Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.fdb_latexmk
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--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.fdb_latexmk (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.fdb_latexmk (revision 1419)
@@ -0,0 +1,114 @@
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Index: /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.aux
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.aux (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.aux (revision 1419)
@@ -0,0 +1,1 @@
+\relax 
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.thm
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.thm (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.thm (revision 1419)
@@ -0,0 +1,18 @@
+\contentsline {definition}{{Definice}{2.{1}}{Agent}}{2}{definition.2.1}
+\contentsline {definition}{{Definice}{2.{2}}{Uspořádání na množině všech stavů}}{3}{definition.2.2}
+\contentsline {definition}{{Definice}{3.{1}}{Dominance množiny}}{5}{definition.3.1}
+\contentsline {definition}{{Definice}{3.{2}}{Množina výsledků}}{6}{definition.3.2}
+\contentsline {definition}{{Definice}{3.{3}}{Dominance strategie}}{6}{definition.3.3}
+\contentsline {definition}{{Definice}{3.{4}}{Nashova rovnost}}{6}{definition.3.4}
+\contentsline {definition}{{Definice}{3.{5}}{Matice zisků}}{7}{definition.3.5}
+\contentsline {definition}{{Definice}{3.{6}}{Rekursivní modelová struktura}}{7}{definition.3.6}
+\contentsline {definition}{{Definice}{3.{7}}{Rekursivní model}}{7}{definition.3.7}
+\contentsline {definition}{{Definice}{3.{8}}{Užitečnost}}{8}{definition.3.8}
+\contentsline {definition}{{Definice}{3.{9}}{Markovův rozhodovací proces}}{9}{definition.3.9}
+\contentsline {definition}{{Definice}{3.{10}}{V-funkce}}{10}{definition.3.10}
+\contentsline {definition}{{Definice}{3.{11}}{Q-function}}{10}{definition.3.11}
+\contentsline {definition}{{Definice}{3.{12}}{Bellmanova rovnice optimality}}{11}{definition.3.12}
+\contentsline {definition}{{Definice}{3.{13}}{MLM}}{12}{definition.3.13}
+\contentsline {definition}{{Definice}{3.{14}}{Podmíněná pravděpodobnost}}{13}{definition.3.14}
+\contentsline {proposition}{{Věta}{3.{1}}{Bayesova věta}}{13}{proposition.3.1}
+\contentsline {definition}{{Definice}{3.{15}}{Věrohodnostní funkce}}{14}{definition.3.15}
Index: /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.tex (revision 1419)
@@ -0,0 +1,133 @@
+\section{LQ řízení}
+
+LQ je zkratka slovního spojení linaer-quadratic, tedy lineárně kvadratický. 
+Jedná se obecně o metodu, kdy je systém v diskrétním časovém kroku $t$ 
+popsán vektorem proměnných $x(t) = ( x_1(t), ..., x_n(t) )$
+a my můžeme nastavovat vektor parametrů $y(t) = ( y_1(t), ..., y_n(t) )$.
+Metoda je popsána a použita v článku \cite{6_tuc_lq} pro nastavování časů zelených na křižovatce.
+Princip přechodu z času $t$ do $t+1$ je popsán lineárním vztahem
+\begin{equation}
+  x(t+1) = A x(t) + B y(t)
+\end{equation}
+.
+kde matice $A$ a $B$ jsou matice stavů a vstupů vyjadřující odezvu systému vzhledem 
+k $x(t)$ a $y(t)$. Účelem LQ řízení je najít optimální hodnoty $y(t)$ v závislosti
+na $x(t)$ dané zpětnovazebnou maticí $L$ vztahem 
+\begin{equation}\label{eq_lq_feedback}
+y(t) = -L x(t)
+\end{equation}
+. Optimalita je definována pomocí
+kvadratického kritéria 
+\begin{equation}\label{eq_quadratic_criterion}
+J = \sum_{t=1}^{\infty} x(t)^T Q x(t) + y(t)^T R y(t) 
+\end{equation}
+
+
+, kde $Q$ a $R$ jsou diagonální pozitivně semidefinitní matice vah určující významnost jednotlivých členů kritéria.
+Zpětnovazebná matice $L$ se podle \cite{6_tuc_lq} dostane minimalizací kritéria $J$ jako
+\begin{equation}\label{eq_riccati}
+L = (R + B^T P B)^{-1} B^T P A
+\end{equation}, kde $P$ je jednoznačné řešení Riccatiho rovnice pro diskrétní časový krok
+
+\begin{equation}\label{eq_riccati_2}
+P = Q + A^T ( P - P B ( R + B^T P B ) B^T P ) A
+\end{equation}
+. Rovnici a její řešení popisuje například \cite{7_lq_methods}.
+
+
+\subsection{Použití LQ řízení ve strategii TUC}
+LQ řízení bylo použito v \cite{6_tuc_lq} k nalezení optimální délky zelených v systému 
+13-ti signálních skupin. Proměnné $x_i(t)$ zde představují obsazenost ramene $i$ 
+spojující křižovatky $M$ a $N$. Účelem strategie je nalezení optimální délky zelených
+$g$, $g_{N,i}$ značí délku zelené na signální skupiny křižovatky $N$ zprůjezdňující
+směr do ramene $i$. Předpokládaný vztah pro přechod systému z času $t$ do času $t+1$ je
+\begin{equation}\label{eq_tuc_1}
+ x_i(t+1) = x_i(t) + T [ q_i(t) + s_i(t) + d_i(t) + u_i(t) ]
+\end{equation}, kde proměnné značí:
+
+\begin{itemize}
+ \item $T$ - časový krok
+ \item $q_i(t)$ - přírůstek vozidel z křižovatek
+ \item $u_i(t)$ - úbytek vozidel do ostatních křižovatek
+ \item $s_i(t)$ - přírůstek vozidel z okolí sítě
+ \item $d_i(t)$ - úbytek vozidel mimo síť
+\end{itemize}
+
+Přírůstek vozidel z křižovatek je dán vztahem
+\begin{equation}
+ q_i(t) = \sum_{k\in I_m} t_{k,i} u_k(t)
+\end{equation}
+, je to tedy součet úbytků vozidel z ramen ústících do křižovatky $N$ vynásobených
+koeficinety $t_{k,i}$, což jsou odbočovací poměry z ramene $k$ do ramene $i$.
+V podovném tvaru se předpokládá $s_i(t)$
+\begin{equation}
+s_i(t) = t_{i,0} q_i(t)
+\end{equation}
+, kde $t_{i,0}$ je odbočovací koeficient ramene $i$ mimo sledovanou síť.
+Při délce cyklu $C$, saturovaném toku $S_i$ a délce zelených $g_{N,i}(t)$ ramene $i$ platí
+\begin{equation} \label{eq:tuc_u}
+ u_i(t) = \frac{S_i \sum g_{N,i}(t)}{C}
+\end{equation}.
+Rovnice \ref{eq_tuc_1} tedy přechází do tvaru
+\begin{equation}\label{eq_tuc_2}
+ x_i(t+1) = x_i(t) + T \left[ 
+    (1-t_{i,0}) \sum_{k\in I_m} t_{k,i} \frac{S_k \sum g_{M,k}(t)}{C} 
+    - \frac{S_i \sum g_{N,i}(t)}{C}
+    + d_i(t) \right]
+\end{equation}. Uvažujeme-li nominální hodnoty $d^n$ a $g^n$ vedoucí
+vždy na stav $x^n$, platí podle rovnice \ref{eq_tuc_2} 
+\begin{equation}\label{eq_tuc_nom}
+ 0 = T \left[ 
+    (1-t_{i,0}) \sum_{k\in I_m} t_{k,i} \frac{S_k \sum g_{M,k}^n}{C} 
+    - \frac{S_i \sum g_{N,i}^n}{C}
+    + d_i^n \right]
+\end{equation}. Označíme-li 
+\begin{equation}\label{eq_delta_g}
+ \Delta g(t) = g(t) - g^n
+\end{equation}, můžeme psát rovnici \ref{eq_tuc_2} jako
+\begin{equation}\label{eq_tuc_3}
+ x_i(t+1) = x_i(t) + T \left[ 
+    (1-t_{i,0}) \sum_{k\in I_m} t_{k,i} \frac{S_k \sum \Delta g_{M,k}(t)}{C} 
+    - \frac{S_i \sum \Delta g_{N,i}(t)}{C}
+     \right]
+\end{equation}, což dovoluje tuto rovnici zapsat pomocí matic v požadovaném tvaru
+\begin{equation}\label{eq_tuc_4}
+ x(t+1) = A x(t) + B \Delta g(t)
+\end{equation}, kde $A$ je jednotková matice. 
+
+\subsubsection{Kvadratické kritérium}
+Účelem lagoritmu je minimalizovat obsazenost ramen, tedy vektor $x(t)$
+a penalizovat změnu délky trvání zelené oproti nominálním hodnotám.
+Kvadratické kritérium optimálního řízení \ref{eq_quadratic_criterion} jetedy v \cite{6_tuc_lq}
+definováno vztahem
+\begin{equation}\label{eq_tuc_crit}
+ J = \sum_{t=0}^{\infty} x(t)^T Q x(t) + \Delta g(t)^T R \Delta g(t)
+\end{equation}. Diagonální matice $Q$ je zde zodpovědná za vyvažování
+počtu vozidel jednotlivých úseků. V \cite{6_tuc_lq} je každý diagonální
+prvek $Q_{i,i}$ matice $Q$ položen převrácené hodnotě maximálního
+povoleného počtu vozidel daného úseku $i$. $R = rI$ penalizuje změnu
+časů zelených. Parametr $r$ ovlivňuje míru reakce systému a ja volen metodu pokus-oprava.
+Minimalizací tohoto kritéria pomcí \ref{eq_riccati} získáme zpětnovazebnou matici $L$,
+která určuje $g(t)$. Z rovnic \ref{eq_lq_feedback} a \ref{eq_delta_g} dostaneme výsledný vztah
+\begin{equation}\label{eq_tuc_feedback}
+ g(t) = g^n - L x(t)
+\end{equation}. Toto řešení předpokládá, že známe hodnotu $g^n$, při které systém
+zůstává ve stavu $x^n$. Tak tomu ale většinou není. Při absenci znalosti $g^n$
+podle \cite{6_tuc_lq} odečteme $g(t) - g(t-1)$ a rovnice \ref{eq_tuc_feedback} nabývá tvaru
+\begin{equation}\label{eq_tuc_feedback_2}
+ g(t) = g(t-1) - L( x(t) - x(t-1) )
+\end{equation}.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/czechiso.bst
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/czechiso.bst (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/czechiso.bst (revision 1419)
@@ -0,0 +1,1602 @@
+%%
+%% This is file `czechiso.bst',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% merlin.mbs  (with options: `head,exlang,lang,vonx,nm-rev,jnrlst,aunm-semi,nmlm,x3,m3,atit-u,vnum-nr,volp-sp,jwdpg,pp-last,jwdvol,num-xser,ser-vol,ser-ed,pg-bk,add-pub,isbn,issn,doi,edpar,edby,blk-tit,au-col,čeątina,pp,and-xcom,xand,eprint,url,url-nl,nfss,,{}')
+%% czech.mbs  (with options: `exlang,lang,vonx,nm-rev,jnrlst,aunm-semi,nmlm,x3,m3,atit-u,vnum-nr,volp-sp,jwdpg,pp-last,jwdvol,num-xser,ser-vol,ser-ed,pg-bk,add-pub,isbn,issn,doi,edpar,edby,blk-tit,au-col,čeątina,pp,and-xcom,xand,eprint,url,url-nl,nfss,,{}')
+%% merlin.mbs  (with options: `tail,exlang,lang,vonx,nm-rev,jnrlst,aunm-semi,nmlm,x3,m3,atit-u,vnum-nr,volp-sp,jwdpg,pp-last,jwdvol,num-xser,ser-vol,ser-ed,pg-bk,add-pub,isbn,issn,doi,edpar,edby,blk-tit,au-col,čeątina,pp,and-xcom,xand,eprint,url,url-nl,nfss,,{}')
+%% ----------------------------------------
+%% *** Styl snaľící se být v souladu s normou ISO 690. Pomocí latex makebst vytvořil David Martinek. ***
+%% 
+%% Copyright 1994-2004 Patrick W Daly
+ % ===============================================================
+ % IMPORTANT NOTICE:
+ % This bibliographic style (bst) file has been generated from one or
+ % more master bibliographic style (mbs) files, listed above.
+ %
+ % This generated file can be redistributed and/or modified under the terms
+ % of the LaTeX Project Public License Distributed from CTAN
+ % archives in directory macros/latex/base/lppl.txt; either
+ % version 1 of the License, or any later version.
+ % ===============================================================
+ % Name and version information of the main mbs file:
+ % \ProvidesFile{merlin.mbs}[2004/02/09 4.13 (PWD, AO, DPC)]
+ %   For use with BibTeX version 0.99a or later
+ %-------------------------------------------------------------------
+ % This bibliography style file is intended for texts in
+ % This is a numerical citation style, and as such is standard LaTeX.
+ % It requires no extra package to interface to the main text.
+ % The form of the \bibitem entries is
+ %   \bibitem{key}...
+ % Usage of \cite is as follows:
+ %   \cite{key} ==>>          [#]
+ %   \cite[chap. 2]{key} ==>> [#, chap. 2]
+ % where # is a number determined by the ordering in the reference list.
+ % The order in the reference list is alphabetical by authors.
+ %---------------------------------------------------------------------
+
+ENTRY
+  { address
+    archive
+    author
+    booktitle
+    chapter
+    doi
+    edition
+    editor
+    eid
+    eprint
+    howpublished
+    institution
+    isbn
+    issn
+    journal
+    key
+    language
+    month
+    note
+    number
+    organization
+    pages
+    publisher
+    school
+    series
+    title
+    type
+    url
+    volume
+    year
+  }
+  {}
+  { label }
+INTEGERS { output.state before.all mid.sentence after.sentence after.block }
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+  #1 'mid.sentence :=
+  #2 'after.sentence :=
+  #3 'after.block :=
+}
+STRINGS { s t}
+FUNCTION {output.nonnull}
+{ 's :=
+  output.state mid.sentence =
+    { ", " * write$ }
+    { output.state after.block =
+        { add.period$ write$
+          newline$
+          "\newblock " write$
+        }
+        { output.state before.all =
+            'write$
+            { add.period$ " " * write$ }
+          if$
+        }
+      if$
+      mid.sentence 'output.state :=
+    }
+  if$
+  s
+}
+FUNCTION {output}
+{ duplicate$ empty$
+    'pop$
+    'output.nonnull
+  if$
+}
+FUNCTION {output.check}
+{ 't :=
+  duplicate$ empty$
+    { pop$ "empty " t * " in " * cite$ * warning$ }
+    'output.nonnull
+  if$
+}
+FUNCTION {fin.entry}
+{ add.period$
+  write$
+  newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+    'skip$
+    { after.block 'output.state := }
+  if$
+}
+FUNCTION {new.sentence}
+{ output.state after.block =
+    'skip$
+    { output.state before.all =
+        'skip$
+        { after.sentence 'output.state := }
+      if$
+    }
+  if$
+}
+FUNCTION {add.blank}
+{  " " * before.all 'output.state :=
+}
+
+FUNCTION {add.colon}
+{ duplicate$ empty$
+    'skip$
+    { ":" * add.blank }
+  if$
+}
+
+FUNCTION {date.block}
+{
+  skip$
+}
+
+FUNCTION {not}
+{   { #0 }
+    { #1 }
+  if$
+}
+FUNCTION {and}
+{   'skip$
+    { pop$ #0 }
+  if$
+}
+FUNCTION {or}
+{   { pop$ #1 }
+    'skip$
+  if$
+}
+FUNCTION {new.block.checka}
+{ empty$
+    'skip$
+    'new.block
+  if$
+}
+FUNCTION {new.block.checkb}
+{ empty$
+  swap$ empty$
+  and
+    'skip$
+    'new.block
+  if$
+}
+FUNCTION {new.sentence.checka}
+{ empty$
+    'skip$
+    'new.sentence
+  if$
+}
+FUNCTION {new.sentence.checkb}
+{ empty$
+  swap$ empty$
+  and
+    'skip$
+    'new.sentence
+  if$
+}
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+    { pop$ "" }
+    'skip$
+  if$
+}
+FUNCTION {emphasize}
+{ duplicate$ empty$
+    { pop$ "" }
+    { "\emph{" swap$ * "}" * }
+  if$
+}
+FUNCTION {tie.or.space.prefix}
+{ duplicate$ text.length$ #3 <
+    { "~" }
+    { " " }
+  if$
+  swap$
+}
+
+FUNCTION {capitalize}
+{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {space.word}
+{ " " swap$ * " " * }
+ % Here are the language-specific definitions for explicit words.
+ % Each function has a name bbl.xxx where xxx is the English word.
+ %-------------------------------------------------------------------
+ % Begin module:
+ % \ProvidesFile{czech.mbs}[2006/03/31 1.0 (DM)]
+
+ % The language selected here is CZECH
+FUNCTION {bbl.and}
+{ "a"}
+
+FUNCTION {bbl.etal}
+{ "aj." }
+
+FUNCTION {bbl.editors}
+{ "editoři" }
+
+FUNCTION {bbl.editor}
+{ "editor" }
+
+FUNCTION {bbl.edby}
+{ "editace" }
+
+FUNCTION {bbl.edition}
+{ "vydání" }
+
+FUNCTION {bbl.volume}
+{ "ročník" }
+
+FUNCTION {bbl.of}
+{ "" }
+
+FUNCTION {bbl.number}
+{ "číslo" }
+
+FUNCTION {bbl.nr}
+{ "č." }
+
+FUNCTION {bbl.in}
+{ "in" }
+
+FUNCTION {bbl.pages}
+{ "s." }
+
+FUNCTION {bbl.page}
+{ "str." }
+
+FUNCTION {bbl.chapter}
+{ "kapitola" }
+
+FUNCTION {bbl.techrep}
+{ "Technická Zpráva" }
+
+FUNCTION {bbl.mthesis}
+{ "Diplomová práce" }
+
+FUNCTION {bbl.phdthesis}
+{ "Dizertační práce" }
+
+FUNCTION {bbl.first}
+{ "První" }
+
+FUNCTION {bbl.second}
+{ "Druhé" }
+
+FUNCTION {bbl.third}
+{ "Třetí" }
+
+FUNCTION {bbl.fourth}
+{ "Čtvrté" }
+
+FUNCTION {bbl.fifth}
+{ "Páté" }
+
+FUNCTION {bbl.st}
+{ "" }
+
+FUNCTION {bbl.nd}
+{ "" }
+
+FUNCTION {bbl.rd}
+{ "" }
+
+FUNCTION {bbl.th}
+{ "" }
+
+MACRO {jan} {"Leden"}
+
+MACRO {feb} {"Únor"}
+
+MACRO {mar} {"Březen"}
+
+MACRO {apr} {"Duben"}
+
+MACRO {may} {"Květen"}
+
+MACRO {jun} {"Červen"}
+
+MACRO {jul} {"Červenec"}
+
+MACRO {aug} {"Srpen"}
+
+MACRO {sep} {"Září"}
+
+MACRO {oct} {"Říjen"}
+
+MACRO {nov} {"Listopad"}
+
+MACRO {dec} {"Prosinec"}
+
+ % End module: czech.mbs
+%% Copyright 1994-2004 Patrick W Daly
+MACRO {acmcs} {"ACM Computing Surveys"}
+
+MACRO {acta} {"Acta Informatica"}
+
+MACRO {cacm} {"Communications of the ACM"}
+
+MACRO {ibmjrd} {"IBM Journal of Research and Development"}
+
+MACRO {ibmsj} {"IBM Systems Journal"}
+
+MACRO {ieeese} {"IEEE Transactions on Software Engineering"}
+
+MACRO {ieeetc} {"IEEE Transactions on Computers"}
+
+MACRO {ieeetcad}
+ {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"}
+
+MACRO {ipl} {"Information Processing Letters"}
+
+MACRO {jacm} {"Journal of the ACM"}
+
+MACRO {jcss} {"Journal of Computer and System Sciences"}
+
+MACRO {scp} {"Science of Computer Programming"}
+
+MACRO {sicomp} {"SIAM Journal on Computing"}
+
+MACRO {tocs} {"ACM Transactions on Computer Systems"}
+
+MACRO {tods} {"ACM Transactions on Database Systems"}
+
+MACRO {tog} {"ACM Transactions on Graphics"}
+
+MACRO {toms} {"ACM Transactions on Mathematical Software"}
+
+MACRO {toois} {"ACM Transactions on Office Information Systems"}
+
+MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"}
+
+MACRO {tcs} {"Theoretical Computer Science"}
+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$
+}
+FUNCTION {format.eprint}
+{ eprint duplicate$ empty$
+    'skip$
+    { "\eprint"
+      archive empty$
+        'skip$
+        { "[" * archive * "]" * }
+      if$
+      "{" * swap$ * "}" *
+    }
+  if$
+}
+FUNCTION {write.url}
+{ url empty$
+    { skip$ }
+    { "\newline\urlprefix\url{" url * "}" * write$ newline$ }
+  if$
+}
+
+STRINGS  { bibinfo}
+INTEGERS { nameptr namesleft numnames }
+
+FUNCTION {format.names}
+{ 'bibinfo :=
+  duplicate$ empty$ 'skip$ {
+  's :=
+  "" 't :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      "{vv~}{ll}{, f.}{, jj}"
+      format.name$
+      bibinfo bibinfo.check
+      't :=
+      nameptr #1 >
+        {
+          nameptr #3
+          #1 + =
+          numnames #3
+          > and
+            { "others" 't :=
+              #1 'namesleft := }
+            'skip$
+          if$
+          namesleft #1 >
+            { "; " * t * }
+            {
+              ";" *
+              s nameptr "{ll}" format.name$ duplicate$ "others" =
+                { 't := }
+                { pop$ }
+              if$
+              t "others" =
+                {
+                  " " * bbl.etal *
+                }
+                { " " * t * }
+              if$
+            }
+          if$
+        }
+        't
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+  } if$
+}
+FUNCTION {format.names.ed}
+{
+  'bibinfo :=
+  duplicate$ empty$ 'skip$ {
+  's :=
+  "" 't :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      "{f.~}{vv~}{ll}{, jj}"
+      format.name$
+      bibinfo bibinfo.check
+      't :=
+      nameptr #1 >
+        {
+          namesleft #1 >
+            { "; " * t * }
+            {
+              ";" *
+              s nameptr "{ll}" format.name$ duplicate$ "others" =
+                { 't := }
+                { pop$ }
+              if$
+              t "others" =
+                {
+
+                  " " * bbl.etal *
+                }
+                { " " * t * }
+              if$
+            }
+          if$
+        }
+        't
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+  } if$
+}
+FUNCTION {format.authors}
+{ author "author" format.names
+}
+FUNCTION {get.bbl.editor}
+{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ }
+
+FUNCTION {format.editors}
+{ editor "editor" format.names duplicate$ empty$ 'skip$
+    {
+      " " *
+      get.bbl.editor
+   "(" swap$ * ")" *
+      *
+    }
+  if$
+}
+FUNCTION {format.book.pages}
+{ pages "pages" bibinfo.check
+  duplicate$ empty$ 'skip$
+    { " " * bbl.pages * }
+  if$
+}
+FUNCTION {format.isbn}
+{ isbn "isbn" bibinfo.check
+  duplicate$ empty$ 'skip$
+    {
+      "ISBN " swap$ *
+    }
+  if$
+}
+
+FUNCTION {format.issn}
+{ issn "issn" bibinfo.check
+  duplicate$ empty$ 'skip$
+    {
+      "ISSN " swap$ *
+    }
+  if$
+}
+
+FUNCTION {format.doi}
+{ doi "doi" bibinfo.check
+  duplicate$ empty$ 'skip$
+    {
+      "\doi{" swap$ * "}" *
+    }
+  if$
+}
+FUNCTION {select.language}
+{ duplicate$ empty$
+    'pop$
+    { language empty$
+        'skip$
+        { "{\selectlanguage{" language * "}" * swap$ * "}" * }
+      if$
+    }
+    if$
+}
+
+FUNCTION {format.note}
+{
+ note empty$
+    { "" }
+    { note #1 #1 substring$
+      duplicate$ "{" =
+        'skip$
+        { output.state mid.sentence =
+          { "l" }
+          { "u" }
+        if$
+        change.case$
+        }
+      if$
+      note #2 global.max$ substring$ * "note" bibinfo.check
+    }
+  if$
+}
+
+FUNCTION {format.title}
+{ title
+  "title" bibinfo.check
+  duplicate$ empty$ 'skip$
+    {
+      select.language
+    }
+  if$
+}
+FUNCTION {output.bibitem}
+{ newline$
+  "\bibitem{" write$
+  cite$ write$
+  "}" write$
+  newline$
+  ""
+  before.all 'output.state :=
+}
+
+FUNCTION {n.dashify}
+{
+  '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$
+}
+
+FUNCTION {word.in}
+{ bbl.in capitalize
+  " " * }
+
+FUNCTION {format.date}
+{
+  month "month" bibinfo.check
+  duplicate$ empty$
+  year  "year"  bibinfo.check duplicate$ empty$
+    { swap$ 'skip$
+        { "there's a month but no year in " cite$ * warning$ }
+      if$
+      *
+    }
+    { swap$ 'skip$
+        {
+          swap$
+          " " * swap$
+        }
+      if$
+      *
+    }
+  if$
+}
+FUNCTION {format.btitle}
+{ title "title" bibinfo.check
+  duplicate$ empty$ 'skip$
+    {
+      emphasize
+      select.language
+    }
+  if$
+}
+FUNCTION {either.or.check}
+{ empty$
+    'pop$
+    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+  if$
+}
+FUNCTION {format.bvolume}
+{ volume empty$
+    { "" }
+    { bbl.volume volume tie.or.space.prefix
+      "volume" bibinfo.check * *
+      series "series" bibinfo.check
+      duplicate$ empty$ 'pop$
+        { emphasize ", " * swap$ * }
+      if$
+      "volume and number" number either.or.check
+    }
+  if$
+}
+FUNCTION {format.number.series}
+{ volume empty$
+    { number empty$
+        { series field.or.null }
+        { series empty$
+            { number "number" bibinfo.check }
+            { output.state mid.sentence =
+                { bbl.number }
+                { bbl.number capitalize }
+              if$
+              number tie.or.space.prefix "number" bibinfo.check * *
+              bbl.in space.word *
+              series "series" bibinfo.check *
+            }
+          if$
+        }
+      if$
+    }
+    { "" }
+  if$
+}
+FUNCTION {is.num}
+{ chr.to.int$
+  duplicate$ "0" chr.to.int$ < not
+  swap$ "9" chr.to.int$ > not and
+}
+
+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$
+}
+
+FUNCTION {convert.edition}
+{ extract.num "l" change.case$ 's :=
+  s "first" = s "1" = or
+    { bbl.first 't := }
+    { s "second" = s "2" = or
+        { bbl.second 't := }
+        { s "third" = s "3" = or
+            { bbl.third 't := }
+            { s "fourth" = s "4" = or
+                { bbl.fourth 't := }
+                { s "fifth" = s "5" = or
+                    { bbl.fifth 't := }
+                    { s #1 #1 substring$ is.num
+                        { s bbl.th * 't := }
+                        { edition 't := }
+                      if$
+                    }
+                  if$
+                }
+              if$
+            }
+          if$
+        }
+      if$
+    }
+  if$
+  t
+}
+
+FUNCTION {format.edition}
+{ edition duplicate$ empty$ 'skip$
+    {
+      convert.edition
+      output.state mid.sentence =
+        { "l" }
+        { "t" }
+      if$ change.case$
+      "edition" bibinfo.check
+      " " * bbl.edition *
+    }
+  if$
+}
+INTEGERS { multiresult }
+FUNCTION {multi.page.check}
+{ '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 {format.pages}
+{ pages duplicate$ empty$ 'skip$
+    { duplicate$ multi.page.check
+        {
+          bbl.pages swap$
+          n.dashify
+        }
+        {
+          bbl.page swap$
+        }
+      if$
+      tie.or.space.prefix
+      "pages" bibinfo.check
+      * *
+    }
+  if$
+}
+FUNCTION {format.journal.pages}
+{ pages duplicate$ empty$ 'pop$
+    { swap$ duplicate$ empty$
+        { pop$ pop$ format.pages }
+        {
+          ": " *
+          swap$
+          n.dashify
+          pages multi.page.check
+            'bbl.pages
+            'bbl.page
+          if$
+          swap$ tie.or.space.prefix
+          "pages" bibinfo.check
+          * *
+          *
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {format.journal.eid}
+{ eid "eid" bibinfo.check
+  duplicate$ empty$ 'pop$
+    { swap$ duplicate$ empty$ 'skip$
+      {
+          ": " *
+      }
+      if$
+      swap$ *
+    }
+  if$
+}
+FUNCTION {format.vol.num.pages}
+{ volume field.or.null
+  duplicate$ empty$ 'skip$
+    {
+      bbl.volume swap$ tie.or.space.prefix
+      "volume" bibinfo.check
+      * *
+    }
+  if$
+  number "number" bibinfo.check duplicate$ empty$ 'skip$
+    {
+      swap$ duplicate$ empty$
+        { "there's a number but no volume in " cite$ * warning$ }
