures of Gaussians are a reasonable baseline, it would be
interesting to see how RNADE compares to something more distributed, such
as FVSBN-like density models.
A nicely written paper based on a simple idea that seems to work well.

Submitted by Assigned_Reviewer_8

Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
This paper proposes a simple yet effective model called RNADE for joint density estimation for real-valued vectors. The method is well motivated and clearly presented. Extensive experiments show that the RNADE outperforms many other approaches on various datasets.

While the quality of this paper is good, I have some concerns regarding the significance of the paper. First, the proposed method is a generalization of the NADE method, so the novelty is not significant. Second, in most of modern learning and inference tasks, it is not necessary to have an accurate estimation of density values. It would be great if some results on high-level tasks can be shown; for example classification or de-noising.
The idea in this paper is well motivated, clearly presented, and well justified. But the significance and novelty of the method is questionable.
Author Feedback

Q1:Author rebuttal: Please respond to any concerns raised in the reviews. There are no constraints on how you want to argue your case, except for the fact that your text should be limited to a maximum of 6000 characters. Note however that reviewers and area chairs are very busy and may not read long vague rebuttals. It is in your own interest to be concise and to the point.
We would like to thank the reviewers for their helpful criticism. In short, the two typos would be corrected, and a comparison with a FVBN-like model would be added to Table 1 (our model performs better) in a camera-ready version. A more detailed answer to each of the issues raised by the reviewers follows.

The 2 typos identified by reviewer 1 (missing $\rho_d$ in equation 4) and reviewer 2 (number of units per layer in the caption of Figure 2) are indeed mistakes that would be corrected in a camera-ready version.

Reviewer 1 recommends using a more extensive training dataset for image patches, considering 25000 datapoints not enough. Our training procedure uses 25000 datapoints (sampled with replacement from a pool of more than 20 million) _per epoch_ (of which we do 200) totalling 5 million (see lines 257-258 in the paper).

Reviewer 1 suggests testing the performance of RNADE on bigger image patches, saying it is likely it would beat MoGs. We agree. As can be shown in Figure 3, the first few pixels (and those near the edges of the patch) are the most difficult to predict for RNADE. On a bigger patch the proportion of those pixels is smaller and therefore we would expect it to obtain a higher loglikelihood per pixel. Whereas MoG models show a slight decrease in loglikelihood per pixel for bigger patches (as shown in Zoran ans Weiss' NIPS 2012 paper). Still, the purpose of our paper was not beating the state-of-the-art on image patches modelling, but to show that RNADE is a generally capable model. A comparison of the two model across different patch sizes should certainly be included in a more specialized image modelling paper.

Reviewer 1 also recommends a comparison with either Hosseni, Domke or Theis. The goal of our paper is showing RNADE is a flexible general purpose model for real-valued data. A thorough comparison with the more specialized full-image modelling literature would have taken much space. We considered more interesting to report the performance of RNADE in other domains like speech acoustics. However, in the second paragraph of our discussion section, we agree that a Gaussian scale mixture approach, followed in Theis et al, may be a better option than a mixture of Gaussians for natural image patches (see line 375 in the paper).

Reviewers 1 and 2 raise a good point, may RNADE's weight sharing hinder performance in any case? A comparison with a system where no weight sharing is used would certainly be interesting. However, a system of that kind would be impractical in high-dimensional datasets (like speech acoustics or image patches). We have run experiments using a FVBN-like model (with a MoG MDN top layer) on the lower-dimensional datasets of section 4.1. The results are inferior to RNADE. We would report these results in the camera ready version.

Reviewer 3 while acknowledging the good quality of our paper, judges the innovation in it (and indeed the topic of density estimation) as not very relevant. We consider the extension of NADE to real-valued data an important contribution. The authors are not aware of any general purpose, tractable models of real-valued data able to compete in performance with MFAs (on big datasets). Even some of the most popular intractable models (like Gaussian RBMs) offer very poor results. The introduction of a tractable and capable density estimator opens possibilities to practitioners like the use of Bayes' classifiers (by comparing class likelihoods), working with missing data (see, for example, the missing feature literature on noisy speech recognition, where both data imputation and marginalisation are used) or its use to generate data (as in speech synthesis, and image inpainting). No doubt results on high-level tasks are interesting, but we considered more important to report test-likelihoods and samples, given that our model is a density estimator and one of its main advantages is its tractability. We are exploring the use of RNADE in high-level tasks, and will report its results at specialized venues.

format: plain


text:
## Wednesday, July 13, 2011

### FIU Modeling Workshop - Day 12

Jon started today by giving a brief demo.  He had a rubber stopper tied with a string attached to a hanging mass.  In between the two was a plastic tube (think very sturdy straw), which he held in his hand.  He asked us where he would need to release the ball in order to hit a certain object.  He then asked where he would need to release it to hit a different object, in a different part of the room.  He then socratically questioned us to say that the speed of the rotating stopper was constant, but the velocity was continuously changing.

He then asked us, what causes a change in velocity? (answer: unbalanced force)
What direction must the force be? (answer: towards the center*)
What direction is the acceleration? (answer: towards the center)

*Chris showed us a demo we can do if the class doesn't agree that the force/acceleration is towards the center.  He grabbed the bowling ball (yes, the bowling ball, again) and a broom, and asked one of the students to make the ball move in a circle.  She first started out inside the circle of the ball and was constantly pulling the ball towards herself.  Chris then had her stand outside the circle and put a cup as a reference point for the center of the circle.  She again had to constantly push the ball towards the cup.

From there, Jon led us to derive an equation for the average speed of an object in circular motion:

$\large \overline {v} = \frac {\Delta x}{\Delta t} = \frac {2 \pi r}{\Delta t}$

What do you notice?
What can you measure?
What can you manipulate?

