diff --git a/Abstract.tex b/Abstract.tex
new file mode 100644
index 0000000..db2713a
--- /dev/null
+++ b/Abstract.tex
@@ -0,0 +1,34 @@
+\documentclass[12pt,letterpaper]{report}
+\usepackage[fancyhdr]{UMCCsThesis} % Thesis style
+\usepackage{setspace}
+\usepackage{myowndef}
+\linespread{1.67} % Linespacing for entire thesis
+\newlength{\defbaselineskip}
+\setlength{\defbaselineskip}{\baselineskip}
+\newcommand{\setlinespacing}[1]%
+           {\setlength{\baselineskip}{#1 \defbaselineskip}}
+\renewcommand{\doublespacing}{\setlength{\baselineskip}%
+                           {1.0 \defbaselineskip}}
+\renewcommand{\singlespacing}{\setlength{\baselineskip}{\defbaselineskip}}
+
+%========= Document start
+\begin {document}
+
+\thispagestyle{empty}
+\smalltitle
+\vspace{20pt}
+\begin{center}
+Ryan J. Calhoun
+\end{center}
+
+\vspace{10pt}
+\begin{center}
+Dr. Jeffrey Uhlmann, Thesis Supervisor 
+\end{center}
+\vspace{5pt}
+\section*{\centering ABSTRACT}
+\vspace{40pt}
+
+\input{chapters/abstract_text}
+\thispagestyle{empty}
+\end{document}
diff --git a/IEEEtran.bst b/IEEEtran.bst
new file mode 100644
index 0000000..70af79c
--- /dev/null
+++ b/IEEEtran.bst
@@ -0,0 +1,2369 @@
+%%
+%% IEEEtran.bst
+%% BibTeX Bibliography Style file for IEEE Journals and Conferences (unsorted)
+%% Version 1.11 (2003/04/02)
+%% 
+%% Copyright (c) 2003 Michael Shell
+%% 
+%% Original starting code base and algorithms obtained from the output of
+%% Patrick W. Daly's makebst package as well as from prior versions of
+%% IEEE BibTeX styles:
+%% 
+%% 1. Howard Trickey and Oren Patashnik's ieeetr.bst  (1985/1988)
+%% 2. Silvano Balemi and Richard H. Roy's IEEEbib.bst (1993)
+%% 
+%% 
+%% See:
+%% http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/
+%% for latest version and current contact information.
+%% 
+%% For use with BibTeX version 0.99a or later
+%%
+%% This is a numerical citation style.
+%% 
+%%**********************************************************************
+%% 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.
+%%
+%% This code is distributed under the Perl Artistic License 
+%% ( http://language.perl.com/misc/Artistic.html ) 
+%% and may be freely used, distributed and modified - subject to the
+%% constraints therein.
+%% Retain all contribution notices, credits and disclaimers.
+%% 
+%% All comments are the opinions of their respective authors and are not
+%% necessarily endorsed by the IEEE.
+%%**********************************************************************
+%
+%
+% Changelog:
+% 
+% 1.00 (2002/08/13) Initial release
+% 
+% 1.10 (2002/09/27)
+%  1. Corrected minor bug for improperly formed warning message when a
+%     book was not given a title. Thanks to Ming Kin Lai for reporting this.
+%  2. Added support for CTLname_format_string and CTLname_latex_cmd fields
+%     in the BST control entry type.
+% 
+% 1.11 (2003/04/02)
+%  1. Fixed bug with URLs containing underscores when using url.sty. Thanks
+%     to Ming Kin Lai for reporting this.
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEFAULTS FOR THE CONTROLS OF THE BST STYLE %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% These are the defaults for the user adjustable controls. The values used
+% here can be overridden by the user via IEEEtranBSTCTL entry type.
+
+% NOTE: The recommended LaTeX command to invoke a control entry type is:
+% 
+%\makeatletter
+%\def\bstctlcite#1{\@bsphack
+%  \@for\@citeb:=#1\do{%
+%    \edef\@citeb{\expandafter\@firstofone\@citeb}%
+%    \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi}%
+%  \@esphack}
+%\makeatother
+%
+% It is called at the start of the document, before the first \cite, like:
+% \bstctlcite{IEEEexample:BSTcontrol}
+%
+% IEEEtran.cls V1.6 and later does provide this command.
+
+
+
+% #0 turns off the display of the number for articles.
+% #1 enables
+FUNCTION {default.is.use.number.for.article} { #1 }
+
+
+% #0 turns off the display of the paper and type fields in @inproceedings.
+% #1 enables
+FUNCTION {default.is.use.paper} { #1 }
+
+
+% #0 turns off the forced use of "et al."
+% #1 enables
+FUNCTION {default.is.forced.et.al} { #0 }
+
+% The maximum number of names that can be present beyond which an "et al."
+% usage is forced. Be sure that num.names.shown.with.forced.et.al (below)
+% is not greater than this value!
+% Note: There are many instances of references in IEEE journals which have
+% a very large number of authors as well as instances in which "et al." is
+% used profusely.
+FUNCTION {default.max.num.names.before.forced.et.al} { #10 }
+
+% The number of names that will be shown with a forced "et al.".
+% Must be less than or equal to max.num.names.before.forced.et.al
+FUNCTION {default.num.names.shown.with.forced.et.al} { #1 }
+
+
+% #0 turns off the alternate interword spacing for entries with URLs.
+% #1 enables
+FUNCTION {default.is.use.alt.interword.spacing} { #1 }
+
+% If alternate interword spacing for entries with URLs is enabled, this is
+% the interword spacing stretch factor that will be used. For example, the
+% default "4" here means that the interword spacing in entries with URLs can
+% stretch to four times normal. Does not have to be an integer. Note that
+% the value specified here can be overridden by the user in their LaTeX
+% code via a command such as: 
+% "\providecommand\BIBentryALTinterwordstretchfactor{1.5}" in addition to
+% that via the IEEEtranBSTCTL entry type.
+FUNCTION {default.ALTinterwordstretchfactor} { "4" }
+
+
+% #0 turns off the "dashification" of repeated (i.e., identical to those
+% of the previous entry) names. IEEE normally does this.
+% #1 enables
+FUNCTION {default.is.dash.repeated.names} { #1 }
+
+
+% The default name format control string.
+FUNCTION {default.name.format.string}{ "{f.~}{vv~}{ll}{, jj}" }
+
+
+% The default LaTeX font command for the names.
+FUNCTION {default.name.latex.cmd}{ "" }
+
+
+% Other controls that cannot be accessed via IEEEtranBSTCTL entry type.
+
+% #0 turns off the terminal startup banner/completed message so as to
+% operate more quietly.
+% #1 enables
+FUNCTION {is.print.banners.to.terminal} { #1 }
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FILE VERSION AND BANNER %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION{bst.file.version} { "1.11" }
+FUNCTION{bst.file.date} { "2003/04/02" }
+FUNCTION{bst.file.website} { "http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/" }
+
+FUNCTION {banner.message}
+{ is.print.banners.to.terminal
+     { "-- IEEEtran.bst version" " " * bst.file.version *
+       " (" * bst.file.date * ") " * "by Michael Shell." *
+       top$
+       "-- " bst.file.website *
+       top$
+       "-- See the " quote$ * "IEEEtran_bst_HOWTO.pdf" * quote$ * " manual for usage information." *
+       top$
+     }
+     { skip$ }
+   if$
+}
+
+FUNCTION {completed.message}
+{ is.print.banners.to.terminal
+     { ""
+       top$
+       "Done."
+       top$
+     }
+     { skip$ }
+   if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%
+%% STRING CONSTANTS %%
+%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION {bbl.and}{ "and" }
+FUNCTION {bbl.etal}{ "et~al." }
+FUNCTION {bbl.editors}{ "eds." }
+FUNCTION {bbl.editor}{ "ed." }
+FUNCTION {bbl.edition}{ "ed." }
+FUNCTION {bbl.volume}{ "vol." }
+FUNCTION {bbl.of}{ "of" }
+FUNCTION {bbl.number}{ "no." }
+FUNCTION {bbl.in}{ "in" }
+FUNCTION {bbl.pages}{ "pp." }
+FUNCTION {bbl.page}{ "p." }
+FUNCTION {bbl.chapter}{ "ch." }
+FUNCTION {bbl.paper}{ "paper" }
+FUNCTION {bbl.part}{ "pt." }
+FUNCTION {bbl.patent}{ "Patent" }
+FUNCTION {bbl.patentUS}{ "U.S." }
+FUNCTION {bbl.revision}{ "Rev." }
+FUNCTION {bbl.series}{ "ser." }
+FUNCTION {bbl.standard}{ "Std." }
+FUNCTION {bbl.techrep}{ "Tech. Rep." }
+FUNCTION {bbl.mthesis}{ "Master's thesis" }
+FUNCTION {bbl.phdthesis}{ "Ph.D. dissertation" }
+FUNCTION {bbl.urlprefix}{ "[Online]. Available:" }
+FUNCTION {bbl.st}{ "st" }
+FUNCTION {bbl.nd}{ "nd" }
+FUNCTION {bbl.rd}{ "rd" }
+FUNCTION {bbl.th}{ "th" }
+
+
+% This is the LaTeX spacer that is used when a larger than normal space
+% is called for (such as just before the address:publisher).
+FUNCTION {large.space} { "\hskip 1em plus 0.5em minus 0.4em\relax " }
+
+% The LaTeX code for dashes that are used to represent repeated names.
+% Note: Some older IEEE journals used something like
+% "\rule{0.275in}{0.5pt}\," which is fairly thick and runs right along
+% the baseline. However, IEEE now uses a thinner, above baseline,
+% six dash long sequence.
+FUNCTION {repeated.name.dashes} { "------" }
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% PREDEFINED STRING MACROS %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+MACRO {jan} {"Jan."}
+MACRO {feb} {"Feb."}
+MACRO {mar} {"Mar."}
+MACRO {apr} {"Apr."}
+MACRO {may} {"May"}
+MACRO {jun} {"June"}
+MACRO {jul} {"July"}
+MACRO {aug} {"Aug."}
+MACRO {sep} {"Sept."}
+MACRO {oct} {"Oct."}
+MACRO {nov} {"Nov."}
+MACRO {dec} {"Dec."}
+
+
+
+%%%%%%%%%%%%%%%%%%
+%% ENTRY FIELDS %%
+%%%%%%%%%%%%%%%%%%
+
+ENTRY
+  { address
+    assignee
+    author
+    booktitle
+    chapter
+    day
+    dayfiled
+    edition
+    editor
+    howpublished
+    institution
+    intype
+    journal
+    key
+    language
+    month
+    monthfiled
+    nationality
+    note
+    number
+    organization
+    pages
+    paper
+    publisher
+    school
+    series
+    revision
+    title
+    type
+    url
+    volume
+    year
+    yearfiled
+    CTLuse_article_number
+    CTLuse_paper
+    CTLuse_forced_etal
+    CTLmax_names_forced_etal
+    CTLnames_show_etal
+    CTLuse_alt_spacing
+    CTLalt_stretch_factor
+    CTLdash_repeated_names
+    CTLname_format_string
+    CTLname_latex_cmd
+  }
+  {}
+  { label }
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%
+%% INTEGER VARIABLES %%
+%%%%%%%%%%%%%%%%%%%%%%%
+
+INTEGERS { prev.status.punct this.status.punct punct.std
+           punct.no punct.comma punct.period 
+           prev.status.space this.status.space space.std
+           space.no space.normal space.large
+           prev.status.quote this.status.quote quote.std
+           quote.no quote.close
+           prev.status.nline this.status.nline nline.std
+           nline.no nline.newblock 
+           status.cap cap.std
+           cap.no cap.yes}
+
+INTEGERS { longest.label.width multiresult nameptr namesleft number.label numnames }
+
+INTEGERS { is.use.number.for.article
+           is.use.paper
+           is.forced.et.al
+           max.num.names.before.forced.et.al
+           num.names.shown.with.forced.et.al
+           is.use.alt.interword.spacing
+           is.dash.repeated.names}
+
+
+%%%%%%%%%%%%%%%%%%%%%%
+%% STRING VARIABLES %%
+%%%%%%%%%%%%%%%%%%%%%%
+
+STRINGS { bibinfo
+          longest.label
+          oldname
+          s
+          t
+          ALTinterwordstretchfactor
+          name.format.string
+          name.latex.cmd}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%
+%% LOW LEVEL FUNCTIONS %%
+%%%%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION {initialize.controls}
+{ default.is.use.number.for.article 'is.use.number.for.article :=
+  default.is.use.paper 'is.use.paper :=
+  default.is.forced.et.al 'is.forced.et.al :=
+  default.max.num.names.before.forced.et.al 'max.num.names.before.forced.et.al :=
+  default.num.names.shown.with.forced.et.al 'num.names.shown.with.forced.et.al :=
+  default.is.use.alt.interword.spacing 'is.use.alt.interword.spacing :=
+  default.is.dash.repeated.names 'is.dash.repeated.names :=
+  default.ALTinterwordstretchfactor 'ALTinterwordstretchfactor :=
+  default.name.format.string 'name.format.string :=
+  default.name.latex.cmd 'name.latex.cmd :=
+}
+
+
+% This IEEEtran.bst features a very powerful and flexible mechanism for
+% controlling the capitalization, punctuation, spacing, quotation, and
+% newlines of the formatted entry fields. (Note: IEEEtran.bst does not need
+% or use the newline/newblock feature, but it has been implemented for
+% possible future use.) The output states of IEEEtran.bst consist of
+% multiple independent attributes and, as such, can be thought of as being
+% vectors, rather than the simple scalar values ("before.all", 
+% "mid.sentence", etc.) used in most other .bst files.
+% 
+% The more flexible and complex design used here was motivated in part by
+% IEEE's rather unusual bibliography style. For example, IEEE ends the
+% previous field item with a period and large space prior to the publisher
+% address; the @electronic entry types use periods as inter-item punctuation
+% rather than the commas used by the other entry types; and URLs are never
+% followed by periods even though they are the last item in the entry.
+% Although it is possible to accommodate these features with the conventional
+% output state system, the seemingly endless exceptions make for convoluted,
+% unreliable and difficult to maintain code.
+%
+% IEEEtran.bst's output state system can be easily understood via a simple
+% illustration of two most recently formatted entry fields (on the stack):
+%
+%               CURRENT_ITEM
+%               "PREVIOUS_ITEM
+%
+% which, in this example, is to eventually appear in the bibliography as:
+% 
+%               "PREVIOUS_ITEM," CURRENT_ITEM
+%
+% It is the job of the output routine to take the previous item off of the
+% stack (while leaving the current item at the top of the stack), apply its
+% trailing punctuation (including closing quote marks) and spacing, and then
+% to write the result to BibTeX's output buffer:
+% 
+%               "PREVIOUS_ITEM," 
+% 
+% Punctuation (and spacing) between items is often determined by both of the
+% items rather than just the first one. The presence of quotation marks
+% further complicates the situation because, in standard English, trailing
+% punctuation marks are supposed to be contained within the quotes.
+% 
+% IEEEtran.bst maintains two output state (aka "status") vectors which
+% correspond to the previous and current (aka "this") items. Each vector
+% consists of several independent attributes which track punctuation,
+% spacing, quotation, and newlines. Capitalization status is handled by a
+% separate scalar because the format routines, not the output routine,
+% handle capitalization and, therefore, there is no need to maintain the
+% capitalization attribute for both the "previous" and "this" items.
+% 
+% When a format routine adds a new item, it copies the current output status
+% vector to the previous output status vector and (usually) resets the
+% current (this) output status vector to a "standard status" vector. Using a
+% "standard status" vector in this way allows us to redefine what we mean by
+% "standard status" at the start of each entry handler and reuse the same
+% format routines under the various inter-item separation schemes. For
+% example, the standard status vector for the @book entry type may use
+% commas for item separators, while the @electronic type may use periods,
+% yet both entry handlers exploit many of the exact same format routines.
+% 
+% Because format routines have write access to the output status vector of
+% the previous item, they can override the punctuation choices of the
+% previous format routine! Therefore, it becomes trivial to implement rules
+% such as "Always use a period and a large space before the publisher." By
+% pushing the generation of the closing quote mark to the output routine, we
+% avoid all the problems caused by having to close a quote before having all
+% the information required to determine what the punctuation should be.
+%
+% The IEEEtran.bst output state system can easily be expanded if needed.
+% For instance, it is easy to add a "space.tie" attribute value if the
+% bibliography rules mandate that two items have to be joined with an
+% unbreakable space. 
+
+FUNCTION {initialize.status.constants}
+{ #0 'punct.no :=
+  #1 'punct.comma :=
+  #2 'punct.period :=
+  #0 'space.no := 
+  #1 'space.normal :=
+  #2 'space.large :=
+  #0 'quote.no :=
+  #1 'quote.close :=
+  #0 'cap.no :=
+  #1 'cap.yes :=
+  #0 'nline.no :=
+  #1 'nline.newblock :=
+}
+
+FUNCTION {std.status.using.comma}
+{ punct.comma 'punct.std :=
+  space.normal 'space.std :=
+  quote.no 'quote.std :=
+  nline.no 'nline.std :=
+  cap.no 'cap.std :=
+}
+
+FUNCTION {std.status.using.period}
+{ punct.period 'punct.std :=
+  space.normal 'space.std :=
+  quote.no 'quote.std :=
+  nline.no 'nline.std :=
+  cap.yes 'cap.std :=
+}
+
+FUNCTION {initialize.prev.this.status}
+{ punct.no 'prev.status.punct :=
+  space.no 'prev.status.space :=
+  quote.no 'prev.status.quote :=
+  nline.no 'prev.status.nline :=
+  punct.no 'this.status.punct :=
+  space.no 'this.status.space :=
+  quote.no 'this.status.quote :=
+  nline.no 'this.status.nline :=
+  cap.yes 'status.cap :=
+}
+
+FUNCTION {this.status.std}
+{ punct.std 'this.status.punct :=
+  space.std 'this.status.space :=
+  quote.std 'this.status.quote :=
+  nline.std 'this.status.nline :=
+}
+
+FUNCTION {cap.status.std}{ cap.std 'status.cap := }
+
+FUNCTION {this.to.prev.status}
+{ this.status.punct 'prev.status.punct :=
+  this.status.space 'prev.status.space :=
+  this.status.quote 'prev.status.quote :=
+  this.status.nline 'prev.status.nline :=
+}
+
+
+FUNCTION {not}
+{   { #0 }
+    { #1 }
+  if$
+}
+
+FUNCTION {and}
+{   { skip$ }
+    { pop$ #0 }
+  if$
+}
+
+FUNCTION {or}
+{   { pop$ #1 }
+    { skip$ }
+  if$
+}
+
+
+% convert the strings "yes" or "no" to #1 or #0 respectively
+FUNCTION {yes.no.to.int}
+{ "l" change.case$ duplicate$
+    "yes" =
+    { pop$  #1 }
+    { duplicate$ "no" =
+        { pop$ #0 }
+        { "unknown boolean " quote$ * swap$ * quote$ *
+          " in " * cite$ * warning$
+          #0
+        }
+      if$
+    }
+  if$
+}
+
+
+% pushes true if the single char string on the stack is in the
+% range of "0" to "9"
+FUNCTION {is.num}
+{ chr.to.int$
+  duplicate$ "0" chr.to.int$ < not
+  swap$ "9" chr.to.int$ > not and
+}
+
+% multiplies the integer on the stack by a factor of 10
+FUNCTION {bump.int.mag}
+{ #0 'multiresult :=
+    { duplicate$ #0 > }
+    { #1 -
+      multiresult #10 +
+      'multiresult :=
+    }
+  while$
+pop$
+multiresult
+}
+
+% converts a single character string on the stack to an integer
+FUNCTION {char.to.integer}
+{ duplicate$ 
+  is.num
+    { chr.to.int$ "0" chr.to.int$ - }
+    {"noninteger character " quote$ * swap$ * quote$ *
+          " in integer field of " * cite$ * warning$
+    #0
+    }
+  if$
+}
+
+% converts a string on the stack to an integer
+FUNCTION {string.to.integer}
+{ duplicate$ text.length$ 'namesleft :=
+  #1 'nameptr :=
+  #0 'numnames :=
+    { nameptr namesleft > not }
+    { duplicate$ nameptr #1 substring$
+      char.to.integer numnames bump.int.mag +
+      'numnames :=
+      nameptr #1 +
+      'nameptr :=
+    }
+  while$
+pop$
+numnames
+}
+
+
+
+
+% The output routines write out the *next* to the top (previous) item on the
+% stack, adding punctuation and such as needed. Since IEEEtran.bst maintains
+% the output status for the top two items on the stack, these output
+% routines have to consider the previous output status (which corresponds to
+% the item that is being output). Full independent control of punctuation,
+% closing quote marks, spacing, and newblock is provided.
+% 
+% "output.nonnull" does not check for the presence of a previous empty
+% item.
+% 
+% "output" does check for the presence of a previous empty item and will
+% remove an empty item rather than outputing it.
+% 
+% "output.warn" is like "output", but will issue a warning if it detects
+% an empty item.
+
+FUNCTION {output.nonnull}
+{ swap$
+  prev.status.punct punct.comma =
+     { "," * }
+     { skip$ }
+   if$
+  prev.status.punct punct.period =
+     { add.period$ }
+     { skip$ }
+   if$ 
+  prev.status.quote quote.close =
+     { "''" * }
+     { skip$ }
+   if$
+  prev.status.space space.normal =
+     { " " * }
+     { skip$ }
+   if$
+  prev.status.space space.large =
+     { large.space * }
+     { skip$ }
+   if$
+  write$
+  prev.status.nline nline.newblock =
+     { newline$ "\newblock " write$ }
+     { skip$ }
+   if$
+}
+
+FUNCTION {output}
+{ duplicate$ empty$
+    'pop$
+    'output.nonnull
+  if$
+}
+
+FUNCTION {output.warn}
+{ 't :=
+  duplicate$ empty$
+    { pop$ "empty " t * " in " * cite$ * warning$ }
+    'output.nonnull
+  if$
+}
+
+% "fin.entry" is the output routine that handles the last item of the entry
+% (which will be on the top of the stack when "fin.entry" is called).
+
+FUNCTION {fin.entry}
+{ this.status.punct punct.no =
+     { skip$ }
+     { add.period$ }
+   if$
+   this.status.quote quote.close =
+     { "''" * }
+     { skip$ }
+   if$
+write$
+newline$
+}
+
+
+FUNCTION {is.last.char.not.punct}
+{ duplicate$
+   "}" * add.period$
+   #-1 #1 substring$ "." =
+}
+
+FUNCTION {is.multiple.pages}
+{ 't :=
+  #0 'multiresult :=
+    { multiresult not
+      t empty$ not
+      and
+    }
+    { t #1 #1 substring$
+      duplicate$ "-" =
+      swap$ duplicate$ "," =
+      swap$ "+" =
+      or or
+        { #1 'multiresult := }
+        { t #2 global.max$ substring$ 't := }
+      if$
+    }
+  while$
+  multiresult
+}
+
+FUNCTION {capitalize}{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {emphasize}
+{ duplicate$ empty$
+    { pop$ "" }
+    { "\emph{" swap$ * "}" * }
+  if$
+}
+
+FUNCTION {do.name.latex.cmd}
+{ name.latex.cmd
+  empty$
+    { skip$ }
+    { name.latex.cmd "{" * swap$ * "}" * }
+  if$
+}
+
+% IEEEtran.bst uses its own \BIBforeignlanguage command which directly
+% invokes the TeX hyphenation patterns without the need of the Babel
+% package. Babel does a lot more than switch hyphenation patterns and
+% its loading can cause unintended effects in many class files (such as
+% IEEEtran.cls).
+FUNCTION {select.language}
+{ duplicate$ empty$ 'pop$
+    { language empty$ 'skip$
+        { "\BIBforeignlanguage{" language * "}{" * swap$ * "}" * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {tie.or.space.prefix}
+{ duplicate$ text.length$ #3 <
+    { "~" }
+    { " " }
+  if$
+  swap$
+}
+
+FUNCTION {get.bbl.editor}
+{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ }
+
+FUNCTION {space.word}{ " " swap$ * " " * }
+
+
+% Field Conditioners, Converters, Checkers and External Interfaces
+
+FUNCTION {empty.field.to.null.string}
+{ duplicate$ empty$
+    { pop$ "" }
+    { skip$ }
+  if$
+}
+
+FUNCTION {either.or.check}
+{ empty$
+    { pop$ }
+    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+  if$
+}
+
+FUNCTION {empty.entry.warn}
+{ author empty$ title empty$ howpublished empty$
+  month empty$ year empty$ note empty$ url empty$
+  and and and and and and
+    { "all relevant fields are empty in " cite$ * warning$ }
+    'skip$
+  if$
+}
+
+
+% The bibinfo system provides a way for the electronic parsing/acquisition
+% of a bibliography's contents as is done by ReVTeX. For example, a field
+% could be entered into the bibliography as:
+% \bibinfo{volume}{2}
+% Only the "2" would show up in the document, but the LaTeX \bibinfo command
+% could do additional things with the information. IEEEtran.bst does provide
+% a \bibinfo command via "\providecommand{\bibinfo}[2]{#2}". However, it is
+% currently not used as the bogus bibinfo functions defined here output the
+% entry values directly without the \bibinfo wrapper. The bibinfo functions
+% themselves (and the calls to them) are retained for possible future use.
+% 
+% bibinfo.check avoids acting on missing fields while bibinfo.warn will
+% issue a warning message if a missing field is detected. Prior to calling
+% the bibinfo functions, the user should push the field value and then its
+% name string, in that order.
+
+FUNCTION {bibinfo.check}
+{ swap$ duplicate$ missing$
+    { pop$ pop$ "" }
+    { duplicate$ empty$
+        { swap$ pop$ }
+        { swap$ pop$ }
+      if$
+    }
+  if$
+}
+
+FUNCTION {bibinfo.warn}
+{ swap$ duplicate$ missing$
+    { swap$ "missing " swap$ * " in " * cite$ * warning$ pop$ "" }
+    { duplicate$ empty$
+        { swap$ "empty " swap$ * " in " * cite$ * warning$ }
+        { swap$ pop$ }
+      if$
+    }
+  if$
+}
+
+
+% IEEE separates large numbers with more than 4 digits into groups of
+% three. IEEE uses a small space to separate these number groups. 
+% Typical applications include patent and page numbers.
+
+% number of consecutive digits required to trigger the group separation.
+FUNCTION {large.number.trigger}{ #5 }
+
+% For numbers longer than the trigger, this is the blocksize of the groups.
+% The blocksize must be less than the trigger threshold, and 2 * blocksize
+% must be greater than the trigger threshold (can't do more than one
+% separation on the initial trigger).
+FUNCTION {large.number.blocksize}{ #3 }
+
+% What is actually inserted between the number groups.
+FUNCTION {large.number.separator}{ "\," }
+
+% So as to save on integer variables by reusing existing ones, numnames
+% holds the current number of consecutive digits read and nameptr holds
+% the number that will trigger an inserted space.
+FUNCTION {large.number.separate}
+{ 't :=
+  ""
+  #0 'numnames :=
+  large.number.trigger 'nameptr :=
+  { t empty$ not }
+  { t #-1 #1 substring$ is.num
+      { numnames #1 + 'numnames := }
+      { #0 'numnames := 
+        large.number.trigger 'nameptr :=
+      }
+    if$
+    t #-1 #1 substring$ swap$ *
+    t #-2 global.max$ substring$ 't :=
+    numnames nameptr =
+      { duplicate$ #1 nameptr large.number.blocksize - substring$ swap$
+        nameptr large.number.blocksize - #1 + global.max$ substring$
+        large.number.separator swap$ * *
+        nameptr large.number.blocksize - 'numnames :=
+        large.number.blocksize #1 + 'nameptr :=
+      }
+      { skip$ }
+    if$
+  }
+  while$
+}
+
+% Converts all single dashes "-" to double dashes "--".
+FUNCTION {n.dashify}
+{ large.number.separate
+  't :=
+  ""
+    { t empty$ not }
+    { t #1 #1 substring$ "-" =
+        { t #1 #2 substring$ "--" = not
+            { "--" *
+              t #2 global.max$ substring$ 't :=
+            }
+            {   { t #1 #1 substring$ "-" = }
+                { "-" *
+                  t #2 global.max$ substring$ 't :=
+                }
+              while$
+            }
+          if$
+        }
+        { t #1 #1 substring$ *
+          t #2 global.max$ substring$ 't :=
+        }
+      if$
+    }
+  while$
+}
+
+
+% This function detects entries with names that are identical to that of
+% the previous entry and replaces the repeated names with dashes (if the
+% "is.dash.repeated.names" user control is nonzero).
+FUNCTION {name.or.dash}
+{ 's :=
+   oldname empty$
+     { s 'oldname := s }
+     { s oldname =
+         { is.dash.repeated.names
+              { repeated.name.dashes }
+              { s 'oldname := s }
+            if$
+         }
+         { s 'oldname := s }
+       if$
+     }
+   if$
+}
+
+% Converts the number string on the top of the stack to
+% "numerical ordinal form" (e.g., "7" to "7th"). There is
+% no artificial limit to the upper bound of the numbers as the
+% least significant digit always determines the ordinal form.