+        'skip$
+      if$
+      swap$
+      ", " bbl.nr * number tie.or.space.prefix pop$ * swap$ *
+    }
+  if$ *
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+    { "" }
+    { type empty$
+        { bbl.chapter }
+        { type "l" change.case$
+          "type" bibinfo.check
+        }
+      if$
+      chapter tie.or.space.prefix
+      "chapter" bibinfo.check
+      * *
+    }
+  if$
+}
+
+FUNCTION {format.booktitle}
+{
+  booktitle "booktitle" bibinfo.check
+  emphasize
+}
+FUNCTION {format.in.ed.booktitle}
+{ format.booktitle duplicate$ empty$ 'skip$
+    {
+      format.bvolume duplicate$ empty$ 'pop$
+        { ", " swap$ * * }
+      if$
+      editor "editor" format.names.ed duplicate$ empty$ 'pop$
+        {
+          bbl.edby
+          " " * swap$ *
+          swap$
+          "," *
+          " " * swap$
+          * }
+      if$
+      word.in swap$ *
+    }
+  if$
+}
+FUNCTION {empty.misc.check}
+{ author empty$ title empty$ howpublished empty$
+  month empty$ year empty$ note empty$
+  and and and and and
+  key empty$ not and
+    { "all relevant fields are empty in " cite$ * warning$ }
+    'skip$
+  if$
+}
+FUNCTION {format.thesis.type}
+{ type duplicate$ empty$
+    'pop$
+    { swap$ pop$
+      "t" change.case$ "type" bibinfo.check
+    }
+  if$
+}
+FUNCTION {format.tr.number}
+{ number "number" bibinfo.check
+  type duplicate$ empty$
+    { pop$ bbl.techrep }
+    'skip$
+  if$
+  "type" bibinfo.check
+  swap$ duplicate$ empty$
+    { pop$ "t" change.case$ }
+    { tie.or.space.prefix * * }
+  if$
+}
+FUNCTION {format.article.crossref}
+{
+  key duplicate$ empty$
+    { pop$
+      journal duplicate$ empty$
+        { "need key or journal for " cite$ * " to crossref " * crossref * warning$ }
+        { "journal" bibinfo.check emphasize word.in swap$ * }
+      if$
+    }
+    { word.in swap$ * " " *}
+  if$
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.crossref.editor}
+{ editor #1 "{vv~}{ll}" format.name$
+  "editor" bibinfo.check
+  editor num.names$ duplicate$
+  #2 >
+    { pop$
+      "editor" bibinfo.check
+      " " * bbl.etal
+      *
+    }
+    { #2 <
+        'skip$
+        { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+            {
+              "editor" bibinfo.check
+              " " * bbl.etal
+              *
+            }
+            {
+             bbl.and space.word
+              * editor #2 "{vv~}{ll}" format.name$
+              "editor" bibinfo.check
+              *
+            }
+          if$
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {format.book.crossref}
+{ volume duplicate$ empty$
+    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+      pop$ word.in
+    }
+    { bbl.volume
+      capitalize
+      swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of space.word *
+    }
+  if$
+  editor empty$
+  editor field.or.null author field.or.null =
+  or
+    { key empty$
+        { series empty$
+            { "need editor, key, or series for " cite$ * " to crossref " *
+              crossref * warning$
+              "" *
+            }
+            { series emphasize * }
+          if$
+        }
+        { key * }
+      if$
+    }
+    { format.crossref.editor * }
+  if$
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.incoll.inproc.crossref}
+{
+  editor empty$
+  editor field.or.null author field.or.null =
+  or
+    { key empty$
+        { format.booktitle duplicate$ empty$
+            { "need editor, key, or booktitle for " cite$ * " to crossref " *
+              crossref * warning$
+            }
+            { word.in swap$ * }
+          if$
+        }
+        { word.in key * " " *}
+      if$
+    }
+    { word.in format.crossref.editor * " " *}
+  if$
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.org.or.pub}
+{ 't :=
+  ""
+  address empty$ t empty$ and
+    'skip$
+    {
+      address "address" bibinfo.check *
+      t empty$
+        'skip$
+        { address empty$
+            'skip$
+            { ": " * }
+          if$
+          t *
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {format.publisher.address}
+{ publisher "publisher" bibinfo.warn format.org.or.pub
+}
+
+FUNCTION {format.organization.address}
+{ organization "organization" bibinfo.check format.org.or.pub
+}
+
+FUNCTION {article}
+{ output.bibitem
+  format.authors "author" output.check
+  add.colon
+  format.title "title" output.check
+  new.sentence
+  crossref missing$
+    {
+      journal
+      "journal" bibinfo.check
+      emphasize
+      "journal" output.check
+      format.vol.num.pages output
+      format.date "year" output.check
+    }
+    { format.article.crossref output.nonnull
+    }
+  if$
+  eid empty$
+    { format.journal.pages }
+    { format.journal.eid }
+  if$
+  format.issn output
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+FUNCTION {book}
+{ output.bibitem
+  author empty$
+    { format.editors "author and editor" output.check
+      add.colon
+    }
+    { format.authors output.nonnull
+      add.colon
+      crossref missing$
+        { "author and editor" editor either.or.check }
+        'skip$
+      if$
+    }
+  if$
+  format.btitle "title" output.check
+  crossref missing$
+    { format.bvolume output
+  new.sentence
+      format.number.series output
+      format.publisher.address output
+    }
+    {
+  new.sentence
+      format.book.crossref output.nonnull
+    }
+  if$
+  format.edition output
+  format.date "year" output.check
+  format.isbn output
+  format.book.pages output
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+FUNCTION {booklet}
+{ output.bibitem
+  format.authors output
+  add.colon
+  format.title "title" output.check
+  new.sentence
+  howpublished "howpublished" bibinfo.check output
+  address "address" bibinfo.check output
+  format.date output
+  format.isbn output
+  format.book.pages output
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+
+FUNCTION {inbook}
+{ output.bibitem
+  author empty$
+    { format.editors "author and editor" output.check
+      add.colon
+    }
+    { format.authors output.nonnull
+      add.colon
+      crossref missing$
+        { "author and editor" editor either.or.check }
+        'skip$
+      if$
+    }
+  if$
+  format.btitle "title" output.check
+  crossref missing$
+    {
+      format.bvolume output
+      format.chapter.pages "chapter and pages" output.check
+  new.sentence
+      format.number.series output
+      format.publisher.address output
+    }
+    {
+      format.chapter.pages "chapter and pages" output.check
+  new.sentence
+      format.book.crossref output.nonnull
+    }
+  if$
+  format.edition output
+  format.date "year" output.check
+  crossref missing$
+    { format.isbn output }
+    'skip$
+  if$
+  format.pages "pages" output.check
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+
+FUNCTION {incollection}
+{ output.bibitem
+  format.authors "author" output.check
+  add.colon
+  format.title "title" output.check
+  new.sentence
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      format.number.series output
+      format.chapter.pages output
+      format.publisher.address output
+      format.edition output
+      format.date "year" output.check
+      format.isbn output
+    }
+    { format.incoll.inproc.crossref output.nonnull
+      format.chapter.pages output
+    }
+  if$
+  format.pages "pages" output.check
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+FUNCTION {inproceedings}
+{ output.bibitem
+  format.authors "author" output.check
+  add.colon
+  format.title "title" output.check
+  new.sentence
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      format.number.series output
+      publisher empty$
+        { format.organization.address output }
+        { organization "organization" bibinfo.check output
+          format.publisher.address output
+        }
+      if$
+      format.date "year" output.check
+      format.isbn output
+      format.issn output
+    }
+    { format.incoll.inproc.crossref output.nonnull
+    }
+  if$
+  format.pages "pages" output.check
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+FUNCTION {conference} { inproceedings }
+FUNCTION {manual}
+{ output.bibitem
+  author empty$
+    { organization "organization" bibinfo.check
+      duplicate$ empty$ 'pop$
+        { output
+          address "address" bibinfo.check output
+        }
+      if$
+    }
+    { format.authors output.nonnull }
+  if$
+  add.colon
+  format.btitle "title" output.check
+  new.sentence
+  author empty$
+    { organization empty$
+        {
+          address "address" bibinfo.check output
+        }
+        'skip$
+      if$
+    }
+    {
+      organization "organization" bibinfo.check output
+      address "address" bibinfo.check output
+    }
+  if$
+  format.edition output
+  format.date output
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+
+FUNCTION {mastersthesis}
+{ output.bibitem
+  format.authors "author" output.check
+  add.colon
+  format.btitle
+  "title" output.check
+  new.sentence
+  bbl.mthesis format.thesis.type output.nonnull
+  school "school" bibinfo.warn output
+  address "address" bibinfo.check output
+  format.date "year" output.check
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+
+FUNCTION {misc}
+{ output.bibitem
+  format.authors output
+  add.colon
+  format.title output
+  new.sentence
+  howpublished "howpublished" bibinfo.check output
+  format.date output
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+  empty.misc.check
+}
+FUNCTION {phdthesis}
+{ output.bibitem
+  format.authors "author" output.check
+  add.colon
+  format.btitle
+  "title" output.check
+  new.sentence
+  bbl.phdthesis format.thesis.type output.nonnull
+  school "school" bibinfo.warn output
+  address "address" bibinfo.check output
+  format.date "year" output.check
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+
+FUNCTION {proceedings}
+{ output.bibitem
+  editor empty$
+    { organization "organization" bibinfo.check output
+    }
+    { format.editors output.nonnull }
+  if$
+  add.colon
+  format.btitle "title" output.check
+  format.bvolume output
+  format.number.series output
+  editor empty$
+    { publisher empty$
+        'skip$
+        {
+          format.publisher.address output
+        }
+      if$
+    }
+    { publisher empty$
+        {
+          format.organization.address output }
+        {
+          organization "organization" bibinfo.check output
+          format.publisher.address output
+        }
+      if$
+     }
+  if$
+      format.date "year" output.check
+  format.isbn output
+  format.issn output
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+
+FUNCTION {techreport}
+{ output.bibitem
+  format.authors "author" output.check
+  add.colon
+  format.title
+  "title" output.check
+  new.sentence
+  format.tr.number output.nonnull
+  institution "institution" bibinfo.warn output
+  address "address" bibinfo.check output
+  format.date "year" output.check
+  format.doi output
+  format.note output
+  format.eprint output
+  fin.entry
+  write.url
+}
+
+FUNCTION {unpublished}
+{ output.bibitem
+  format.authors "author" output.check
+  add.colon
+  format.title "title" output.check
+  format.date output
+  format.doi output
+  format.note "note" output.check
+  format.eprint output
+  fin.entry
+  write.url
+}
+
+FUNCTION {default.type} { misc }
+READ
+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 > }
+    { s nameptr
+      "{ll{ }}{  f{ }}{  jj{ }}"
+      format.name$ 't :=
+      nameptr #1 >
+        {
+          nameptr #3
+          #1 + =
+          numnames #3
+          > and
+            { "others" 't :=
+              #1 'namesleft := }
+            'skip$
+          if$
+          "   "  *
+          namesleft #1 = t "others" = and
+            { "zzzzz" * }
+            { t sortify * }
+          if$
+        }
+        { 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 {presort}
+{ type$ "book" =
+  type$ "inbook" =
+  or
+    'author.editor.sort
+    { type$ "proceedings" =
+        'editor.organization.sort
+        { type$ "manual" =
+            'author.organization.sort
+            'author.sort
+          if$
+        }
+      if$
+    }
+  if$
+  "    "
+  *
+  year field.or.null sortify
+  *
+  "    "
+  *
+  title field.or.null
+  sort.format.title
+  *
+  #1 entry.max$ substring$
+  'sort.key$ :=
+}
+ITERATE {presort}
+SORT
+STRINGS { longest.label }
+INTEGERS { number.label longest.label.width }
+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$
+}
+EXECUTE {initialize.longest.label}
+ITERATE {longest.label.pass}
+FUNCTION {begin.bib}
+{ preamble$ empty$
+    'skip$
+    { preamble$ write$ newline$ }
+  if$
+  "\begin{thebibliography}{"  longest.label  * "}" *
+  write$ newline$
+  "\providecommand{\url}[1]{\texttt{#1}}"
+  write$ newline$
+  "\providecommand{\urlprefix}{URL }"
+  write$ newline$
+  "\expandafter\ifx\csname urlstyle\endcsname\relax"
+  write$ newline$
+  "  \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else"
+  write$ newline$
+  "  \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup \urlstyle{rm}\Url}\fi"
+  write$ newline$
+  "\providecommand{\selectlanguage}[1]{\relax}"
+  write$ newline$
+  "\providecommand{\eprint}[2][]{\url{#2}}"
+  write$ newline$
+}
+EXECUTE {begin.bib}
+EXECUTE {init.state.consts}
+ITERATE {call.type$}
+FUNCTION {end.bib}
+{ newline$
+  "\end{thebibliography}" write$ newline$
+}
+EXECUTE {end.bib}
+%% End of customized bst file
+%%
+%% End of file `czechiso.bst'.
Index: /applications/doprava/texty/novotny_vyzk_LQ/Results.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Results.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Results.tex (revision 1419)
@@ -0,0 +1,1 @@
+\chapter{Výsledky} 
Index: /applications/doprava/texty/novotny_vyzk_LQ/Implementation.log
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Implementation.log (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Implementation.log (revision 1419)
@@ -0,0 +1,214 @@
+This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=latex 2011.7.1)  9 AUG 2011 20:37
+entering extended mode
+ %&-line parsing enabled.
+**Implementation.tex
+(./Implementation.tex
+LaTeX2e <2009/09/24>
+Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
+yphenation, loaded.
+! Undefined control sequence.
+l.1 \chapter
+            {Implementace}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.1 \chapter{I
+              mplementace}
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no I in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
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Index: /applications/doprava/texty/novotny_vyzk_LQ/04_Bayes/Bayes.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/04_Bayes/Bayes.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/04_Bayes/Bayes.tex (revision 1419)
@@ -0,0 +1,74 @@
+\section{Bayesovské učení}
+
+% \section{Úvod}
+V této kapitole je naznačena metoda bayesovského učení
+, což je bodový odhadu parametru rozdělení náhodné veličiny 
+založený na Bayesovuě větě. 
+Tato metoda byla použita v článku \cite{4_rmm_formalization} ke zlepšení
+odhadu pravděpodobnosti uskutečnění se modelového chování ostatních agentů.
+Jeho výhodou je využití experimentální i expertní znalosti.
+V praxi se této metody hojně využívá tam, kde jsou data získávána postupně a zpočátku je nutné parametr
+odhadnout na základě zkušenosti a nadále ho podle výsledků měření zpřesňovat.
+
+\begin{definition}[Podmíněná pravděpodobnost]\label{de:podm_pravd}
+ Nechť $A$ a $B$ jsou náhodné jevy. Podmíněná pravděpodobnost jevu $A$ na jevu $B$, tedy pravděpodobnost že nastane
+ jev $A$ pokud nastane jev $B$, je definována jako
+  $$ P(A|B) = \frac{P(A \cap B )}{P(B)} $$
+\end{definition}
+
+\begin{proposition}[Bayesova věta]\label{v:bayes}
+ Nechť $A$ a $B$ jsou náhodné jevy a platí $P(B) > 0$. Potom
+  $$ P(A|B) = \frac{P(B|A) P(A) }{P(B)} $$
+\end{proposition}
+
+% \subsection{Značení}
+
+V souladu s \cite{5_bayes_learn} zavedeme následující značení:
+
+\begin{itemize}
+ \item $y(t) = [ y_1, ..., y_T ] $ - vetor $T \in \mathbb{N}$ naměřených hodnot, kde $y_t \in \{ 0,1 \}$ a $y_t = 1$ značí, 
+				      že výsledek experimentu v čase $t \in \{ 1, ..., T \}$ dopadlu v souladu s naší hypotézou
+ \item $\Theta$  - parametr rozdělení
+ \item $ \hat{\Theta}_{T} $  - odhad parametru při $T$ naměřených hodnotách
+ \item $f(y_t|\Theta)$ - hustota pravděpodobnosti náhodné veličiny v čase $t$ při parametru $\Theta$ 
+\end{itemize}
+
+\subsection{Věrohodnostní funkce}
+
+K odhadu parametru se v této metodě využívá věrohodnostní funkce, která vyjadřuje
+pravděpodobnost, že při daném parametru se bude vektor naměřených výsledků bude rovnat 
+teoretické hodnotě. V \cite{5_bayes_learn} se tato funkce definuje jako: \footnotemark
+
+\footnotetext{Tato definice je poněkud zjednodušena a předpokládá, že výsledek $t$-tého pokusu nezávisí na 
+předchozích pokusech, ani na počátečních podmínkách před $t$-tým pokusem.}
+
+\begin{definition}[Věrohodnostní funkce]\label{de:ver_fce}
+ $$f(y(T)|\Theta) = \prod_{t=1}^T f(y_t|\Theta) $$
+\end{definition}
+
+Při použití těchtu veličin nabývá Bayesova věta podle \cite{5_bayes_learn} tvaru
+
+$$ f(\Theta|y(T)) = \frac{f(y(T)|\Theta) f(\Theta)}{f(y(T))} $$
+
+kde jsou
+
+\begin{itemize}
+ \item $ f(\Theta|y(T)) $ aposteriorní hustota pravděpodobnosti
+ \item $ f(y(T)|\Theta) $ Věrohodnostní funkce
+ \item $ f(\Theta) = f(\Theta|y(0)) $ je tzv. apriorní hustota pravděpodobnosti
+ \item $ f(y(T)) $ normalizační konstanta ($ f(\Theta|y(T)) $ se bere jako funkce $\Theta$ a parametrů $y(t)$)
+\end{itemize}
+
+Apriorní hustota pravděpodobnosti zde vyjadřuje odhad parametru při nenaměřených datech. Jedná se tedy
+o expertní odhad, předpokládané chování náhodné veličiny založené na známých faktech a zkušenosti.
+Aposteriorní hustota pravděpodobnosti představuje pravděpodobnost parametru $\Theta$ závislou
+na naměřených hodnotách náhodné veličiny a její střední hodnota je odhadem tohoto parametru.
+Tedy platí:
+
+$$ \hat{\Theta}_T = \int_{\mathbb{R}} f(\Theta|y(T)) d\Theta $$
+
+
+
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/04_Bayes/Bayes.tex.backup
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/04_Bayes/Bayes.tex.backup (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/04_Bayes/Bayes.tex.backup (revision 1419)
@@ -0,0 +1,70 @@
+\section{Bayesovské učení}
+
+% \section{Úvod}
+V této kapitole je naznačena metoda bayesovského učení, což je bodový odhadu parametru rozdělení náhodné veličiny 
+založený na Bayesovuě větě. Jeho výhodou je využití experimentální i expertní znalosti.
+V praxi se této metody hojně využívá tam, kde jsou data získávána postupně a zpočátku je nutné parametr
+odhadnout na základě zkušenosti a nadále ho podle výsledků měření zpřesňovat.
+
+\begin{definition}[Podmíněná pravděpodobnost]\label{de:podm_pravd}
+ Nechť $A$ a $B$ jsou náhodné jevy. Podmíněná pravděpodobnost jevu $A$ na jevu $B$, tedy pravděpodobnost že nastane
+ jev $A$ pokud nastane jev $B$, je definována jako
+  $$ P(A|B) = \frac{P(A \cap B )}{P(B)} $$
+\end{definition}
+
+\begin{proposition}[Bayesova věta]\label{v:bayes}
+ Nechť $A$ a $B$ jsou náhodné jevy a platí $P(B) > 0$. Potom
+  $$ P(A|B) = \frac{P(B|A) P(A) }{P(B)} $$
+\end{proposition}
+
+% \section{Značení}
+
+V souladu s \cite{5_bayes_learn} zavedeme následující značení:
+
+\begin{itemize}
+ \item $y(t) = [ y_1, ..., y_T ] $ - vetor $T \in \mathbb{N}$ naměřených hodnot, kde $y_t \in \{ 0,1 \}$ a $y_t = 1$ značí, 
+				      že výsledek experimentu v čase $t \in \{ 1, ..., T \}$ dopadlu v souladu s naší hypotézou
+ \item $\Theta$  - parametr rozdělení
+ \item $ \hat{\Theta}_{T} $  - odhad parametru při $T$ naměřených hodnotách
+ \item $f(y_t|\Theta)$ - hustota pravděpodobnosti náhodné veličiny v čase $t$ při parametru $\Theta$ 
+\end{itemize}
+
+\section{Věrohodnostní funkce}
+
+K odhadu parametru se v této metodě využívá věrohodnostní funkce, která vyjadřuje
+pravděpodobnost, že při daném parametru se bude vektor naměřených výsledků bude rovnat 
+teoretické hodnotě. V \cite{5_bayes_learn} se tato funkce definuje jako: \footnotemark
+
+\footnotetext{Tato definice je poněkud zjednodušena a předpokládá, že výsledek $t$-tého pokusu nezávisí na 
+předchozích pokusech, ani na počátečních podmínkách před $t$-tým pokusem.}
+
+\begin{definition}[Věrohodnostní funkce]\label{de:ver_fce}
+ $$f(y(T)|\Theta) = \prod_{t=1}^T f(y_t|\Theta) $$
+\end{definition}
+
+Při použití těchtu veličin nabývá Bayesova věta podle \cite{5_bayes_learn} tvaru
+
+$$ f(\Theta|y(T)) = \frac{f(y(T)|\Theta) f(\Theta)}{f(y(T))} $$
+
+kde jsou
+
+\begin{itemize}
+ \item $ f(\Theta|y(T)) $ aposteriorní hustota pravděpodobnosti
+ \item $ f(y(T)|\Theta) $ Věrohodnostní funkce
+ \item $ f(\Theta) = f(\Theta|y(0)) $ je tzv. apriorní hustota pravděpodobnosti
+ \item $ f(y(T)) $ normalizační konstanta ($ f(\Theta|y(T)) $ se bere jako funkce $\Theta$ a parametrů $y(t)$)
+\end{itemize}
+
+Apriorní hustota pravděpodobnosti zde vyjadřuje odhad parametru při nenaměřených datech. Jedná se tedy
+o expertní odhad, předpokládané chování náhodné veličiny založené na známých faktech a zkušenosti.
+Aposteriorní hustota pravděpodobnosti představuje pravděpodobnost parametru $\Theta$ závislou
+na naměřených hodnotách náhodné veličiny a její střední hodnota je odhadem tohoto parametru.
+Tedy platí:
+
+$$ \hat{\Theta}_T = \int_{\mathbb{R}} f(\Theta|y(T)) d\Theta $$
+
+
+
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzkumak.kilepr
===================================================================
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Index: /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.fdb_latexmk
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.fdb_latexmk (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.fdb_latexmk (revision 1419)
@@ -0,0 +1,7 @@
+# Fdb version 3
+["pdflatex"] 1320508920 "LQ_rizeni.tex" "LQ_rizeni.pdf" "LQ_rizeni" 
+  "LQ_rizeni.aux" 1320508920 8 a94a2480d3289e625eea47cd1b285758 ""
+  "LQ_rizeni.tex" 1320508920 23 ba1ceccc510c3400729cc9abfda149f7 ""
+  (generated)
+  "LQ_rizeni.pdf"
+  "LQ_rizeni.log"
Index: /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning.tex (revision 1419)
@@ -0,0 +1,154 @@
+
+
+\section{Markovův rozhodvací proces}
+Markovův rozhodvací proces je alternativní metoda sloužící
+k volbě strategií odhadem zisků z nich plynoucích do budoucna.
+Modeluje prostředí jako množinu stavů a akcí, které 
+je možné provést a mění stav prostředí s určitou pravděpodobností.
+Čas je zde vnímán v diskrétní formě kroků a prostředí jako částečně známé, částečně
+ovlivnitelné a do jisté míry měnící se náhodně.\\
+
+Účelem tohoto procesu je najít funkci $\pi(s): S \rightarrow A$
+která každému stavu prostředí jednoznačně přiřadí akci maximalizující
+zisky do určitého bodu v budoucnosti, teoreticky do nekonečna.
+V \cite{3_i_traff_light_c} je Markovův rozhodovací proces definován takto:
+
+\begin{definition}[Markovův rozhodovací proces]\label{de:markov_decision_process}
+  Markovův rozhodovací proces je definován jako uspořádaná čtveřice
+  $$ (S, A, P, R) $$
+  kde jsou
+  \begin{itemize}
+    \item $S$ - množina stavů prostředí
+    \item $A$ - množina možných akcí
+    \item $P(i,a,j) := p(s_{t+1} = j | s_t = i \wedge a = a_t)$ - pravděpodobnost, že při aplikování akce $a$
+								  za stavu $i$ přejde systém do stavu $j$
+    \item $R(i,a,j)$ - okamžitý užitek přechodu systému ze stavu $i$ do stavu $j$ při akci $a$
+  \end{itemize}
+\end{definition}
+
+
+
+\subsection{Dynamické programování}\label{sec:dynamic_programming}
+
+%asi trochu poupravit podle \cite{tlc_using_sarsa}
+Dynamické programování je proces sloužící k nalezení optimální
+strategie dané $\pi(s)$. K tomu slouží funkce očekávaných kumulativních diskontních zisků
+$V^{\pi}(i) : \rightarrow \mathbb{R}$ 
+reprezentující předpokládané dlouhodobé zisky při určité $\pi(s)$. Agent se tedy snaží 
+zvolit strategii tak, aby funkci $V^{\pi}$ při daném počátečním stavu $s_0 = i$ maximalizoval.