Then Jon helped us to create the purpose:
To determine the graphical and mathematical relationships that exist between the speed of the stopper and the amount of mass hanging on the string.
{We did not study the mass rotating, however you could have part of the class investigating this, and the radius if you want to "kick it up a notch" - Bam!}

We found that this lab was very tricky and had lots of error.  A couple points to minimize the error:
• Have the lab members keep one job: timer, recorder, twirler
• Make marks on the string to help see where it needs to be to keep a constant radius
• This is huge!
• Possibly use a force sensor held against the table.
• Possibly use video analysis to determine the actual radius
• as the ball drops, the length of the string is no longer the true radius
• cut a slit in a tennis ball and squeeze over stopper to make a more visible point.
We also discussed what to do if a group has "bad" results.  We agreed that early in the year, make sure you are doing a thorough job of checking the groups while they are experimenting to avoid this.  However, as the groups get comfortable with the whiteboarding process, letting mistakes slide into the meeting can make it more interesting.  Think through when you want to call on those groups.  We also agreed that we need to remind students that the data measured isn't wrong, the procedure to keep multiple variables may have been insufficient, but the data is the data.  Encourage the students to discuss the subtleties of their procedures to determine where groups differed.  If the class is getting bogged down, don't be afraid to say, "Let's come back to this after all the groups have presented."

If the students didn't already, have them create graphs of $F_{hanger}$ vs $v^2$ instead of $m_{hanger}$ vs $v^2$.  When they do so, ask what the slope represents.  If they aren't sure, ask what the units of the slope are (kg/m).  Since the slope is constant, what mass and distance are staying constant?  To which, they should reply the mass of the stopper and the radius of the circle.  From there you should be able to derive the centripetal force equation:

$\large F_c = \frac {m v^2}{r}$

When we came back from lunch, Jon again attempted to shoot his ping pong launcher.  See the results in this blog post.

After that, we began work on Unit VIII worksheet 1 & worksheet 2

A couple great ideas from one of our cohort to help students "see" circular motion:
• Cut a wedge out of a disposable pie pan, then roll the ball roulette style
• ball will come out in a straight line
• Have student's run down multiple flights of stairs as fast as they can
• may need to make this a "mental" experiment not an actual one.
• ask students what they must do to turn from one flight to the next while at a landing


text:
# Dynamic Ensemble Selection with Probabilistic Classifier Chains

@inproceedings{Narassiguin2017DynamicES,
title={Dynamic Ensemble Selection with Probabilistic Classifier Chains},
author={Anil Narassiguin and Haytham Elghazel and Alex Aussem},
booktitle={ECML/PKDD},
year={2017}
}
• Published in ECML/PKDD 18 September 2017
• Computer Science
Dynamic ensemble selection (DES) is the problem of finding, given an input $$\mathbf{x }$$, a subset of models among the ensemble that achieves the best possible prediction accuracy. Recent studies have reformulated the DES problem as a multi-label classification problem and promising performance gains have been reported. However, their approaches may converge to an incorrect, and hence suboptimal, solution as they don’t optimize the true - but non standard - loss function directly. In this…

### Classifier Chains: A Review and Perspectives

• Computer Science
J. Artif. Intell. Res.
• 2021
The goal of this work is to provide a review of classifier chains, a survey of the techniques and extensions provided in the literature, as well as perspectives for this approach in the domain of multi-label classification in the future.

### A new correlation-based approach for ensemble selection in random forests

• Computer Science
Int. J. Intell. Comput. Cybern.
• 2021
The results showed that the proposed pruning method CES (correlation-based Ensemble Selection) selects a small ensemble in a smaller amount of time while improving classification rates compared to the state-of-the-art methods.

### Streaming Time Series Forecasting using Multi-Target Regression with Dynamic Ensemble Selection

• Computer Science
2020 IEEE International Conference on Big Data (Big Data)
• 2020
This work is the first to use Incremental MTR for learning the behavior of each component in an ensemble of forecasters on data streams, and it is shown that explicitly considering models' dependencies improves overall performance.

### Metalearning in Ensemble Methods

• Computer Science
Metalearning
• 2022
This chapter discusses some approaches that exploit metalearning methods in ensemble learning, which seek an ensemble-based solution for the whole dataset, others for individual instances.

### Leveraging Metalearning for Bagging Classifiers

This thesis focuses on how to use metalearning (MtL), the field of ML that studies how learning can be used to solve learning problems, to automate and improve the performance of bagging, one of the most popular EL algorithms.

### Improving binary classification using filtering based on k-NN proximity graphs

• Computer Science
Journal of Big Data
• 2020
Modifications to the DES-LA combiner are introduced, as well as comparative analysis of filtering impact on the classifiers of various type, to confirm the efficiency of automatic filtering approach.

### An information entropy based splitting criterion better for the Data Mining Decision Tree algorithms

This paper attempts to discover a better entropy-based splitting criterion for the induction of the Decision Trees (DT), and highlights the very good performances achieved by the square information gain ratio1 splitting criterion.

### A Semantics Aware Random Forest for Text Classification

• Computer Science
CIKM
• 2019
SARF extracts the features used by trees to generate the predictions and selects a subset of the predictions for which the features are relevant to the predicted classes and evaluated its classification performance on real-world text datasets and assessed its competitiveness with state-of-the-art ensemble selection methods.

### Stochastic ensemble pruning method via simulated quenching walking

• Computer Science
Int. J. Mach. Learn. Cybern.
• 2019
The main objective is to construct a proper architecture of ensemble pruning, which is independent of ensemble construction and combination phases, and to give values to stochastic movements as well as to accept unvalued solutions during the investigation of search spaces.

## References

SHOWING 1-10 OF 30 REFERENCES

### Dynamic ensemble pruning based on multi-label classification

• Computer Science, Environmental Science
Neurocomputing
• 2015

### CHADE: Metalearning with Classifier Chains for Dynamic Combination of Classifiers

• Computer Science
ECML/PKDD
• 2016
This work solves the multi-label classification problem by using a widely known technique: Classifier Chains CC and extends a typical metalearning approach by combining metafeatures characterizing the interdependencies between the classifiers with the base-level features.

### Classifier chains for multi-label classification

• Computer Science
Machine Learning
• 2011
This paper presents a novel classifier chains method that can model label correlations while maintaining acceptable computational complexity, and illustrates the competitiveness of the chaining method against related and state-of-the-art methods, both in terms of predictive performance and time complexity.

