From a2125147b1941b68503fad0c2a75a90c7d77fc23 Mon Sep 17 00:00:00 2001
From: Jon Whiteaker <jbw@berkeley.edu>
Date: Sat, 15 Sep 2012 10:34:53 -0700
Subject: new sty file

---
 ieeeconf.cls | 4591 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 4591 insertions(+)
 create mode 100644 ieeeconf.cls

(limited to 'ieeeconf.cls')

diff --git a/ieeeconf.cls b/ieeeconf.cls
new file mode 100644
index 0000000..c3ff411
--- /dev/null
+++ b/ieeeconf.cls
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+%%
+%% IEEEtran.cls 2002/11/18 version V1.6b
+%% 
+%% NOTE: This text file uses MS Windows line feed conventions. When (human)
+%% reading this file on other platforms, you may have to use a text
+%% editor that can handle lines terminated by the MS Windows line feed
+%% characters (0x0D 0x0A).
+%% 
+%% 
+%% This is the official IEEE LaTeX class for authors of the Institute of 
+%% Electrical and Electronics Engineers (IEEE) Transactions journals and
+%% conferences.
+%% 
+%% The latest version and documentation of IEEEtran can be obtained at:
+%% http://www.ieee.org
+%% and/or
+%% http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/
+%% 
+%% The CTAN page may have additional files related to obscure, 
+%% non-IEEE standard and/or platform dependent use of this tool.
+%%
+%% Based on the original 1993 IEEEtran.cls, but with many bug fixes
+%% and enhancements (from both JVH and MDS) over the 1996/7 version.
+%%
+%%
+%% Contributors:
+%% Gerry Murray (1993), Silvano Balemi (1993),
+%% Jon Dixon (1996), Peter N"uchter (1996),
+%% Juergen von Hagen (2000), and Michael Shell (2001-2002)
+%% 
+%% 
+%% Copyright (c) 1993-2002 by Gerry Murray, Silvano Balemi, 
+%%                         Jon Dixion, Peter N"uchter,
+%%                         Juergen von Hagen and Michael Shell
+%%
+%% Current maintainer (V1.3 to V1.6): Michael Shell
+%%                                    mshell@ece.gatech.edu
+%%                                    See the CTAN website above
+%%                                    for current contact information.
+%%
+%% Special thanks to Peter Wilson (CUA) and Donald Arseneau
+%% for allowing the inclusion of the \@ifmtarg command 
+%% from their ifmtarg LaTeX package. 
+%% 
+%%**********************************************************************
+%% Legal Notice:
+%% This code is offered as-is without any warranty either
+%% expressed or implied; without even the implied warranty of
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE!
+%% User assumes all risk.
+%% In no event shall IEEE or any contributor to this code
+%% be liable for any damages or losses, including, but not limited to,
+%% incidental, consequential, or any other damages, resulting from the
+%% use or misuse of any information contained here.
+%% 
+%% All comments are the opinions of their respective authors and are not
+%% necessarily endorsed by the IEEE.
+%%
+%% This code is distributed under the Perl Artistic License 
+%% ( http://language.perl.com/misc/Artistic.html ) 
+%% and may be freely used, distributed and modified.
+%% Retain the contribution notices and credits.
+%% 
+%% Major changes to the user interface should be indicated by an 
+%% increase in the version numbers. If a version is a beta, it will 
+%% be indicated with a BETA suffix, i.e., 1.4 BETA.
+%% Small changes can be indicated by appending letters to the version
+%% such as "IEEEtran_v14a.cls".
+%% In all cases, \Providesclass, any \typeout messages to the user,
+%% \IEEEtransversionmajor and \IEEEtransversionminor must reflect the
+%% correct version information.
+%% The changes should also be documented via source comments.
+%%**********************************************************************
+%%
+%
+% Available class options 
+% (e.g., \documentclass[10pt,conference]{ieeeconf} 
+% 
+%             *** choose only one from each category ***
+%
+% 9pt, 10pt, 11pt, 12pt
+%    Sets normal font size. The default is 10pt.
+% 
+% conference, journal, technote, peerreview, peerreviewca
+%    determines format mode - conference papers, journal papers,
+%    correspondence papers (technotes), or peer review papers. The user
+%    should also select 9pt when using technote. peerreview is like
+%    journal mode, but provides for a single-column "cover" title page for
+%    anonymous peer review. The paper title (without the author names) is
+%    repeated at the top of the page after the cover page. For peer review
+%    papers, the \IEEEpeerreviewmaketitle command must be executed (will
+%    automatically be ignored for non-peerreview modes) at the place the
+%    cover page is to end, usually just after the abstract (keywords are
+%    not normally used with peer review papers). peerreviewca is like
+%    peerreview, but allows the author names to be entered and formatted
+%    as with conference mode so that author affiliation and contact
+%    information can be easily seen on the cover page.
+%    The default is journal.
+%
+% draft, draftcls, draftclsnofoot, final
+%    determines if paper is formatted as a widely spaced draft (for
+%    handwritten editor comments) or as a properly typeset final version.
+%    draftcls restricts draft mode to the class file while all other LaTeX
+%    packages (i.e., \usepackage{graphicx}) will behave as final - allows
+%    for a draft paper with visible figures, etc. draftclsnofoot is like
+%    draftcls, but does not display the date and the word "DRAFT" at the foot
+%    of the pages. If using one of the draft modes, the user will probably
+%    also want to select onecolumn.
+%    The default is final.
+%
+% letterpaper, a4paper
+%    determines paper size: 8.5in X 11in or 210mm X 297mm. CHANGING THE PAPER
+%    SIZE WILL NOT ALTER THE TYPESETTING OF THE DOCUMENT - ONLY THE MARGINS
+%    WILL BE AFFECTED. In particular, documents using the a4paper option will
+%    have reduced side margins (A4 is narrower than US letter) and a longer
+%    bottom margin (A4 is longer than US letter). For both cases, the top
+%    margins will be the same and the text will be horizontally centered. 
+%    For final submission to IEEE, authors should use US letter (8.5 X 11in)
+%    paper. Note that authors should ensure that all post-processing 
+%    (ps, pdf, etc.) uses the same paper specificiation as the .tex document.
+%    Problems here are by far the number one reason for incorrect margins.
+%    IEEEtran will automatically set the default paper size under pdflatex 
+%    (without requiring a change to pdftex.cfg), so this issue is more
+%    important to dvips users. Fix config.ps, config.pdf, or ~/.dvipsrc for
+%    dvips, or use the dvips -t papersize option instead as needed. See the
+%    testflow documentation
+%    http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/testflow
+%    for more details on dvips paper size configuration.
+%    The default is letterpaper.
+%
+% oneside, twoside
+%    determines if layout follows single sided or two sided (duplex)
+%    printing. The only notable change is with the headings at the top of
+%    the pages.
+%    The default is oneside.
+%
+% onecolumn, twocolumn
+%    determines if text is organized into one or two columns per page. One
+%    column mode is usually used only with draft papers.
+%    The default is twocolumn.
+%
+% nofonttune
+%    turns off tuning of the font interword spacing. Maybe useful to those
+%    not using the standard Times fonts or for those who have already "tuned"
+%    their fonts.
+%    The default is to enable IEEEtran to tune font parameters.
+%
+%
+%*******
+% 11/2002 V1.6b (MDS) changes:
+%
+% 1) Fixed problem with figure captions when using hyperref. Thanks to 
+%    Leandro Barajas and Michael Bassetti for reporting this bug.
+%
+% 2) Provide a fake nabib command \NAT@parse so that hyperref will not
+%    interfere with the operation of cite.sty. However, as a result citation
+%    numbers will not be hyperlinked. Also, natbib will not be able to work
+%    with IEEEtran. However, this is perhaps the best solution until cite.sty
+%    and hyperref.sty are able to co-exist with each other.
+%    It easy enough to override the fake command via:
+%    \makeatletter
+%    \let\NAT@parse\undefined
+%    \makeatother
+%
+% 3) Revised font selection method so as not to have problems when used
+%    with setspace.sty. Thanks to Zhang Yan for reporting this bug.
+%
+% 4) Added \special to feed papersize to dvips. Thanks to Moritz Borgmann 
+%    for suggesting this feature.
+%
+% 5) In addition to the IEEE IED lists, the original IED style list
+%    environments (as is done in article.cls) are now provided as
+%    LaTeXitemize, LaTeXenumerate, and LaTeXdescription. Also, users can
+%    now redefine \makelabel within IEEE IED list controls. There may be
+%    some use for this in specialized applications. Thanks to Eli Barzilay
+%    for suggesting this feature.
+%
+% 6) \table* now defaults to \footnotesize text like \table.
+%
+% 7) The draft modes now no longer force a pagebreak after the title.
+%    Thanks to Christian Peel for suggesting this change.
+%
+% 8) New draftclsnofoot mode is like draftcls, but does not display the
+%    date and the word "DRAFT" at the foot of the page. Thanks to
+%    Christian Peel for suggesting this feature.
+%
+% 9) New peerreview and peerreviewca modes with \IEEEpeerreviewmaketitle
+%    command allows for a "cover" titlepage for anonymous peer review.
+%    Except for the cover titlepage, peerreview is much like journal mode.
+%    peerreviewca is like peerreview, but allows the author names to be
+%    entered and formatted as under conference mode so that author
+%    affiliations and contact information can be easily seen on the cover
+%    page. Thanks to Eric Benedict for suggesting this feature.
+%
+%
+%*******
+% 7/2002 V1.6 (MDS) changes:
+% 
+% 1) Added conference mode via conference option. Defaults to the traditional
+%    journal mode. i.e., \documentclass[conference]{IEEEtran}
+% 
+% 2) Added support for A4 paper via new a4paper option. Pdflatex's paper size
+%    lengths are now automatically set to the proper paper size being used.
+% 
+% 3) Revised margins again. Page text is now horizontally centered.
+%    Conference mode increases the top and bottom margins with the bottom
+%    margin being slightly larger. For A4 paper, the top margin and text
+%    typesetting will not change from those of US letter paper, but the side
+%    margins will be smaller and the bottom margin will be larger than that of
+%    US letter. All per IEEE specs.
+%
+% 4) Fixed footnote line spacing anomaly in draft mode. 
+%    Thanks to Alberto Rodriguez for reporting this bug.
+%    
+%    Also, slightly revised footnote and \thanks note spacing.
+%    Set \interfootnotelinepenalty=10000 to prevent LaTeX
+%    from breaking footnotes across multiple pages or columns.
+%
+% 5) Fixed bug that caused overwritten photo areas and sometimes anomalous
+%    spacing when a new paragraph was started within a biography. Also,
+%    the presence of \par's, new lines or spaces at the beginning of
+%    abstract, keywords, biography, or biographynophoto will no longer
+%    affect the first word spacing.
+%    Thanks to Eric Durant for reporting this bug.
+%    
+%    The biography environment now does a better job in preventing
+%    a biography photo area from being broken across pages or columns.
+%
+% 6) Fixed whitespace between \cite entries bug. i.e.,
+%    both \cite{einstein24, knuth84} and \cite{einstein24,knuth84}
+%    are now valid. \cite is now a robust command as it should be.
+%    IEEEtran now no longer defines the old non-standard \shortcite or 
+%    \citename.
+%    
+%    The base IEEEtran.cls does not sort citation numbers or produce ranges
+%    for three or more consecutive numbers. However, V1.6 of IEEEtran.cls 
+%    now pre-defines the following format control macros to facilitate easy 
+%    use with Donald Arseneau's cite.sty package (tested with cite.sty V3.9):  
+%
+%    \def\citepunct{], [}
+%    \def\citedash{]--[}
+%    
+%    cite.sty is standard on most LaTeX sytems and can be obtained from
+%    www.ctan.org. Thanks to Donald Arseneau for creating cite.sty, providing
+%    the required format arguments to produce the IEEE style. and
+%    designing a cite interface capable of handling the IEEE citation
+%    style.
+%    
+%    Note: Historically, IEEE has wanted authors to "hardcode" symbolics.
+%    (i.e., replace all \cite{} with fixed [x]). However, it now seems that
+%    most electronic manuscript submissions to IEEE are in .pdf format, and 
+%    as such, do not require the LaTeX document reference numbers to be hard
+%    coded. If an author is required to submit actual LaTeX files, I do 
+%    recommend that the bibliography file (.bbl) be copied into the .tex 
+%    document and the \bibliographystyle{} and \bibliography{} commands be 
+%    commented out so that the .tex file does not depend on (potentially 
+%    lengthy and/or confidential) external bibliography database files.
+%
+% 7) Adjusted some spacing parameters. The spacing above and below equations
+%    has been revised (to a typical IEEE value). \jot now has a decent value.
+%    The title text is now exactly 24pt. (On a related note, \fontsubfuzz has
+%    been increased to 0.9pt to prevent annoying font substitution warnings
+%    when using the Computer Modern fonts that use the 24.88pt size.)
+%    In V1.6, \small is now 8.5pt in 9pt docs because \footnotesize is 8pt. 
+%    For 9pt docs, you should probably go ahead and use \footnotesize when you
+%    need text a little smaller than \normalsize.
+%    The interword spacing has been adjusted to be extremely close to that
+%    which IEEE uses. You can use a new class option, nofonttune, if you need
+%    to disable the adjusting of the interword spacing. This adjustment and
+%    an increase to \hyphenpenalty have greatly reduced the amount of
+%    hyphenation in a typical paper.
+%       The baselineskip for the normalsize fonts has been tweaked to reduce
+%    underfull vboxes on journal paper columns with only paragraphs. 
+%    Conference mode does the same thing but by also tweaking the \textheight
+%    slightly off 9.25in (IEEE spec) to ensure an integer number of lines per
+%    page. Draft (also draftcls) mode has also been revised to reduce 
+%    underfull vbox warnings. However, draft mode can still produce underfull
+%    vboxes (a direct result of the increase in line spacing and margins) if:
+%    A non-normalsize font occupies an entire column (abstract and index terms
+%    take up a whole column by themselves); or the beginning of a section
+%    occurs near the end of a column and cannot be squeezed into the bottom,
+%    etc. This is normal as draft mode's liberal spacings cannot guarantee
+%    perfect formatting.
+%
+% 8) New biographynophoto environment for biographies without photos.
+%    Usage: 
+%    
+%    \begin{biographynophoto}{author name}
+%    biography text here 
+%    \end{biographynophoto}
+%    
+% 9) Fixed bug that produced multiple table of contents entries for papers
+%    with more than one biography. Also, biography now works better with
+%    hyperref.
+% 
+%10) New \sublargesize font size command provides for 11pt text in a 10pt
+%    document. (Needed for things like author names.) For documents not
+%    using 10pt normal size text, \sublargesize is currently identical 
+%    to \large.
+%
+%11) New \IEEEmembership command to provide correct font to indicate IEEE
+%    membership for journal papers.
+%
+%12) Fixed author name line overflow problem when in journal mode. This
+%    problem had been introduced in V1.5 in my rush to get \and to work for
+%    conferences. \and is unneeded (and invalid) in journal mode. For 
+%    conference mode, \and will work as expected and features an optional
+%    spacing argument. i.e., \and[\hspace{5ex}] 
+%    \and will default (recommended) to using \hfill which will result in
+%    equal spacing between author blocks.
+% 
+%13) New \authorblockN, \authorblockA and \authorrefmark commands to 
+%    facilitate easy formatting of author names, affiliations and cross
+%    reference symbols, respectively, when in conference mode. These 
+%    three commands are to be used only for conference papers.
+%    In conference mode, \author text is placed within a modified tabular
+%    environment (somewhat like article.cls). So, within \author in conference
+%    mode, you should not try to enclose multiple \\ within an environment or
+%    command (other than the argument braces of \authorblockX{}). For example:
+%    
+%    \author{\authorblockN{{John Doe \\ Jane Doe}}} % WRONG!
+%    
+%    will generate an error. 
+%  
+%    Note that font size/attribute changes will now persists across \\ within
+%    \author. (But, not across author blocks nor across \and.)
+%    However, with the new commands, there should be no need to alter any
+%    font attributes within \author. All text sizing and spacing within 
+%    \author{} and the author block commands is per IEEE specs for both 
+%    conference and journal modes. (In conference mode, the author names
+%    are only very slightly larger than the affiliations which are in normal
+%    size.) For specialized applications you can alter the justification of
+%    author lines by placing \hfill at the beginning or at the end of a line.
+%    The interline spacing within \author is determined by the font attributes
+%    that are in effect at the end of each line within author.
+% 
+%14) Because the titles and author name blocks use different font sizes/styles
+%    from the main text, it was possible that two column papers with titles that
+%    span both columns (standard journal and conference papers, but not technotes)
+%    with certain numbers of lines for the title and authors' name/affiliations
+%    can cause underfull vbox problems (paragraphs with large spacings between
+%    them) in the second column of the main text on the title page - if there were
+%    no new sections, equations or figures in this column (they would provide some
+%    needed rubber spacing). The use of things like special paper notices and
+%    publisher ID marks also affected this issue. The problem could not happen
+%    in the first column because the first column has a rubber length around the
+%    heading of the first section. Furthermore, problems seldom occurred on pages
+%    after the first as the margins had been chosen not to cause it with the popular
+%    font sizes. Rubber lengths after the author names would not fix this problem.
+%       Auto-calculating a "good" spacing after the title is a tad difficult
+%    to do in LaTeX. However, I am pleased to report that V1.6 has this new
+%    capability - "dynamically determined title spacing". IEEEtran will now
+%    measure the height of all the title and author text in \maketitle
+%    and then calculate a rigid (non-rubber) spacer to follow that meets
+%    IEEE specs and also produces a \textheight on the title page that ensures
+%    an integer number of normalsized lines on the rest of the page. Single
+%    column  papers, and two column papers with the title entirely in column
+%    one (technotes) do not need dynamic rigid spacing and therefore use
+%    standard rubber spacers.
+%    
+%    Note: This problem can still crop up if you use floats that span both
+%    columns (i.e., figure*). It has been a decade+ long limitation with LaTeX
+%    that the stretchable portion of \dbltextfloatsep is ignored. 
+%    If you get a problem with underful vbox warnings and paragraphs that "are
+%    pulled apart" on page with a float that spans both columns, tweak the 
+%    space between the figure and the main text a little:
+%    
+%    \vskip 5pt
+%    \end{figure*}
+%    
+%    If you can't find a value that fixes both columns, you are going to
+%    have to put a rubber spacer somewhere in one or both of the columns.
+% 
+%15) Because of change #14 above, those of you using \pubid will, as of V1.6,
+%    have to place it *before* \maketitle in order for it have the intended 
+%    affect. The dynamic spacer algorithm must see if you are using \pubid when
+%    \maketitle is called. \pubidadjcol works as before except that it now 
+%    has additional logic to prevent it from doing anything if \pubid was never
+%    called.
+%    
+%16) In some unusual, non-standard circumstances, an author may desire to
+%    alter the spacing after the title area or put some unusual text above
+%    the main text. For instance, to stop a bad break when a new section
+%    occurs right at the start of the second page. This is difficult to do
+%    when the title spans both columns of two column text since LaTeX treats
+%    such title text as a type of float. A new command, \IEEEaftertitletext{}, 
+%    gives access to the end of that produced by \maketitle. The types of
+%    things that can go into \IEEEaftertitletext are the same as those into 
+%    \twocolumn[] - no \par, but \\ are OK. There is no restriction on the
+%    range of spacings that can be used. 
+%    i.e., \IEEEaftertitletext{\vspace{-100pt}} will push the main text well
+%    into the title and \IEEEaftertitletext{\vspace{100pt}} will push it far down
+%    the page. You will have complete control. If used, place
+%    \IEEEaftertitletext{} before \maketitle like \title and \author. IEEEtran's
+%    dynamic title spacing intentionally does not take into consideration the 
+%    contents of \IEEEaftertitletext{} when determining the spacer after the title
+%    area (otherwise it would try to second guess you), so the user will have
+%    manually adjust the height of the contents in \IEEEaftertitletext{} if the
+%    problem discussed in #14 above should develop. A safe bet is to keep
+%    the height of contents of \IEEEaftertitletext{} to integer multiples of 
+%    \baselineskip, i.e., \IEEEaftertitletext{\vspace{-1\baselineskip}} 
+%    
+%    Because it can result in an IEEE nonstandard format, the use of
+%    \IEEEaftertitletext{} is discouraged. Possible uses include (1) the use of
+%    IEEEtran for non-IEEE work with different title spacing requirements,
+%    or (2) as an emergency manual override if a problem should develop in 
+%    IEEEtran's automatic spacing algorithm.
+% 
+%17) completely rewritten \PARstart to:
+%    a. no longer have problems when the user begins an environment
+%       within the paragraph that uses \PARstart.
+%    b. auto-detect and use the current font family
+%    c. revise handling of the space at the end of the first word so that
+%       interword glue will now work as normal.
+%    d. produce correctly aligned edges for the (two) indented lines.
+%
+%    Because the current font family is now auto-detected, there is no
+%    longer any need for \CMPARstart - it is now the same as \PARstart.
+%   
+%18) There is now a new "open box" Q.E.D. symbol (\QEDopen) as well as the
+%    original default (\QED) closed one (\QEDclosed). Some journals use
+%    the open form. To make \proof use the open form, just do:
+%    \renewcommand{\QED}{\QEDopen}
+%
+%19) Additional \typeout{} notices added to warn the user when unusual 
+%    settings/commands are detected or as reminders to avoid common errors
+%    when in conference mode.
+%
+%20) IEEEtran now provides \abovecaptionskip and \belowcaptionskip skip
+%    registers because article class provides them and some packages
+%    may error if they are missing. However, IEEEtran only uses 
+%    \abovecaptionskip for actual caption spacing.
+%
+%21) Fixed bug that prevented users from redefining the section headings
+%    to use arabic digits. Thanks to Richardt H. Wilkinson for reporting
+%    this bug.
+%
+%22) Code cleaned up to be more efficient with the use of TeX registers;
+%    removed some old LaTeX 2.09 code; revised option processing to 
+%    LaTeX2e standard; eliminated unwanted "phantom" spaces in some
+%    environments.
+%
+%23) Added new \IEEEeqnarray, \IEEEeqnarraybox, \IEEEeqnarrayboxm and 
+%    \IEEEeqnarrayboxt environments to provide superior alternatives to the
+%    standard LaTeX \eqnarray, \array and \tabular. Additional new support
+%    commands include \IEEEeqnarraydecl, \IEEEeqnarrayboxdecl,
+%    \IEEEeqnarraymathstyle, \IEEEeqnarraytextstyle, \yesnumber. \IEEEnonumber,
+%    \IEEEyesnumber, \IEEEyessubnumber, \IEEEeqnarraynumspace, \IEEEeqnarraymulticol,
+%    \IEEEeqnarrayomit, \IEEEeqnarraydefcol, \IEEEeqnarraydefcolsep, \IEEEeqnarrayseprow,
+%    \IEEEeqnarrayseprowcut, \IEEEeqnarrayrulerow, \IEEEeqnarraydblrulerowcut,
+%    \IEEEeqnarraystrutmode, \IEEEeqnarraystrutsize, \IEEEeqnarraystrutsizeadd, 
+%    \IEEEvisiblestrutstrue, \IEEEvisiblestrutsfalse and \IEEEstrut.
+%    These are documented in the user's guide.
+%    
+%24) V1.6 changed back to using () around theorem names (which are also now in italics)
+%    as this is what IEEE is using now. Thanks to Christian Peel for reporting this.
+%    Also, when section numbers are used as the first part of theorem numbers, display
+%    them in arabic, not Roman.