+V \cite{3_i_traff_light_c} je tato funkce definována násedovně:
+
+\begin{definition}[V-funkce]\label{de:v_function}
+ $$
+    V^{\pi}(i) = \sum_{k=0}^{\infty} E( \gamma^{k} R(s_k, \pi(s_k), s_{k+1}))
+ $$
+při $s_0 = i$ kde jsou
+\begin{itemize}
+ \item $\gamma \in <0,1> $ diskontní faktor určující snižování významnosti odhadu s narůstajícím časem
+ \item $E$ operator odhadu %střední hodnota přes všechny možnosti cesty stav/akce
+\end{itemize}
+\end{definition}
+
+Tento zápis je spíše formální, proto se tato funkce v \cite{3_i_traff_light_c} definuje pomocí
+pomocí $Q$-funkce $Q^{\pi}(i,a)$, funkce odhadující zisk při aplikování akce $a$ při stavu $a$.
+
+\begin{definition}[Q-function]\label{de:q_function}
+ $$
+    Q(i, a)^{\pi} = \sum_{j \in S} P(i,a,j) ( R(i,a,j) + \gamma V^{\pi}(j) )
+ $$
+
+kde jsou
+ $$ V^{\pi}(i) = \max_a Q^{\pi}(i,a) $$,
+ $$ \pi(i) = \arg \max_a Q^{\pi}(i,a) $$
+\end{definition}
+
+Postupným iterativním přepočítáváním $V$, $Q$ a $\pi$ dostaneme Bellmanovu rovnici optimality definovanou v \cite{dynamic_programming}
+jako:
+
+\begin{definition}[Bellmanova rovnice optimality]\label{de:bellman_equation_of_optimality}
+ $$
+    Q(i, a)^{*} = \sum_{j \in S} P(i,a,j) ( R(i,a,j) + \gamma V^{*}(j) )
+ $$
+\end{definition}
+
+kde funkce $Q$ a $V$ nezávisí na strategii $\pi$.
+Bellmanova rovnice optimality říká, že pokud jsou $Q$ a $V$ optimální, 
+nemění se s dalšími kroky iterace. V praxi se stanoví nějaká dostatečně malá konstanta $\epsilon$, a 
+pokud se v dalším kroku $Q$ a $V$ nezmění o vícejak $\epsilon$, považujeme je za optimální.
+Navíc bylo dokázáno, že vždy existuje právě jedna dvojice dvojice těchto funkcí, která je optimální
+a vždy ji lze tedy iterací určit.\\
+
+Algoritmus pro určení funkce $\pi$ tedy iterativně přes všechny stavy, akce a časové
+kroky upravuje funkce $V$, $Q$ a $\pi$ podle rovnic \ref{de:q_function}, a v \cite{3_i_traff_light_c}
+je v krocích popsán takto:
+
+\begin{enumerate}
+ \item Inicializace počátečních hodnot funkcí $V$ a $Q$
+ \item Opakovat kroky 3-5 do dosažení podmínek optimality
+ \item Upravit hodnotu $Q$-funkce podle rovnice
+   $$ Q(i, a) = \sum_{j \in S} P(i,a,j) ( R(i,a,j) + \gamma V(j) ) $$
+ \item dopočítat hodnotu funkce $V$ jako
+  $$ V(i) = \max_a Q(i,a) $$
+ \item nastavit hodnotu funkce $pi$ na akci maximálního zisku jako
+  $$ \pi(i) = \arg \max_a Q(i,a) $$ 
+\end{enumerate}
+
+\section{Zpětnovazebné učení (Reinforcement learning)}
+V praxi jsou z počátku hodnoty funkcí $P$ a $R$ popsané v \ref{de:markov_decision_process}
+neznámé a je potřeba je určit pozorováním. Prakticky se tedy agent musí naučit jak prostředí
+reaguje na provedení každé akce v určitém stavu. Podle \cite{3_i_traff_light_c} se tedy
+na začátku procesu nastaví všechny hodnoty na nulu a po každé provedené akci se pozoruje
+jak prostředí reaguje, tedy hodnota funkce $P(i, a, j)$, a jaký okamžitý zisk z toho plyne, tedy
+$R(i, a, j)$. K určení těchto hodnot se používají různé algoritmy.
+ 
+\subsection{Q-učení (Q-learning)}
+Q-učení je bezmodelová metoda popsaná v \cite{q_learning} a \cite{learning_to_predict}. 
+K určení požadovaných hodnot, jak název napovídá, používá
+úpravu funkce $Q$ definované v \ref{de:q_function} 
+v každém časovém kroce $t$ podle rovnice:
+
+$$
+  Q_t(i,a) = \left\{
+     \begin{array}{lr}
+       (1 - \alpha_t) Q_{t-1}(i,a) + \alpha_t ( r_t + \gamma V_{t-1}(i) ) & : i = i_t \wedge a = a_t \\
+       Q_{t-1}(i,a) & : jinak
+     \end{array}
+   \right.
+$$
+
+kde $ \alpha_t \in <0,1> $ je učící faktor v časovém kroce $t$ a $r_t$ je okamžitý
+zisk akce $a$. Funkce $P$ a $R$ popisující prostředí se zde tedy nevyskytují a 
+$Q$-funkce se zde upravuje přímo z naměřených hodnot za použití snižujícího se
+učícího koeficientu $\alpha$.
+
+
+\subsection{Učení na základě modelu (Model-based learning)}\label{sec:model_based_learning}
+V této metodě, popsané v \cite{3_i_traff_light_c}, se modeluje
+prostředí funkcemi $P(i,a,j)$ a $R(i,a,j)$, které jsou definované v
+\ref{de:markov_decision_process}. Ty jsou z počátku neznámé
+a jejich hodnoty se určují metodou maximální věrohodnosti
+podle četnosti naměřených údajů. Agent popsaný v \cite{3_i_traff_light_c}
+používal následující veličiny:
+
+\begin{itemize}
+ \item $C_{i}(a)$ - počet, kolikrát agent zvolil akci $a$ ve stavu $i$
+ \item $C_{i,j}(a)$ - počet, kolikrát prostředí přešlo ze stavu $i$ do stavu $j$ při aplikace akce $a$
+ \item $R_{i,j}(a)$ - součet okamžitých zisků při použití akce $a$ ve stavu $i$ a následném přechodu do stavu $j$
+\end{itemize}
+
+Model maximální věrohodnosti (MLM) je v \cite{3_i_traff_light_c} definován jako:
+
+\begin{definition}[MLM]\label{de:mlm} 
+ $$ \hat{P} (i,a,j) = \frac{C_{i,j}(a)}{C_i(a)} $$
+ $$ \hat{R} (i,a,j) = \frac{R_{i,j}(a)}{C_{i,j}(a)} $$
+\end{definition}
+
+V každém časovém kroce je po aplikaci akce $a$ model přepočítán. Poté
+je znovu použito dynamické programování popsané v sekci \ref{sec:dynamic_programming}.
+
+
+
+
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/test
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/test (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/test (revision 1419)
@@ -0,0 +1,6 @@
+@comment{This file has been generated by Pybliographer}
+
+@Article{test,
+
+}
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/05_I_a_in_dec_t_c/I_a_in_dec_t_c.tex.backup
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/05_I_a_in_dec_t_c/I_a_in_dec_t_c.tex.backup (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/05_I_a_in_dec_t_c/I_a_in_dec_t_c.tex.backup (revision 1419)
@@ -0,0 +1,7 @@
+\chapter{Agenti v decentralizovaném řízení dopravy}
+
+V této kapitole uvedeme příklady použití multiagentních systémů k řízení dopravy.
+
+% \section{Běžný způsob použití multiagentních systémů v řízení}
+% 
+% tady by to chtělo nakombinovat \cite{2_int_a_in_dec} a \cite{3_i_traff_light_c}
Index: /applications/doprava/texty/novotny_vyzk_LQ/05_I_a_in_dec_t_c/I_a_in_dec_t_c.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/05_I_a_in_dec_t_c/I_a_in_dec_t_c.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/05_I_a_in_dec_t_c/I_a_in_dec_t_c.tex (revision 1419)
@@ -0,0 +1,7 @@
+\chapter{Agenti v decentralizovaném řízení dopravy}
+
+V této kapitole uvedeme příklady použití multiagentních systémů k řízení dopravy.
+
+% \section{Běžný způsob použití multiagentních systémů v řízení}
+% 
+% tady by to chtělo nakombinovat \cite{2_int_a_in_dec} a \cite{3_i_traff_light_c}
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.lof
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.lof (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.lof (revision 1419)
@@ -0,0 +1,9 @@
+\select@language {czech}
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\contentsline {figure}{\numberline {3.1}{\ignorespaces T\IeC {\v r}\IeC {\'\i }\IeC {\'u}rov\IeC {\v n}ov\IeC {\'a} rekurzivn\IeC {\'\i } modelov\IeC {\'a} struktura agenta $R_1$\relax }}{15}{figure.caption.5}
+\contentsline {figure}{\numberline {3.2}{\ignorespaces V\IeC {\'y}sledky m\IeC {\v e}\IeC {\v r}en\IeC {\'\i }. M1 - RMM, M2 - pevn\IeC {\'e} cykly, M3 - "Hill-climbing" \relax }}{16}{figure.caption.6}
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\addvspace {10\p@ }
Index: /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning.tex.backup
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning.tex.backup (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning.tex.backup (revision 1419)
@@ -0,0 +1,141 @@
+
+
+\section{Markovův rozhodvací proces}
+Markovův rozhodvací proces je alternativní metoda sloužící
+k volbě strategií odhadem zisků z nich plynoucích do budoucna.
+Modeluje prostředí jako množinu stavů a akcí, které 
+je možné provést a mění stav prostředí s určitou pravděpodobností.
+Čas je zde vnímán v diskrétní formě kroků a prostředí jako částečně známé, částečně
+ovlivnitelné a do jisté míry měnící se náhodně.\\
+
+Účelem tohoto procesu je najít funkci $\pi(s): S \rightarrow A$
+která každému stavu prostředí jednoznačně přiřadí akci maximalizující
+zisky do určitého bodu v budoucnosti, teoreticky do nekonečna.
+V \cite{3_i_traff_light_c} je Markovův rozhodovací proces definován takto:
+
+\begin{definition}[Markovův rozhodovací proces]\label{de:markov_decision_process}
+  Markovův rozhodovací proces je definován jako uspořádaná čtveřice
+  $$ (S, A, P, R) $$
+  kde jsou
+  \begin{itemize}
+    \item $S$ - množina stavů prostředí
+    \item $A$ - množina možných akcí
+    \item $P(i,a,j) := p(s_{t+1} = j | s_t = i \wedge a = a_t)$ - pravděpodobnost, že při aplikování akce $a$
+								  za stavu $i$ přejde systém do stavu $j$
+    \item $R(i,a,j)$ - okamžitý užitek přechodu systému ze stavu $i$ do stavu $j$ při akci $a$
+  \end{itemize}
+\end{definition}
+
+
+
+\subsubsection{Dynamické programování}
+
+%asi trochu poupravit podle \cite{tlc_using_sarsa}
+Dynamické programování je proces sloužící k nalezení optimální
+strategie dané $\pi(s)$. K tomu slouží funkce očekávaných kumulativních diskontních zisků
+$V^{\pi}(i) : \rightarrow \mathbb{R}$ 
+reprezentující předpokládané dlouhodobé zisky při určité $\pi(s)$. Agent se tedy snaží 
+zvolit strategii tak, aby funkci $V^{\pi}$ při daném počátečním stavu $s_0 = i$ maximalizoval.
+V \cite{3_i_traff_light_c} je tato funkce definována násedovně:
+
+\begin{definition}[V-funkce]\label{de:v_function}
+ $$
+    V^{\pi}(i) = \sum_{k=0}^{\infty} E( \gamma^{k} R(s_k, \pi(s_k), s_{k+1}))
+ $$
+při $s_0 = i$ kde jsou
+\begin{itemize}
+ \item $\gamma \in <0,1> $ diskontní faktor určující snižování významnosti odhadu s narůstajícím časem
+ \item $E$ operator odhadu %střední hodnota přes všechny možnosti cesty stav/akce
+\end{itemize}
+\end{definition}
+
+Tento zápis je spíše formální, proto se tato funkce v \cite{3_i_traff_light_c} definuje pomocí
+pomocí $Q$-funkce $Q^{\pi}(i,a)$, funkce odhadující zisk při aplikování akce $a$ při stavu $a$.
+
+\begin{definition}[Q-function]\label{de:q_function}
+ $$
+    Q(i, a)^{\pi} = \sum_{j \in S} P(i,a,j) ( R(i,a,j) + \gamma V^{\pi}(j) )
+ $$
+
+kde jsou
+ $$ V^{\pi}(i) = \max_a Q^{\pi}(i,a) $$,
+ $$ \pi(i) = \arg \max_a Q^{\pi}(i,a) $$
+\end{definition}
+
+Postupným iterativním přepočítáváním $V$, $Q$ a $\pi$ dostaneme Bellmanovu rovnici optimality definovanou v \cite{dynamic_programming}
+jako:
+
+\begin{definition}[Bellmanova rovnice optimality]\label{de:bellman_equation_of_optimality}
+ $$
+    Q(i, a)^{*} = \sum_{j \in S} P(i,a,j) ( R(i,a,j) + \gamma V^{*}(j) )
+ $$
+\end{definition}
+
+kde funkce $Q$ a $V$ nezávisí na strategii $\pi$.
+Bellmanova rovnice optimality říká, že pokud jsou $Q$ a $V$ optimální, 
+nemění se s dalšími kroky iterace. V praxi se stanoví nějaká dostatečně malá konstanta $\epsilon$, a 
+pokud se v dalším kroku $Q$ a $V$ nezmění o vícejak $\epsilon$, považujeme je za optimální.
+Navíc bylo dokázáno, že vždy existuje právě jedna dvojice dvojice těchto funkcí, která je optimální
+a vždy ji lze tedy iterací určit.\\
+
+Algoritmus pro určení funkce $\pi$ tedy iterativně přes všechny stavy, akce a časové
+kroky upravuje funkce $V$, $Q$ a $\pi$ podle rovnic \ref{de:q_function}, a v \cite{3_i_traff_light_c}
+je v krocích popsán takto:
+
+\begin{enumerate}
+ \item Inicializace počátečních hodnot funkcí $V$ a $Q$
+ \item Opakovat kroky 3-5 do dosažení podmínek optimality
+ \item Upravit hodnotu $Q$-funkce podle rovnice
+   $$ Q(i, a) = \sum_{j \in S} P(i,a,j) ( R(i,a,j) + \gamma V(j) ) $$
+ \item dopočítat hodnotu funkce $V$ jako
+  $$ V(i) = \max_a Q(i,a) $$
+ \item nastavit hodnotu funkce $pi$ na akci maximálního zisku jako
+  $$ \pi(i) = \arg \max_a Q(i,a) $$ 
+\end{enumerate}
+
+\section{Zpětnovazebné učení (Reinforcement learning)}
+V praxi jsou z počátku hodnoty funkcí $P$ a $R$ popsané v \ref{de:markov_decision_process}
+neznámé a je potřeba je určit pozorováním. Prakticky se tedy agent musí naučit jak prostředí
+reaguje na provedení každé akce v určitém stavu. Podle \cite{3_i_traff_light_c} se tedy
+na začátku procesu nastaví všechny hodnoty na nulu a po každé provedené akci se pozoruje
+jak prostředí reaguje, tedy hodnota funkce $P(i, a, j)$, a jaký okamžitý zisk z toho plyne, tedy
+$R(i, a, j)$. K určení těchto hodnot se používají různé algoritmy.
+ 
+\subsection{Q-učení (Q-learning)}
+Q-učení je bezmodelová metoda popsaná v \cite{q_learning} a \cite{learning_to_predict}. 
+K určení požadovaných hodnot, jak název napovídá, používá
+úpravu funkce $Q$ definované v \ref{de:q_function} 
+v každém časovém kroce $t$ podle rovnice:
+
+$$
+  Q_t(i,a) = \left\{
+     \begin{array}{lr}
+       (1 - \alpha_t) Q_{t-1}(i,a) + \alpha_t ( r_t + \gamma V_{t-1}(i) ) & : i = i_t \wedge a = a_t \\
+       Q_{t-1}(i,a) & : jinak
+     \end{array}
+   \right.
+$$
+
+kde $ \alpha_t \in <0,1> $ je učící faktor v časovém kroce $t$ a $r_t$ je okamžitý
+zisk akce $a$. Funkce $P$ a $R$ popisující prostředí se zde tedy nevyskytují a 
+$Q$-funkce se zde upravuje přímo z naměřených hodnot za použití snižujícího se
+učícího koeficientu $\alpha$.
+
+
+\subsection{Učení na základě modelu (Model-based learning)}
+V této metodě, popsané v \cite{3_i_traff_light_c}, se modeluje
+prostředí funkcemi $P(i,a,j)$ a $R(i,a,j)$, které jsou definované v
+\ref{de:markov_decision_process}. Ty jsou z počátku neznámé
+a jejich hodnoty se určují metodou maximální věrohodnosti
+podle četnosti naměřených údajů. Agent popsaný v \cite{3_i_traff_light_c}
+používal následující veličiny:
+
+\begin{itemize}
+ \item $C_{i}(a)$
+ \item $C_{i,j}(a)$
+ \item $C_{i,j}(a)$
+\end{itemize}
+
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/02_Agents/Agents.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/02_Agents/Agents.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/02_Agents/Agents.tex (revision 1419)
@@ -0,0 +1,149 @@
+\chapter{Multiagentní systémy}
+
+\section{Úvod}
+
+Multiagentní systém je druh distribuované umělé inteligence. Tento systém se skládá z
+jednotlivých výpočetních prvků, tzv. agentů, které musí mít dvě základní schopnosti.
+Zaprvé musí být schopni autonomní akce rozhodnutí - zjistit jak nejlépe dosáhnout
+požadovaných cílů - a zadruhé je to schopnost interakce s ostatními agenty. V druhém případě nejde
+jen o pouhou výměnu dat, ale o typ kolektivní aktivity - návrh, potvrzení, odmítnutí.
+
+\subsection{Historie}
+
+Multiagentní systémy jsou na poli počítačové vědy relativní novinkou. Studium tohoto 
+tématu probíhá od začátku osmdesátých let dvacátého století. Větší pozornosti
+se jim dostalo v polovině let devadesátých s rozvojem internetu. 
+
+\subsection{Agent}
+
+Neexistuje obecně uznávaná definice agenta. Přikloníme se k definici použité v publikaci 
+\cite{wooldridge}.
+
+\begin{definition}[Agent]\label{de:agent01}
+Agent je počítačový systém umístěný do nějakého prostředí, který je schopen autonomní akce
+k přiblížení se navrženým cílům.
+\end{definition}
+
+
+Agent v naprosté většině případů nemá celkovou kontrolu nad prostředím. Prostředí může ovlivňovat
+jen částečně. Obecně je prostředí nedeterministické. Stejná akce provedená dvakrát za sebou 
+nemusí vést ke stejnému výsledku.
+
+\section{Druhy prostředí}
+
+Způsob práce agentů se liší podle druhu prostředí, ve kterém pracují. Podle \cite{wooldridge} se
+prostředí dají klasifikovat následovně:
+
+\begin{itemize}
+ \item Deterministické vs. nedeterministické
+ \item Dostupné vs. nedostupné
+ \item Statické vs. dynamické
+\end{itemize}
+Deterministické prostředí je takové, ve kterém má každá jednotlivá akce předem daný efekt.
+Prostředí je dostupné, pokud agent může zjistit jeho úplný stav v kteroukoliv dobu.
+Statické prostředí se na rozdíl od dynamického mění pouze vlivem akcí vyvolanými agenty.
+V diskrétním prostředí existuje pevné konečné číslo možných vjemů a akcí.
+% \\
+% \\
+% V našem případě je prostředí nedeterministické (agent pouze odhaduje vliv přenastavení parametru),
+% nedostupné (hodnoty se měří pouze jednou za 90 sekund, a ještě jsou zkreslené) a dynamické 
+% (intenzita dopravy se mění nezávisle na akcích agenta). Je zřejmé, že prostředí s těmito vlastnostmi
+% znesnadňuje rozhodování a kontrolu vyvolaného výsledku.
+
+
+\section{Interakce agentů}
+
+\subsection{Stavy prostředí a preference agentů}
+
+Mějme pro jednoduchost 2 agenty. Označme si je $i$ a $j$.
+Předpokládejme, že máme množinu $$\Omega = \{\omega_1, \omega_2, ...\}$$ obsahující všechny možné stavy
+prostředí, v kterém agenti operují. Aby byl agent schopen efektivně ovlivňovat prostření, musí být schopen
+ohodnotit, jak je pro něj daný stav příznivý. Hodnocení daného stavu agenta $i$ a $j$ formálně definujeme jako funkce
+$$u_i : \Omega \rightarrow \mathbb{R}, $$
+$$u_j : \Omega \rightarrow \mathbb{R}. $$
+Čím je stav $\omega$ příznivější pro agenta $i$, tím je větší hodnota funkce $u_i$.
+
+\begin{definition}[Uspořádání na množině všech stavů]
+ Mějme 2 stavy prostředí $\omega_1$, $\omega_2$. Řekněme, že stav $\omega_1$ je preferován agentem $i$ nad stavem $\omega_2$,
+pokud platí $u_i(\omega_1) \geqq u_i(\omega_2)$. Značíme
+$$ \omega_1 \succeq_i \omega_2. $$
+Stav $\omega_1$ je silně preferován agentem $i$ nad stavem $\omega_2$,
+pokud platí $u_i(\omega_1) > u_i(\omega_2)$. Značíme
+$$ \omega_1 \succ_i \omega_2 $$
+\end{definition}
+
+Relace $ \succeq_i $ je zřejmě uspořádání, protože má všechny potřebné vlastnosti.
+\newline
+Reflexivitu:
+$$  \forall \omega \in \Omega : \omega \succeq_i \omega $$
+Tranzitivitu:
+$$  \forall \omega_1, \omega_2, \omega_3 \in \Omega : \omega_1 \succeq_i \omega_2 \wedge \omega_2 \succeq_i \omega_3 \Rightarrow \omega_1 \succeq_i \omega_3$$
+Porovnatelnost:
+$$  \forall \omega_1, \omega_2 \in \Omega : \omega_1 \succeq_i \omega_2 \vee \omega_2 \succeq_i \omega_1 $$
+
+Relace $\succ_i$ zjevně nesplňuje podmínky reflexivity.
+
+\chapter{Výběr strategie genta}
+Nyní popíšeme, jak mají agenti možnost ovlivňovat prostředí.
+Opět předpokládejme existenci dvou agentů $i$ a $j$. Obecně mají
+různí agenti různou oblast působnosti. Množina
+$$ A = \{ a_1, a_2, ... \} $$
+znázorňuje množinu všech akcí, které jsou agenti schopni provézt.
+Na tyto akce reaguje prostředí přechodem do nějakého stavu $\omega \in \Omega$.
+Formálně můžeme tento přechod zapsat jako funkci
+$$ \tau : A \times A \rightarrow \Omega. $$
+
+
+
+
+\section{Výběr strategie podle teorie her}
+
+Popišme zde způsob, jak se agent rozhodne pro realizaci určité akce.
+Agent je nyní schopen ohodnotit, který stav prostředí je pro něj příznivější než jiný,
+neví však jak budou reagovat ostatní agenti, není schopen určit tudíž, i za předpokladu,
+že by systém byl deterministický, do jakého stavu systém přejde. K výběru optimální akce
+se používají prvky z teorie her. Zadefinujme nejprve v souladu s touto teorií základní pojmy.
+
+\begin{definition}[Dominance množiny]
+ Mějme 2 podmnožiny $ \Omega_1, \Omega_2 \subset \Omega $. 
+Řekneme, že $\Omega_1$ je pro agenta $i$ dominantní nad množinou $\Omega_2$, pokud platí
+$$
+\forall \omega \in \Omega_1, \forall \omega' \in \Omega_2 : \omega \succeq_i \omega'.
+$$
+Řekneme že $\Omega_1$ je pro agenta $i$ silně dominantní nad množinou $\Omega_2$, pokud platí
+$$
+\forall \omega \in \Omega_1, \forall \omega' \in \Omega_2 : \omega \succ_i \omega'.
+$$
+\end{definition}
+
+Abychom používali terminologii teorie her, budeme nyní akce $a_i \in A$ jednotlivých agentů
+nazývat strategiemi.
+
+\begin{definition}[Množina výsledků]
+Nazvěme množinu všech stavů, do kterých může prostředí přejít při hraní strategie $a_i \in A$,
+množinou možných výsledků. Označme ji
+$$
+a_i^* \subset \Omega.
+$$
+\end{definition}
+
+\begin{definition}[Dominance strategie]
+ Řekneme, že strategie $a_i$ je dominantní nad strategií $a_j$,
+pokud je množina $a_i^*$ dominantní nad množinou $a_j^*$.
+Strategie $a_i$ je silně dominantní nad strategií $a_j$,
+pokud je množina $a_i^*$ silně dominantní nad množinou $a_j^*$.
+\end{definition}
+
+Racionálně uvažující agent tedy vyloučí všechny strategie $a_i$, jestliže existuje
+strategie $a_j$, která nad strategií $a_i$ silně dominuje. K zúžení výběru zbývajících
+strategií slouží Nashova rovnost. Pro zjednodušení uvažujme 2 agenty, $i$ a $j$
+\begin{definition}[Nashova rovnost]\label{de:nash_equlibrium}
+ Dvě strategie, $a_1$ a $a_2$ jsou v Nashově rovnosti, pokud za předpokladu že agent 
+  $i$ zvolí strategii $a_1$, je nejvýhodnější strategií pro agenta $j$ je strategie $a_2$ a zároveň
+  pokud agent $j$ zvolí strategii $a_2$, je pro agenta i nejvýhodnější strategií $a_1$.
+\end{definition}
+
+
+  
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/Styles/Colors.sty
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Styles/Colors.sty (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Styles/Colors.sty (revision 1419)
@@ -0,0 +1,15 @@
+\usepackage[dvips]{color}                   %for using colors
+
+%-----<<< Color definition >>>-----
+\definecolor{gold}{rgb}{0.85,.66,0}         %color definition
+\definecolor{Gold}{rgb}{1.,0.84,0.}
+\definecolor{pink}{rgb}{1, 0.506, 0.82}
+\definecolor{brown}{rgb}{0.51, 0.337, 0}
+\definecolor{orange}{rgb}{0.984, 0.431, 0.341}
+\definecolor{gray}{rgb}{0.753, 0.753, 0.753}
+\definecolor{dred}{rgb}{0.78, 0, 0}
+\definecolor{dgreen}{rgb}{0, 0.6, 0}
+\definecolor{dblue}{rgb}{0, 0, 0.6}
+\definecolor{dmagenta}{rgb}{0.569, 0.098, 0.788}
+\definecolor{dgray}{rgb}{0.5, 0.5, 0.5}
+%-----<<< ---------------- >>>-----
Index: /applications/doprava/texty/novotny_vyzk_LQ/Styles/Skripta.bst
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Styles/Skripta.bst (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Styles/Skripta.bst (revision 1419)
@@ -0,0 +1,1370 @@
+% BibTeX standard bibliography style `agsm' (one of the harvard family)
+    % version 0.99a for BibTeX versions 0.99a or later, LaTeX version 2.09.