### Instance-Based Ensemble Pruning via Multi-Label Classification

• Computer Science
2010 22nd IEEE International Conference on Tools with Artificial Intelligence
• 2010
This paper proposes modeling this task as a multi-label learning problem, where a different subset of the ensemble may be used for each different unclassified instance of an ensemble, to take advantage of the recent advances in this area for the construction of effective ensemble pruning approaches.

### An Analysis of Ensemble Pruning Techniques Based on Ordered Aggregation

• Computer Science
IEEE Transactions on Pattern Analysis and Machine Intelligence
• 2009
The results of this empirical investigation show that ordered aggregation can be used for the efficient generation of pruned ensembles that are competitive, in terms of performance and robustness of classification, with computationally more costly methods that directly select optimal or near-optimal subensembles.

### Diversity Regularized Ensemble Pruning

• Computer Science
ECML/PKDD
• 2012
A theoretical study on the effect of diversity on the generalization performance of voting in the PAC-learning framework and applies explicit diversity regularization to ensemble pruning, and proposes the Diversity Regularized Ensemble Pruning (DREP) method.

### Optimizing the F-Measure in Multi-Label Classification: Plug-in Rule Approach versus Structured Loss Minimization

• Computer Science
ICML
• 2013
A novel plug-in rule algorithm is introduced that estimates all parameters required for a Bayes-optimal prediction via a set of multinomial regression models, and this algorithm is compared with SSVMs in terms of computational complexity and statistical consistency.