+%    
+%25) New \IEEEtriggeratref{X} command allows a page break to be triggered just
+%    before the given reference number "X". This is most useful when balancing
+%    the columns on the last page and a \newpage between references is desired.
+%    \IEEEtriggercmd{X} allows a different command to be executed at trigger.
+%
+%
+%*******
+% 7/2001 V1.5 (MDS) changes:
+%
+%
+% 1) Fixed \and within \author bug: (! Misplaced \crcr. \endtabular ->\crcr)
+%    Thanks to Rainer Dorsch for discovering and reporting that \and 
+%    did not work.
+%    
+% 2) Fixed the biography environment so that if a biography's text is shorter
+%    than the area allocated for the photo, a collision with the next
+%    biography does not occur. You can now put real graphics (using the
+%    graphicx package) into the biography photo box with a new optional 
+%    argument of the biography command! For example:
+%    
+%    \begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{./tux.eps}}]{Linux Penguin}
+%    
+%    will use the specified graphic as the author's photo. The photo area is
+%    exactly 1in wide by 1.25in high - as is done in IEEE Transactions. Try
+%    to keep the same 4:5 aspect ratio if scanning/cropping your photos. 
+%    Note the need for the extra set of enclosing braces around the
+%    \includegraphics. Without it, The LaTeX parser may get confused when it
+%    sees the \includegraphics's brackets within the biography's optional
+%    argument. Due to the length of the \includegraphics command, you may wish
+%    to define your own shorthand form of it. I have not done so with IEEEtran 
+%    to prevent dependence on the graphicx package. If you do not use the 
+%    optional argument, or leave it empty, a standard frame box with the 
+%    words "Place Photo Here" will be used. If you want the space to remain
+%    completely empty, you can do:
+%    
+%    \begin{biography}[\mbox{}]{The Invisible Man} 
+%    
+%    The interface to biography's optional argument is into a
+%    1in X 1.25in minipage in which the argument text is centered both 
+%    horizontally and vertically:
+%    
+%    \begin{minipage}[b][1.25in][c]{1in}%
+%    \centering
+%    #1%
+%    \end{minipage}
+%    
+%    Within the biography environment, \unitlength is set to 1in.
+%    With this in mind, you can even design your own custom frameboxes.
+%    For instance:
+%    
+%    \begin{biography}[\framebox(1,1.25){\parbox[][\height][c]{0.9in}{\centering PLACE\\ PHOTO\\ HERE}}]{Author Name}
+%    
+%    will yield the same type of result as the default photo box.
+%    
+%    Thanks to Herbert Voss for discovering the collision bug, suggesting the ability
+%    to handle graphics and providing some prototype code.
+%
+%
+%
+%*******
+% 3/2001 V1.4 (MDS) changes:
+%
+%
+% 1) New "draftcls" and "final" options have been added.
+%    Thanks to Dragan Cvetkovic for suggesting an option like draftcls.
+%    
+% 2) Documentation changes to reflect the fact that this IEEEtran.cls 
+%    is no longer beta test.
+%
+% 3) Slightly revised caption sizes. Figure and table captions are now 
+%    in \footnotesize, not \small as before.
+%
+% 4) Allow user to control figure caption justification. IEEEtran.cls 
+%    normally defaults to left justified as is done in Transactions.
+%    However, for conferences, you may wish to issue the command:
+%    \centerfigcaptionstrue
+%    in the preamble. Short (less than one line long) figure captions
+%    will then be centered. Multi-line figure captions will always be 
+%    properly left justified. V1.6: This is already done for you when
+%    using the conference mode.
+%
+%
+%
+%*******
+% 1/2001 V1.3 
+% Michael Shell (MDS) made extensive changes and additions:
+%
+%
+% BUGS FIXED (and many others too numerous to mention!):
+% 1) Fixed improper alignment with itemized, enumerated and
+%    description lists. Added new controls to these three
+%    environments so that it is easy to get the alignment IEEE
+%    uses. Furthermore, the itemize, enumerate and description lists
+%    no longer force a new paragraph to begin at the end the list
+%    (\par). (Sometimes lists are used within paragraphs.) 
+% 
+% 2) JVH's fixes now allow things like $\mathbf{N}(0,P(0))$
+%    to work properly without needing the extra braces:
+%    ${\mathbf{N}}(0,P(0))$. There is no longer any dependence
+%    on the "rawfonts" and "oldlfont" packages. Thanks Juergen! 
+% 
+% 3) Fixed underfull hbox errors and incorrect reference number
+%    alignment when the number of references in the bibliography
+%    exceeded 9 entries (which is almost every paper!).
+%  
+% 4) Removed dependence on the LaTeX sizexx.clo files.
+%    Now, 9pt documents should work correctly even on systems that
+%    lack a size9.clo file. This is most often used in conjunction
+%    with the option "technote" for "correspondence" papers like those
+%    in IEEE Transactions on Information Theory. For virtually all
+%    other papers, 10pt is used and so it is the default.
+%    Some improper font sizes have been corrected. \footnotesize is
+%    now 8pt in 9pt docs, so footnotes in technotes should be the
+%    correct size now. 
+% 
+% 5) Added \interlinepenalty within the bibliography section to discourage
+%    LaTeX from breaking within a reference. IEEE almost never breaks within
+%    a reference and when they do it is usually in technotes
+%    (correspondence papers). You may get an underfull vbox warning in the
+%    bibliography indicating that the spacing just before the "REFERENCES" 
+%    section is larger than normal, but the final result will be more like 
+%    what IEEE will publish. See the comments in the BIBLIOGRAPHY section
+%    around line 2034 below if you want to change this behavior.
+%
+% 6) No longer "blows up" when you use \paragraph and have a table
+%    of contents.
+% 
+% 7) Theorem environment changed, (but for V1.6, back to the old way, sigh).
+% 
+% 8) Figure captions adjusted: IEEE left (not center) justifies
+%    figure captions (for journals) and does not indent figure caption text.
+% 
+% 9) Adjusted some spacings in the table of contents(TOC))/list-of-figures/
+%    list-of-tables so that section/table numbers will not so easily 
+%    collide with the titles. Section VIII was usually the worst offender.
+%    Still doesn't right justify the section numbers, but neither does 
+%    article.cls (This must be why LaTeX likes the x.y.z section numbering
+%    scheme unlike I, II, III, etc. of IEEE. )
+%    It may be "normal" as it is (left justified). sigh.
+% 
+%10) Now uses "index terms" now as a heading instead of "keywords".
+%    Furthermore, the "index terms" and "abstract" headings are in bold
+%    italic. This is how IEEE does things.
+%
+%11) \thebibliography and \biography now put entries into
+%    the table of contents for you.
+%
+% *******
+%
+%
+%
+%
+%
+% *******
+% 9/2000 (JVH) changes: (now designated as V1.2)
+% 
+% made some corrections to get closer to LaTeX2e
+% 20000906 Juergen v.Hagen
+% vonhagen@ihefiji.etec.uni-karlsruhe.de
+% 
+% Permission to redistribute granted as of December 2000.
+% *******
+%
+%
+%
+%
+%
+% *******
+% 
+% 1996 (JWD) LaTeX2e version: (now designated as V1.1)
+%  
+% In the most recent TeXhax digest, there was a request for a copy of
+% IEEEtrans.sty modified to work with LaTeX2e.  I have a version I
+% modified to make it IEEEtrans.cls, which I have sent to the person
+% making the request and am now sending to you to consider posting to
+% the archives.
+% --
+% Jon Dixon
+% dixonj@colorado.edu
+% http://spot.colorado.edu/~dixonj/
+%
+%*******
+%
+%
+%
+%
+%
+%*******
+%
+% 30-August-1993 original LaTeX 2.09 version (IEEEtran.sty),
+% (now designated as V1.0):
+%
+% by Gerry Murray and Silvano Balemi
+% Automatic Control Lab, ETH Zurich, Switzerland
+% balemi@aut.ee.ethz.ch
+%
+%*******
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%
+%
+%
+%
+\ProvidesClass{cssconf}[2004/1/15 revision V1.6b by Pradeep Misra]
+%\ProvidesClass{IEEEtran}[2002/11/18 revision V1.6b by Michael Shell]
+%\typeout{-- See the "IEEEtran_HOWTO" manual for usage information.}
+%\typeout{-- The source comments contain changelog notes.}
+\NeedsTeXFormat{LaTeX2e}
+
+% define new needed flags to indicate document options
+% and set a few "failsafe" defaults
+\newif\if@twocolumnmode      \global\@twocolumnmodetrue
+\newif\if@draftversion       \global\@draftversionfalse
+\newif\if@draftclsmode       \global\@draftclsmodefalse
+\newif\if@draftclsmodefoot   \global\@draftclsmodefootfalse
+\newif\if@confmode           \global\@confmodefalse
+\newif\if@peerreviewoption   \global\@peerreviewoptionfalse
+\newif\if@peerreviewcaoption \global\@peerreviewcaoptionfalse
+
+% we HAVE to turn off technote as there is no
+% "not a tech note" option
+\newif\if@technote      \global\@technotefalse
+
+% V1.6 we allow the user to control whether or not the
+% font interword spacings are tuned to be more like
+% that of IEEE. The default is to tune things.
+\newif\if@fonttunesettings   \global\@fonttunesettingstrue
+
+% V1.6b flag to show if using a4paper
+\newif\if@IEEEusingAfourpaper      \global\@IEEEusingAfourpaperfalse
+
+% IEEEtran class scratch pad registers
+% dimen
+\newdimen\@IEEEtrantmpdimenA
+\newdimen\@IEEEtrantmpdimenB
+% count
+\newcount\@IEEEtrantmpcountA
+\newcount\@IEEEtrantmpcountB
+% token list
+\newtoks\@IEEEtrantmptoksA
+
+% we use \@IEEEptsize so that we can ID the point size (even for 9pt docs)
+% as well as LaTeX's \@ptsize to retain some compatability with some
+% external packages
+\def\@IEEEptsize{10}
+\def\@ptsize{0}
+% LaTeX does not support 9pt, so we set \@ptsize to 0 - same as that of 10pt
+\DeclareOption{9pt}{\def\@IEEEptsize{9}\def\@ptsize{0}}
+\DeclareOption{10pt}{\def\@IEEEptsize{10}\def\@ptsize{0}}
+\DeclareOption{11pt}{\def\@IEEEptsize{11}\def\@ptsize{1}}
+\DeclareOption{12pt}{\def\@IEEEptsize{12}\def\@ptsize{2}}
+
+
+% \@IEEEmarginE is the side margin for equal margins
+% \@IEEEmarginW is the wider side margin when the margins are not equal
+% NOTE: BOTH of the above margins are as they appear
+% on the paper - they are NOT offset by 1 inch
+%\DeclareOption{letterpaper}{\setlength{\paperheight}{11in}%
+%                            \setlength{\paperwidth}{8.5in}%
+%                            \def\@IEEEmarginE{0.680in}%
+%                            \def\@IEEEmarginW{0.775in}%
+%                            \@IEEEusingAfourpaperfalse}
+%
+%
+%\DeclareOption{a4paper}{\setlength{\paperheight}{297mm}%
+%                        \setlength{\paperwidth}{210mm}%
+%                        \def\@IEEEmarginE{14.32mm}%
+%                        \def\@IEEEmarginW{17mm}
+%                        \@IEEEusingAfourpapertrue}
+%
+% [2004/1/15 revision V1.6b by Pradeep Misra]
+\DeclareOption{letterpaper}{\setlength{\paperheight}{11in}%
+                            \setlength{\paperwidth}{8.5in}%
+%			    \setlength{\topmargin}{0in}%
+                            \def\@IEEEmarginE{0.75in}%
+                            \def\@IEEEmarginW{0.75in}}
+
+
+\DeclareOption{a4paper}{\setlength{\paperheight}{297mm}%
+                        \setlength{\paperwidth}{210mm}%
+			\setlength{\topmargin}{-0.69in}%
+                        \def\@IEEEmarginE{13.15mm}%
+                        \def\@IEEEmarginW{0.75in}}
+
+
+\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}
+\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue}
+
+\DeclareOption{onecolumn}{\global\@twocolumnmodefalse}
+% the file twocolumn.sty is not read as it changes \textwidth.
+\DeclareOption{twocolumn}{\global\@twocolumnmodetrue}
+
+% If the user selects draft, then this class AND any packages
+% will go into draft mode.
+\DeclareOption{draft}{\global\@draftversiontrue \global\@draftclsmodetrue
+\global\@draftclsmodefoottrue} 
+% draftcls is for a draft mode which will not affect any packages
+% used by the document.
+\DeclareOption{draftcls}{\global\@draftversionfalse \global\@draftclsmodetrue
+\global\@draftclsmodefoottrue} 
+% draftclsnofoot is like draftcls, but without the footer.
+\DeclareOption{draftclsnofoot}{\global\@draftversionfalse \global\@draftclsmodetrue
+\global\@draftclsmodefootfalse} 
+% we provide a final option just for completeness (article.cls has one)
+\DeclareOption{final}{\global\@draftversionfalse \global\@draftclsmodefalse
+\global\@draftclsmodefootfalse}
+
+\DeclareOption{journal}{\global\@peerreviewoptionfalse \global\@peerreviewcaoptionfalse
+\global\@confmodefalse \global\@technotefalse}
+
+\DeclareOption{conference}{\global\@peerreviewoptionfalse \global\@peerreviewcaoptionfalse
+\global\@confmodetrue \global\@technotefalse}
+
+\DeclareOption{technote}{\global\@peerreviewoptionfalse \global\@peerreviewcaoptionfalse
+\global\@confmodefalse \global\@technotetrue}
+
+\DeclareOption{peerreview}{\global\@peerreviewoptiontrue \global\@peerreviewcaoptionfalse
+\global\@confmodefalse \global\@technotefalse}
+
+\DeclareOption{peerreviewca}{\global\@peerreviewoptiontrue \global\@peerreviewcaoptiontrue
+\global\@confmodefalse \global\@technotefalse}
+
+\DeclareOption{nofonttune}{\global\@fonttunesettingsfalse}
+
+
+% IEEE uses Times font, so we'll default to times.
+% These three commands make up the entire times.sty package.
+\renewcommand{\sfdefault}{phv}
+\renewcommand{\rmdefault}{ptm}
+\renewcommand{\ttdefault}{pcr}
+% enable Times now - so that all class options can see the correct font families
+\normalfont\selectfont
+
+
+% default to US letter paper, 10pt, twocolumn, one sided, final, journal
+\ExecuteOptions{letterpaper,10pt,twocolumn,oneside,final,journal}
+% overrride these defaults per user requests
+\ProcessOptions
+
+% we can send console reminder messages to the user here
+\AtEndDocument{\if@confmode%
+\typeout{}%
+\typeout{** Conference Paper **}%
+\typeout{Before submitting the final camera ready copy, remember to:}%
+\typeout{}%
+\typeout{ 1. Manually equalize the lengths of two columns on the last page}%
+\typeout{ of your paper;}%
+\typeout{}%
+\typeout{ 2. Ensure that any PostScript and/or PDF output post-processing}%
+\typeout{ uses only Type 1 fonts and that every step in the generation}%
+\typeout{ process uses the US letter (8.5in X 11in) paper size.}%
+\typeout{}%
+\fi}
+
+
+% warn about the use of single column other than for draft mode
+\if@twocolumnmode\else%
+  \if@draftclsmode\else%
+   \typeout{** ATTENTION: Single column mode is not normally used with IEEE publications.}%
+  \fi%
+\fi
+
+
+% V1.6, if the user is using pdflatex, go ahead and set the output paper size.
+% Otherwise, we declare the papersize via a \special for dvips.
+% We keep the tests within braces because otherwise, if not using pdflatex,
+% \pdfpageheight and \pdfpagewidth will be set to \relax - possibly affecting
+% similar tests of other packages.
+{\@ifundefined{pdfpageheight}{% not using pdflatex, setup paper size for dvips
+\if@IEEEusingAfourpaper
+\special{papersize=210mm,297mm}%
+\else
+\special{papersize=8.5in,11in}%
+\fi}%
+{% using pdftex, set paper size for pdftex
+\global\pdfpageheight\paperheight\global\pdfpagewidth\paperwidth}}
+
+
+
+% The idea hinted here is for LaTeX to generate markleft{} and markright{}
+% automatically for you after you enter \author{}, \journal{},
+% \journaldate{}, journalvol{}, \journalnum{}, etc.
+% However, there may be some backward compatibility issues here as
+% well as some special applications for IEEEtran.cls and special issues
+% that may require the flexible \markleft{}, \markright{} and/or \markboth{}.
+% We'll leave this as an open future suggestion.
+%\newcommand{\journal}[1]{\def\@journal{#1}}
+%\def\@journal{}
+
+
+
+% pointsize values
+% used with ifx to determine the document's normal size
+\def\@IEEEptsizenine{9}
+\def\@IEEEptsizeten{10}
+\def\@IEEEptsizeeleven{11}
+\def\@IEEEptsizetwelve{12}
+
+
+
+% FONT DEFINITIONS (No sizexx.clo file needed) 
+% V1.6 revised font sizes, displayskip values and
+%      revised normalsize baselineskip to reduce underfull vbox problems
+%      on the 58pc = 696pt = 9.5in text height we want
+%      normalsize     #lines/column  baselineskip (aka leading)
+%             9pt     63             11.0476pt (truncated down)
+%            10pt     58             12pt      (exact)
+%            11pt     52             13.3846pt (truncated down)
+%            12pt     50             13.92pt   (exact)
+%
+
+% we need to store the nominal baselineskip for the given font size
+% in case baselinestretch ever changes.
+\newskip\@IEEEnormalsizefontbaselineskip
+\@IEEEnormalsizefontbaselineskip\baselineskip
+
+\ifx\@IEEEptsize\@IEEEptsizenine
+\typeout{-- This is a 9 point document.}
+\def\normalsize{\@setfontsize{\normalsize}{9}{11.0476pt}}%
+\setlength{\@IEEEnormalsizefontbaselineskip}{11.0476pt}%
+\normalsize
+\abovedisplayskip 1.5ex plus3pt minus1pt%
+\belowdisplayskip \abovedisplayskip%
+\abovedisplayshortskip 0pt plus3pt%
+\belowdisplayshortskip 1.5ex plus3pt minus1pt
+\def\small{\@setfontsize{\small}{8.5}{10pt}}
+\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}
+\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}
+\def\tiny{\@setfontsize{\tiny}{5}{6pt}}
+% sublargesize is the same as large - 10pt
+\def\sublargesize{\@setfontsize{\sublargesize}{10}{12pt}}
+\def\large{\@setfontsize{\large}{10}{12pt}}
+\def\Large{\@setfontsize{\Large}{12}{14pt}}
+\def\LARGE{\@setfontsize{\LARGE}{14}{17pt}}
+\def\huge{\@setfontsize{\huge}{17}{20pt}}
+\def\Huge{\@setfontsize{\Huge}{20}{24pt}}
+\fi
+
+
+% Check if we have selected 10 points
+\ifx\@IEEEptsize\@IEEEptsizeten
+\typeout{-- This is a 10 point document.}
+\def\normalsize{\@setfontsize{\normalsize}{10}{12.00pt}}%
+\setlength{\@IEEEnormalsizefontbaselineskip}{12pt}%
+\normalsize
+\abovedisplayskip 1.5ex plus4pt minus2pt%
+\belowdisplayskip \abovedisplayskip%
+\abovedisplayshortskip 0pt plus4pt%
+\belowdisplayshortskip 1.5ex plus4pt minus2pt
+\def\small{\@setfontsize{\small}{9}{10pt}}
+\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}
+\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}
+\def\tiny{\@setfontsize{\tiny}{5}{6pt}}
+% sublargesize is a tad smaller than large - 11pt
+\def\sublargesize{\@setfontsize{\sublargesize}{11}{13.4pt}}
+\def\large{\@setfontsize{\large}{12}{14pt}}
+\def\Large{\@setfontsize{\Large}{14}{17pt}}
+\def\LARGE{\@setfontsize{\LARGE}{16}{20pt}}
+\def\huge{\@setfontsize{\huge}{20}{24pt}}
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
+\fi
+
+
+% Check if we have selected 11 points
+\ifx\@IEEEptsize\@IEEEptsizeeleven
+\typeout{-- This is an 11 point document.}
+\def\normalsize{\@setfontsize{\normalsize}{11}{13.3846pt}}%
+\setlength{\@IEEEnormalsizefontbaselineskip}{13.3846pt}%
+\normalsize
+\abovedisplayskip 1.5ex plus5pt minus3pt%
+\belowdisplayskip \abovedisplayskip%
+\abovedisplayshortskip 0pt plus5pt%
+\belowdisplayshortskip 1.5ex plus5pt minus3pt
+\def\small{\@setfontsize{\small}{10}{12pt}}
+\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
+\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
+\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
+% sublargesize is the same as large - 12pt
+\def\sublargesize{\@setfontsize{\sublargesize}{12}{14pt}}
+\def\large{\@setfontsize{\large}{12}{14pt}}
+\def\Large{\@setfontsize{\Large}{14}{17pt}}
+\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}
+\def\huge{\@setfontsize{\huge}{20}{24pt}}
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
+\fi
+
+
+% Check if we have selected 12 points
+\ifx\@IEEEptsize\@IEEEptsizetwelve
+\typeout{-- This is a 12 point document.}
+\def\normalsize{\@setfontsize{\normalsize}{12}{13.92pt}}%
+\setlength{\@IEEEnormalsizefontbaselineskip}{13.92pt}%
+\normalsize
+\abovedisplayskip 1.5ex plus6pt minus4pt%
+\belowdisplayskip \abovedisplayskip%
+\abovedisplayshortskip 0pt plus6pt%
+\belowdisplayshortskip 1.5ex plus6pt minus4pt
+\def\small{\@setfontsize{\small}{10}{12pt}}
+\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
+\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
+\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
+% sublargesize is the same as large - 14pt
+\def\sublargesize{\@setfontsize{\sublargesize}{14}{17pt}}
+\def\large{\@setfontsize{\large}{14}{17pt}}
+\def\Large{\@setfontsize{\Large}{17}{20pt}}
+\def\LARGE{\@setfontsize{\LARGE}{20}{24pt}}
+\def\huge{\@setfontsize{\huge}{22}{26pt}}
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
+\fi
+
+
+% V1.6 The Computer Modern Fonts will issue a substitution warning for
+% 24pt titles (24.88pt is used instead) increase the substitution
+% tolerance to turn off this warning
+\def\fontsubfuzz{.9pt}
+% However, the default (and correct) Times font will scale exactly as needed.
+
+
+% warn the user in case they forget to use the 9pt option with
+% technote
+\if@technote%
+ \ifx\@IEEEptsize\@IEEEptsizenine\else%
+  \typeout{** ATTENTION: Technotes are normally 9pt documents.}%
+ \fi%
+\fi
+
+
+% set \baselinestretch
+\def\baselinestretch{1}
+\if@draftclsmode% draft mode uses larger than normal spacing
+\def\baselinestretch{1.5} % controls line spacing for draft version
+\fi                       % some people may like 1.7 or greater
+                          % so that there will be even more space
+                          % for hand written comments 
+
+\normalsize % make \baselinestretch take affect
+
+
+% V1.6
+% store the normalsize baselineskip
+\newskip\normalsizebaselineskip
+\normalsizebaselineskip=\baselineskip\relax
+% store the nominal value of jot
+\newskip\normaljot
+\normaljot=0.25\normalsizebaselineskip\relax
+
+% set \jot
+\jot=\normaljot\relax
+
+
+% abstract and keywords are in \small, except 
+% for 9pt docs in which they are in \footnotesize
+% Since 9pt docs use an 8pt footnotesize, \small
+% becomes a rather awkward 8.5pt
+\let\@IEEEabskeysecsize=\small
+\ifx\@IEEEptsize\@IEEEptsizenine
+ \let\@IEEEabskeysecsize=\footnotesize
+\fi
+
+
+
+% V1.6, we are now going to fine tune the interword spacing
+% The default interword glue for Times under TeX appears to use a
+% nominal interword spacing of 25% (relative to the font size, i.e., 1em)
+% a maximum of 40% and a minimum of 19%.