+    % Copyright (C) 1991, all rights reserved.
+    % Copying of this file is authorized only if either
+    % (1) you make absolutely no changes to your copy, including name, or
+    % (2) if you do make changes, you name it something other than
+    % btxbst.doc, plain.bst, unsrt.bst, alpha.bst, abbrv.bst, agsm.bst,
+        % dcu.bst or kluwer.bst.
+    % This restriction helps ensure that all standard styles are identical.
+    % The file harvard.tex has the documentation for this style.
+
+ % Includes fields ISBN and ISSN by JmR.
+ %
+
+% ACKNOWLEDGEMENT:
+%   This document is a modified version of alpha.bst to which it owes much of
+%   its functionality.
+
+% AUTHOR
+%   Peter Williams, Key Centre for Design Quality, Sydney University
+%   e-mail: peterw@archsci.arch.su.oz.au
+
+ENTRY
+  { address
+    author
+    booktitle
+    chapter
+    edition
+    editor
+    howpublished
+    institution
+    journal
+    key
+    month
+    note
+    number
+    organization
+    pages
+    publisher
+    school
+    series
+    title
+    type
+    URL
+    volume
+    year
+    isbn
+  }
+  { field.used etal.allowed etal.required} %%%XXX change
+  { extra.label sort.label list.year }
+
+INTEGERS { output.state before.all mid.sentence after.sentence after.block }
+
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+  #1 'mid.sentence :=
+  #2 'after.sentence :=
+  #3 'after.block :=
+}
+
+STRINGS { s t f }
+
+FUNCTION {output.nonnull}
+{ 's :=
+  output.state mid.sentence =
+    { ", " * write$ }
+    { output.state after.block =
+    { add.period$ write$
+      newline$
+      "\newblock " write$
+    }
+    { output.state before.all =
+        'write$
+        { add.period$ " " * write$ }
+      if$
+    }
+      if$
+      mid.sentence 'output.state :=
+    }
+  if$
+  s
+}
+
+FUNCTION {output}
+{ duplicate$ empty$
+    'pop$
+    'output.nonnull
+  if$
+}
+
+FUNCTION {output.check}
+{ 't :=
+  duplicate$ empty$
+    { pop$ "empty " t * " in " * cite$ * warning$ }
+    'output.nonnull
+  if$
+}
+
+FUNCTION {item.check}
+{ 't :=
+  empty$
+    { "empty " t * " in " * cite$ * warning$ }
+    { skip$ }
+  if$
+}
+
+FUNCTION {fin.entry}
+{ add.period$
+  write$
+  newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+    'skip$
+    { after.block 'output.state := }
+  if$
+}
+
+FUNCTION {not}
+{   { #0 }
+    { #1 }
+  if$
+}
+
+FUNCTION {and}
+{   'skip$
+    { pop$ #0 }
+  if$
+}
+
+FUNCTION {or}
+{   { pop$ #1 }
+    'skip$
+  if$
+}
+
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+    { pop$ "" }
+    'skip$
+  if$
+}
+
+FUNCTION {emphasize}
+{ duplicate$ empty$
+    { pop$ "" }
+    { "{\em " swap$ * "}" * }
+  if$
+}
+
+FUNCTION {embolden}
+{ duplicate$ empty$
+    { pop$ "" }
+    { "{\bf " swap$ * "}" * }
+  if$
+}
+
+FUNCTION {quote}
+{ duplicate$ empty$
+    { pop$ "" }
+    { "`" swap$ * "'" * }
+  if$
+}
+
+FUNCTION {write.url}
+{ URL empty$
+    { skip$ }
+    { "\newline\harvardurl{" URL * "}" * write$ newline$ }
+  if$
+}
+
+INTEGERS { nameptr namesleft numnames }
+
+FUNCTION {format.names}
+{ 's :=
+  'f :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr f format.name$ 't :=
+      nameptr #1 >
+    { namesleft #1 >
+        { ", " * t * }
+        { t "others" =
+        { " et~al." * }
+        { " \harvardand\ " * t * }
+          if$
+        }
+      if$
+    }
+    't
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+}
+
+FUNCTION {format.authors}
+{ author empty$
+    { "" }
+    { "{vv~}{ll}{, jj}{, f.}" author format.names }
+  if$
+}
+
+FUNCTION {format.editors}
+{ editor empty$
+    { "" }
+    { "{vv~}{ll}{, jj}{, f.}" editor format.names
+      editor num.names$ #1 >
+    { ", eds" * }
+    { ", ed." * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.isbn}
+{ isbn empty$
+    { "" }
+    { new.block "ISBN~" isbn * }
+  if$
+}
+
+FUNCTION {format.editors.reverse}
+{ editor empty$
+    { "" }
+    { "{f.~}{vv~}{ll}{, jj}" editor format.names
+      editor num.names$ #1 >
+    { ", eds" * }
+    { ", ed." * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.title}
+{ title empty$
+    { "" }
+    { title "t" change.case$ }
+  if$
+}
+
+FUNCTION {n.dashify}
+{ '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$
+}
+
+FUNCTION {format.btitle}
+{ title emphasize
+}
+
+FUNCTION {tie.or.space.connect}
+{ duplicate$ text.length$ #3 <
+    { "~" }
+    { " " }
+  if$
+  swap$ * *
+}
+
+FUNCTION {either.or.check}
+{ empty$
+    'pop$
+    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+  if$
+}
+
+FUNCTION {format.bvolume}
+{ volume empty$
+    { "" }
+    { "Vol." volume tie.or.space.connect
+      series empty$
+    'skip$
+    { " of " * series emphasize * }
+      if$
+      "volume and number" number either.or.check
+    }
+  if$
+}
+
+FUNCTION {format.number.series}
+{ volume empty$
+    { number empty$
+    { series field.or.null }
+    { output.state mid.sentence =
+        { "number" }
+        { "Number" }
+      if$
+      number tie.or.space.connect
+      series empty$
+        { "there's a number but no series in " cite$ * warning$ }
+        { " {\em in} " * series quote * }
+      if$
+    }
+      if$
+    }
+    { "" }
+  if$
+}
+
+FUNCTION {format.edition}
+{ edition empty$
+    { "" }
+    { output.state mid.sentence =
+    { edition "l" change.case$ " edn" * }
+    { edition "t" change.case$ " edn" * }
+      if$
+    }
+  if$
+}
+
+INTEGERS { multiresult }
+
+FUNCTION {multi.page.check}
+{ '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 {format.pages}
+{ pages empty$
+    { "" }
+    { pages multi.page.check
+    { "pp.~" pages n.dashify * }
+    { "p.~" pages * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.vol.num.pages}
+{ volume embolden field.or.null
+  number empty$
+    'skip$
+    { "(" number * ")" * *
+      volume empty$
+    { "there's a number but no volume in " cite$ * warning$ }
+    'skip$
+      if$
+    }
+  if$
+  pages empty$
+    'skip$
+    { duplicate$ empty$
+    { pop$ format.pages }
+    { ",~" * pages n.dashify * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+    'format.pages
+    { type empty$
+    { "chapter" }
+    { type "l" change.case$ }
+      if$
+      chapter tie.or.space.connect
+      pages empty$
+    'skip$
+    { ", " * format.pages * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.in.ed.booktitle}
+{ booktitle empty$
+    { "" }
+    { editor empty$
+    { "{\em in} " booktitle quote * }
+    { "{\em in} " format.editors.reverse * ", " * booktitle quote * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {empty.misc.check}
+{ author empty$ title empty$ howpublished empty$
+  month empty$ year empty$ note empty$
+  and and and and and
+  key empty$ not and
+    { "all relevant fields are empty in " cite$ * warning$ }
+    'skip$
+  if$
+}
+
+FUNCTION {format.thesis.type}
+{ type empty$
+    'skip$
+    { pop$
+      type "t" change.case$
+    }
+  if$
+}
+
+FUNCTION {format.tr.number}
+{ type empty$
+    { "Technical Report" }
+    'type
+  if$
+  number empty$
+    { "t" change.case$ }
+    { number tie.or.space.connect }
+  if$
+}
+
+FUNCTION {format.article.crossref}
+{ key empty$
+    { journal empty$
+    { "need key or journal for " cite$ * " to crossref " * crossref *
+      warning$
+      ""
+    }
+    { "in {\em " journal * "\/} \cite{" * crossref * "}" *}
+      if$
+    }
+    { "{\em in} \citeasnoun{" crossref * "}" * }
+  if$
+ 
+}
+
+FUNCTION {format.book.crossref}
+{ volume empty$
+    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+      "in "
+    }
+    { "Vol." volume tie.or.space.connect
+      " of " *
+    }
+  if$
+  editor empty$
+  editor field.or.null author field.or.null =
+  or
+    { key empty$
+    { series empty$
+        { "need editor, key, or series for " cite$ * " to crossref " *
+          crossref * warning$
+          "" *
+        }
+        { "{\em " * series * "\/} \cite{" * crossref * "}" *}
+      if$
+    }
+    { " \citeasnoun{" * crossref * "}" * }
+      if$
+    }
+    { " \citeasnoun{" * crossref * "}" * }
+  if$
+}
+
+FUNCTION {format.incoll.inproc.crossref}
+{ editor empty$
+  editor field.or.null author field.or.null =
+  or
+    { key empty$
+    { booktitle empty$
+        { "need editor, key, or booktitle for " cite$ * " to crossref " *
+          crossref * warning$
+          ""
+        }
+        { "in {\em " booktitle * "\/}" * " \cite{" * crossref * "}" *}
+      if$
+    }
+    { "{\em in} \citeasnoun{" crossref * "}" * }
+      if$
+    }
+    { "{\em in} \citeasnoun{" crossref * "}" * }
+  if$
+  
+}
+
+INTEGERS { len }
+
+FUNCTION {chop.word}
+{ 's :=
+  'len :=
+  s #1 len substring$ =
+    { s len #1 + global.max$ substring$ }
+    's
+  if$
+}
+
+INTEGERS { ind tsslen }
+
+STRINGS { tss ret rss istr }
+
+FUNCTION {replace.substring}{
+  'rss :=
+  'tss :=
+  'istr :=
+  "" 'ret :=
+  tss text.length$ 'tsslen :=
+  #1 'ind :=
+    { istr ind tsslen substring$ "" = not }
+    { istr ind tsslen substring$ tss =
+        { ret rss * 'ret :=
+          ind tsslen + 'ind :=
+        }
+        { ret istr ind #1 substring$ * 'ret :=
+          ind #1 + 'ind :=
+        }
+      if$
+    }
+  while$
+  ret
+}
+
+FUNCTION {format.lab.names.abbr}
+{ 's :=
+  s num.names$ 'numnames :=
+  numnames #1 >
+    { numnames #2 >
+    { s #1 "{vv~}{ll}" format.name$ " et~al." * }
+    { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+            { s #1 "{vv~}{ll}" format.name$ " et~al." * }
+        { s #1 "{vv~}{ll}" format.name$ " \harvardand\ " *
+              s #2 "{vv~}{ll}" format.name$ * 
+            }
+          if$
+        }
+      if$
+    }
+    { s #1 "{vv~}{ll}" format.name$ }
+  if$
+}
+
+FUNCTION {format.lab.names.full}
+{ 's :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr "{vv~}{ll}" format.name$ 't :=
+      nameptr #1 >
+    { namesleft #1 >
+        { ", " * t * }
+        { t "others" =
+        { " et~al." * }
+        { " \harvardand\ " * t * }
+          if$
+        }
+      if$
+    }
+    't
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+}
+
+INTEGERS { author.field editor.field organization.field title.field key.field }
+
+FUNCTION {init.field.constants}
+{ #0 'author.field :=
+  #1 'editor.field :=
+  #2 'organization.field :=
+  #3 'title.field :=
+  #4 'key.field :=
+}
+
+FUNCTION {make.list.label}
+{ author.field field.used =
+    { format.authors }
+    { editor.field field.used =
+        { format.editors }
+        { organization.field field.used =
+            { "The " #4 organization chop.word #3 text.prefix$ }
+            { title.field field.used =
+                { format.btitle }
+                { key.field field.used =
+                    { key #3 text.prefix$ }
+                    { "Internal error :001 on " cite$ * " label" * warning$ }
+                  if$
+                }
+              if$
+            }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+FUNCTION {make.full.label}
+{ author.field field.used =
+    { author format.lab.names.full }
+    { editor.field field.used =
+        { editor format.lab.names.full }
+        { organization.field field.used =
+            { "The " #4 organization chop.word #3 text.prefix$ }
+            { title.field field.used =
+                { format.btitle }
+                { key.field field.used =
+                    { key #3 text.prefix$ }
+                    { "Internal error :001 on " cite$ * " label" * warning$ }
+                  if$
+                }
+              if$
+            }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+FUNCTION {make.abbr.label} %%%XXX change
+{
+  etal.allowed
+    { author.field field.used =
+        { author format.lab.names.abbr }
+        { editor.field field.used =
+            { editor format.lab.names.abbr }
+            { organization.field field.used =
+                { "The " #4 organization chop.word #3 text.prefix$ }
+                { title.field field.used =
+                    { format.btitle }
+                    { key.field field.used =
+                        { key #3 text.prefix$ }
+                        {"Internal error :001 on " cite$ * " label" * warning$ }
+                      if$
+                    }
+                  if$
+                }
+              if$
+            }
+          if$
+        }
+      if$
+    }
+    { make.full.label }
+  if$
+}
+
+FUNCTION {output.bibitem}
+{ newline$
+  etal.allowed        %%%XXX change
+  etal.required
+  and
+    {
+      "\harvarditem[" write$
+      make.abbr.label write$
+      "]{" write$
+    }
+    {
+      "\harvarditem{" write$
+    }
+  if$
+  make.full.label write$
+  "}{" write$
+  list.year write$
+  "}{" write$
+  cite$ write$
+  "}" write$
+  newline$
+  ""
+  before.all 'output.state :=
+}
+
+FUNCTION {list.label.output}
+{ make.list.label " " * write$
+}
+
+FUNCTION {article}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  author "author" item.check
+  title.field field.used =
+    { skip$ }
+    { format.title quote "title" output.check }
+  if$
+  crossref missing$
+    { journal emphasize "journal" duplicate$ item.check
+      " " * format.vol.num.pages * output
+    }
+    { format.article.crossref output.nonnull
+      format.pages output
+    }
+  if$
+  new.block
+  note output
+  format.isbn output
+  fin.entry
+  write.url
+}
+
+FUNCTION {book}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  author empty$
+    { editor "author and editor" item.check }
+    { crossref missing$
+    { "author and editor" editor either.or.check }
+    'skip$
+      if$
+    }
+  if$
+  title.field field.used =
+    { skip$ }
+    { format.btitle "title" output.check }
+  if$
+  crossref missing$
+    { format.bvolume output
+      format.number.series output
+      format.edition output
+      publisher "publisher" output.check
+      address output
+    }
+    { format.book.crossref output.nonnull
+      format.edition output
+    }
+  if$
+  new.block
+  note output
+  format.isbn output
+  fin.entry
+  write.url
+}
+
+FUNCTION {booklet}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  title.field field.used =
+    { skip$ }
+    { format.title quote "title" output.check }
+  if$
+  howpublished output
+  address output
+  new.block
+  note output
+  fin.entry
+  write.url
+  format.isbn output
+}
+
+FUNCTION {inbook}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  author empty$
+    { editor "author and editor" item.check }
+    { crossref missing$
+    { "author and editor" editor either.or.check }
+    'skip$
+      if$
+    }
+  if$
+  title.field field.used =
+    { skip$ }
+    { format.btitle "title" output.check }
+  if$
+  crossref missing$
+    { format.bvolume output
+      format.number.series output
+      format.edition output
+      publisher "publisher" output.check
+      address output
+    }
+    { format.book.crossref output.nonnull
+      format.edition output
+    }
+  if$
+  format.chapter.pages "chapter and pages" output.check
+  new.block
+  note output
+  fin.entry
+  write.url
+  format.isbn output
+}
+
+FUNCTION {incollection}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  title.field field.used =
+    { skip$ }
+    { format.title "title" output.check }
+  if$
+  author "author" item.check
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      format.edition output
+      format.bvolume output
+      format.number.series output
+      publisher "publisher" output.check
+      address output
+    }
+    { format.incoll.inproc.crossref output.nonnull
+    }
+  if$
+  format.chapter.pages output
+  new.block
+  note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {inproceedings}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  title.field field.used =
+    { skip$ }
+    { format.title "title" output.check }
+  if$
+  author "author" item.check
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      format.bvolume output
+      format.number.series output
+      address empty$
+    { organization output
+      publisher output
+    }
+    { organization output
+      publisher output
+          address output.nonnull
+    }
+      if$
+    }
+    { format.incoll.inproc.crossref output.nonnull
+    }
+  if$
+  format.pages output
+  new.block
+  note output
+  fin.entry
+  write.url
+  format.isbn output
+}
+
+FUNCTION {conference} { inproceedings }
+
+FUNCTION {manual}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  title.field field.used =
+    { skip$ }
+    { format.btitle "title" output.check }
+  if$
+  format.edition output
+  author empty$
+    { organization empty$
+    { address output }
+    'skip$
+      if$
+    }
+    { organization output
+      address output
+    }
+  if$
+  new.block
+  note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {mastersthesis}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  author "author" item.check
+  title.field field.used =
+    { skip$ }
+    { format.title "title" output.check }
+  if$
+  "Master's thesis" format.thesis.type output.nonnull
+  school "school" output.check
+  address output
+  new.block
+  note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {misc}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  title.field field.used =
+    { skip$ }
+    { format.title quote output }
+  if$
+  howpublished output
+  new.block
+  note output
+  fin.entry
+  write.url
+  empty.misc.check
+}
+
+FUNCTION {phdthesis}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  author "author" item.check
+  title.field field.used =
+    { skip$ }
+    { title "title" output.check }
+  if$
+  "PhD thesis" format.thesis.type output.nonnull
+  school "school" output.check
+  address output
+  new.block
+  note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {proceedings}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  title.field field.used =
+    { skip$ }
+    { format.btitle "title" output.check }
+  if$
+  format.bvolume output
+  format.number.series output
+  address empty$
+    { editor empty$
+    { skip$ }
+    { organization output
+    }
+      if$
+      publisher output
+    }
+    { editor empty$
+    'skip$
+    { organization output }
+      if$
+      publisher output
+      address output.nonnull
+    }
+  if$
+  new.block
+  note output
+  fin.entry
+  write.url
+  format.isbn output
+}
+
+FUNCTION {techreport}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  author "author" item.check
+  title.field field.used =
+    { skip$ }
+    { format.title "title" output.check }
+  if$
+  format.tr.number output.nonnull
+  institution "institution" output.check
+  address output
+  new.block
+  note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {unpublished}
+{ output.bibitem
+  list.label.output
+  " \harvardyearleft " list.year * "\harvardyearright " * output.nonnull
+  author "author" item.check
+  title.field field.used =
+    { skip$ }
+    { format.title "title" output.check }
+  if$
+  new.block
+  note "note" output.check
+  fin.entry
+  write.url
+}
+
+FUNCTION {default.type} { misc }
+
+MACRO {jan} {"January"}
+
+MACRO {feb} {"February"}
+
+MACRO {mar} {"March"}
+
+MACRO {apr} {"April"}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"June"}
+
+MACRO {jul} {"July"}
+
+MACRO {aug} {"August"}
+
+MACRO {sep} {"September"}
+
+MACRO {oct} {"October"}
+
+MACRO {nov} {"November"}
+
+MACRO {dec} {"December"}
+
+MACRO {acmcs} {"ACM Computing Surveys"}
+
+MACRO {acta} {"Acta Informatica"}
+
+MACRO {cacm} {"Communications of the ACM"}
+
+MACRO {ibmjrd} {"IBM Journal of Research and Development"}
+
+MACRO {ibmsj} {"IBM Systems Journal"}
+
+MACRO {ieeese} {"IEEE Transactions on Software Engineering"}
+
+MACRO {ieeetc} {"IEEE Transactions on Computers"}
+
+MACRO {ieeetcad}
+ {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"}
+
+MACRO {ipl} {"Information Processing Letters"}
+
+MACRO {jacm} {"Journal of the ACM"}
+
+MACRO {jcss} {"Journal of Computer and System Sciences"}
+
+MACRO {scp} {"Science of Computer Programming"}
+
+MACRO {sicomp} {"SIAM Journal on Computing"}
+
+MACRO {tocs} {"ACM Transactions on Computer Systems"}
+
+MACRO {tods} {"ACM Transactions on Database Systems"}
+
+MACRO {tog} {"ACM Transactions on Graphics"}
+
+MACRO {toms} {"ACM Transactions on Mathematical Software"}
+
+MACRO {toois} {"ACM Transactions on Office Information Systems"}
+
+MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"}
+
+MACRO {tcs} {"Theoretical Computer Science"}
+
+READ
+
+EXECUTE {init.field.constants}
+
+FUNCTION {sortify}
+{ purify$
+  "l" change.case$
+}
+
+FUNCTION {sortify.names}
+{ " \harvardand\ " " " replace.substring
+  " et~al." " zzz" replace.substring
+  sortify
+}
+
+FUNCTION {author.key.label}
+{ author empty$
+    { key empty$
+    { title.field 'field.used := }
+    { key.field 'field.used := }
+      if$
+    }
+    { author.field 'field.used := }
+  if$
+}
+
+FUNCTION {author.editor.key.label}
+{ author empty$
+    { editor empty$
+    { key empty$
+        { title.field 'field.used := }
+        { key.field 'field.used := }
+      if$
+    }
+    { editor.field 'field.used := }
+      if$
+    }
+    { author.field 'field.used := }
+  if$
+}
+
+FUNCTION {author.key.organization.label}
+{ author empty$
+    { key empty$
+    { organization empty$
+        { title.field 'field.used := }
+        { organization.field 'field.used := }
+      if$
+    }
+    { key.field 'field.used := }
+      if$
+    }
+    { author.field 'field.used := }
+  if$
+}
+
+FUNCTION {editor.key.organization.label}
+{ editor empty$
+    { key empty$
+    { organization empty$
+        { title.field 'field.used := }
+        { organization.field 'field.used := }
+      if$
+    }
+    { key.field 'field.used := }
+      if$
+    }
+    { editor.field 'field.used := }
+  if$
+}
+
+FUNCTION {sort.format.title}
+{ 't :=
+  "A " #2
+    "An " #3
+      "The " #4 t chop.word
+    chop.word
+  chop.word
+  sortify
+  #1 global.max$ substring$
+}
+
+FUNCTION {calc.label} %%%XXX change
+{ make.abbr.label
+  title.field field.used =
+    { sort.format.title }
+    { sortify.names }
+  if$
+  year field.or.null purify$ #-1 #4 substring$ sortify
+  *
+  'sort.label :=
+}
+
+FUNCTION {preliminaries} %%%XXX change
+{ type$ "book" =
+  type$ "inbook" =
+  or
+    'author.editor.key.label
+    { type$ "proceedings" =
+    'editor.key.organization.label
+    { type$ "manual" =
+        'author.key.organization.label
+        'author.key.label
+      if$
+    }
+      if$
+    }
+  if$
+  author.field field.used = %%%XXX change
+    {
+      author num.names$ #2 >
+        { #1 }
+        { #0 }
+      if$
+      'etal.required :=
+    }
+    {
+      editor.field field.used = 
+        {
+          editor num.names$ #2 >
+            { #1 }
+            { #0 }
+          if$
+        }
+        { #0 }
+      if$
+      'etal.required :=
+    }
+  if$
+  #1 'etal.allowed :=
+}
+
+FUNCTION {first.presort}
+{ calc.label
+  sort.label
+  title.field field.used =
+    { skip$ }
+    { "    "
+      *
+      make.list.label sortify.names
+      *
+      "    "
+      *
+      title field.or.null
+      sort.format.title
+      *
+    }
+  if$
+  #1 entry.max$ substring$
+  'sort.key$ :=
+}
+
+ITERATE {preliminaries}
+
+ITERATE {first.presort}
+
+SORT
+
+STRINGS { last.sort.label next.extra last.full.label}
+
+INTEGERS { last.extra.num last.etal.allowed}
+
+FUNCTION {initialize.confusion}
+{ #0 int.to.chr$ 'last.sort.label :=
+  #0 int.to.chr$ 'last.full.label :=
+  #1 'last.etal.allowed :=
+}
+
+FUNCTION {confusion.pass}
+{ last.sort.label sort.label =
+    { last.etal.allowed 
+        { last.full.label make.full.label sortify.names =
+            { skip$ }
+            { #0 'etal.allowed :=
+              #0 'last.etal.allowed :=
+            }
+          if$
+        }
+        { #0 'etal.allowed := }
+      if$
+    }
+    { sort.label 'last.sort.label :=
+      make.full.label sortify.names 'last.full.label :=
+      #1 'last.etal.allowed :=
+    }
+  if$
+}
+
+EXECUTE {initialize.confusion}
+
+ITERATE {confusion.pass}
+
+EXECUTE {initialize.confusion}
+
+REVERSE {confusion.pass}
+
+FUNCTION {initialize.last.extra.num}
+{ #0 int.to.chr$ 'last.sort.label :=
+  "" 'next.extra :=
+  #0 'last.extra.num :=
+}
+
+FUNCTION {forward.pass}
+{ last.sort.label sort.label =
+    { last.extra.num #1 + 'last.extra.num :=
+      last.extra.num int.to.chr$ 'extra.label :=
+    }
+    { "a" chr.to.int$ 'last.extra.num :=
+      "" 'extra.label :=
+      sort.label 'last.sort.label :=
+    }
+  if$
+}
+
+FUNCTION {reverse.pass}
+{ next.extra "b" =
+    { "a" 'extra.label := }
+    'skip$
+  if$
+  year empty$
+    { "n.d." extra.label emphasize * 'list.year := }
+    { year extra.label emphasize * 'list.year := }
+  if$
+  extra.label 'next.extra :=
+}
+
+ITERATE {first.presort}
+
+SORT
+
+EXECUTE {initialize.last.extra.num}
+
+ITERATE {forward.pass}
+
+REVERSE {reverse.pass}
+
+FUNCTION {second.presort}
+{ make.list.label
+  title.field field.used =
+    { sort.format.title }
+    { sortify.names }
+  if$
+  "    "
+  *
+  list.year field.or.null sortify
+  *
+  "    "
+  *
+  title.field field.used =
+    { skip$ }
+    { title field.or.null
+      sort.format.title
+      *
+    }
+  if$
+  #1 entry.max$ substring$
+  'sort.key$ :=
+}
+
+ITERATE {second.presort}
+
+SORT
+
+FUNCTION {begin.bib}
+{ preamble$ empty$
+    'skip$
+    { "\harvardpreambledefs{%" write$ newline$
+      preamble$ write$ "}" write$ newline$
+      "\harvardpreambletext{%" write$ newline$
+      preamble$ write$ "}" write$ newline$ }
+  if$
+  "\begin{thebibliography}{xx}" write$ newline$
+}
+
+EXECUTE {begin.bib}
+
+EXECUTE {init.state.consts}
+
+ITERATE {call.type$}
+
+FUNCTION {end.bib}
+{ newline$
+  "\end{thebibliography}" write$ newline$
+}
+
+EXECUTE {end.bib}
Index: /applications/doprava/texty/novotny_vyzk_LQ/Styles/Skripta.sty
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Styles/Skripta.sty (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Styles/Skripta.sty (revision 1419)
@@ -0,0 +1,290 @@
+%%% ====================================================================
+%%% @LaTeX-file{
+%%%   filename  = "Skripta.sty",
+%%%   version   = "1.00",
+%%%   date      = "2006/01/16",
+%%%   time      = "01:20:10 CET",
+%%%   author    = "Jirka Roubal",
+%%%   copyright = "Copyright 2006, Jirka Roubal,
+%%%                all rights reserved.  Copying of this file is
+%%%                authorized only if either:
+%%%                (1) you make absolutely no changes to your copy,