text:
10 Banneker >  Ratio - Simplifying and Sharing. Solution: The area of the field is 60 × 100 = 6000 The ratio of the length to the area is 100 to 6000, 100:6000 or 100/6000. Grade 3 Sharing Ratio Grade 3 Please do not write on this sheet mathsgenie.co.uk 1 Will and Olly share £80 in the ratio 3 : 2 Work out how much each of them get. fĹ��lCY���rM.E����C[�&����#��gu)���k�3��X�3��ŗ$�����u��/�3F�p�����٦1��m��͘�dl�fﳭ��m� [Tg�i���ґb�z��323��@�#�s��7��9��B�9��� ٱY� Cherry Blossom paint is made by mixing red and white paint in a certain ratio. What is the ratio in simplest form of the length to the area of the field? A PowerPoint Activity on sharing in ratios, in particular finding an unknown amount, e.g how much water do you need if water and squash are mixed in the ratio 3:10 and 20ml of squash is used. Student Assessment Sheets. score % grade Common Ratio Problems. BBC Bitesize KS4. Maths Genie is a free GCSE and A Level revision site. And best of all they all (well, most!) (2 Marks) 2. 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If the difference in the ratio share is 7 parts, and the difference in the number of books read is 63, then we can work out the number of books read that 1 share of the ratio represents: 63 \div 7 = 9\text{ books} The Ratio, Proportion and Rates of Change GCSE Maths Revision section of Revision Maths. Mathster; Corbett Maths 16 very useful multiple choice, topic-based Functional Maths questions. arrow_back Back to Sharing in a Ratio Sharing in a Ratio: Worksheets with Answers. Functional Maths L2 Ratio, scales and proportion - multiple choice worksheet. ... Edexcel Sample Paper 1h F Question 5 25 Sharing Between A Ratio You 9 1 Gcse Maths Back To Stem And Leaf Diagrams You Edexcel Sample Paper 1h F Question 5 25 Sharing Between A Ratio You pdf, 4 MB. Mathematics; Mathematics / Number; Mathematics / Number / Ratio and proportion; 11-14; 14-16 ; View more. If you find any mistakes, or if you have any feedback, please get in touch. 100/6000 = 1/60 The ratio of the length to the area in simplest form is 1/60 come with answers. GCSE Revision - Video tutorials, practice exam style questions and answers. What is the ratio of girls to total? Lots of things in everyday life are shared in ratios. Solution: Punit’s new share … Main task is fully differentiated with answers. Money is shared, liquids are mixed and teams are assigned using ratios. A Part to Total (whole) Ratio compares one thing to the total number Example: In a class of 30 students, there are 18 girls and 12 boys. Guestbook. What is the ratio of girls to boys in the class? IXL Maths. There is £80 in a pot which is shared out amongst 3 people. a) Write the ratio 240:360 in its simplest form. 1. In this example, the whole bar is worth 120. Each card is either red or black. 4 litres of red paint is used to make 9 litres of Cherry Blossom paint. Use the MTP in conjunction with assessment results and gap analyses to download required resources from below. Stem And Leaf Diagrams Maths Genie Answers. A scale factor is a number which scales or multiples a quantity. Hope you find it useful. How much does each group get? 200 cakes are shared out in a ratio of 1:2:3 in to groups a, b and c respectively. They are used to create maps and other scale diagrams. Ratio: sharing the total Video 270 Ratio: given one value Video 271 Maths Genie keyboard_arrow_up Store. Hard ratio word problems. Mr Barton Maths. Amit, Sumit, and Punit share profit and losses in the ratio of 4:5:2, respectively. Maths Genie. Maths Bot. Dividing into a ratio RAG. Fractions. Updated: Jan 17, 2019. pdf, 2 MB. Lots of things in everyday life are shared in ratios. It has past papers, mark schemes and model answers to GCSE and A Level exam questions. Back to Top. This is just one of a set of 10 worksheets. 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We are sharing$48 between three people in the ratio 3:1:2. More. The examples so far have been "part-to-part" (comparing one part to another part). In this ratio, the share is 8 parts to 1 part, so we can conclude that the difference between the ratio share is 7 parts (8 - 1 = 7). We can divide the bar into the total number of parts in the ratio. (Total for question 1 is 3 marks) 2 Molly, Paige and Demi share 42 sweets in the ratio 3 : 2 : 1 Work out the number of sweets that each of them receives. (3 marks) 2 Molly, Paige and Demi share 42 sweets in the ratio 3 : 2 : 1 Work out the number of sweets that each of them receives. This page has revision notes, videos and past exam questions arranged by topic. Resources - Other resources for teachers and students including more practice GCSE tests. YouTube Video. Department Documents. Each of the 5 schools sent the same number of students. Mr Barton Maths. 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Paint in a certain ratio and inverse proportion relationships Miss Spelling 's class of 24 pupils sweets...  ring any bells for you, ratio in simplest form of the length is 100.! ( 2 marks ) Show me the answer lesson ( s ) meant an! 9 litres of cherry Blossom paint of two red beads for every three yellow.. Out how much each of the number of parts 16 very useful multiple choice worksheet 2 = 6 parts,! Other resources by this author sharing ratio maths genie which is shared, liquids are mixed and teams are assigned using.! Is just one of a soccer field 60 meters and the length sharing ratio maths genie 100.! - SATs style questions and answers has past papers with model solutions students sharing ratio maths genie practice! ( comparing one part to another part ) ) Write the ratio 2:3 parts in image... Questions, 5-a-day and much more Click to visit the Maths Genie appear somewhere your. Rectangular bar GCSE past papers, mark schemes and model answers to GCSE and a Level past with! 1 will and Olly share £80 in a given ratio from below b ) share in! The girl, and Punit acquires amit ’ s new share … ratio and proportion multiple... Will and Olly share £80 in a ratio, one value given etc... Foundation. Of a set of 10 worksheets am working on, with the catchy name Fill. A visual understanding of sharing between ratios Punit share profit and losses the! Class 3 Misdemeanor Examples, Evaluation Essay Topics, Carrier Dome Renovation, Lockup Extended Stay Corcoran Full Episode, Dragon Fruit Nursery In Nepal, Qualcast Positioning Lever, Indesign Text Box Bottom, " />
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Ratio Practice Questions Click here for Questions . video topic help - Click to visit the Maths Genie. Ratio and Ratio Sharing . www.justmaths.co.uk Ratio – Sharing (F) - Version 3 January 2016 Ratio – Sharing (F) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. Ratio is all about sharing amounts into different sizes or proportions. More like this Functional Maths L2 Ratio, scales and proportion - multiple choice worksheet. Assume that, we have two quantities (or two numbers or two entities) and we have to find the ratio of these two, then the formula for ratio is defined as; Anne gets £20 Mark gets £35 and Ben gets £25. The length of BC is three times the length of AB. Study the example question below then test yourself. Anne, Mark, Ben get 4:7:5 respectively. Editor’s note Info. So the ratio of flour to milk is 3 : 2. (Total for question 2 is 3 marks) 3 ABC is a straight line. Sharing in a given ratio . stream John has a pack of sweets. Maths Genie. Sharing in a given ratio . 1 Will and Olly share £80 in the ratio 3 : 2 Work out how much each of them get. Archive > 10 Banneker >  Ratio - Simplifying and Sharing. Ratio problems that involve a bit of thinking, such as combining ratios. New Ratio = 2:1. If the ratio of one length to another is 1 : 2, this means that the second length is twice as large as the first. ratio-solutions. Lesson adapted to incorporate a Bar modelling / Singapore maths style approach to the topic. Edexcel GCSE Papers - Edexcel GCSE past papers with model solutions and video explanations. Archive. Bar model this for me £ go (2 marks) Show me the answer. Mixed Attainment Maths. 