+FUNCTION {num.to.ordinal}
+{ duplicate$ #-1 #1 substring$ "1" =
+     { bbl.st * }
+     { duplicate$ #-1 #1 substring$ "2" =
+         { bbl.nd * }
+         { duplicate$ #-1 #1 substring$ "3" =
+             { bbl.rd * }
+             { bbl.th * }
+           if$
+         }
+       if$
+     }
+   if$
+}
+
+% If the string on the top of the stack begins with a number,
+% (e.g., 11th) then replace the string with the leading number
+% it contains. Otherwise retain the string as-is. s holds the
+% extracted number, t holds the part of the string that remains
+% to be scanned.
+FUNCTION {extract.num}
+{ duplicate$ 't :=
+  "" 's :=
+  { t empty$ not }
+  { t #1 #1 substring$
+    t #2 global.max$ substring$ 't :=
+    duplicate$ is.num
+      { s swap$ * 's := }
+      { pop$ "" 't := }
+    if$
+  }
+  while$
+  s empty$
+    'skip$
+    { pop$ s }
+  if$
+}
+
+% Converts the word number string on the top of the stack to
+% Arabic string form. Will be successful up to "tenth".
+FUNCTION {word.to.num}
+{ duplicate$ "l" change.case$ 's :=
+  s "first" =
+    { pop$ "1" }
+    { skip$ }
+  if$
+  s "second" =
+    { pop$ "2" }
+    { skip$ }
+  if$
+  s "third" =
+    { pop$ "3" }
+    { skip$ }
+  if$
+  s "fourth" =
+    { pop$ "4" }
+    { skip$ }
+  if$
+  s "fifth" =
+    { pop$ "5" }
+    { skip$ }
+  if$
+  s "sixth" =
+    { pop$ "6" }
+    { skip$ }
+  if$
+  s "seventh" =
+    { pop$ "7" }
+    { skip$ }
+  if$
+  s "eighth" =
+    { pop$ "8" }
+    { skip$ }
+  if$
+  s "ninth" =
+    { pop$ "9" }
+    { skip$ }
+  if$
+  s "tenth" =
+    { pop$ "10" }
+    { skip$ }
+  if$
+}
+
+
+% Converts the string on the top of the stack to numerical
+% ordinal (e.g., "11th") form.
+FUNCTION {convert.edition}
+{ duplicate$ empty$ 'skip$
+    { duplicate$ #1 #1 substring$ is.num
+        { extract.num
+          num.to.ordinal
+        }
+        { word.to.num
+          duplicate$ #1 #1 substring$ is.num
+            { num.to.ordinal }
+            { "edition ordinal word " quote$ * edition * quote$ *
+              " may be too high (or improper) for conversion" * " in " * cite$ * warning$
+            }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% LATEX BIBLIOGRAPHY CODE %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION {start.entry}
+{ newline$
+  "\bibitem{" write$
+  cite$ write$
+  "}" write$
+  newline$
+  ""
+  initialize.prev.this.status
+}
+
+% Here we write out all the LaTeX code that we will need. The most involved
+% code sequences are those that control the alternate interword spacing and
+% foreign language hyphenation patterns. The heavy use of \providecommand
+% gives users a way to override the defaults. Special thanks to Javier Bezos,
+% Johannes Braams, Robin Fairburns, Heiko Oberdiek, Donald Arseneau and all
+% the other gurus on comp.text.tex for their help and advice on the topic of
+% \selectlanguage, Babel and BibTeX.
+FUNCTION {begin.bib}
+{ preamble$ empty$ 'skip$
+    { preamble$ write$ newline$ }
+  if$
+  "\begin{thebibliography}{"  longest.label  * "}" *
+  write$ newline$
+  "\providecommand{\url}[1]{#1}"
+  write$ newline$
+  "\csname url@rmstyle\endcsname"
+  write$ newline$
+  "\providecommand{\newblock}{\relax}"
+  write$ newline$
+  "\providecommand{\bibinfo}[2]{#2}"
+  write$ newline$
+  "\providecommand\BIBentrySTDinterwordspacing{\spaceskip=0pt\relax}"
+  write$ newline$
+  "\providecommand\BIBentryALTinterwordstretchfactor{"
+  ALTinterwordstretchfactor * "}" *
+  write$ newline$
+  "\providecommand\BIBentryALTinterwordspacing{\spaceskip=\fontdimen2\font plus "
+  write$ newline$
+  "\BIBentryALTinterwordstretchfactor\fontdimen3\font minus \fontdimen4\font\relax}"
+  write$ newline$
+  "\providecommand\BIBforeignlanguage[2]{{%"
+  write$ newline$
+  "\expandafter\ifx\csname l@#1\endcsname\relax"
+  write$ newline$
+  "\typeout{** WARNING: IEEEtran.bst: No hyphenation pattern has been}%"
+  write$ newline$
+  "\typeout{** loaded for the language `#1'. Using the pattern for}%"
+  write$ newline$
+  "\typeout{** the default language instead.}%"
+  write$ newline$
+  "\else"
+  write$ newline$
+  "\language=\csname l@#1\endcsname"
+  write$ newline$
+  "\fi"
+  write$ newline$
+  "#2}}"
+  write$ newline$
+}
+
+FUNCTION {end.bib}
+{ newline$ "\end{thebibliography}" write$ newline$ }
+
+FUNCTION {if.url.alt.interword.spacing}
+{ is.use.alt.interword.spacing 
+     {url empty$ 'skip$ {"\BIBentryALTinterwordspacing" write$ newline$} if$}
+     { skip$ }
+   if$
+}
+
+FUNCTION {if.url.std.interword.spacing}
+{ is.use.alt.interword.spacing 
+     {url empty$ 'skip$ {"\BIBentrySTDinterwordspacing" write$ newline$} if$}
+     { skip$ }
+   if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% LONGEST LABEL PASS %%
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION {initialize.longest.label}
+{ "" 'longest.label :=
+  #1 'number.label :=
+  #0 'longest.label.width :=
+}
+
+FUNCTION {longest.label.pass}
+{ number.label int.to.str$ 'label :=
+  number.label #1 + 'number.label :=
+  label width$ longest.label.width >
+    { label 'longest.label :=
+      label width$ 'longest.label.width :=
+    }
+    'skip$
+  if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%
+%% FORMAT HANDLERS %%
+%%%%%%%%%%%%%%%%%%%%%
+
+%% Lower Level Formats (used by higher level formats)
+
+FUNCTION {format.address.org.or.pub.date}
+{ 't :=
+  ""
+  year empty$
+    { "empty year in " cite$ * warning$ }
+    { skip$ }
+  if$
+  address empty$ t empty$ and
+  year empty$ and month empty$ and
+    { skip$ }
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      address "address" bibinfo.check *
+      t empty$
+        { skip$ }
+        { punct.period 'prev.status.punct :=
+          space.large 'prev.status.space :=
+          address empty$
+            { skip$ }
+            { ": " * }
+          if$
+          t *
+        }
+      if$
+      year empty$ month empty$ and
+        { skip$ }
+        { t empty$ address empty$ and
+            { skip$ }
+            { ", " * }
+          if$
+          month empty$
+            { year empty$
+                { skip$ }
+                { year "year" bibinfo.check * }
+              if$
+            }
+            { month "month" bibinfo.check *
+              year empty$
+                 { skip$ }
+                 { " " * year "year" bibinfo.check * }
+              if$
+            }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+
+FUNCTION {format.names}
+{ 'bibinfo :=
+  duplicate$ empty$ 'skip$ {
+  this.to.prev.status
+  this.status.std
+  's :=
+  "" 't :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      name.format.string
+      format.name$
+      bibinfo bibinfo.check
+      't :=
+      nameptr #1 >
+        { nameptr num.names.shown.with.forced.et.al #1 + =
+          numnames max.num.names.before.forced.et.al >
+          is.forced.et.al and and
+            { "others" 't :=
+              #1 'namesleft :=
+            }
+            { skip$ }
+          if$
+          namesleft #1 >
+            { ", " * t do.name.latex.cmd * }
+            {
+              numnames #2 >
+                { "," * }
+                'skip$
+              if$
+              s nameptr "{ll}" format.name$ duplicate$ "others" =
+                { 't := }
+                { pop$ }
+              if$
+              t "others" =
+                {
+                  " " * bbl.etal emphasize *
+                }
+                {
+                  bbl.and
+                  space.word * t do.name.latex.cmd *
+                }
+              if$
+            }
+          if$
+        }
+        { t do.name.latex.cmd }
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+  cap.status.std
+  } if$
+}
+
+
+
+
+%% Higher Level Formats
+
+%% addresses/locations
+
+FUNCTION {format.address}
+{ address duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+
+
+%% author/editor names
+
+FUNCTION {format.authors}{ author "author" format.names }
+
+FUNCTION {format.editors}
+{ editor "editor" format.names duplicate$ empty$ 'skip$
+    { ", " *
+      get.bbl.editor
+      capitalize
+      *
+    }
+  if$
+}
+
+
+
+%% date
+
+FUNCTION {format.date}
+{
+  month "month" bibinfo.check duplicate$ empty$
+  year  "year" bibinfo.check duplicate$ empty$
+    { swap$ 'skip$
+        { this.to.prev.status
+          this.status.std
+          cap.status.std
+         "there's a month but no year in " cite$ * warning$ }
+      if$
+      *
+    }
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      swap$ 'skip$
+        {
+          swap$
+          " " * swap$
+        }
+      if$
+      *
+    }
+  if$
+}
+
+FUNCTION {format.date.electronic}
+{ month "month" bibinfo.check duplicate$ empty$
+  year  "year" bibinfo.check duplicate$ empty$
+    { swap$ 
+        { pop$ }
+        { "there's a month but no year in " cite$ * warning$
+        pop$ ")" * "(" swap$ *
+        this.to.prev.status
+        punct.no 'this.status.punct :=
+        space.normal 'this.status.space :=
+        quote.no 'this.status.quote :=
+        cap.yes  'status.cap :=
+        }
+      if$
+    }
+    { swap$ 
+        { swap$ pop$ ")" * "(" swap$ * }
+        { "(" swap$ * ", " * swap$ * ")" * }
+      if$
+    this.to.prev.status
+    punct.no 'this.status.punct :=
+    space.normal 'this.status.space :=
+    quote.no 'this.status.quote :=
+    cap.yes  'status.cap :=
+    }
+  if$
+}
+
+
+
+%% edition/title
+
+% Note: IEEE considers the edition to be closely associated with
+% the title of a book. So, in IEEEtran.bst the edition is normally handled 
+% within the formatting of the title. The format.edition function is 
+% retained here for possible future use.
+FUNCTION {format.edition}
+{ edition duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      convert.edition
+      status.cap
+        { "t" }
+        { "l" }
+      if$ change.case$
+      "edition" bibinfo.check
+      "~" * bbl.edition *
+      cap.status.std
+    }
+  if$
+}
+
+% This is used to format the booktitle of a conference proceedings.
+% Here we use the "intype" field to provide the user a way to 
+% override the word "in" (e.g., with things like "presented at")
+% Use of intype stops the emphasis of the booktitle to indicate that
+% we no longer mean the written conference proceedings, but the
+% conference itself.
+FUNCTION {format.in.booktitle}
+{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      select.language
+      intype missing$
+        { emphasize
+          bbl.in " " *
+        }
+        { intype " " * }
+      if$
+      swap$ *
+      cap.status.std
+    }
+  if$
+}
+
+% This is used to format the booktitle of collection.
+% Here the "intype" field is not supported, but "edition" is.
+FUNCTION {format.in.booktitle.edition}
+{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      select.language
+      emphasize
+      edition empty$ 'skip$
+        { ", " *
+          edition
+          convert.edition
+          "l" change.case$
+          * "~" * bbl.edition *
+        }
+      if$
+      bbl.in " " * swap$ *
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.article.title}
+{ title duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      "t" change.case$
+    }
+  if$
+  "title" bibinfo.check
+  duplicate$ empty$ 'skip$
+    { quote.close 'this.status.quote :=
+      is.last.char.not.punct
+        { punct.std 'this.status.punct := }
+        { punct.no 'this.status.punct := }
+      if$
+      select.language
+      "``" swap$ *
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.article.title.electronic}
+{ title duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      "t" change.case$ 
+    }
+  if$
+  "title" bibinfo.check
+  duplicate$ empty$ 
+    { skip$ } 
+    { select.language }
+  if$
+}
+
+FUNCTION {format.book.title.edition}
+{ title "title" bibinfo.check
+  duplicate$ empty$
+    { "empty title in " cite$ * warning$ }
+    { this.to.prev.status
+      this.status.std
+      select.language
+      emphasize
+      edition empty$ 'skip$
+        { ", " *
+          edition
+          convert.edition
+          status.cap
+            { "t" }
+            { "l" }
+          if$
+          change.case$
+          * "~" * bbl.edition *
+        }
+      if$
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.book.title}
+{ title "title" bibinfo.check
+  duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      select.language
+      emphasize
+    }
+  if$
+}
+
+
+
+%% journal
+
+FUNCTION {format.journal}
+{ journal duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      select.language
+      emphasize
+    }
+  if$
+}
+
+
+
+%% how published
+
+FUNCTION {format.howpublished}
+{ howpublished duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+
+
+%% institutions/organization/publishers/school
+
+FUNCTION {format.institution}
+{ institution duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.organization}
+{ organization duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.address.publisher.date}
+{ publisher "publisher" bibinfo.warn format.address.org.or.pub.date }
+
+FUNCTION {format.address.publisher.date.nowarn}
+{ publisher "publisher" bibinfo.check format.address.org.or.pub.date }
+
+FUNCTION {format.address.organization.date}
+{ organization "organization" bibinfo.check format.address.org.or.pub.date }
+
+FUNCTION {format.school}
+{ school duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+
+
+%% volume/number/series/chapter/pages
+
+FUNCTION {format.volume}
+{ volume empty.field.to.null.string
+  duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      bbl.volume 
+      status.cap
+        { capitalize }
+        { skip$ }
+      if$
+      swap$ tie.or.space.prefix
+      "volume" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.number}
+{ number empty.field.to.null.string
+  duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      status.cap
+         { bbl.number capitalize }
+         { bbl.number }
+       if$
+      swap$ tie.or.space.prefix
+      "number" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.number.if.use.for.article}
+{ is.use.number.for.article 
+     { format.number }
+     { "" }
+   if$
+}
+
+% IEEE does not seem to tie the series so closely with the volume
+% and number as is done in other bibliography styles. Instead the
+% series is treated somewhat like an extension of the title.
+FUNCTION {format.series}
+{ series empty$ 
+   { "" }
+   { this.to.prev.status
+     this.status.std
+     bbl.series " " *
+     series "series" bibinfo.check *
+     cap.status.std
+   }
+ if$
+}
+
+
+FUNCTION {format.chapter}
+{ chapter empty$
+    { "" }
+    { this.to.prev.status
+      this.status.std
+      type empty$
+        { bbl.chapter }
+        { type "l" change.case$
+          "type" bibinfo.check
+        }
+      if$
+      chapter tie.or.space.prefix
+      "chapter" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+
+% The intended use of format.paper is for paper numbers of inproceedings.
+% The paper type can be overridden via the type field.
+% We allow the type to be displayed even if the paper number is absent
+% for things like "postdeadline paper"
+FUNCTION {format.paper}
+{ is.use.paper
+     { paper empty$
+        { type empty$
+            { "" }
+            { this.to.prev.status
+              this.status.std
+              type "type" bibinfo.check
+              cap.status.std
+            }
+          if$
+        }
+        { this.to.prev.status
+          this.status.std
+          type empty$
+            { bbl.paper }
+            { type "type" bibinfo.check }
+          if$
+          " " * paper
+          "paper" bibinfo.check
+          *
+          cap.status.std
+        }
+      if$
+     }
+     { "" } 
+   if$
+}
+
+
+FUNCTION {format.pages}
+{ pages duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      duplicate$ is.multiple.pages
+        {
+          bbl.pages swap$
+          n.dashify
+        }
+        {
+          bbl.page swap$
+        }
+      if$
+      tie.or.space.prefix
+      "pages" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+
+
+%% technical report number
+
+FUNCTION {format.tech.report.number}
+{ number "number" bibinfo.check
+  type duplicate$ empty$
+    { pop$ 
+      this.to.prev.status
+      this.status.std
+      cap.status.std
+      bbl.techrep
+    }
+    { skip$ }
+  if$
+  "type" bibinfo.check 
+  swap$ duplicate$ empty$
+    { pop$ }
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      tie.or.space.prefix * * }
+  if$
+}
+
+
+
+%% note
+
+FUNCTION {format.note}
+{ note empty$
+    { "" }
+    { this.to.prev.status
+      this.status.std
+      punct.period 'this.status.punct :=
+      note #1 #1 substring$
+      duplicate$ "{" =
+        { skip$ }
+        { status.cap
+          { "u" }
+          { "l" }
+        if$
+        change.case$
+        }
+      if$
+      note #2 global.max$ substring$ * "note" bibinfo.check
+      cap.yes  'status.cap :=
+    }
+  if$
+}
+
+
+
+%% patent
+
+FUNCTION {format.patent.date}
+{ this.to.prev.status
+  this.status.std
+  year empty$
+    { monthfiled duplicate$ empty$
+        { "monthfiled" bibinfo.check pop$ "" }
+        { "monthfiled" bibinfo.check }
+      if$
+      dayfiled duplicate$ empty$
+        { "dayfiled" bibinfo.check pop$ "" * }
+        { "dayfiled" bibinfo.check 
+          monthfiled empty$ 
+             { "dayfiled without a monthfiled in " cite$ * warning$
+               * 
+             }
+             { " " swap$ * * }
+           if$
+        }
+      if$
+      yearfiled empty$
+        { "no year or yearfiled in " cite$ * warning$ }
+        { yearfiled "yearfiled" bibinfo.check 
+          swap$
+          duplicate$ empty$
+             { pop$ }
+             { ", " * swap$ * }
+           if$
+        }
+      if$
+    }
+    { month duplicate$ empty$
+        { "month" bibinfo.check pop$ "" }
+        { "month" bibinfo.check }
+      if$
+      day duplicate$ empty$
+        { "day" bibinfo.check pop$ "" * }
+        { "day" bibinfo.check 
+          month empty$ 
+             { "day without a month in " cite$ * warning$
+               * 
+             }
+             { " " swap$ * * }
+           if$
+        }
+      if$
+      year "year" bibinfo.check 
+      swap$
+      duplicate$ empty$
+        { pop$ }
+        { ", " * swap$ * }
+      if$
+    }
+  if$
+  cap.status.std
+}
+
+FUNCTION {format.patent.nationality.type.number}
+{ this.to.prev.status
+  this.status.std
+  nationality duplicate$ empty$
+    { "nationality" bibinfo.warn pop$ "" }
+    { "nationality" bibinfo.check
+      duplicate$ "l" change.case$ "united states" =
+        { pop$ bbl.patentUS }
+        { skip$ }
+      if$
+      " " *
+    }
+  if$
+  type empty$
+    { bbl.patent "type" bibinfo.check }
+    { type "type" bibinfo.check }
+  if$  
+  *
+  number duplicate$ empty$
+    { "number" bibinfo.warn pop$ }
+    { "number" bibinfo.check
+      large.number.separate
+      swap$ " " * swap$ *
+    }
+  if$ 
+  cap.status.std
+}
+
+
+
+%% standard
+
+FUNCTION {format.organization.institution.standard.type.number}
+{ this.to.prev.status
+  this.status.std
+  organization duplicate$ empty$
+    { pop$ 
+      institution duplicate$ empty$
+        { "institution" bibinfo.warn }
+        { "institution" bibinfo.warn " " * }
+      if$
+    }
+    { "organization" bibinfo.warn " " * }
+  if$
+  type empty$
+    { bbl.standard "type" bibinfo.check }
+    { type "type" bibinfo.check }
+  if$  
+  *
+  number duplicate$ empty$
+    { "number" bibinfo.check pop$ }
+    { "number" bibinfo.check
+      large.number.separate
+      swap$ " " * swap$ *
+    }
+  if$ 
+  cap.status.std
+}
+
+FUNCTION {format.revision}
+{ revision empty$
+    { "" }
+    { this.to.prev.status
+      this.status.std
+      bbl.revision
+      revision tie.or.space.prefix
+      "revision" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+
+%% thesis
+
+FUNCTION {format.master.thesis.type}
+{ this.to.prev.status
+  this.status.std
+  type empty$
+    {
+      bbl.mthesis
+    }
+    { 
+      type "type" bibinfo.check
+    }
+  if$
+cap.status.std
+}
+
+FUNCTION {format.phd.thesis.type}
+{ this.to.prev.status
+  this.status.std
+  type empty$
+    {
+      bbl.phdthesis
+    }
+    { 
+      type "type" bibinfo.check
+    }
+  if$
+cap.status.std
+}
+
+
+
+%% URL
+
+FUNCTION {format.url}
+{ url empty$
+    { "" }
+    { this.to.prev.status
+      this.status.std
+      cap.yes 'status.cap :=
+      bbl.urlprefix " " * 
+      "\url{" * url * "}" *
+      punct.no 'this.status.punct :=
+      punct.period 'prev.status.punct :=
+      space.normal 'this.status.space :=
+      space.normal 'prev.status.space :=
+      quote.no 'this.status.quote :=
+    }
+  if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% ENTRY HANDLERS %%
+%%%%%%%%%%%%%%%%%%%%
+
+
+% Note: In many journals, IEEE (or the authors) tend not to show the number
+% for articles, so the display of the number is controlled here by the
+% switch "is.use.number.for.article"
+FUNCTION {article}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.journal "journal" bibinfo.check "journal" output.warn
+  format.volume output
+  format.number.if.use.for.article output
+  format.pages output
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {book}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  author empty$
+    { format.editors "author and editor" output.warn }
+    { format.authors output.nonnull }
+  if$
+  name.or.dash
+  format.book.title.edition output
+  format.series output
+  author empty$
+    { skip$ }
+    { format.editors output }
+  if$
+  format.address.publisher.date output
+  format.volume output
+  format.number output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {booklet}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.article.title "title" output.warn
+  format.howpublished "howpublished" bibinfo.check output
+  format.organization "organization" bibinfo.check output
+  format.address "address" bibinfo.check output
+  format.date output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {electronic}
+{ std.status.using.period
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.date.electronic output
+  format.article.title.electronic output
+  format.howpublished "howpublished" bibinfo.check output
+  format.organization "organization" bibinfo.check output
+  format.address "address" bibinfo.check output
+  format.note output
+  format.url output
+  fin.entry
+  empty.entry.warn
+  if.url.std.interword.spacing
+}
+
+FUNCTION {inbook}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  author empty$
+    { format.editors "author and editor" output.warn }
+    { format.authors output.nonnull }
+  if$
+  name.or.dash
+  format.book.title.edition output
+  format.series output
+  format.address.publisher.date output
+  format.volume output
+  format.number output
+  format.chapter output
+  format.pages output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {incollection}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.in.booktitle.edition "booktitle" output.warn
+  format.series output
+  format.editors output
+  format.address.publisher.date.nowarn output
+  format.volume output
+  format.number output
+  format.chapter output
+  format.pages output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {inproceedings}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.in.booktitle "booktitle" output.warn
+  format.series output
+  format.editors output
+  format.volume output
+  format.number output
+  publisher empty$
+    { format.address.organization.date output }
+    { format.organization "organization" bibinfo.check output
+      format.address.publisher.date output
+    }
+  if$
+  format.paper output
+  format.pages output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {manual}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.book.title.edition "title" output.warn
+  format.howpublished "howpublished" bibinfo.check output 
+  format.organization "organization" bibinfo.check output
+  format.address "address" bibinfo.check output
+  format.date output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {mastersthesis}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.master.thesis.type output.nonnull
+  format.school "school" bibinfo.warn output
+  format.address "address" bibinfo.check output
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {misc}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.article.title output
+  format.howpublished "howpublished" bibinfo.check output 
+  format.organization "organization" bibinfo.check output
+  format.address "address" bibinfo.check output
+  format.pages output
+  format.date output
+  format.note output
+  format.url output
+  fin.entry
+  empty.entry.warn
+  if.url.std.interword.spacing
+}
+
+FUNCTION {patent}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.article.title output
+  format.patent.nationality.type.number output
+  format.patent.date output
+  format.note output
+  format.url output
+  fin.entry
+  empty.entry.warn
+  if.url.std.interword.spacing
+}
+
+FUNCTION {periodical}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.editors output
+  name.or.dash
+  format.book.title "title" output.warn
+  format.series output
+  format.volume output
+  format.number output
+  format.organization "organization" bibinfo.check output
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {phdthesis}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.phd.thesis.type output.nonnull
+  format.school "school" bibinfo.warn output
+  format.address "address" bibinfo.check output
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {proceedings}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.editors output
+  name.or.dash
+  format.book.title "title" output.warn
+  format.series output
+  format.volume output
+  format.number output
+  publisher empty$
+    { format.address.organization.date output }
+    { format.organization "organization" bibinfo.check output
+      format.address.publisher.date output
+    }
+  if$
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {standard}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.book.title "title" output.warn
+  format.howpublished "howpublished" bibinfo.check output 
+  format.organization.institution.standard.type.number output
+  format.revision output
+  format.date output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {techreport}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.howpublished "howpublished" bibinfo.check output 
+  format.institution "institution" bibinfo.warn output
+  format.address "address" bibinfo.check output
+  format.tech.report.number output.nonnull
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {unpublished}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.date output
+  format.note "note" output.warn
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+
+% The special entry type which provides the user interface to the
+% BST controls
+FUNCTION {IEEEtranBSTCTL}
+{ is.print.banners.to.terminal
+    { "** IEEEtran BST control entry " quote$ * cite$ * quote$ * " detected." *
+      top$
+    }
+    { skip$ }
+  if$
+  CTLuse_article_number
+  empty$
+    { skip$ }
+    { CTLuse_article_number
+      yes.no.to.int
+      'is.use.number.for.article :=
+    }
+  if$
+  CTLuse_paper
+  empty$
+    { skip$ }
+    { CTLuse_paper
+      yes.no.to.int
+      'is.use.paper :=
+    }
+  if$
+  CTLuse_forced_etal
+  empty$
+    { skip$ }
+    { CTLuse_forced_etal
+      yes.no.to.int
+      'is.forced.et.al :=
+    }
+  if$
+  CTLmax_names_forced_etal
+  empty$
+    { skip$ }
+    { CTLmax_names_forced_etal
+      string.to.integer
+      'max.num.names.before.forced.et.al :=
+    }
+  if$
+  CTLnames_show_etal
+  empty$
+    { skip$ }
+    { CTLnames_show_etal
+      string.to.integer
+      'num.names.shown.with.forced.et.al :=
+    }
+  if$
+  CTLuse_alt_spacing
+  empty$
+    { skip$ }
+    { CTLuse_alt_spacing
+      yes.no.to.int
+      'is.use.alt.interword.spacing :=
+    }
+  if$
+  CTLalt_stretch_factor
+  empty$
+    { skip$ }
+    { CTLalt_stretch_factor
+      'ALTinterwordstretchfactor :=
+      "\renewcommand\BIBentryALTinterwordstretchfactor{"
+      ALTinterwordstretchfactor * "}" *
+      write$ newline$
+    }
+  if$
+  CTLdash_repeated_names
+  empty$
+    { skip$ }
+    { CTLdash_repeated_names
+      yes.no.to.int
+      'is.dash.repeated.names :=
+    }
+  if$
+  CTLname_format_string
+  empty$
+    { skip$ }
+    { CTLname_format_string
+      'name.format.string :=
+    }
+  if$
+  CTLname_latex_cmd
+  empty$
+    { skip$ }
+    { CTLname_latex_cmd
+      'name.latex.cmd :=
+    }
+  if$
+  
+  
+  num.names.shown.with.forced.et.al max.num.names.before.forced.et.al >
+    { "CTLnames_show_etal cannot be greater than CTLmax_names_forced_etal in " cite$ * warning$ 
+      max.num.names.before.forced.et.al 'num.names.shown.with.forced.et.al :=
+    }
+    { skip$ }
+  if$
+}
+
+
+%%%%%%%%%%%%%%%%%%%
+%% ENTRY ALIASES %%
+%%%%%%%%%%%%%%%%%%%
+FUNCTION {conference}{inproceedings}
+FUNCTION {online}{electronic}
+FUNCTION {internet}{electronic}
+FUNCTION {webpage}{electronic}
+FUNCTION {default.type}{misc}
+
+
+
+%%%%%%%%%%%%%%%%%%
+%% MAIN PROGRAM %%
+%%%%%%%%%%%%%%%%%%
+
+READ
+
+EXECUTE {initialize.controls}
+EXECUTE {initialize.status.constants}
+EXECUTE {banner.message}
+
+EXECUTE {initialize.longest.label}
+ITERATE {longest.label.pass}
+
+EXECUTE {begin.bib}
+ITERATE {call.type$}
+EXECUTE {end.bib}
+
+EXECUTE{completed.message}
+
+
+%% That's all folks, mds.
diff --git a/IEEEtran.sty b/IEEEtran.sty
new file mode 100644
index 0000000..6e7fff4
--- /dev/null
+++ b/IEEEtran.sty
@@ -0,0 +1,105 @@
+% \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}}
diff --git a/IEEEtranS.bst b/IEEEtranS.bst
new file mode 100644
index 0000000..412347e
--- /dev/null
+++ b/IEEEtranS.bst
@@ -0,0 +1,2550 @@
+%%
+%% IEEEtranS.bst
+%% BibTeX Bibliography Style file
+%% Sorting version of IEEEtran.bst
+%% *** Not for use with work to be submitted to the IEEE ***
+%% Version 1.11 (2003/04/02)
+%% 
+%% Copyright (c) 2003 Michael Shell
+%% 
+%% Original starting code base and algorithms obtained from the output of
+%% Patrick W. Daly's makebst package as well as from prior versions of
+%% IEEE BibTeX styles:
+%% 
+%% 1. Howard Trickey and Oren Patashnik's ieeetr.bst  (1985/1988)
+%% 2. Silvano Balemi and Richard H. Roy's IEEEbib.bst (1993)
+%% 
+%% Added sorting code is from plain.bst.