+% For example, 10pt text uses an interword glue of:
+% 
+% 2.5pt plus 1.49998pt minus 0.59998pt
+% 
+% However, IEEE allows for a more generous range which reduces the need
+% for hyphenation, especially for two column text. Furthermore, IEEE
+% tends to use a little bit more nominal space between the words.
+% IEEE's interword spacing percentages appear to be:
+% 35% nominal
+% 23% minimum
+% 50% maximum
+% (They may even be using a tad more for the largest fonts such as 24pt.)
+% 
+% for bold text, IEEE increases the spacing a little more:
+% 37.5% nominal
+% 23% minimum
+% 55% maximum
+
+% here are the interword spacing ratios we'll use
+% for medium (normal weight)
+\def\@IEEEinterspaceratioM{0.35}
+\def\@IEEEinterspaceMINratioM{0.23}
+\def\@IEEEinterspaceMAXratioM{0.50}
+
+% for bold
+\def\@IEEEinterspaceratioB{0.375}
+\def\@IEEEinterspaceMINratioB{0.23}
+\def\@IEEEinterspaceMAXratioB{0.55}
+
+
+% command to revise the interword spacing for the current font under TeX:
+% \fontdimen2 = nominal interword space
+% \fontdimen3 = interword stretch
+% \fontdimen4 = interword shrink
+% since all changes to the \fontdimen are global, we can enclose these commands
+% in braces to confine any font attribute or length changes
+\def\@@@IEEEsetfontdimens#1#2#3{{%
+\setlength{\@IEEEtrantmpdimenB}{\f@size pt}% grab the font size in pt, could use 1em instead.
+\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
+\fontdimen2\font=\@IEEEtrantmpdimenA\relax
+\addtolength{\@IEEEtrantmpdimenA}{-#2\@IEEEtrantmpdimenB}%
+\fontdimen3\font=-\@IEEEtrantmpdimenA\relax
+\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
+\addtolength{\@IEEEtrantmpdimenA}{-#3\@IEEEtrantmpdimenB}%
+\fontdimen4\font=\@IEEEtrantmpdimenA\relax}}
+
+% revise the interword spacing for each font weight
+\def\@@IEEEsetfontdimens{{%
+\mdseries
+\@@@IEEEsetfontdimens{\@IEEEinterspaceratioM}{\@IEEEinterspaceMAXratioM}{\@IEEEinterspaceMINratioM}%
+\bfseries
+\@@@IEEEsetfontdimens{\@IEEEinterspaceratioB}{\@IEEEinterspaceMAXratioB}{\@IEEEinterspaceMINratioB}%
+}}
+
+% revise the interword spacing for each font shape
+% \slshape is not often used for IEEE work and is not altered here. The \scshape caps are
+% already a tad too large in the free LaTeX fonts (as compared to what IEEE uses) so we
+% won't alter these either.
+\def\@IEEEsetfontdimens{{%
+\normalfont
+\@@IEEEsetfontdimens
+\normalfont\itshape
+\@@IEEEsetfontdimens
+}}
+
+% if the nofonttune class option is not given, revise the interword spacing
+% for each font size (and shape and weight). Only the \rmfamily is done here
+% as \ttfamily uses a fixed spacing and \sffamily is not used as the main
+% text of IEEE papers.
+\def\@IEEEtunefonts{%
+\if@fonttunesettings
+{\selectfont\rmfamily
+\tiny\@IEEEsetfontdimens
+\scriptsize\@IEEEsetfontdimens
+\footnotesize\@IEEEsetfontdimens
+\small\@IEEEsetfontdimens
+\normalsize\@IEEEsetfontdimens
+\sublargesize\@IEEEsetfontdimens
+\large\@IEEEsetfontdimens
+\LARGE\@IEEEsetfontdimens
+\huge\@IEEEsetfontdimens
+\Huge\@IEEEsetfontdimens}\fi}
+
+% if needed, revise the interword spacing now - in case IEEEtran makes any default
+% length measurements, and make sure all the default fonts are loaded
+\@IEEEtunefonts
+
+% and again at the start of the document in case the user loaded different fonts
+\AtBeginDocument{\@IEEEtunefonts}
+
+
+
+% V1.6 
+% LaTeX is a little to quick to use hyphenations
+% So, we increase the penalty for their use and raise
+% the badness level that triggers an underfull hbox
+% warning. The author may still have to tweak things,
+% but the appearance will be much better "right out
+% of the box" than that under V1.5 and prior.
+% TeX default is 50
+\hyphenpenalty=750
+% If we didn't adjust the interword spacing, 2200 might be better.
+% The TeX default is 1000
+\hbadness=1350
+% IEEE does not use extra spacing after punctuation
+\frenchspacing
+
+
+% we want to maintain textheight as an integer multiple of
+% \baselineskip.  Keep \topsep in with this game plan too.
+\topskip=\baselineskip
+% set sizes and margins
+% Book typesetting is a world where point and pica (12pt) reign supreme.
+% IEEE textwidth is 21 pica. They have a colsep of 1 pica.
+% V1.6 conference mode margins
+\if@confmode
+  % [2004/10/15 revision V1.6c by Pradeep Misra]
+ \topmargin        -0.25in
+ \textheight        9.5in % The standard for conferences
+  % However, we will adjust this a  tad so that an integer number
+  % of lines will always fit on each page
+  % The baselineskip (leading) for each document point size is used 
+  % to determine these values
+  % rounded up an extra 0.1pt or so to prevent trouble with any rounding errors
+ \ifx\@IEEEptsize\@IEEEptsizenine\textheight=682.0pt\fi      %9.4722in  61 lines/page
+ \ifx\@IEEEptsize\@IEEEptsizeten\textheight=684.0pt\fi       %9.5in  57 lines/page
+ \ifx\@IEEEptsize\@IEEEptsizeeleven\textheight=673.2pt\fi   %9.2611in  51 lines/page
+ \ifx\@IEEEptsize\@IEEEptsizetwelve\textheight=676.8pt\fi   %9.2473in  47 lines/page
+\else
+ \topmargin        -49.0pt
+ \textheight        58pc % = 9.63in or 696pt
+\fi
+
+  % [2004/1/15 revision V1.6b by Pradeep Misra]
+%\textwidth         43pc   % 2 x 21pc + 1pc = 43pc
+%\columnsep          1pc
+
+\textwidth         7.0in   % 2 x 21pc + 1pc = 43pc
+\columnsep         0.2in
+
+% IEEE MARGIN INFO and new \overrideIEEEmargins command
+% V1.6 revised margins again
+% IEEE wants the side margins to be equal under both US letter
+% and A4 paper
+% 
+% However, for those of you who need to bind copies of your work
+% (for review distribution, etc.) the \overrideIEEEmargins
+% command will shift the text a tad away from the binding
+% edge.
+% 
+%
+
+
+% the default side margins are equal
+\oddsidemargin    \@IEEEmarginE
+\addtolength{\oddsidemargin}{-1in}% compensate for LaTeX's 1in offset
+\evensidemargin   \@IEEEmarginE
+\addtolength{\evensidemargin}{-1in}% compensate for LaTeX's 1in offset
+
+% execute \overrideIEEEmargins in the preamble to make the side margin
+% near the spine slightly wider so that the paper will be much more 
+% agreeable to being bound.  \overrideIEEEmargins will have no effect
+% when in draft or draftcls mode.
+\def\overrideIEEEmargins{\if@draftclsmode\relax\else%
+ \typeout{** ATTENTION: Overriding IEEE standard margins (line \the\inputlineno).}%
+ \if@twoside
+  % for double sided, odd pages have the bound side on the left
+  % make this the wide margin
+  \oddsidemargin\@IEEEmarginW
+  % and even pages have the narrow margin on the left
+  % as they are bound on the right
+  % evensidemargin is to be the narrow margin
+  % calculate the narrow margin and set evensidemargin
+  \setlength{\evensidemargin}{\paperwidth}%
+  \addtolength{\evensidemargin}{-\@IEEEmarginW}%
+  \addtolength{\evensidemargin}{-\textwidth}%
+ \else
+  % for single sided the bound side is always on the left
+  % make this the wide margin
+  \oddsidemargin\@IEEEmarginW
+  \evensidemargin\@IEEEmarginW
+ \fi
+ \addtolength{\oddsidemargin}{-1.0in}%  compensate for LaTeX's 1in offset
+ \addtolength{\evensidemargin}{-1.0in}%
+\fi}
+
+
+\parindent        1.0em
+
+% conference papers do not have headers, other papers need
+% to reserve space for them
+\if@confmode
+\headsep          0in
+\headheight       0in
+\else
+\headsep          0.25in
+\headheight       12pt
+\fi
+
+% V1.6, if things get too close, go ahead and let them touch
+\lineskip            0pt
+\normallineskip      0pt
+\lineskiplimit       0pt
+\normallineskiplimit 0pt
+
+
+% The distance from the lower edge of the text body to the
+% footline
+\footskip 0.4in
+
+% normally zero, should be relative to font height.
+% put in a little rubber to help stop some bad breaks (underfull vboxes)
+\parskip 0ex plus 0.2ex minus 0.1ex
+
+
+
+% draft mode settings override that of all other modes
+% provides a nice 1" margin all around the paper and extra
+% space between the lines for editor's comments
+\if@draftclsmode 
+\headsep          0.25in
+\headheight       12pt
+% want 1" from top of paper to text
+\setlength{\topmargin}{-\headsep}%
+\addtolength{\topmargin}{-\headheight}%
+
+% we want 1in side margins regardless of paper type
+\oddsidemargin      0in
+\evensidemargin     0in
+
+% set the text width - start with the entire page
+\setlength{\textwidth}{\paperwidth}%
+% subtract for the 1" top/bottom margins
+\addtolength{\textwidth}{-2.0in}%
+% give them a textheight that won't have underfull
+% vbox problems, but can't help them if they later change 
+% baselinestretch from its default
+\setlength{\textheight}{\paperheight}%
+\addtolength{\textheight}{-2.0in}%
+% subtract of first line taken by \topskip
+\addtolength{\textheight}{-1\topskip}%
+% now digitize \textheight so that the length after
+% the first line is an integer multiple of  \baselineskip
+% to cut down on underfull vbox errors in draft mode
+\divide\textheight  by \baselineskip%
+\multiply\textheight  by \baselineskip%
+% add back the first line
+\addtolength{\textheight}{\topskip}%
+\fi
+
+
+
+% margin note stuff
+\marginparsep      10pt
+\marginparwidth    20pt
+\marginparpush     25pt
+
+
+% LIST SPACING CONTROLS
+
+% Controls the amount of EXTRA spacing
+% above and below \trivlist 
+% Both \list and IED lists override this.
+% However, \trivlist will use this as will most
+% things built from \trivlist like the \center
+% environment.
+\topsep           0.5\baselineskip
+
+% Controls the additional spacing around lists preceded
+% or followed by blank lines. IEEE does not increase
+% spacing before or after paragraphs so it is set to zero.
+% \z@ is the same as zero, but faster.
+\partopsep          \z@
+
+% Controls the spacing between paragraphs in lists. 
+% IEEE does not increase spacing before or after paragraphs
+% so this is also zero. 
+% With IEEEtran.cls, global changes to
+% this value DO affect lists (but not IED lists).
+\parsep             \z@
+
+% Controls the extra spacing between list items. 
+% IEEE does not put extra spacing between items.
+% With IEEEtran.cls, global changes to this value DO affect
+% lists (but not IED lists).
+\itemsep            \z@
+
+% \itemindent is the amount to indent the FIRST line of a list
+% item. It is auto set to zero within the \list environment. To alter
+% it, you have to do so when you call the \list.
+% However, IEEE uses this for the theorem environment
+% There is an alternative value for this near \leftmargini below
+\itemindent         -1em
+
+% \leftmargin, the spacing from the left margin of the main text to
+% the left of the main body of a list item is set by \list.
+% Hence this statement does nothing for lists.
+% But, quote and verse do use it for indention.
+\leftmargin         2em
+
+% we retain this stuff from the older IEEEtran.cls so that \list
+% will work the same way as before. However, itemize, enumerate and
+% description (IED) could care less about what these are as they
+% all are overridden.
+\leftmargini        2em
+%\itemindent         2em  % Alternative values: sometimes used.
+%\leftmargini        0em
+\leftmarginii       1em
+\leftmarginiii    1.5em
+\leftmarginiv     1.5em
+\leftmarginv      1.0em
+\leftmarginvi     1.0em
+\labelsep         0.5em 
+\labelwidth         \z@
+
+
+% The old IEEEtran.cls behavior of \list is retained.
+% However, the new V1.3 IED list environments override all the
+% @list stuff (\@listX is called within \list for the
+% appropriate level just before the user's list_decl is called). 
+% \topsep is now 2pt as IEEE puts a little extra space around
+% lists - used by those non-IED macros that depend on \list.
+% Note that \parsep and \itemsep are not redefined as in 
+% the sizexx.clo \@listX (which article.cls uses) so global changes
+% of these values DO affect \list
+% 
+\def\@listi{\leftmargin\leftmargini \topsep 2pt plus 1pt minus 1pt}
+\let\@listI\@listi
+\def\@listii{\leftmargin\leftmarginii\labelwidth\leftmarginii%
+    \advance\labelwidth-\labelsep \topsep 2pt}
+\def\@listiii{\leftmargin\leftmarginiii\labelwidth\leftmarginiii%
+    \advance\labelwidth-\labelsep \topsep 2pt}
+\def\@listiv{\leftmargin\leftmarginiv\labelwidth\leftmarginiv%
+    \advance\labelwidth-\labelsep \topsep 2pt}
+\def\@listv{\leftmargin\leftmarginv\labelwidth\leftmarginv%
+    \advance\labelwidth-\labelsep \topsep 2pt}
+\def\@listvi{\leftmargin\leftmarginvi\labelwidth\leftmarginvi%
+    \advance\labelwidth-\labelsep \topsep 2pt}
+
+
+% IEEE uses 5) not 5.
+\def\labelenumi{\theenumi)}     \def\theenumi{\arabic{enumi}}
+
+% IEEE uses a) not (a)
+\def\labelenumii{\theenumii)}  \def\theenumii{\alph{enumii}}
+
+% IEEE uses iii) not iii.
+\def\labelenumiii{\theenumiii)} \def\theenumiii{\roman{enumiii}}
+
+% IEEE uses A) not A.
+\def\labelenumiv{\theenumiv)}   \def\theenumiv{\Alph{enumiv}}
+
+% exactly the same as in article.cls
+\def\p@enumii{\theenumi}
+\def\p@enumiii{\theenumi(\theenumii)}
+\def\p@enumiv{\p@enumiii\theenumiii}
+
+% itemized list label styles
+\def\labelitemi{$\scriptstyle\bullet$}
+\def\labelitemii{\textbf{--}}
+\def\labelitemiii{$\ast$}
+\def\labelitemiv{$\cdot$}
+
+
+% IEEEtran.cls version numbers, provided as of V1.3
+% These values serve as a way a .tex file can
+% determine if the new features are provided.
+% The version number of this IEEEtrans.cls can be obtained from 
+% these values. i.e., V1.4
+% KEEP THESE AS INTEGERS! i.e., NO {4a} or anything like that-
+% (no need to enumerate "a" minor changes here)
+\def\IEEEtransversionmajor{1}
+\def\IEEEtransversionminor{6}
+
+
+% **** V1.3 ENHANCEMENTS ****
+% Itemize, Enumerate and Description (IED) List Controls
+% ***************************
+% 
+% 
+% IEEE seems to use at least two different values by
+% which ITEMIZED list labels are indented to the right
+% For The Journal of Lightwave Technology (JLT) and The Journal
+% on Selected Areas in Communications (JSAC), they tend to use
+% an indention equal to \parindent. For Transactions on Communications
+% they tend to indent ITEMIZED lists a little more--- 1.3\parindent.
+% We'll provide both values here for you so that you can choose 
+% which one you like in your document using a command such as:
+% setlength{\IEEEilabelindent}{\IEEEilabelindentB}
+\newdimen\IEEEilabelindentA
+\IEEEilabelindentA \parindent
+
+\newdimen\IEEEilabelindentB
+\IEEEilabelindentB 1.3\parindent
+% However, we'll default to using \parindent
+% which makes more sense to me
+\newdimen\IEEEilabelindent
+\IEEEilabelindent \IEEEilabelindentA
+
+
+% This controls the default amount the enumerated list labels
+% are indented to the right.
+% Normally, this is the same as the paragraph indention
+\newdimen\IEEEelabelindent
+\IEEEelabelindent \parindent
+
+% This controls the default amount the description list labels
+% are indented to the right.
+% Normally, this is the same as the paragraph indention
+\newdimen\IEEEdlabelindent
+\IEEEdlabelindent \parindent
+
+% This is the value actually used within the IED lists.
+% The IED environments automatically set its value to
+% one of the three values above, so global changes do 
+% not have any effect
+\newdimen\labelindent
+\labelindent \parindent
+
+% The actual amount labels will be indented is
+% \labelindent multiplied by the factor below
+% corresponding to the level of nesting depth
+% This provides a means by which the user can
+% alter the effective \labelindent for deeper
+% levels
+% There may not be such a thing as correct "standard IEEE"
+% values. What IEEE actually does may depend on the specific
+% circumstances.
+% The first list level almost always has full indention.
+% The second levels I've seen have only 75% of the normal indentation
+% Three level or greater nestings are very rare. I am guessing
+% that they don't use any indentation.
+\def\IEEElabelindentfactori{1.0}   % almost always one
+\def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases
+\def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0?
+\def\IEEElabelindentfactoriv{0.0}
+\def\IEEElabelindentfactorv{0.0}
+\def\IEEElabelindentfactorvi{0.0}
+
+% value actually used within IED lists, it is auto
+% set to one of the 6 values above
+% global changes here have no effect
+\def\labelindentfactor{1.0}
+
+% This controls the default spacing between the end of the IED
+% list labels and the list text, when normal text is used for
+% the labels.
+\newdimen\IEEEiednormlabelsep
+\IEEEiednormlabelsep 0.6em
+
+% This controls the default spacing between the end of the IED
+% list labels and the list text, when math symbols are used for
+% the labels (nomenclature lists). IEEE usually increases the 
+% spacing in these cases
+\newdimen\IEEEiedmathlabelsep
+\IEEEiedmathlabelsep 1.2em
+
+% This controls the extra vertical separation put above and
+% below each IED list. IEEE usually puts a little extra spacing
+% around each list. However, this spacing is barely noticeable.
+\newskip\IEEEiedtopsep
+\IEEEiedtopsep 2pt plus 1pt minus 1pt
+
+
+% This command is executed within each IED list environment
+% at the beginning of the list. You can use this to set the 
+% parameters for some/all your IED list(s) without disturbing 
+% global parameters that affect things other than lists.
+% i.e., renewcommand{\iedlistdecl}{\setlength{\labelsep}{5em}}
+% will alter the \labelsep for the next list(s) until 
+% \iedlistdecl is redefined. 
+\def\iedlistdecl{\relax}
+
+% This command provides an easy way to set \leftmargin based
+% on the \labelwidth, \labelsep and the argument \labelindent
+% Usage: \calcleftmargin{width-to-indent-the-label}
+% output is in the \leftmargin variable, i.e., effectively:
+% \leftmargin = argument + \labelwidth + \labelsep
+% Note controlled spacing here, shield end of lines with %
+\def\calcleftmargin#1{\setlength{\leftmargin}{#1}%
+\addtolength{\leftmargin}{\labelwidth}%
+\addtolength{\leftmargin}{\labelsep}}
+
+% This command provides an easy way to set \labelwidth to the
+% width of the given text. It is the same as
+% \settowidth{\labelwidth}{label-text}
+% and useful as a shorter alternative.
+% Typically used to set \labelwidth to be the width
+% of the longest label in the list
+\def\setlabelwidth#1{\settowidth{\labelwidth}{#1}}
+
+% When this command is executed, IED lists will use the 
+% IEEEiedmathlabelsep label separation rather than the normal
+% spacing. To have an effect, this command must be executed via
+% the \iedlistdecl or within the option of the IED list
+% environments.
+\def\usemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}}
+
+% A flag which controls whether the IED lists automatically
+% calculate \leftmargin from \labelindent, \labelwidth and \labelsep
+% Useful if you want to specify your own \leftmargin
+% This flag must be set (\nocalcleftmargintrue or \nocalcleftmarginfalse) 
+% via the \iedlistdecl or within the option of the IED list
+% environments to have an effect.
+\newif\ifnocalcleftmargin
+\nocalcleftmarginfalse
+
+% A flag which controls whether \labelindent is multiplied by
+% the \labelindentfactor for each list level.
+% This flag must be set via the \iedlistdecl or within the option 
+% of the IED list environments to have an effect.
+\newif\ifnolabelindentfactor
+\nolabelindentfactorfalse
+
+
+% internal variable to indicate type of IED label
+% justification
+% 0 - left; 1 - center; 2 - right
+\def\@iedjustify{0}
+
+
+% commands to allow the user to control IED
+% label justifications. Use these commands within
+% the IED environment option or in the \iedlistdecl
+% Note that changing the normal list justifications
+% is nonstandard and IEEE may not like it if you do so!
+% I include these commands as they may be helpful to
+% those who are using these enhanced list controls for
+% other non-IEEE related LaTeX work.
+% itemize and enumerate automatically default to right
+% justification, description defaults to left.