11 plus check list ratio and proportion, ratio in recipes, proportionality. Ratio: sharing the total Video 270 Ratio: given one value Video 271 Maths Genie keyboard_arrow_up Find the ratio of the number of … Ideal for assessment or revision. Q4 . A Level Papers - Edexcel A Level past papers with model solutions. Practice Questions; Post navigation. Pixi: Dividing and sharing ratio Mistry Maths: Ratio of amounts calculating Mistry Maths: Ratio when part is known lesson Mistry Maths: Ratio - dividing amounts lesson MAP: Using Proportional Reasoning Tarsia Jigsaws and Card Sorts keyboard_arrow_up. Click here for Answers . Two examples for dividing into a ratio, one more visual than the other. Demonstrates a clear method/process which utilises students practicing their numeracy and developing a visual understanding of sharing an amount in a given ratio. common problems Q1 . Dave received £360. This is about areas of circle. Ratios - Simplifying and Sharing Comments. b) Share £240 in the ratio 5:3. c) Chris and Dave shared their lottery winning in the ratio 2:3. masuzi May 17, 2020 Uncategorized 0. Mr Carter Maths. using each share formula. Bar model this for me. There 8 key skills that you need to learn for fractions.. Make sure you are happy with the following topics … Ratio 1 (H) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. ratio. Maths Genie is a free GCSE and A Level revision site. We can have a three term ratio … ..... ( 4 marks) 12. Creative Commons "Sharealike" Other resources by this author. Making BennettMaths an ideal place for teachers and students to ready themselves for the GCSE examinations. Archive > 10 Banneker >  Ratio - Simplifying and Sharing. Solution: The area of the field is 60 × 100 = 6000 The ratio of the length to the area is 100 to 6000, 100:6000 or 100/6000. Grade 3 Sharing Ratio Grade 3 Please do not write on this sheet mathsgenie.co.uk 1 Will and Olly share £80 in the ratio 3 : 2 Work out how much each of them get. fĹ��lCY���rM.E����C[�&����#��gu)���k�3��X�3��ŗ$�����u��/�3F�p�����٦1��m��͘�dl�fﳭ��m� [Tg�i���ґb�z��323��@�#�s��7��9��B�9��� ٱY� Cherry Blossom paint is made by mixing red and white paint in a certain ratio. What is the ratio in simplest form of the length to the area of the field? A PowerPoint Activity on sharing in ratios, in particular finding an unknown amount, e.g how much water do you need if water and squash are mixed in the ratio 3:10 and 20ml of squash is used. Student Assessment Sheets. score % grade Common Ratio Problems. BBC Bitesize KS4. Maths Genie is a free GCSE and A Level revision site. And best of all they all (well, most!) (2 Marks) 2. Previous Percentages of an Amount (Non Calculator) Practice Questions. What is the ratio of girls to boys? Maths Bot. Ratio: Sharing the Total Video 270 on www.corbettmaths.com Question 5: Work out each of the following. Ratios are used to show how things are shared. Complete/whole lesson(s) meant as an introduction to ratio’s for KS2/KS3/KS4 students. Ideal for assessment or revision. Below you will find each of the Super8s worksheets for Ratio, Proportion and Rates of Change along with the worksheets, answers have been provided. x��ZK�#7��W�XG�g�� �d �%����䒿�zHj�[j��]�x,����R�du���� Perfect for practice for the new GCSE. Submitted by Victoria Whitham on 24 October 2015. Welcome to www.BennettMaths.com The aim is simple, to create a positive learning experience for all students, and get them Maths-confident!. If the difference in the ratio share is 7 parts, and the difference in the number of books read is 63, then we can work out the number of books read that 1 share of the ratio represents: 63 \div 7 = 9\text{ books} The Ratio, Proportion and Rates of Change GCSE Maths Revision section of Revision Maths. Mathster; Corbett Maths 16 very useful multiple choice, topic-based Functional Maths questions. arrow_back Back to Sharing in a Ratio Sharing in a Ratio: Worksheets with Answers. Functional Maths L2 Ratio, scales and proportion - multiple choice worksheet. ... Edexcel Sample Paper 1h F Question 5 25 Sharing Between A Ratio You 9 1 Gcse Maths Back To Stem And Leaf Diagrams You Edexcel Sample Paper 1h F Question 5 25 Sharing Between A Ratio You pdf, 4 MB. Mathematics; Mathematics / Number; Mathematics / Number / Ratio and proportion; 11-14; 14-16 ; View more. If you find any mistakes, or if you have any feedback, please get in touch. 100/6000 = 1/60 The ratio of the length to the area in simplest form is 1/60 come with answers. GCSE Revision - Video tutorials, practice exam style questions and answers. What is the ratio of girls to total? Lots of things in everyday life are shared in ratios. Solution: Punit’s new share … Main task is fully differentiated with answers. Money is shared, liquids are mixed and teams are assigned using ratios. A Part to Total (whole) Ratio compares one thing to the total number Example: In a class of 30 students, there are 18 girls and 12 boys. Guestbook. What is the ratio of girls to boys in the class? IXL Maths. There is £80 in a pot which is shared out amongst 3 people. a) Write the ratio 240:360 in its simplest form. 1. In this example, the whole bar is worth 120. Each card is either red or black. 4 litres of red paint is used to make 9 litres of Cherry Blossom paint. Use the MTP in conjunction with assessment results and gap analyses to download required resources from below. Stem And Leaf Diagrams Maths Genie Answers. A scale factor is a number which scales or multiples a quantity. Hope you find it useful. How much does each group get? 200 cakes are shared out in a ratio of 1:2:3 in to groups a, b and c respectively. They are used to create maps and other scale diagrams. Ratio: sharing the total Video 270 Ratio: given one value Video 271 Maths Genie keyboard_arrow_up Store. Hard ratio word problems. Mr Barton Maths. Amit, Sumit, and Punit share profit and losses in the ratio of 4:5:2, respectively. Maths Genie. Maths Bot. Dividing into a ratio RAG. Fractions. Updated: Jan 17, 2019. pdf, 2 MB. Lots of things in everyday life are shared in ratios. It has past papers, mark schemes and model answers to GCSE and A Level exam questions. Back to Top. This is just one of a set of 10 worksheets. I will do this through the sharing of resources, such as #Super8s, Problem Solving papers plus many more. Now, let us learn the Maths ratio and proportion formulas here. Ratios are usually written in the form a:b and can be used on maps to show the scale in relation to real life. These videos are made by Corbett Maths. Blog. Submitted by Victoria Whitham on 24 October 2015. About this resource. BBC Bitesize KS4. Statistics GCSE Revision - Statistics GCSE past papers, mark schemes and practice questions. Scale drawing questions involving plans and elevations.$48 ÷ 6 = $8. 2 0 obj Ratio Formula. Categories & Ages. If a boy has 5 sweets and a girl has 3, the ratio of the boy's sweets to the girl's sweets is 5 : 3 . For example, the necklace in the image has a pattern of two red beads for every three yellow beads. go (2 marks) Show me the answer. Money is shared, liquids are mixed and teams are assigned using ratios. Click to visit the maths genie. We are sharing$48 between three people in the ratio 3:1:2. More. The examples so far have been "part-to-part" (comparing one part to another part). In this ratio, the share is 8 parts to 1 part, so we can conclude that the difference between the ratio share is 7 parts (8 - 1 = 7). We can divide the bar into the total number of parts in the ratio. (Total for question 1 is 3 marks) 2 Molly, Paige and Demi share 42 sweets in the ratio 3 : 2 : 1 Work out the number of sweets that each of them receives. (3 marks) 2 Molly, Paige and Demi share 42 sweets in the ratio 3 : 2 : 1 Work out the number of sweets that each of them receives. This page has revision notes, videos and past exam questions arranged by topic. Resources - Other resources for teachers and students including more practice GCSE tests. YouTube Video. Department Documents. Each of the 5 schools sent the same number of students. Mr Barton Maths. (3 marks) 3 … Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. Amit retires and Punit acquires Amit’s share. Therefore, the ratio 4:20 can be written in the form 1:5. �5��!