+%% 
+%% See:
+%% http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/
+%% for latest version and current contact information.
+%% 
+%% For use with BibTeX version 0.99a or later
+%%
+%% This is a numerical citation style.
+%% 
+%%**********************************************************************
+%% 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.
+%%
+%% This code is distributed under the Perl Artistic License 
+%% ( http://language.perl.com/misc/Artistic.html ) 
+%% and may be freely used, distributed and modified - subject to the
+%% constraints therein.
+%% Retain all contribution notices, credits and disclaimers.
+%% 
+%% All comments are the opinions of their respective authors and are not
+%% necessarily endorsed by the IEEE.
+%%**********************************************************************
+%
+%
+% Changelog:
+% 
+% 1.10 (2002/09/27) Initial release
+%
+% 1.11 (2003/04/02)
+%  1. Fixed bug with URLs containing underscores when using url.sty. Thanks
+%     to Ming Kin Lai for reporting this.
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEFAULTS FOR THE CONTROLS OF THE BST STYLE %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% These are the defaults for the user adjustable controls. The values used
+% here can be overridden by the user via IEEEtranBSTCTL entry type.
+
+% NOTE: The recommended LaTeX command to invoke a control entry type is:
+% 
+%\makeatletter
+%\def\bstctlcite#1{\@bsphack
+%  \@for\@citeb:=#1\do{%
+%    \edef\@citeb{\expandafter\@firstofone\@citeb}%
+%    \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi}%
+%  \@esphack}
+%\makeatother
+%
+% It is called at the start of the document, before the first \cite, like:
+% \bstctlcite{IEEEexample:BSTcontrol}
+%
+% IEEEtran.cls V1.6 and later does provide this command.
+
+
+
+% #0 turns off the display of the number for articles.
+% #1 enables
+FUNCTION {default.is.use.number.for.article} { #1 }
+
+
+% #0 turns off the display of the paper and type fields in @inproceedings.
+% #1 enables
+FUNCTION {default.is.use.paper} { #1 }
+
+
+% #0 turns off the forced use of "et al."
+% #1 enables
+FUNCTION {default.is.forced.et.al} { #0 }
+
+% The maximum number of names that can be present beyond which an "et al."
+% usage is forced. Be sure that num.names.shown.with.forced.et.al (below)
+% is not greater than this value!
+% Note: There are many instances of references in IEEE journals which have
+% a very large number of authors as well as instances in which "et al." is
+% used profusely.
+FUNCTION {default.max.num.names.before.forced.et.al} { #10 }
+
+% The number of names that will be shown with a forced "et al.".
+% Must be less than or equal to max.num.names.before.forced.et.al
+FUNCTION {default.num.names.shown.with.forced.et.al} { #1 }
+
+
+% #0 turns off the alternate interword spacing for entries with URLs.
+% #1 enables
+FUNCTION {default.is.use.alt.interword.spacing} { #1 }
+
+% If alternate interword spacing for entries with URLs is enabled, this is
+% the interword spacing stretch factor that will be used. For example, the
+% default "4" here means that the interword spacing in entries with URLs can
+% stretch to four times normal. Does not have to be an integer. Note that
+% the value specified here can be overridden by the user in their LaTeX
+% code via a command such as: 
+% "\providecommand\BIBentryALTinterwordstretchfactor{1.5}" in addition to
+% that via the IEEEtranBSTCTL entry type.
+FUNCTION {default.ALTinterwordstretchfactor} { "4" }
+
+
+% #0 turns off the "dashification" of repeated (i.e., identical to those
+% of the previous entry) names. IEEE normally does this.
+% #1 enables
+FUNCTION {default.is.dash.repeated.names} { #1 }
+
+
+% The default name format control string.
+FUNCTION {default.name.format.string}{ "{f.~}{vv~}{ll}{, jj}" }
+
+
+% The default LaTeX font command for the names.
+FUNCTION {default.name.latex.cmd}{ "" }
+
+
+% Other controls that cannot be accessed via IEEEtranBSTCTL entry type.
+
+% #0 turns off the terminal startup banner/completed message so as to
+% operate more quietly.
+% #1 enables
+FUNCTION {is.print.banners.to.terminal} { #1 }
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FILE VERSION AND BANNER %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION{bst.file.version} { "1.11" }
+FUNCTION{bst.file.date} { "2003/04/02" }
+FUNCTION{bst.file.website} { "http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/" }
+
+FUNCTION {banner.message}
+{ is.print.banners.to.terminal
+     { "-- IEEEtranS.bst version" " " * bst.file.version *
+       " (" * bst.file.date * ") " * "by Michael Shell." *
+       top$
+       "-- " bst.file.website *
+       top$
+       "-- See the " quote$ * "IEEEtran_bst_HOWTO.pdf" * quote$ * " manual for usage information." *
+       top$
+       "** Sorting version - not for use with work to be submitted to the IEEE."
+       top$
+     }
+     { skip$ }
+   if$
+}
+
+FUNCTION {completed.message}
+{ is.print.banners.to.terminal
+     { ""
+       top$
+       "Done."
+       top$
+     }
+     { skip$ }
+   if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%
+%% STRING CONSTANTS %%
+%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION {bbl.and}{ "and" }
+FUNCTION {bbl.etal}{ "et~al." }
+FUNCTION {bbl.editors}{ "eds." }
+FUNCTION {bbl.editor}{ "ed." }
+FUNCTION {bbl.edition}{ "ed." }
+FUNCTION {bbl.volume}{ "vol." }
+FUNCTION {bbl.of}{ "of" }
+FUNCTION {bbl.number}{ "no." }
+FUNCTION {bbl.in}{ "in" }
+FUNCTION {bbl.pages}{ "pp." }
+FUNCTION {bbl.page}{ "p." }
+FUNCTION {bbl.chapter}{ "ch." }
+FUNCTION {bbl.paper}{ "paper" }
+FUNCTION {bbl.part}{ "pt." }
+FUNCTION {bbl.patent}{ "Patent" }
+FUNCTION {bbl.patentUS}{ "U.S." }
+FUNCTION {bbl.revision}{ "Rev." }
+FUNCTION {bbl.series}{ "ser." }
+FUNCTION {bbl.standard}{ "Std." }
+FUNCTION {bbl.techrep}{ "Tech. Rep." }
+FUNCTION {bbl.mthesis}{ "Master's thesis" }
+FUNCTION {bbl.phdthesis}{ "Ph.D. dissertation" }
+FUNCTION {bbl.urlprefix}{ "[Online]. Available:" }
+FUNCTION {bbl.st}{ "st" }
+FUNCTION {bbl.nd}{ "nd" }
+FUNCTION {bbl.rd}{ "rd" }
+FUNCTION {bbl.th}{ "th" }
+
+
+% This is the LaTeX spacer that is used when a larger than normal space
+% is called for (such as just before the address:publisher).
+FUNCTION {large.space} { "\hskip 1em plus 0.5em minus 0.4em\relax " }
+
+% The LaTeX code for dashes that are used to represent repeated names.
+% Note: Some older IEEE journals used something like
+% "\rule{0.275in}{0.5pt}\," which is fairly thick and runs right along
+% the baseline. However, IEEE now uses a thinner, above baseline,
+% six dash long sequence.
+FUNCTION {repeated.name.dashes} { "------" }
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% PREDEFINED STRING MACROS %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+MACRO {jan} {"Jan."}
+MACRO {feb} {"Feb."}
+MACRO {mar} {"Mar."}
+MACRO {apr} {"Apr."}
+MACRO {may} {"May"}
+MACRO {jun} {"June"}
+MACRO {jul} {"July"}
+MACRO {aug} {"Aug."}
+MACRO {sep} {"Sept."}
+MACRO {oct} {"Oct."}
+MACRO {nov} {"Nov."}
+MACRO {dec} {"Dec."}
+
+
+
+%%%%%%%%%%%%%%%%%%
+%% ENTRY FIELDS %%
+%%%%%%%%%%%%%%%%%%
+
+ENTRY
+  { address
+    assignee
+    author
+    booktitle
+    chapter
+    day
+    dayfiled
+    edition
+    editor
+    howpublished
+    institution
+    intype
+    journal
+    key
+    language
+    month
+    monthfiled
+    nationality
+    note
+    number
+    organization
+    pages
+    paper
+    publisher
+    school
+    series
+    revision
+    title
+    type
+    url
+    volume
+    year
+    yearfiled
+    CTLuse_article_number
+    CTLuse_paper
+    CTLuse_forced_etal
+    CTLmax_names_forced_etal
+    CTLnames_show_etal
+    CTLuse_alt_spacing
+    CTLalt_stretch_factor
+    CTLdash_repeated_names
+    CTLname_format_string
+    CTLname_latex_cmd
+  }
+  {}
+  { label }
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%
+%% INTEGER VARIABLES %%
+%%%%%%%%%%%%%%%%%%%%%%%
+
+INTEGERS { prev.status.punct this.status.punct punct.std
+           punct.no punct.comma punct.period 
+           prev.status.space this.status.space space.std
+           space.no space.normal space.large
+           prev.status.quote this.status.quote quote.std
+           quote.no quote.close
+           prev.status.nline this.status.nline nline.std
+           nline.no nline.newblock 
+           status.cap cap.std
+           cap.no cap.yes}
+
+INTEGERS { longest.label.width multiresult nameptr namesleft number.label numnames }
+
+INTEGERS { is.use.number.for.article
+           is.use.paper
+           is.forced.et.al
+           max.num.names.before.forced.et.al
+           num.names.shown.with.forced.et.al
+           is.use.alt.interword.spacing
+           is.dash.repeated.names}
+
+
+%%%%%%%%%%%%%%%%%%%%%%
+%% STRING VARIABLES %%
+%%%%%%%%%%%%%%%%%%%%%%
+
+STRINGS { bibinfo
+          longest.label
+          oldname
+          s
+          t
+          ALTinterwordstretchfactor
+          name.format.string
+          name.latex.cmd}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%
+%% LOW LEVEL FUNCTIONS %%
+%%%%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION {initialize.controls}
+{ default.is.use.number.for.article 'is.use.number.for.article :=
+  default.is.use.paper 'is.use.paper :=
+  default.is.forced.et.al 'is.forced.et.al :=
+  default.max.num.names.before.forced.et.al 'max.num.names.before.forced.et.al :=
+  default.num.names.shown.with.forced.et.al 'num.names.shown.with.forced.et.al :=
+  default.is.use.alt.interword.spacing 'is.use.alt.interword.spacing :=
+  default.is.dash.repeated.names 'is.dash.repeated.names :=
+  default.ALTinterwordstretchfactor 'ALTinterwordstretchfactor :=
+  default.name.format.string 'name.format.string :=
+  default.name.latex.cmd 'name.latex.cmd :=
+}
+
+
+% This IEEEtran.bst features a very powerful and flexible mechanism for
+% controlling the capitalization, punctuation, spacing, quotation, and
+% newlines of the formatted entry fields. (Note: IEEEtran.bst does not need
+% or use the newline/newblock feature, but it has been implemented for
+% possible future use.) The output states of IEEEtran.bst consist of
+% multiple independent attributes and, as such, can be thought of as being
+% vectors, rather than the simple scalar values ("before.all", 
+% "mid.sentence", etc.) used in most other .bst files.
+% 
+% The more flexible and complex design used here was motivated in part by
+% IEEE's rather unusual bibliography style. For example, IEEE ends the
+% previous field item with a period and large space prior to the publisher
+% address; the @electronic entry types use periods as inter-item punctuation
+% rather than the commas used by the other entry types; and URLs are never
+% followed by periods even though they are the last item in the entry.
+% Although it is possible to accommodate these features with the conventional
+% output state system, the seemingly endless exceptions make for convoluted,
+% unreliable and difficult to maintain code.
+%
+% IEEEtran.bst's output state system can be easily understood via a simple
+% illustration of two most recently formatted entry fields (on the stack):
+%
+%               CURRENT_ITEM
+%               "PREVIOUS_ITEM
+%
+% which, in this example, is to eventually appear in the bibliography as:
+% 
+%               "PREVIOUS_ITEM," CURRENT_ITEM
+%
+% It is the job of the output routine to take the previous item off of the
+% stack (while leaving the current item at the top of the stack), apply its
+% trailing punctuation (including closing quote marks) and spacing, and then
+% to write the result to BibTeX's output buffer:
+% 
+%               "PREVIOUS_ITEM," 
+% 
+% Punctuation (and spacing) between items is often determined by both of the
+% items rather than just the first one. The presence of quotation marks
+% further complicates the situation because, in standard English, trailing
+% punctuation marks are supposed to be contained within the quotes.
+% 
+% IEEEtran.bst maintains two output state (aka "status") vectors which
+% correspond to the previous and current (aka "this") items. Each vector
+% consists of several independent attributes which track punctuation,
+% spacing, quotation, and newlines. Capitalization status is handled by a
+% separate scalar because the format routines, not the output routine,
+% handle capitalization and, therefore, there is no need to maintain the
+% capitalization attribute for both the "previous" and "this" items.
+% 
+% When a format routine adds a new item, it copies the current output status
+% vector to the previous output status vector and (usually) resets the
+% current (this) output status vector to a "standard status" vector. Using a
+% "standard status" vector in this way allows us to redefine what we mean by
+% "standard status" at the start of each entry handler and reuse the same
+% format routines under the various inter-item separation schemes. For
+% example, the standard status vector for the @book entry type may use
+% commas for item separators, while the @electronic type may use periods,
+% yet both entry handlers exploit many of the exact same format routines.
+% 
+% Because format routines have write access to the output status vector of
+% the previous item, they can override the punctuation choices of the
+% previous format routine! Therefore, it becomes trivial to implement rules
+% such as "Always use a period and a large space before the publisher." By
+% pushing the generation of the closing quote mark to the output routine, we
+% avoid all the problems caused by having to close a quote before having all
+% the information required to determine what the punctuation should be.
+%
+% The IEEEtran.bst output state system can easily be expanded if needed.
+% For instance, it is easy to add a "space.tie" attribute value if the
+% bibliography rules mandate that two items have to be joined with an
+% unbreakable space. 
+
+FUNCTION {initialize.status.constants}
+{ #0 'punct.no :=
+  #1 'punct.comma :=
+  #2 'punct.period :=
+  #0 'space.no := 
+  #1 'space.normal :=
+  #2 'space.large :=
+  #0 'quote.no :=
+  #1 'quote.close :=
+  #0 'cap.no :=
+  #1 'cap.yes :=
+  #0 'nline.no :=
+  #1 'nline.newblock :=
+}
+
+FUNCTION {std.status.using.comma}
+{ punct.comma 'punct.std :=
+  space.normal 'space.std :=
+  quote.no 'quote.std :=
+  nline.no 'nline.std :=
+  cap.no 'cap.std :=
+}
+
+FUNCTION {std.status.using.period}
+{ punct.period 'punct.std :=
+  space.normal 'space.std :=
+  quote.no 'quote.std :=
+  nline.no 'nline.std :=
+  cap.yes 'cap.std :=
+}
+
+FUNCTION {initialize.prev.this.status}
+{ punct.no 'prev.status.punct :=
+  space.no 'prev.status.space :=
+  quote.no 'prev.status.quote :=
+  nline.no 'prev.status.nline :=
+  punct.no 'this.status.punct :=
+  space.no 'this.status.space :=
+  quote.no 'this.status.quote :=
+  nline.no 'this.status.nline :=
+  cap.yes 'status.cap :=
+}
+
+FUNCTION {this.status.std}
+{ punct.std 'this.status.punct :=
+  space.std 'this.status.space :=
+  quote.std 'this.status.quote :=
+  nline.std 'this.status.nline :=
+}
+
+FUNCTION {cap.status.std}{ cap.std 'status.cap := }
+
+FUNCTION {this.to.prev.status}
+{ this.status.punct 'prev.status.punct :=
+  this.status.space 'prev.status.space :=
+  this.status.quote 'prev.status.quote :=
+  this.status.nline 'prev.status.nline :=
+}
+
+
+FUNCTION {not}
+{   { #0 }
+    { #1 }
+  if$
+}
+
+FUNCTION {and}
+{   { skip$ }
+    { pop$ #0 }
+  if$
+}
+
+FUNCTION {or}
+{   { pop$ #1 }
+    { skip$ }
+  if$
+}
+
+
+% convert the strings "yes" or "no" to #1 or #0 respectively
+FUNCTION {yes.no.to.int}
+{ "l" change.case$ duplicate$
+    "yes" =
+    { pop$  #1 }
+    { duplicate$ "no" =
+        { pop$ #0 }
+        { "unknown boolean " quote$ * swap$ * quote$ *
+          " in " * cite$ * warning$
+          #0
+        }
+      if$
+    }
+  if$
+}
+
+
+% pushes true if the single char string on the stack is in the
+% range of "0" to "9"
+FUNCTION {is.num}
+{ chr.to.int$
+  duplicate$ "0" chr.to.int$ < not
+  swap$ "9" chr.to.int$ > not and
+}
+
+% multiplies the integer on the stack by a factor of 10
+FUNCTION {bump.int.mag}
+{ #0 'multiresult :=
+    { duplicate$ #0 > }
+    { #1 -
+      multiresult #10 +
+      'multiresult :=
+    }
+  while$
+pop$
+multiresult
+}
+
+% converts a single character string on the stack to an integer
+FUNCTION {char.to.integer}
+{ duplicate$ 
+  is.num
+    { chr.to.int$ "0" chr.to.int$ - }
+    {"noninteger character " quote$ * swap$ * quote$ *
+          " in integer field of " * cite$ * warning$
+    #0
+    }
+  if$
+}
+
+% converts a string on the stack to an integer
+FUNCTION {string.to.integer}
+{ duplicate$ text.length$ 'namesleft :=
+  #1 'nameptr :=
+  #0 'numnames :=
+    { nameptr namesleft > not }
+    { duplicate$ nameptr #1 substring$
+      char.to.integer numnames bump.int.mag +
+      'numnames :=
+      nameptr #1 +
+      'nameptr :=
+    }
+  while$
+pop$
+numnames
+}
+
+
+
+
+% The output routines write out the *next* to the top (previous) item on the
+% stack, adding punctuation and such as needed. Since IEEEtran.bst maintains
+% the output status for the top two items on the stack, these output
+% routines have to consider the previous output status (which corresponds to
+% the item that is being output). Full independent control of punctuation,
+% closing quote marks, spacing, and newblock is provided.
+% 
+% "output.nonnull" does not check for the presence of a previous empty
+% item.
+% 
+% "output" does check for the presence of a previous empty item and will
+% remove an empty item rather than outputing it.
+% 
+% "output.warn" is like "output", but will issue a warning if it detects
+% an empty item.
+
+FUNCTION {output.nonnull}
+{ swap$
+  prev.status.punct punct.comma =
+     { "," * }
+     { skip$ }
+   if$
+  prev.status.punct punct.period =
+     { add.period$ }
+     { skip$ }
+   if$ 
+  prev.status.quote quote.close =
+     { "''" * }
+     { skip$ }
+   if$
+  prev.status.space space.normal =
+     { " " * }
+     { skip$ }
+   if$
+  prev.status.space space.large =
+     { large.space * }
+     { skip$ }
+   if$
+  write$
+  prev.status.nline nline.newblock =
+     { newline$ "\newblock " write$ }
+     { skip$ }
+   if$
+}
+
+FUNCTION {output}
+{ duplicate$ empty$
+    'pop$
+    'output.nonnull
+  if$
+}
+
+FUNCTION {output.warn}
+{ 't :=
+  duplicate$ empty$
+    { pop$ "empty " t * " in " * cite$ * warning$ }
+    'output.nonnull
+  if$
+}
+
+% "fin.entry" is the output routine that handles the last item of the entry
+% (which will be on the top of the stack when "fin.entry" is called).
+
+FUNCTION {fin.entry}
+{ this.status.punct punct.no =
+     { skip$ }
+     { add.period$ }
+   if$
+   this.status.quote quote.close =
+     { "''" * }
+     { skip$ }
+   if$
+write$
+newline$
+}
+
+
+FUNCTION {is.last.char.not.punct}
+{ duplicate$
+   "}" * add.period$
+   #-1 #1 substring$ "." =
+}
+
+FUNCTION {is.multiple.pages}
+{ 't :=
+  #0 'multiresult :=
+    { multiresult not
+      t empty$ not
+      and
+    }
+    { t #1 #1 substring$
+      duplicate$ "-" =
+      swap$ duplicate$ "," =
+      swap$ "+" =
+      or or
+        { #1 'multiresult := }
+        { t #2 global.max$ substring$ 't := }
+      if$
+    }
+  while$
+  multiresult
+}
+
+FUNCTION {capitalize}{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {emphasize}
+{ duplicate$ empty$
+    { pop$ "" }
+    { "\emph{" swap$ * "}" * }
+  if$
+}
+
+FUNCTION {do.name.latex.cmd}
+{ name.latex.cmd
+  empty$
+    { skip$ }
+    { name.latex.cmd "{" * swap$ * "}" * }
+  if$
+}
+
+% IEEEtran.bst uses its own \BIBforeignlanguage command which directly
+% invokes the TeX hyphenation patterns without the need of the Babel
+% package. Babel does a lot more than switch hyphenation patterns and
+% its loading can cause unintended effects in many class files (such as
+% IEEEtran.cls).
+FUNCTION {select.language}
+{ duplicate$ empty$ 'pop$
+    { language empty$ 'skip$
+        { "\BIBforeignlanguage{" language * "}{" * swap$ * "}" * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {tie.or.space.prefix}
+{ duplicate$ text.length$ #3 <
+    { "~" }
+    { " " }
+  if$
+  swap$
+}
+
+FUNCTION {get.bbl.editor}
+{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ }
+
+FUNCTION {space.word}{ " " swap$ * " " * }
+
+
+% Field Conditioners, Converters, Checkers and External Interfaces
+
+FUNCTION {empty.field.to.null.string}
+{ duplicate$ empty$
+    { pop$ "" }
+    { skip$ }
+  if$
+}
+
+FUNCTION {either.or.check}
+{ empty$
+    { pop$ }
+    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+  if$
+}
+
+FUNCTION {empty.entry.warn}
+{ author empty$ title empty$ howpublished empty$
+  month empty$ year empty$ note empty$ url empty$
+  and and and and and and
+    { "all relevant fields are empty in " cite$ * warning$ }
+    'skip$
+  if$
+}
+
+
+% The bibinfo system provides a way for the electronic parsing/acquisition
+% of a bibliography's contents as is done by ReVTeX. For example, a field
+% could be entered into the bibliography as:
+% \bibinfo{volume}{2}
+% Only the "2" would show up in the document, but the LaTeX \bibinfo command
+% could do additional things with the information. IEEEtran.bst does provide
+% a \bibinfo command via "\providecommand{\bibinfo}[2]{#2}". However, it is
+% currently not used as the bogus bibinfo functions defined here output the
+% entry values directly without the \bibinfo wrapper. The bibinfo functions
+% themselves (and the calls to them) are retained for possible future use.
+% 
+% bibinfo.check avoids acting on missing fields while bibinfo.warn will
+% issue a warning message if a missing field is detected. Prior to calling
+% the bibinfo functions, the user should push the field value and then its
+% name string, in that order.
+
+FUNCTION {bibinfo.check}
+{ swap$ duplicate$ missing$
+    { pop$ pop$ "" }
+    { duplicate$ empty$
+        { swap$ pop$ }
+        { swap$ pop$ }
+      if$
+    }
+  if$
+}
+
+FUNCTION {bibinfo.warn}
+{ swap$ duplicate$ missing$
+    { swap$ "missing " swap$ * " in " * cite$ * warning$ pop$ "" }
+    { duplicate$ empty$
+        { swap$ "empty " swap$ * " in " * cite$ * warning$ }
+        { swap$ pop$ }
+      if$
+    }
+  if$
+}
+
+
+% IEEE separates large numbers with more than 4 digits into groups of
+% three. IEEE uses a small space to separate these number groups. 
+% Typical applications include patent and page numbers.
+
+% number of consecutive digits required to trigger the group separation.
+FUNCTION {large.number.trigger}{ #5 }
+
+% For numbers longer than the trigger, this is the blocksize of the groups.
+% The blocksize must be less than the trigger threshold, and 2 * blocksize
+% must be greater than the trigger threshold (can't do more than one
+% separation on the initial trigger).
+FUNCTION {large.number.blocksize}{ #3 }
+
+% What is actually inserted between the number groups.
+FUNCTION {large.number.separator}{ "\," }
+
+% So as to save on integer variables by reusing existing ones, numnames
+% holds the current number of consecutive digits read and nameptr holds
+% the number that will trigger an inserted space.
+FUNCTION {large.number.separate}
+{ 't :=
+  ""
+  #0 'numnames :=
+  large.number.trigger 'nameptr :=
+  { t empty$ not }
+  { t #-1 #1 substring$ is.num
+      { numnames #1 + 'numnames := }
+      { #0 'numnames := 
+        large.number.trigger 'nameptr :=
+      }
+    if$
+    t #-1 #1 substring$ swap$ *
+    t #-2 global.max$ substring$ 't :=
+    numnames nameptr =
+      { duplicate$ #1 nameptr large.number.blocksize - substring$ swap$
+        nameptr large.number.blocksize - #1 + global.max$ substring$
+        large.number.separator swap$ * *
+        nameptr large.number.blocksize - 'numnames :=
+        large.number.blocksize #1 + 'nameptr :=
+      }
+      { skip$ }
+    if$
+  }
+  while$
+}
+
+% Converts all single dashes "-" to double dashes "--".
+FUNCTION {n.dashify}
+{ large.number.separate
+  't :=
+  ""
+    { t empty$ not }
+    { t #1 #1 substring$ "-" =
+        { t #1 #2 substring$ "--" = not
+            { "--" *
+              t #2 global.max$ substring$ 't :=
+            }
+            {   { t #1 #1 substring$ "-" = }
+                { "-" *
+                  t #2 global.max$ substring$ 't :=
+                }
+              while$
+            }
+          if$
+        }
+        { t #1 #1 substring$ *
+          t #2 global.max$ substring$ 't :=
+        }
+      if$
+    }
+  while$
+}
+
+
+% This function detects entries with names that are identical to that of
+% the previous entry and replaces the repeated names with dashes (if the
+% "is.dash.repeated.names" user control is nonzero).
+FUNCTION {name.or.dash}
+{ 's :=
+   oldname empty$
+     { s 'oldname := s }
+     { s oldname =
+         { is.dash.repeated.names
+              { repeated.name.dashes }
+              { s 'oldname := s }
+            if$
+         }
+         { s 'oldname := s }
+       if$
+     }
+   if$
+}
+
+% Converts the number string on the top of the stack to
+% "numerical ordinal form" (e.g., "7" to "7th"). There is
+% no artificial limit to the upper bound of the numbers as the
+% least significant digit always determines the ordinal form.
+FUNCTION {num.to.ordinal}
+{ duplicate$ #-1 #1 substring$ "1" =
+     { bbl.st * }
+     { duplicate$ #-1 #1 substring$ "2" =
+         { bbl.nd * }
+         { duplicate$ #-1 #1 substring$ "3" =
+             { bbl.rd * }
+             { bbl.th * }
+           if$
+         }
+       if$
+     }
+   if$
+}
+
+% If the string on the top of the stack begins with a number,
+% (e.g., 11th) then replace the string with the leading number
+% it contains. Otherwise retain the string as-is. s holds the
+% extracted number, t holds the part of the string that remains
+% to be scanned.