+%%%                including name; OR
+%%%                (2) if you do make changes, you first rename it
+%%%                to some other name.",
+%%%   address   = "Jirka Roubal,
+%%%                Department of Control Engineering,
+%%%                Faculty of Electrical Engineering,
+%%%                Czech Technical University in Prague,
+%%%                Karlovo náměstí 13,
+%%%                121 35 Prague 2,
+%%%                Czech Republic",
+%%%   telephone = "+420-2-2435-7687",
+%%%   FAX       = "",
+%%%   checksum  = "38084 5829 21569 202795",
+%%%   email     = "roubalj@control.felk.cvut.cz",
+%%%   website   = "http://dce.felk.cvut.cz/roubal/",
+%%%   codetable = "ISO/ASCII",
+%%%   keywords  = "latex, amsmath, ntheorem, inputenc, czech",
+%%%   supported = "yes",
+%%%   abstract  = "This is a \LaTeX{} template for students bachelorsor
+%%%                diploma thesis.",
+%%% }
+%%% ====================================================================
+
+%-----<<< ----------- >>>-----
+%-----<<< USEPACKAGES >>>-----
+\usepackage[utf8]{inputenc}
+\usepackage[czech]{babel}
+\usepackage{fancyhdr}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage[amsmath,thmmarks]{ntheorem}
+\usepackage{latexsym}
+\usepackage[dvips]{graphicx}
+\usepackage{float}
+% \usepackage{picins}                     %text beside figure
+\usepackage[width=.90\textwidth,hang,small]{caption}
+\usepackage{subfigure}                  %text beside figure
+%-----<<< USEPACKAGES >>>-----
+%-----<<< ----------- >>>-----
+
+
+
+%-----<<< ---------------------------------- >>>-----
+%-----<<< PAGE, TITLE AND SECTION DEFINITION >>>-----
+\linespread{1.3}                        %line spacing 1.5
+
+\setlength{\oddsidemargin}{0mm}
+\setlength{\textwidth}{159.2mm}\setlength{\topmargin}{0mm}
+\setlength{\textheight}{230mm}
+\setlength{\headheight}{14.5pt}         %height of head
+\setlength{\oddsidemargin}{5mm}         %odd left margin
+\setlength{\evensidemargin}{-\oddsidemargin} %even left margin
+
+
+\newcommand\titulek{\@startsection {paragraph}{5}{\z@}%
+                                   {-0.5ex \@plus -.1ex \@minus -.2ex}%
+                                   {2.3ex \@plus.2ex}%
+                                   {\LARGE\bfseries}}
+\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
+                                    {3.25ex \@plus1ex \@minus.2ex}%
+                                    {-1em}%
+                                    {\normalfont\normalsize\bfseries}}
+\renewcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}%
+                                       {3.25ex \@plus1ex \@minus .2ex}%
+                                       {-1em}%
+                                      {\normalfont\normalsize\bfseries}}
+\renewcommand\section{\@startsection {section}{1}{\z@}%
+                                   {-8.5ex \@plus -.1ex \@minus -.2ex}%
+                                   {2.3ex \@plus.2ex}%
+                                   {\raggedright\normalfont\Large\bfseries}}
+\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
+                                     {-5.25ex\@plus -1ex \@minus -.2ex}%
+                                     {1.5ex \@plus .2ex}%
+                                     {\raggedright\normalfont\large\bfseries}}
+\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+                                     {-3.25ex\@plus -1ex \@minus -.2ex}%
+                                     {1.5ex \@plus .2ex}%
+                                     {\raggedright\normalsize\bfseries}}
+
+%\newtheorem{definition}{Definice}[chapter]
+%\newenvironment{Definition}{\begin{definition}\noindent\rm}{\hspace*{\fill}$\Box$\end{definition}\par\bigskip}
+%\newtheorem{proposition}{Věta}[chapter]
+%\newenvironment{Proposition}{\begin{proposition}\noindent}{\end{proposition}\par\bigskip}
+%\newtheorem{example}{Příklad}[chapter]
+%\newenvironment{Example}{\begin{example}\noindent\rm}{\end{example}\par\bigskip}
+
+\theorembodyfont{\normalfont}
+\theoremseparator{\?:}
+\theoremsymbol{\ensuremath{\blacktriangleright}}
+\newtheorem{definition}{Definice}[chapter]
+
+\theorembodyfont{\em}
+\theoremsymbol{}
+\theoremseparator{\?:}
+\newtheorem{proposition}{Věta}[chapter]
+
+\theorembodyfont{\normalfont}
+\theoremseparator{\?:}
+\theoremsymbol{\ensuremath{\Box}}
+\newtheorem*{note}{Poznámka}
+
+\def\qed{\includegraphics[width=1.5cm]{\cestaFiles Figures/Proved.eps}}
+\theorembodyfont{\normalfont}
+\theoremseparator{\normalfont{\?:}}
+\theoremsymbol{\qed}
+\newtheorem*{proof}{Důkaz}
+
+\theorembodyfont{\normalfont}
+\theoremsymbol{}
+\theoremseparator{\?:}
+\newtheorem{example}{Příklad}[chapter]
+
+\theoremheaderfont{\em}
+\theorembodyfont{\normalfont}
+\theoremseparator{\normalfont{\?:}}
+\theoremsymbol{\ensuremath{\checkmark}}
+\newtheorem*{solution}{Řešení}
+
+
+
+%\setlength\abovecaptionskip{1mm}
+%\setlength\belowcaptionskip{-5mm}
+%-----<<< PAGE, TITLE AND SECTION DEFINITION >>>-----
+%-----<<< ---------------------------------- >>>-----
+
+
+
+%-----<<< ---------- >>>-----
+%-----<<< TITLE PAGE >>>-----
+\def \CVUT {České vysoké učení technické v~Praze}
+\def \FJFI {Fakulta jaderná a fyzikálně inženýrská}
+
+\def \BookHead {
+    \begin{center}
+    {\LARGE \textsc \CVUT}\\[2ex]
+    {\LARGE \textsc \FJFI}\\
+
+    \vspace{2cm}
+    \begin{figure}[H]
+    \begin{center}
+      {\includegraphics[width=5cm]{\cestaFiles Figures/lev.eps}}
+    \end{center}
+    \end{figure}
+    \vspace{1cm}
+
+    {\textbf {\Huge \BookName \\[8ex]}
+%    {\Large \bf \em \Bookname}
+    }
+
+    {\large \bf \Authors}\\[6ex]
+
+    \begin{figure}[H]
+    \begin{center}
+      {\includegraphics[width=3cm]{\cestaFiles Figures/DCE.eps}}
+    \end{center}
+    \end{figure}
+    \vspace{-1cm}
+    {\large \em \DCE}
+    \newpage
+    \end{center}
+    }
+%-----<<< ---------- >>>-----
+
+%-----<<< TITLE PAGE 2 >>>-----
+\def\title#1{
+\vspace*{-1cm}
+\thispagestyle{plain}\begin{center}
+{\scriptsize\sc \school}\par\medskip
+{\subject}\par\bigskip
+\titulek{\bf\uppercase{#1}}
+\end{center}\def\popis{#1}}
+
+\def\author#1{\small\centerline{#1}\def\Authors{#1}
+\fancyhead{}
+\fancyhead[R]{\thepage}
+\fancyhead[L]{\small\it\BookName}%
+\fancyfoot{}
+\pagestyle{fancy}
+\hypersetup{
+    pdftitle = {\BookName},
+    pdfauthor = {\Authors}
+}\par\vspace{15mm}}
+
+\def\maketitle{
+\fancyhead{}
+\fancyhead[R]{\thepage}
+\fancyhead[L]{\small\it\BookName}%
+\fancyfoot{}
+\pagestyle{fancy}
+\hypersetup{
+    pdftitle = {\BookName},
+    pdfauthor = {\Authors}
+}
+}
+%-----<<< TITLE PAGE >>>-----
+%-----<<< ---------- >>>-----
+
+
+
+%-----<<< ------ >>>-----
+%-----<<< MATLAB >>>-----
+\usepackage{fancybox}
+\usepackage{verbatim}
+\newenvironment{matlab}[1]
+    {\VerbatimEnvironment
+    \bigskip\par\begin{minipage}{#1}\scriptsize\begin{Verbatim}}
+    {\end{Verbatim}\end{minipage}\par\bigskip\noindent}
+%-----<<< MATLAB >>>-----
+%-----<<< ------ >>>-----
+
+
+
+%-----<<< ------ >>>-----
+%-----<<< MACROS >>>-----
+\def\?{\kern.07em}                      %inseparable space, for instance before colon, semicolon, question mark, ...
+\mathchardef\.="013B                    %space after decimal point
+%\mathcode`\,="013B
+
+%-----<<< České uvozovky
+\DeclareTextCommandDefault\clqq{\leavevmode
+  \set@low@box{''}%
+  \setbox1=\hbox{l\/}\dimen1=\wd1
+  \setbox1=\hbox{l}\advance\dimen1 by -\wd1
+  \ifdim\dimen1>0pt\kern-.1em\box0\kern.1em
+    \else\kern.1em\box0\kern-.1em\fi\nobreak\hskip0pt}
+\DeclareTextCommandDefault\crqq{\edef\@SF{\spacefactor\the\spacefactor}%
+  \nobreak\kern-.07em\hbox{``}\kern.07em\@SF\relax}
+\def\uv#1{\clqq#1\crqq}
+%>>>-----
+
+%-----<<< Množiny
+\DeclareFontFamily{OT1}{mnozina}{}
+%\DeclareFontShape{OT1}{mnozina}{m}{n}{ <10> <12> msbm10 }{}
+\DeclareFontShape{OT1}{mnozina}{m}{n}{ <6> msbm7 <8> msbm9 <10> <12> msbm10}{}
+\DeclareSymbolFont{matsym}{OT1}{mnozina}{m}{n}
+\DeclareMathSymbol{\N}{\mathord}{matsym}{78}
+\DeclareMathSymbol{\Z}{\mathord}{matsym}{90}
+\DeclareMathSymbol{\R}{\mathord}{matsym}{82}
+%\DeclareMathSymbol{\C}{\mathord}{matsym}{67}
+%>>>-----
+
+%-----<<< Odkazy na tabulky, obrázky a kapitoly
+%\newcommand{\eqref}[1]{\mbox{(\ref{#1})}}
+\newcommand{\tabref}[1]{tabulka~\mbox{\ref{#1}}}
+\newcommand{\figref}[1]{obr.~\mbox{\ref{#1}}}
+\newcommand{\charef}[1]{kapitola~\mbox{\ref{#1}}}
+\newcommand{\dcvref}[2]{\mbox{\ref{#1}}\?: #2\?;\,\,\,}
+%>>>-----
+
+%-----<<< Tučné matice kurzívou
+%\newcommand{\mat}[1]{{\bf #1}}              %bold matrix
+%\newcommand{\matt}[1]{{\pmb{#1}}}           %bold matrix for Greek
+\newcommand{\mat}[1]{\mbox{\boldmath $#1$}} %bold italic matrix
+\newcommand{\matt}[1]{\pmb{\mathit #1}}     %bold italic matrix for Greek
+\newcommand{\matit}[1]{\mathit #1}          %italic for Greek
+\newcommand{\pruh}[1]{\overline{#1}}        %overline na matrix
+%>>>-----
+
+\newcommand \Bod[1]{\vspace{0.5cm}\noindent{\bf\em  \textcolor{blue}{#1}}}
+\newcommand \Bodd[1]{\vspace{0.3cm}\noindent{\em  \textcolor{magenta}{$\star$~#1}}}
+\newcommand \Boddd[1]{\noindent{\em  \textcolor{brown}{#1}}}
+
+\def\fracc#1#2{{\displaystyle{#1\over#2}}\,}%redefinition of fraction (normal size)
+\def\frac#1#2{{\begingroup#1\endgroup\over#2}\,}
+\newcommand{\quantity}[2]{#1~[#2]}          %physics variables with unit
+\newcommand{\e}[1]{e^{\displaystyle #1}}    %exponential
+\newcommand{\Lap}{\mathcal{L}}              %Laplace operator
+\newcommand{\Ztf}{\mathcal{Z}}              %Laplace operator
+\def\rank{\qopname\relax n{hod}}            %rank of matrix
+\newcommand{\PID}[2]{#1_{_{#2}}}            %smaller subscript at PID controllers gains
+%-----<<< MACROS >>>-----
+%-----<<< ------ >>>-----
+
+
+
+%-----<<< Styl pro literaturu
+% \def\bibTeX{\textsc{bib}\TeX}
+% \renewcommand{\harvardand}{a}
+%>>>-----
Index: /applications/doprava/texty/novotny_vyzk_LQ/Styles/Diplomka.sty
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Styles/Diplomka.sty (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Styles/Diplomka.sty (revision 1419)
@@ -0,0 +1,34 @@
+%-----<<< ---------- >>>-----
+%-----<<< TITLE PAGE >>>-----
+\def \BookHeadDP {
+    \begin{center}
+    {\LARGE \textsc \CVUT}\\[2ex]
+    {\LARGE \textsc \FJFI}\\
+
+    \vspace{2cm}
+    \begin{figure}[H]
+    \begin{center}
+      {\includegraphics[width=5cm]{\cestaFiles Figures/lev.eps}}
+    \end{center}
+    \end{figure}
+    \vspace{1cm}
+
+    {\textbf {\Huge \BookName \\[4ex]}
+    {\LARGE \bf \Bookname}
+    }
+
+    \vfill
+
+   {\large
+    \begin{tabular}{rl}
+    Vypracoval: & \autor\\
+    Vedoucí práce: & \vedouci\\
+    Konzultant: & \konzultant\\
+    \multicolumn{2}{c}\DatumDP
+    \end{tabular}
+   }
+\end {center}
+}
+
+    
+%-----<<< ---------- >>>-----
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.log
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.log (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.log (revision 1419)
@@ -0,0 +1,1036 @@
+This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=latex 2011.10.24)  4 JAN 2012 16:58
+entering extended mode
+ %&-line parsing enabled.
+**vyzk.tex
+(./vyzk.tex
+LaTeX2e <2009/09/24>
+Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
+yphenation, loaded.
+(/usr/share/texmf-texlive/tex/latex/base/report.cls
+Document Class: report 2007/10/19 v1.4h Standard LaTeX document class
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+File: size12.clo 2007/10/19 v1.4h Standard LaTeX file (size option)
+)
+\c@part=\count79
+\c@chapter=\count80
+\c@section=\count81
+\c@subsection=\count82
+\c@subsubsection=\count83
+\c@paragraph=\count84
+\c@subparagraph=\count85
+\c@figure=\count86
+\c@table=\count87
+\abovecaptionskip=\skip41
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+\bibindent=\dimen102
+)
+(/usr/share/texmf-texlive/tex/latex/hyperref/hyperref.sty
+Package: hyperref 2009/10/09 v6.79a Hypertext links for LaTeX
+
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+Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
+\KV@toks@=\toks14
+)
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+Package: ifpdf 2009/04/10 v2.0 Provides the ifpdf switch (HO)
+Package ifpdf Info: pdfTeX in pdf mode not detected.
+)
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+Package: xcolor-patch 2009/10/02 xcolor patch
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+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
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+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
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+%%EndFont 
+%%BeginFont: CMR10
+%!PS-AdobeFont-1.0: CMR10 003.002
+%%Title: CMR10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
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+/FontName /CMR10 def
+/FontBBox {-40 -250 1009 750 }readonly def
+/UniqueID 5000793 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
+/FullName (CMR10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
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+{restore}if
+%%EndFont 
+%%BeginFont: MSBM10
+%!PS-AdobeFont-1.0: MSBM10 003.002
+%%Title: MSBM10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name MSBM10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/MSBM10 known{/MSBM10 findfont dup/UniqueID known{dup
+/UniqueID get 5031982 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /MSBM10 def
+/FontBBox {-55 -420 2343 920 }readonly def
+/UniqueID 5031982 def
+/PaintType 0 def
+/FontInfo 7 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name MSBM10.) readonly def
+/FullName (MSBM10) readonly def
+/FamilyName (Euler) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 78 /N put
+dup 82 /R put
+readonly def
+currentdict end
+currentfile eexec
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+%%EndFont 
+%%BeginFont: CMTI12
+%!PS-AdobeFont-1.0: CMTI12 003.002
+%%Title: CMTI12
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMTI12.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+{save true}{false}ifelse}{false}ifelse
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+/FontName /CMTI12 def
+/FontBBox {-36 -251 1103 750 }readonly def
+/UniqueID 5000829 def
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+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMTI12.) readonly def
+/FullName (CMTI12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
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+%%EndFont 
+%%BeginFont: CMMI7
+%!PS-AdobeFont-1.0: CMMI7 003.002
+%%Title: CMMI7
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI7.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMMI7 known{/CMMI7 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
+11 dict begin
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+/FontName /CMMI7 def
+/FontBBox {-1 -250 1171 750 }readonly def
+/UniqueID 5087382 def
+/PaintType 0 def
+/FontInfo 10 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI7.) readonly def
+/FullName (CMMI7) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+/ascent 750 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
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+readonly def
+currentdict end
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+%%EndFont 
+%%BeginFont: CMSY10
+%!PS-AdobeFont-1.0: CMSY10 003.002
+%%Title: CMSY10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup
+/UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMSY10 def
+/FontBBox {-29 -960 1116 775 }readonly def
+/UniqueID 5096651 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY10.) readonly def
+/FullName (CMSY10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 0 /minus put
+dup 2 /multiply put
+dup 15 /bullet put
+dup 23 /followsequal put
+dup 26 /propersubset put
+dup 31 /follows put
+dup 33 /arrowright put
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+dup 56 /universal put
+dup 92 /intersection put
+dup 94 /logicaland put
+dup 95 /logicalor put
+dup 102 /braceleft put
+dup 103 /braceright put
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+currentdict end
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+%%EndFont 
+%%BeginFont: CMR7
+%!PS-AdobeFont-1.0: CMR7 003.002
+%%Title: CMR7
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR7.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR7 known{/CMR7 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
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+/FontName /CMR7 def
+/FontBBox {-27 -250 1122 750 }readonly def
+/UniqueID 5000790 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR7.) readonly def
+/FullName (CMR7) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
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+0 1 255 {1 index exch /.notdef put} for
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+readonly def
+currentdict end
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+%!PS-AdobeFont-1.0: CMEX10 003.002
+%%Title: CMEX10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMEX10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+%%EndFont 
+%%BeginFont: CMSY6
+%!PS-AdobeFont-1.0: CMSY6 003.002
+%%Title: CMSY6
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY6.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMSY6 known{/CMSY6 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMSY6 def
+/FontBBox {-4 -948 1329 786 }readonly def
+/UniqueID 5096647 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY6.) readonly def
+/FullName (CMSY6) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/isFixedPitch false def
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+/UnderlineThickness 50 def
+end readonly def
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+0 1 255 {1 index exch /.notdef put} for
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+readonly def
+currentdict end
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+%%EndFont 
+%%BeginFont: CMR6
+%!PS-AdobeFont-1.0: CMR6 003.002
+%%Title: CMR6
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR6.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR6 known{/CMR6 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMR6 def
+/FontBBox {-20 -250 1193 750 }readonly def
+/UniqueID 5000789 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR6.) readonly def
+/FullName (CMR6) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 43 /plus put
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+readonly def
+currentdict end
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+%%Title: CMMI6
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI6.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+%%EndFont 
+%%BeginFont: CMSY8
+%!PS-AdobeFont-1.0: CMSY8 003.002
+%%Title: CMSY8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+{save true}{false}ifelse}{false}ifelse
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+/FontName /CMSY8 def
+/FontBBox {-30 -955 1185 779 }readonly def
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+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY8.) readonly def
+/FullName (CMSY8) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
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+0 1 255 {1 index exch /.notdef put} for
+dup 0 /minus put
+dup 3 /asteriskmath put
+dup 48 /prime put
+dup 49 /infinity put
+dup 50 /element put
+dup 102 /braceleft put
+dup 103 /braceright put
+dup 106 /bar put
+readonly def
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+%%EndFont 
+%%BeginFont: CMMI8
+%!PS-AdobeFont-1.0: CMMI8 003.002
+%%Title: CMMI8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+/FontName /CMMI8 def
+/FontBBox {-24 -250 1110 750 }readonly def
+/UniqueID 5087383 def
+/PaintType 0 def
+/FontInfo 10 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI8.) readonly def
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+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/ascent 750 def
+end readonly def
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+{restore}if
+%%EndFont 
+%%BeginFont: CMSL12
+%!PS-AdobeFont-1.0: CMSL12 003.002
+%%Title: CMSL12
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSL12.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMSL12 known{/CMSL12 findfont dup/UniqueID known{dup
+/UniqueID get 5000799 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMSL12 def
+/FontBBox {-56 -251 1102 750 }readonly def
+/UniqueID 5000799 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSL12.) readonly def
+/FullName (CMSL12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -9.46 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 19 /acute put
+dup 20 /caron put
+dup 46 /period put
+dup 50 /two put
+dup 51 /three put
+dup 65 /A put
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+dup 83 /S put
+dup 84 /T put
+dup 85 /U put
+dup 86 /V put
+dup 89 /Y put
+readonly def
+currentdict end
+currentfile eexec
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+%!PS-AdobeFont-1.0: MSAM10 003.002
+%%Title: MSAM10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name MSAM10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+%%EndFont 
+%%BeginFont: CMBX12
+%!PS-AdobeFont-1.0: CMBX12 003.002
+%%Title: CMBX12
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMBX12.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+{save true}{false}ifelse}{false}ifelse
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+/FontName /CMBX12 def
+/FontBBox {-53 -251 1139 750 }readonly def
+/UniqueID 5000769 def
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+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMBX12.) readonly def
+/FullName (CMBX12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Bold) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
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+readonly def
+currentdict end
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+%%EndFont 
+%%BeginFont: CMR8
+%!PS-AdobeFont-1.0: CMR8 003.002
+%%Title: CMR8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+{save true}{false}ifelse}{false}ifelse
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+/FontName /CMR8 def
+/FontBBox {-36 -250 1070 750 }readonly def
+/UniqueID 5000791 def
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+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR8.) readonly def
+/FullName (CMR8) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
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+%%BeginFont: CMMI12
+%!PS-AdobeFont-1.0: CMMI12 003.002
+%%Title: CMMI12
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI12.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+/FontName /CMMI12 def
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+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI12.) readonly def
+/FullName (CMMI12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/UnderlineThickness 50 def
+/ascent 750 def
+end readonly def
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+%%BeginFont: CMR12
+%!PS-AdobeFont-1.0: CMR12 003.002
+%%Title: CMR12
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR12.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+%%EndFont 
+%%BeginFont: CMCSC10
+%!PS-AdobeFont-1.0: CMCSC10 003.002
+%%Title: CMCSC10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMCSC10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMCSC10 known{/CMCSC10 findfont dup/UniqueID known{dup
+/UniqueID get 5087402 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMCSC10 def
+/FontBBox {14 -250 1077 750 }readonly def
+/UniqueID 5087402 def
+/PaintType 0 def
+/FontInfo 10 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMCSC10.) readonly def
+/FullName (CMCSC10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+/ascent 750 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 16 /dotlessi put
+dup 19 /acute put
+dup 20 /caron put
+dup 67 /C put
+dup 70 /F put
+dup 80 /P put
+dup 97 /a put
+dup 99 /c put
+dup 100 /d put
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+dup 110 /n put
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+dup 114 /r put
+dup 115 /s put
+dup 116 /t put
+dup 117 /u put
+dup 118 /v put
+dup 121 /y put
+dup 122 /z put
+readonly def
+currentdict end
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Index: /applications/doprava/texty/novotny_vyzk_LQ/Implementation.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Implementation.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Implementation.tex (revision 1419)
@@ -0,0 +1,272 @@
+\chapter{Implementace}
+
+\section{Seznam proměnných}
+Všechny proměnné jsou zavedeny pro každého agenta reprezentujícího jednu křižovatku zvlášť
+a jsou označeny indexem $i$ signální skupiny. Tavždy ovládá jeden jízdní pruh. Pokud jsou bez indexu,
+jedná se o proměnnou agenta, případně oblasti simulace.
+
+\begin{tabular}{ccp{5cm}p{5cm}}
+  \textbf{V textu} & \textbf{V programu} & \textbf{Název} & \textbf{Popis} \\
+  $T \in \mathbb{N}$ & \texttt{T} & Vzorkovací perioda & ...\\
+  $C \in \mathbb{N}$ & \texttt{Tc} & Délka cyklu & ... \\
+  $S = 0,5$ & \texttt{Tc} & Saturovaný tok & Maximální počet vozidel, která projedou křižovatkou za sekundu \\
+  $L \in \mathbb{R}^+$ &  \texttt{L} & Ztrátový čas & Čas potřebný k vyklizení křižovatky mezi dvěma fázemi\\ 
+  $J = \{j_1, ..., j_n\}$ &  & Množina signálních skupin &  \\
+  $J_A \subset J$ & \texttt{} & Množina signálních skupin agenta $A$ & Skupiny náležící jednomu agentovi \\
+  $I_j \subset J$ & \texttt{} & Množina vstupů signální skupiny & Signální skupiny ostatních agentů ústících do příslušné skupiny $g$ \\
+  $g_j^N \in <0,1>$ & & Nominální poměr zelené & Defi novaný poměr fází \\
+  $g_j(t) \in <0,1>$ & & Efektivní poměr zelené & Část z délky cyklu, kdy je signální skupina  průjezdná \\
+  $i_j(t) \in \mathbb{R}^+$ & \texttt{i\_g} & Hustota vstupů & Počet přijíždějících vozidel do pruhu signální skupiny za jednotku času \\
+  $o_j(t) \in \mathbb{R}^+$ & \texttt{} & Hustota výstupů & Počet vyjíždějících vozidel z pruhu signální skupiny za jednotku času \\
+  $q_j(t) \in \mathbb{N}_0^+$ & \texttt{} & Fronta & Počet vozidel jedoucí menší rychlostí než $3,6 km/h$ \\
+  $\alpha_{j,k}  \in <0,1>$ & \texttt{} & Odbočovací poměr z $j$ do $k$ &  
+\end{tabular}
+
+\section{Použitá metoda}
+Účelem této práce je řídit provoz pomocí nastavení optimální délky cyklu za použití multiagentního systému, kde
+každý agent ovládá signální skupiny jedné křižovatky a jsou mu dostupné příslušné údaje.
+Jako vhodná metoda bylo zvoleno LQ řízení, které se snaží minimalizovat fronty a penalizovat délku cyklu.