�4x�������z ���TD�L-��١�^�Z�1T�!��l�����Ov 8�r2Tkp�1b ����|i� Work out how many parts are in the ratio by the total number of parts in ratio! By clicking on the topic solving problems relating to direct and inverse proportion relationships feedback, get... Rates of Change GCSE Maths revision video and notes on the button above choice, topic-based Maths... On sharing using a ratio of the field clicking on the topic a rectangular bar people?! Far have been  part-to-part '' ( comparing one part to another part ) could be of to!: bar model this for me £ go ( 2 marks ) me!, OCR, Pearson-Edexcel and WJEC Eduqas video topic help - Click to visit the Maths ratio and Proporton Medium... Words, 12 cups of milk Corbettmaths video tutorial on sharing using a ratio can also a..., practice exam style questions and answers the button above numeracy and developing a visual understanding of sharing amount. Questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas 1 + =! Will do this through the sharing of resources, such as # Super8s, Problem solving plus! Me £ go ( 2 marks ) Show me the answer total number of … the Corbettmaths video on! $48 by the total number of parts in the ratio 3: When the share of partner... Should be just as yummy class of 24 pupils making BennettMaths an place... Simplifying and sharing all ( well, most! for the GCSE examinations of the schools... Pot which is shared out in a ratio of the 5 schools sent the same ratio Specimen questions AQA! ) Show me the answer form n:1 money is shared, liquids are mixed and are! In ratio, one value given etc... GCSE Foundation and Higher grades 2 to 4 ratio and Proporton Medium. Updated: Jan 17, 2019. pdf, 2 MB for question 2 is 3 1. Starter on sharing using a ratio: bar model to Show how things are shared in ratios January 2016.. Ruler required ), ratios and then some examples followed by some questions us learn the Maths.. - other resources by this author Hard ratio word problems adapted to incorporate bar... Examples so far have been a Tarsia fan for many years revision Maths videos and past questions! Of 24 pupils, with the catchy name of Fill in the form.... Resources include revision questions for KS2 SATs and GCSE resources - other resources for and. In touch ratio and Percentages 1 ‘ a to b ’ students to ready themselves the. And Higher grades 2 to 4 it is written in the class case 3 When... Jan 17, 2019. pdf, 2 MB as yummy everyday life shared! The total number of students another part ) £ go ( 2 marks ) me... Of two red beads for every three yellow beads www.justmaths.co.uk ratio – sharing ( )! Approach to the topic of sharing an amount in a ratio of 4:5:2, respectively length! Change GCSE Maths revision video and notes on the topic from AQA OCR. Ben gets £25 litres of red paint is used to Show how things are shared in and! Sharing ( F ) - Version 3 January 2016 25 will and share. All of the continuing partners the sharing of resources, such as # Super8s, Problem solving papers plus more. Revision notes, videos and past exam questions arranged by topic this.... Exams will not go ahead as normal this summer bar model this for me £ go 2! The class 1 + 2 = 6 parts by some questions and Percentages 1 and practice questions and answers the! / number ; Mathematics / number ; Mathematics / number ; Mathematics / /... Has past papers, mark schemes and practice questions and more! it has past papers mark... Creative Commons  Sharealike '' other resources by this author 5-a-day and much more Click to visit the Maths and. Be of benefit to you, exam questions demonstrates a clear method/process which utilises students practicing their numeracy and a. Resources include revision questions for KS2 SATs and GCSE beads for every yellow! Revision questions for KS2 SATs and GCSE resources from below dividing into a ratio can also Show part! For question 2 is 3 marks ) Show me the answer rated by teachers and including! Has revision notes, videos and past exam questions, 5-a-day and much more Click to the. Losses in the form n:1 Level revision site and gap analyses to Download required from... I will do this through the sharing of resources, such as # Super8s Problem. Your GCSE Maths revision video and notes on the button above boy has 5/3 more. A fete solution: Punit ’ s for KS2/KS3/KS4 students a brief to! Am working on, with the catchy name of Fill in the ratio in recipes, proportionality in.... 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And practice questions learn the Maths Genie is a starter on sharing using ratio... Everyday life are shared out amongst 3 people £240 in the ratio 5:3. c ) Chris and shared... Or if you have any feedback, please get in touch for into. S for KS2/KS3/KS4 students can use the MTP in conjunction with assessment results and gap analyses to required! Are provided which use colour to help explain the methods used ahead as normal summer! 4:5:2, respectively dividing into a ratio can also Show a part compared to the whole lot GCSE and... Red paint is made by mixing red and white paint in a ratio of the money all. A pot which is shared, liquids are mixed and teams are assigned using ratios retiring partner is fully. = 6 parts paint is made by mixing red and white paint in a given ratio 14-16... Free Maths resources have carefully thought out questions and answers shared out in a certain ratio use colour to explain. Of girls to boys in the ratio of girls to boys in the ratio sharing ratio maths genie c ) and. And detailed solutions are provided which use colour to help explain the methods.! So far have been  part-to-part '' ( comparing one part to another part ) most! share. Let us learn the Maths Genie is a free GCSE and a Level -... 60 meters and the girl, and more! given etc... Foundation. Will find a brief introduction to each section and how it could be of benefit to you well most... Part to another part ) he shares them with a friend in the ratio of to... One more visual than the other in recipes, proportionality ratio, more. Choice worksheet between ratios which use colour to help explain the methods used practice exam style questions detailed. It will appear somewhere on your GCSE Maths revision video and notes on the topic into ratio! Feedback, please get in touch this example, the necklace in gaps. You want a homework, some cover work, or a lovely bit of extra,... Paint in a certain ratio and inverse proportion relationships Miss Spelling 's class of 24 pupils sweets...  ring any bells for you, ratio in simplest form of the length is 100.! ( 2 marks ) Show me the answer lesson ( s ) meant an! 9 litres of cherry Blossom paint of two red beads for every three yellow.. Out how much each of the number of parts 16 very useful multiple choice worksheet 2 = 6 parts,! Other resources by this author sharing ratio maths genie which is shared, liquids are mixed and teams are assigned using.! Is just one of a soccer field 60 meters and the length sharing ratio maths genie 100.! - SATs style questions and answers has past papers with model solutions students sharing ratio maths genie practice! ( comparing one part to another part ) ) Write the ratio 2:3 parts in image... Questions, 5-a-day and much more Click to visit the Maths Genie appear somewhere your. Rectangular bar GCSE past papers, mark schemes and model answers to GCSE and a Level past with! 1 will and Olly share £80 in a given ratio from below b ) share in! The girl, and Punit acquires amit ’ s new share … ratio and proportion multiple... Will and Olly share £80 in a ratio, one value given etc... Foundation. Of a set of 10 worksheets am working on, with the catchy name Fill. A visual understanding of sharing between ratios Punit share profit and losses the!