+FUNCTION {extract.num}
+{ duplicate$ 't :=
+  "" 's :=
+  { t empty$ not }
+  { t #1 #1 substring$
+    t #2 global.max$ substring$ 't :=
+    duplicate$ is.num
+      { s swap$ * 's := }
+      { pop$ "" 't := }
+    if$
+  }
+  while$
+  s empty$
+    'skip$
+    { pop$ s }
+  if$
+}
+
+% Converts the word number string on the top of the stack to
+% Arabic string form. Will be successful up to "tenth".
+FUNCTION {word.to.num}
+{ duplicate$ "l" change.case$ 's :=
+  s "first" =
+    { pop$ "1" }
+    { skip$ }
+  if$
+  s "second" =
+    { pop$ "2" }
+    { skip$ }
+  if$
+  s "third" =
+    { pop$ "3" }
+    { skip$ }
+  if$
+  s "fourth" =
+    { pop$ "4" }
+    { skip$ }
+  if$
+  s "fifth" =
+    { pop$ "5" }
+    { skip$ }
+  if$
+  s "sixth" =
+    { pop$ "6" }
+    { skip$ }
+  if$
+  s "seventh" =
+    { pop$ "7" }
+    { skip$ }
+  if$
+  s "eighth" =
+    { pop$ "8" }
+    { skip$ }
+  if$
+  s "ninth" =
+    { pop$ "9" }
+    { skip$ }
+  if$
+  s "tenth" =
+    { pop$ "10" }
+    { skip$ }
+  if$
+}
+
+
+% Converts the string on the top of the stack to numerical
+% ordinal (e.g., "11th") form.
+FUNCTION {convert.edition}
+{ duplicate$ empty$ 'skip$
+    { duplicate$ #1 #1 substring$ is.num
+        { extract.num
+          num.to.ordinal
+        }
+        { word.to.num
+          duplicate$ #1 #1 substring$ is.num
+            { num.to.ordinal }
+            { "edition ordinal word " quote$ * edition * quote$ *
+              " may be too high (or improper) for conversion" * " in " * cite$ * warning$
+            }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% LATEX BIBLIOGRAPHY CODE %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION {start.entry}
+{ newline$
+  "\bibitem{" write$
+  cite$ write$
+  "}" write$
+  newline$
+  ""
+  initialize.prev.this.status
+}
+
+% Here we write out all the LaTeX code that we will need. The most involved
+% code sequences are those that control the alternate interword spacing and
+% foreign language hyphenation patterns. The heavy use of \providecommand
+% gives users a way to override the defaults. Special thanks to Javier Bezos,
+% Johannes Braams, Robin Fairburns, Heiko Oberdiek, Donald Arseneau and all
+% the other gurus on comp.text.tex for their help and advice on the topic of
+% \selectlanguage, Babel and BibTeX.
+FUNCTION {begin.bib}
+{ preamble$ empty$ 'skip$
+    { preamble$ write$ newline$ }
+  if$
+  "\begin{thebibliography}{"  longest.label  * "}" *
+  write$ newline$
+  "\providecommand{\url}[1]{#1}"
+  write$ newline$
+  "\csname url@rmstyle\endcsname"
+  write$ newline$
+  "\providecommand{\newblock}{\relax}"
+  write$ newline$
+  "\providecommand{\bibinfo}[2]{#2}"
+  write$ newline$
+  "\providecommand\BIBentrySTDinterwordspacing{\spaceskip=0pt\relax}"
+  write$ newline$
+  "\providecommand\BIBentryALTinterwordstretchfactor{"
+  ALTinterwordstretchfactor * "}" *
+  write$ newline$
+  "\providecommand\BIBentryALTinterwordspacing{\spaceskip=\fontdimen2\font plus "
+  write$ newline$
+  "\BIBentryALTinterwordstretchfactor\fontdimen3\font minus \fontdimen4\font\relax}"
+  write$ newline$
+  "\providecommand\BIBforeignlanguage[2]{{%"
+  write$ newline$
+  "\expandafter\ifx\csname l@#1\endcsname\relax"
+  write$ newline$
+  "\typeout{** WARNING: IEEEtran.bst: No hyphenation pattern has been}%"
+  write$ newline$
+  "\typeout{** loaded for the language `#1'. Using the pattern for}%"
+  write$ newline$
+  "\typeout{** the default language instead.}%"
+  write$ newline$
+  "\else"
+  write$ newline$
+  "\language=\csname l@#1\endcsname"
+  write$ newline$
+  "\fi"
+  write$ newline$
+  "#2}}"
+  write$ newline$
+}
+
+FUNCTION {end.bib}
+{ newline$ "\end{thebibliography}" write$ newline$ }
+
+FUNCTION {if.url.alt.interword.spacing}
+{ is.use.alt.interword.spacing 
+     {url empty$ 'skip$ {"\BIBentryALTinterwordspacing" write$ newline$} if$}
+     { skip$ }
+   if$
+}
+
+FUNCTION {if.url.std.interword.spacing}
+{ is.use.alt.interword.spacing 
+     {url empty$ 'skip$ {"\BIBentrySTDinterwordspacing" write$ newline$} if$}
+     { skip$ }
+   if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% LONGEST LABEL PASS %%
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+FUNCTION {initialize.longest.label}
+{ "" 'longest.label :=
+  #1 'number.label :=
+  #0 'longest.label.width :=
+}
+
+FUNCTION {longest.label.pass}
+{ number.label int.to.str$ 'label :=
+  number.label #1 + 'number.label :=
+  label width$ longest.label.width >
+    { label 'longest.label :=
+      label width$ 'longest.label.width :=
+    }
+    'skip$
+  if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%
+%% FORMAT HANDLERS %%
+%%%%%%%%%%%%%%%%%%%%%
+
+%% Lower Level Formats (used by higher level formats)
+
+FUNCTION {format.address.org.or.pub.date}
+{ 't :=
+  ""
+  year empty$
+    { "empty year in " cite$ * warning$ }
+    { skip$ }
+  if$
+  address empty$ t empty$ and
+  year empty$ and month empty$ and
+    { skip$ }
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      address "address" bibinfo.check *
+      t empty$
+        { skip$ }
+        { punct.period 'prev.status.punct :=
+          space.large 'prev.status.space :=
+          address empty$
+            { skip$ }
+            { ": " * }
+          if$
+          t *
+        }
+      if$
+      year empty$ month empty$ and
+        { skip$ }
+        { t empty$ address empty$ and
+            { skip$ }
+            { ", " * }
+          if$
+          month empty$
+            { year empty$
+                { skip$ }
+                { year "year" bibinfo.check * }
+              if$
+            }
+            { month "month" bibinfo.check *
+              year empty$
+                 { skip$ }
+                 { " " * year "year" bibinfo.check * }
+              if$
+            }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+
+FUNCTION {format.names}
+{ 'bibinfo :=
+  duplicate$ empty$ 'skip$ {
+  this.to.prev.status
+  this.status.std
+  's :=
+  "" 't :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      name.format.string
+      format.name$
+      bibinfo bibinfo.check
+      't :=
+      nameptr #1 >
+        { nameptr num.names.shown.with.forced.et.al #1 + =
+          numnames max.num.names.before.forced.et.al >
+          is.forced.et.al and and
+            { "others" 't :=
+              #1 'namesleft :=
+            }
+            { skip$ }
+          if$
+          namesleft #1 >
+            { ", " * t do.name.latex.cmd * }
+            {
+              numnames #2 >
+                { "," * }
+                'skip$
+              if$
+              s nameptr "{ll}" format.name$ duplicate$ "others" =
+                { 't := }
+                { pop$ }
+              if$
+              t "others" =
+                {
+                  " " * bbl.etal emphasize *
+                }
+                {
+                  bbl.and
+                  space.word * t do.name.latex.cmd *
+                }
+              if$
+            }
+          if$
+        }
+        { t do.name.latex.cmd }
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+  cap.status.std
+  } if$
+}
+
+
+
+
+%% Higher Level Formats
+
+%% addresses/locations
+
+FUNCTION {format.address}
+{ address duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+
+
+%% author/editor names
+
+FUNCTION {format.authors}{ author "author" format.names }
+
+FUNCTION {format.editors}
+{ editor "editor" format.names duplicate$ empty$ 'skip$
+    { ", " *
+      get.bbl.editor
+      capitalize
+      *
+    }
+  if$
+}
+
+
+
+%% date
+
+FUNCTION {format.date}
+{
+  month "month" bibinfo.check duplicate$ empty$
+  year  "year" bibinfo.check duplicate$ empty$
+    { swap$ 'skip$
+        { this.to.prev.status
+          this.status.std
+          cap.status.std
+         "there's a month but no year in " cite$ * warning$ }
+      if$
+      *
+    }
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      swap$ 'skip$
+        {
+          swap$
+          " " * swap$
+        }
+      if$
+      *
+    }
+  if$
+}
+
+FUNCTION {format.date.electronic}
+{ month "month" bibinfo.check duplicate$ empty$
+  year  "year" bibinfo.check duplicate$ empty$
+    { swap$ 
+        { pop$ }
+        { "there's a month but no year in " cite$ * warning$
+        pop$ ")" * "(" swap$ *
+        this.to.prev.status
+        punct.no 'this.status.punct :=
+        space.normal 'this.status.space :=
+        quote.no 'this.status.quote :=
+        cap.yes  'status.cap :=
+        }
+      if$
+    }
+    { swap$ 
+        { swap$ pop$ ")" * "(" swap$ * }
+        { "(" swap$ * ", " * swap$ * ")" * }
+      if$
+    this.to.prev.status
+    punct.no 'this.status.punct :=
+    space.normal 'this.status.space :=
+    quote.no 'this.status.quote :=
+    cap.yes  'status.cap :=
+    }
+  if$
+}
+
+
+
+%% edition/title
+
+% Note: IEEE considers the edition to be closely associated with
+% the title of a book. So, in IEEEtran.bst the edition is normally handled 
+% within the formatting of the title. The format.edition function is 
+% retained here for possible future use.
+FUNCTION {format.edition}
+{ edition duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      convert.edition
+      status.cap
+        { "t" }
+        { "l" }
+      if$ change.case$
+      "edition" bibinfo.check
+      "~" * bbl.edition *
+      cap.status.std
+    }
+  if$
+}
+
+% This is used to format the booktitle of a conference proceedings.
+% Here we use the "intype" field to provide the user a way to 
+% override the word "in" (e.g., with things like "presented at")
+% Use of intype stops the emphasis of the booktitle to indicate that
+% we no longer mean the written conference proceedings, but the
+% conference itself.
+FUNCTION {format.in.booktitle}
+{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      select.language
+      intype missing$
+        { emphasize
+          bbl.in " " *
+        }
+        { intype " " * }
+      if$
+      swap$ *
+      cap.status.std
+    }
+  if$
+}
+
+% This is used to format the booktitle of collection.
+% Here the "intype" field is not supported, but "edition" is.
+FUNCTION {format.in.booktitle.edition}
+{ booktitle "booktitle" bibinfo.check duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      select.language
+      emphasize
+      edition empty$ 'skip$
+        { ", " *
+          edition
+          convert.edition
+          "l" change.case$
+          * "~" * bbl.edition *
+        }
+      if$
+      bbl.in " " * swap$ *
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.article.title}
+{ title duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      "t" change.case$
+    }
+  if$
+  "title" bibinfo.check
+  duplicate$ empty$ 'skip$
+    { quote.close 'this.status.quote :=
+      is.last.char.not.punct
+        { punct.std 'this.status.punct := }
+        { punct.no 'this.status.punct := }
+      if$
+      select.language
+      "``" swap$ *
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.article.title.electronic}
+{ title duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      "t" change.case$ 
+    }
+  if$
+  "title" bibinfo.check
+  duplicate$ empty$ 
+    { skip$ } 
+    { select.language }
+  if$
+}
+
+FUNCTION {format.book.title.edition}
+{ title "title" bibinfo.check
+  duplicate$ empty$
+    { "empty title in " cite$ * warning$ }
+    { this.to.prev.status
+      this.status.std
+      select.language
+      emphasize
+      edition empty$ 'skip$
+        { ", " *
+          edition
+          convert.edition
+          status.cap
+            { "t" }
+            { "l" }
+          if$
+          change.case$
+          * "~" * bbl.edition *
+        }
+      if$
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.book.title}
+{ title "title" bibinfo.check
+  duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      select.language
+      emphasize
+    }
+  if$
+}
+
+
+
+%% journal
+
+FUNCTION {format.journal}
+{ journal duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      select.language
+      emphasize
+    }
+  if$
+}
+
+
+
+%% how published
+
+FUNCTION {format.howpublished}
+{ howpublished duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+
+
+%% institutions/organization/publishers/school
+
+FUNCTION {format.institution}
+{ institution duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.organization}
+{ organization duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.address.publisher.date}
+{ publisher "publisher" bibinfo.warn format.address.org.or.pub.date }
+
+FUNCTION {format.address.publisher.date.nowarn}
+{ publisher "publisher" bibinfo.check format.address.org.or.pub.date }
+
+FUNCTION {format.address.organization.date}
+{ organization "organization" bibinfo.check format.address.org.or.pub.date }
+
+FUNCTION {format.school}
+{ school duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+    }
+  if$
+}
+
+
+
+%% volume/number/series/chapter/pages
+
+FUNCTION {format.volume}
+{ volume empty.field.to.null.string
+  duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      bbl.volume 
+      status.cap
+        { capitalize }
+        { skip$ }
+      if$
+      swap$ tie.or.space.prefix
+      "volume" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.number}
+{ number empty.field.to.null.string
+  duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      status.cap
+         { bbl.number capitalize }
+         { bbl.number }
+       if$
+      swap$ tie.or.space.prefix
+      "number" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+FUNCTION {format.number.if.use.for.article}
+{ is.use.number.for.article 
+     { format.number }
+     { "" }
+   if$
+}
+
+% IEEE does not seem to tie the series so closely with the volume
+% and number as is done in other bibliography styles. Instead the
+% series is treated somewhat like an extension of the title.
+FUNCTION {format.series}
+{ series empty$ 
+   { "" }
+   { this.to.prev.status
+     this.status.std
+     bbl.series " " *
+     series "series" bibinfo.check *
+     cap.status.std
+   }
+ if$
+}
+
+
+FUNCTION {format.chapter}
+{ chapter empty$
+    { "" }
+    { this.to.prev.status
+      this.status.std
+      type empty$
+        { bbl.chapter }
+        { type "l" change.case$
+          "type" bibinfo.check
+        }
+      if$
+      chapter tie.or.space.prefix
+      "chapter" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+
+% The intended use of format.paper is for paper numbers of inproceedings.
+% The paper type can be overridden via the type field.
+% We allow the type to be displayed even if the paper number is absent
+% for things like "postdeadline paper"
+FUNCTION {format.paper}
+{ is.use.paper
+     { paper empty$
+        { type empty$
+            { "" }
+            { this.to.prev.status
+              this.status.std
+              type "type" bibinfo.check
+              cap.status.std
+            }
+          if$
+        }
+        { this.to.prev.status
+          this.status.std
+          type empty$
+            { bbl.paper }
+            { type "type" bibinfo.check }
+          if$
+          " " * paper
+          "paper" bibinfo.check
+          *
+          cap.status.std
+        }
+      if$
+     }
+     { "" } 
+   if$
+}
+
+
+FUNCTION {format.pages}
+{ pages duplicate$ empty$ 'skip$
+    { this.to.prev.status
+      this.status.std
+      duplicate$ is.multiple.pages
+        {
+          bbl.pages swap$
+          n.dashify
+        }
+        {
+          bbl.page swap$
+        }
+      if$
+      tie.or.space.prefix
+      "pages" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+
+
+%% technical report number
+
+FUNCTION {format.tech.report.number}
+{ number "number" bibinfo.check
+  type duplicate$ empty$
+    { pop$ 
+      this.to.prev.status
+      this.status.std
+      cap.status.std
+      bbl.techrep
+    }
+    { skip$ }
+  if$
+  "type" bibinfo.check 
+  swap$ duplicate$ empty$
+    { pop$ }
+    { this.to.prev.status
+      this.status.std
+      cap.status.std
+      tie.or.space.prefix * * }
+  if$
+}
+
+
+
+%% note
+
+FUNCTION {format.note}
+{ note empty$
+    { "" }
+    { this.to.prev.status
+      this.status.std
+      punct.period 'this.status.punct :=
+      note #1 #1 substring$
+      duplicate$ "{" =
+        { skip$ }
+        { status.cap
+          { "u" }
+          { "l" }
+        if$
+        change.case$
+        }
+      if$
+      note #2 global.max$ substring$ * "note" bibinfo.check
+      cap.yes  'status.cap :=
+    }
+  if$
+}
+
+
+
+%% patent
+
+FUNCTION {format.patent.date}
+{ this.to.prev.status
+  this.status.std
+  year empty$
+    { monthfiled duplicate$ empty$
+        { "monthfiled" bibinfo.check pop$ "" }
+        { "monthfiled" bibinfo.check }
+      if$
+      dayfiled duplicate$ empty$
+        { "dayfiled" bibinfo.check pop$ "" * }
+        { "dayfiled" bibinfo.check 
+          monthfiled empty$ 
+             { "dayfiled without a monthfiled in " cite$ * warning$
+               * 
+             }
+             { " " swap$ * * }
+           if$
+        }
+      if$
+      yearfiled empty$
+        { "no year or yearfiled in " cite$ * warning$ }
+        { yearfiled "yearfiled" bibinfo.check 
+          swap$
+          duplicate$ empty$
+             { pop$ }
+             { ", " * swap$ * }
+           if$
+        }
+      if$
+    }
+    { month duplicate$ empty$
+        { "month" bibinfo.check pop$ "" }
+        { "month" bibinfo.check }
+      if$
+      day duplicate$ empty$
+        { "day" bibinfo.check pop$ "" * }
+        { "day" bibinfo.check 
+          month empty$ 
+             { "day without a month in " cite$ * warning$
+               * 
+             }
+             { " " swap$ * * }
+           if$
+        }
+      if$
+      year "year" bibinfo.check 
+      swap$
+      duplicate$ empty$
+        { pop$ }
+        { ", " * swap$ * }
+      if$
+    }
+  if$
+  cap.status.std
+}
+
+FUNCTION {format.patent.nationality.type.number}
+{ this.to.prev.status
+  this.status.std
+  nationality duplicate$ empty$
+    { "nationality" bibinfo.warn pop$ "" }
+    { "nationality" bibinfo.check
+      duplicate$ "l" change.case$ "united states" =
+        { pop$ bbl.patentUS }
+        { skip$ }
+      if$
+      " " *
+    }
+  if$
+  type empty$
+    { bbl.patent "type" bibinfo.check }
+    { type "type" bibinfo.check }
+  if$  
+  *
+  number duplicate$ empty$
+    { "number" bibinfo.warn pop$ }
+    { "number" bibinfo.check
+      large.number.separate
+      swap$ " " * swap$ *
+    }
+  if$ 
+  cap.status.std
+}
+
+
+
+%% standard
+
+FUNCTION {format.organization.institution.standard.type.number}
+{ this.to.prev.status
+  this.status.std
+  organization duplicate$ empty$
+    { pop$ 
+      institution duplicate$ empty$
+        { "institution" bibinfo.warn }
+        { "institution" bibinfo.warn " " * }
+      if$
+    }
+    { "organization" bibinfo.warn " " * }
+  if$
+  type empty$
+    { bbl.standard "type" bibinfo.check }
+    { type "type" bibinfo.check }
+  if$  
+  *
+  number duplicate$ empty$
+    { "number" bibinfo.check pop$ }
+    { "number" bibinfo.check
+      large.number.separate
+      swap$ " " * swap$ *
+    }
+  if$ 
+  cap.status.std
+}
+
+FUNCTION {format.revision}
+{ revision empty$
+    { "" }
+    { this.to.prev.status
+      this.status.std
+      bbl.revision
+      revision tie.or.space.prefix
+      "revision" bibinfo.check
+      * *
+      cap.status.std
+    }
+  if$
+}
+
+
+%% thesis
+
+FUNCTION {format.master.thesis.type}
+{ this.to.prev.status
+  this.status.std
+  type empty$
+    {
+      bbl.mthesis
+    }
+    { 
+      type "type" bibinfo.check
+    }
+  if$
+cap.status.std
+}
+
+FUNCTION {format.phd.thesis.type}
+{ this.to.prev.status
+  this.status.std
+  type empty$
+    {
+      bbl.phdthesis
+    }
+    { 
+      type "type" bibinfo.check
+    }
+  if$
+cap.status.std
+}
+
+
+
+%% URL
+
+FUNCTION {format.url}
+{ url empty$
+    { "" }
+    { this.to.prev.status
+      this.status.std
+      cap.yes 'status.cap :=
+      bbl.urlprefix " " * 
+      "\url{" * url * "}" *
+      punct.no 'this.status.punct :=
+      punct.period 'prev.status.punct :=
+      space.normal 'this.status.space :=
+      space.normal 'prev.status.space :=
+      quote.no 'this.status.quote :=
+    }
+  if$
+}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% ENTRY HANDLERS %%
+%%%%%%%%%%%%%%%%%%%%
+
+
+% Note: In many journals, IEEE (or the authors) tend not to show the number
+% for articles, so the display of the number is controlled here by the
+% switch "is.use.number.for.article"
+FUNCTION {article}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.journal "journal" bibinfo.check "journal" output.warn
+  format.volume output
+  format.number.if.use.for.article output
+  format.pages output
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {book}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  author empty$
+    { format.editors "author and editor" output.warn }
+    { format.authors output.nonnull }
+  if$
+  name.or.dash
+  format.book.title.edition output
+  format.series output
+  author empty$
+    { skip$ }
+    { format.editors output }
+  if$
+  format.address.publisher.date output
+  format.volume output
+  format.number output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {booklet}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.article.title "title" output.warn
+  format.howpublished "howpublished" bibinfo.check output
+  format.organization "organization" bibinfo.check output
+  format.address "address" bibinfo.check output
+  format.date output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {electronic}
+{ std.status.using.period
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.date.electronic output
+  format.article.title.electronic output
+  format.howpublished "howpublished" bibinfo.check output
+  format.organization "organization" bibinfo.check output
+  format.address "address" bibinfo.check output
+  format.note output
+  format.url output
+  fin.entry
+  empty.entry.warn
+  if.url.std.interword.spacing
+}
+
+FUNCTION {inbook}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  author empty$
+    { format.editors "author and editor" output.warn }
+    { format.authors output.nonnull }
+  if$
+  name.or.dash
+  format.book.title.edition output
+  format.series output
+  format.address.publisher.date output
+  format.volume output
+  format.number output
+  format.chapter output
+  format.pages output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {incollection}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.in.booktitle.edition "booktitle" output.warn
+  format.series output
+  format.editors output
+  format.address.publisher.date.nowarn output
+  format.volume output
+  format.number output
+  format.chapter output
+  format.pages output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {inproceedings}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.in.booktitle "booktitle" output.warn
+  format.series output
+  format.editors output
+  format.volume output
+  format.number output
+  publisher empty$
+    { format.address.organization.date output }
+    { format.organization "organization" bibinfo.check output
+      format.address.publisher.date output
+    }
+  if$
+  format.paper output
+  format.pages output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {manual}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.book.title.edition "title" output.warn
+  format.howpublished "howpublished" bibinfo.check output 
+  format.organization "organization" bibinfo.check output
+  format.address "address" bibinfo.check output
+  format.date output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {mastersthesis}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.master.thesis.type output.nonnull
+  format.school "school" bibinfo.warn output
+  format.address "address" bibinfo.check output
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {misc}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.article.title output
+  format.howpublished "howpublished" bibinfo.check output 
+  format.organization "organization" bibinfo.check output
+  format.address "address" bibinfo.check output
+  format.pages output
+  format.date output
+  format.note output
+  format.url output
+  fin.entry
+  empty.entry.warn
+  if.url.std.interword.spacing
+}
+
+FUNCTION {patent}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.article.title output
+  format.patent.nationality.type.number output
+  format.patent.date output
+  format.note output
+  format.url output
+  fin.entry
+  empty.entry.warn
+  if.url.std.interword.spacing
+}
+
+FUNCTION {periodical}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.editors output
+  name.or.dash
+  format.book.title "title" output.warn
+  format.series output
+  format.volume output
+  format.number output
+  format.organization "organization" bibinfo.check output
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {phdthesis}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.phd.thesis.type output.nonnull
+  format.school "school" bibinfo.warn output
+  format.address "address" bibinfo.check output
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {proceedings}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.editors output
+  name.or.dash
+  format.book.title "title" output.warn
+  format.series output
+  format.volume output
+  format.number output
+  publisher empty$
+    { format.address.organization.date output }
+    { format.organization "organization" bibinfo.check output
+      format.address.publisher.date output
+    }
+  if$
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {standard}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors output
+  name.or.dash
+  format.book.title "title" output.warn
+  format.howpublished "howpublished" bibinfo.check output 
+  format.organization.institution.standard.type.number output
+  format.revision output
+  format.date output
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {techreport}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.howpublished "howpublished" bibinfo.check output 
+  format.institution "institution" bibinfo.warn output
+  format.address "address" bibinfo.check output
+  format.tech.report.number output.nonnull
+  format.date "year" output.warn
+  format.note output
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+FUNCTION {unpublished}
+{ std.status.using.comma
+  start.entry
+  if.url.alt.interword.spacing
+  format.authors "author" output.warn
+  name.or.dash
+  format.article.title "title" output.warn
+  format.date output
+  format.note "note" output.warn
+  format.url output
+  fin.entry
+  if.url.std.interword.spacing
+}
+
+
+% The special entry type which provides the user interface to the
+% BST controls
+FUNCTION {IEEEtranBSTCTL}
+{ is.print.banners.to.terminal
+    { "** IEEEtran BST control entry " quote$ * cite$ * quote$ * " detected." *
+      top$
+    }
+    { skip$ }
+  if$
+  CTLuse_article_number
+  empty$
+    { skip$ }
+    { CTLuse_article_number
+      yes.no.to.int
+      'is.use.number.for.article :=
+    }
+  if$
+  CTLuse_paper
+  empty$
+    { skip$ }
+    { CTLuse_paper
+      yes.no.to.int
+      'is.use.paper :=
+    }
+  if$
+  CTLuse_forced_etal
+  empty$
+    { skip$ }
+    { CTLuse_forced_etal
+      yes.no.to.int
+      'is.forced.et.al :=
+    }
+  if$
+  CTLmax_names_forced_etal
+  empty$
+    { skip$ }
+    { CTLmax_names_forced_etal
+      string.to.integer
+      'max.num.names.before.forced.et.al :=
+    }
+  if$
+  CTLnames_show_etal
+  empty$
+    { skip$ }
+    { CTLnames_show_etal
+      string.to.integer
+      'num.names.shown.with.forced.et.al :=
+    }
+  if$
+  CTLuse_alt_spacing
+  empty$
+    { skip$ }
+    { CTLuse_alt_spacing
+      yes.no.to.int
+      'is.use.alt.interword.spacing :=
+    }
+  if$
+  CTLalt_stretch_factor
+  empty$
+    { skip$ }
+    { CTLalt_stretch_factor
+      'ALTinterwordstretchfactor :=
+      "\renewcommand\BIBentryALTinterwordstretchfactor{"
+      ALTinterwordstretchfactor * "}" *
+      write$ newline$
+    }
+  if$
+  CTLdash_repeated_names
+  empty$
+    { skip$ }
+    { CTLdash_repeated_names
+      yes.no.to.int
+      'is.dash.repeated.names :=
+    }
+  if$
+  CTLname_format_string
+  empty$
+    { skip$ }
+    { CTLname_format_string
+      'name.format.string :=
+    }
+  if$
+  CTLname_latex_cmd
+  empty$
+    { skip$ }
+    { CTLname_latex_cmd
+      'name.latex.cmd :=
+    }
+  if$
+  
+  
+  num.names.shown.with.forced.et.al max.num.names.before.forced.et.al >
+    { "CTLnames_show_etal cannot be greater than CTLmax_names_forced_etal in " cite$ * warning$ 
+      max.num.names.before.forced.et.al 'num.names.shown.with.forced.et.al :=
+    }
+    { skip$ }
+  if$
+}
+
+
+%%%%%%%%%%%%%%%%%%%
+%% ENTRY ALIASES %%
+%%%%%%%%%%%%%%%%%%%
+FUNCTION {conference}{inproceedings}
+FUNCTION {online}{electronic}
+FUNCTION {internet}{electronic}
+FUNCTION {webpage}{electronic}
+FUNCTION {default.type}{misc}
+
+
+
+%%%%%%%%%%%%%%%%%%
+%% MAIN PROGRAM %%
+%%%%%%%%%%%%%%%%%%
+
+READ
+
+EXECUTE {initialize.controls}
+EXECUTE {initialize.status.constants}
+EXECUTE {banner.message}
+
+
+
+% BEGIN sort code based on that of plain.bst
+
+FUNCTION {sortify}
+{ purify$
+  "l" change.case$
+}
+
+INTEGERS { len }
+
+FUNCTION {chop.word}
+{ 's :=
+  'len :=
+  s #1 len substring$ =
+    { s len #1 + global.max$ substring$ }
+    { s }
+  if$
+}
+
+FUNCTION {sort.format.names}
+{ 's :=
+  #1 'nameptr :=
+  ""
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { nameptr #1 >
+        { "   " * }
+        { skip$ }
+      if$
+      s nameptr "{vv{ } }{ll{ }}{  ff{ }}{  jj{ }}" format.name$ 't :=
+      nameptr numnames = t "others" = and
+        { "et al" * }
+        { t sortify * }
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+}
+
+FUNCTION {sort.format.title}
+{ 't :=
+  "A " #2
+    "An " #3
+      "The " #4 t chop.word
+    chop.word
+  chop.word
+  sortify
+  #1 global.max$ substring$
+}
+
+FUNCTION {author.sort}
+{ author empty$
+    { key empty$
+        { "to sort, need author or key in " cite$ * warning$ "" }
+        { key sortify }
+      if$
+    }
+    { author sort.format.names }
+  if$
+}
+
+FUNCTION {author.editor.sort}
+{ author empty$
+    { editor empty$
+        { key empty$
+            { "to sort, need author, editor, or key in " cite$ * warning$ "" }
+            { key sortify }
+          if$
+        }
+        { editor sort.format.names }
+      if$
+    }
+    { author sort.format.names }
+  if$
+}
+
+FUNCTION {author.organization.sort}
+{ author empty$
+    { organization empty$
+        { key empty$
+            { "to sort, need author, organization, or key in " cite$ * warning$ "" }
+            { key sortify }
+          if$
+        }
+        { "The " #4 organization chop.word sortify }
+      if$
+    }
+    { author sort.format.names }
+  if$
+}
+
+FUNCTION {editor.organization.sort}
+{ editor empty$
+    { organization empty$
+        { key empty$
+            { "to sort, need editor, organization, or key in " cite$ * warning$ "" }
+            { key sortify }
+          if$
+        }
+        { "The " #4 organization chop.word sortify }
+      if$
+    }
+    { editor sort.format.names }
+  if$
+}
+
+FUNCTION {author.organization.institution.sort}
+{ author empty$
+    { organization empty$
+        { institution empty$
+            { key empty$
+                { "to sort, need author, organization, institution or key in " cite$ * warning$ "" }
+                { key sortify }
+              if$
+            }
+            { "The " #4 institution chop.word sortify }
+          if$
+        }
+        { "The " #4 organization chop.word sortify }
+      if$
+    }
+    { author sort.format.names }
+  if$
+}
+
+
+FUNCTION {presort}
+{ type$ "ieeetranbstctl" =
+    { key empty$
+        { "_" }
+        { key sortify }
+      if$
+    }
+    { type$ "book" =
+      type$ "inbook" =
+      or 
+        { author.editor.sort }
+        { type$ "proceedings" =
+          type$ "periodical" =
+          or
+            { editor.organization.sort }
+            { type$ "manual" =
+              type$ "electronic" =
+              type$ "misc" =
+              or or
+                { author.organization.sort }
+                { type$ "standard" =
+                   { author.organization.institution.sort }
+                   { author.sort }
+                 if$ 
+                }
+              if$
+            }
+          if$
+        }
+      if$
+      "    "
+      *
+      year empty.field.to.null.string sortify
+      *
+      "    "
+      *
+      title empty.field.to.null.string
+      sort.format.title
+      *
+    }
+  if$
+  #1 entry.max$ substring$
+  'sort.key$ :=
+}
+
+ITERATE {presort}
+
+SORT
+
+% END sort code based on that of plain.bst
+
+
+
+EXECUTE {initialize.longest.label}
+ITERATE {longest.label.pass}
+
+EXECUTE {begin.bib}
+ITERATE {call.type$}
+EXECUTE {end.bib}
+
+EXECUTE{completed.message}
+
+
+%% That's all folks, mds.
diff --git a/IEEEtrantools.sty b/IEEEtrantools.sty
new file mode 100644
index 0000000..c5dec9d
--- /dev/null
+++ b/IEEEtrantools.sty
@@ -0,0 +1,1754 @@
+%%
+%% IEEEtrantools.sty 2002/11/18 version V1.1
+%% 
+%% NOTE: This text file uses UNIX 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 UNIX line feed
+%% character (0x0A).