+
+\subsection{Přechodové vztahy}
+Jako údaj popisující stav systému byla zvolena délka fronty $q_j(t)$, což je počet aut v jízdním pruhu jedoucích 
+méně než 3,6 km/h. Pro danou frontu v čase $t+1$ platí zřejmě vztah
+\begin{equation}\label{eq:my_trans_01}
+ q_j(t+1) = q_j(t) + T ( i_j(t) - o_j(t) )
+\end{equation}, kde hustota vstupu $i_j(t)$ je součtem výstupů sousedů pronásobený odbočovacími poměry,
+případně vstupu do systému $i_{j,0}(t)$, pokud se jedná o koncové rameno řízené oblasti, tedy
+\begin{equation}
+  i_j(t) = i_{j,0}(t) + \sum_{k \in I_j} \alpha_{k,j} o_k(t)
+\end{equation}.
+Křižovtkou z daného jízdního pruhu v průjezdné fázi projede $S$ vozidel za sekundu, kde 
+délka průjezdné fáze závisí na nastaveném poměru a délce cyklu. Před přechodem do nové
+fáze signálího plánu je potřeba vklidit křižovatku, což vede ke ztrátovému času $L$, který
+se projeví vždy jednou za cyklus. Efektivní délka zelené je tedy
+\begin{equation}
+ g_j(t) = (C(t) - L) g_j^N
+\end{equation}
+a pro hustotu výstupu platí
+\begin{equation}
+ o_j(t) = \frac{S_j g_j(t)}{C(t)} = S_j g_j^N \left( 1 - LC(t)^{-1} \right)
+\end{equation}. Rovnice \ref{eq:my_trans_01} tedy přechází do tvaru
+\begin{equation}\label{eq:my_trans_02}
+ q_j(t+1) = q_j(t) + T \left( i_{j,0}(t) + \sum_{k \in I_j} \alpha_{k,j} S_k g_k^N \left( 1 - LC(t)^{-1} \right)  - S_j g_j^N \left( 1 - LC(t)^{-1} \right) \right)
+\end{equation}.
+Pokud budeme podobně jako v \cite{6_tuc_lq} předpokládat existenci nominální délky cyklu $C^N$, při níž se
+nemění délka fronty, platíc(
+\begin{equation}\label{eq:my_trans_nom}
+ 0 = T \left( i_{j,0}(t) + \sum_{k \in I_j} \alpha_{k,j} S_k g_k^N \left( 1 - LC^{N -1} \right)  - S_j g_j^N \left( 1 - LC^{N -1} \right) \right)
+\end{equation}. Odečtením rovnice \ref{eq:my_trans_nom} od \ref{eq:my_trans_02} dostaneme
+\begin{equation}\label{eq:my_trans_03}
+ q_j(t+1) = q_j(t) + T \left( - \sum_{k \in I_j} \alpha_{k,j} S_k g_k^N  + S_j g_j^N  \right) L \Delta C^{-1}(t)
+\end{equation}, kde $ \Delta C^{-1}(t) = C(t)^{-1} - C^{N -1}$. Pro ramena $j \in J_A$ náležící agentovi $A$ se
+tedy rovnice pro fronty dají zapsat maticově ve tvaru
+\begin{equation}\label{eq:my_trans_mat}
+ \vec{q}(t+1) = A \vec{q}(t) + B \Delta C^{-1}(t) 
+\end{equation}
+
+Kostantni saturovany tok neni optimalni, pouzije aprox podle Pecherkove (viz bak.), 
+prujezd odpovida bud sat. toku, pokud neodjede cela fronta, nebo je primo umerny
+fronte (+ prijezdum). prolozi se funkci a aprox se primkou podle hodnoty fronty v case t.
+Napocte se rizen pro horizont a podle vyvoje fronty se prepocte misto pro prolozeni pri
+
+
+\subsubsection{Model toku}
+V článku \cite{6_tuc_lq} se úbytek vozidel modeluje podle rovnice \ref{eq:tuc_u}, kde je uvažován
+tok vozidel křižovatkou za jednotku času jako konstanta $S$, což je saturovaný tok. Tento vztah
+platí pouze když je příslušný pruh naplněn vozidly do té míry, že křižovatkou projede maximální
+možný počet vozidel. To však neplatí, pokud není pruh dostatečně vytížen, například pokud se zmenší
+délka fronty v nějaký časový okamžik na nulu. Pokud je vytížení menší je tok lineárně závislý na součtu
+fronty $q(t)/T$ a počtu vstupujících vozidel $i(t)$. Pro teoretickou hodnotu toku $S$ tedy dostáváme vztah
+\begin{equation}\label{eq:teor_tok}
+ S_{teor}(q(t) + i(t)) = \left\{
+			\begin{array}{lr}
+			  \frac{q(t)}{T} + i(t) & \frac{q(t)}{T} + i(t) <= S_{max} \\
+			  S_{max} &  \frac{q(t)}{T} + i(t) > S_{max}
+                        \end{array}
+		  \right.
+\end{equation}
+. tento vztah vyjadřuje to, že pokud je fronta plus přírůstrek vozidel ve vzorkovací periodě
+$(q(t), i(t)T)$ menší než maximální počet vozidel, který je křižovatka za periodu $T$ schopna
+propustit $(T S_{max})$, projedou všechna vozidla. Abychom se vyhnuli podmínce podle $S_{max}$,
+aproximuje se tento vztah funkcí
+\begin{equation}\label{eq:exp_tok}
+ S_{exp}(q(t), i(t)) = S_{max} \left(1 - e^{- \frac{1}{S_{max}} \left( \frac{q(t)}{T} + i(t) \right) } \right)
+\end{equation}
+, která splňuje podmínku 
+\begin{equation} 
+\frac{ dS_{exp} }{d(q/T+i)}(0,0) = 1  
+\end{equation}
+, tedy při malé frontě a hustotě provozu
+je přírůstek toku roven $q/T+i$, a podmínku 
+\begin{equation}
+\lim_{q/T+i\to\infty} S_{exp} = S_{max}  
+\end{equation}
+, tedy při velké frontě a hustotě provozu
+se tok blíží konstantě $S_{max}$. Pro malý časový interval můžeme tuto funkci dále zjednodušit na lineární vztah
+\begin{equation}\label{eq:lin_tok}
+ S(q(t)) = \sigma(q(t)/T + i_0)
+\end{equation}
+, kde je $i_0 = i(0)$ a
+\begin{equation}
+ \sigma = \frac{ dS_{exp} }{d(q/T+i)}(q(0),i(0))
+\end{equation}
+\\
+vlozit graf s ruznymi S
+\\
+
+\subsubsection{Přechodové vztahy s proměnným tokem}
+Pro vyjádření přechodových vzthů použijeme lineární odel toku a rovnice \ref{eq:my_trans_02}
+přejde na tvar
+\begin{equation}
+ q_j(t+1) = q_j(t) + T \left( i_{j,0}(t) + \sum_{k \in I_j} \alpha_{k,j} S_k(q_k(t)) g_k^N \left( 1 - LC(t)^{-1} \right)  - S_j(q_j(t)) g_j^N \left( 1 - LC(t)^{-1} \right) \right)
+\end{equation}
+, a po dosazení \ref{eq:lin_tok} dostaneme
+\begin{equation}
+ q_j(t+1) = q_j(t) + T \left( \begin{array}{c}
+				i_{j,0}(t) + \\
+				+ \sum_{k \in I_j} \alpha_{k,j} \delta_k(q_k(t) T^{-1} + i_{0,k}) g_k^N \left( 1 - LC(t)^{-1} \right) - \\
+				- \delta_j(q_j(t) T^{-1} + i_{0,j}) g_j^N \left( 1 - LC(t)^{-1} \right)
+                              \end{array}
+  \right)
+\end{equation}
+
+\begin{equation}\label{eq:my_trans_mod_tok_03}
+ q_j(t+1) = q_j(t) + T \left( \begin{array}{c}
+				i_{j,0}(t) + \\
+				+ \sum_{k \in I_j} \alpha_{k,j} \delta_k g_k^N T^{-1} q_k(t)  - \delta_j g_j^N T^{-1} q_j(t) + \\
+				+ \sum_{k \in I_j} \alpha_{k,j} \delta_k i_{0,k} g_k^N - \delta_j i_{0,j} g_j^N - \\
+				- \sum_{k \in I_j} \alpha_{k,j} \delta_k g_k^N L T^{-1} q_k(t) C(t)^{-1} + \delta_j  g_j^N L T^{-1} q_j(t) C(t)^{-1} - \\				
+				- \sum_{k \in I_j} \alpha_{k,j} \delta_k i_{0,k} g_k^N L C(t)^{-1} + \delta_j i_{0,j} g_j^N L C(t)^{-1} 				
+                              \end{array}
+  \right)
+\end{equation}
+
+. Pokud budeme podobně jako v rovnici \ref{eq:my_trans_nom} uvažovat nominální $C^N$, pro které se $q(t+1)$ rovná $q(t)$,
+dostaneme dosazením $\Delta C^{-1}(t) = C(t)^{-1} - C^{N -1} $ do \ref{eq:my_trans_mod_tok_03} rovnici
+
+\begin{equation}\label{eq:my_trans_mod_tok_04}
+\begin{array}{ccc}
+ q_j(t+1) &= q_j(t) +& L \left( \delta_j  g_j^N q_j(t)   - \sum_{k \in I_j} \alpha_{k,j} \delta_k g_k^N q_k(t) \right) C(t)^{-1} +\\
+  & & + L T \left( \delta_j i_{0,j} g_j^N - \sum_{k \in I_j} \alpha_{k,j} \delta_k i_{0,k} g_k^N  \right) C(t)^{-1} 
+\end{array} 
+\end{equation}
+
+
+
+
+\subsection{Minimalizační kritérium}
+Podobně jako v předchozí kapitole, minimalizovat kvaratické kritérium $J$.
+Minimalizaci budeme provádět v proměnných $\Delta C(t)$ pro časový horizont $h$,
+tedy pro vektory $\Delta C(t_0), \Delta C(t_0 + 1), ..., \Delta C(t_0 + h)$. Pro zpřehlednění
+zápisu položíme bez újmy na obecnosti $t_0 = 0$.
+Kvadratické kritérium
+ve tvaru
+\begin{equation}\label{eq:J}
+ J = \sum_{t=0}^h q(t)^T Q q(t) + \Delta C(t)^T R \Delta C(t)
+\end{equation}, 
+kde $Q$ a $R$ jsou diagonální pozitivně definitní matice vah,
+rozepíšeme pomocí vztahu
+\begin{equation}\label{eq:prechod}
+ q(t+1) = Aq(t) + Bq(t)
+\end{equation} a budeme minimalizovat pro jednotlivá $t$ podle  $\Delta C(t)$.
+$\Delta C(h)$ se v kritériu vyskytuje pouze jako člen
+\begin{equation}
+\Delta C(h)^T R \Delta C(h)
+\end{equation}
+a tedy musí být $\Delta C(h) 0$. $\Delta C(h - 1)$ se vyskytuje ve členech
+\begin{equation}
+  \Delta C(h - 1)^T R \Delta C(h - 1) + (q(h - 1)^T A^T + \Delta C(h - 1)^T B^T ) Q ( A q(h - 1) + B \Delta C(h - 1))
+\end{equation}
+, což lze pomocí složených vektorů a matic přepsat do tvaru
+\begin{equation} \label{eq:J_sloz}
+ (\Delta C(h-1)^T, q(h - 1)^T ) 
+  \left( \begin{array}{cc}
+          B^T \sqrt{Q} & \sqrt{R} \\
+	  A^T \sqrt{Q} & 0
+	  \end{array}
+  \right)  
+  \left( \begin{array}{cc}
+           \sqrt{Q} B & \sqrt{Q} A \\
+	  \sqrt{R} & 0
+	  \end{array}
+  \right)
+  \left( \begin{array}{c}
+	    \Delta C(h-1) \\
+	    q(h - 1)
+	  \end{array}
+  \right)
+\end{equation}, kde $\sqrt{Q}$ je matice, pro níž platí $\sqrt{Q} \sqrt{Q} = Q$.
+Složenou matici
+\begin{equation}
+  \left( \begin{array}{cc}
+          B^T \sqrt{Q} & \sqrt{R} \\
+	  A^T \sqrt{Q} & 0
+	  \end{array}
+  \right)  
+  \left( \begin{array}{cc}
+           \sqrt{Q} B & \sqrt{Q} A \\
+	  \sqrt{R} & 0
+	  \end{array}
+  \right) = 
+  \left( \begin{array}{cc}
+          B^T Q B + R & B^T Q A \\
+	  A^T Q B & A^T Q A
+	  \end{array}
+  \right)
+\end{equation}
+můžeme pomocí Choleského dekompozici na součin dolní a horní trojúhelníkové matice.
+Člen \ref{eq:J_sloz} poté přejde na tvar
+\begin{equation}
+ (\Delta C(h-1)^T, q(h - 1)^T ) 
+  \left( \begin{array}{cc}
+          L_q^T & 0 \\
+	  L^T & L_C^T
+	  \end{array}
+  \right)  
+  \left( \begin{array}{cc}
+          L_C & L \\
+	  0 & L_q
+	  \end{array}
+  \right)
+  \left( \begin{array}{c}
+	    \Delta C(h-1) \\
+	    q(h - 1)
+	  \end{array}
+  \right)
+\end{equation}, který můžeme dále upravit na
+\begin{equation}
+ ( L_C \Delta C(h-1) +  L_q q(h-1) )^T ( L_C \Delta C(h-1) +  L_q q(h-1) ) + q(h-1)^T L_q^T L_q q(h-1) 
+\end{equation}. Pokud tento člen chceme minimalizovat v proměnné $q(h-1)$, musí nutně platit
+\begin{equation}
+ \Delta C(h-1) = - L_C^{-1} L q(h-1)
+\end{equation}. Zbývající nenulová část $q(h-1)^T L_q^T L_q q(h-1) $ lze přepsat pomocí rovnice \ref{eq:prechod} do tvaru 
+\begin{equation}
+ q(h-1)^T L_q^T L_q q(h-1) = ( A q(h-2) + B \Delta C(h-2) )^T L_q^T L_q ( A q(h-2) + B \Delta C(h-2) )
+\end{equation}, kde se vyskytuje $\Delta C(t)$ pouze pro $t = h-2$. Minimalizace přes
+$\Delta C(h-2)$ bude probíhat analogicky, pouze se matice $Q$ nahradí maticí 
+\begin{equation}
+\widetilde{Q} = Q + L_q^T L_q
+\end{equation}, která zahrnuje zbytek po členu s $\Delta C(h-1)$.
+Pro další $\Delta C(t)$ se pouze upraví matice $\widetilde{Q}$ výše popsaným způsoen a minimalizace již probíhá stejně.\\
+
+DOTAZY:\\
+QR - obecne nerozklada na trojuhelnikove matice $L L^{-1}$, ale na jednu troj a na druhou ortogonal.
+Cholesky rozklada pouze pozitivně definitní matice - je pozitivně definitní? dokazovat? pouzit QR?
+Matice L se v tomto pripade meni v kazdem kroku. V poradku?
+
+
+
+
+
+
+
+
+
+
+
+\section{Simulace}
+
+\subsection{Simulátor AIMSUN}
+
+\subsection{Oblast simulace}
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.toc
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.toc (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.toc (revision 1419)
@@ -0,0 +1,42 @@
+\select@language {czech}
+\contentsline {chapter}{Seznam obr\IeC {\'a}zk\IeC {\r u}}{vii}{chapter*.2}
+\contentsline {chapter}{Seznam tabulek}{viii}{chapter*.3}
+\contentsline {chapter}{\numberline {1}\IeC {\'U}vod}{1}{chapter.1}
+\contentsline {chapter}{\numberline {2}Multiagentn\IeC {\'\i } syst\IeC {\'e}my}{2}{chapter.2}
+\contentsline {section}{\numberline {2.1}\IeC {\'U}vod}{2}{section.2.1}
+\contentsline {subsection}{\numberline {2.1.1}Historie}{2}{subsection.2.1.1}
+\contentsline {subsection}{\numberline {2.1.2}Agent}{2}{subsection.2.1.2}
+\contentsline {section}{\numberline {2.2}Druhy prost\IeC {\v r}ed\IeC {\'\i }}{3}{section.2.2}
+\contentsline {section}{\numberline {2.3}Interakce agent\IeC {\r u}}{3}{section.2.3}
+\contentsline {subsection}{\numberline {2.3.1}Stavy prost\IeC {\v r}ed\IeC {\'\i } a preference agent\IeC {\r u}}{3}{subsection.2.3.1}
+\contentsline {chapter}{\numberline {3}V\IeC {\'y}b\IeC {\v e}r strategie genta}{5}{chapter.3}
+\contentsline {section}{\numberline {3.1}V\IeC {\'y}b\IeC {\v e}r strategie podle teorie her}{5}{section.3.1}
+\contentsline {section}{\numberline {3.2}RMM - Rekurzivn\IeC {\'\i } modelov\IeC {\'e} metody}{6}{section.3.2}
+\contentsline {subsection}{\numberline {3.2.1}Form\IeC {\'a}ln\IeC {\'\i } definice}{6}{subsection.3.2.1}
+\contentsline {subsection}{\numberline {3.2.2}Rozhodovac\IeC {\'\i } algoritmus}{8}{subsection.3.2.2}
+\contentsline {section}{\numberline {3.3}Markov\IeC {\r u}v rozhodvac\IeC {\'\i } proces}{9}{section.3.3}
+\contentsline {subsection}{\numberline {3.3.1}Dynamick\IeC {\'e} programov\IeC {\'a}n\IeC {\'\i }}{10}{subsection.3.3.1}
+\contentsline {section}{\numberline {3.4}Zp\IeC {\v e}tnovazebn\IeC {\'e} u\IeC {\v c}en\IeC {\'\i } (Reinforcement learning)}{11}{section.3.4}
+\contentsline {subsection}{\numberline {3.4.1}Q-u\IeC {\v c}en\IeC {\'\i } (Q-learning)}{12}{subsection.3.4.1}
+\contentsline {subsection}{\numberline {3.4.2}U\IeC {\v c}en\IeC {\'\i } na z\IeC {\'a}klad\IeC {\v e} modelu (Model-based learning)}{12}{subsection.3.4.2}
+\contentsline {section}{\numberline {3.5}Bayesovsk\IeC {\'e} u\IeC {\v c}en\IeC {\'\i }}{13}{section.3.5}
+\contentsline {subsection}{\numberline {3.5.1}V\IeC {\v e}rohodnostn\IeC {\'\i } funkce}{13}{subsection.3.5.1}
+\contentsline {section}{\numberline {3.6}Pou\IeC {\v z}it\IeC {\'\i } RMM a Bayesova u\IeC {\v c}en\IeC {\'\i } v decentralizovan\IeC {\'e}m \IeC {\v r}\IeC {\'\i }zen\IeC {\'\i } dopravy}{14}{section.3.6}
+\contentsline {section}{\numberline {3.7}Pou\IeC {\v z}it\IeC {\'\i } zp\IeC {\v e}tnovazebn\IeC {\'e}ho u\IeC {\v c}en\IeC {\'\i }}{16}{section.3.7}
+\contentsline {subsection}{\numberline {3.7.1}Zp\IeC {\v e}tnovazebn\IeC {\'e} u\IeC {\v c}en\IeC {\'\i } na z\IeC {\'a}klad\IeC {\v e} modelu}{16}{subsection.3.7.1}
+\contentsline {section}{\numberline {3.8}LQ \IeC {\v r}\IeC {\'\i }zen\IeC {\'\i }}{17}{section.3.8}
+\contentsline {subsection}{\numberline {3.8.1}Pou\IeC {\v z}it\IeC {\'\i } LQ \IeC {\v r}\IeC {\'\i }zen\IeC {\'\i } ve strategii TUC}{18}{subsection.3.8.1}
+\contentsline {subsubsection}{\numberline {3.8.1.1}Kvadratick\IeC {\'e} krit\IeC {\'e}rium}{20}{subsubsection.3.8.1.1}
+\contentsline {chapter}{\numberline {4}Implementace}{21}{chapter.4}
+\contentsline {section}{\numberline {4.1}Seznam prom\IeC {\v e}nn\IeC {\'y}ch}{21}{section.4.1}
+\contentsline {section}{\numberline {4.2}Pou\IeC {\v z}it\IeC {\'a} metoda}{22}{section.4.2}
+\contentsline {subsection}{\numberline {4.2.1}P\IeC {\v r}echodov\IeC {\'e} vztahy}{23}{subsection.4.2.1}
+\contentsline {subsubsection}{\numberline {4.2.1.1}Model toku}{24}{subsubsection.4.2.1.1}
+\contentsline {subsubsection}{\numberline {4.2.1.2}P\IeC {\v r}echodov\IeC {\'e} vztahy s prom\IeC {\v e}nn\IeC {\'y}m tokem}{25}{subsubsection.4.2.1.2}
+\contentsline {subsection}{\numberline {4.2.2}Minimaliza\IeC {\v c}n\IeC {\'\i } krit\IeC {\'e}rium}{25}{subsection.4.2.2}
+\contentsline {section}{\numberline {4.3}Simulace}{27}{section.4.3}
+\contentsline {subsection}{\numberline {4.3.1}Simul\IeC {\'a}tor AIMSUN}{27}{subsection.4.3.1}
+\contentsline {subsection}{\numberline {4.3.2}Oblast simulace}{27}{subsection.4.3.2}
+\contentsline {chapter}{\numberline {5}V\IeC {\'y}sledky}{28}{chapter.5}
+\contentsline {chapter}{Literatura}{30}{chapter*.7}
+\contentsline {chapter}{\numberline {A}P\IeC {\v r}\IeC {\'\i }loha 1}{I}{appendix.A}
Index: /applications/doprava/texty/novotny_vyzk_LQ/Implementation.tex.backup
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Implementation.tex.backup (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Implementation.tex.backup (revision 1419)
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+\chapter{Implementace}
+
+\section{Seznam proměnných}
+Všechny proměnné jsou zavedeny pro každého agenta reprezentujícího jednu křižovatku zvlášť
+a jsou označeny indexem $i$ signální skupiny. Tavždy ovládá jeden jízdní pruh. Pokud jsou bez indexu,
+jedná se o proměnnou agenta, případně oblasti simulace.
+
+\begin{tabular}{ccp{5cm}p{5cm}}
+  \textbf{V textu} & \textbf{V programu} & \textbf{Název} & \textbf{Popis} \\
+  $T \in \mathbb{N}$ & \texttt{T} & Vzorkovací perioda & ...\\
+  $C \in \mathbb{N}$ & \texttt{Tc} & Délka cyklu & ... \\
+  $S = 0,5$ & \texttt{Tc} & Saturovaný tok & Maximální počet vozidel, která projedou křižovatkou za sekundu \\
+  $L \in \mathbb{R}^+$ &  \texttt{L} & Ztrátový čas & Čas potřebný k vyklizení křižovatky mezi dvěma fázemi\\ 
+  $J = \{j_1, ..., j_n\}$ &  & Množina signálních skupin &  \\
+  $J_A \subset J$ & \texttt{} & Množina signálních skupin agenta $A$ & Skupiny náležící jednomu agentovi \\
+  $I_j \subset J$ & \texttt{} & Množina vstupů signální skupiny & Signální skupiny ostatních agentů ústících do příslušné skupiny $g$ \\
+  $g_j^N \in <0,1>$ & & Nominální poměr zelené & Defi novaný poměr fází \\
+  $g_j(t) \in <0,1>$ & & Efektivní poměr zelené & Část z délky cyklu, kdy je signální skupina  průjezdná \\
+  $i_j(t) \in \mathbb{R}^+$ & \texttt{i\_g} & Hustota vstupů & Počet přijíždějících vozidel do pruhu signální skupiny za jednotku času \\
+  $o_j(t) \in \mathbb{R}^+$ & \texttt{} & Hustota výstupů & Počet vyjíždějících vozidel z pruhu signální skupiny za jednotku času \\
+  $q_j(t) \in \mathbb{N}_0^+$ & \texttt{} & Fronta & Počet vozidel jedoucí menší rychlostí než $3,6 km/h$ \\
+  $\alpha_{j,k}  \in <0,1>$ & \texttt{} & Odbočovací poměr z $j$ do $k$ &  
+\end{tabular}
+
+\section{Použitá metoda}
+Účelem této práce je řídit provoz pomocí nastavení optimální délky cyklu za použití multiagentního systému, kde
+každý agent ovládá signální skupiny jedné křižovatky a jsou mu dostupné příslušné údaje.
+Jako vhodná metoda bylo zvoleno LQ řízení, které se snaží minimalizovat fronty a penalizovat délku cyklu.
+
+\subsection{Přechodové vztahy}
+Jako údaj popisující stav systému byla zvolena délka fronty $q_j(t)$, což je počet aut v jízdním pruhu jedoucích 
+méně než 3,6 km/h. Pro danou frontu v čase $t+1$ platí zřejmě vztah
+\begin{equation}\label{eq:my_trans_01}
+ q_j(t+1) = q_j(t) + T ( i_j(t) - o_j(t) )
+\end{equation}, kde hustota vstupu $i_j(t)$ je součtem výstupů sousedů pronásobený odbočovacími poměry,
+případně vstupu do systému $i_{j,0}(t)$, pokud se jedná o koncové rameno řízené oblasti, tedy
+\begin{equation}
+  i_j(t) = i_{j,0}(t) + \sum_{k \in I_j} \alpha_{k,j} o_k(t)
+\end{equation}.
+Křižovtkou z daného jízdního pruhu v průjezdné fázi projede $S$ vozidel za sekundu, kde 
+délka průjezdné fáze závisí na nastaveném poměru a délce cyklu. Před přechodem do nové
+fáze signálího plánu je potřeba vklidit křižovatku, což vede ke ztrátovému času $L$, který
+se projeví vždy jednou za cyklus. Efektivní délka zelené je tedy
+\begin{equation}
+ g_j(t) = (C(t) - L) g_j^N
+\end{equation}
+a pro hustotu výstupu platí
+\begin{equation}
+ o_j(t) = \frac{S_j g_j(t)}{C(t)} = S_j g_j^N \left( 1 - LC(t)^{-1} \right)
+\end{equation}. Rovnice \ref{eq:my_trans_01} tedy přechází do tvaru
+\begin{equation}\label{eq:my_trans_02}
+ q_j(t+1) = q_j(t) + T \left( i_{j,0}(t) + \sum_{k \in I_j} \alpha_{k,j} S_k g_k^N \left( 1 - LC(t)^{-1} \right)  - S_j g_j^N \left( 1 - LC(t)^{-1} \right) \right)
+\end{equation}.
+Pokud budeme podobně jako v \cite{6_tuc_lq} předpokládat existenci nominální délky cyklu $C^N$, při níž se
+nemění délka fronty, platíc(
+\begin{equation}\label{eq:my_trans_nom}
+ 0 = T \left( i_{j,0}(t) + \sum_{k \in I_j} \alpha_{k,j} S_k g_k^N \left( 1 - LC^{N -1} \right)  - S_j g_j^N \left( 1 - LC^{N -1} \right) \right)
+\end{equation}. Odečtením rovnice \ref{eq:my_trans_nom} od \ref{eq:my_trans_02} dostaneme
+\begin{equation}\label{eq:my_trans_03}
+ q_j(t+1) = q_j(t) + T \left( - \sum_{k \in I_j} \alpha_{k,j} S_k g_k^N  + S_j g_j^N  \right) L \Delta C^{-1}(t)
+\end{equation}, kde $ \Delta C^{-1}(t) = C(t)^{-1} - C^{N -1}$. Pro ramena $j \in J_A$ náležící agentovi $A$ se
+tedy rovnice pro fronty dají zapsat maticově ve tvaru
+\begin{equation}\label{eq:my_trans_mat}
+ \vec{q}(t+1) = A \vec{q}(t) + B \Delta C^{-1}(t) 
+\end{equation}
+
+Kostantni saturovany tok neni optimalni, pouzije aprox podle Pecherkove (viz bak.), 
+prujezd odpovida bud sat. toku, pokud neodjede cela fronta, nebo je primo umerny
+fronte (+ prijezdum). prolozi se funkci a aprox se primkou podle hodnoty fronty v case t.