+\def\iedlabeljustifyl{\def\@iedjustify{0}}%left
+\def\iedlabeljustifyc{\def\@iedjustify{1}}%center
+\def\iedlabeljustifyr{\def\@iedjustify{2}}%right
+
+
+
+
+% commands to save to and restore from the list parameter copies
+% this allows us to set all the list parameters within
+% the list_decl and prevent \list (and its \@list) 
+% from overriding any of our parameters
+% V1.6 use \edefs instead of dimen's to conserve dimen registers
+% Note controlled spacing here, shield end of lines with %
+\def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}%
+\edef\@IEEEiedlabelwidth{\the\labelwidth}%
+\edef\@IEEEiedlabelsep{\the\labelsep}%
+\edef\@IEEEiedleftmargin{\the\leftmargin}%
+\edef\@IEEEiedpartopsep{\the\partopsep}%
+\edef\@IEEEiedparsep{\the\parsep}%
+\edef\@IEEEieditemsep{\the\itemsep}%
+\edef\@IEEEiedrightmargin{\the\rightmargin}%
+\edef\@IEEEiedlistparindent{\the\listparindent}%
+\edef\@IEEEieditemindent{\the\itemindent}}
+
+% Note controlled spacing here
+\def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax%
+\labelwidth\@IEEEiedlabelwidth\relax%
+\labelsep\@IEEEiedlabelsep\relax%
+\leftmargin\@IEEEiedleftmargin\relax%
+\partopsep\@IEEEiedpartopsep\relax%
+\parsep\@IEEEiedparsep\relax%
+\itemsep\@IEEEieditemsep\relax%
+\rightmargin\@IEEEiedrightmargin\relax%
+\listparindent\@IEEEiedlistparindent\relax%
+\itemindent\@IEEEieditemindent\relax}
+
+
+% v1.6b provide original LaTeX IED list environments
+% note that latex.ltx defines \itemize and \enumerate, but not \description
+% which must be created by the base classes
+% save original LaTeX itemize and enumerate
+\let\LaTeXitemize\itemize
+\let\endLaTeXitemize\enditemize
+\let\LaTeXenumerate\enumerate
+\let\endLaTeXenumerate\endenumerate
+
+% provide original LaTeX description environment from article.cls
+\newenvironment{LaTeXdescription}
+               {\list{}{\labelwidth\z@ \itemindent-\leftmargin
+                        \let\makelabel\descriptionlabel}}
+               {\endlist}
+\newcommand*\descriptionlabel[1]{\hspace\labelsep
+                                 \normalfont\bfseries #1}
+
+
+% override LaTeX's default IED lists
+\def\itemize{\@IEEEitemize}
+\def\enditemize{\@endIEEEitemize}
+\def\enumerate{\@IEEEenumerate}
+\def\endenumerate{\@endIEEEenumerate}
+\def\description{\@IEEEdescription}
+\def\enddescription{\@endIEEEdescription}
+
+% provide the user with aliases - may help those using packages that
+% override itemize, enumerate, or description
+\def\IEEEitemize{\@IEEEitemize}
+\def\endIEEEitemize{\@endIEEEitemize}
+\def\IEEEenumerate{\@IEEEenumerate}
+\def\endIEEEenumerate{\@endIEEEenumerate}
+\def\IEEEdescription{\@IEEEdescription}
+\def\endIEEEdescription{\@endIEEEdescription}
+
+
+% V1.6 we want to keep the IEEEtran IED list definitions as our own internal
+% commands so they are protected against redefinition
+\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}}
+\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}}
+\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}}
+\def\@endIEEEitemize{\endlist}
+\def\@endIEEEenumerate{\endlist}
+\def\@endIEEEdescription{\endlist}
+
+
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
+% IEEEtran itemized list MDS 1/2001
+% Note controlled spacing here, shield end of lines with %
+\def\@@IEEEitemize[#1]{%
+                \ifnum\@itemdepth>3\relax\@toodeep\else%
+                \ifnum\@listdepth>5\relax\@toodeep\else%
+                \advance\@itemdepth\@ne%
+                \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
+                % get the labelindentfactor for this level
+                \advance\@listdepth\@ne% we need to know what the level WILL be
+                \edef\labelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
+                \advance\@listdepth-\@ne% undo our increment
+                \def\@iedjustify{2}% right justified labels are default
+                % set other defaults
+                \nocalcleftmarginfalse%
+                \nolabelindentfactorfalse%
+                \topsep\IEEEiedtopsep%
+                \labelindent\IEEEilabelindent%
+                \labelsep\IEEEiednormlabelsep%
+                \partopsep 0ex%
+                \parsep 0ex%
+                \itemsep 0ex%
+                \rightmargin 0em%
+                \listparindent 0em%
+                \itemindent 0em%
+                % calculate the label width
+                % the user can override this later if
+                % they specified a \labelwidth
+                \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}%
+                \@IEEEsavelistparams% save our list parameters
+                \list{\csname\@itemitem\endcsname}{%
+                \@IEEErestorelistparams% override any list{} changes
+                                       % to our globals
+                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
+                \iedlistdecl% let user alter parameters
+                #1\relax%
+                % If the user has requested not to use the
+                % labelindent factor, don't revise \labelindent
+                \ifnolabelindentfactor\relax%
+                \else\labelindent=\labelindentfactor\labelindent%
+                \fi%
+                % Unless the user has requested otherwise,
+                % calculate our left margin based
+                % on \labelindent, \labelwidth and
+                % \labelsep
+                \ifnocalcleftmargin\relax%
+                \else\calcleftmargin{\labelindent}%
+                \fi}\fi\fi}%
+
+
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
+% IEEEtran enumerate list MDS 1/2001
+% Note controlled spacing here, shield end of lines with %
+\def\@@IEEEenumerate[#1]{%
+                \ifnum\@enumdepth>3\relax\@toodeep\else%
+                \ifnum\@listdepth>5\relax\@toodeep\else%
+                \advance\@enumdepth\@ne%
+                \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
+                % get the labelindentfactor for this level
+                \advance\@listdepth\@ne% we need to know what the level WILL be
+                \edef\labelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
+                \advance\@listdepth-\@ne% undo our increment
+                \def\@iedjustify{2}% right justified labels are default
+                % set other defaults
+                \nocalcleftmarginfalse%
+                \nolabelindentfactorfalse%
+                \topsep\IEEEiedtopsep%
+                \labelindent\IEEEelabelindent%
+                \labelsep\IEEEiednormlabelsep%
+                \partopsep 0ex%
+                \parsep 0ex%
+                \itemsep 0ex%
+                \rightmargin 0em%
+                \listparindent 0em%
+                \itemindent 0em%
+                % calculate the label width
+                % We'll set it to the width suitable for all labels using
+                % normalfont 1) to 9)
+                % The user can override this later
+                \settowidth{\labelwidth}{9)}%
+                \@IEEEsavelistparams% save our list parameters
+                \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}%
+                \@IEEErestorelistparams% override any list{} changes
+                                       % to our globals
+                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
+                \iedlistdecl% let user alter parameters 
+                #1\relax%
+                % If the user has requested not to use the
+                % labelindent factor, don't revise \labelindent
+                \ifnolabelindentfactor\relax%
+                \else\labelindent=\labelindentfactor\labelindent%
+                \fi%
+                % Unless the user has requested otherwise,
+                % calculate our left margin based
+                % on \labelindent, \labelwidth and
+                % \labelsep
+                \ifnocalcleftmargin\relax%
+                \else\calcleftmargin{\labelindent}%
+                \fi}\fi\fi}%
+
+
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
+% IEEEtran description list MDS 1/2001
+% Note controlled spacing here, shield end of lines with %
+\def\@@IEEEdescription[#1]{%
+                \ifnum\@listdepth>5\relax\@toodeep\else%
+                % get the labelindentfactor for this level
+                \advance\@listdepth\@ne% we need to know what the level WILL be
+                \edef\labelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
+                \advance\@listdepth-\@ne% undo our increment
+                \def\@iedjustify{0}% left justified labels are default
+                % set other defaults
+                \nocalcleftmarginfalse%
+                \nolabelindentfactorfalse%
+                \topsep\IEEEiedtopsep% 
+                \labelindent\IEEEdlabelindent%
+                % assume normal labelsep
+                \labelsep\IEEEiednormlabelsep%
+                \partopsep 0ex%
+                \parsep 0ex%
+                \itemsep 0ex%
+                \rightmargin 0em%
+                \listparindent 0em%
+                \itemindent 0em%
+                % Bogus label width in case the user forgets
+                % to set it.
+                % TIP: If you want to see what a variable's width is you
+                % can use the TeX command \showthe\width-variable to 
+                % display it on the screen during compilation 
+                % (This might be helpful to know when you need to find out
+                % which label is the widest)
+                \settowidth{\labelwidth}{Hello}%
+                \@IEEEsavelistparams% save our list parameters
+                \list{}{\@IEEErestorelistparams% override any list{} changes
+                                               % to our globals
+                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
+                \iedlistdecl% let user alter parameters 
+                #1\relax%
+                % If the user has requested not to use the
+                % labelindent factor, don't revise \labelindent
+                \ifnolabelindentfactor\relax%
+                \else\labelindent=\labelindentfactor\labelindent%
+                \fi%
+                % Unless the user has requested otherwise,
+                % calculate our left margin based
+                % on \labelindent, \labelwidth and
+                % \labelsep
+                \ifnocalcleftmargin\relax%
+                \else\calcleftmargin{\labelindent}\relax%
+                \fi}\fi}
+
+% v1.6b we use one makelabel that does justification as needed.
+\def\@IEEEiedmakelabel#1{\relax\if\@iedjustify 0\relax
+\makebox[\labelwidth][l]{\normalfont #1}\else
+\if\@iedjustify 1\relax
+\makebox[\labelwidth][c]{\normalfont #1}\else
+\makebox[\labelwidth][r]{\normalfont #1}\fi\fi}
+
+
+% VERSE and QUOTE
+\def\verse{\let\\=\@centercr
+    \list{}{\itemsep\z@ \itemindent -1.5em \listparindent \itemindent
+    \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
+\let\endverse\endlist
+\def\quotation{\list{}{\listparindent 1.5em \itemindent\listparindent
+    \rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}
+\let\endquotation=\endlist
+\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
+\let\endquote=\endlist
+
+
+% \titlepage
+% provided only for backward compatibility. \maketitle is the correct
+% way to create the title page. 
+\newif\if@restonecol
+\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
+    \else \newpage \fi \thispagestyle{empty}\c@page\z@}
+\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}
+
+% standard values from article.cls
+\arraycolsep     5pt
+\arrayrulewidth .4pt
+\doublerulesep   2pt
+
+\tabcolsep       6pt
+\tabbingsep      0.5em
+
+
+%% FOOTNOTES
+%
+%\skip\footins 10pt plus 4pt minus 2pt
+% V1.6 respond to changes in font size
+% space added above the footnotes (if present)
+\skip\footins 0.9\baselineskip  plus 0.4\baselineskip  minus 0.2\baselineskip
+
+% V1.6, we need to make \footnotesep responsive to changes
+% in \baselineskip or strange spacings will result when in
+% draft mode. Here is a little LaTeX secret - \footnotesep
+% determines the height of an invisible strut that is placed
+% *above* the baseline of footnotes after the first. Since
+% LaTeX considers the space for characters to be 0.7/baselineskip
+% above the baseline and 0.3/baselineskip below it, we need to
+% use 0.7/baselineskip as a \footnotesep to maintain equal spacing
+% between all the lines of the footnotes. IEEE often uses a tad
+% more, so use 0.8\baselineskip. This slightly larger value also helps
+% the text to clear the footnote marks. Note that \thanks now uses
+% its own value of \footnotesep.
+{\footnotesize
+\global\footnotesep 0.8\baselineskip}
+
+
+\skip\@mpfootins = \skip\footins
+\fboxsep = 3pt
+\fboxrule = .4pt
+% V1.6 use 1em, the use LaTeX2e's \@makefnmark
+% Note that IEEE normally *left* aligns the footnote marks, so we don't need
+% box resizing tricks here.
+\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@makefnmark}#1}% V1.6 use 1em
+
+\def\footnoterule{}
+
+% V1.6 do not allow LaTeX to break a footnote across multiple pages
+\interfootnotelinepenalty=10000
+
+% V1.6 discourage breaks within equations
+% Note that amsmath normally sets this to 10000,
+% but LaTeX2e normally uses 100.
+\interdisplaylinepenalty=2500
+
+
+\if@technote
+   \setcounter{secnumdepth}{3}
+\else
+   \setcounter{secnumdepth}{4}
+\fi
+
+
+\newcounter{section}
+\newcounter{subsection}[section]
+\newcounter{subsubsection}[subsection]
+\newcounter{paragraph}[subsubsection]
+
+% used only by IEEEtran's IEEEeqnarray as other packages may
+% have their own, different, implementations
+\newcounter{IEEEsubequation}[equation]
+
+% as shown when called by user from \ref, \label and in table of contents
+\def\thesection{\Roman{section}}                             % I
+\def\thesubsection{\thesection-\Alph{subsection}}            % I-A
+\def\thesubsubsection{\thesubsection.\arabic{subsubsection}} % I-A.1
+\def\theparagraph{\thesubsubsection.\alph{paragraph}}        % I-A.1.a
+\def\theequation{\arabic{equation}}                          % 1
+\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}}  % 1a (used only by IEEEtran's IEEEeqnarray)
+
+% Main text forms (how shown in main text headings)
+% V1.6, using \thesection in \thesectiondis allows changes
+% in the former to automatically appear in the latter
+\def\thesectiondis{\thesection.}                   % I.
+\def\thesubsectiondis{\Alph{subsection}.}          % B.
+\def\thesubsubsectiondis{\arabic{subsubsection})}  % 3)
+\def\theparagraphdis{\alph{paragraph})}            % d)
+% just like LaTeX2e's \@eqnnum
+\def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1)
+% IEEEsubequation used only by IEEEtran's IEEEeqnarray
+\def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a)
+% redirect LaTeX2e's equation number display and all that depend on
+% it, through IEEEtran's \theequationdis
+\def\@eqnnum{\theequationdis}
+
+% LIST OF FIGURES AND TABLES AND TABLE OF CONTENTS
+%
+\def\@pnumwidth{1.55em}
+\def\@tocrmarg{2.55em}
+\def\@dotsep{4.5}
+\setcounter{tocdepth}{3}
+
+% adjusted some spacings here so that section numbers will not easily 
+% collide with the section titles. 
+% VIII; VIII-A; and VIII-A.1 are usually the worst offenders.
+% MDS 1/2001
+\def\tableofcontents{\section*{Contents}\@starttoc{toc}}
+\def\l@section#1#2{\addpenalty{\@secpenalty}\addvspace{1.0em plus 1pt}%
+    \@tempdima 2.75em \begingroup \parindent \z@ \rightskip \@pnumwidth%
+    \parfillskip-\@pnumwidth {\bfseries\leavevmode #1}\hfil\hbox to\@pnumwidth{\hss #2}\par%
+    \endgroup}
+% argument format #1:level, #2:labelindent,#3:labelsep
+\def\l@subsection{\@dottedtocline{2}{2.75em}{3.75em}}
+\def\l@subsubsection{\@dottedtocline{3}{6.5em}{4.5em}}
+% must provide \l@ defs for ALL sublevels EVEN if tocdepth
+% is such as they will not appear in the table of contents
+% these defs are how TOC knows what level these things are!
+\def\l@paragraph{\@dottedtocline{4}{6.5em}{5.5em}}
+\def\l@subparagraph{\@dottedtocline{5}{6.5em}{6.5em}}
+\def\listoffigures{\section*{List of Figures}\@starttoc{lof}}
+\def\l@figure{\@dottedtocline{1}{0em}{2.75em}}
+\def\listoftables{\section*{List of Tables}\@starttoc{lot}}
+\let\l@table\l@figure
+
+
+%% Definitions for floats
+%%
+%% Normal Floats
+\floatsep 1\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip
+\textfloatsep 1.7\baselineskip plus  0.2\baselineskip minus  0.4\baselineskip
+\@fptop 0pt plus 1fil
+\@fpsep 0.75\baselineskip plus 2fil 
+\@fpbot 0pt plus 1fil
+\def\topfraction{1.0}
+\def\bottomfraction{.4}
+\def\floatpagefraction{0.8}
+\def\textfraction{.2}
+
+%% Double Column Floats
+\dblfloatsep 1\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip
+
+\dbltextfloatsep 1.7\baselineskip plus  0.2\baselineskip minus  0.4\baselineskip
+% Note that it would be nice if the rubber here actually worked in LaTeX2e.
+% There is a long standing limitation in LaTeX, first discovered (to the best
+% of my knowledge) by Alan Jeffrey in 1992. LaTeX ignores the stretchable
+% portion of \dbltextfloatsep, and as a result, double column figures can and
+% do result in an non-integer number of lines in the main text columns with
+% underfull vbox errors as a consequence. A post to comp.text.tex
+% by Donald Arseneau confirms that this had not yet been fixed in 1998.
+% IEEEtran V1.6 will fix this problem for you in the titles, but it doesn't
+% protect you from other double floats. Happy vspace'ing.
+
+\@dblfptop 0pt plus 1fil
+\@dblfpsep 0.75\baselineskip plus 2fil
+\@dblfpbot 0pt plus 1fil
+\def\dbltopfraction{1.0}
+\def\dblfloatpagefraction{0.8}
+\setcounter{dbltopnumber}{4}
+
+\intextsep 1\baselineskip plus 0.2\baselineskip minus  0.2\baselineskip
+\setcounter{topnumber}{2}
+\setcounter{bottomnumber}{2}
+\setcounter{totalnumber}{4}
+
+
+%% redefine CAPTION
+% V1.4 add user control for short figure caption justification
+\newif\ifcenterfigcaptions
+
+% V1.6 set the default according to conference mode
+\if@confmode
+\centerfigcaptionstrue
+\else
+\centerfigcaptionsfalse
+\fi
+
+% article class provides these, we should too.
+\newlength\abovecaptionskip
+\newlength\belowcaptionskip
+% but only \abovecaptionskip is used above figure captions and *below* table
+% captions
+\setlength\abovecaptionskip{0.5\baselineskip}
+\setlength\belowcaptionskip{0pt}
+% V1.6 create hooks in case the caption spacing ever needs to be
+% overridden by a user
+\def\@IEEEfigurecaptionsepspace{\vskip\abovecaptionskip\relax}%
+\def\@IEEEtablecaptionsepspace{\vskip\abovecaptionskip\relax}%
+
+
+% 1.6b revise caption system so that \@makecaption uses two arguments
+% as with LaTeX2e. Otherwise, there will be problems when using hyperref.
+\def\@IEEEtablestring{table}
+
+\long\def\@makecaption#1#2{%
+% test if is a for a figure or table
+\ifx\@captype\@IEEEtablestring%
+% if a table, do table caption
+\begin{center}{\footnotesize #1}\\{\footnotesize\scshape #2}\end{center}%
+\@IEEEtablecaptionsepspace% V1.6 was a hard coded 8pt
+% if not a table, format it as a figure
+\else
+\@IEEEfigurecaptionsepspace% V1.6 was a hard coded 5pt
+% 3/2001 use footnotesize, not small; use two nonbreaking spaces, not one
+\setbox\@tempboxa\hbox{\footnotesize #1.~~ #2}%
+\ifdim \wd\@tempboxa >\hsize%
+% if caption is longer than a line, let it wrap around
+\setbox\@tempboxa\hbox{\footnotesize #1.~~ }%
+\parbox[t]{\hsize}{\footnotesize \noindent\unhbox\@tempboxa#2}%
+% if caption is shorter than a line,
+% allow user to control short figure caption justification (left or center)
+\else%
+\ifcenterfigcaptions \hbox to\hsize{\footnotesize\hfil\box\@tempboxa\hfil}%
+\else \hbox to\hsize{\footnotesize\box\@tempboxa\hfil}%
+\fi\fi\fi}
+
+
+\newcounter{figure}
+\def\thefigure{\@arabic\c@figure}
+\def\fps@figure{tbp}
+\def\ftype@figure{1}
+\def\ext@figure{lof}
+\def\fnum@figure{Fig.~\thefigure}
+\def\figure{\@float{figure}}
+\let\endfigure\end@float
+\@namedef{figure*}{\@dblfloat{figure}}
+\@namedef{endfigure*}{\end@dblfloat}
+\newcounter{table}
+\def\thetable{\@Roman\c@table}
+\def\fps@table{tbp}
+\def\ftype@table{2}
+\def\ext@table{lot}
+\def\fnum@table{TABLE~\thetable}
+% V1.6 IEEE uses 8pt text for tables
+% to default to footnotesize, we hack into LaTeX2e's \@floatboxreset and pray
+\def\table{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@float{table}}
+\let\endtable\end@float
+% v1.6b double column tables need to default to footnotesize as well.
+\@namedef{table*}{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@dblfloat{table}}
+\@namedef{endtable*}{\end@dblfloat}
+
+
+
+
+%%
+%% START OF IEEEeqnarry DEFINITIONS
+%%
+%% Inspired by the concepts, examples, and previous works of LaTeX 
+%% coders and developers such as Donald Arseneau, Fred Bartlett, 
+%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum, 
+%% Roland Winkler and Mark Wooding.
+%% I don't make the claim that my work here is even near their calibre. ;)
+
+
+% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting
+\def\@IEEEclspkgerror{\ClassError{IEEEtran}}
+
+\newif\if@IEEEeqnarraystarform% flag to indicate if the environment was called as the star form
+\@IEEEeqnarraystarformfalse
+
+\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter
+% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray
+% used by IEEEeqnarraymulticol so that it can work properly in both
+\@advanceIEEEeqncolcnttrue
+
+\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined
+\newcount\@IEEEeqncolcnt  % tracks how many IEEEeqnarray cols the user actually used
+
+
+% The default math style used by the columns
+\def\IEEEeqnarraymathstyle{\displaystyle}
+% The default text style used by the columns
+% default to using the current font
+\def\IEEEeqnarraytextstyle{\relax}
+
+% like the iedlistdecl but for \IEEEeqnarray
+\def\IEEEeqnarraydecl{\relax}
+\def\IEEEeqnarrayboxdecl{\relax}
+
+% \yesnumber is the opposite of \nonumber
+% a novel concept with the same def as the equationarray package
+% However, we give IEEE versions too since some LaTeX packages such as 
+% the MDWtools mathenv.sty redefine \nonumber to something else.
+\providecommand{\yesnumber}{\global\@eqnswtrue}
+\def\IEEEyesnumber{\global\@eqnswtrue}
+\def\IEEEnonumber{\global\@eqnswfalse}
+
+
+\def\IEEEyessubnumber{\global\@IEEEissubequationtrue\global\@eqnswtrue%
+\if@IEEEeqnarrayISinner% only do something inside an IEEEeqnarray
+\if@IEEElastlinewassubequation\addtocounter{equation}{-1}\else\setcounter{IEEEsubequation}{1}\fi%
+\def\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\fi}
+
+% flag to indicate that an equation is a sub equation
+\newif\if@IEEEissubequation%
+\@IEEEissubequationfalse
+
+% allows users to "push away" equations that get too close to the equation numbers
+\def\IEEEeqnarraynumspace{\hphantom{\if@IEEEissubequation\theIEEEsubequationdis\else\theequationdis\fi}}
+
+% provides a way to span multiple columns within IEEEeqnarray environments
+% will consider \if@advanceIEEEeqncolcnt before globally advancing the
+% column counter - so as to work within \IEEEeqnarraybox
+% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text}
+\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}%
+% check if column is defined
+\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined%
+\csname @IEEEeqnarraycolPRE#2\endcsname#3\relax\relax\relax\relax\relax%
+\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST#2\endcsname%
+\else% if not, error and use default type
+\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak
+Using a default centering column instead}%
+{You must define IEEEeqnarray column types before use.}%
+\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname#3\relax\relax\relax\relax\relax%
+\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname%
+\fi%
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi}
+
+% like \omit, but maintains track of the column counter for \IEEEeqnarray
+\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi}
+
+
+% provides a way to define a letter referenced column type
+% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text}
+\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}%
+\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}%
+\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}}
+
+
+% provides a way to define a numerically referenced inter-column glue types
+% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition}
+\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}%
+\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}}
+
+
+\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types
+
+
+% expands and appends the given argument to the \@IEEEtrantmptoksA token list
+% used to build up the \halign preamble
+\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}%
+\@@IEEEappendtoksA}
+
+% also appends to \@IEEEtrantmptoksA, but does not expand the argument
+% uses \toks8 as a scratchpad register
+\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}%
+\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}%
+\@@IEEEappendNOEXPANDtoksA}
+
+% define some common column types for the user
+% math
+\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil}
+\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
+\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$}
+\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil}
+\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil}
+\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$}
+% text
+\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil}
+\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil}
+\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{}
+
+% vertical rules
+\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth}
+\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth}
+\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
+\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}%
+{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
+
+% horizontal rules
+\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil}
+\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil}
+
+% plain
+\IEEEeqnarraydefcol{x}{}{}
+\IEEEeqnarraydefcol{X}{$}{$}
+
+% the default column type to use in the event a column type is not defined
+\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
+
+
+% a zero tabskip (used for "-" col types)
+\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt}
+% a centering tabskip (used for "+" col types)
+\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt}
+
+% top level default tabskip glues for the start, end, and inter-column
+% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox
+\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue
+\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue
+\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue
+
+
+
+% creates a vertical rule that extends from the bottom to the top a a cell
+% Provided in case other packages redefine \vline some other way.