+%% 
+%% 
+%% This package provides several popular and unique commands from the
+%% IEEEtran.cls class (version 1.6b) file.
+%% 
+%% The provided commands include \PARstart, \IEEEitemize, \IEEEenumerate,
+%% \IEEEdescription as well as the \IEEEeqnarray, \IEEEeqnarraybox family
+%% of commands including support commands such as \IEEEstrut.
+%% Also provides the \bstctlcite command for the control entry types of
+%% IEEEtran.bst V1.00 and later.
+%% 
+%% IEEEtrantools.sty should not be used with IEEEtran.cls.
+%% 
+%% The latest version and documentation of IEEEtrantools can be obtained at:
+%% http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/
+%% 
+%% 
+%% Copyright (c) 2002 by Michael Shell
+%%                       mshell@ece.gatech.edu
+%%                       See the CTAN website above
+%%                       for current contact information.
+%%
+%%**********************************************************************
+%% 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.
+%% Please retain the contribution notices and credits.
+%% 
+%%**********************************************************************
+%%
+%%
+%%
+%% Available package options (e.g., \usepackage[retainorgcmds]{IEEEtrantools}
+%%
+%% retainorgcmds
+%%    Prevents IEEEtrantools from overriding existing LaTeX commands.
+%%    Currently, the only effect is to preserve the original definitions
+%%    of itemize, enumerate and description. The IEEEtran versions are
+%%    always available as IEEEitemize, IEEEenumerate and IEEEdescription.
+%%
+%%*******
+% 11/2002 V1.1 (v1.6b of IEEEtran.cls) changes:
+% 
+% 1) In addition to the IEEE IED lists, the original LaTeX IED style list
+%    environments are now preserved as LaTeXitemize, LaTeXenumerate, and
+%    LaTeXdescription. Also, users can now redefine \makelabel within
+%    IEEE IED list controls. There may be some use for these in specialized
+%    applications. Thanks to Eli Barzilay for suggesting this feature.
+% 
+%%**********************************************************************
+
+
+\ProvidesPackage{IEEEtrantools}[2002/11/18 revision V1.1 by Michael Shell]
+\typeout{-- See the "IEEEtrantools_doc.txt" manual for usage information.}
+\NeedsTeXFormat{LaTeX2e}
+
+
+% If IEEEtran.cls is detected, error.
+{\@ifundefined{IEEEtransversionmajor}{\relax}{%
+\PackageError{IEEEtrantools}{IEEEtrantools is not for use with the\MessageBreak
+                             IEEEtran class}%
+    {Do not load IEEEtrantools - you don't need it.}%
+}}
+
+
+% define new needed flags to indicate document options
+% and set a few "failsafe" defaults
+\newif\if@retainorgcmds       
+\global\@retainorgcmdsfalse
+
+
+
+% IEEEtran class scratch pad registers
+% dimen
+\newdimen\@IEEEtrantmpdimenA
+\newdimen\@IEEEtrantmpdimenB
+% count
+\newcount\@IEEEtrantmpcountA
+\newcount\@IEEEtrantmpcountB
+% token list
+\newtoks\@IEEEtrantmptoksA
+
+
+% declare the options
+\DeclareOption{retainorgcmds}{\@retainorgcmdstrue}
+
+% get and process any supplied options
+\ProcessOptions
+
+
+
+% store the normalsize baselineskip
+\newskip\normalsizebaselineskip
+{\normalsize \global\normalsizebaselineskip\baselineskip\relax}
+% store the nominal value of jot
+\newskip\normaljot
+\normaljot\jot\relax
+
+
+
+
+
+% 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
+% 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, shield end of lines with %
+\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
+% base class should define \description
+\let\LaTeXdescription\description
+\let\endLaTeXdescription\enddescription
+
+
+% override LaTeX's default IED lists, unless the user requested they be retained
+\if@retainorgcmds\relax\else
+\def\itemize{\@IEEEitemize}
+\def\enditemize{\@endIEEEitemize}
+\def\enumerate{\@IEEEenumerate}
+\def\endenumerate{\@endIEEEenumerate}
+\def\description{\@IEEEdescription}
+\def\enddescription{\@endIEEEdescription}
+\fi
+
+
+% provide the user with the IEEE IED commands
+\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}
+
+
+
+
+
+% used only by IEEEtran's IEEEeqnarray as other packages may
+% have their own, different, implementations
+\newcounter{IEEEsubequation}[equation]
+
+% e.g., "1a" (used only by IEEEtran's IEEEeqnarray)
+\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}}
+% just like LaTeX2e's \@eqnnum
+\def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1)
+% IEEEsubequation used only by IEEEtran's IEEEeqnarray
+\def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a)
+
+
+
+
+%%
+%% 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{\PackageError{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
+%%
+
+
+
+
+
+
+
+
+
+% \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.
+% 
+% We generalize things via control macros - playing with these is fun too.
+% For IEEEtrantools, we do not use a "@" in the names as these are user
+% alterable controls.
+% 
+% 
+% the number of lines that are indented to clear it
+\providecommand{\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
+\providecommand{\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.
+\providecommand{\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. 
+\providecommand{\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}}
+
+
+% 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}
+
+
+
+
+% Provide support for the control entries of IEEEtran.bst V1.00 and later.
+\providecommand{\bstctlcite}[1]{\@bsphack
+  \@for\@citeb:=#1\do{%
+    \edef\@citeb{\expandafter\@firstofone\@citeb}%
+    \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi}%
+  \@esphack}
+
+
+
+
+\endinput
+%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtrantools.sty  %%%%%%%%%%%%%%%%%%%%%%
+% That's all folks!
+
diff --git a/Public.tex b/Public.tex
new file mode 100644
index 0000000..596811c
--- /dev/null
+++ b/Public.tex
@@ -0,0 +1,45 @@
+\documentclass[12pt,letterpaper]{report}
+\usepackage{fullpage}
+
+%========= Document start
+\begin {document}
+
+
+\thispagestyle{empty}
+
+\noindent{\bf Public Abstract }\\
+\\
+First Name: Ryan\\
+Middle Name: James\\
+Last Name: Calhoun\\
+Adviser's First Name: Jeffrey\\
+Adviser's Last Name: Uhlmann\\
+Co-Adviser's First Name:\\
+Co-Adviser's Last Name:\\
+Graduation Term: SP 2008\\
+Department: Computer Science\\
+Degree: MS\\
+Title: On the Relationship Between Generalized Covariance Union and the Minimal Enclosing Ellipsoid
+Problem
+\\
+\\
+\indent An important tool in the field of data fusion called Generalized Covariance Union (GCU) is used to combine
+or merge probabilistic estimates or measurements, given in standard statistical notation. For easier
+visualization during the course of research, it is common to represent the quantities involved using a set of
+ellipsoids (in two dimensions, a set of ellipses). In the case of GCU, the results surprisingly appear
+equivalent to finding a Minimal Enclosing Ellipsoid of Ellipsoids (MEEE), a problem from computational
+geometry.
+\\
+\indent This thesis presents a means to analyze and test this described behavior numerically, detailing the one-
+and two-dimensional cases, using mathematics which can be easily extended into higher dimensions. The
+current hypothesis, supported by experimental evidence, is that the relationship between GCU and the
+MEEE problem is one of equivalence.
+\\
+\indent Subsequent to this finding, pending a formal proof, it will be possible
+to apply tools from computational geometry to solve data fusion problems.
+
+
+\thispagestyle{empty}
+
+
+\end{document}
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..a01eadc
--- /dev/null
+++ b/README.md
@@ -0,0 +1,3 @@
+# thesis
+
+This is my thesis.
diff --git a/Thesis.tex b/Thesis.tex
new file mode 100644
index 0000000..b55a468
--- /dev/null
+++ b/Thesis.tex
@@ -0,0 +1,138 @@
+%\documentclass[12pt,letterpaper,twoside]{report}
+\documentclass[12pt,letterpaper]{report}
+\linespread{1.67} % Linespacing for entire thesis
+% Standard packages
+\usepackage{graphicx} % PostScript figures
+\usepackage[centertags,fleqn]{amsmath}
+\usepackage{amsfonts} 
+\usepackage{amsbsy}
+\usepackage{amssymb}
+\usepackage{subfig}
+\usepackage{caption}
+\usepackage{amsthm,amstext}
+\usepackage{newlfont} 
+%\usepackage[hang]{subfigure} \usepackage{portland}
+\usepackage{multirow}
+\usepackage{verbatim}
+\usepackage{url}
+\usepackage{euscript}
+\usepackage{algorithmic}
+%\usepackage{dashbox}
+\usepackage{setspace} % 1.5 spacing
+\usepackage{longtable}
+\usepackage[fancyhdr]{UMCCsThesis} % Thesis style
+\usepackage{color}
+\usepackage{float}
+\floatstyle{ruled}
+%\newfloat{algorithm}{htbp}{loa}
+%\floatname{algorithm}{Algorithm}
+\usepackage{upgreek,fontenc}
+\usepackage[retainorgcmds]{IEEEtrantools}
+
+%\usepackage{parsetree}
+
+\hyphenpenalty=100
+\tolerance=5000
+
+
+% Defines name, thesis title, etc.
+\usepackage{myowndef}
+\include{myeqns}
+
+%Define some commonly used macros here
+\newcommand{\nl}{\newline\indent} 
+\renewcommand{\algorithmiccomment}[1]{ //\texttt{#1}}
+\newcommand{\ac}{\algorithmiccomment}
+\def\headrulehook{\color{black}} % Color the header rule
+
+% Line spacing -----------------------------------------------------------
+\newlength{\defbaselineskip}
+\setlength{\defbaselineskip}{\baselineskip}
+\newcommand{\setlinespacing}[1]%
+           {\setlength{\baselineskip}{#1 \defbaselineskip}}
+\renewcommand{\doublespacing}{\setlength{\baselineskip}%
+                           {1.0 \defbaselineskip}}
+\renewcommand{\singlespacing}{\setlength{\baselineskip}{\defbaselineskip}}
+
+%========= Document start
+\begin {document}
+% Title pages
+\include{chapters/cover}
+%===== Justification, spacing for the main text
+%\raggedbottom
+
+%========= Acknowledgments
+\pagenumbering{roman}
+\typeout{}
+\setcounter{page}{2}
+\addcontentsline{toc}{chapter}{Acknowledgments}
+\include{chapters/acknowledgment}
+
+%========== Tables of contents, figures, tables
+\tableofcontents
+\setcounter{tocdepth}{3}
+\newpage
+\addcontentsline{toc}{chapter}{List of Figures}
+\listoffigures
+\newpage
+\addcontentsline{toc}{chapter}{List of Tables}
+\listoftables
+
+%========= List of acronyms
+%\newpage
+%\typeout{}
+%\clearpage
+%\addcontentsline{toc}{chapter}{Acronyms}
+%\include{chapters/acronyms}
+
+%========= Definition of terms
+%\newpage
+%\typeout{}
+%\clearpage
+%\addcontentsline{toc}{chapter}{Definitions}
+%\include{chapters/definitions}
+
+
+%========== Abstract ==============
+\newpage
+\addcontentsline{toc}{chapter}{Abstract}
+\typeout{}
+\clearpage
+\include{chapters/abstract}
+
+
+%========= Main Body ==============
+\cleardoublepage
+\pagenumbering{arabic}
+
+\typeout{}
+\include{chapters/chapter1}
+
+\typeout{}
+\include{chapters/chapter2}
+
+\typeout{}
+\include{chapters/chapter3}
+
+\typeout{}
+\include{chapters/chapter4}
+
+\typeout{}
+\include{chapters/chapter5}
+
+
+%========== Appendices==================
+%\appendix
+
+%========== Bibliography
+\typeout{}
+\linespread{1.0}
+\setlinespacing{1.0}
+\bibliography{chapters/citations.bib}
+\bibliographystyle{IEEEtran}	
+
+%========== VITA
+%\typeout{}
+%\linespread{1.66}
+%\include{chapters/vita}
+\end{document}
diff --git a/ThesisPresentation.ppt b/ThesisPresentation.ppt
new file mode 100644
index 0000000..6b4097d
Binary files /dev/null and b/ThesisPresentation.ppt differ
diff --git a/UMCCsThesis.sty b/UMCCsThesis.sty
new file mode 100644
index 0000000..5f8af3c
--- /dev/null
+++ b/UMCCsThesis.sty
@@ -0,0 +1,259 @@
+% Style file for LaTeX2e
+%   - for use with documentclass report
+%     \usepackage [fancyhdr]{McECEThesis}
+
+% $Id: McECEThesis.sty,v 1.9 2000/03/26 12:46:34 pkabal Exp $
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{UMCCsThesis}[2000/03/15]
+
+\newif\if@fancyhdr
+\DeclareOption{fancyhdr}{\@fancyhdrtrue}
+\DeclareOption{plainhdr}{\@fancyhdrfalse}
+
+\ExecuteOptions{plainhdr}
+\ProcessOptions
+
+%================== page layout
+\newdimen \insidemargin
+\newdimen \outsidemargin
+\newdimen \abovemargin
+\newdimen \belowmargin
+
+%===== page layout defined by 4 dimensions, others are calculated from these
+% Define the side margins for a right-side page
+\insidemargin = 1.5in		% Actual space
+\outsidemargin = 1.0in
+
+% Above margin is space above the header
+% Below margin is space below footer
+\abovemargin = 1.0in		% Actual space
+\belowmargin = 1.0in
+%=====
+
+% Leave more space for the header (originally 12pt)
+\headheight = 15pt
+
+% Other parameters retain their default values (values for 12pt documents)
+% \headsep - space from bottom of header to top of text (25pt)
+% \footskip - distance from the bottom of text to bottom of footer (30pt)
+
+% The rest of the dimensions are calculated from the above values
+% (compensation for TeX 1in margin offsets is done here)
+\textwidth = \paperwidth
+  \advance\textwidth by -\insidemargin
+  \advance\textwidth by -\outsidemargin
+\textheight = \paperheight
+  \advance \textheight by -\abovemargin
+  \advance \textheight by -\headheight
+  \advance \textheight by -\headsep
+  \advance \textheight by -\belowmargin
+  \advance \textheight by -\footskip
+\topmargin = \abovemargin
+  \advance \topmargin by -1in
+
+\oddsidemargin = \insidemargin
+  \advance\oddsidemargin by -1in
+\if@twoside
+  \evensidemargin = \outsidemargin
+    \advance\evensidemargin by -1in
+\else
+  \evensidemargin = \oddsidemargin
+\fi
+
+%========= Redefine \cleardoublepage to use pagestyle plain
+% Notes:
+%  \include xxx
+%      expands to \clearpage \input xxx.tex \clearpage
+%  \chapter
+%      expands to \clearpage  OR \cleardoublepage
+%                 \thispagestyle{plain}
+%                  ...
+% \cleardoublepage is modified to output an empty page with pagestyle plain
+% for headings and footers.
+\renewcommand{\cleardoublepage}{%
+  \clearpage
+  \if@twoside
+    \ifodd\c@page
+    \else
+      \hbox{}\thispagestyle{plain}\newpage
+      \if@twocolumn \hbox{}\newpage \fi
+    \fi
+  \fi}
+
+%========= Redefine \thebibliography to put a entry in the TOC
+%========= Change the name from "Bibliography" to "References"
+\renewcommand\bibname{References}
+\let\SV@thebibliography\thebibliography
+\renewcommand{\thebibliography}[1]{%
+  \if@twoside
+    \cleardoublepage
+  \else
+    \clearpage
+  \fi
+  \addcontentsline{toc}{chapter}{\bibname}
+  \SV@thebibliography{#1}}
+
+%========= Dummy definitions if datestamp package is not loaded
+\ifx\datestampbox\@undefined
+  \let\datestampbox=\relax
+  \def\rcs #1{}
+\fi
+
+%========= Fancy headings setup
+% Single-sided printing
+%   header:   3.2 Section        5
+%             --------------------
+% Double-sided printing
+%   header:   4            Chapter
+%   even      --------------------
+%
+%   header:   3.2 Section        5
+%   odd       --------------------
+%
+
+\if@fancyhdr
+  \RequirePackage{fancyhdr}
+  \pagestyle{fancy}
+  \if@twoside
+    \renewcommand{\chaptermark}[1]{\markboth{\upshape \bfseries \scriptsize #1}{}}
+    \renewcommand{\sectionmark}[1]{\markright { \upshape \bfseries \scriptsize \thesection\hspace{5pt} #1}}
+    \fancyhf{}			% clear all fields
+    \fancyhead[LE,RO]{\bfseries \thepage}
+    \fancyhead[LO]{\bfseries \nouppercase{\rightmark}}
+    \fancyhead[RE]{\bfseries \nouppercase{\leftmark}}
+    \fancyfoot[LO,RE]{}
+  \else
+  	\renewcommand{\chaptermark}[1]{\markboth{\upshape \bfseries \scriptsize #1}{}}
+    \renewcommand{\sectionmark}[1]{\markright { \upshape \bfseries \scriptsize \thesection\hspace{5pt} #1}}
+    \fancyhf{}			% clear all fields
+    \fancyhead[LE,RO]{\bfseries \thepage}
+    \fancyhead[LO]{\bfseries \nouppercase{\rightmark}}
+    \fancyhead[RE]{\bfseries \nouppercase{\leftmark}}
+    \fancyfoot[LO,RE]{}
+    %\renewcommand{\chaptermark}[1]{\markright{\thechapter\ #1}}
+    %\renewcommand{\sectionmark}[1]{}
+    %\fancyhf{}			% clear all fields
+    %\fancyhead[RE,RO]{\bfseries \thepage}
+    %\fancyhead[LE,LO]{\bfseries \nouppercase{\rightmark}}
+    %\fancyfoot[LO,RE]{\datestampbox}
+  \fi
+
+  \renewcommand{\footrulewidth}{0pt}
+  \renewcommand{\headrulewidth}{0.4pt}
+  \def\headrule{{\headrulehook
+                 \hrule height\headrulewidth width\headwidth
+                 \vskip-\headrulewidth}}
+  \def\headrulehook{}
+% Notes:
+%  - \nouppercase is to knock out the hardwired uppercase in
+%    contents and bibliography
+%  - \headrulehook can used for colour, e.g. \def\headrulehook{color{red}}
+
+% Redefine plain style (used by \chapter) to just a page number at the top
+  \fancypagestyle{plain}{%
+    \fancyhf{}			% clear all fields
+    \fancyhead[LE,RO]{\bfseries \thepage}%
+    \fancyfoot[LO,RE]{\datestampbox}}
+
+\fi
+
+%================== title page
+
+% Date set as "August 1996"
+\def\Month{\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}
+\date{\Month\ \number\year}
+
+% Organization
+\newcommand\organization[1]{\def\@organization{#1}}
+\def\@organization{\@latex@warning@no@line{No \noexpand\organization given}}
+
+% Note
+\newcommand\note[1]{\def\@note{#1}}
+\def\@note{\@latex@warning@no@line{No \noexpand\note given}}
+
+% Redefine the \maketitle macro (separate page) with new layout
+% This is a simplified version of the LaTeX \maketitle macro, since we
+% need only worry about a single author and a single institution.
+\renewcommand\maketitle{\begin{titlepage}%
+  \let\footnotesize\small
+  \let\footnoterule\relax
+  \let \footnote \thanks
+
+% Reset the page style to empty
+  \pagestyle{empty}
+
+% -- vertical space --
+% Title with \LARGE \bfseries
+% Author with \Large \itshape
+% Organization with \large
+% Date with \large
+% -- vertical space --
+% Note
+
+  \begin{center}%
+    \null\vfil \vskip 60\p@	% vertical centering (extra 60pt at top)
+    {\LARGE \bfseries \@title \par}%
+    \vskip 10ex%
+   {\Large \itshape \@author}%
+    \vskip 6ex%
+    {\normalsize
+     \lineskip 0.5em%
+     \begin{tabular}[t]{c}%
+       \@organization
+     \end{tabular}\par}%
+    \vskip 6ex%
+    {\large \@date \par}%
+    \vskip 5em%
+    \vfil\null			% vertical centering
+    \@note
+  \end{center}\par
+  \@thanks
+
+  \end{titlepage}%
+
+% Reset macros
+  \setcounter{footnote}{0}%
+  \global\let\thanks\relax
+  \global\let\maketitle\relax
+  \global\let\@thanks\@empty
+  \global\let\@author\@empty
+  \global\let\@date\@empty
+  \global\let\@title\@empty
+  \global\let\title\relax
+  \global\let\author\relax
+  \global\let\date\relax
+  \global\let\and\relax
+}
+
+%================== general changes
+% Smaller section and subsection heads, ragged right
+% [classes.dtx]
+\def\veryraggedright{\advance\rightskip by 0pt plus 1fil\relax}
+\renewcommand\section{\@startsection {section}{1}{\z@}%
+	{-3.5ex \@plus -1ex \@minus -.2ex}%
+	{2.3ex \@plus.2ex}%
+	{\normalfont\large\bfseries\veryraggedright}}
+\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
+	{-3.25ex\@plus -1ex \@minus -.2ex}%
+	{1.5ex \@plus .2ex}%
+	{\normalfont\bfseries\veryraggedright}}
+
+
+% Placement of figures and tables htbp instead of tbp
+% Figure name, Table name in bold
+% [classes.dtx]
+\renewcommand\fps@figure{htbp}
+\renewcommand\fps@table{htbp}
+\renewcommand\fnum@figure{{\reset@font\bfseries\figurename~\thefigure}}
+\renewcommand\fnum@table{{\reset@font\bfseries\tablename~\thetable}}
+
+% Less space between the number and the section title (1em -> 0.5em)
+% [ltsect.dtx]
+\renewcommand\@seccntformat[1]{\csname the#1\endcsname\hskip 0.5em}
+
+
+% Figure name becomes "Fig." (was "Figure")
+\renewcommand\figurename{Fig.}
diff --git a/chapters/abstract.tex b/chapters/abstract.tex
new file mode 100644
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--- /dev/null
+++ b/chapters/abstract.tex
@@ -0,0 +1,6 @@
+\thispagestyle{plain}
+\section*{\centering Abstract}
+\vspace{40pt}
+\hspace{15pt}
+\input{chapters/abstract_text}
+\thispagestyle{plain}
diff --git a/chapters/abstract_text.tex b/chapters/abstract_text.tex
new file mode 100644
index 0000000..f5af79d
--- /dev/null
+++ b/chapters/abstract_text.tex
@@ -0,0 +1,10 @@
+\hspace{15pt} Examination of the behavior of Generalized Covariance Union (GCU) reveals a previously unsuspected superficial
+relationship to the problem of finding a minimal enclosing ellipsoid of ellipsoids, also called a L\"owner ellipsoid. By
+interpreting any mean and covariance pair of some estimate or measurement as the 1-$\sigma$ contour ellipsoid of its
+associated Gaussian probability density function, the results of GCU appear to form a L\"owner 1-$\sigma$ ellipsoid
+about the 1-$\sigma$ ellipsoids of its $n$ inputs. This thesis presents a means to analyze and test this behavior
+numerically, detailing the one- and two-dimensional cases, using mathematics easily extensible into higher dimensions.
+The current hypothesis, supported by experimental evidence, is that the relationship between GCU and the minimal
+enclosing ellipsoid problem is one of equivalence. Subsequent to this finding, pending a formal proof, it will be
+possible to apply tools from computational geometry to solve data fusion problems.
+
diff --git a/chapters/acknowledgment.tex b/chapters/acknowledgment.tex
new file mode 100644
index 0000000..d262d6e
--- /dev/null
+++ b/chapters/acknowledgment.tex
@@ -0,0 +1,7 @@
+%\setcounter{page}{2} 
+\section*{\centering Acknowledgments}
+\hspace{15pt} I extend my greatest appreciation to my adviser, Dr. Jeffrey Uhlmann, for his constant support and
+guidance. I thank him for his endless patience and dedication, without which this thesis could not have been realized.
+He is the greatest mentor, teacher and friend, for which any student could ask. I also thank Dr. Simon Julier and Ottmar
+Boschardt for their ideas and insight, which proved invaluable as this thesis progressed.
+       
diff --git a/chapters/chapter1.tex b/chapters/chapter1.tex
new file mode 100644
index 0000000..6bab4df
--- /dev/null
+++ b/chapters/chapter1.tex
@@ -0,0 +1,100 @@
+\chapter{Introduction}\label{chapter:introduction}
+
+\section{Background Information}
+
+\PARstart{O}{ver} the last decade, Level-1 information management has matured significantly, with the development of
+rigorous algorithms robust to the effects of unmodeled correlations, and corrupt and/or spurious information, in the
+context of general distributed data fusion networks. Recent inroads into the development of higher level information
+management applications have yielded significant improvements to the data fusion tool called Covariance Union
+(CU)~\cite{uhlmann03,julier05}. CU is used to find the union of a set of input modes or state estimates in a way that
+guarantees an accurate representation of the system's true state in circumstances when other tools may not; simply put,
+it is a method to reduce many modes to one.