+Napocte se rizen pro horizont a podle vyvoje fronty se prepocte misto pro prolozeni pri
+
+
+\subsubsection{Model toku}
+V článku \cite{6_tuc_lq} se úbytek vozidel modeluje podle rovnice \ref{eq:tuc_u}, kde je uvažován
+tok vozidel křižovatkou za jednotku času jako konstanta $S$, což je saturovaný tok. Tento vztah
+platí pouze když je příslušný pruh naplněn vozidly do té míry, že křižovatkou projede maximální
+možný počet vozidel. To však neplatí, pokud není pruh dostatečně vytížen, například pokud se zmenší
+délka fronty v nějaký časový okamžik na nulu. Pokud je vytížení menší je tok lineárně závislý na součtu
+fronty $q(t)/T$ a počtu vstupujících vozidel $i(t)$. Pro teoretickou hodnotu toku $S$ tedy dostáváme vztah
+\begin{equation}\label{eq:teor_tok}
+ S_{teor}(q(t) + i(t)) = \left\{
+			\begin{array}{lr}
+			  \frac{q(t)}{T} + i(t) & \frac{q(t)}{T} + i(t) <= S_{max} \\
+			  S_{max} &  \frac{q(t)}{T} + i(t) > S_{max}
+                        \end{array}
+		  \right.
+\end{equation}
+. tento vztah vyjadřuje to, že pokud je fronta plus přírůstrek vozidel ve vzorkovací periodě
+$(q(t), i(t)T)$ menší než maximální počet vozidel, který je křižovatka za periodu $T$ schopna
+propustit $(T S_{max})$, projedou všechna vozidla. Abychom se vyhnuli podmínce podle $S_{max}$,
+aproximuje se tento vztah funkcí
+\begin{equation}\label{eq:exp_tok}
+ S_{exp}(q(t), i(t)) = S_{max} \left(1 - e^{- \frac{1}{S_{max}} \left( \frac{q(t)}{T} + i(t) \right) } \right)
+\end{equation}
+, která splňuje podmínku 
+\begin{equation} 
+\frac{ dS_{exp} }{d(q/T+i)}(0,0) = 1  
+\end{equation}
+, tedy při malé frontě a hustotě provozu
+je přírůstek toku roven $q/T+i$, a podmínku 
+\begin{equation}
+\lim_{q/T+i\to\infty} S_{exp} = S_{max}  
+\end{equation}
+, tedy při velké frontě a hustotě provozu
+se tok blíží konstantě $S_{max}$. Pro malý časový interval můžeme tuto funkci dále zjednodušit na lineární vztah
+\begin{equation}\label{eq:lin_tok}
+ S(q(t)) = \sigma(q(t)/T + i_0)
+\end{equation}
+, kde je $i_0 = i(0)$ a
+\begin{equation}
+ \sigma = \frac{ dS_{exp} }{d(q/T+i)}(q(0),i(0))
+\end{equation}
+\\
+vlozit graf s ruznymi S
+\\
+
+\subsubsection{Přechodové vztahy s proměnným tokem}
+Pro vyjádření přechodových vzthů použijeme lineární odel toku a rovnice \ref{eq:my_trans_02}
+přejde na tvar
+\begin{equation}
+ q_j(t+1) = q_j(t) + T \left( i_{j,0}(t) + \sum_{k \in I_j} \alpha_{k,j} S_k(q_k(t)) g_k^N \left( 1 - LC(t)^{-1} \right)  - S_j(q_j(t)) g_j^N \left( 1 - LC(t)^{-1} \right) \right)
+\end{equation}
+, a po dosazení \ref{eq:lin_tok} dostaneme
+\begin{equation}
+ q_j(t+1) = q_j(t) + T \left( \begin{array}{c}
+				i_{j,0}(t) + \\
+				+ \sum_{k \in I_j} \alpha_{k,j} \delta_k(q_k(t) T^{-1} + i_{0,k}) g_k^N \left( 1 - LC(t)^{-1} \right) - \\
+				- \delta_j(q_j(t) T^{-1} + i_{0,j}) g_j^N \left( 1 - LC(t)^{-1} \right)
+                              \end{array}
+  \right)
+\end{equation}
+
+\begin{equation}\label{eq:my_trans_mod_tok_03}
+ q_j(t+1) = q_j(t) + T \left( \begin{array}{c}
+				i_{j,0}(t) + \\
+				+ \sum_{k \in I_j} \alpha_{k,j} \delta_k g_k^N T^{-1} q_k(t)  - \delta_j g_j^N T^{-1} q_j(t) + \\
+				+ \sum_{k \in I_j} \alpha_{k,j} \delta_k i_{0,k} g_k^N - \delta_j i_{0,j} g_j^N - \\
+				- \sum_{k \in I_j} \alpha_{k,j} \delta_k g_k^N L T^{-1} q_k(t) C(t)^{-1} + \delta_j  g_j^N L T^{-1} q_j(t) C(t)^{-1} - \\				
+				- \sum_{k \in I_j} \alpha_{k,j} \delta_k i_{0,k} g_k^N L C(t)^{-1} + \delta_j i_{0,j} g_j^N L C(t)^{-1} 				
+                              \end{array}
+  \right)
+\end{equation}
+
+. Pokud budeme podobně jako v rovnici \ref{eq:my_trans_nom} uvažovat nominální $C^N$, pro které se $q(t+1)$ rovná $q(t)$,
+dostaneme dosazením $\Delta C^{-1}(t) = C(t)^{-1} - C^{N -1} $ do \ref{eq:my_trans_mod_tok_03} rovnici
+
+\begin{equation}\label{eq:my_trans_mod_tok_04}
+\begin{array}{ccc}
+ q_j(t+1) &= q_j(t) +& L \left( \delta_j  g_j^N q_j(t)   - \sum_{k \in I_j} \alpha_{k,j} \delta_k g_k^N q_k(t) \right) C(t)^{-1} +\\
+  & & + L T \left( \delta_j i_{0,j} g_j^N - \sum_{k \in I_j} \alpha_{k,j} \delta_k i_{0,k} g_k^N  \right) C(t)^{-1} 
+\end{array} 
+\end{equation}
+
+
+
+
+\subsection{Minimalizační kritérium}
+Podobně jako v předchozí kapitole, minimalizovat kvaratické kritérium $J$.
+Minimalizaci budeme provádět v proměnných $\Delta C(t)$ pro časový horizont $h$,
+tedy pro vektory $\Delta C(t_0), \Delta C(t_0 + 1), ..., \Delta C(t_0 + h)$. Pro zpřehlednění
+zápisu položíme bez újmy na obecnosti $t_0 = 0$.
+Kvadratické kritérium
+ve tvaru
+\begin{equation}\label{eq:J}
+ J = \sum_{t=0}^h q(t)^T Q q(t) + \Delta C(t)^T R \Delta C(t)
+\end{equation}, 
+kde $Q$ a $R$ jsou diagonální pozitivně definitní matice vah,
+rozepíšeme pomocí vztahu
+\begin{equation}
+ q(t+1) = Aq(t) + Bq(t)
+\end{equation} a budeme minimalizovat pro jednotlivá $t$ podle  $\Delta C(t)$.
+$\Delta C(h)$ se v kritériu vyskytuje pouze jako člen
+\begin{equation}
+\Delta C(h)^T R \Delta C(h)
+\end{equation}
+a tedy musí být $\Delta C(h) 0$. $\Delta C(h - 1)$ se vyskytuje ve tvaru
+\begin{equation}
+  \Delta C(h - 1)^T R \Delta C(h - 1) + (q(h - 1)^T A^T + \Delta C(h - 1)^T B^T ) Q ( A q(h - 1) + B \Delta C(h - 1))
+\end{equation}
+, což lze pomocí složených vektorů a matic přepsat do tvaru
+\begin{equation} \label{eq:J_sloz}
+ (\Delta C(h-1)^T, q(h - 1)^T ) 
+  \left( \begin{array}{cc}
+          B^T \sqrt{Q} & \sqrt{R} \\
+	  A^T \sqrt{Q} & 0
+	  \end{array}
+  \right)  
+  \left( \begin{array}{cc}
+           \sqrt{Q} B & \sqrt{Q} A \\
+	  \sqrt{R} & 0
+	  \end{array}
+  \right)
+  \left( \begin{array}{c}
+	    \Delta C(h-1) \\
+	    q(h - 1)
+	  \end{array}
+  \right)
+\end{equation}, kde $\sqrt{Q}$ je matice, pro níž platí $\sqrt{Q} \sqrt{Q} = Q$.
+Složenou matici
+\begin{equation}
+ 
+  \left( \begin{array}{cc}
+          B^T \sqrt{Q} & \sqrt{R} \\
+	  A^T \sqrt{Q} & 0
+	  \end{array}
+  \right)  
+  \left( \begin{array}{cc}
+           \sqrt{Q} B & \sqrt{Q} A \\
+	  \sqrt{R} & 0
+	  \end{array}
+  \right) = 
+  \left( \begin{array}{cc}
+          B^T Q B + R & B^T Q A \\
+	  A^T Q B & A^T Q A
+	  \end{array}
+  \right)
+\end{equation}
+můžeme pomocí Choleského dekompozici na součin dolní a horní trojúhelníkové matice.
+Rovnice 
+
+
+
+
+
+
+
+
+\section{Simulace}
+
+\subsection{Simulátor AIMSUN}
+
+\subsection{Oblast simulace}
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/01_Intro/Intro.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/01_Intro/Intro.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/01_Intro/Intro.tex (revision 1419)
@@ -0,0 +1,18 @@
+\chapter{Úvod}
+
+Multiagentní systémy jsou dnes rychle se rozvijející formou decentralizované
+umělé inteligence a s úspěchem se aplikují na celou řadu problémů, kde 
+není možné použít centrální řízení a je zapotřebí komunikace, koordinace a spolupráce.\\
+
+V této práci si nejdříve definujeme základní pojmy, a poté se hlouběji
+podíváme na problém interakce agentů. Popíšeme zde různé způsoby
+výběru vhodných strategií za pomoci komunikace, teorie her a
+modelování chování. Prozkoumáme některé způsoby učení agentů,
+které pomáhají zlepšovat jejich reakce na neustále se měníci prostředí
+a na chování ostatních.\\
+
+V další části prozkoumáme nasazení těchto metod k řízení dopravy a
+zhodnotíme úspěch těchto aplikací.
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/01_Intro/Intro.tex.backup
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/01_Intro/Intro.tex.backup (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/01_Intro/Intro.tex.backup (revision 1419)
@@ -0,0 +1,15 @@
+\chapter{Úvod}
+
+Multiagentní systémy jsou dnes rychle se rozvijející formou decentralizované
+umělé inteligence a s úspěchem se aplikují na celou řadu problémů, kde 
+není možné použít centrální řízení a je zapotřebí komunikace, koordinace a spolupráce.\\
+
+V této práci si nejdříve definujeme základní pojmy, a poté se hlouběji
+podíváme na problém interakce agentů. Popíšeme zde různé způsoby
+výběru vhodných strategií za pomoci komunikace, teorie her a
+modelování chování. Prozkoumáme některé způsoby učení agentů,
+které pomáhají zlepšovat jejich reakce na neustále se měníci prostředí
+a na chování ostatních.
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/03_RMM/RMM.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/03_RMM/RMM.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/03_RMM/RMM.tex (revision 1419)
@@ -0,0 +1,119 @@
+\section{RMM - Rekurzivní modelové metody} 
+
+
+Rekurzivní modelová metoda, která byla použita
+v článku \cite{4_rmm_formalization} k modelování chování
+agentů ovládajících ostatní dopravní uzly, slouží k odhadu chování ostatních a gentů.
+Akce každého agenta z pravidlo ovlivňuje do určité míry celý systém, tudíž
+výběr strategie každého agenta závisí na předpokládaném chování ostatních
+agentů. Tato metoda minimalizuje nutnost komunikace a vyjednávání o provedení jisté akce tím,
+že každý agent je schopen modelovat rozhodnutí ostatních a podle známých parametrů
+prostředí s určitou pravděpodobností stanovit jejich volbu.
+
+
+
+\subsection{Formální definice}
+
+Základním stavebním kamenem RMM je matice zisků agenta, Definovaná v souladu s teorií her v \cite{4_rmm_formalization}
+
+\begin{definition}[Matice zisků]\label{de:payoff_matrix}
+  Matice zisků $P_{R_i}$ agenta $R_i$ je definována trojicí
+  $$(R, A, U)$$
+  kde $R$ je množina všech agentů v systému, 
+  $A$ je množina množin $A_j = \{a_1^j, a_2^j, ...\}$ alternativních akcí agenta $R_j$. 
+  $A_j$ budeme nazývat rozhodovací prostor agenta $R_j$.
+  U je funkce 
+  $$U : A_1 \times A_2 \times ... \times A_n \rightarrow \mathbb{R}$$
+  přiřazující hodnoty zisku všem kombinacím akcí všech agentů.
+\end{definition}
+Každý agent provádí danou akci z nějakého důvodu. Zisky agenta $R_i$ jsou spojeny s
+provedením jeho určité akce $a_m^i \in A_i$ za předpokladu, že ostatní agenti $R_j, j \in \{1 .. n \} / \{i\} $
+provedou akci $a_k^j \in A_j$. Matice je tedy $n$-dimenzionální, kde $n$ je počet agentů v systému, a sestává
+se z prvků $u^{R_i}_{a_k^1 ... a_l^i ... a_m^n}$, reprezentující zisky v dané situaci.
+\\
+K určení pravděpodobnosti provedení strategií ostatních agentů se definuje rekursivní modelová struktura. \cite{4_rmm_formalization}
+
+\begin{definition}[Rekursivní modelová struktura]\label{de:rms}
+ Rekursivní modelová struktura $RMS_{R_i}$ agenta $R_i$ je definována jako dvojice
+  $$ (P_{R_i}, RM_{R_i}) $$,
+ kde $P_{R_i}$ je matice zisků definovaná v \ref{de:payoff_matrix} a $RM_{R_i}$
+ je rekurzivní model \ref{de:rm}, který je použit k modelování rozhodování ostatních agentů. 
+\end{definition}
+
+Rekursivní model je definován v \cite{4_rmm_formalization} takto:
+
+\begin{definition}[Rekursivní model]\label{de:rm}
+  Rekursivní model $MR_{R_i}$ agenta $R_i$ je definován jako $m$-tice dvojic \footnotemark
+  $$ MR_{R_i} = ( (p^{R_i}_1, M^{(R_i, 1)}_{\{-R_i\}}), ... ,(p^{R_i}_m, M^{(R_i, m)}_{\{-R_i\}}) )  $$ 
+  kde
+  $$ M^{(R_i, k )}_{\{-R_i\}} = ( M^{(R_i, k )}_{R_1}, ... , M^{(R_i, k )}_{R_{i-1}}, M^{(R_i, k )}_{R_{i+1}}, ... ,M^{(R_i, k )}_{R_n} )$$
+  představuje jednu z $m$ $(n-1)$-tic rozhodovacích modelů ostatních agentů a $p_i^k$ jeho subjektivní předpokládanou pravděpodobnost.  
+\end{definition}
+\footnotetext{$\{-R_i\}$ je zkrácený zápis množiny ostatních agentů $ \{R_1, ..., R_n\} / \{R_i\} $}
+
+$M^{(R_i, k )}_{R_j}$ je tedy jeden z možných modelů agenta $R_j$, který předpokládá agent $R_i$
+s pravděpodobností $p^{R_i}_k$. Platí samozřejmě podmínka $\sum_{k=1}^m p^{R_i}_k = 1$.
+\\
+Model $M^{(R_i, k )}_{R_j}$ se dá podle \cite{4_rmm_formalization} rozdělit do tří forem:
+
+\begin{itemize}
+ \item $IM^{(R_i, k )}_{R_j}$ - Recionální model
+ \item $NM^{(R_i, k )}_{R_j}$ - Neinformovaný model
+ \item $SM^{(R_i, k )}_{R_j}$ - Neracionální model
+\end{itemize}
+
+Recionální model odpovídá tomu, že agent $R_i$ předpokládá o agentovi $R_j$, že se chová racionálně.
+V \cite{4_rmm_formalization} je definován jako
+
+$$IM^{(R_i, k )}_{R_j} = RMS_{R_j}^{(R_i, k)}$$,
+
+s parametry $p^{(R_i, k)}_{a^j_l}$ a $P_{R_j}^{(R_i, k)} $.
+$P_{R_j}^{(R_i, k)} $ je matice zisků, kterou podle agenta $R_i$ v modelu $k$ agent $R_j$ použije.
+což je Rekurzivní modelové struktura s $k$-tými daty, o kterých agent $R_i$ předpokládá,
+že je agent $R_j$ použije k rozhodování.\\
+
+Neinformovaný model vychází z toho, že agent $R_i$ nemá o agentovi $R_j$ žádné informace, tudíž přiřadí každé
+akci $a^{R_j}_l$ pravděpodobnost $p^{(R_i, k)}_{a^j_l} = \frac{1}{|A_j|}$, kde $|A_j|$ je počet možných akcí agenta $R_j$, 
+což odpovídá rovnoměrnému rozdělení.
+$p^{(R_i, k)}_{a^j_l}$ značí pravďěpodobnost, že podle agenta $R_i$ nastane v $k$-tém modelu agenta $R_j$ akce $a^j_l$.\\
+
+Neracionální model odpovídá tomu, že se agent $A_j$ chová iracionálně. Chování se v tompto případě modeluje 
+podle situace pokaždé jinak.\\
+
+Systém se tedy rekurzivně rozvijí, dokud jsou dostupné informace. Pokud nejsou, rekurze skončí neinformovaným modelem
+s rovnoměrným rozdělením pravděpodobnosti všech akcí. Rekurze také může skončit iracionálním modelem, což ovšem není 
+v našem případě příliš časté.
+
+\subsection{Rozhodovací algoritmus}
+
+Po zkonstruování rekurzivní modelové struktury se prochází tento systém od konce rekurze, kde jsou pravděpodobnosti
+známi, z důvodu ukončení rekurzivního rozvijení neinformovaným modelem. K výběru nejpravděpodobnější situace se používá
+tzv. užitečnosti. \cite{4_rmm_formalization}
+
+\begin{definition}[Užitečnost]\label{de:utility}
+  Užitečnost akce $a^i_m$ podle agenta $R_i$ je definována jako
+  $$ 
+  u^{R_i}_{a^i_m}  = 
+  \sum_{a^1_q \in A_1} ...
+  \sum_{a^{i-1}_v \in A_{i-1}}
+  \sum_{a^{i+1}_w \in A_{i+1}} ...
+  \sum_{a^n_x \in A_n} 
+  ( p^{R_i}_{a^1_q} ... p^{R_i}_{a^{i-1}_v} p^{R_i}_{a^{i-1}_w} ...  p^{R_i}_{a^n_x}  u^{R_i}_{ a^1_q ... a^i_m ... a^n_x } )
+  $$,
+  kde 
+  $$ u^{R_i}_{ a^1_q ... a^n_x } $$ 
+  je prvek matice zisků $P_{R_i}$ a pravděpodobnost $ p^{R_i}_{a_o^j} $ je definována jako
+  $$ p^{R_i}_{a_k^j} = \sum_{o} p^{R_i}_o p^{(R_i, o)}_{a_k^j} $$. 
+  
+  
+\end{definition}
+
+kde $p^{R_i}_o$ je pravděpodobnost modelu z definice \ref{de:rm} a 
+$p^{(R_i, o)}_{a_k^j} $ značí pravďěpodobnost, že podle agenta $R_i$ 
+nastane v $o$-tém modelu agenta $R_j$ akce $a^j_k$. V případě, že je algoritmus v bodě racionálního modelu,
+určí se tato hodnota rekurzivně, pokud je model neinformovaný, je rovna $\frac{1}{|A_j|}$.
+$ p^{R_i}_{a_k^j}$ je tedy součet pravděpodobností dané akce v modelu vyvážený pravděpodobností modelu
+a $ u^{R_i}_{a^i_m} $ se definuje jako součet všech prvků matice zisků, kromě těch, které zahrnují jiné akce agenta 
+$R_i$, než je $a_k^j$, vyvažený touto pravděpodobností.
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.tex.backup
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.tex.backup (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.tex.backup (revision 1419)
@@ -0,0 +1,134 @@
+\section{LQ řízení}
+
+LQ je zkratka slovního spojení linaer-quadratic, tedy lineárně kvadratický. 
+Jedná se obecně o metodu, kdy je systém v diskrétním časovém kroku $t$ 
+popsán vektorem proměnných $x(t) = ( x_1(t), ..., x_n(t) )$
+a my můžeme nastavovat vektor parametrů $y(t) = ( y_1(t), ..., y_n(t) )$.
+Metoda je popsána a použita v článku \cite{6_tuc_lq} pro nastavování časů zelených na křižovatce.
+Princip přechodu z času $t$ do $t+1$ je popsán lineárním vztahem
+\begin{equation}
+  x(t+1) = A x(t) + B y(t)
+\end{equation}
+.
+kde matice $A$ a $B$ jsou matice stavů a vstupů vyjadřující odezvu systému vzhledem 
+k $x(t)$ a $y(t)$. Účelem LQ řízení je najít optimální hodnoty $y(t)$ v závislosti
+na $x(t)$ dané zpětnovazebnou maticí $L$ vztahem 
+\begin{equation}\label{eq_lq_feedback}
+y(t) = -L x(t)
+\end{equation}
+. Optimalita je definována pomocí
+kvadratického kritéria 
+\begin{equation}\label{eq_quadratic_criterion}
+J = \sum_{t=1}^{\infty} x(t)^t Q x(t) + y(t)^t R y(t) 
+\end{equation}
+
+
+, kde $Q$ a $R$ jsou diagonální pozitivně semidefinitní matice vah určující významnost jednotlivých členů kritéria.
+Zpětnovazebná matice $L$ se podle \cite{6_tuc_lq} dostane minimalizací kritéria $J$ pomocí řešení
+Riccatiho rovnice pro diskrétní časový krok
+\begin{equation}\label{eq_riccati}
+L = 
+\end{equation}
+
+\begin{equation}\label{eq_riccati_2}
+P = Q + A^T ( P - P B ( R + B^T P B ) B^T P ) A
+\end{equation}
+, popsané například v \cite{7_lq_methods}.
+
+
+\subsection{Použití LQ řízení ve strategii TUC}
+LQ řízení bylo použito v \cite{6_tuc_lq} k nalezení optimální délky zelených v systému 
+13-ti signálních skupin. Proměnné $x_i(t)$ zde představují obsazenost ramene $i$ 
+spojující křižovatky $M$ a $N$. Účelem strategie je nalezení optimální délky zelených
+$g$, $g_{N,i}$ značí délku zelené na signální skupiny křižovatky $N$ zprůjezdňující
+směr do ramene $i$. Předpokládaný vztah pro přechod systému z času $t$ do času $t+1$ je
+\begin{equation}\label{eq_tuc_1}
+ x_i(t+1) = x_i(t) + T [ q_i(t) + s_i(t) + d_i(t) + u_i(t) ]
+\end{equation}, kde proměnné značí:
+
+\begin{itemize}
+ \item $T$ - časový krok
+ \item $q_i(t)$ - přírůstek vozidel z křižovatek
+ \item $u_i(t)$ - úbytek vozidel do křižovatek
+ \item $s_i(t)$ - přírůstek vozidel z okolí sítě
+ \item $d_i(t)$ - úbytek vozidel mimo síť
+\end{itemize}
+
+Přírůstek vozidel z křižovatek je dán vztahem
+\begin{equation}
+ q_i(t) = \sum_{k\in I_m} t_{k,i} u_k(t)
+\end{equation}
+, je to tedy součet úbytků vozidel z ramen ústících do křižovatky $N$ vynásobených
+koeficinety $t_{k,i}$, což jsou odbočovací poměry z ramene $k$ do ramene $i$.
+V podovném tvaru se předpokládá $s_i(t)$
+\begin{equation}
+s_i(t) = t_{i,0} q_i(t)
+\end{equation}
+, kde $t_{i,0}$ je odbočovací koeficient ramene $i$ mimo sledovanou síť.
+Při délce cyklu $C$, saturovaném toku $S_i$ a délce zelených $g_{N,i}(t)$ remene $i$ platí
+\begin{equation}
+ u_i(t) = \frac{S_i \sum g_{N,i}(t)}{C}
+\end{equation}.
+Rovnice \ref{eq_tuc_1} tedy přechází do tvaru
+\begin{equation}\label{eq_tuc_2}
+ x_i(t+1) = x_i(t) + T \left[ 
+    (1-t_{i,0}) \sum_{k\in I_m} t_{k,i} \frac{S_k \sum g_{M,k}(t)}{C} 
+    - \frac{S_i \sum g_{N,i}(t)}{C}
+    + d_i(t) \right]
+\end{equation}. Uvažujeme-li nominální hodnoty $d^n$ a $g^n$ vedoucí
+vždy na stav $x^n$, platí podle rovnice \ref{eq_tuc_2} 
+\begin{equation}\label{eq_tuc_nom}
+ 0 = T \left[ 
+    (1-t_{i,0}) \sum_{k\in I_m} t_{k,i} \frac{S_k \sum g_{M,k}^n}{C} 
+    - \frac{S_i \sum g_{N,i}^n}{C}
+    + d_i^n \right]
+\end{equation}. Označíme-li 
+\begin{equation}\label{eq_delta_g}
+ \Delta g(t) = g(t) - g^n
+\end{equation}, můžeme psát rovnici \ref{eq_tuc_2} jako
+\begin{equation}\label{eq_tuc_3}
+ x_i(t+1) = x_i(t) + T \left[ 
+    (1-t_{i,0}) \sum_{k\in I_m} t_{k,i} \frac{S_k \sum \Delta g_{M,k}(t)}{C} 
+    - \frac{S_i \sum \Delta g_{N,i}(t)}{C}
+     \right]
+\end{equation}, což dovoluje tuto rovnici zapsat pomocí matic v požadovaném tvaru
+\begin{equation}\label{eq_tuc_4}
+ x(t+1) = A x(t) + B \Delta g(t)
+\end{equation}, kde $A$ je jednotková matice. 
+
+\subsubsection{Kvadratické kritérium}
+Účelem lagoritmu je minimalizovat obsazenost ramen, tedy vektor $x(t)$
+a penalizovat změnu délky trvání zelené oproti nominálním hodnotám.
+Kvadratické kritérium optimálního řízení \ref{eq_quadratic_criterion} jetedy v \cite{6_tuc_lq}
+definováno vztahem
+\begin{equation}\label{eq_tuc_crit}
+ J = \sum_{t=0}^{\infty} x^T Q x + \Delta g^T R \Delta g
+\end{equation}. Diagonální matice $Q$ je zde zodpovědná za vyvažování
+počtu vozidel jednotlivých úseků. V \cite{6_tuc_lq} je každý diagonální
+prvek $Q_{i,i}$ matice $Q$ položen převrácené hodnotě maximálního
+povoleného počtu vozidel daného úseku $i$. $R = rI$ penalizuje změnu
+časů zelených. Parametr $r$ ovlivňuje míru reakce systému a ja volen metodu pokus-oprava.