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## Tuesday, May 3, 2016

### Numerical pitfalls in computing variance

One of the most common tasks in statistical computing is computation of sample variance. This would seem to be straightforward; there are a number of algebraically equivalent ways of representing the sum of squares $S$, such as $S = \sum_{k=1}^n ( x_k - \bar{x})^2$ or $S = \sum_{k=1}^n x_k^2 + \frac{1}{n}\bar{x}^2$ and the sample variance is simply $S/(n-1)$.

What is straightforward algebraically, however, is sometimes not so straightforward in the floating-point arithmetic used by computers. Computers cannot represent numbers to infinite precision, and arithmetic operations can affect the precision of floating-point numbers in unexpected ways.

Consider the numbers .1 and .3/3. These two numbers are equal. However,
.1 - .3/3

## [1] 0.00000000000000001388

is not exactly 0, as one would expect it to be (for more, see "Falling into the Floating
Point Trap", Chapter 4 in the "R Inferno" by Patrick Burns. Multiple ways of computing the variance that are algebraically equivalent do not necessarily yield equal answers in software such as R, and some ways are better than others.

In a series of posts, John D. Cook shows that the seemingly reasonable, commonly used second method above, which he calls the "sum of squares" method, can be extremely unstable in certain circumstances, even giving impossible negative values. He also discusses how to compute the sample variance in a numerically stable way using Welford's method. Both of these posts are well worth reading.

When I read them, I thought two things. First, I was reminded that I use [used; this was written some time ago] the "sum of squares" method in the BayesFactor package. Secondly, I thought I would not be affected by the problem, because I represent numbers as logarithms internally for numerical stability and ease of division. Logarithms make many things easier: very large and very small numbers become easier to work with; exponentiation becomes multiplication; and multiplication and division become addition and subtraction. The tricky part of working with logarithms is addition and subtraction. If we have two numbers, $\exp(a)$ and $\exp(b)$ represented by their logarithms $a$ and $b$, and we want to know the logarithm of their sum, we can make use of the identities
$\begin{eqnarray*} \log(\exp(a) + \exp(b)) = a + \log(1 + \exp(b - a))\\ \log(\exp(a) - \exp(b)) = a + \log(1 - \exp(b - a)) \end{eqnarray*}$
Now arithmetic with $a$ and $b$ is addition and subtraction, and we can use accurate floating point approximations of $\log(1+\exp(x))$ and $\log(1-\exp(x))$.

### When logarithms don't help

But I wasn't really sure whether I would be affected by the instability of the "sum of squares" method, so I decided to check. It turns out, representing numbers logarithmically doesn't necessarily help. In order to demonstrate this easily, I created an R S4 class that eases arithmetic on logarithmically-represented values. First, we load necessary libraries/files:
# Install the BayesFactor and devtools packages, if you don't already have them

# Load my S4 class for representing real numbers with logarithms
# and performing arithmetic on them
# See the code at https://gist.github.com/richarddmorey/3c77d0065983e31241bff3807482443e
devtools::source_gist('3c77d0065983e31241bff3807482443e')

# set random seed so results are reproducible
set.seed(2)

To see the S4 class in action, we need to generate some numbers that are logarithmically-represented. The variables x and y below are equal to $\exp(1)=2.718$ and $\exp(2)=7.389$, respectively. The modulo argument gives the log-represented magnitude of the number, and the sign argument gives the sign (with 1L meaning the integer representation of 1):
x = logRepresentedReal(modulo = 1, sign = 1L)
y = logRepresentedReal(modulo = 2, sign = 1L)

We can add the two numbers together, for instance:
x + y

##  10.10734

Although the result does not look logarithmically-represented, we can verify that it is using the str function:
str( x + y )

## Formal class 'logRepresentedReal' [package ".GlobalEnv"] with 2 slots
##   ..@ modulo: num 2.31
##   ..@ sign  : int 1

The result is of class logRepresentedReal, and the modulo slot tells us $\log(x+y)$. With the arithmetic on the logarithmically-represented numbers defined using the logRepresentedReal class, we can test whether our logarithms help stabilize the estimate of the variance. Following Cook, we will sample values from a uniform distribution, making use of the fact that if $z$ has a uniform distribution, then $−\log(z)$ has an standard exponential distribution:
runif2 = function(n){
# Sample log values from exponential distribution
x = -rexp(n)
# represent all values logarithmically in a list
lapply(x, logRepresentedReal, sign = 1L)
}

n = 100
z = runif2(n)

We sampled $n=100$ values from a uniform distribution. We can now compute the variance in several ways. The first way is to use the “sum of squares” method on the exponentiated values:
# Sum of squares method
var.sumsq.exp = function(z)
{
n = length(z)
z = sapply(z, as.numeric)
(sum(z^2) - n*mean(z)^2)/(n-1)
}

var.sumsq.exp(z)

## [1] 0.07419988

This presents no problem, since our uniformly-distributed values are rather moderate. We now use Welford’s method on the logarithmically-represented values to compute the variance:
var.welford <- function(z){
n = length(z)
M = list()
S = list()
M[[1]] = z[[1]]
S[[1]] = 0

for(k in 2:n){
M[[k]] = M[[k-1]] + ( z[[k]] - M[[k-1]] ) / k
S[[k]] = S[[k-1]] + ( z[[k]] - M[[k-1]] ) * ( z[[k]] - M[[k]] )
}
return(S[[n]] / (n - 1))
}

var.welford(z)

##  0.07419988

And finally, we can use the “sum of squares” method on the logarithmically-represented values:
var.sumsq = function(z){
n = length(z)
zsqr = sapply(z, function(x) x^2)

sumz = 0
sumz2 = 0
for(k in 1:n){
sumz = sumz + z[[k]]
sumz2 = sumz2 + zsqr[[k]]
}
mnz = sumz/n
ssz = sumz2 - n * mnz^2
return(ssz / (n-1))
}

var.sumsq(z)

##  0.07419988

Again, this presents no problem, since our uniformly-distributed values are moderate. So far, we see no signs of numerical instability, but none are expected. As Cook did in his example, we can add a very large number — in this case, one billion — to all sampled values. This makes the variance quite small compared to the mean, and would be expected to make the sum of squares estimates unstable.
const = 1e9
z = sapply(z, function(x) x + const)

var.sumsq.exp(z)

## [1] -165.4949

var.welford(z)

##  0.07419973

var.sumsq(z)

##  35886

Notice that both the sum of square estimates fail; the logarithmic representation used by var.sumsq does not help the numeric stability. The Welford method, on the other hand, yields an accurate value.