+
+A higher level data fusion application is likely manage information in a multimodal scheme, using either Multi
+Hypothesis Tracking (MHT) or a Gaussian Mixture Model (GMM). MHT maintains multiple location and uncertainly estimates
+corresponding to distinct possible states~\cite{barshalom88}. GMM is a parametrization of the Probability Density
+Function (PDF) that describes the uncertainty distribution across the application. Since PDF approximations typically
+only represent the significant modes of the distribution in terms of their mean and covariance, the representation
+differs from that of MHT only in that a GMM interprets each mode as an explicit Gaussian PDF~\cite{fusion06}. Since
+the implementation of these two techniques is identical, this thesis will use the GMM convention, of the form
+  \begin{equation}\label{eqn:gmm}
+    p(\mathbf{x})=\sum_{i=1}^Np_i\gaussN{\mathbf{x};\mu{_i},\sigma_i\sigma_i^T},
+  \end{equation}
+whenever referring to a multimodal state estimate, with the understanding that a Gaussian MHT model will be equivalent.
+
+The fusion of a set $S$ of location and uncertainty estimates---each defining a possible state of the target, only one
+of which is guaranteed to be consistent---with another set $T$ can be accomplished simply by forming the Cartesian
+product $S\times T$ and applying the appropriate fusion algorithm (Kalman or Covariance Intersection) to the pairs.
+Unfortunately, this yields a combined estimate that has $O(|S|*|T|)$ modes, which implies that the complexity of the
+fused estimate exceeds that of the original estimates. This increasing complexity will tend to exhaust available
+resources and therefore must be mitigated. CU can be used to combine modes, instead of pruning those deemed unnecessary
+by some metric, and therefore reduce the information complexity of the fused set in a way that correctly estimates the
+cumulative effect of the remaining modes~\cite{fusion06}.
+
+\section{Notation}
+
+Determining how to represent information and uncertainty, in either a single-target application or a multimodal system,
+is a key first step that impacts all aspects of the data fusion problem. The representation must provide both an
+estimate of the state of the target or system of interest {\em and} its associated degree of error or uncertainty, and
+the uncertainty must be defined in a form that permits it to be empirically determined. There must be a rigorous
+algorithm for fusing information in the representation, and the computational complexity of the representation and its
+associated fusion algorithms must be bounded for practical application~\cite{fusion06}.
+
+By far the most widely used information representation is the mean and covariance form, where the mean vector defines
+the best estimate of the state of the target and the error covariance provides an upper bound on the expected squared
+error associated with the mean. For example, the measured position of an object in two dimensions can be represented as
+a vector $\v{m}$ consisting of the object's estimated mean position, e.g., $\v{m} = [x,y]^T$, and an
+error covariance matrix $\m{M}$ that expresses the uncertainty associated with the estimated mean.  If the error in
+the estimated mean vector is denoted as $\ea$, then the error covariance matrix is an estimate of the expected squared
+error, E$[\ea\ea^T]$. The estimate is said to be {\em consistent} (or conservative) if and only if $\m{M}$ $\geq$
+E$[\ea\ea^T]$ or, equivalently, $\m{M}$ - E$[\ea\ea^T]$ is positive definite or semidefinite (i.e., has no negative
+eigenvalues). The full estimate of a target's state is given by the mean and covariance pair
+$(\v{m},\m{M})$~\cite{fusion06,uhlmann03}. Although the GMM convention explicitly defines its own notation, as in
+equation \ref{eqn:gmm}, the mean and covariance notation will be used throughout this thesis whenever referring to any
+probabilistic estimate.
+
+
+\section{Problem Definition}
+
+Generalized Covariance Union (GCU) forms an important part of the hierarchy of data fusion tools which includes the
+Kalman filter, Covariance Intersection, and the optimal form of CU. Each of these tools is capable of generating a
+consistent result over a set of $n$ input estimates $(\v{m}_i,\m{M}_i)$, given certain preconditions. However, practical
+running times for the current implementation of CU and GCU prohibit the use of these tools in any real-time
+applications (operational cost is roughly proportional to the number of estimates $n$, and the cube of the
+dimensionality of the state space)~\cite{fusion06}.
+
+Research into GCU has revealed a remarkable superficial similarity to the problem of finding a Minimal Enclosing
+Ellipsoid of Ellipsoids (MEEE), a common technique from computational geometry and computer graphics. These two problems
+are very different, in the sense that mean and covariance estimates in tracking and data fusion refer to moments of a
+possibly unknown underlying probability distribution, whereas ellipsoidal intersection and containment involves finite
+volumes of space. Despite any differences between GCU and MEEE in representation and formulation, the similarities
+between the results are suggestive of some level of equivalence.
+
+This thesis will examine the GCU optimization problem and the possible applicability of techniques from computational
+geometry, by presenting evidence that GCU and MEEE techniques may in fact be used to solve the same problem.
+
+
+\section{Organization of Thesis}
+
+
+The organization of this thesis is outlined as follows. Chapter \ref{chapter:introduction} begins by providing background
+information and motivation for the research proposed in this thesis. A definition of the problem is given next, to
+outline the scope of the research.
+
+Work leading up to the research presented here is detailed in Chapter \ref{chapter:gcu}. This chapter will present the
+Kalman filter, Covariance Intersection, and Covariance Union as part of a framework of data fusion tools. Generalized
+Covariance Union is presented here as well, after this framework has been established.
+
+Chapter \ref{chapter:meee} will define the problem of finding a Minimal Enclosing Ellipsoid of Ellipsoids, and give a
+method to test whether a proposed enclosing ellipsoid properly contains its enclosed ellipsoids, as it should. Also given
+in this chapter is a transformation between mean-covariance space and ellipsoid space, in order to provide a way for the
+GCU and MEEE results to be compared.
+
+Chapter \ref{chapter:analysis} will present the results of this research, experimental evidence and mathematical
+analysis that demonstrate the relationship between GCU and MEEE.
+
+This thesis concludes with a summary of accomplishments and dialog for future work in Chapter
+\ref{chapter:conclusion}.
+
+
+
diff --git a/chapters/chapter2.tex b/chapters/chapter2.tex
new file mode 100644
index 0000000..bec5fe0
--- /dev/null
+++ b/chapters/chapter2.tex
@@ -0,0 +1,313 @@
+\chapter{Generalized Covariance Union}\label{chapter:gcu}
+
+\section{Data Fusion Framework}\label{section:framework}
+
+\PARstart{C}{ovariance Union}, in both its Optimal and Generalized forms, is part of a larger hierarchy of data fusion
+tools which when used properly together cover a broad range of possible situations, and form a robust framework with
+which to build higher-level applications~\cite{fusion06,uhlmann03}. The remainder of this section is given to present
+the previously published portions of this framework, the Kalman filter, Covariance Intersection, and Optimal Covariance
+Union; both as background information and to provide the proper context for Generalized Covariance Union, which is 
+detailed in sections \ref{section:motivation} and \ref{section:gcu}.
+
+
+% SECTION Kalman
+\subsection{Kalman Filter}
+
+The most basic concept of data fusion is the idea that two pieces of information can be ``fused'' to create
+a new piece of information which is ``better'' than the two inputs by some metric. One tool used to perform this action
+is the Kalman filter. The Kalman filter addresses the general problem of trying to estimate the state $\v{x}\in\Re$  of
+a discrete-time controlled process that is governed by the linear stochastic difference equation
+\begin{equation}\label{eqn:kalsto}
+    \v{x}_k = \m{A}\v{x}_{k-1} + \m{B}\v{u}_k + \v{w}_{k-1} ,
+\end{equation}
+with a measurement $\v{z}\in\Re$ that is
+\begin{equation}\label{eqn:kalmeasure}
+\v{z}_k = \m{H}\v{x}_k + \v{v}_k.
+\end{equation}
+where $\v{w}_k$ and $\v{v}_k$ are random variables which represent the process and measurement noise, respectively,
+where $\m{H}_i$ is the transformation for the state space of the fused estimate to the state space of the
+estimate~\cite{siggraph01}.
+
+The filter operates in two steps for every discrete unit of time. The first step is the projection step, in which the 
+future state of a system is estimated, projecting forward from time step $k-1$ to the current time step $k$. This is 
+given by
+\begin{align}
+    \v{x}^-_k &= \m{A}\v{x}_{k-1}+\m{B}\v{u}_k\\
+    \m{P}^-_k &= \m{A}\m{P}_{k-1}\m{A}^T+\m{Q}
+\end{align}
+where $\m{Q}$ is the process noise covariance defining the PDF for the variable $\v{w}_k$ from equation \ref{eqn:kalsto}.
+The second step is the update step, in which the actual measurements are used to correct the predicted state. This is
+given by
+\begin{align}
+    \v{x}_k &= \v{x}^-_k+\m{K}_k(\v{z}_k-\m{H}\v{x}^-_k)\\
+    \m{P}_k &= (\m{I}-\m{K}_k\m{H})\m{P}^-_k,\\
+\intertext{with}
+    \m{K}_k &= \m{P}^-_k\m{H}^T(\m{H}\m{P}^-_k\m{H}^T+\m{R})^{-1},
+\end{align}
+where $\m{R}$ is the measurement noise covariance defining the PDF for the variable $\v{v}_k$ from equation
+\ref{eqn:kalmeasure}~\cite{siggraph01}.
+
+In addition to a time-sequence of measurements received from the same source, the Kalman filter may also be applied to a
+set of separate measurements from different sources. Given a set of statistically {\em independent} (uncorrelated) estimates
+$(\v{m}_1,\m{M}_1),(\v{m}_2,\m{M}_2),\dots,(\v{m}_n,\m{M}_n)$, the Kalman fusion equations can be written
+as~\cite{uhlmann03,maybeck79}
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/kalman2d.png}
+    \caption{\it 1-$\sigma$ contour plots of two 2D inputs (blue) together with the Kalman fused result (red). Note that
+        these contours are a distance of $\sigma$ away from the mean on a 2D Gaussian surface, and do not represent a
+        closed volume or area. }
+    \label{fig:kalman2d}
+\end{figure}
+\begin{align}
+    \m{C} &= (\m{M}^{-1}_1+\m{M}^{-1}_2+\dots+\m{M}^{-1}_n)^{-1}\label{eqn:kalmanP}\\
+    \v{c} &= \m{C}(\m{M}^{-1}_1\v{m}_1+\m{M}^{-1}_2\v{m}_2+\dots+\m{M}^{-1}_n\v{m}_n).\label{eqn:kalmanx}
+\end{align}
+Figure \ref{fig:kalman2d} illustrates the correct operation of the Kalman filter on two estimates known to be both
+consistent and independent. Although the two input estimates and the fused Kalman result in the example are all 2D
+Gaussian surfaces (which are greater than or equal to some unknown underlying PDF), it is convenient to represent these
+probabilistic models simply by showing the 1-$\sigma$ contour centered at the mean.
+
+In either form, the underlying assumptions in all Kalman applications are consistency and independence. However, any
+presumption of statistical independence should be carefully considered, since virtually any sensor is subject to
+time-correlated errors resulting from the particular conditions of its use; additionally errors associated with the 
+non-linear transformation of its measurements are deterministic and therefore non-independent~\cite{uhlmann03}. For
+example, any changes in temperature, barometric pressure, or humidity which affect the operation of a sensor's internal
+electronics, and their effect on the sensor's accuracy, must be known {\em exactly}, or the assumption of independence
+does not hold.
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/kalman2d-i.png}
+    \caption{\it 1-$\sigma$ contour plots of two 2D inputs (blue) together with the Kalman fused result (red),
+        illustrating a potentially inconsistent result. Note that the 1-$\sigma$ contours of the inputs, which are
+        supposed to be independent estimates of the same position, do not overlap, suggesting that one may be the result
+        of spurious data. One of the means is clear outlier when compared to the Kalman contour.}
+    \label{fig:kalman2d-i}
+\end{figure}
+Figure \ref{fig:kalman2d-i} shows an example of what happens when the precondition for consistency is violated. The two
+input estimates in this example are interpreted by the Kalman filter to be estimates of the same position, yet they are
+far enough apart to suggest that one estimate might be the result of spurious data. Note that the 2D Gaussian surfaces
+represented by the plotted 1-$\sigma$ contours do overlap, but not in the part of the surface that contains the highest
+probability. The Kalman result shown will most likely not be consistent, but there is no way to correct for this
+behavior.
+
+To reiterate, the Kalman filter operates correctly if all its estimates are both consistent and independent.
+
+
+% SECTION 1.2 CI
+\subsection{Covariance Intersection}
+
+Consider here the fusion of two estimates using either the Kalman filter or the data fusion technique known as
+Covariance Intersection (CI), under the following circumstances:~\cite{uhlmann03}
+\begin{enumerate}
+\item {\em The two estimates are independent.} In this case the Kalman filter produces an optimal fused estimate while
+CI produces a consistent, though suboptimal, estimate.
+\item {\em The two estimates are completely correlated.} In this case CI produces an optimal fused estimate while
+Kalman produces an inconsistent estimate.
+\item {\em The two estimates are partially correlated.} In this case CI produces a consistent, though suboptimal,
+estimate while the Kalman filter produces an inconsistent estimate.  \end{enumerate}
+In each case, CI produces a consistent result, allowing it to operate safely in conditions which cause the Kalman filter
+to fail.
+
+The formulation of the CI equations follows from the joint covariance structure which exists between a given pair of
+estimates $(\v{m}_1,\m{M}_1)$ and $(\v{m}_2,\m{M}_2)$
+\begin{equation}\label{eqn:jointcov}
+\left[\begin{array}{cc}
+    \m{M}_1 & \m{X} \\
+    \m{X}^T & \m{M}_2
+\end{array}\right]
+\end{equation}
+where $\m{X}$ represents the actual, but unknown, cross covariance between the two estimates~\cite{uhlmann03}. Without
+complete and exact knowledge of $\m{X}$, the only way to ensure consistency is to identify a joint covariance that is
+guaranteed to be consistent based on the information available. This can be achieved by selecting a scalar value
+$\omega, 0\leq1,$ and verifying that
+\begin{equation}\label{eqn:cijointcov}
+\left[\begin{array}{cc}
+    \frac{1}{\omega}\m{M}_1 & 0 \\
+    0                       & \frac{1}{1-\omega}\m{M}_2
+\end{array}\right]
+\leq
+\left[\begin{array}{cc}
+    \m{M}_1 & \m{X} \\
+    \m{X}^T & \m{M}_2
+\end{array}\right].
+\end{equation}
+
+
+This formulation of the $\omega$-parametrized covariance can be expanded from $2$ to $n$ estimates as follows
+\begin{equation}\label{eqn:ncijointcov}
+\left[\begin{array}{cccc}
+    \omega_1\m{M}^{-1}_1 &                    0 &                    0 &                    0 \\
+                       0 & \omega_2\m{M}^{-1}_2 &                    0 &                    0 \\
+                       0 &                    0 &               \ddots &                    0 \\
+                       0 &                    0 &                    0 & \omega_n\m{M}^{-1}_n
+\end{array}\right],
+\end{equation}
+by selecting $\omega_1\dots\omega_n$ such that $1=\sum_{i=1}^n\omega_i$. By applying the inverse Kalman filter equations
+\ref{eqn:kalmanP} and \ref{eqn:kalmanx} to \ref{eqn:ncijointcov}, the CI fusion equations for $n$ estimates with 
+completely unknown degrees of correlation can be written as
+\begin{figure}[tbp]
+    \centering
+        \subfloat[$\omega_1$=0.05]{\label{fig:ci2d05}\includegraphics[width=0.4\textwidth]{figures/ci2d-05.png}}
+        \subfloat[$\omega_1$=0.25]{\label{fig:ci2d25}\includegraphics[width=0.4\textwidth]{figures/ci2d-25.png}}
+        \subfloat[$\omega_1$=0.50]{\label{fig:ci2d50}\includegraphics[width=0.4\textwidth]{figures/ci2d-50.png}}
+        \subfloat[$\omega_1$=0.75]{\label{fig:ci2d75}\includegraphics[width=0.4\textwidth]{figures/ci2d-75.png}}
+        \subfloat[$\omega_1$=0.95]{\label{fig:ci2d95}\includegraphics[width=0.4\textwidth]{figures/ci2d-95.png}}
+    \caption{\it 1-$\sigma$ contour plots for two 2D input estimates (blue) together with the CI fused result (red), for
+        different values of $\omega$. Note how the CI result contour behaves like an interpolation between these two
+        inputs as $\omega$ varies from 0 to 1. }
+    \label{fig:ci2d}
+\end{figure}
+\begin{align}
+    \m{C} &= \left(\omega_1\m{H}_1^T\m{M}^{-1}_1\m{H}_1+\omega_2\m{H}_2^T\m{M}^{-1}_2\m{H}_2+\dots+\omega_n\m{H}_n^T\m{M}^{-1}_n\m{H}_n\right)\label{eqn:cicov}\\
+    \v{c} &= \m{C}\left(\omega_1\m{H}_1^T\m{M}^{-1}_1\v{m}_1+\omega_2\m{H}_2^T\m{M}^{-1}_2\v{m}_2+\dots+\omega_n\m{H}_n^T\m{M}^{-1}_n\v{m}_n\right)\label{eqn:cimean}
+\end{align}
+where $\m{H}_i$ is the transformation for the state space of the fused estimate to the state space of the estimate $i$
+\cite{uhlmann03,fusion01}.
+
+Figure \ref{fig:ci2d} shows an example of CI performed on a set of two input estimates. Different CI results are shown
+for different values of $\omega$ in the range $(0,1)$, and each possible result is numerically consistent. An application which
+performs CI should select the appropriate $\omega$ to minimize the size, e.g. the determinant, of the fused
+covariance~\cite{uhlmann03}.
+
+To reiterate, CI requires that all of its inputs be consistent, but it will function correctly in the face of partially
+or completely correlated input data \footnote{CI as described here finds the optimal fused result when the correlation
+between its inputs is completely unknown; but another form of CI called Split CI is optimal when the degree of
+correlation is partially known, and the estimates can be represented in split covariance form. See Appendix B
+of~\cite{uhlmann03} for more information.}.
+
+
+
+% SECTION 3 CU
+\subsection{Optimal Covariance Union}\label{section:cu}
+
+In order to develop a completely robust data fusion application, it may be necessary to handle possibly spurious
+measurements prior to any data fusion being performed. If two given estimates $(\v{m}_1,\m{M}_1)$ and
+$(\v{m}_2,\m{M}_2)$ are determined to be mutually inconsistent with each other, i.e. the difference between their means
+is much larger than what can be expected based on their respective error covariance estimates, then using either the
+Kalman filter or CI equations will yield an inconsistent fused result~\cite{uhlmann03}.
+
+Computing the Mahalanobis distance between the two estimates,
+\begin{equation}\label{eqn:mahalanobis}
+(\v{m}_1-\v{m}_2)^T(\m{M}_1+\m{M}_2)^{-1}(\v{m}_1-\v{m}_2),
+\end{equation}
+is one method to detect statistically significant deviations between these estimates (for example, as in figure
+\ref{fig:kalman2d-i}). If such a deviation is detected, it can be assumed one of the estimates is the result of
+spurious measurements or corrupted data, but it may not be possible to detect which of the estimates is at
+fault~\cite{uhlmann03}.
+
+Covariance Union (CU) is a data fusion technique which can be used to resolve such a confliction by finding a union
+estimate which is consistent with both (or all of) its inputs. This union $(\v{u},\m{U})$ is found by minimizing some
+measure of $\m{U}$, e.g. the determinant, subject to the following constraints,
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/cu2d.png}
+    \caption{\it 1-$\sigma$ contour plots of two 2D input estimates (blue) together with the CU result (red).}
+    \label{fig:cu2d}
+\end{figure}
+\begin{align}
+    \m{U}   &\geq   \m{M}_1 + (\v{u}-\v{m}_1)(\v{u}-\v{m}_1)^T\nonumber\\
+    \m{U}   &\geq   \m{M}_2 + (\v{u}-\v{m}_2)(\v{u}-\v{m}_2)^T\nonumber\\
+    ~       &\qquad\vdots\nonumber\\
+    \m{U}   &\geq   \m{M}_n + (\v{u}-\v{m}_n)(\v{u}-\v{m}_n)^T,\label{eqn:cu}
+\end{align}
+for inputs $1$ to $n$. The goal of this operation is to find the location of the mean vector $\v{u}$ having the smallest
+covariance $\m{U}$ that is large enough to guarantee consistency with its $n$ input estimates, regardless of which of the
+$n$ estimates is consistent~\cite{fusion06,uhlmann03}.
+
+In multimodal applications, the inputs to CU are not separate estimates of the same object to be deconflicted, but
+separate modes used to represent the state of a complex or compound object. Performing CU on some or all of these modes
+can be used to reduce the overall information complexity by combining modes, instead of pruning ``unimportant'' modes
+(which would lead to an overestimation of the importance of the remaining modes).
+This is necessary when considering the fusion of a complex set $S$ with another set $T$, which yields a combined
+estimate that has $O(|S|*|T|)$ modes, formed from the Cartesian product $S\times T$. When the fused estimate exceeds the
+complexity of the original estimates for each fusion step, the increasing complexity will tend to exhaust available
+resources~\cite{fusion06}. The CU result is a faithful representation of all the modes it has replaced~\cite{uhlmann03}.
+
+To reiterate, CU operates correctly even if one or more of its modes are inconsistent (as long as one is consistent), at
+the cost of a much larger (less certain) error covariance that the Kalman filter or CI would provide.
+
+
+% MOTIVATION for GCU
+\section{Motivation for Generalized Covariance Union}\label{section:motivation}
+
+The use of Covariance Union in data fusion is intended to guarantee consistency in the presence of spurious
+data. CU is only useful if it will produce a result that is consistent with all of its inputs. However, a common
+scenario arises in which CU will generate a result that is consistent with only one of its inputs (and inconsistent with
+some or all of the others).
+
+Consider the set of measurements $(\v{m}_1,\m{M}_1),(\v{m}_2,\m{M}_2),(\v{m}_3,\m{M}_3)$, which must be combined using
+CU. The union may be computed in two ways:
+\begin{enumerate}
+\item {\em CU is applied to all three estimates simultaneously.}\\
+    $(\v{u},\m{U})=\CU\left((\v{m}_1,\m{M}_1),(\v{m}_2,\m{M}_2),(\v{m}_3,\v{M}_3)\right)$
+\item {\em CU is applied in a pair-wise fashion.}\\
+    $(\v{u}',\m{U}')=\CU\left((\v{m}_1,\m{M}_1),(\v{m}_2,\m{M}_2)\right),$\\
+    $(\v{u},\m{U})=\CU\left((\v{m}_3,\m{M}_3),(\v{u}',\m{U}')\right)$
+\end{enumerate}
+By its definition, given in equation \ref{eqn:cu}, the CU result is guaranteed to be consistent with its inputs. In the
+first case, this means $(\v{u},\m{U})$ is consistent with $(\v{m}_1,\m{M}_1)$, $(\v{m}_2,\m{M}_2)$, and
+$(\v{m}_3,\m{M}_3)$.  In the second case, however, all that is known for certain is that $(\v{u},\m{U})$ is consistent
+with $(\v{m}_3,\m{M}_3)$ and $(\v{u}',\m{U}')$, and separately that $(\v{u}',\m{U}')$ is consistent with
+$(\v{m}_1,\m{M}_1)$ and $(\v{m}_2,\m{M}_2)$. 
+\begin{figure}[tbp]
+    \centering
+        \subfloat[First, the intermediate pairwise result is calculated.]{\label{fig:gcu-i1}\includegraphics[width=0.4\textwidth]{figures/cu2d-i1.png}}
+        \subfloat[Then, that intermediate result is used as input for the final result.]{\label{fig:gcu-iall}\includegraphics[width=0.4\textwidth]{figures/cu2d-iall.png}}
+    \caption{\it 1-$\sigma$ contour plots of three 2D inputs (blue) together with the intermediate (pairwise) Optimal CU result
+        (green) and the final (pairwise) CU result (red). Note that although the intermediate result is consistent with
+        its two inputs, one of the original (blue) inputs is a clear outlier with the final (red) result.}
+    \label{fig:cu2d-i}
+\end{figure}
+
+The nature of CU is to consider only the current state of the problem, i.e. its immediate inputs, and it functions with
+no knowledge of any previous states. Consider an application which gathers a set of $n$ measurements at each discrete
+time step, and may perform CU on some or all of those measurements for later use. If at time step $k$ CU replaces a
+given estimate $(\v{m}_{i|k},\m{M}_{i|k})$ with a consistent union $(\v{u}_{k},\m{U}_{k})$, it does so by shifting the
+mean from $\v{m}_{i|k}$ to $\v{u}_{k}$, and enlarging the covariance by at least the outer product of
+$(\v{u}_{k}-\v{m}_{i|k})$ \cite{uhlmann03}. But if the estimate $(\v{u}_{k},\m{U}_{k})$ is used at time step $k+1$ as an
+input to another CU operation, $\CU_{k+1}$ will have no knowledge of the mean shift that occurred during $\CU_{k}$. Since
+CU finds the optimal, i.e. the tightest, covariance possible for all the inputs, any mean shifting that occurred during
+prior time steps may cause this optimal covariance to be inconsistent for the inputs to those prior time steps
+\cite{fusion06}.
+
+
+% GCU
+\section{Formulation of Generalized Covariance Union}\label{section:gcu}
+In order to address the problems with Optimal CU as defined in section \ref{section:cu}, with regard to inconsistencies
+that arise from a pair-wise or time-sequence application as described in section \ref{section:motivation}, it is
+necessary to use Generalized CU. The generalized form of CU includes an additional parameter $\alpha_i$ per estimate in
+the constraint equations. As with Optimal CU, the goal is to minimize some measure of $\m{U}$, e.g. the determinant. The
+constraints are
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/cu2d-gen-batch.png}
+    \caption{\it 1-$\sigma$ contour plots of three 2D inputs (blue) together with the batch Generalized CU result (red).
+        This is the first time that these 1-$\sigma$ plots appear to exhibit a minimally enclosing behavior.}
+    \label{fig:cu2d-gen-batch}
+\end{figure}
+\begin{align}
+    \m{U}   &\geq    \frac{\m{M}_1}{\alpha_1} + \frac{(\v{u}-\v{m}_1)(\v{u}-\v{m}_1)^T}{1-\alpha_1}\nonumber\\
+    \m{U}   &\geq    \frac{\m{M}_2}{\alpha_2} + \frac{(\v{u}-\v{m}_2)(\v{u}-\v{m}_2)^T}{1-\alpha_2}\nonumber\\
+    ~       &\qquad\vdots\nonumber\\
+    \m{U}   &\geq    \frac{\m{M}_n}{\alpha_n} + \frac{(\v{u}-\v{m}_n)(\v{u}-\v{m}_n)^T}{1-\alpha_n},\label{eqn:gcu}
+\end{align}
+where $\alpha_1\dots\alpha_n$ are in the range $(0,1)$ \cite{fusion06}. Each $\alpha_i$ is equivalent to the $\omega$
+parameter in equation \ref{eqn:cijointcov}~\cite{uhlmann03}, in this context used to prevent either a single covariance
+$\m{M}_i$ or a single mean shift term $(\v{u}-\v{m}_i)$ from dominating the CU calculation. The $\alpha_i$ parameters
+are optimized as part of this calculation to generate the tightest union possible~\cite{fusion06}. The result is
+sub-optimal, but it is necessary to use this form of CU if it is used as part of a pair-wise or time-sequence
+application as described above.  Generalized CU guarantees consistency regardless of how many times its result is
+re-used in future CU operations.
+\begin{figure}[tbp]
+    \centering
+        \subfloat[First, the intermediate pairwise result is calculated.]{\label{fig:gcu-s1}\includegraphics[width=0.4\textwidth]{figures/cu2d-gen-s1.png}}
+        \subfloat[Then, that intermediate result is used as input for the final result.]{\label{fig:gcu-sall}\includegraphics[width=0.4\textwidth]{figures/cu2d-gen-sall.png}}
+    \caption{\it 1-$\sigma$ contour plots of three 2D inputs (blue) together with the intermediate (pairwise) Generalized CU result
+        (green) and the final (pairwise) GCU result (red). Note that the final (red) result is consistent with all of
+        its inputs, including all the original (blue) inputs, even those that were not used as direct inputs.}
+    \label{fig:cu2d-gen-s}
+\end{figure}
+Figure \ref{fig:cu2d-gen-batch} shows GCU applied as a single batch operation, and figure \ref{fig:cu2d-gen-s} shows GCU
+applied pairwise to the same three input estimates. The pairwise application of GCU is shown for completeness, but the
+batch application is of main interest. It is this batch GCU operation, specifically its 1-$\sigma$ contour ellipsoid,
+which will be compared to the MEEE problem.