+% usage: \IEEEeqnarrayvrule[rule thickness]
+% If no argument is provided, \arrayrulewidth will be used for the rule thickness. 
+\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax}
+
+% creates a blank separator row
+% usage: \IEEEeqnarrayseprow[separation length][font size commands]
+% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax]
+% blank arguments inherit the default values
+% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
+\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}}
+\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}}
+\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
+\ifx\@IEEEeqnarrayseprowARGONE\@empty%
+% get the skip value, based on the font commands
+% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
+% assign within a bogus box to confine the font changes
+{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
+\else%
+{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
+\fi%
+\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}
+
+% creates a blank separator row, but omits all the column templates
+% usage: \IEEEeqnarrayseprowcut[separation length][font size commands]
+% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax]
+% blank arguments inherit the default values
+% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
+\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}}
+\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}}
+\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
+\ifx\@IEEEeqnarrayseprowARGONE\@empty%
+% get the skip value, based on the font commands
+% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
+% assign within a bogus box to confine the font changes
+{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
+\else%
+{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
+\fi%
+\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}
+
+
+
+% draws a single rule across all the columns optional
+% argument determines the rule width, \arrayrulewidth is the default
+% updates column counter as needed and turns off struts
+% usage: \IEEEeqnarrayrulerow[rule line thickness]
+\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}}
+\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule 
+% turn off any struts
+\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax}
+
+
+% draws a double rule by using a single rule row, a separator row, and then
+% another single rule row 
+% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
+% second optional argument determines the rule spacing, \doublerulesep is the default
+% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
+\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}}
+\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}%
+{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}}
+\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
+% we allow the user to say \IEEEeqnarraydblrulerow[][]
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%
+\else%
+\@IEEEeqnarrayrulerow[#1]\relax%
+\fi%
+\def\@IEEEeqnarraydblrulerowARG{#2}%
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\\\IEEEeqnarrayseprow[\doublerulesep][\relax]%
+\else%
+\\\IEEEeqnarrayseprow[#2][\relax]%
+\fi%
+\\\multispan{\@IEEEeqnnumcols}%
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\def\@IEEEeqnarraydblrulerowARG{#1}%
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%
+\else%
+\@IEEEeqnarrayrulerow[#1]%
+\fi%
+}
+
+% draws a double rule by using a single rule row, a separator (cutting) row, and then
+% another single rule row 
+% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
+% second optional argument determines the rule spacing, \doublerulesep is the default
+% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
+\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}}
+\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}%
+{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}}
+\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
+% we allow the user to say \IEEEeqnarraydblrulerow[][]
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%
+\else%
+\@IEEEeqnarrayrulerow[#1]%
+\fi%
+\def\@IEEEeqnarraydblrulerowARG{#2}%
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]%
+\else%
+\\\IEEEeqnarrayseprowcut[#2][\relax]%
+\fi%
+\\\multispan{\@IEEEeqnnumcols}%
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\def\@IEEEeqnarraydblrulerowARG{#1}%
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%
+\else%
+\@IEEEeqnarrayrulerow[#1]%
+\fi%
+}
+
+
+
+% inserts a full row's worth of &'s
+% relies on \@IEEEeqnnumcols to provide the correct number of columns
+% uses \@IEEEtrantmptoksA, \count0 as scratch registers
+\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax%
+\loop% add cols if the user did not use them all
+\ifnum\count0<\@IEEEeqnnumcols\relax%
+\@IEEEappendtoksA{&}%
+\advance\count0 by 1\relax% update the col count
+\repeat%
+\the\@IEEEtrantmptoksA%execute the &'s
+}
+
+
+
+\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines
+\@IEEEeqnarrayISinnerfalse    % of an IEEEeqnarray - after the IEEEeqnarraydecl
+
+\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts
+\edef\@IEEEeqnarrayTHEstrutdepth{0pt}
+
+\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt}  % struts within an IEEEeqnarray
+
+\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height
+\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth
+
+\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value
+\@IEEEeqnarrayusemasterstruttrue     % is to be used
+
+
+
+% saves the strut height and depth of the master strut
+\def\@IEEEeqnarraymasterstrutsave{\relax%
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
+% remove stretchability
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% save values
+\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}}
+
+% restores the strut height and depth of the master strut
+\def\@IEEEeqnarraymasterstrutrestore{\relax%
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax%
+% remove stretchability
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% restore values
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}}
+
+
+% globally restores the strut height and depth to the 
+% master values and sets the master strut flag to true
+\def\@IEEEeqnarraystrutreset{\relax%
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
+% remove stretchability
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% restore values
+\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\global\@IEEEeqnarrayusemasterstruttrue}
+
+
+% if the master strut is not to be used, make the current
+% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth
+% and the use master strut flag, global
+% this allows user strut commands issued in the last column to be carried
+% into the isolation/strut column
+\def\@IEEEeqnarrayglobalizestrutstatus{\relax%
+\if@IEEEeqnarrayusemasterstrut\else%
+\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}%
+\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}%
+\global\@IEEEeqnarrayusemasterstrutfalse%
+\fi}
+
+
+
+% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands]
+% If called outside the lines of an IEEEeqnarray, sets the height
+% and depth of both the master and local struts. If called inside
+% an IEEEeqnarray line, sets the height and depth of the local strut
+% only and sets the flag to indicate the use of the local strut
+% values. If the height or depth is left blank, 0.7\normalbaselineskip
+% and 0.3\normalbaselineskip will be used, respectively.
+% The optional argument can be used to evaluate the lengths under
+% a different font size and styles. If none is specified, the current
+% font is used.
+% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
+\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}}
+\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}%
+\ifx\@IEEEeqnarraystrutsizeARG\@empty%
+{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}%
+\skip0=\skip3\relax%
+\else% arg one present
+{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}%
+\skip0=\skip3\relax%
+\fi% if null arg
+\def\@IEEEeqnarraystrutsizeARG{#2}%
+\ifx\@IEEEeqnarraystrutsizeARG\@empty%
+{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}%
+\skip2=\skip3\relax%
+\else% arg two present
+{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}%
+\skip2=\skip3\relax%
+\fi% if null arg
+% remove stretchability, just to be safe
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% dimen0 = height, dimen2 = depth
+\if@IEEEeqnarrayISinner% inner does not touch master strut size
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\@IEEEeqnarrayusemasterstrutfalse% do not use master
+\else% outer, have to set master strut too
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\@IEEEeqnarrayusemasterstruttrue% use master strut
+\fi}
+
+
+% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands]
+% If called outside the lines of an IEEEeqnarray, adds the given height
+% and depth to both the master and local struts.
+% If called inside an IEEEeqnarray line, adds the given height and depth
+% to the local strut only and sets the flag to indicate the use 
+% of the local strut values.
+% In both cases, if a height or depth is left blank, 0pt is used instead.
+% The optional argument can be used to evaluate the lengths under
+% a different font size and styles. If none is specified, the current
+% font is used.
+% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
+\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}}
+\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}%
+\ifx\@IEEEeqnarraystrutsizearg\@empty%
+\skip0=0pt\relax%
+\else% arg one present
+{\setbox0=\hbox{#3\relax\global\skip3=#1}}%
+\skip0=\skip3\relax%
+\fi% if null arg
+\def\@IEEEeqnarraystrutsizearg{#2}%
+\ifx\@IEEEeqnarraystrutsizearg\@empty%
+\skip2=0pt\relax%
+\else% arg two present
+{\setbox0=\hbox{#3\relax\global\skip3=#2}}%
+\skip2=\skip3\relax%
+\fi% if null arg
+% remove stretchability, just to be safe
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% dimen0 = height, dimen2 = depth
+\if@IEEEeqnarrayISinner% inner does not touch master strut size
+% get local strut size
+\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
+% add it to the user supplied values
+\advance\dimen0 by \skip0\relax%
+\advance\dimen2 by \skip2\relax%
+% update the local strut size
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\@IEEEeqnarrayusemasterstrutfalse% do not use master
+\else% outer, have to set master strut too
+% get master strut size
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
+% add it to the user supplied values
+\advance\dimen0 by \skip0\relax%
+\advance\dimen2 by \skip2\relax%
+% update the local and master strut sizes
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\@IEEEeqnarrayusemasterstruttrue% use master strut
+\fi}
+
+
+% allow user a way to see the struts
+\newif\ifIEEEvisiblestruts
+\IEEEvisiblestrutsfalse
+
+% inserts an invisible strut using the master or local strut values
+% uses scratch registers \skip0, \skip2, \dimen0, \dimen2
+\def\@IEEEeqnarrayinsertstrut{\relax%
+\if@IEEEeqnarrayusemasterstrut
+% get master strut size
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
+\else%
+% get local strut size
+\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
+\fi%
+% remove stretchability, probably not needed
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% dimen0 = height, dimen2 = depth
+% allow user to see struts if desired
+\ifIEEEvisiblestruts%
+\vrule width0.2pt height\dimen0 depth\dimen2\relax%
+\else%
+\vrule width0pt height\dimen0 depth\dimen2\relax\fi}
+
+
+% creates an invisible strut, useable even outside \IEEEeqnarray
+% if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide. 
+% usage: \IEEEstrut[height][depth][font size commands]
+% default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax]
+% blank arguments inherit the default values
+% uses \dimen0, \dimen2, \skip0, \skip2
+\def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}}
+\def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}}
+\def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}}
+\def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax%
+\def\@IEEEstrutARG{#1}%
+\ifx\@IEEEstrutARG\@empty%
+\skip0=0.7\normalbaselineskip\relax%
+\else%
+\skip0=#1\relax%
+\fi%
+\def\@IEEEstrutARG{#2}%
+\ifx\@IEEEstrutARG\@empty%
+\skip2=0.3\normalbaselineskip\relax%
+\else%
+\skip2=#2\relax%
+\fi%
+% remove stretchability, probably not needed
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+\ifIEEEvisiblestruts%
+\vrule width0.2pt height\dimen0 depth\dimen2\relax%
+\else%
+\vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}}
+
+
+% enables strut mode by setting a default strut size and then zeroing the
+% \baselineskip, \lineskip, \lineskiplimit and \jot
+\def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]%
+\baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt}
+
+
+
+\def\IEEEeqnarray{\@IEEEeqnarraystarformfalse\@IEEEeqnarray}
+\def\endIEEEeqnarray{\end@IEEEeqnarray}
+
+\@namedef{IEEEeqnarray*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarray}
+\@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray}
+
+
+% \IEEEeqnarray is an enhanced \eqnarray. 
+% The star form defaults to not putting equation numbers at the end of each row.
+% usage: \IEEEeqnarray[decl]{cols}
+\def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}}
+\def\@@IEEEeqnarray[#1]#2{%
+   % default to showing the equation number or not based on whether or not
+   % the star form was involked
+   \if@IEEEeqnarraystarform\global\@eqnswfalse
+   \else% not the star form
+   \global\@eqnswtrue
+   \fi% if star form
+   \@IEEEissubequationfalse% default to no subequations
+   \@IEEElastlinewassubequationfalse% assume last line is not a sub equation
+   \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign
+   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default
+   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise
+   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off
+   % no extra space unless the user specifically requests it
+   \lineskip=0pt\relax
+   \lineskiplimit=0pt\relax
+   \baselineskip=\normalbaselineskip\relax%
+   \jot=\normaljot\relax%
+   \mathsurround\z@\relax% no extra spacing around math
+   \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses, 
+                             % used in \IEEEeqnarraymulticol and in the preamble build
+   \stepcounter{equation}% advance equation counter before first line
+   \setcounter{IEEEsubequation}{0}% no subequation yet 
+   \def\@currentlabel{\p@equation\theequation}% redefine the ref label
+   \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides
+   #1\relax% allow user to override defaults
+   \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers
+   \global\@IEEEeqncolcnt\z@% col. count = 0 for first line
+   \@IEEEbuildpreamble #2\end\relax% build the preamble and put it into \@IEEEtrantmptoksA 
+   % put in the column for the equation number
+   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first
+   \toks0={##}%
+   % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking
+   \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}%
+   % add the isolation column
+   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}%
+   % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking
+   \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}%
+   % add the equation number col to the preamble
+   \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}%
+   % note \@IEEEeqnnumcols does not count the equation col or isolation col
+   % set the starting tabskip glue as determined by the preamble build
+   \tabskip=\@IEEEBPstartglue\relax
+   % begin the display alignment
+   \@IEEEeqnarrayISinnertrue% commands are now within the lines
+   $$\everycr{}\halign to\displaywidth\bgroup
+   % "exspand" the preamble
+   \span\the\@IEEEtrantmptoksA\cr}
+
+% enter isolation/strut column (or the next column if the user did not use
+% every column), record the strut status, complete the columns, do the strut if needed,
+% restore counters to correct values and exit
+\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup%
+\if@IEEElastlinewassubequation\global\advance\c@IEEEsubequation\m@ne\fi%
+\global\advance\c@equation\m@ne%
+$$\@ignoretrue}
+
+% need a way to remember if last line is a subequation
+\newif\if@IEEElastlinewassubequation%
+\@IEEElastlinewassubequationfalse
+
+% IEEEeqnarray uses a modifed \\ instead of the plain \cr to
+% end rows. This allows for things like \\*[vskip amount]
+% This "cr" macros are modified versions those for LaTeX2e's eqnarray
+% the {\ifnum0=`} braces must be kept away from the last column to avoid
+% altering spacing of its math, so we use & to advance to the next column
+% as there is an isolation/strut column after the user's columns
+\def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column
+   {\ifnum0=`}\fi
+   \@ifstar{%
+      \global\@eqpen\@M\@IEEEeqnarrayYCR
+   }{%
+      \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR
+   }%
+}
+
+\def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip}
+
+\def\@IEEEeqnarrayXCR[#1]{%
+   \ifnum0=`{\fi}%
+   \@@IEEEeqnarraycr
+   \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}%
+
+\def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register
+    \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column
+    \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax
+    \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak
+                          environment}%
+    {Use fewer \string &'s or put more columns in the IEEEeqnarry column\MessageBreak 
+     specifications.}\relax%
+    \else
+    \loop% add cols if the user did not use them all
+    \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax
+    \@IEEEappendtoksA{&}%
+    \advance\@IEEEeqncolcnt by 1\relax% update the col count
+    \repeat
+    % this number of &'s will take us the the isolation column
+    \fi
+    % execute the &'s
+    \the\@IEEEtrantmptoksA%
+    % handle the strut/isolation column
+    \@IEEEeqnarrayinsertstrut% do the strut if needed
+    \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray
+    &% and enter the equation number column
+    % is this line needs an equation number, display it and advance the
+    % (sub)equation counters, record what type this line was
+    \if@eqnsw%
+     \if@IEEEissubequation\theIEEEsubequationdis\addtocounter{equation}{1}\stepcounter{IEEEsubequation}%
+     \global\@IEEElastlinewassubequationtrue%
+     \else% display a standard equation number, initialize the IEEEsubequation counter
+     \theequationdis\stepcounter{equation}\setcounter{IEEEsubequation}{0}%
+     \global\@IEEElastlinewassubequationfalse\fi%
+    \fi%
+    % reset the eqnsw flag to indicate default preference of the display of equation numbers
+    \if@IEEEeqnarraystarform\global\@eqnswfalse\else\global\@eqnswtrue\fi
+    \global\@IEEEissubequationfalse% reset the subequation flag
+    % reset the number of columns the user actually used
+    \global\@IEEEeqncolcnt\z@\relax
+    % the real end of the line
+    \cr}
+
+
+
+
+
+% \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything
+% inside a vtop, vbox, or vcenter box depending on the letter in the second
+% optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray,
+% equation numbers are not displayed and \IEEEeqnarraybox can be nested.
+% \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox
+% within an hbox.
+% \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within
+% a \hbox{$ $} construct.
+% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or 
+% \IEEEeqnarrayboxt depending on the math mode.
+% The third optional argument specifies the width this box is to be set to -
+% natural width is the default.
+% The * forms do not add \jot line spacing
+% usage: \IEEEeqnarraybox[decl][pos][width]{cols}
+\def\IEEEeqnarrayboxm{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
+\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox}
+\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
+\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox}
+
+\def\IEEEeqnarrayboxt{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
+\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox}
+\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
+\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox}
+
+\def\IEEEeqnarraybox{\@IEEEeqnarraystarformfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
+\@IEEEeqnarraybox}
+\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox}
+
+\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarraystarformtrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
+\@IEEEeqnarraybox}
+\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox}
+
+% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $} 
+% for \vcenter in non-math mode
+\newif\if@IEEEeqnarrayboxHBOXSW%
+\@IEEEeqnarrayboxHBOXSWfalse
+
+\def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}}
+\def\@@IEEEeqnarraybox[#1]{\relax\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}}
+\def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}}
+
+% #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs
+\def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign
+   \@IEEEeqnarraymasterstrutsave% save current master strut values
+   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default
+   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise
+   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off
+   % no extra space unless the user specifically requests it
+   \lineskip=0pt\relax%
+   \lineskiplimit=0pt\relax%
+   \baselineskip=\normalbaselineskip\relax%
+   \jot=\normaljot\relax%
+   \mathsurround\z@\relax% no extra spacing around math
+   % the default end glues are zero for an \IEEEeqnarraybox
+   \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue
+   \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue
+   \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue
+   \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses, 
+                              % used in \IEEEeqnarraymulticol and in the preamble build
+   \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides
+   #1\relax% allow user to override defaults
+   \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing
+   \@IEEEbuildpreamble #4\end\relax% build the preamble and put it into \@IEEEtrantmptoksA
+   % add an isolation column to the preamble to stop \\'s {} from getting into the last col
+   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first
+   \toks0={##}%
+   % add the isolation column to the preamble
+   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% 
+   % set the starting tabskip glue as determined by the preamble build
+   \tabskip=\@IEEEBPstartglue\relax
+   % begin the alignment
+   \everycr{}%
+   % use only the very first token to determine the positioning
+   % this stops some problems when the user uses more than one letter,
+   % but is probably not worth the effort
+   % \noindent is used as a delimiter
+   \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
+   \@IEEEgrabfirstoken#2\relax\relax\noindent
+   % \@IEEEgrabbedfirstoken has the first token, the rest are discarded
+   % if we need to put things into and hbox and go into math mode, do so now
+   \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi%
+   % use the appropriate vbox type
+   \if\@IEEEgrabbedfirstoken t\relax\vtop\else\if\@IEEEgrabbedfirstoken c\relax%
+   \vcenter\else\vbox\fi\fi\bgroup%
+   \@IEEEeqnarrayISinnertrue% commands are now within the lines
+   \ifx#3\relax\halign\else\halign to #3\relax\fi%
+   \bgroup
+   % "exspand" the preamble
+   \span\the\@IEEEtrantmptoksA\cr}
+
+% carry strut status and enter the isolation/strut column, 
+% exit from math mode if needed, and exit
+\def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status
+&% enter isolation/strut column
+\@IEEEeqnarrayinsertstrut% do strut if needed
+\@IEEEeqnarraymasterstrutrestore% restore the previous master strut values
+% reset the strut system for next IEEEeqnarray
+% (sets local strut values back to previous master strut values)
+\@IEEEeqnarraystrutreset%
+% ensure last line, exit from halign, close vbox
+\crcr\egroup\egroup%
+% exit from math mode and close hbox if needed
+\if@IEEEeqnarrayboxHBOXSW $\egroup\fi}
+
+
+
+% IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to
+% end rows. This allows for things like \\[vskip amount]
+% This "cr" macros are modified versions those for LaTeX2e's eqnarray
+% For IEEEeqnarraybox, \\* is the same as \\
+% the {\ifnum0=`} braces must be kept away from the last column to avoid
+% altering spacing of its math, so we use & to advance to the isolation/strut column
+% carry strut status into isolation/strut column
+\def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status
+&% enter isolation/strut column
+\@IEEEeqnarrayinsertstrut% do strut if needed
+% reset the strut system for next line or IEEEeqnarray
+\@IEEEeqnarraystrutreset%
+{\ifnum0=`}\fi%
+\@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}}
+
+% test and setup the optional argument to \\[]
+\def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip}
+
+% IEEEeqnarraybox does not automatically increase line spacing by \jot
+\def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}%
+\cr\noalign{\if@IEEEeqnarraystarform\else\vskip\jot\fi\vskip#1\relax}}
+
+
+
+% starts the halign preamble build
+\def\@IEEEbuildpreamble{\@IEEEtrantmptoksA={}% clear token register
+\let\@IEEEBPcurtype=u%current column type is not yet known
+\let\@IEEEBPprevtype=s%the previous column type was the start
+\let\@IEEEBPnexttype=u%next column type is not yet known
+% ensure these are valid
+\def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}%
+\def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition
+% currently acquired numerically referenced glue
+% use a name that is easier to remember
+\let\@IEEEBPcurnum=\@IEEEtrantmpcountA%
+\@IEEEBPcurnum=0%
+% tracks number of columns in the preamble
+\@IEEEeqnnumcols=0%
+% record the default end glues
+\edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}%
+\edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}%
+% now parse the user's column specifications
+\@@IEEEbuildpreamble}
+
+
+% parses and builds the halign preamble
+\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble%
+% use only the very first token to check the end
+% \noindent is used as a delimiter as \end can be present here
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
+\@IEEEgrabfirstoken#1\relax\relax\noindent
+\ifx\@IEEEgrabbedfirstoken\end\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else%
+% identify current and next token type
+\@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid
+\@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next
+% if curtype is a glue, get the glue def
+\if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi%
+% if curtype is a column, get the column def and set the current column name
+\if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi%
+% if curtype is a numeral, acquire the user defined glue
+\if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi%
+% process the acquired glue 
+\if\@IEEEBPcurtype g\@IEEEprocessGcol\fi%
+% process the acquired col 
+\if\@IEEEBPcurtype c\@IEEEprocessCcol\fi%
+% ready prevtype for next col spec.