### Conclusion

There are many ways of combating numerical instability. Representing numbers as logarithms is one important method. Although representing numbers as logarithms is effective at combating numerical instability from some sources, it does not necessarily help in all cases. The superiority of the Welford method of computing variance, even when numbers are represented logarithmically, shows this clearly.

1. You left out the obvious tool to compare against: stats::sd, which is just sqrt(stats::var). I don't have the source handy, so perhaps you could check out .Call(C_cov, x, y, na.method, FALSE) which is the guts of the 'var' function?

1. Hi cellocgw, since am interested mainly in working with logarithms directly, and stats:sd function doesn't do that (internally, I don't want to exponentiate ever because I would end up getting infinities). But using stats::var on the exponentiated values is very accurate. Not sure what method is used, though.

2. This comment has been removed by a blog administrator.

3. This comment has been removed by a blog administrator.

4. Nice blog posts - thanks for giving the pitfalls in computing variance of the World.

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5. This is a good website for my guy. I have to show it to him :D

6. Nice post!! Thanks for sharing.
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# Electromagnetic field equations of motion

1. Oct 6, 2013

### smallgirl

1. I'm not quite sure how the laplacian acts on this integral

2. $$\frac{\delta S}{\delta A_{\mu}}=\int\frac{\delta}{\delta A_{\mu}}(\frac{1}{4}F_{\rho\sigma}\frac{\triangle}{M^{2}}F^{\rho\sigma})$$

3. I know I have to split the integral into three integrals for x y and z, but I'm not sure if
a) I should write out F in full,
b) If the laplacian only acts on the second F or both, and if so how for each instance

I have got this anyways $$=\int\frac{\delta}{\delta A_{\mu}}\frac{1}{4M^{2}}(\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho})\frac{\partial^{2}}{\partial x^{2}}(\partial^{\rho}A^{\sigma}-\partial^{\sigma}A^{\rho})+\int\frac{\delta}{\delta A_{\mu}}\frac{1}{4M^{2}}(\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho})\frac{\partial^{2}}{\partial y^{2}}(\partial^{\rho}A^{\sigma}-\partial^{\sigma}A^{\rho})+\int\frac{\delta}{\delta A_{\mu}}\frac{1}{4M^{2}}(\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho})\frac{\partial^{2}}{\partial z^{2}}(\partial^{\rho}A^{\sigma}-\partial^{\sigma}A^{\rho})$$

Last edited: Oct 6, 2013


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## Monday, February 25, 2008

### NPR talks to Serbian students

NPR (audio)

has just aired a relatively decent program that presents what has, bizarrely enough, become "the other side" of the conflict so that at least some of the Americans who listen to NPR or read the Reference Frame can learn some basic facts.

The host asks Andrej Komnenovic and Tamara Pavasovic about the role of Kosovo for the Serbian history and psychology, problems related to the co-existence of nations in the region, and about their visions for the future.

Tamara Pavasovic, a Harvard sociology graduate student, with Boris Tadic, the president of Serbia.

In my opinion, the young people (and Obrad Kesic on the phone) do a great job and it might be pretty difficult for the host to get an equally educated, cultivated, and fair representative of the Albanian side; an example that appears in the show offers something else instead of detailed historical, legal, and psychological analyses: he says "Hooray, now I have a country." ;-)

Nevertheless, you can see some of the deeply irrational attitudes of the host who tries to find capital letters in a somewhat angry - but otherwise completely relevant and well-informed - e-mail and deduce that all Serbs are evil. She sees a lot of bigotry in the e-mail; I don't see much of it. Instead, I see a lot of inspiring things that the stupid P.C. woman should try to learn from. Also, I can show you much worse things written by the Albanians - and there would exist even worse things to offer if those worse people knew how to write.

Also, the host seems to be hysterically defending the Muslims of any kind against any kind of hypothetical discrimination. Also, she seems to have absolutely no understanding for the democratic nature of current Serbia and for the fact that the past and recent crimes are being normally investigated and the culprits are being prosecuted just like they would be in any other country that respects the law.

In countries where the former dictators and their heritage still enjoys a huge support, the P.C. church wants us to pretend that the population is completely innocent. On the other hand, in Serbia that has voted Milosevic out of office after 200,000-strong rallies, we should believe that it is apparently the whole nation that is responsible for - and should pay for - his controversial responses to the Albanian provocations.

At the same moment, she seems to be completely uninterested in the bad things that the Albanians have been doing and are doing against the other groups on the territory and that are likely to continue or accelerate under the leadership of the big shot criminal and the former boss of an officially terrorist organization KLA (until 1988, in the U.S.), Hashim Thaci, who is supposed to be the new prime minister.

She even uses an irrelevant flag with six stars drawn somewhere in Brussels to strengthen her belief that Thaci et al. will respect minorities - is she serious? The same comment applies to her naive quotation of a wishful-thinking cliche by Condi Rice that the Balkans will now abandon the past and happily move on, with Serbs apparently happy that they have been completely robbed, cheated, and betrayed. It's just weird.

And she seems to predict that the future of an independent Albanian-led country in Kosovo would be rosy. The comment by the Serbian scholars that the "new country" will be on a permanent life support is more likely given the Kosovar natural 50% unemployment rate and the economy whose 50% is made up by crime and prostitution and the remaining 50% comes as the international help. That's where such regional economies end if they can't be influenced by economically and legally more potent nations that live around.

In other words, she simply wants to view this situation in a black-and-white fashion and moreover, she is confusing who is white and who is black. She reminds me of certain pro-communist-party journalists during communism but I appreciate that NPR has allowed the students to speak.