+
+
+
diff --git a/chapters/chapter3.tex b/chapters/chapter3.tex
new file mode 100644
index 0000000..d0023f4
--- /dev/null
+++ b/chapters/chapter3.tex
@@ -0,0 +1,198 @@
+\chapter{Minimal Enclosing Ellipsoid of Ellipsoids}\label{chapter:meee}
+
+\section{Uses of MEEE}
+
+\PARstart{T}{he idea} of approximating complicated objects using simpler ones is widely used in computational geometry
+and computer graphics. A common approach is to replace a complicated object by a simpler model covering it, such as a
+minimum volume box or a sphere. More recently, ellipsoidal models have been proposed in the literature as they usually
+provide better approximations than bounding boxes or spheres~\cite{yildirim06,sturm03,shiang00,ju01}. The use of simpler
+objects inevitably leads to faster processing times for more responsive applications, ideally with minimal---though not
+insignificant---loss of detail resolution. Recently new algorithms have been developed for the calculation of a minimal
+enclosing ellipsoid; specifically, such an ellipsoid bounding the convex hull of a set of ellipsoids, also known as a
+L\"owner ellipsoid, or L\"owner-John ellipsoid~\cite{yildirim06}.
+
+
+% MAXDET 
+\section{Solving with MAXDET}
+
+The maxdet-problem is a convex optimization problem, minimizing the objective function
+\begin{equation}\label{eqn:maxdetobj}
+    c^T\v{x} + \log \det G(\v{x})^{-1}
+\end{equation}
+subject to
+\begin{align}
+     G(\v{x}) &>     0,\qquad\text{and}\nonumber\\
+     F(\v{x}) &\geq  0,\label{eqn:maxdetcons}
+\end{align}
+where the optimization variable is the vector $\v{x}\in\Re^m$. The Functions 
+$G:\Re^m\rightarrow\Re^{\left|\v{x}\right|}$ and $F:\Re^m\rightarrow\Re^{n\times n}$ are affine:
+\begin{align}
+    G(\v{x}) &= G_0 + \v{x}_1G_1 + \dots + \v{x}_mG_m\nonumber\\
+    F(\v{x}) &= F_0 + \v{x}_1F_1 + \dots + \v{x}_mF_m\label{eqn:maxdet},
+\end{align} 
+where $G_i=G_i^T$ and $F_i=F_i^T$. The objective function is convex on $\{x|G(x)>0\}$ and the constraint set is
+convex~\cite{vandenberghe96}.
+
+A wide class of computational geometry problems can be formulated at maxdet-problems. The formulation of interest is
+that of a minimal volume ellipsoid $\varepsilon_0$ containing $n$ given ellipsoids $\varepsilon_1\dots\varepsilon_n$. The
+given ellipsoids are described as sublevel sets of convex quadratic functions:~\cite{vandenberghe96,boyd04}
+\begin{equation}\label{eqn:ellipse}
+    \varepsilon_i = \{ x | x^TA_ix + 2b_i^Tx + c_i \leq 0 \},\qquad i=0,\dots,n.
+\end{equation}
+The solution can be found by, in the variables $A_0 = A_0^T$, $b_0$, and
+$n$ scalar variables $\tau_i$, minimizing:~\cite{vandenberghe96}
+\begin{equation}\label{eqn:maxdetfun}
+    \log\det A_0^{-1}
+\end{equation}
+subject to
+\begin{equation}\label{eqn:maxdetconstraints}
+    \begin{array}{l}
+    A_0 = A_0^T > 0 ,\\
+    \tau_1 \geq 0,\dots,\tau_n\geq 0 ,\qquad\text{and}\\
+    \left[ \begin{array}{ccc}
+        A_0   & b_0 &  0     \\
+        b_0^T & -1  & b_0^T  \\
+        0     & b_0 & -A_0
+    \end{array} \right]
+    -\tau_i
+    \left[ \begin{array}{ccc}
+        A_i   & b_i & 0 \\
+        b_i^T & c_i & 0 \\
+        0     &   0 & 0 
+    \end{array} \right]
+    \leq 0,\qquad i=1,\dots,n.
+    \end{array}
+\end{equation}
+Here, $c_0$ is given by~\cite{boyd94}
+\begin{equation}
+    c_0=b_0^TA_0^{-1}b_0-1\\
+\end{equation}
+and the final ellipsoid is
+\begin{equation}
+    \varepsilon_0=\{x|x^TA_0x+2b_0^Tx+c_0\leq 0\},
+\end{equation}
+which defines the ellipsoid of least volume containing $\varepsilon_1,\dots,\varepsilon_n$. The formulation for the MEEE
+constraints given in equation \ref{eqn:maxdetconstraints} as a maxdet-problem, as in equation \ref{eqn:maxdet}, 
+is~\cite{vandenberghe96}.
+\begin{align}
+    G(\v{x}) &= I_{n\times n}\nonumber\\
+    F(\v{x}) &= \left[\begin{array}{cccc}
+        A_0 &   &  &  \\
+            & \left[ \begin{array}{ccc}
+                \tau_i A_i - A_0   & \tau_i b_i - b_0 &  0     \\
+                \tau_i b_i^T - b_0^T & \tau_i c_i -1  & -b_0^T  \\
+                0     & -b_0 & A_0
+                \end{array}\right]  &  &  \\
+            &   & \ddots & \\
+            &   &  & 
+                \left[ \begin{array}{ccc}
+                \tau_1 &  &  \\
+                       & \ddots & \\
+                       &       & \tau_n
+            \end{array}\right]
+    \end{array}\right]
+\end{align}
+The variables $A_0$ and $b_0$, and $\tau_1\dots \tau_n$, are solved in-place during the minimization process.
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/ellipse01.png}
+    \caption{\it An example of a minimally enclosing L\"owner 2D ellipsoid containing five ellipsoids,
+        from~\cite{boyd04}. Comparing this plot with figure \ref{fig:cu2d-gen-batch} will illustrate the superficial
+        similarities between GCU and MEEE. }
+    \label{fig:ellipse}
+\end{figure}
+
+Other convex optimization tools may be easily used with the objective function and constraints given in equations
+\ref{eqn:maxdetfun} and \ref{eqn:maxdetconstraints} as well~\cite{boyd04}.
+
+
+% CONTAINMENT
+\section{Testing for Ellipsoid Containment}\label{section:containment}
+
+In the development of any algorithm which finds a minimally enclosing object, it is necessary to also develop a test to
+compare this theoretically enclosing result with its enclosed set. For the MEEE problem, the goal is to test whether one
+ellipsoid properly contains another, i.e. the properly contained ellipsoid does not have any points which fall outside
+the bounding perimeter of the containing ellipsoid~\cite{yildirim06}.
+
+This analysis follows the test for ellipse intersection presented in~\cite{eberly00}. Consider an $n$--dimensional
+ellipsoid $\varepsilon_0$ given by the curve,
+\begin{equation}
+    Q_0 = x^TA_0x + 2b_0^Tx + c_0,
+\end{equation}
+which should contain the $n$--dimensional ellipsoid $\varepsilon_1$ given by the curve,
+\begin{equation}
+    Q_1 = x^TA_1x + 2b_1^Tx + c_1.
+\end{equation}
+All level curves defined by $Q_0(x)=\lambda$ are ellipsoids, except for the minimum negative value of $\lambda$ for
+which the equation defined a single point, the center of every level curve ellipsoid. The ellipsoid defined by
+$Q_1(x)=0$ generally intersects many level curves of $Q_0$. By finding the minimum level value $\lambda_{min}$ and the
+maximum level value $\lambda_{max}$ of $Q_0$ attained by any $x$ on the curve $Q_1$, it is possible to determine the
+spatial relationship between $\varepsilon_0$ and $\varepsilon_1$. If $\lambda_{max}\leq 0$, then only a level curve
+$Q_0(x)\leq 0$ will intersect $Q_1(x)=0$, and $\varepsilon_0$ must properly contain $\varepsilon_1$.
+
+This can be formulated as a constrained minimization that can be solved by the method of Lagrange multipliers: Minimize
+$Q_0(x)$ subject to the constraint that $Q_1(x)=0$. Define $F(x,t)=Q_0(x)+tQ_1(x)$. Differentiating yields $\nabla
+F=\nabla Q_0+t\nabla Q_1$, where the gradient indicated derivative in $x$. Since $\partial{F}/\partial{t}=Q_1$, setting the
+$t$-derivative equal to zero reproduces the constraint $Q_1=0$. Setting the $x$-derivative equal to zero yields $\nabla
+Q_0+t\nabla Q_1=0$ for some $t$. Geometrically, this means the gradients are parallel.
+
+Note that $\nabla Q_i=2A_ix+2b_i$, so
+\begin{equation}
+    0 = \nabla Q_0 + t\nabla Q_1 = 2(A_0+tA_1)x+2(b_0+tb_1).
+\end{equation}
+Solving for $x$ yields
+\begin{equation}\label{eqn:solvex}
+    x = -(A_0+tA_1)^{-1}(b_0+tb_1)=\frac{1}{\delta(t)}Y(t),
+\end{equation}
+where $\delta(t)$ is the determinant of $(A_0+tA_1)$, a polynomial in $t$ of degree $n$, and $Y(t)$ has components in
+$t$ of degree $n$ as well. Replacing this in $Q_1(x)=0$ yields
+\begin{equation}\label{eqn:poly}
+    P(t) = Y(t)^TA_1Y(t)+\delta(t)b_1^TY(t)+\delta(t)^2c_1=0,
+\end{equation}
+a degree $2n$ polynomial in $t$. The roots of $P(t)$ in equation \ref{eqn:poly} can be applied to equation
+\ref{eqn:solvex} to find the critical values for $x$ of $Q_1$. The minimum and maximum values of the evaluation of
+$Q_0(x)$ at the roots of $P(t)$ are respectively $\lambda_{min}$ and $\lambda_{max}$, the minimum and maximum level
+curves which intersect $Q_1$. 
+
+As stated previously, if $\lambda_{max}\leq 0$, then $\varepsilon_0$ properly contains $\varepsilon_1$.
+
+
+% TRANSFORM
+\section{Relating to Generalized Covariance Union}
+
+Before any MEEE results can be compared to GCU, it is necessary to define a set of transforms between the ellipsoid and
+statistical measurement domains.  Since this thesis interprets all estimates (means and covariances) as unweighted
+Gaussian PDFs, i.e.
+\begin{equation}
+    (\v{m}_i,\m{M}_i) := \gaussN{\v{m}_i,\m{M}_i},
+\end{equation}
+each estimate is uniquely transformable to and from the ellipsoid domain, given in equation \ref{eqn:ellipse},
+by representing each as only the 1-$\sigma$ contour ellipsoid on its Gaussian surface. The
+forward transformation into ellipse notation is~\cite{boyd04}
+\begin{align}
+\label{eqn:cu2e}
+\mathbb{T}(\v{m}_i,\m{M}_i) &:= \left\{
+    \begin{aligned}
+        A_i &= \m{M}_i^{-1}\\
+        b_i &= -\m{M}_i^{-1}\v{m}_i\\
+        c_i &= \v{m}_i^T\m{M}_i^{-1}\v{m}_i-1,
+    \end{aligned}
+    \right.
+\intertext{and the backward transformation is}
+\label{eqn:e2cu}
+\mathbb{T}^{-1}(A_i,b_i,c_i) &:= \left\{
+    \begin{aligned}
+        \m{M}_i &= A_i^{-1}\\
+        \m{m}_i &= -A_i^{-1}b_i.
+    \end{aligned}
+    \right.
+\end{align}
+The ellipsoid described by $(A_i,b_i,c_i)$ is centered at $\v{m}_i$, with a radial distance of $\m{M}_i^{\frac{1}{2}}$.
+By interpreting a given Gaussian PDF as an ellipsoid, or a given ellipsoid as the 1-$\sigma$ contour which defines a
+Gaussian PDF, it is possible to directly compare the results of GCU and MEEE.
+
+
+
+
+
+
+
diff --git a/chapters/chapter4.tex b/chapters/chapter4.tex
new file mode 100644
index 0000000..ba59491
--- /dev/null
+++ b/chapters/chapter4.tex
@@ -0,0 +1,453 @@
+\chapter{Analysis}\label{chapter:analysis}
+
+\section{Explanation of $\mathbf{\alpha}$--Parametrized Behavior}\label{section:explanation}
+
+\PARstart{I}{ncluding} the $\alpha_i$ parameter in the Generalized CU constraints, given in equation \ref{eqn:gcu},
+creates an asymptotic scale on which the terms $\m{M}_i$ and $(\v{u}-\v{m}_i)$ are balanced. At the two extremes are the
+following cases:
+\begin{enumerate}
+\item If $\m{M}_i$ is a zero matrix, $\alpha_i$ is allowed to approach 0 as well, and the constraint reduces to
+$\m{U}\geq (\v{u}-\v{m}_i)(\v{u}-\v{m}_i)^T$, and
+\item If $\v{u}$ and $\v{m}_i$ are coincident, $\alpha_i$ is allowed to approach 1, and the constraint reduces to
+$\m{U}\geq \m{M}_i$.
+\end{enumerate}
+For the general case, in which both terms are nonzero, the actual value of $\alpha_i$ will be bounded somewhere between
+0 and 1. It is not important to know this actual value, since it is determined by the optimization process in
+conjunction with the other $n-1$ estimates.
+
+With this knowledge, it is possible to logically reduce the question of whether Generalized CU and MEEE are equivalent.
+First, since it is necessary to satisfy all $n$ constraints in equation \ref{eqn:gcu}, a minimal L\"owner
+ellipsoid $\varepsilon_0$ for $(\v{u},\m{U})$ will be one that completely contains the ellipsoid $\varepsilon_i$ for
+each $(\v{m}_i,\m{M}_i)$ in $i=1\dots n$~\cite{yildirim06}. Second, if the ellipsoid $\tau_i$ for
+$(\v{u},\frac{\m{M}_i}{\alpha_i}+\frac{(\v{u}-\v{m}_i)(\v{u}-\v{m}_i)^T}{1-\alpha_i})$ completely contains
+$\varepsilon_i$, it follows that $\varepsilon_0$ will completely contain $\varepsilon_i$ as well, since $\tau_i$ and
+$\varepsilon_0$ are both centered at $\v{u}$ and $\varepsilon_0$ is at least as large as $\tau_i$. Therefore, if
+$\tau_i$ can be shown to completely enclose $\varepsilon_i$ for all values of $\alpha_i\in (0,1)$, for
+all $i=1\dots n$, then $\varepsilon_0$ is a L\"owner ellipsoid, and Generalized CU and MEEE are in fact equivalent.
+
+Formally, $\varepsilon_i$ and $\tau_i$ are the 1-$\sigma$ ellipsoids transformed by equation \ref{eqn:cu2e}; of
+\begin{align}
+    \displaystyle
+    \varepsilon_i    &= \mathbb{T}\left(\v{m}_i,\m{M}_i\right)\label{eqn:coveps}\\
+    \tau_i(\alpha_i) &=
+\mathbb{T}\left(\v{u},\frac{\m{M}_i}{\alpha_i}+\frac{(\v{u}-\v{m}_i)(\v{u}-\v{m}_i)^T}{1-\alpha_i}\right)\label{eqn:covtau}
+\end{align}
+The containing ellipsoid $\tau_i$ varies with $\alpha_i$, with all other terms constant. An analysis of this behavior
+follows.
+
+
+% 1D
+\section{Describing the Behavior in One Dimension}
+
+Since the 1-$\sigma$ ellipsoid of a Gaussian curve in one variable is a line, the mathematics are extremely simple; it
+becomes extremely easy to visualize and plot the data, and to check the results by hand. Notationally,
+$(\v{m}_i,\m{M}_i)$ is just $(\mu_i,\sigma_i^2)$, and the PDF of the estimate is given by the unweighted Gaussian
+function
+\begin{equation}\label{eqn:gauss1d}
+    \varphi_{\mu_i,\sigma_i^2}(x)=e^\frac{-(\mu_i-x)^2}{2\sigma_i^2}, \end{equation}
+and the 1-$\sigma$ ellipsoid is the band between $\mu_i-1\sigma_i$ and $\mu_i+1\sigma_i$. The $y$ value of the
+1-$\sigma$ line is $\varphi_{\mu_i,\sigma_i^2}(x=\mu_i\pm\sigma_i)=e^{-\frac{1}{2}}\approx0.6065$.
+
+% EXAMPLE 1D CU
+\begin{example}[Generalized CU in One Dimension]\label{ex:gcu1d}
+
+Consider a set of four estimates $(\mu_i,\sigma_i^2)$, given by
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/est1d-4.png}
+    \caption{\it 1D Gaussian curves for four estimate means and covariances, for example \ref{ex:gcu1d}.}
+    \label{fig:est1d-4}
+\end{figure}
+\begin{align}
+    (\mu_1,\sigma_1^2) &= (0.3000,0.1000^2)\\\nonumber
+    (\mu_2,\sigma_2^2) &= (0.1000,0.2000^2)\\\nonumber
+    (\mu_3,\sigma_3^2) &= (0.0000,0.3000^2)\\\nonumber
+    (\mu_4,\sigma_4^2) &= (-0.4000,0.0500^2),\label{ex:est1d-4}
+\end{align}
+shown in figure \ref{fig:est1d-4}. Applying batch Generalized CU to these inputs,
+\begin{equation}
+    (\mu_u,\sigma_u^2) = \GCU\left((\mu_1,\sigma_1^2),(\mu_2,\sigma_2^2),(\mu_3,\sigma_3^2),(\mu_4,\sigma_4^2)\right)
+\end{equation}
+yields the values
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/cu1d.png}
+    \caption{\it 1D Gaussian curves for four inputs (blue), together with the batch Generalized CU result (red) and
+            its 1-$\sigma$ ellipsoid (dashed), for example \ref{ex:gcu1d}.}
+    \label{fig:cu1d}
+\end{figure}
+\begin{equation}
+    (\mu_u,\sigma_u^2) = (-0.0250,0.4250^2).
+\end{equation}
+Figure \ref{fig:cu1d} shows the inputs plotted with the Gaussian curve for $(\mu_u,\sigma_u^2)$. The 1-$\sigma$ line,
+from $x=\mu_u-\sigma_u$ to $x=\mu_u+\sigma_u$, at $y=e^{-\frac{1}{2}}$, corresponds to the outermost intersection points
+between the inputs and the CU result curves. The boundary points for each 1-$\sigma$ ellipsoid are $x=\mu_i\pm\sigma_i$:
+\begin{align}
+    \mu_1-\sigma_1 &= 0.2000 & \mu_1+\sigma_1 &= 0.4000\nonumber\\
+    \mu_2-\sigma_2 &= -0.1000 & \mu_2+\sigma_2 &= 0.3000\nonumber\\
+    \mu_3-\sigma_3 &= -0.3000 & \mu_3+\sigma_3 &= 0.3000\nonumber\\
+    \mu_4-\sigma_4 &= -0.4500 & \mu_4+\sigma_4 &= -0.3500\\
+\intertext{Of these points, $\mu_4-\sigma_4$ and $\mu_1+\sigma_1$ exactly equal the 1-$\sigma$ points on the CU curve,}
+    \mu_u-\sigma_u &= -0.4500 & \mu_u+\sigma_u &= 0.4000,
+\end{align}
+and the remaining points are all within the range $(-0.4500,0.4000)$.
+
+Following the logic outlined in section \ref{section:explanation}, it is
+necessary to consider the ellipsoid $\varepsilon_1$ from equation \ref{eqn:coveps} and $\tau_1(\alpha_1)$ from equation
+\ref{eqn:covtau}:
+\begin{align}
+    \varepsilon_1 &= \mathbb{T}\left(\mu_1,\sigma_1^2\right) = \mathbb{T}\left(0.3000,0.0100\right)\\
+    \tau_1(\alpha_1) &= \mathbb{T}\left(\mu_u,\frac{\sigma_1^2}{\alpha_1}+\frac{(\mu_u-\mu_1)^2}{1-\alpha_1}\right)
+        = \mathbb{T}\left(-0.0250,\frac{0.0100}{\alpha_1}+\frac{0.1056}{1-\alpha_1}\right).
+\end{align}
+From equation \ref{eqn:cu2e}, the transformation into ellipsoid space is:
+\begin{align}
+    \varepsilon_1 &= \left\{
+        \begin{aligned}
+            A_{\varepsilon,1} &= 100\\
+            b_{\varepsilon,1} &= -30\\
+            c_{\varepsilon,1} &= 8
+        \end{aligned}\right.,\\\nonumber
+    \tau_1(\alpha_1) &= \left\{
+        \begin{aligned}
+            A_{\tau,1} &= \frac{\begin{smallmatrix}1\end{smallmatrix}}{\frac{0.0100}{\alpha_1}+\frac{0.1056}{1-\alpha_1}} \\
+            b_{\tau,1} &= \frac{\begin{smallmatrix}0.0250\end{smallmatrix}}{\frac{0.0100}{\alpha_1}+\frac{0.1056}{1-\alpha_1}} \\
+            c_{\tau,1} &= \frac{\begin{smallmatrix}0.0062\end{smallmatrix}}{\frac{0.0100}{\alpha_1}+\frac{0.1056}{1-\alpha_1}} -1 \\
+        \end{aligned}\right.
+\end{align}
+Equation \ref{eqn:ellipse} (repeated here)
+\begin{equation}
+    \varepsilon_i = \{ x | x^TA_ix + 2b_i^Tx + c_i \leq 0 \}\nonumber
+\end{equation}
+gives the quadratic formulation for an $n$-dimensional ellipsoid. In one dimension, $\varepsilon_1$ can be written as
+\begin{equation}
+    \varepsilon_1 = 100x^2-60x+8 \leq 0,
+\end{equation}
+and solving for the roots gives
+\begin{equation}
+    x = 0.2, \qquad x = 0.4,
+\end{equation}
+which are exactly equal to $\mu_1\pm\sigma_1$. For $\tau_1(\alpha_1)$ to completely contain $\varepsilon_1$, its roots
+must bound the roots of $\varepsilon_1$ for all values of $\alpha_1\in(0,1)$.
+\begin{figure}[tbp]
+    \centering
+        \subfloat[$\alpha_1$=0.05]{\label{fig:alpha1d05}\includegraphics[width=0.4\textwidth]{figures/alpha1d-05.png}}
+        \subfloat[$\alpha_1$=0.25]{\label{fig:alpha1d25}\includegraphics[width=0.4\textwidth]{figures/alpha1d-25.png}}
+        \subfloat[$\alpha_1$=0.50]{\label{fig:alpha1d50}\includegraphics[width=0.4\textwidth]{figures/alpha1d-50.png}}
+        \subfloat[$\alpha_1$=0.75]{\label{fig:alpha1d75}\includegraphics[width=0.4\textwidth]{figures/alpha1d-75.png}}
+        \subfloat[$\alpha_1$=0.95]{\label{fig:alpha1d95}\includegraphics[width=0.4\textwidth]{figures/alpha1d-95.png}}
+    \caption{\it 1D Gaussian curves for estimate $(\v{m}_1,\m{M}_1)$ and the intermediate error covariance (red), and
+            its 1D 1-$\sigma$ ellipsoid (dashed), for example \ref{ex:gcu1d}.}
+    \label{fig:alpha1d}
+\end{figure}
+By choosing a value for $\alpha_1$, it is possible to numerically determine the intermediate error covariance
+$\left(\mu_u,\frac{\sigma_1^2}{\alpha_1}+\frac{(\mu_u-\mu_1)^2}{1-\alpha_1}\right)$, and the 1-$\sigma$ ellipsoid
+$\tau_1(\alpha_1)$ and its roots. Using the ellipsoid transformation (equation \ref{eqn:cu2e}) and quadratic ellipsoid
+equation (\ref{eqn:ellipse}) as above, the roots of $\tau_1(\alpha_1)$ are:
+\begin{equation}
+    x = \begin{cases}
+            -0.5828, 0.5328 \qquad \text{for $\alpha_1 = 0.05$}\\
+            -0.4502, 0.4002 \qquad \text{for $\alpha_1 = 0.25$}\\
+            -0.5059, 0.4559 \qquad \text{for $\alpha_1 = 0.50$}\\
+            -0.6852, 0.6352 \qquad \text{for $\alpha_1 = 0.75$}\\
+            -1.4821, 1.4321 \qquad \text{for $\alpha_1 = 0.95$}
+        \end{cases}
+\end{equation}
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/alpha1dcurve.png}
+    \caption{\it $\alpha_1$ vs $\sigma_{intermediate,1}$ for example \ref{ex:gcu1d}.}
+    \label{fig:alpha1dcurve}
+\end{figure}
+Since the roots of $\tau_1(\alpha_1)$ can also be written as $\mu_u\pm\sigma_{intermediate,1}$, it is also useful to
+find the value of the intermediate standard deviation
+\begin{equation}
+    \sigma_{intermediate,1} = \sqrt{\frac{\sigma_1^2}{\alpha_1}+\frac{(\mu_u-\mu_1)^2}{1-\alpha_1}}
+\end{equation}
+and plot it versus $\alpha_1$, as shown in figure \ref{fig:alpha1dcurve}. The minimum value for
+$\sigma_{intermediate,1}$ occurs at $\alpha_1=0.2350$, so the smallest ellipsoid $\tau_1(\alpha_1)$ is:
+\begin{equation}
+    \tau_1(\alpha_1=0.2350) = \left\{
+        \begin{aligned}
+            A_{\varepsilon,1} &= 5.5373\\
+            b_{\varepsilon,1} &= 0.1384\\
+            c_{\varepsilon,1} &= -0.9654
+        \end{aligned}\right.
+\end{equation}
+The quadratic form is
+\begin{equation}
+    \varepsilon_1 = 5.5373x^2+2768x-0.9654 \leq 0,
+\end{equation}
+and solving for the roots gives
+\begin{equation}
+    x = -0.4499, \qquad x = 0.3999,
+\end{equation}
+which are within acceptable floating-point rounding error of $\mu_u\pm\sigma_{intermediate,1}$.
+
+This procedure can be repeated for $(\mu_2,\sigma_2^2)$, $(\mu_3,\sigma_3^2)$, and $(\mu_4,\sigma_4^2)$ to confirm the
+same behavior. The fact that the roots of $\varepsilon_i$ are bounded by the roots of $\tau_i(\alpha_i)$ for all
+$\alpha_i\in(0,1)$ implies that $\varepsilon_0 = \mathbb{T}\left(\mu_u,\sigma_u^2\right)$ completely contains each
+$\varepsilon_i$, and is therefore a minimal L\"owner ellipsoid.
+
+\end{example}
+
+% 2D
+\section{Describing the Behavior in Two Dimensions}
+
+In two dimensions, relative positions between estimate means become more complex, and additionally rotations must be
+considered for each covariance body. Regarding notation, $\v{m}_i$ is
+$\left[\begin{smallmatrix}\mu_{x,i}\\\mu_{y,i}\end{smallmatrix}\right]$ and $\m{M}_i$ is at least as large as
+$\left[\begin{smallmatrix}\sigma_{x,i}\\\sigma_{y,i}\end{smallmatrix}\right]
+ \left[\begin{smallmatrix}\sigma_{x,i}&\sigma_{y,i}\end{smallmatrix}\right]$, though $\sigma_{x,i}$ and $\sigma_{y,i}$
+may be rotated by any arbitrary amount. The PDF of the estimate is given by the unweighted Gaussian function
+\begin{equation}\label{eqn:gauss2d}
+    \varphi_{(\mu_{x,i},\mu_{y,i}),(\sigma_{x,i},\sigma_{y,i})} = 
+        e^{-\left(\frac{(\mu_{x,i}-x)^2}{2\sigma_{x,i}^2}\right)-\left(\frac{(\mu_{y,i}-y)^2}{2\sigma_{y,i}^2}\right)},
+\end{equation}
+and the 1-$\sigma$ ellipsoid is a two dimensional ellipse centered at $(\mu_{x,i},\mu_{y,i})$ with axes of length
+$2\sigma_{x,i}$ and $2\sigma_{y,i}$, rotated to match $\varphi_{(\mu_{x,i},\mu_{y,i}),(\sigma_{x,i},\sigma_{y,i})}$. The
+behavior of the $\alpha$--parametrized intermediate covariance is also more complex, since it is a linear combination
+of both the shape of $\m{M}_i$ and the relative distance between the means $\v{m}_i$ and $\v{u}$.