+\let\@IEEEBPprevtype=\@IEEEBPcurtype%
+% be sure and put back the future token(s) as a group
+\fi\@@nextIEEEbuildpreamble{#2}}
+
+
+% executed just after preamble build is completed
+% warn about zero cols, and if prevtype type = u, put in end tabskip glue
+\def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax
+\@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}%
+{At least one column type must be declared for each IEEEeqnarray.}%
+\fi%num cols less than 1
+%if last type undefined, set default end tabskip glue
+\if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi}
+
+
+% Identify and return the column specifier's type code
+\def\@IEEEgetcoltype#1#2#3{%
+% use only the very first token to determine the type
+% \noindent is used as a delimiter as \end can be present here
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
+\@IEEEgrabfirstoken#1\relax\relax\noindent
+% \@IEEEgrabfirstoken has the first token, the rest are discarded
+% n = number
+% g = glue (any other char in catagory 12)
+% c = letter
+% e = \end
+% u = undefined
+% third argument: 0 = no error message, 1 = error on invalid char
+\let#2=u\relax% assume invalid until know otherwise
+\ifx\@IEEEgrabbedfirstoken\end\let#2=e\else
+\ifcat\@IEEEgrabbedfirstoken\relax\else% screen out control sequences
+\if0\@IEEEgrabbedfirstoken\let#2=n\else
+\if1\@IEEEgrabbedfirstoken\let#2=n\else
+\if2\@IEEEgrabbedfirstoken\let#2=n\else
+\if3\@IEEEgrabbedfirstoken\let#2=n\else
+\if4\@IEEEgrabbedfirstoken\let#2=n\else
+\if5\@IEEEgrabbedfirstoken\let#2=n\else
+\if6\@IEEEgrabbedfirstoken\let#2=n\else
+\if7\@IEEEgrabbedfirstoken\let#2=n\else
+\if8\@IEEEgrabbedfirstoken\let#2=n\else
+\if9\@IEEEgrabbedfirstoken\let#2=n\else
+\ifcat,\@IEEEgrabbedfirstoken\let#2=g\relax
+\else\ifcat a\@IEEEgrabbedfirstoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+\if#2u\relax
+\if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}%
+{Only letters, numerals and certain other symbols are allowed \MessageBreak
+as IEEEeqnarray column specifiers.}\fi\fi}
+
+
+% identify the current letter referenced column
+% if invalid, use a default column
+\def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined%
+\def\@IEEEBPcurcolname{#1}\else% invalid column name
+\@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak
+Using a default centering column instead}%
+{You must define IEEEeqnarray column types before use.}%
+\def\@IEEEBPcurcolname{@IEEEdefault}\fi}
+
+
+% identify and return the predefined (punctuation) glue value
+\def\@IEEEgetcurglue#1#2{%
+% ! = \! (neg small)  -0.16667em (-3/18 em)
+% , = \, (small)       0.16667em ( 3/18 em)
+% : = \: (med)         0.22222em ( 4/18 em)
+% ; = \; (large)       0.27778em ( 5/18 em)
+% ' = \quad            1em
+% " = \qquad           2em
+% . = 0.5\arraycolsep
+% / = \arraycolsep
+% ? = 2\arraycolsep
+% * = 1fil
+% + = \@IEEEeqnarraycolSEPcenter
+% - = \@IEEEeqnarraycolSEPzero
+% Note that all em values are referenced to the math font (textfont2) fontdimen6
+% value for 1em.
+% 
+% use only the very first token to determine the type
+% this prevents errant tokens from getting in the main text
+% \noindent is used as a delimiter here
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
+\@IEEEgrabfirstoken#1\relax\relax\noindent
+% get the math font 1em value
+% LaTeX2e's NFSS2 does not preload the fonts, but \IEEEeqnarray needs
+% to gain access to the math (\textfont2) font's spacing parameters.
+% So we create a bogus box here that uses the math font to ensure
+% that \textfont2 is loaded and ready. If this is not done,
+% the \textfont2 stuff here may not work.
+% Thanks to Bernd Raichle for his 1997 post on this topic.
+{\setbox0=\hbox{$\displaystyle\relax$}}%
+% fontdimen6 has the width of 1em (a quad).
+\@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax%
+% identify the glue value based on the first token
+% we discard anything after the first
+\if!\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if,\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if:\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if;\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if'\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if"\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if.\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if/\@IEEEgrabbedfirstoken\edef#2{\the\arraycolsep}\else
+\if?\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if *\@IEEEgrabbedfirstoken\edef#2{0pt plus 1fil minus 0pt}\else
+\if+\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else
+\if-\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPzero}\else
+\edef#2{\@IEEEeqnarraycolSEPzero}%
+\@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak
+column specifications. Using a default value of\MessageBreak
+0pt instead}%
+{Only !,:;'"./?*+ and - are valid predefined glue types in the\MessageBreak 
+IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
+
+
+
+% process a numerical digit from the column specification
+% and look up the corresponding user defined glue value
+% can transform current type from n to g or a as the user defined glue is acquired
+\def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g%
+\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak
+specifications. Ignoring consecutive glue specifiers\MessageBreak
+after the first}%
+{You cannot have two or more glue types next to each other\MessageBreak 
+in the IEEEeqnarray column specifications.}%
+\let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded
+\@IEEEBPcurnum=0\relax%
+\else% if we previously aborted a glue
+\if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion
+\else%acquire this number
+% save the previous type before the numerical digits started
+\if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi%
+\multiply\@IEEEBPcurnum by 10\relax%
+\advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX's number scan
+\if\@IEEEBPnexttype n\else%close acquisition
+\expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined%
+\edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}%
+\else%user glue not defined
+\@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak
+column specifications. Using a default value of\MessageBreak
+0pt instead}%
+{You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak
+\string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}%
+\edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}%
+\fi% glue defined or not
+\let\@IEEEBPcurtype=g% change the type to reflect the acquired glue
+\let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue
+\@IEEEBPcurnum=0\relax%ready for next acquisition
+\fi%close acquisition, get glue
+\fi%discard or acquire number
+\fi%prevtype glue or not
+}
+
+
+% process an acquired glue
+% add any acquired column/glue pair to the preamble
+\def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions
+\else
+% if this is the start glue, save it, but do nothing else 
+% as this is not used in the preamble, but before
+\if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}%
+\else%not the start glue
+\if\@IEEEBPprevtype g%ignore if back to back glues
+\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak
+specifications. Ignoring consecutive glue specifiers\MessageBreak
+after the first}%
+{You cannot have two or more glue types next to each other\MessageBreak 
+in the IEEEeqnarray column specifications.}%
+\let\@IEEEBPcurtype=a% abort this glue
+\else% not a back to back glue
+\if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble
+\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi
+\toks0={##}%
+% make preamble advance col counter if this environment needs this
+\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi
+% insert the column defintion into the preamble, being careful not to expand
+% the column definition
+\@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}%
+\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%
+\@IEEEappendtoksA{\@IEEEBPcurcolname}%
+\@IEEEappendNOEXPANDtoksA{\endcsname}%
+\@IEEEappendtoksA{\the\toks0}%
+\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%
+\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%
+\@IEEEappendtoksA{\@IEEEBPcurcolname}%
+\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%
+\relax\relax\relax\relax\relax\endgroup}%
+\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble
+\else% error: non-start glue with no pending column
+\@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak
+type in the column specifications. Ignoring this glue\MessageBreak 
+specifier}%
+{Except for the first and last positions, glue can be placed only\MessageBreak
+between column types.}%
+\let\@IEEEBPcurtype=a% abort this glue
+\fi% previous was a column
+\fi% back-to-back glues
+\fi% is start column glue
+\fi% prev type not a
+}
+
+
+% process an acquired letter referenced column and, if necessary, add it to the preamble
+\def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else
+\if\@IEEEBPnexttype n\else
+% we have a column followed by something other than a glue (or numeral glue)
+% so we must add this column to the preamble now
+\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first
+\if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue
+\@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue
+\toks0={##}%
+% make preamble advance col counter if this environment needs this
+\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi
+% insert the column definition into the preamble, being careful not to expand
+% the column definition
+\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%
+\@IEEEappendtoksA{\@IEEEBPcurcolname}%
+\@IEEEappendNOEXPANDtoksA{\endcsname}%
+\@IEEEappendtoksA{\the\toks0}%
+\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%
+\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%
+\@IEEEappendtoksA{\@IEEEBPcurcolname}%
+\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%
+\relax\relax\relax\relax\relax\endgroup}%
+\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble
+\fi%next type not numeral
+\fi%next type not glue
+}
+
+
+%%
+%% END OF IEEEeqnarry DEFINITIONS
+%%
+
+
+
+
+% set up the running headings, this complex because of all the different
+% modes IEEEtran supports
+\if@twoside
+ \if@technote
+   \def\ps@headings{%
+       \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
+       \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
+       \if@draftclsmode
+            \if@draftclsmodefoot
+               \def\@oddfoot{\scriptsize\@date\hfil DRAFT}
+               \def\@evenfoot{\scriptsize DRAFT\hfil\@date}
+            \else
+               \def\@oddfoot{}\def\@evenfoot{}%
+            \fi
+       \else
+            \def\@oddfoot{}\def\@evenfoot{}
+       \fi}
+ \else % not a technote
+   \def\ps@headings{%
+       \if@confmode
+        \def\@oddhead{}
+        \def\@evenhead{}
+       \else
+        \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}
+        \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
+       \fi
+       \if@draftclsmode
+            \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}
+            \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
+            \if@draftclsmodefoot
+               \def\@oddfoot{\scriptsize\@date\hfil DRAFT}
+               \def\@evenfoot{\scriptsize DRAFT\hfil\@date}
+            \else
+               \def\@oddfoot{}\def\@evenfoot{}%
+            \fi
+       \else
+            \def\@oddfoot{}\def\@evenfoot{}%
+       \fi}
+ \fi
+\else % single side
+\def\ps@headings{%
+    \if@confmode
+     \def\@oddhead{}
+     \def\@evenhead{}
+    \else
+     \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
+     \def\@evenhead{}
+    \fi
+    \if@draftclsmode
+          \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
+          \def\@evenhead{}
+          \if@draftclsmodefoot
+             \def\@oddfoot{\scriptsize \@date \hfil DRAFT}
+          \else
+             \def\@oddfoot{}
+          \fi
+    \else
+         \def\@oddfoot{}
+    \fi
+    \def\@evenfoot{}}
+\fi
+
+
+% title page style
+\def\ps@titlepagestyle{\def\@oddfoot{}\def\@evenfoot{}%
+\if@confmode
+   \def\@oddhead{}%
+   \def\@evenhead{}%
+\else
+   \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%
+   \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%
+\fi
+\if@draftclsmode
+   \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%
+   \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%
+   \if@draftclsmodefoot
+      \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%
+      \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%
+   \fi
+\else
+   % all non-draft mode footers
+   \if@IEEEusingpubid
+      % for title pages that are using a pubid
+      % do not repeat pubid if using peer review option
+      \if@peerreviewoption
+      \else
+         \footskip 0pt%
+         \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@pubid}\hss}%
+         \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@pubid}\hss}%
+      \fi
+   \fi
+\fi}
+
+
+% peer review cover page style
+\def\ps@peerreviewcoverpagestyle{%
+\def\@oddhead{}\def\@evenhead{}%
+\def\@oddfoot{}\def\@evenfoot{}%
+\if@draftclsmode
+   \if@draftclsmodefoot
+      \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%
+      \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%
+   \fi
+\else
+   % non-draft mode footers
+   \if@IEEEusingpubid
+      \footskip 0pt%
+      \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@pubid}\hss}%
+      \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@pubid}\hss}%
+   \fi
+\fi}
+
+
+% start with empty headings
+\def\rightmark{}\def\leftmark{}
+
+
+%% Defines the command for putting the header. \footernote{TEXT} is the same
+%% as \markboth{TEXT}{TEXT}. 
+%% Note that all the text is forced into uppercase, if you have some text
+%% that needs to be in lower case, for instance et. al., then either manually
+%% set \leftmark and \rightmark or use \MakeLowercase{et. al.} within the
+%% arguments to \markboth.
+\def\markboth#1#2{\def\leftmark{\MakeUppercase{#1}}\def\rightmark{\MakeUppercase{#2}}}
+\def\footernote#1{\markboth{#1}{#1}}
+
+\def\today{\ifcase\month\or
+    January\or February\or March\or April\or May\or June\or
+    July\or August\or September\or October\or November\or December\fi
+    \space\number\day, \number\year}
+
+
+
+
+%% CITATION AND BIBLIOGRAPHY COMMANDS
+%% 
+%% V1.6 no longer supports the older, nonstandard \shortcite and \citename setup stuff
+% 
+% 
+% Modify Latex2e \@citex to separate citations with "], ["
+\def\@citex[#1]#2{%
+  \let\@citea\@empty
+  \@cite{\@for\@citeb:=#2\do
+    {\@citea\def\@citea{], [}%
+     \edef\@citeb{\expandafter\@firstofone\@citeb\@empty}%
+     \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
+     \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%
+       \G@refundefinedtrue
+       \@latex@warning
+         {Citation `\@citeb' on page \thepage \space undefined}}%
+       {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}
+
+% V1.6 we create hooks for the optional use of Donald Arseneau's
+% cite.sty package. cite.sty is "smart" and will notice that the
+% following format controls are already defined and will not
+% redefine them. The result will be the proper sorting of the
+% citation numbers and auto detection of 3 or more entry "ranges" -
+% all in IEEE style:  [1], [2], [5]--[7], [12]
+% This also allows for an optional note, i.e., \cite[mynote]{..}.
+% If the \cite with note has more than one reference, the note will
+% be applied to the last of the listed references. It is generally
+% desired that if a note is given, only one reference is listed in
+% that \cite.
+% Thanks to Mr. Arseneau for providing the required format arguments
+% to produce the IEEE style.
+\def\citepunct{], [}
+\def\citedash{]--[}
+
+
+% V1.6b providing this command makes hyperref think the natbib package is
+% in use so that it will not interfere with cite.sty. However, as a result,
+% citation numbers will not be hyperlinked.
+\def\NAT@parse{\typeout{IEEEtran error: Attempt to use fake Natbib command 
+which is provided to fool Hyperref.}}
+% it easy enough to override via:
+% \let\NAT@parse\undefined
+
+
+% V1.6 class files should always provide these
+\def\newblock{\hskip .11em\@plus.33em\@minus.07em}
+\let\@openbib@code\@empty
+
+
+
+% Provide support for the control entries of IEEEtran.bst V1.00 and later.
+\def\bstctlcite#1{\@bsphack
+  \@for\@citeb:=#1\do{%
+    \edef\@citeb{\expandafter\@firstofone\@citeb}%
+    \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi}%
+  \@esphack}
+
+% V1.6 provide a way for a user to execute a command just before 
+% a given reference number - used to insert a \newpage to balance
+% the columns on the last page
+\edef\@IEEEtriggerrefnum{0}   % the default of zero means that
+                              % the command is not executed
+\def\@IEEEtriggercmd{\newpage}
+
+% allow the user to alter the triggered command
+\long\def\IEEEtriggercmd#1{\long\def\@IEEEtriggercmd{#1}}
+
+% allow user a way to specify the reference number just before the
+% command is executed
+\def\IEEEtriggeratref#1{\@IEEEtrantmpcountA=#1%
+\edef\@IEEEtriggerrefnum{\the\@IEEEtrantmpcountA}}%
+
+% trigger command at the given reference
+\def\@IEEEbibitemprefix{\@IEEEtrantmpcountA=\@IEEEtriggerrefnum\relax%
+\advance\@IEEEtrantmpcountA by -1\relax%
+\ifnum\c@enumiv=\@IEEEtrantmpcountA\relax\@IEEEtriggercmd\relax\fi}
+
+\def\@biblabel#1{[#1]}
+
+\def\thebibliography#1{\section*{References}%
+    \addcontentsline{toc}{section}{References}%
+    % V1.6 add some rubber space here and provide a command trigger
+    \footnotesize \vskip 0.3\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip%
+    \list{\@biblabel{\@arabic\c@enumiv}}%
+    {\settowidth\labelwidth{\@biblabel{#1}}%
+    \leftmargin\labelwidth
+    \advance\leftmargin\labelsep\relax
+    \itemsep 0pt plus .5pt\relax%
+    \usecounter{enumiv}%
+    \let\p@enumiv\@empty
+    \renewcommand\theenumiv{\@arabic\c@enumiv}}%
+    \let\@IEEElatexbibitem\bibitem%
+    \def\bibitem{\@IEEEbibitemprefix\@IEEElatexbibitem}%
+\def\newblock{\hskip .11em plus .33em minus .07em}%
+% originally:
+%   \sloppy\clubpenalty4000\widowpenalty4000%
+% by adding the \interlinepenalty here, we make it more
+% difficult, but not impossible, for LaTeX to break within a reference.
+% IEEE almost never breaks a reference (but they do it more often with
+% technotes). You may get an underfull vbox warning around the bibliography, 
+% but the final result will be much more like what IEEE will publish. 
+% MDS 11/2000
+\if@technote\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty100%
+\else\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty500\fi%
+    \sfcode`\.=1000\relax}
+\let\endthebibliography=\endlist
+
+
+
+
+% TITLE PAGE COMMANDS
+% 
+% 
+% \IEEEmembership is used to produce the sublargesize italic font used to indicate author 
+% IEEE membership.
+\def\IEEEmembership#1{{\sublargesize\normalfont\textit{#1}}}
+ 
+
+% \authorrefmark{} produces a footnote type symbol to indicate author affiliation.
+% When given an argument of 1 to 9, \authorrefmark{} follows the standard LaTeX footnote
+% symbol sequence convention. However, for arguments 10 and above, \authorrefmark{} 
+% reverts to using lower case roman numerals, so it cannot overflow. Do note that you 
+% cannot use \footnotemark[] in place of \authorrefmark{} within \author as the footnote
+% symbols will have been turned off to prevent \thanks from creating footnote marks.
+% \authorrefmark{} produces a symbol that appears to LaTeX as having zero vertical
+% height - this allows for a more compact line packing, but the user must ensure that
+% the interline spacing is large enough to prevent \authorrefmark{} from colliding
+% with the text above.
+\def\authorrefmark#1{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or%
+    \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger%
+    \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}}
+
+
+% FONT CONTROLS AND SPACINGS FOR CONFERENCE MODE AUTHOR NAME AND AFFILIATION BLOCKS
+% 
+% The default font styles for the author name and affiliation blocks (confmode)
+\def\@IEEEauthorblockNstyle{\normalfont\sublargesize}
+\def\@IEEEauthorblockAstyle{\normalfont\normalsize}
+% The default if the user does not use an author block
+\def\@IEEEauthordefaulttextstyle{\normalfont\sublargesize}
+
+% spacing from title (or special paper notice) to author name blocks (confmode)
+% can be negative
+\def\@IEEEauthorblockconfadjspace{-0.25em}
+
+% spacing between name and affiliation blocks (confmode)
+% This can be negative.
+% IEEE doesn't want any added spacing here, but I will leave these
+% controls in place in case they ever change their mind.
+% Personally, I like 0.75ex.
+%\def\@IEEEauthorblockNtopspace{0.75ex}
+%\def\@IEEEauthorblockAtopspace{0.75ex}
+\def\@IEEEauthorblockNtopspace{0.0ex}
+\def\@IEEEauthorblockAtopspace{0.0ex}
+% baseline spacing within name and affiliation blocks (confmode)
+% must be positive, spacings below certain values will make 
+% the position of line of text sensitive to the contents of the
+% line above it i.e., whether or not the prior line has descenders, 
+% subscripts, etc. For this reason it is a good idea to keep
+% these above 2.6ex
+\def\@IEEEauthorblockNinterlinespace{2.6ex}
+\def\@IEEEauthorblockAinterlinespace{2.75ex}
+
+% This tracks the required strut size.
+% See the \@IEEEauthorhalign command for the actual default value used.
+\def\@IEEEauthorblockXinterlinespace{2.7ex}
+
+% variables to retain font size and style across groups
+% values given here have no effect as they will be overwritten later
+\gdef\@IEEESAVESTATEfontsize{10}
+\gdef\@IEEESAVESTATEfontbaselineskip{12}
+\gdef\@IEEESAVESTATEfontencoding{OT1}
+\gdef\@IEEESAVESTATEfontfamily{ptm}
+\gdef\@IEEESAVESTATEfontseries{m}
+\gdef\@IEEESAVESTATEfontshape{n}
+
+% saves the current font attributes
+\def\@IEEEcurfontSAVE{\global\let\@IEEESAVESTATEfontsize\f@size%
+\global\let\@IEEESAVESTATEfontbaselineskip\f@baselineskip%
+\global\let\@IEEESAVESTATEfontencoding\f@encoding%
+\global\let\@IEEESAVESTATEfontfamily\f@family%
+\global\let\@IEEESAVESTATEfontseries\f@series%
+\global\let\@IEEESAVESTATEfontshape\f@shape}
+
+% restores the saved font attributes
+\def\@IEEEcurfontRESTORE{\fontsize{\@IEEESAVESTATEfontsize}{\@IEEESAVESTATEfontbaselineskip}%
+\fontencoding{\@IEEESAVESTATEfontencoding}%
+\fontfamily{\@IEEESAVESTATEfontfamily}%
+\fontseries{\@IEEESAVESTATEfontseries}%
+\fontshape{\@IEEESAVESTATEfontshape}%
+\selectfont}
+
+
+% variable to indicate if the current block is the first block in the column
+\newif\if@IEEEprevauthorblockincol   \@IEEEprevauthorblockincolfalse
+
+
+% the command places a strut with height and depth = \@IEEEauthorblockXinterlinespace
+% we use this technique to have complete manual control over the spacing of the lines
+% within the halign environment.
+% We set the below baseline portion at 30%, the above
+% baseline portion at 70% of the total length.
+% Responds to changes in the document's \baselinestretch
+\def\@IEEEauthorstrutrule{\@IEEEtrantmpdimenA\@IEEEauthorblockXinterlinespace%
+\@IEEEtrantmpdimenA=\baselinestretch\@IEEEtrantmpdimenA%
+\rule[-0.3\@IEEEtrantmpdimenA]{0pt}{\@IEEEtrantmpdimenA}}
+
+
+% blocks to hold the authors' names and affilations. 
+% Makes formatting easy for conferences
+%
+% use real definitions in conference mode
+% name block
+\def\authorblockN#1{\relax\@IEEEauthorblockNstyle% set the default text style
+\gdef\@IEEEauthorblockXinterlinespace{0pt}% disable strut for spacer row
+% the \expandafter hides the \cr in conditional tex, see the array.sty docs
+% for details, probably not needed here as the \cr is in a macro
+% do a spacer row if needed
+\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockNtopspaceline\fi
+\global\@IEEEprevauthorblockincoltrue% we now have a block in this column
+%restore the correct strut value
+\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockNinterlinespace}%
+% input the author names
+#1%
+% end the row if the user did not already
+\crcr}
+% spacer row for names
+\def\@IEEEauthorblockNtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockNtopspace}}
+%
+% affiliation block
+\def\authorblockA#1{\relax\@IEEEauthorblockAstyle% set the default text style
+\gdef\@IEEEauthorblockXinterlinespace{0pt}%disable strut for spacer row
+% the \expandafter hides the \cr in conditional tex, see the array.sty docs
+% for details, probably not needed here as the \cr is in a macro
+% do a spacer row if needed
+\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockAtopspaceline\fi
+\global\@IEEEprevauthorblockincoltrue% we now have a block in this column
+%restore the correct strut value
+\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockAinterlinespace}%
+% input the author affiliations
+#1%
+% end the row if the user did not already
+\crcr}
+% spacer row for affiliations
+\def\@IEEEauthorblockAtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockAtopspace}}
+
+
+% allow papers to compile even if author blocks are used in modes other
+% than conference or peerreviewca. For such cases, we provide dummy blocks.