+
+
+% EXAMPLE 2D CU
+\begin{example}[Generalized CU in Two Dimensions]\label{ex:gcu2d}
+
+Consider as set of four estimates $(\v{m}_i,\m{M}_i)$, given by
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/est2d-4.png}
+    \caption{\it 1-$\sigma$ contour ellipsoids for four 2D input estimate means and covariances used in example \ref{ex:gcu2d}.}
+    \label{fig:est2d-4}
+\end{figure}
+\begin{align}
+    (\v{m}_1,\m{M}_1) &= \left(\left[
+        \begin{smallmatrix}
+            0.3000\\
+            0.5000
+        \end{smallmatrix}\right],
+        \left[
+        \begin{smallmatrix}
+            0.1225 &  0.0650\\
+            0.0650 &  0.0475
+        \end{smallmatrix}\right]\right)\nonumber\\
+    (\v{m}_2,\m{M}_2) &= \left(\left[
+        \begin{smallmatrix}
+            0.4000\\
+            0.6000
+        \end{smallmatrix}\right],
+        \left[
+        \begin{smallmatrix}
+            0.0900 &  0.0000\\
+            0.0000 &  0.0100
+        \end{smallmatrix}\right]\right)\nonumber\\
+    (\v{m}_3,\m{M}_3) &= \left(\left[
+        \begin{smallmatrix}
+            0.8000\\
+            0.9000
+        \end{smallmatrix}\right],
+        \left[
+        \begin{smallmatrix}
+            0.0250 & -0.0150\\
+           -0.0150 &  0.0250
+        \end{smallmatrix}\right]\right)\nonumber\\
+    (\v{m}_4,\m{M}_4) &= \left(\left[
+        \begin{smallmatrix}
+            0.5000\\
+            0.4000
+        \end{smallmatrix}\right],
+        \left[
+        \begin{smallmatrix}
+            0.0573 &  0.0238\\
+            0.0238 &  0.0727
+        \end{smallmatrix}\right]\right)
+\end{align}
+shown in figure \ref{fig:est2d-4}. Applying batch GCU to these inputs,
+\begin{equation}
+    (\v{u},\m{U}) = \GCU\left((\v{m}_1,\m{M}_1),(\v{m}_2,\m{M}_2),(\v{m}_3,\m{M}_3),(\v{m}_4,\m{M}_4)\right),
+\end{equation}
+yields the values
+\begin{figure}[tbp]
+    \centering\includegraphics[width=0.6\textwidth]{figures/cu2d-4.png}
+    \caption{\it 1-$\sigma$ contour ellipsoids for four inputs (blue) together with the batch Generalized CU result
+        (red) for example \ref{ex:gcu2d}.}
+    \label{fig:cu2d-4}
+\end{figure}
+\begin{equation}
+    (\v{u},\m{U}) = \left(\left[
+        \begin{smallmatrix}
+            0.4499\\
+            0.5342
+        \end{smallmatrix}\right],
+        \left[
+        \begin{smallmatrix}
+            0.2606 &  0.1559\\
+            0.1559 &  0.2778
+        \end{smallmatrix}\right]\right)
+\end{equation}
+
+
+
+
+It is next necessary to consider the ellipsoid $\varepsilon_1$ from equation
+\ref{eqn:coveps} and $\tau_1(\alpha_1)$ from equation \ref{eqn:covtau}:
+\begin{align}
+    \varepsilon_1 &= \mathbb{T}\left(\v{m}_1,\m{M}_1\right) =
+        \mathbb{T}\left(\left[\begin{smallmatrix}0.3000\\0.5000\end{smallmatrix}\right],
+            \left[\begin{smallmatrix}0.1224 & 0.0650\\0.0650&0.0475\end{smallmatrix}\right]\right)\\
+    \tau_1(\alpha_1) &= \mathbb{T}\left(\v{u},\frac{\m{M}_1}{\alpha_1}+\frac{(\v{u}-\v{m}_1)(\v{u}-\v{m}_1)'}{1-\alpha_1}\right)\\
+        &= \mathbb{T}\left(\left[\begin{smallmatrix}0.4499\\0.5342\end{smallmatrix}\right],
+        \frac{\left[\begin{smallmatrix}0.1225&0.0650\\0.0650&0.0475\end{smallmatrix}\right]}{\alpha_1}+
+        \frac{\left[\begin{smallmatrix}0.0225&0.0051\\0.0051&0.0012\end{smallmatrix}\right]}{1-\alpha_1}\right).
+\end{align}
+From equation \ref{eqn:cu2e}, the transformation into ellipsoid space is:
+\begin{align}
+    \varepsilon_1 &= \left\{
+        \begin{aligned}
+            A_{\varepsilon,1} &= \left[\begin{smallmatrix}29.6875& -40.5949\\ -40.5949& 76.5625\end{smallmatrix}\right]\\
+            b_{\varepsilon,1} &= \left[\begin{smallmatrix}11.3912\\-26.1028\end{smallmatrix}\right]\\
+            c_{\varepsilon,1} &= \begin{smallmatrix}9.6340\end{smallmatrix}
+        \end{aligned}\right.,\\\nonumber
+    \tau_1(\alpha_1) &= \left\{
+        \begin{aligned}
+            A_{\tau,1} &= \left({\frac{\left[\begin{smallmatrix}0.1224 & 0.0650\\0.0650& 0.0475\end{smallmatrix}\right]}{\alpha_1}
+                                  +\frac{\left[\begin{smallmatrix}0.0225 & 0.0051\\0.0051& 0.0012\end{smallmatrix}\right]}{1-\alpha_1}}\right)^{-1} \\
+            b_{\tau,1} &= -\left({\frac{\left[\begin{smallmatrix}0.1224 & 0.0650\\0.0650& 0.0475\end{smallmatrix}\right]}{\alpha_1}
+                                  +\frac{\left[\begin{smallmatrix}0.0225 & 0.0051\\0.0051& 0.0012\end{smallmatrix}\right]}{1-\alpha_1}}\right)^{-1} 
+                          \left[\begin{smallmatrix}0.3\\0.5\end{smallmatrix}\right]\\
+            c_{\tau,1} &= \left[\begin{smallmatrix}0.3&0.5\end{smallmatrix}\right] 
+                            \left({\frac{\left[\begin{smallmatrix}0.1224 & 0.0650\\0.0650& 0.0475\end{smallmatrix}\right]}{\alpha_1}
+                                  +\frac{\left[\begin{smallmatrix}0.0225 & 0.0051\\0.0051& 0.0012\end{smallmatrix}\right]}{1-\alpha_1}}\right)^{-1} 
+                          \left[\begin{smallmatrix}0.3\\0.5\end{smallmatrix}\right] -1\\
+        \end{aligned}\right.
+\end{align}
+
+\begin{figure}[tbp]
+    \centering
+        \subfloat[$\alpha_1$=0.05]{\label{fig:alpha2d05}\includegraphics[width=0.4\textwidth]{figures/alpha2d-05.png}}
+        \subfloat[$\alpha_1$=0.25]{\label{fig:alpha2d25}\includegraphics[width=0.4\textwidth]{figures/alpha2d-25.png}}
+        \subfloat[$\alpha_1$=0.50]{\label{fig:alpha2d50}\includegraphics[width=0.4\textwidth]{figures/alpha2d-50.png}}
+        \subfloat[$\alpha_1$=0.75]{\label{fig:alpha2d75}\includegraphics[width=0.4\textwidth]{figures/alpha2d-75.png}}
+        \subfloat[$\alpha_1$=0.95]{\label{fig:alpha2d95}\includegraphics[width=0.4\textwidth]{figures/alpha2d-95.png}}
+    \caption{\it 1-$\sigma$ contour ellipse for estimate $(\v{m}_1,\m{M}_1)$ and the mean shift term
+        $(\v{u}-\v{m}_1)(\v{u}-\v{m}_1)'$ (blue), together with the intermediate covariance 1-$\sigma$ ellipse (red),
+        for example \ref{ex:gcu2d}.}
+    \label{fig:alpha2d}
+\end{figure}
+Figure \ref{fig:alpha2d} shows the 1-$\sigma$ contour ellipse of $(\v{m}_1,\m{M}_1)$ and
+$\left(\v{u},\frac{\m{M}_1}{\alpha_1}+\frac{(\v{u}-\v{m}_1)(\v{u}-\v{m}_1)'}{1-\alpha_1}\right)$ for different values of
+$\alpha_1$. The input $(\v{m}_1,\m{M}_1)$ is given. The mean shift term $(\v{u}-\v{m}_1)(\v{u}-\v{m}_1)'$ is a
+single-component matrix which forms an ellipse with major axis twice the length of the shift, and minor axis of
+length zero, centered at $\v{u}$ and aligned with both means. The intermediate covariance is a linear sum of these two
+components, with the interpolation between $\alpha_1=0$ and $\alpha_1=1$ creating an unbounded asymptotic behavior which
+is roughly similar to that shown in figure \ref{fig:alpha1dcurve} in the 1-D case. The 1-$\sigma$ ellipse given by
+$\tau_1(\alpha_1=0)$ will be infinite in size, with the same shape as $\varepsilon_1$; at the other end,
+$\tau_1(\alpha_1=1)$ will be infinite in length, with the same orientation as the mean shift term and the exact width of
+the projection of $\varepsilon_1$ in the orthogonal direction.
+
+By choosing values for $\alpha_1$ it is possible to compare $\tau_1(\alpha_1)$ with $\varepsilon_1$ and test for
+containment and confirm that $\varepsilon_1$ is always completely contained. Taking $\alpha_1=0.75$, $\tau_1$ becomes
+\begin{equation}
+    \tau_1(\alpha_1=0.75)=\left\{
+        \begin{aligned}
+            A_{\tau,1} &=
+            \left[\begin{smallmatrix}
+                 11.8286 & -18.6285\\
+                -18.6285 &  44.0408
+            \end{smallmatrix}\right]\\
+            b_{\tau,1} &=
+            \left[\begin{smallmatrix}
+                  4.6295\\
+                -15.1454
+            \end{smallmatrix}\right]\\
+            c_{\tau,1} &=  \begin{smallmatrix}6.0078\end{smallmatrix}
+        \end{aligned}\right.
+\end{equation}
+and the solution to $\lambda_{max}$ described in section \ref{section:containment} is $-0.0696$, so the condition
+$\lambda_{max}\leq 0$ for $\tau_1$ to properly contain $\varepsilon_1$~\cite{eberly00}, holds.
+
+
+\end{example}
+
+
+% ND, projections
+\section{Extension to Higher Dimensions}
+
+
+It becomes increasingly difficult to visualize any of the covariance or ellipsoid components as the dimensionality
+increases. For example, in three dimensions, the 1-$\sigma$ contour ellipsoid is a three-dimensional cross-section of a
+four-dimensional Gaussian volume, which is rotated by both an elevation angle $\phi$ and an azimuth angle
+$\theta$. However, even in these higher state spaces, the mathematics operate in the same fashion as described for the
+one- and two-dimensional cases.
+
+One rough method to check a higher-dimensional GCU result for ellipsoid enclosure (although not strictly {\em minimal}
+enclosure) is to project the set of $n$-dimensional ellipsoids into all possible two-dimensional major axis component
+planes. Properly contained ellipsoids should still be properly contained in any lower-dimensional projection. Figure
+\ref{fig:cu3d} illustrates this property by projecting a set of three-dimensional 1-$\sigma$ contour ellipsoids into the
+$xy$, $xz$, and $yz$ planes.
+\begin{figure}[tbp]
+    \centering
+        \subfloat[Projection into $xy$ plane]{\label{fig:cu3dxy}\includegraphics[width=0.4\textwidth]{figures/cu3dxy.png}}
+        \subfloat[Projection into $xz$ plane]{\label{fig:cu3dxz}\includegraphics[width=0.4\textwidth]{figures/cu3dxz.png}}
+        \subfloat[Projection into $yz$ plane]{\label{fig:cu3dyz}\includegraphics[width=0.4\textwidth]{figures/cu3dyz.png}}
+    \caption{\it 1-$\sigma$ contour plots of three 3D input estimates (blue) together with the batch GCU result (red),
+        projected down into the three 2D major axis component planes. }
+    \label{fig:cu3d}
+\end{figure}
+Computation of the sixth-order $P(t)$ polynomial (equation \ref{eqn:poly}) for the Lagrange test confirms that the GCU
+result 1-$\sigma$ contour ellipsoid properly contains its inputs in three-dimensional space as well, the space in which
+this result is known to be minimized.
+
+
+% Additional 2D figures
+\section{Additional Examples}\label{section:examples}
+
+In this section, further examples of two-dimensional GCU are plotted as 1-$\sigma$ contour ellipses to provide further
+evidence that a GCU solution satisfies the MEEE requirements. The procedure used for each example is:
+\begin{enumerate}
+    \item Randomly generate five mean and covariance estimates, $(\v{m}_i,\m{M}_i)$, $i=1\dots 5$.
+    \item Calculate $(\v{u},\m{U})$ as the batch GCU of $(\v{m}_i,\m{M}_i)$, $i=1\dots 5$.
+    \item Use the transformation in equation \ref{eqn:cu2e} to find the ellipses $\varepsilon_0=\mathbb{T}(\v{u},\m{U})$
+        and $\varepsilon_i=\mathbb{T}(\v{m}_i,\m{M}_i)$, $i=1\dots 5$.
+    \item Use the procedure in section \ref{section:containment} to find $\lambda_{max}$ for each $Q_0$ and $Q_i$,
+        $i=1\dots 5$.
+\end{enumerate}
+The fives values of $\lambda_{max}\leq 0$ are given as numerical results to support the claim that each GCU ellipse
+actually does properly contain all of its inputs~\cite{eberly00}. The 1-$\sigma$ contour plots are shown in figure
+\ref{fig:cu2d-5}, and the numerical values of $\lambda_{max}$ are listed in table \ref{tab:cu2d-5}.
+
+\begin{figure}[tbp]
+    \centering
+        \subfloat[]{\label{fig:cu2d-5a}\includegraphics[width=0.4\textwidth]{figures/cu2d-5a.png}}
+        \subfloat[]{\label{fig:cu2d-5b}\includegraphics[width=0.4\textwidth]{figures/cu2d-5b.png}}
+        \subfloat[]{\label{fig:cu2d-5c}\includegraphics[width=0.4\textwidth]{figures/cu2d-5c.png}}
+        \subfloat[]{\label{fig:cu2d-5d}\includegraphics[width=0.4\textwidth]{figures/cu2d-5d.png}}
+        \subfloat[]{\label{fig:cu2d-5e}\includegraphics[width=0.4\textwidth]{figures/cu2d-5e.png}}
+        \subfloat[]{\label{fig:cu2d-5f}\includegraphics[width=0.4\textwidth]{figures/cu2d-5f.png}}
+    \caption{\it 1-$\sigma$ contour plots of five 2D input estimates (blue) together with the batch GCU result (red). Figures
+        (a) through (f) are independent examples, and the numerical results for
+        $\lambda_{max}$ are given in table \ref{tab:cu2d-5}. }
+    \label{fig:cu2d-5}
+\end{figure}
+
+\begin{table}
+\centering
+\begin{tabular*}{0.8\textwidth}{@{\extracolsep{\fill}}r@{.}lr@{.}lr@{.}lr@{.}lr@{.}lr@{.}l}
+\multicolumn{2}{c}{Ex. (a)} &
+\multicolumn{2}{c}{Ex. (b)} &
+\multicolumn{2}{c}{Ex. (c)} &
+\multicolumn{2}{c}{Ex. (d)} &
+\multicolumn{2}{c}{Ex. (e)} &
+\multicolumn{2}{c}{Ex. (f)}\\
+\hline
+-1&40e-4    &  -0&0264      &  -0&1592  &  -2&24e-5 &  -6&64e-5 &  -0&1353 \\
+-0&1374     &  -2&31e-5     &  -0&0095  &  -9&24e-4 &  -0&7482  &  -0&0078 \\
+-1&99e-5    &  -0&1508      &  -3&96e-5 &  -4&44e-5 &  -1&51e-4 &  -1&64e-4 \\
+-0&3566     &  -1&21e-4     &  -5&16e-5 &  -1&53e-5 &  -0&1234  &  -0&2035 \\
+-0&4794     &  -1&79e-4     &  -0&2109  &  -1&19e-5 &  -0&0356  &  -1&72e-5\\
+\end{tabular*}
+    \caption{\it Five $\lambda_{max}$ values for the six GCU trials shown in figure \ref{fig:cu2d-5}. Note that all of these
+        values satisfy the condition $\lambda_{max}\leq 0$ to show that the GCU 1-$\sigma$ contour ellipse properly contains its 
+        five inputs. } 
+    \label{tab:cu2d-5}
+\end{table}
+
+
+
+
diff --git a/chapters/chapter5.tex b/chapters/chapter5.tex
new file mode 100644
index 0000000..0108183
--- /dev/null
+++ b/chapters/chapter5.tex
@@ -0,0 +1,37 @@
+\chapter{Conclusion}\label{chapter:conclusion}
+
+\section{Discussion}
+
+\PARstart{T}{his thesis} has presented a technique from data fusion called Generalized Covariance Union, an important
+member in the hierarchy of data fusion tools. GCU allows data fusion operations to be performed in the presence of
+possibly correlated and/or spurious input, but its current implementation does not provide a real-time response in
+higher-dimensional state spaces.
+
+GCU can be graphically plotted in such a way as to suggest equivalence with the Minimal Enclosing Ellipsoid of
+Ellipsoids problem, which would allow computational geometry tools to be applied to solve the GCU optimization problem.
+The 1-$\sigma$ contour ellipsoids which uniquely define the Gaussian PDF associated with an error covariance, and the
+covariance-to-ellipsoid transformation given in equation \ref{eqn:cu2e}, are interchangeable, and this provides a
+mechanism for testing whether Generalized CU and MEEE do in fact solve the same problem. The logic outlined in section
+\ref{section:explanation} and the experimental evidence illustrated in examples \ref{ex:gcu1d} and \ref{ex:gcu2d}, and
+in section \ref{section:examples}, suggest that the answer to this question is yes.
+
+
+\section{Future Work}
+
+Although the experimental evidence presented is suggestive, it is not conclusive. Before research on GCU and MEEE can be
+merged, there must be a rigorous proof in place showing that these two techniques are equivalent in any dimensionality.
+Once this proof is established, it will be possible to solve GCU using MEEE algorithms, and vice-versa. The immediate
+benefit will be a direct comparison of software running time of implementations of each technique, leading toward
+improved real-time responses in both domains. Additionally, once it becomes accepted that GCU and MEEE are
+interchangeable, this will allow for further investigation into other relationships between the fields of data fusion
+and computational geometry. Perhaps these relationships exist not only between the two techniques used in this thesis,
+but are in fact an indication of a larger degree of compatibility between two previously unrelated classes of problems.
+
+This thesis contains the first formal analysis of GCU, following its initial presentation to the 9th International
+Conference on Information Fusion in 2006, in~\cite{fusion06}. Planned future work includes a journal article covering
+the GCU--MEEE equivalence. Although past and current research has been hampered by the lack of available tools---e.g. the
+current implementation of CU/GCU is the first of its kind---continuing refinement to the CU/GCU optimization problem
+will no doubt prove invaluable to further study, eventually leading to a robust real-time tool for mainstream data fusion
+applications.
+
+
diff --git a/chapters/citations.bib b/chapters/citations.bib
new file mode 100644
index 0000000..eb40300
--- /dev/null
+++ b/chapters/citations.bib
@@ -0,0 +1,152 @@
+@inproceedings{fusion06,
+    author          = {Ottmar Boschardt{, Ryan Calhoun, Simon Julier, and Jeffrey Ulhmann}},
+    title           = {Generalized Information Representation and Compresssion Using Covariance Union},
+    booktitle       = {9th Internation Conference on Information Fusion},
+    address         = {Florence, Italy},
+    month           = {10--13 July},
+    year            = {2006} 
+    }
+
+@inproceedings{julier05,
+    author          = {S. Julier{ and J. K. Uhlmann}},
+    title           = {Fusion of Time Delayed Measurements With Uncertain Time Delays},
+    booktitle       = {2005 American Control Conference},
+    address         = {Portland, OR, USA},
+    month           = {8--10 June},
+    year            = {2005} 
+    }
+
+@article{uhlmann03,
+    author          = {Jeffrey Uhlmann},
+    title           = {Covariance Consistency Methods for Fault-Tolerant Distributed Data Fusion},
+    journal         = {Information Fusion},
+    pages           = {201--215},
+    volume          = {4},
+    number          = {3},
+    month           = {September},
+    year            = {2003}
+    }
+
+@book{siggraph01,
+    author          = {Greg Welch and Gary Bishop},
+    title           = {SIGGRAPH 2001 Course 8: An Introduction to the Kalman Filter},
+    publisher       = {ACM Press/Addison-Wesley Publishing Co.},
+    address         = {Los Angeles, CA, USA},
+    year            = {2001}
+    }
+
+@book{maybeck79,
+    author          = {P.S. Maybeck},
+    title           = {Stochastic Models, Estimation, and Control},
+    publisher       = {Academic Press},
+    address         = {New York, NY, USA},
+    volume          = {141},
+    series          = {Mathematics in Science and Engineering},
+    year            = {1979}
+    }
+
+@book{barshalom88,
+    author          = {Y. Bar-Shalom{ and T. E. Fortmann}},
+    title           = {Tracking and Data Association},
+    publisher       = {Academic Press Professional, Inc.},
+    address         = {San Diego, CA, USA},
+    year            = {1988}
+    }
+
+@incollection{fusion01,
+    author          = {Simon Julier{ and Jeffrey Uhlmann}},
+    editor          = {David L. Hall{ and James Llinas}},
+    title           = {General Decentralized Data Fusion with Covariance Intersection (CI)},
+    booktitle       = {Handbook of Multisensor Data Fusion}, 
+    chapter         = {12},
+    publisher       = {CRC Press},
+    address         = {Boca Raton, FL, USA},
+    year            = {2001}
+    }
+
+
+@article{yildirim06,
+    author          = {E. Alper Yildirim},
+    title           = {On the Minimum Volume Covering Ellipsoid of Ellipsoids},
+    journal         = {SIAM Journal on Optimization},
+    pages           = {621--641},
+    volume          = {17},
+    number          = {3},
+    month           = {September},
+    year            = {2006}
+    }
+
+@article{vandenberghe96,
+    author          = {Lieven Vandenberghe{, Stephen Boyd, and Shao-Po Wu}},
+    title           = {Determinant Maximization with Linear Matrix Inequality Constraints},
+    journal         = {SIAM Journal on Matrix Analysis and Applications},
+    pages           = {499--533},
+    volume          = {19},
+    number          = {2},
+    year            = {1998}
+    }
+
+@book{boyd94,
+    author          = {S. Boyd{, L. El Ghaoni, E. Feron, and V. Balakrishnan}},
+    title           = {Linear Matrix Inequalities in System Control Theory},
+    publisher       = {Society for Industrial and Applied Mathematics},
+    address         = {Philadelphia, PA, USA},
+    volume          = {15},
+    series          = {Studies in Applied Mathematics},
+    year            = {1994}
+    }
+
+
+@article{ju01,
+    author          = {M. Ju{, J. Liu, S. Shiang, Y. Chien, K. Hwang, and W. Lee}},
+    title           = {Fast and Accurate Collision Detection Based on Enclosed Ellipsoids},
+    journal         = {Robotica},
+    volume          = {19},
+    number          = {4},
+    pages           = {381--394}, 
+    month           = {June},
+    year            = {2001}
+    }
+
+@inproceedings{shiang00,
+    author          = {S. Shiang{, J. Liu, and Y. Chien}},
+    title           = {Estimate of Minimum Distance Between Convex Polyhedra Based on Enclosed Ellipsoids},
+    booktitle       = {2000 IEEE/RSJ International Conference on Intelligent Robots and Systems},
+    pages           = {739--744}, 
+    address         = {Takamatsu, Japan},
+    month           = {31 October--5 November},
+    year            = {2000}
+    }
+
+@article{sturm03,
+    author          = {J. F. Sturm{ and S. Z. Zhang}},
+    title           = {On Cones of Nonnegative Quadratic Functions},
+    journal         = {Mathematics of Operations Research},
+    volume          = {28},
+    number          = {2},
+    pages           = {246--267},
+    month           = {May},
+    year            = {2003}
+    }
+
+@misc{eberly00,
+    author          = {David Eberly},
+    title           = {Intersection of Ellipsoids},
+    publisher       = {Geometric Tools, Inc.},
+    howpublished    = {\url{http://www.geometrictools.com}},
+    month           = {10 October},
+    year            = {2000}
+    }
+
+@inbook{boyd04,
+    author          = {Stephen Boyd{ and Lieven Vandenberghe}},
+    title           = {Geometric Problems},
+    chapter         = {8},
+    booktitle       = {Convex Optimization},
+    address         = {Cambridge, MA, USA},
+    publisher       = {Cambridge University Press},
+    year            = {2004}
+    }
+
+
+
diff --git a/chapters/cover.tex b/chapters/cover.tex
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index 0000000..dd14742
--- /dev/null
+++ b/chapters/cover.tex
@@ -0,0 +1,77 @@
+\title{\maintitle}
+\thispagestyle{empty}
+\vskip 10mm
+\smalltitle
+\vskip 10mm
+\centerline{\rule{150mm}{0.2mm}}
+\vskip 10mm
+\centerline{A Thesis presented to the Faculty of the Graduate School}
+\centerline{University of Missouri---Columbia}
+\vspace{10mm}
+\centerline{\rule{150mm}{0.2mm}}
+\vspace{10mm}
+\centerline{In Partial Fulfillment}
+\centerline{of the Requirements for the Degree}
+\centerline{of \fulldegree}
+\vspace{10mm}
+\centerline{\rule{150mm}{0.2mm}}
+\vspace{10mm}
+\centerline{by}
+\vskip 4mm
+\centerline{\MYNAME}
+\vskip 4mm
+\centerline{\myadvisor,\hspace{1mm} Thesis Supervisor}
+\vskip 4mm 
+\centerline{\defensedate}
+\newpage
+
+\thispagestyle{empty}
+\vspace*{15cm}
+\begin{center}
+$\mbox{\copyright}$ copyright by \myname~ \defenseyear\\
+All Rights Reserved
+\end{center}
+\newpage
+
+\thispagestyle{empty}
+The undersigned, appointed by the Dean of the Graduate School, have 
+examined the thesis entitled:\par
+\vskip 5mm
+\smalltitle
+\vskip5mm
+presented by \myname \par
+a candidate for the degree of \fulldegree \par
+and hereby certify that in their opinion it is worthy of acceptance.
+%\vskip 15mm
+\vskip 15mm
+\centerline{\rule{100mm}{0.2mm}}
+\centerline{\myadvisor}%\vskip 12mm
+\vskip 10mm
+\centerline{\rule{100mm}{0.2mm}}
+\secondreader%\vskip 12mm
+\vskip 10mm
+\centerline{\rule{100mm}{0.2mm}}
+\thirdreader%\vskip 12mm
+%\vskip 4mm
+%\centerline{\rule{100mm}{0.2mm}}
+%\fourthreader
+\newpage
+
+
+%\newpage
+%\pagenumbering{roman}
+%\setcounter{page}{2}
+%\newpage
+%\addcontentsline{toc}{chapter}{ACKNOWLEDGEMENTS}
+%\vskip 10mm
+%\centerline{\bf \large ACKNOWLEDGMENTS}
+%\vskip 10mm
+%\input{aknowledge}
+%\newpage
+%\addcontentsline{toc}{chapter}{ABSTRACT}
+%\centerline {\large \bf ABSTRACT}
+%\vskip 2mm 
+ 
+%\newpage
+
+%\input{abstract}
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+++ b/myeqns.tex
@@ -0,0 +1,18 @@
+\DeclareMathOperator{\CU}{CU}
+\DeclareMathOperator{\GCU}{GenCU}
+\newcommand{\gaussN}[1]{\mathcal{N}\left\{#1\right\}}
+\newcommand{\m}[1]{\mathbf{#1}}
+\renewcommand{\v}[1]{\mathbf{#1}}
+\newcommand{\ea}{\tilde{\mathbf{m}}}
+
+\newtheoremstyle{example}{\topsep}{\topsep}%
+    {}%           Body font
+    {}%           Indent amount (empty = no indent, \parindent = para indent)
+    {\bfseries}%  Thm head font
+    {}%           Punctuation after thm head
+    {\newline}%   Space after thm head (\newline = linebreak)
+    {\thmname{#1}\thmnumber{ #2}\thmnote{ #3}}%         Thm head spec
+
+    \theoremstyle{example}
+    \newtheorem{example}{Example}[section]
+
diff --git a/myowndef.sty b/myowndef.sty
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index 0000000..72f1078
--- /dev/null
+++ b/myowndef.sty
@@ -0,0 +1,20 @@
+\def\myname{Ryan \ J. \ Calhoun}
+\def\MYNAME{RYAN \ J. \ CALHOUN}
+\def\myadvisor{Dr. Jeffrey Uhlmann}
+\def\maintitle{\bf ON THE RELATIONSHIP BETWEEN GENERALIZED COVARIANCE UNION AND THE MINIMAL ENCLOSING ELLIPSOID PROBLEM}
+\def\smalltitle
+{
+\centerline{\bf ON THE RELATIONSHIP BETWEEN}
+\centerline{\bf GENERALIZED COVARIANCE UNION} 
+\centerline{\bf AND THE MINIMAL ENCLOSING ELLIPSOID PROBLEM}
+}
+\def\firstreader{\centerline{Dr. Jeffrey Uhlmann}}
+\def\secondreader{\centerline{Dr. Ye Duan}}
+\def\thirdreader{\centerline{Dr. Michael Devaney}}
+
+\def\fulldegree{Master of Science}
+\def\defensemonth{MAY}
+\def\defenseyear{2008}
+\def\defensedate{\defensemonth~\defenseyear}
+\def\tc{$T_{AF \rightarrow F}\ $}
+