+\if@confmode
+\else
+   \if@peerreviewcaoption\else
+      % not conference or peerreviewca mode
+      \def\authorblockN#1{#1}%
+      \def\authorblockA#1{#1}%
+   \fi
+\fi
+
+
+
+% we provide our own halign so as not to have to depend on tabular
+\def\@IEEEauthorhalign{\@IEEEauthordefaulttextstyle% default text style
+   \lineskip=0pt\relax% disable line spacing
+   \lineskiplimit=0pt\relax%
+   \baselineskip=0pt\relax%
+   \@IEEEcurfontSAVE% save the current font
+   \mathsurround\z@\relax% no extra spacing around math
+   \let\\\@IEEEauthorhaligncr% replace newline with halign friendly one
+   \tabskip=0pt\relax% no column spacing
+   \everycr{}% ensure no problems here
+   \@IEEEprevauthorblockincolfalse% no author blocks yet
+   \def\@IEEEauthorblockXinterlinespace{2.7ex}% default interline space
+   \vtop\bgroup%vtop box
+   \halign\bgroup&\relax\hfil\@IEEEcurfontRESTORE\relax ##\relax
+   \hfil\@IEEEcurfontSAVE\@IEEEauthorstrutrule\cr}
+
+% ensure last line, exit from halign, close vbox
+\def\end@IEEEauthorhalign{\crcr\egroup\egroup}
+
+% handle bogus star form
+\def\@IEEEauthorhaligncr{{\ifnum0=`}\fi\@ifstar{\@@IEEEauthorhaligncr}{\@@IEEEauthorhaligncr}}
+
+% test and setup the optional argument to \\[]
+\def\@@IEEEauthorhaligncr{\@testopt\@@@IEEEauthorhaligncr\z@skip}
+
+% end the line and do the optional spacer
+\def\@@@IEEEauthorhaligncr[#1]{\ifnum0=`{\fi}\cr\noalign{\vskip#1\relax}}
+
+
+
+% flag to prevent multiple \and warning messages
+\newif\if@IEEEWARNand
+\@IEEEWARNandtrue
+
+% if in conference or peerreviewca modes, we support the use of \and as \author is a
+% tabular environment, otherwise we warn the user that \and is invalid
+% outside of conference or peerreviewca modes.
+\def\and{\relax} % provide a bogus \and that we will then override
+
+\renewcommand{\and}[1][\relax]{\if@IEEEWARNand\typeout{** WARNING: \noexpand\and is valid only
+                               when in conference or peerreviewca}\typeout{modes (line \the\inputlineno).}\fi\global\@IEEEWARNandfalse}
+
+\if@confmode%
+\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
+\fi
+\if@peerreviewcaoption
+\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
+\fi
+
+
+% page clearing command
+% based on LaTeX2e's \cleardoublepage, but allows different page styles
+% for the inserted blank pages
+\def\@IEEEcleardoublepage#1{\clearpage\if@twoside\ifodd\c@page\else
+\hbox{}\thispagestyle{#1}\newpage\if@twocolumn\hbox{}\thispagestyle{#1}\newpage\fi\fi\fi}
+
+
+% user command to invoke the title page
+\def\maketitle{\par%
+  \begingroup%
+  \normalfont%
+  \def\thefootnote{}%  the \thanks{} mark type is empty
+  \def\footnotemark{}% and kill space from \thanks within author
+  \footnotesize%       equal spacing between thanks lines
+  \footnotesep 0.7\baselineskip%see global setting of \footnotesep for more info
+  \normalsize%
+  \if@peerreviewoption
+     \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
+     \thispagestyle{peerreviewcoverpagestyle}\@thanks%
+  \else
+     \if@twocolumn%
+        \if@technote%
+           \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
+        \else
+           \twocolumn[\@maketitle\@IEEEdynamictitlevspace\@IEEEaftertitletext]%
+        \fi
+     \else
+        \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
+     \fi
+     \thispagestyle{titlepagestyle}\@thanks%
+  \fi
+  % pullup page for pubid if used.
+  \if@IEEEusingpubid
+     \enlargethispage{-\@pubidpullup}%
+  \fi 
+  \endgroup
+  \setcounter{footnote}{0}\let\maketitle\relax\let\@maketitle\relax
+  \gdef\@thanks{}
+  % v1.6b do not clear these as we will need the title again for peer review papers
+  % \gdef\@author{}\gdef\@title{}%
+  \let\thanks\relax}
+
+
+% formats the Title, authors names, affiliations and special paper notice
+% THIS IS A CONTROLLED SPACING COMMAND! Do not allow blank lines or unintentional
+% spaces to enter the definition - use % at the end of each line
+% Changed Title font to \LARGE from \Huge
+\def\@maketitle{\newpage
+\begin{center}%
+\if@technote%
+   {\bfseries\large\@title\par}\vskip 1.3em{\lineskip .5em\@author\@specialpapernotice\par}%
+\else% not a technote
+   \vskip0.25in{\LARGE\@title\par}\vskip1.0em\par%
+   % V1.6 handle \author differently if in conference mode
+   \if@confmode%
+      {\@specialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
+      \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}%
+   \else% peerreviewca, peerreview or journal
+      \if@peerreviewcaoption
+         % peerreviewca handles author names just like conference mode
+         {\@specialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
+         \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}%
+      \else % journal or peerreview
+         {\lineskip.5em\sublargesize\@author\@specialpapernotice\par}%
+      \fi
+   \fi
+\fi\end{center}}
+
+
+
+% V1.6b define the \IEEEpeerreviewmaketitle as needed
+\if@peerreviewoption
+\def\IEEEpeerreviewmaketitle{\@IEEEcleardoublepage{empty}%
+\if@twocolumnmode
+\twocolumn[\@IEEEpeerreviewmaketitle\@IEEEdynamictitlevspace]
+\else
+\newpage\@IEEEpeerreviewmaketitle\@IEEEstatictitlevskip
+\fi
+\thispagestyle{titlepagestyle}}
+\else
+% \IEEEpeerreviewmaketitle does nothing if peer review option has not been selected
+\def\IEEEpeerreviewmaketitle{\relax}
+\fi
+
+% peerreview formats the repeated title like the title in journal papers.
+\def\@IEEEpeerreviewmaketitle{\begin{center}%
+\normalfont\normalsize\vskip0.2em{\Huge\@title\par}\vskip1.0em\par
+\end{center}}
+
+
+
+% V1.6 
+% this is a static rubber spacer between the title/authors and the main text
+% used for single column text, or when the title appears in the first column
+% of two column text (technotes). 
+\def\@IEEEstatictitlevskip{{\normalfont\normalsize
+% adjust spacing to next text
+% v1.6b handle peer review papers
+\if@peerreviewoption
+% for peer review papers, the same value is used for both title pages
+% regardless of the other paper modes
+   \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip
+\else
+   \if@confmode% conference
+      \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%
+   \else%
+      \if@technote% technote
+         \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%
+      \else% journal uses more space
+         \vskip 2.5\baselineskip plus 0.75\baselineskip minus 0.375\baselineskip%
+      \fi
+   \fi
+\fi}}
+
+
+% V1.6
+% This is a dynamically determined rigid spacer between the title/authors 
+% and the main text. This is used only for single column titles over two 
+% column text (most common)
+% This is bit tricky because we have to ensure that the textheight of the
+% main text is an integer multiple of \baselineskip
+% otherwise underfull vbox problems may develop in the second column of the
+% text on the titlepage
+% The possible use of \pubid must also be taken into account.
+\def\@IEEEdynamictitlevspace{{%
+    % we run within a group so that all the macros can be forgotten when we are done
+    \def\thanks##1{\relax}%don't allow \thanks to run when we evaluate the vbox height
+    \normalfont\normalsize% we declare more descriptive variable names
+    \let\@maintextheight=\@IEEEtrantmpdimenA%height of the main text columns
+    \let\@INTmaintextheight=\@IEEEtrantmpdimenB%height of the main text columns with integer # lines
+    % set the nominal and minimum values for the title spacer
+    % the dynamic algorithm will not allow the spacer size to
+    % become less than \@MINtitlevspace - instead it will be
+    % lengthened
+    % default to journal values
+    \def\@NORMtitlevspace{2.5\baselineskip}%
+    \def\@MINtitlevspace{2\baselineskip}%
+    % conferences and technotes need tighter spacing
+    \if@confmode%conference
+     \def\@NORMtitlevspace{1\baselineskip}%
+     \def\@MINtitlevspace{0.75\baselineskip}%
+    \fi
+    \if@technote%technote
+      \def\@NORMtitlevspace{1\baselineskip}%
+      \def\@MINtitlevspace{0.75\baselineskip}%
+    \fi%
+    % get the height that the title will take up
+    \if@peerreviewoption
+       \settoheight{\@maintextheight}{\vbox{\hsize\textwidth \@IEEEpeerreviewmaketitle}}%
+    \else
+       \settoheight{\@maintextheight}{\vbox{\hsize\textwidth \@maketitle}}%
+    \fi
+    \@maintextheight=-\@maintextheight% title takes away from maintext, so reverse sign
+    % add the height of the page textheight
+    \advance\@maintextheight by \textheight%
+    % correct for title pages using pubid
+    \if@peerreviewoption\else
+       % peerreview papers use the pubid on the cover page only.
+       % And the cover page uses a static spacer.
+       \if@IEEEusingpubid\advance\@maintextheight by -\@pubidpullup\fi
+    \fi%
+    % subtract off the nominal value of the title bottom spacer
+    \advance\@maintextheight by -\@NORMtitlevspace%
+    % \topskip takes away some too
+    \advance\@maintextheight by -\topskip%
+    % calculate the column height of the main text for lines
+    % now we calculate the main text height as if holding
+    % an integer number of \normalsize lines after the first
+    % and discard any excess fractional remainder
+    % we subtracted the first line, because the first line
+    % is placed \topskip into the maintext, not \baselineskip like the
+    % rest of the lines.
+    \@INTmaintextheight=\@maintextheight%
+    \divide\@INTmaintextheight  by \baselineskip%
+    \multiply\@INTmaintextheight  by \baselineskip%
+    % now we calculate how much the title spacer height will
+    % have to be reduced from nominal (\@REDUCEmaintextheight is always
+    % a positive value) so that the maintext area will contain an integer
+    % number of normal size lines
+    % we change variable names here (to avoid confusion) as we no longer
+    % need \@INTmaintextheight and can reuse its dimen register
+    \let\@REDUCEmaintextheight=\@INTmaintextheight%
+    \advance\@REDUCEmaintextheight by -\@maintextheight%
+    \advance\@REDUCEmaintextheight by \baselineskip%
+    % this is the calculated height of the spacer
+    % we change variable names here (to avoid confusion) as we no longer
+    % need \@maintextheight and can reuse its dimen register
+    \let\@COMPENSATElen=\@maintextheight%
+    \@COMPENSATElen=\@NORMtitlevspace% set the nominal value
+    % we go with the reduced length if it is smaller than an increase
+    \ifdim\@REDUCEmaintextheight < 0.5\baselineskip\relax%
+     \advance\@COMPENSATElen by -\@REDUCEmaintextheight%
+     % if the resulting spacer is too small back out and go with an increase instead
+     \ifdim\@COMPENSATElen<\@MINtitlevspace\relax%
+      \advance\@COMPENSATElen by \baselineskip%
+     \fi%
+    \else%
+     % go with an increase because it is closer to the nominal than a decrease
+     \advance\@COMPENSATElen by -\@REDUCEmaintextheight%
+     \advance\@COMPENSATElen by \baselineskip%
+    \fi%
+    % set the calculated rigid spacer
+    \vspace{\@COMPENSATElen}}}
+
+
+
+% V1.6
+% we allow the user access to the last part of the title area
+% useful in emergencies such as when a different spacing is needed
+% This text is NOT compensated for in the dynamic sizer.
+\let\@IEEEaftertitletext=\relax
+\def\IEEEaftertitletext#1{\def\@IEEEaftertitletext{#1}}
+
+
+% V1.6 have abstract and keywords strip leading spaces, pars and newlines
+% so that spacing is more tightly controlled.
+\def\abstract{\normalfont%
+    \if@twocolumn%
+      \@IEEEabskeysecsize\bfseries\textit{Abstract}---\,%
+    \else%
+      \begin{center}\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{Abstract}\end{center}\quotation\@IEEEabskeysecsize%
+    \fi\@IEEEgobbleleadPARNLSP}
+% V1.6 IEEE wants only 1 pica from end of abstract to introduction heading when in 
+% conference mode (the heading already has this much above it)
+\def\endabstract{\relax\if@confmode\vspace{0ex}\else\vspace{1.34ex}\fi\par\if@twocolumn\else\endquotation\fi%
+    \normalfont\normalsize}
+
+
+\def\keywords{\normalfont%
+    % IEEE uses the term (in bold italics) "Index Terms" now. 
+    \if@twocolumn%
+      \@IEEEabskeysecsize\bfseries\textit{Index Terms}---\,\relax%
+    \else%
+      \begin{center}\@IEEEabskeysecsize\bfseries Index Terms\end{center}\quotation\@IEEEabskeysecsize%
+    \fi\@IEEEgobbleleadPARNLSP}
+\def\endkeywords{\relax\if@technote\vspace{1.34ex}\else\vspace{0.67ex}\fi%
+    \par\if@twocolumn\else\endquotation\fi%
+    \normalsize\normalfont}
+
+
+% gobbles all leading \, \\ and \par, upon finding first token that
+% is not a \ , \\ or a \par, it ceases and returns that token
+% 
+% used to strip leading \, \\ and \par from the input
+% so that such things in the beginning of an environment will not
+% affect the formatting of the text
+\long\def\@IEEEgobbleleadPARNLSP#1{\let\@IEEEswallowthistoken=0%
+\let\@IEEEgobbleleadPARNLSPtoken#1%
+\let\@IEEEgobbleleadPARtoken=\par%
+\let\@IEEEgobbleleadNLtoken=\\%
+\let\@IEEEgobbleleadSPtoken=\ %
+\def\@IEEEgobbleleadSPMACRO{\ }%
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadPARtoken%
+\let\@IEEEswallowthistoken=1%
+\fi%
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadNLtoken%
+\let\@IEEEswallowthistoken=1%
+\fi%
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPtoken%
+\let\@IEEEswallowthistoken=1%
+\fi%
+% a control space will come in as a macro
+% when it is the last one on a line
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPMACRO%
+\let\@IEEEswallowthistoken=1%
+\fi%
+% if we have to swallow this token, do so and taste the next one
+% else spit it out and stop gobbling
+\ifx\@IEEEswallowthistoken 1\let\@IEEEnextgobbleleadPARNLSP=\@IEEEgobbleleadPARNLSP\else%
+\let\@IEEEnextgobbleleadPARNLSP=#1\fi%
+\@IEEEnextgobbleleadPARNLSP}%
+
+
+
+
+% TITLING OF SECTIONS
+\def\@IEEEsectpunct{:\ \,}  % Punctuation after run-in section heading  (headings which are
+                            % part of the paragraphs), need little bit more than a space
+
+\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 0.5em\relax}
+
+\def\@sect#1#2#3#4#5#6[#7]#8{%
+  \ifnum #2>\c@secnumdepth%
+     \def\@svsec{}%
+  \else%
+     \refstepcounter{#1}
+     % load section label and spacer into \@svsec
+     \protected@edef\@svsec{\@seccntformat{#1}\relax}%
+  \fi%
+  \@tempskipa #5\relax%
+  \ifdim \@tempskipa>\z@% tempskipa determines whether is treated as a high
+     \begingroup #6\relax% or low level heading
+      \noindent % subsections are NOT indented
+       % print top level headings. \@svsec is label, #8 is heading title
+       %\@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}
+       % IEEE does not block indent the section title text, it flows like normal
+       \relax{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
+     \endgroup%
+     % got rid of sectionmark stuff
+     % \csname #1mark\endcsname{#7}
+     \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else%
+               \protect\numberline{\csname the#1\endcsname}\fi#7}%
+  \else % printout low level headings
+     % svsechd seems to swallow the trailing space, protect it with \mbox{}
+     % got rid of sectionmark stuff
+     \def\@svsechd{#6\hskip #3\@svsec #8\@IEEEsectpunct\mbox{}%\csname #1mark\endcsname{#7}
+     \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else%
+               \protect\numberline{\csname the#1\endcsname}\fi#7}}
+  \fi%skip down
+  \@xsect{#5}}
+  
+% section* handler
+\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax%
+  \ifdim \@tempskipa>\z@%
+     %\begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup
+     % IEEE does not block indent the section title text, it flows like normal
+     \begingroup \noindent #4\relax{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup%
+  % svsechd swallows the trailing space, protect it with \mbox{}
+  \else \def\@svsechd{#4\hskip #1\relax #5\@IEEEsectpunct\mbox{}}\fi%
+  \@xsect{#3}}
+
+
+%% SECTION heading spacing and font
+%%
+% arguments are: #1 - sectiontype name
+% (for \@sect)   #2 - section level
+%                #3 - section heading indent
+%                #4 - top separation (absolute value used, neg indicates not to indent main text)
+%                     If negative, make stretch parts negative too!
+%                #5 - (absolute value used) positive: bottom separation after heading,
+%                      negative: amount to indent main text after heading
+%                Both #4 and #5 negative means to indent main text and use negative top separation
+%                #6 - font control
+% You've got to have \normalfont\normalsize in the font specs below to prevent
+% trouble when you do something like:
+% \section{Note}{\ttfamily TT-TEXT} is known to ... 
+% IEEE sometimes REALLY stretches the area before a section
+% heading by up to about 0.5in. However, it may not be a good
+% idea to let LaTeX have quite this much rubber.
+\if@confmode%
+% IEEE wants section heading spacing to decrease for conference mode
+\def\section{\@startsection{section}{1}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%
+{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%
+\def\subsection{\@startsection{subsection}{2}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
+\else % for journals
+\def\section{\@startsection{section}{1}{\z@}{3.0ex plus 1.5ex minus 1.5ex}% V1.6 3.0ex from 3.5ex
+{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%
+\def\subsection{\@startsection{subsection}{2}{\z@}{3.5ex plus 1.5ex minus 1.5ex}%
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
+\fi
+% decided to put in a little rubber above the section, might help somebody
+\def\subsubsection{\@startsection{subsubsection}{3}{\parindent}{0ex plus 0.1ex minus 0.1ex}%
+{0ex}{\normalfont\normalsize\itshape}}%
+\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%
+{0ex}{\normalfont\normalsize\itshape}}%
+
+
+
+%% ENVIRONMENTS
+% "box" symbols at end of proofs
+\def\QEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box
+% V1.6 some journals use an open box instead that will just fit around a closed one
+\def\QEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}}
+\def\QED{\QEDclosed} % default to closed
+
+\def\proof{\noindent\hspace{2em}{\itshape Proof: }}
+\def\endproof{\hspace*{\fill}~\QED\par\endtrivlist\unskip}
+%\itemindent is set to \z@ by list, so define new temporary variable
+\newdimen\@IEEEtmpitemindent
+\def\@begintheorem#1#2{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily\trivlist%
+    \item[\hskip \labelsep{\indent\itshape #1\ #2:}]\itemindent\@IEEEtmpitemindent}
+\def\@opargbegintheorem#1#2#3{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily \trivlist%
+% V1.6 IEEE is back to using () around theorem names which are also in italics
+% Thanks to Christian Peel for reporting this.
+    \item[\hskip\labelsep{\indent\itshape #1\ #2\ (#3):}]\itemindent\@IEEEtmpitemindent}
+\def\@endtheorem{\endtrivlist\unskip}
+
+% V1.6
+% display command for the section the theorem is in - so that \thesection
+% is not used as this will be in Roman numerals when we want arabic.
+% LaTeX2e uses \def\@thmcounter#1{\noexpand\arabic{#1}} for the theorem number
+% (second part) display and \def\@thmcountersep{.} as a separator.
+\def\@IEEEthmcounterin#1{\arabic{#1}}
+% redefine the #1#2[#3] form of newtheorem to use a hook to \@IEEEthmcounterin
+\def\@xnthm#1#2[#3]{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}\@newctr{#1}[#3]%
+     \expandafter\xdef\csname the#1\endcsname{%
+     \noexpand\@IEEEthmcounterin{#3}\@thmcountersep\@thmcounter{#1}}%
+     \global\@namedef{#1}{\@thm{#1}{#2}}%
+     \global\@namedef{end#1}{\@endtheorem}}}
+
+
+
+%% SET UP THE DEFAULT PAGESTYLE
+\ps@headings
+\pagenumbering{arabic}
+
+% normally the page counter starts at 1
+\setcounter{page}{1}
+% however, for peerreview the cover sheet is page 0 or page -1
+% (for duplex printing)
+\if@peerreviewoption
+   \if@twoside
+      \setcounter{page}{-1}
+   \else
+      \setcounter{page}{0}
+   \fi
+\fi
+
+% standard book class behavior - let bottom line float up and down as
+% needed when single sided
+\if@twoside\else\raggedbottom\fi
+% if two column - turn on twocolumn, allow word spacings to stretch more and
+% enforce a rigid position for the last lines
+\if@twocolumnmode
+% the peer review option delays invoking twocolumn
+   \if@peerreviewoption\else
+      \twocolumn
+   \fi
+\sloppy 
+\flushbottom
+\fi
+
+
+
+
+% \APPENDIX and \APPENDICES definitions
+
+% This is the \@ifmtarg command from the LaTeX ifmtarg package
+% by Peter Wilson (CUA) and Donald Arseneau
+% \@ifmtarg is used to determine if an argument to a command
+% is present or not.
+% For instance:
+% \@ifmtarg{#1}{\typeout{empty}}{\typeout{has something}}
+% \@ifmtarg is used with our redefined \section command if
+% \appendices is invoked.
+% The command \section will behave slightly differently depending
+% on whether the user specifies a title: 
+% \section{My appendix title}
+% or not:
+% \section{}
+% This way, we can eliminate the blank lines where the title
+% would be, and the unneeded : after Appendix in the table of
+% contents 
+\begingroup
+\catcode`\Q=3
+\long\gdef\@ifmtarg#1{\@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil}
+\long\gdef\@xifmtarg#1#2Q#3#4#5\@nil{#4}
+\endgroup
+% end of \@ifmtarg defs
+
+% save the "original" meaning of \section so we can redefine
+% \section after a call to \appendix or \appendices 
+\let\@IEEEappendixsavesection\section
+
+% neat trick to grab and process the argument from \section{argument}
+% we process differently if the user invoked \section{} with no
+% argument (title)
+% note we reroute the call to the old \section*
+\def\@IEEEprocessthesectionargument#1{%
+\@ifmtarg{#1}{%
+\@IEEEappendixsavesection*{Appendix \thesectiondis}%
+\addcontentsline{toc}{section}{Appendix \thesection}}{%
+\@IEEEappendixsavesection*{Appendix \thesectiondis \\* #1}%
+\addcontentsline{toc}{section}{Appendix \thesection: #1}}}
+
+% we use this if the user calls \section{} after
+% \appendix-- which has no meaning. So, we ignore the
+% command and its argument. Then, warn the user.
+\def\@IEEEdestroythesectionargument#1{\typeout{** WARNING: Ignoring useless
+\protect\section\space in Appendix (line \the\inputlineno).}}
+
+
+% remember \thesection forms will be displayed in \ref calls
+% and in the Table of Contents.
+% The \sectiondis form is used in the actual heading itself
+
+% appendix command for one single appendix
+% normally has no heading. However, if you want a 
+% heading, you can do so via the optional argument:
+% \appendix[Optional Heading]
+\def\appendix{\relax}
+\renewcommand{\appendix}[1][]{\par%
+    % v1.6 keep hyperref's identifiers unique
+    \def\theHsection{Appendix.A}%
+    % v1.6 adjust hyperref's string name for the section
+    \xdef\Hy@chapapp{appendix}%
+    \setcounter{section}{0}%
+    \setcounter{subsection}{0}%
+    \setcounter{subsubsection}{0}%
+    \setcounter{paragraph}{0}%
+    \def\thesection{}%
+    \def\thesectiondis{}% 
+    \def\thesubsection{\Alph{subsection}}%
+    \refstepcounter{section}% update the \ref counter
+    \@ifmtarg{#1}{\@IEEEappendixsavesection*{Appendix}%
+                  \addcontentsline{toc}{section}{Appendix}}{%
+             \@IEEEappendixsavesection*{Appendix \\* #1}%
+             \addcontentsline{toc}{section}{Appendix: #1}}%
+    % redefine \section command for appendix
+    % leave \section* as is
+    \def\section{\@ifstar{\@IEEEappendixsavesection*}{%
+                    \@IEEEdestroythesectionargument}}% throw out the argument
+                                                     % of the normal form
+}
+
+
+% provides the user a way to choose between
+% Appendix A
+%    and
+% Appendix I
+% notation
+% defaults to Roman.
+\newif\ifuseRomanappendices
+\useRomanappendicestrue
+
+
+% appendices command for multiple appendices
+% user then calls \section with an argument (possibly empty) to
+% declare the individual appendices
+\def\appendices{\par%
+    % v1.6 keep hyperref's identifiers unique
+    \def\theHsection{Appendix.\Alph{section}}%
+    % v1.6 adjust hyperref's string name for the section
+    \xdef\Hy@chapapp{appendix}%
+    \setcounter{section}{-1}% we want \refstepcounter to use section 0
+    \setcounter{subsection}{0}%
+    \setcounter{subsubsection}{0}%
+    \setcounter{paragraph}{0}%
+    \ifuseRomanappendices%
+    \def\thesection{\Roman{section}}%
+    \def\thesectiondis{\Roman{section}}%
+    \else%
+    \def\thesection{\Alph{section}}%
+    \def\thesectiondis{\Alph{section}}%
+    \fi%
+    \refstepcounter{section}% update the \ref counter
+    \setcounter{section}{0}% NEXT \section will be the FIRST appendix
+    % redefine \section command for appendices
+    % leave \section* as is
+    \def\section{\@ifstar{\@IEEEappendixsavesection*}{% process the *-form
+                    \refstepcounter{section}% or is a new section so,
+                    \@IEEEprocessthesectionargument}}% process the argument 
+                                                 % of the normal form
+}
+
+
+
+% \PARstart
+% Definition for the big two line drop cap letter at the beginning of the
+% first paragraph of journal papers. The first argument is the first letter
+% of the first word, the second argument is the remaining letters of the
+% first word which will be rendered in upper case.
+% In V1.6 this has been completely rewritten to:
+% 
+% 1. no longer have problems when the user begins an environment
+%    within the paragraph that uses \PARstart.
+% 2. auto-detect and use the current font family
+% 3. revise handling of the space at the end of the first word so that
+%    interword glue will now work as normal.
+% 4. produce correctly aligned edges for the (two) indented lines.
+% 
+% We generalize things via control macros - playing with these is fun too.
+% 
+% the number of lines that are indented to clear it
+\def\@IEEEPARstartDROPLINES{2}
+% minimum number of lines left on a page to allow a \@PARstart
+% Does not take into consideration rubber shrink, so it tends to
+% be overly cautious
+\def\@IEEEPARstartMINPAGELINES{2}
+% the depth the letter is lowered below the baseline
+% the height (and size) of the letter is determined by the sum
+% of this value and the height of a capital "T" in the current
+% font. It is a good idea to set this value in terms of the baselineskip
+% so that it can respond to changes therein.
+\def\@IEEEPARstartDROPDEPTH{1.1\baselineskip}
+% This is the separation distance from the drop letter to the main text.
+% Lengths that depend on the font (i.e., ex, em, etc.) will be referenced
+% to the font that is active when PARstart is called. 
+\def\@IEEEPARstartSEP{0.15em}
+
+
+% definition of \PARstart
+% THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES
+% 
+% The token \@IEEEPARstartfont will be globally defined after the first use
+% of \PARstart and will be a font command which creates the big letter
+% The first argument is the first letter of the first word and the second
+% argument is the rest of the first word(s).
+\def\PARstart#1#2{\par{%
+% if this page does not have enough space, break it and lets start
+% on a new one
+\@IEEEtranneedspace{\@IEEEPARstartMINPAGELINES\baselineskip}{\relax}%
+% calculate the desired height of the big letter
+% it extends from the top of a capital "T" in the current font
+% down to \@IEEEPARstartDROPDEPTH below the current baseline
+\settoheight{\@IEEEtrantmpdimenA}{T}%
+\addtolength{\@IEEEtrantmpdimenA}{\@IEEEPARstartDROPDEPTH}%
+% extract the name of the current font in bold
+% and place it in \@IEEEPARstartFONTNAME
+\def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}%
+{\bfseries%
+\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}%
+\xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}%
+% define a font based on this name with a point size equal to the desired
+% height of the drop letter
+\font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax%
+% save this value as a counter (integer) value (sp points)
+\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA%
+% now get the height of the actual letter produced by this font size
+\settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\MakeUppercase{#1}}%
+% If something bogus happens like the first argument is empty or the
+% current font is strange, do not allow a zero height.
+\ifdim\@IEEEtrantmpdimenB=0pt\relax%
+\typeout{** WARNING: PARstart drop letter has zero height! (line \the\inputlineno)}%
+\typeout{ Forcing the drop letter font size to 10pt.}%
+\@IEEEtrantmpdimenB=10pt%
+\fi%
+% and store it as a counter
+\@IEEEtrantmpcountB=\@IEEEtrantmpdimenB%
+% Since a font size doesn't exactly correspond to the height of the capital
+% letters in that font, the actual height of the letter, \@IEEEtrantmpcountB,
+% will be less than that desired, \@IEEEtrantmpcountA
+% we need to raise the font size, \@IEEEtrantmpdimenA 
+% by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB
+% But, TeX doesn't have floating point division, so we have to use integer
+% division. Hence the use of the counters.
+% We need to reduce the denominator so that the loss of the remainder will
+% have minimal affect on the accuracy of the result
+\divide\@IEEEtrantmpcountB by 200%
+\divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB%
+% Then reequalize things when we use TeX's ability to multiply by
+% floating point values
+\@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA%
+\multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA%
+% \@IEEEPARstartfont is globaly set to the calculated font of the big letter
+% We need to carry this out of the local calculation area to to create the
+% big letter.
+\global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB%
+% Now set \@IEEEtrantmpdimenA to the width of the big letter
+% We need to carry this out of the local calculation area to set the
+% hanging indent
+\settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont\MakeUppercase{#1}}}%
+% end of the isolated calculation environment
+% add in the extra clearance we want
+\advance\@IEEEtrantmpdimenA by \@IEEEPARstartSEP%
+% \@IEEEtrantmpdimenA has the width of the big letter plus the
+% separation space and \@IEEEPARstartfont is the font we need to use
+% Now, we make the letter and issue the hanging indent command
+% The letter is placed in a box of zero width and height so that other
+% text won't be displaced by it.
+\noindent\hangindent\@IEEEtrantmpdimenA\hangafter=-\@IEEEPARstartDROPLINES%
+\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}\raisebox{-\@IEEEPARstartDROPDEPTH}[0pt][0pt]{\@IEEEPARstartfont\MakeUppercase{#1}}}\MakeUppercase{#2}}
+
+
+% V1.6 \CMPARstart is no longer needed as \PARstart now uses whatever
+% the current font family is.
+% \CMPARstart is provided here for backward compatability.
+\let\CMPARstart=\PARstart
+
+
+
+% determines if the space remaining on a given page is equal to or greater
+% than the specified space of argument one
+% if not, execute argument two (only if the remaining space is greater than zero)
+% and issue a \newpage
+% 
+% example: \@IEEEtranneedspace{2in}{\vfill}
+% 
+% Does not take into consideration rubber shrinkage, so it tends to
+% be overly cautious
+% Based on an example posted by Donald Arseneau
+% Note this macro uses \@IEEEtrantmpdimenB internally for calculations,
+% so DO NOT PASS \@IEEEtrantmpdimenB to this routine
+% if you need a dimen register, import with \@IEEEtrantmpdimenA instead
+\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable
+\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left
+\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left
+\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi%
+\newpage%
+\fi\endgroup}
+
+
+
+% BIOGRAPHY ENVIRONMENT
+% Allows user to enter BIOGRAPHY leaving place for picture (adapts to font size)
+% As of V1.5, a new optional argument allows you to have a real graphic!
+% V1.5 and later also fixes the "colliding biographies" which could happen when a 
+% biography's text was shorter than the space for the photo.
+% MDS 7/2001
+% V1.6 prevent multiple biographies from making multiple TOC entries
+\newif\if@biographyTOCentrynotmade
+\global\@biographyTOCentrynotmadetrue
+
+% biography counter so hyperref can jump directly to the biographies
+% and not just the previous section
+\newcounter{biography}
+\setcounter{biography}{0}
+
+% photo area size
+\def\@IEEEBIOphotowidth{1.0in}    % width of the biography photo area
+\def\@IEEEBIOphotodepth{1.25in}   % depth (height) of the biography photo area
+% area cleared for photo
+\def\@IEEEBIOhangwidth{1.14in}    % width cleared for the biography photo area
+\def\@IEEEBIOhangdepth{1.25in}    % depth cleared for the biography photo area
+                                  % actual depth will be a multiple of 
+                                  % \baselineskip, rounded up
+\def\@IEEEBIOskipN{4\baselineskip}% nominal value of the vskip above the biography
+
+\newenvironment{biography}[2][]{\normalfont\footnotesize%
+\unitlength 1in\parskip=0pt\par\parindent 1em\interlinepenalty500%
+% we need enough space to support the hanging indent
+% the nominal value of the spacer
+% and one extra line for good measure
+\@IEEEtrantmpdimenA=\@IEEEBIOhangdepth%
+\advance\@IEEEtrantmpdimenA by \@IEEEBIOskipN%
+\advance\@IEEEtrantmpdimenA by 1\baselineskip%
+% if this page does not have enough space, break it and lets start
+% with a new one
+\@IEEEtranneedspace{\@IEEEtrantmpdimenA}{\relax}%
+% nominal spacer can strech, not shrink use 1fil so user can out stretch with \vfill
+\vskip \@IEEEBIOskipN plus 1fil minus 0\baselineskip%
+% the default box for where the photo goes
+\def\@IEEEtempbiographybox{{\setlength{\fboxsep}{0pt}\framebox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}\centering PLACE\\ PHOTO\\ HERE \end{minipage}}}}%
+%
+% detect if the optional argument was supplied, this requires the
+% \@ifmtarg command as defined in the appendix section above
+% and if so, override the default box with what they want
+\@ifmtarg{#1}{\relax}{\def\@IEEEtempbiographybox{\mbox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}%
+\centering%
+#1%
+\end{minipage}}}}% end if optional argument supplied
+% Make an entry into the table of contents only if we have not done so before
+\if@biographyTOCentrynotmade%
+% link labels to the biography counter so hyperref will jump
+% to the biography, not the previous section
+\setcounter{biography}{-1}%
+\refstepcounter{biography}%
+\addcontentsline{toc}{section}{Biographies}%
+\global\@biographyTOCentrynotmadefalse%
+\fi%
+% one more biography
+\refstepcounter{biography}%
+% Make an entry for this name into the table of contents 
+\addcontentsline{toc}{subsection}{#2}%
+% V1.6 properly handle if a new paragraph should occur while the
+% hanging indent is still active. Do this by redefining \par so
+% that it will not start a new paragraph. (But it will appear to the
+% user as if it did.) Also, strip any leading pars, newlines, or spaces.
+\let\@IEEEBIOORGparCMD=\par% save the original \par command
+\edef\par{\hfil\break\indent}% the new \par will not be a "real" \par
+\settoheight{\@IEEEtrantmpdimenA}{\@IEEEtempbiographybox}% get height of biography box
+\@IEEEtrantmpdimenB=\@IEEEBIOhangdepth%
+\@IEEEtrantmpcountA=\@IEEEtrantmpdimenB% countA has the hang depth
+\divide\@IEEEtrantmpcountA by \baselineskip%  calculates lines needed to produce the hang depth
+\advance\@IEEEtrantmpcountA by 1% ensure we overestimate
+% set the hanging indent
+\hangindent\@IEEEBIOhangwidth%
+\hangafter-\@IEEEtrantmpcountA%
+% reference the top of the photo area to the top of a capital T
+\settoheight{\@IEEEtrantmpdimenB}{\mbox{T}}%
+% set the photo box, give it zero width and height so as not to disturb anything
+\noindent\makebox[0pt][l]{\hspace{-\@IEEEBIOhangwidth}\raisebox{\@IEEEtrantmpdimenB}[0pt][0pt]{\raisebox{-\@IEEEBIOphotodepth}[0pt][0pt]{\@IEEEtempbiographybox}}}%
+% now place the author name and begin the bio text
+\noindent\textbf{#2\ }\@IEEEgobbleleadPARNLSP}{\relax\let\par=\@IEEEBIOORGparCMD\par%
+% 7/2001 V1.5 detect when the biography text is shorter than the photo area
+% and pad the unused area - preventing a collision from the next biography entry
+% MDS
+\ifnum \prevgraf <\@IEEEtrantmpcountA\relax% detect when the biography text is shorter than the photo
+    \advance\@IEEEtrantmpcountA by -\prevgraf% calculate how many lines we need to pad
+    \advance\@IEEEtrantmpcountA by -1\relax% we compensate for the fact that we indented an extra line
+    \@IEEEtrantmpdimenA=\baselineskip% calculate the length of the padding
+    \multiply\@IEEEtrantmpdimenA by \@IEEEtrantmpcountA%
+    \noindent\rule{0pt}{\@IEEEtrantmpdimenA}% insert an invisible support strut
+\fi%
+\par\normalfont}
+
+
+
+% V1.6
+% added biography without a photo environment
+\newenvironment{biographynophoto}[1]{%
+% Make an entry into the table of contents only if we have not done so before
+\if@biographyTOCentrynotmade%
+% link labels to the biography counter so hyperref will jump
+% to the biography, not the previous section
+\setcounter{biography}{-1}%
+\refstepcounter{biography}%
+\addcontentsline{toc}{section}{Biographies}%
+\global\@biographyTOCentrynotmadefalse%
+\fi%
+% one more biography
+\refstepcounter{biography}%
+% Make an entry for this name into the table of contents 
+\addcontentsline{toc}{subsection}{#1}%
+\normalfont\footnotesize\interlinepenalty500%
+\vskip 4\baselineskip plus 1fil minus 0\baselineskip%
+\parskip=0pt\par%
+\noindent\textbf{#1\ }\@IEEEgobbleleadPARNLSP}{\relax\par\normalfont}
+
+
+% provide the user with some old font commands
+% got this from article.cls
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
+\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}
+\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}
+
+
+% SPECIAL PAPER NOTICE COMMANDS
+% 
+% holds the special notice text
+\def\@specialpapernotice{\relax}
+ 
+% for special papers, like invited papers, the user can do:
+% \specialpapernotice{(Invited Paper)} before \maketitle
+\def\specialpapernotice#1{\if@confmode%
+\def\@specialpapernotice{{\sublargesize\textit{#1}\vspace*{1em}}}%
+\else%
+\def\@specialpapernotice{{\\*[1.5ex]\sublargesize\textit{#1}}\vspace*{-2ex}}%
+\fi}
+
+
+
+
+% PUBLISHER ID COMMANDS
+% to insert a publisher's ID footer
+% V1.6 \pubid has been changed so that the change in page size and style
+% occurs in \maketitle. \pubid must now be issued prior to \maketitle
+% use \pubidadjcol as before - in the second column of the title page
+% These changes allow \maketitle to take the reduced page height into
+% consideration when dynamically setting the space between the author 
+% names and the maintext.
+%
+% the amount the main text is pulled up to make room for the
+% publisher's ID footer
+% IEEE uses about 1.3\baselineskip for journals, 
+% dynamic title spacing will clean up the fraction
+\def\@pubidpullup{1.3\baselineskip}
+\if@technote
+% for technotes it must be an integer of baselineskip as there can be no
+% dynamic title spacing for two column mode technotes (the title is in the
+% in first column) and we should maintain an integer number of lines in the
+% second column
+% There are some examples (such as older issues of "Transactions on
+% Information Theory") in which IEEE really pulls the text off the ID for
+% technotes - about 0.55in (or 4\baselineskip). We'll use 2\baselineskip
+% and call it even.
+\def\@pubidpullup{2\baselineskip}
+\fi
+
+% holds the ID text
+\def\@pubid{\relax}
+
+% flag so \maketitle can tell if \pubid was called
+\newif\if@IEEEusingpubid
+\global\@IEEEusingpubidfalse
+% issue this command in the page to have the ID at the bottom
+% V1.6 use before \maketitle
+\def\pubid#1{\def\@pubid{#1} \global\@IEEEusingpubidtrue}
+
+
+% command which will pull up (shorten) the column it is executed in
+% to make room for the publisher ID. Place in the second column of
+% the title page when using \pubid
+% Is smart enough not to do anything when in single column text or
+% if the user hasn't called \pubid
+% currently needed in for the second column of a page with the
+% publisher ID. If not needed in future releases, please provide this
+% command and define it as \relax for backward compatibility
+% v1.6b do not allow command to operate if the peer review option has been 
+% selected because \pubidadjcol will not be on the cover page.
+\def\pubidadjcol{\if@peerreviewoption\else\if@twocolumn\if@IEEEusingpubid\enlargethispage{-\@pubidpullup}\fi\fi\fi}
+
+% Special thanks to Peter Wilson, Daniel Luecking, and the other
+% gurus at comp.text.tex, for helping me to understand how best to
+% implement the pubid command in LaTeX.
+
+
+
+%% Lockout some commands under various conditions
+
+% general purpose bit bucket
+\newsavebox{\@IEEEtranrubishbin}
+
+% flags to prevent multiple warning messages
+\newif\if@IEEEWARNthanks
+\newif\if@IEEEWARNPARstart
+\newif\if@IEEEWARNCMPARstart
+\newif\if@IEEEWARNkeywords
+\newif\if@IEEEWARNbiography
+\newif\if@IEEEWARNbiographynophoto
+\newif\if@IEEEWARNpubid
+\newif\if@IEEEWARNpubidadjcol
+\newif\if@IEEEWARNIEEEmembership
+\newif\if@IEEEWARNIEEEaftertitletext
+\@IEEEWARNthankstrue
+\@IEEEWARNPARstarttrue
+\@IEEEWARNCMPARstarttrue
+\@IEEEWARNkeywordstrue
+\@IEEEWARNbiographytrue
+\@IEEEWARNbiographynophototrue
+\@IEEEWARNpubidtrue
+\@IEEEWARNpubidadjcoltrue
+\@IEEEWARNIEEEmembershiptrue
+\@IEEEWARNIEEEaftertitletexttrue
+
+
+%% Lockout some commands when in various modes, but allow them to be restored if needed
+%%
+% save commands which might be locked out
+% so that the user can later restore them if needed
+\let\@IEEESAVECMDthanks\thanks
+\let\@IEEESAVECMDPARstart\PARstart
+\let\@IEEESAVECMDCMPARstart\CMPARstart
+\let\@IEEESAVECMDkeywords\keywords
+\let\@IEEESAVECMDendkeywords\endkeywords
+\let\@IEEESAVECMDbiography\biography
+\let\@IEEESAVECMDendbiography\endbiography
+\let\@IEEESAVECMDbiographynophoto\biographynophoto
+\let\@IEEESAVECMDendbiographynophoto\endbiographynophoto
+\let\@IEEESAVECMDpubid\pubid
+\let\@IEEESAVECMDpubidadjcol\pubidadjcol
+\let\@IEEESAVECMDIEEEmembership\IEEEmembership
+\let\@IEEESAVECMDIEEEaftertitletext\IEEEaftertitletext
+
+
+% disable \PARstart when in draft mode
+% This may have originally been done because the pre-V1.6 drop letter
+% algorithm had problems with a non-unity baselinestretch
+% At any rate, it seems too formal to have a drop letter in a draft
+% paper.
+\if@draftclsmode
+\def\PARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** ATTENTION: \noexpand\PARstart is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNPARstartfalse}
+\def\CMPARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** ATTENTION: \noexpand\CMPARstart is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNCMPARstartfalse}
+\fi
+% and for technotes
+\if@technote
+\def\PARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** WARNING: \noexpand\PARstart is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNPARstartfalse}
+\def\CMPARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** WARNING: \noexpand\CMPARstart is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNCMPARstartfalse}
+\fi
+
+
+% lockout unneeded commands when in conference mode
+\if@confmode
+% when locked out, \thanks, \keywords, \biography, \biographynophoto, \pubid,
+% \IEEEmembership and \IEEEaftertitletext will all swallow their given text. 
+% \PARstart and \CMPARstart will output a normal character instead
+% warn the user about these commands only once to prevent the console screen
+% from filling up with redundant messages
+\def\thanks#1{\if@IEEEWARNthanks\typeout{** WARNING: \noexpand\thanks is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNthanksfalse}
+\def\PARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** WARNING: \noexpand\PARstart is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNPARstartfalse}
+\def\CMPARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** WARNING: \noexpand\CMPARstart is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNCMPARstartfalse}
+
+\renewenvironment{keywords}[1]{\if@IEEEWARNkeywords\typeout{** WARNING: \noexpand\keywords is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNkeywordsfalse%
+\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
+
+% LaTeX treats environments and commands with optional arguments differently.
+% the actual ("internal") command is stored as \\commandname 
+% (accessed via \csname\string\commandname\endcsname )
+% the "external" command \commandname is a macro with code to determine
+% whether or not the optional argument is presented and to provide the 
+% default if it is absent. So, in order to save and restore such a command
+% we would have to save and restore \\commandname as well. But, if LaTeX
+% ever changes the way it names the internal names, the trick would break.
+% Instead let us just define a new environment so that the internal
+% name can be left undisturbed.
+\newenvironment{@IEEEbogusbiography}[2][]{\if@IEEEWARNbiography\typeout{** WARNING: \noexpand\biography is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNbiographyfalse%
+\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
+% and make biography point to our bogus biography
+\let\biography=\@IEEEbogusbiography
+\let\endbiography=\end@IEEEbogusbiography
+
+\renewenvironment{biographynophoto}[1]{\if@IEEEWARNbiographynophoto\typeout{** WARNING: \noexpand\biographynophoto is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNbiographynophotofalse%
+\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
+
+\def\pubid#1{\if@IEEEWARNpubid\typeout{** WARNING: \noexpand\pubid is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNpubidfalse}
+\def\pubidadjcol{\if@IEEEWARNpubidadjcol\typeout{** WARNING: \noexpand\pubidadjcol is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNpubidadjcolfalse}
+\def\IEEEmembership#1{\if@IEEEWARNIEEEmembership\typeout{** WARNING: \noexpand\IEEEmembership is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEmembershipfalse}
+\def\IEEEaftertitletext#1{\if@IEEEWARNIEEEaftertitletext\typeout{** WARNING: \noexpand\IEEEaftertitletext is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEaftertitletextfalse}
+\fi
+
+
+% provide a way to restore the commands that are locked out
+\def\IEEEoverridecommandlockouts{%
+\typeout{** ATTENTION: Overriding command lockouts (line \the\inputlineno).}%
+\let\thanks\@IEEESAVECMDthanks%
+\let\PARstart\@IEEESAVECMDPARstart%
+\let\CMPARstart\@IEEESAVECMDCMPARstart%
+\let\keywords\@IEEESAVECMDkeywords%
+\let\endkeywords\@IEEESAVECMDendkeywords%
+\let\biography\@IEEESAVECMDbiography%
+\let\endbiography\@IEEESAVECMDendbiography%
+\let\biographynophoto\@IEEESAVECMDbiographynophoto%
+\let\endbiographynophoto\@IEEESAVECMDendbiographynophoto%
+\let\pubid\@IEEESAVECMDpubid%
+\let\pubidadjcol\@IEEESAVECMDpubidadjcol%
+\let\IEEEmembership\@IEEESAVECMDIEEEmembership%
+\let\IEEEaftertitletext\@IEEESAVECMDIEEEaftertitletext}
+
+
+\endinput
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtran.cls  %%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% That's all folks!
+
-- 
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