+Minimalizací tohoto kritéria pomcí \ref{eq_riccati} získáme zpětnovazebnou matici $L$,
+která určuje $g(t)$. Z rovnic \ref{eq_lq_feedback} a \ref{eq_delta_g} dostaneme výsledný vztah
+\begin{equation}\label{eq_tuc_feedback}
+ g(t) = g^n - L x(t)
+\end{equation}. Toto řešení předpokládá, že známe hodnotu $g^n$, při které systém
+zůstává ve stavu $x^n$. Tak tomu ale většinou není. Při absenci znalosti $g^n$
+podle \cite{6_tuc_lq} odečteme $g(t) - g(t-1)$ a rovnice \ref{eq_tuc_feedback} nabývá tvaru
+\begin{equation}\label{eq_tuc_feedback_2}
+ g(t) = g(t-1) - L( x(t) - x(t-1) )
+\end{equation}.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.aux
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.aux (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.aux (revision 1419)
@@ -0,0 +1,212 @@
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+\newlabel{eq_tuc_1}{{3.6}{18}{Použití LQ řízení ve strategii TUC\relax }{equation.3.8.6}{}}
+\citation{6_tuc_lq}
+\newlabel{eq:tuc_u}{{3.9}{19}{Použití LQ řízení ve strategii TUC\relax }{equation.3.8.9}{}}
+\newlabel{eq_tuc_2}{{3.10}{19}{Použití LQ řízení ve strategii TUC\relax }{equation.3.8.10}{}}
+\newlabel{eq_tuc_nom}{{3.11}{19}{Použití LQ řízení ve strategii TUC\relax }{equation.3.8.11}{}}
+\newlabel{eq_delta_g}{{3.12}{19}{Použití LQ řízení ve strategii TUC\relax }{equation.3.8.12}{}}
+\newlabel{eq_tuc_3}{{3.13}{19}{Použití LQ řízení ve strategii TUC\relax }{equation.3.8.13}{}}
+\newlabel{eq_tuc_4}{{3.14}{19}{Použití LQ řízení ve strategii TUC\relax }{equation.3.8.14}{}}
+\citation{6_tuc_lq}
+\citation{6_tuc_lq}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.8.1.1}Kvadratick\IeC {\'e} krit\IeC {\'e}rium}{20}{subsubsection.3.8.1.1}}
+\newlabel{eq_tuc_crit}{{3.15}{20}{Kvadratické kritérium\relax }{equation.3.8.15}{}}
+\newlabel{eq_tuc_feedback}{{3.16}{20}{Kvadratické kritérium\relax }{equation.3.8.16}{}}
+\newlabel{eq_tuc_feedback_2}{{3.17}{20}{Kvadratické kritérium\relax }{equation.3.8.17}{}}
+\@writefile{toc}{\contentsline {chapter}{\numberline {4}Implementace}{21}{chapter.4}}
+\@writefile{lof}{\addvspace {10\p@ }}
+\@writefile{lot}{\addvspace {10\p@ }}
+\@writefile{toc}{\contentsline {section}{\numberline {4.1}Seznam prom\IeC {\v e}nn\IeC {\'y}ch}{21}{section.4.1}}
+\@writefile{toc}{\contentsline {section}{\numberline {4.2}Pou\IeC {\v z}it\IeC {\'a} metoda}{22}{section.4.2}}
+\citation{6_tuc_lq}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}P\IeC {\v r}echodov\IeC {\'e} vztahy}{23}{subsection.4.2.1}}
+\newlabel{eq:my_trans_01}{{4.1}{23}{Přechodové vztahy\relax }{equation.4.2.1}{}}
+\newlabel{eq:my_trans_02}{{4.5}{23}{Přechodové vztahy\relax }{equation.4.2.5}{}}
+\newlabel{eq:my_trans_nom}{{4.6}{23}{Přechodové vztahy\relax }{equation.4.2.6}{}}
+\newlabel{eq:my_trans_03}{{4.7}{23}{Přechodové vztahy\relax }{equation.4.2.7}{}}
+\newlabel{eq:my_trans_mat}{{4.8}{23}{Přechodové vztahy\relax }{equation.4.2.8}{}}
+\citation{6_tuc_lq}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.1.1}Model toku}{24}{subsubsection.4.2.1.1}}
+\newlabel{eq:teor_tok}{{4.9}{24}{Model toku\relax }{equation.4.2.9}{}}
+\newlabel{eq:exp_tok}{{4.10}{24}{Model toku\relax }{equation.4.2.10}{}}
+\newlabel{eq:lin_tok}{{4.13}{24}{Model toku\relax }{equation.4.2.13}{}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.1.2}P\IeC {\v r}echodov\IeC {\'e} vztahy s prom\IeC {\v e}nn\IeC {\'y}m tokem}{25}{subsubsection.4.2.1.2}}
+\newlabel{eq:my_trans_mod_tok_03}{{4.17}{25}{Přechodové vztahy s proměnným tokem\relax }{equation.4.2.17}{}}
+\newlabel{eq:my_trans_mod_tok_04}{{4.18}{25}{Přechodové vztahy s proměnným tokem\relax }{equation.4.2.18}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}Minimaliza\IeC {\v c}n\IeC {\'\i } krit\IeC {\'e}rium}{25}{subsection.4.2.2}}
+\newlabel{eq:J}{{4.19}{25}{Minimalizační kritérium\relax }{equation.4.2.19}{}}
+\newlabel{eq:prechod}{{4.20}{25}{Minimalizační kritérium\relax }{equation.4.2.20}{}}
+\newlabel{eq:J_sloz}{{4.23}{26}{Minimalizační kritérium\relax }{equation.4.2.23}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {4.3}Simulace}{27}{section.4.3}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.1}Simul\IeC {\'a}tor AIMSUN}{27}{subsection.4.3.1}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.2}Oblast simulace}{27}{subsection.4.3.2}}
+\bibstyle{czechiso}
+\bibdata{Bibl/bibl}
+\@writefile{toc}{\contentsline {chapter}{\numberline {5}V\IeC {\'y}sledky}{28}{chapter.5}}
+\@writefile{lof}{\addvspace {10\p@ }}
+\@writefile{lot}{\addvspace {10\p@ }}
+\bibcite{7_lq_methods}{1}
+\bibcite{dynamic_programming}{2}
+\bibcite{2_int_a_in_dec}{3}
+\bibcite{4_rmm_formalization}{4}
+\bibcite{5_bayes_learn}{5}
+\bibcite{1_rmm_bayes_learning}{6}
+\bibcite{17_fronta}{7}
+\bibcite{learning_to_predict}{8}
+\bibcite{tlc_using_sarsa}{9}
+\bibcite{6_tuc_lq}{10}
+\bibcite{leraning_from_delayed_rewards}{11}
+\bibcite{q_learning}{12}
+\bibcite{3_i_traff_light_c}{13}
+\bibcite{wooldridge}{14}
+\citation{*}
+\@writefile{toc}{\contentsline {chapter}{Literatura}{30}{chapter*.7}}
+\HyPL@Entry{39<</S/R>>}
+\@writefile{toc}{\contentsline {chapter}{\numberline {A}P\IeC {\v r}\IeC {\'\i }loha 1}{I}{appendix.A}}
+\@writefile{lof}{\addvspace {10\p@ }}
+\@writefile{lot}{\addvspace {10\p@ }}
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.lot
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.lot (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.lot (revision 1419)
@@ -0,0 +1,7 @@
+\select@language {czech}
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\addvspace {10\p@ }
+\addvspace {10\p@ }
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.bbl
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.bbl (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.bbl (revision 1419)
@@ -0,0 +1,67 @@
+\begin{thebibliography}{10}
+\providecommand{\url}[1]{\texttt{#1}}
+\providecommand{\urlprefix}{URL }
+\expandafter\ifx\csname urlstyle\endcsname\relax
+  \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else
+  \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup
+  \urlstyle{rm}\Url}\fi
+\providecommand{\selectlanguage}[1]{\relax}
+\providecommand{\eprint}[2][]{\url{#2}}
+
+\bibitem{7_lq_methods}
+Anderson, M.~J., B.D.O.: Optimal Control - Linear Quadratic Methods.
+  \emph{Prentice Hall, Englewood Cliffs, NJ}, 1990.
+
+\bibitem{dynamic_programming}
+Bellman, R.: Dynamic programming. \emph{Princeton University Press}, 1957.
+
+\bibitem{2_int_a_in_dec}
+Ferreira, E.; Subrahmanian, E.; Manstetten, D.: Intelligent agents in
+  decentralized traffic control. \emph{Intelligent Transportation Systems},
+  2001.
+
+\bibitem{4_rmm_formalization}
+Gmytrasiewicz, P.~J.; Durfee, E.~H.: A rigorous, operational formalization of
+  recursive modeling. \emph{First International Conference on Multiagent
+  Systems}, 1995.
+
+\bibitem{5_bayes_learn}
+Nagy, I.; Nedoma, P.; Ettler, P.; aj.: O bayesovsk{\'e}m u\v{c}en{\'i}.
+  \emph{Automa}, 2002.
+
+\bibitem{1_rmm_bayes_learning}
+Ou, H.; Zhang, W.; Xu, X.: Urban traffic multi-agent system based on RMM and
+  Bayesian learning. \emph{American Control Conference}, 2002.
+
+\bibitem{17_fronta}
+P., P.; J., D.; Fl{\'i}dr: Modelling and Simultaneous Estimation of State and
+  Parameters of Traffic System. \emph{Robotics, Automation and Control}, 2008.
+
+\bibitem{learning_to_predict}
+Sutton, R.~S.: Learning to predict by the methods of temporal didffrences.
+  \emph{Machine Learning}, 1988.
+
+\bibitem{tlc_using_sarsa}
+Thorpe, T.: Vehicle traffic light controlusing sarsa. \emph{Master’s thesis,
+  Department of Computer Science, Colorado State University}, 1997.
+
+\bibitem{6_tuc_lq}
+Vaya~Dinopoulou, M.~P., Christina~Diakaki: Applications of the urban traffic
+  control strategy TUC. \emph{European Journal of Operational Research}, 2005.
+
+\bibitem{leraning_from_delayed_rewards}
+Watkins, C. J. C.~H.: Leraning from Delayed Rewards. \emph{PhD thesis, King's
+  College, Cambridge, England}, 1989.
+
+\bibitem{q_learning}
+Watkins, C. J. C.~H.; Dayan, P.: Q-leraning. \emph{Machine Learning}, 1992.
+
+\bibitem{3_i_traff_light_c}
+Wiering, M.; {Van Veenen}, J.; Vreeken, J.; aj.: Intelligent traffic light
+  control. \emph{European Research Consortium for Informatics and Mathematics},
+  2003.
+
+\bibitem{wooldridge}
+Wooldridge, M.: \emph{Multi Agent Systems}. MIT Press, Březen 2005.
+
+\end{thebibliography}
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.tex (revision 1419)
@@ -0,0 +1,157 @@
+%\documentclass [a4paper,12pt]{report}                              %print on one side
+\documentclass [a4paper,12pt,onewside,notitlepage,openright]{report} %print on both side
+\usepackage[bookmarks=false, colorlinks=false,unicode]{hyperref}
+% \usepackage[abbr,dcucite]{harvard}      %style ofliterature
+\usepackage{Styles/Skripta}
+\usepackage{Styles/Diplomka}
+\usepackage{Styles/Colors}
+\usepackage{listings}
+\usepackage[dvips]{graphics}
+\usepackage{multirow}
+\usepackage{dcolumn}
+
+%\usepackage{showframe}                  %show edges of pages
+
+%-----<<<<<<<<<<<< NAMES NAD PATHS >>>>>>>>>>>>-----
+\def \BookName {Výzkumný úkol}
+\def \Bookname {Teorie a aplikace multiagentního řízení dopravy}
+\def \BooknameEN {Theory of multiagent traffic control}
+\newcommand{\katedra}{Katedra matematiky}
+\newcommand{\obor}{Inženýrská informatika}
+\newcommand{\zamereni}{Tvorba softwaru}
+% \def \Authors {Autor\?: Jakub Novotný Vedoucí práce\?: Ing. Václav Šmídl, Ph.D.}
+\def \DatumDP {Praha, 2011}
+\def \autor {Jakub Novotný}
+%\def \vedouci {Ing. Václav Šmídl, Ph.D.}
+% \def \konzultant {Dr. Ing. Jan Přikryl, Ph.D.}
+\def \vedouci {Dr. Ing. Jan Přikryl, Ph.D.}
+\def \konzultant {Ing. Václav Šmídl, Ph.D.}
+
+\def \CVUT {České vysoké učení technické v Praze}
+
+\def \cestaFiles {00_Chapters/}
+\def \cesta01 {01_Intro/}
+\def \cestaAP {Appendix/}
+%-----<<< --------------------------------- >>>-----
+
+
+
+%-----<<<<<<<<<<<< DOCUMENT >>>>>>>>>>>>-----
+\begin{document}
+
+
+%-----<<< HEAD >>>-----
+\pagestyle{empty}                       %no pagination
+
+\BookHeadDP
+
+\cleardoublepage
+%-----<<< ---- >>>-----
+
+
+%-----<<< DECLARATION >>>-----
+\pagestyle{plain}                       %no pagination
+\pagenumbering{roman}                   %start roman pagination from 1
+\input{\cestaFiles Declar.tex}          %input file
+\newpage
+%-----<<< ----------- >>>-----
+
+
+%-----<<< ACKNOWLEDGEMENT >>>-----
+\input{\cestaFiles Acknow.tex}          %input file
+\cleardoublepage
+%-----<<< --------------- >>>-----
+
+
+%-----<<< ABSTRACT >>>-----
+\input{\cestaFiles Abstract.tex}        %input file
+\cleardoublepage
+%-----<<< -------- >>>-----
+
+
+%-----<<< ZADÁNÍ BAKALÁŘSKÉ PRÁCE >>>-----
+
+Zadání práce s podpisem děkana
+
+Vypracujte přehled literatury zabývající se použitím multi-agentních systémů v řízení dopravy. 
+Zvláštní pozornost věnujte řízení v městském provozu s množstvím křižovatek.
+Z použitých přístupů sestavte přehled používaných metod autonomního řízení a 
+komunikovaných informací mezi agenty.
+Z dostupných metod zvolte takovou, která je v vhodná pro použití v oblasti Zličína a 
+implementujte ji v prostředí řízení mikrosimulátoru AIMSUN.
+Výsledné řízení zvolenou metodou srovnejte se současným řídícím algoritmem navrženým dopravními experty.
+
+\cleardoublepage
+%-----<<< ---------------------- >>>-----
+
+
+%-----<<< TABLE OF CONTENTS >>>-----
+\setcounter{secnumdepth}{4}             %number of section to 4
+\setcounter{tocdepth}{4}                %number of section in table of contents greater then 3
+\tableofcontents
+\cleardoublepage
+%-----<<< ----------------- >>>-----
+
+
+%-----<<< TABLE OF FIGURES >>>-----
+\addcontentsline{toc}{chapter}{Seznam obrázků}
+\listoffigures
+\cleardoublepage
+%-----<<< ---------------- >>>-----
+
+
+%-----<<< TABLE OF TABLES >>>-----
+\addcontentsline{toc}{chapter}{Seznam tabulek}
+\listoftables
+\cleardoublepage
+%-----<<< --------------- >>>-----
+
+
+%-----<<< TABLE OF CONTENTS PAGINATION >>>-----
+\pagenumbering{arabic}                  %start arabic pagination from 1
+%-----<<< ---------------------------- >>>-----
+
+
+%-----<<< CHAPTERS >>>-----
+\hyphenation{Automatica}                %no divide words
+\pagestyle{headings}
+
+%input fieles
+\input{01_Intro/Intro.tex}              
+\input{02_Agents/Agents.tex}           
+\input{03_RMM/RMM.tex}
+\input{Reinforcement_learning.tex} 
+\input{04_Bayes/Bayes.tex}          
+%\input{05_I_a_in_dec_t_c/I_a_in_dec_t_c.tex}
+\input{06_Bayes_rmm_pouziti/Bayes_rmm_pouziti.tex}
+\input{Reinforcement_learning_pouziti/Reinforcement_learning_pouziti.tex}
+\input{LQ_rizeni.tex}
+\input{Implementation.tex}
+\input{Results.tex}
+
+
+%-----<<< -------- >>>-----
+
+
+%-----<<< REFERENCES >>>-----
+%\input{05_Refer/Refer.tex}
+% \bibliographystyle{Styles/Skripta}
+\bibliographystyle{czechiso}
+\bibliography{Bibl/bibl}\nocite{*}              %references from BIBTEX
+\addcontentsline{toc}{chapter}{Literatura}
+
+%-----<<< ---------- >>>-----
+
+%-----<<< APPENDIXS >>>-----
+\cleardoublepage
+% \def\appendixname{Příloha}
+\pagenumbering{Roman}                   %start arabic pagination from 1
+\begin{appendix}
+\input{\cestaAP/01.tex}   
+         %input file
+\end{appendix}
+%-----<<< --------- >>>-----
+
+\end{document}
+%-----<<<<<<<<< END OF DOCUMENT >>>>>>>>>-----
+ 
Index: /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning_pouziti/Reinforcement_learning_pouziti.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning_pouziti/Reinforcement_learning_pouziti.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning_pouziti/Reinforcement_learning_pouziti.tex (revision 1419)
@@ -0,0 +1,48 @@
+\section{Použití zpětnovazebného učení}
+
+\subsection{Zpětnovazebné učení na základě modelu}
+
+V \cite{3_i_traff_light_c} je popsána simulace používající
+zpětnovazebné učení na základě modelu popsané v \ref{sec:model_based_learning}.
+Na rozdíl od ezperimentu popsaného v předchozí kapitole zde autoři zvolili
+variantu, kde existují 2 druhy agentů: agent-vozidlo a agent-křižovatka. 
+Agent-vozidlo má v každý časový krok následující parametry definující jeho stav,
+které se ukládají v průběhu celé simulace:
+
+\begin{itemize}
+ \item $node$ - dopravní uzel, kde se právě nachází
+ \item $dir$ - směr vůči tomuto uzlu
+ \item $place$ - pozice ve frontě vozidel
+ \item $des$ - místo, kam chce v systému dojet
+\end{itemize}
+
+Algoritmus se snaží minimalizovat celkový čas od vyjetí až po dosažení cíle.
+Každý agent má ve vyjednávání právo hlasovat o nastavení dopravního uzlu,
+tedy jestli bude v průjezdném nebo uzavřeném stavu. Pro každý uzel $node$ a směr $dir$ je to
+tedy akce $g$ - na uzlu $node$, kde se vozidlo nachází ve směru $dir$, svítí červená - uzel je v tomto směru neprůjezdný, 
+a akce $g$ - uzel je v tomto směru průjezdný.
+Funkce definované v \ref{sec:dynamic_programming} se tedy zapisují ve tvarech
+$$ Q([node, dir, place, des], a) $$ $$ V([node, dir, place, des]) $$
+kde $a \in \{r,g\}$. Optimální akce se v \cite{3_i_traff_light_c} volí
+podle maxima sumy z 
+$$ Q([node, dir, place, des], r) - Q([node, dir, place, des], g) $$ 
+přes všechny vozidla ovlivněná frontou u daného uzlu. Komunikace je zde tedy omezena pouze na výměnu
+hodnot $Q$.\\
+
+Metode popsaná v článku \cite{3_i_traff_light_c} používá ohodnocovací funkci
+založenou na parametrech jednotlivých vozidel. Výhodou oproti pojetí, kdy agent
+představuje pouze signální skupinu, jsou například v tom, že není potřeba
+odhadovat délku fronty a úloha se celá zjednoduší. Například v publikaci
+\cite{tlc_using_sarsa} se musí používat k odhadu funkcí $V$ a $Q$ neuronová síť.
+Navíc tento systém umožňuje i výběr optimální cesty vozidla pro průjezd dopravní sítí.
+Nevýhodou tohoto pojetí je ovšem značná neuniverzálnost. Už pro počítačové testování
+tato metode znesnadnuje či úplně znemožňuje použít celou řadu dopravních simulátorů,
+které jsou pro simulaci po dlouhou dobu optimalizovány a 
+jejichž nasazení značně zjednodušuje práci a urychluje vývoj.
+Navíc pokud je použit řadič, který obstarává logiku přepínání průjezdnosti a 
+lze nastavovat pouze vnější parametry jako jsou délka cyklu a offset, je
+metoda, která potřebuje okamžitou změnu signalizace naprosto nevhodná,
+proto je toto řešení pro reálné nasazení v dnešní době nepoužitelné.
+
+
+ 
Index: /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning_pouziti/Reinforcement_learning_pouziti.tex.backup
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning_pouziti/Reinforcement_learning_pouziti.tex.backup (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Reinforcement_learning_pouziti/Reinforcement_learning_pouziti.tex.backup (revision 1419)
@@ -0,0 +1,41 @@
+\section{Použití zpětnovazebného učení}
+
+V \cite{3_i_traff_light_c} je popsána simulace používající
+zpětnovazebné učení na základě modelu popsané v \ref{sec:model_based_learning}.
+Na rozdíl od ezperimentu popsaného v předchozí kapitole zde autoři zvolili
+variantu, kde existují 2 druhy agentů: agent-vozidlo a agent-křižovatka. 
+Agent-vozidlo má v každý časový krok následující parametry definující jeho stav,
+které se ukládají v průběhu celé simulace:
+
+\begin{itemize}
+ \item $node$ - dopravní uzel, kde se právě nachází
+ \item $dir$ - směr vůči tomuto uzlu
+ \item $place$ - pozice ve frontě vozidel
+ \item $des$ - místo, kam chce v systému dojet
+\end{itemize}
+
+Algoritmus se snaží minimalizovat celkový čas od vyjetí až po dosažení cíle.
+Každý agent má ve vyjednávání právo hlasovat o nastavení dopravního uzlu,
+tedy jestli bude v průjezdném nebo uzavřeném stavu. Pro každý uzel $node$ a směr $dir$ je to
+tedy akce $g$ - na uzlu $node$, kde se vozidlo nachází ve směru $dir$, svítí červená - uzel je v tomto směru neprůjezdný, 
+a akce $g$ - uzel je v tomto směru průjezdný.
+Funkce definované v \ref{sec:dynamic_programming} se tedy zapisují ve tvarech
+$$ Q([node, dir, place, des], a) $$ $$ V([node, dir, place, des]) $$
+kde $a \in \{r,g\}$. Optimální akce se v \cite{3_i_traff_light_c} volí
+podle maxima sumy z 
+$$ Q([node, dir, place, des], r) - Q([node, dir, place, des], g) $$ 
+přes všechny vozidla ovlivněná frontou u daného uzlu. Komunikace je zde tedy omezena pouze na výměnu
+hodnot $Q$.\\
+
+Metode popsaná v článku \cite{3_i_traff_light_c} používá ohodnocovací funkci
+založenou na parametrech jednotlivých vozidel. Výhodou oproti pojetí, kdy agent
+představuje pouze signální skupinu, jsou například v tom, že není potřeba
+odhadovat délku fronty a úloha se celá zjednoduší. Například v publikaci
+\cite{tlc_using_sarsa} se musí používat k odhadu funkcí $V$ a $Q$ neuronová síť.
+Navíc tento systém umožňuje i výběr optimální cesty vozidla pro průjezd dopravní sítí.
+Nevýhodou tohoto pojetí je ovšem značná neuniverzálnost. Už pro počítačové testování
+tato metode znesnadnuje či úplně znemožňuje použít celou řadu dopravních simulátorů,
+které jsou pro simulaci po dlouhou dobu optimalizovány a 
+jejichž nasazení značně zjednodušuje práci a urychluje vývoj.
+ 
+ 
Index: /applications/doprava/texty/novotny_vyzk_LQ/vyzk.blg
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/vyzk.blg (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/vyzk.blg (revision 1419)
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Index: /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/Bayes_rmm_pouziti.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/Bayes_rmm_pouziti.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/Bayes_rmm_pouziti.tex (revision 1419)
@@ -0,0 +1,44 @@
+\def \cesta {./06_Bayes_rmm_pouziti}
+
+\section{Použití RMM a Bayesova učení v decentralizovaném řízení dopravy} 
+
+V následujícím textu se budeme zabývat konkrétním využitím
+rekursivních modelovacích metod v kombinaci s bayesovským učením
+v decentralizovaném řízení dopravy pomocí multiagentních systémů.
+Tento koncept byl testován a výsledky zveřejněny v článku \cite{1_rmm_bayes_learning}.\\
+
+Testy byly prováděny na modelu dvou křižovatek klasického typu, kde každý agent $R_1, R_2$
+ovládal jednu z nich. K modelování chování druhého agenta bylo použito třísyupňové RMM
+zakončené neinformovaným modelem. Obrázek \ref{fig:rmm_structure} z článku \cite{1_rmm_bayes_learning}
+znázorňuje RMM agenta $R_1$, kde se na každé úrovni agent rozhoduje mezi dvěma modely, informovaným a
+neinformovaným. Z počátku simulace jsou těmto modelům přiřazeny pravděpodobnosti po řadě 0,8 a 0,2.
+Tyto pravděpodobnosti jsou upravovány metodou bayesovskeho učení podle akcí provedených druhým agentem.
+Pro řešení tohoto modelu je použit algoritmus z \cite{4_rmm_formalization} popsaný v předchozí kapitole.\\
+
+Určujícím faktorem pro sestavení matice zisků je délka fronty čekajících aut. Tento údaj byl také
+použit jako klíčový pro srovnání s ostatními metodami při testování. Metoda byla testována
+za použití simulace psané v jazyce VC++ a porovnávána s dvěma dalšími, a to pevně dané sekvence
+stanovené dopravními experty a stochastická metoda "Hill-climbing process". Z tohoto srovnání
+vychází metoda  využívající RMM a bayesovského učenís podle výsledků prezentovaných v \cite{1_rmm_bayes_learning} nejlépe, 
+jak můžeme vidět na obrázku \ref{fig:rmm_results}.
+
+
+
+\begin{figure}[H]
+\begin{center}
+    \includegraphics[width=70mm]{\cesta/rmm_structure.eps}
+    \caption{Tříúrovňová rekurzivní modelová struktura agenta $R_1$}\label{fig:rmm_structure}
+\end{center}
+\end{figure}
+
+\newpage
+
+\begin{figure}[H]
+\begin{center}
+    \includegraphics[width=70mm]{\cesta/rmm_results.eps}
+    \caption{Výsledky měření. M1 - RMM, M2 - pevné cykly, M3 - "Hill-climbing" }\label{fig:rmm_results}
+\end{center}
+\end{figure}
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/rmm_structure.eps
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/rmm_structure.eps (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/rmm_structure.eps (revision 1419)
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Index: /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/Bayes_rmm_pouziti.tex.backup
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/Bayes_rmm_pouziti.tex.backup (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/06_Bayes_rmm_pouziti/Bayes_rmm_pouziti.tex.backup (revision 1419)
@@ -0,0 +1,40 @@
+\def \cesta {./05_Bayes_rmm_pouziti}
+
+\chapter{Použití RMM a Bayesova učení v decentralizovaném řízení dopravy} 
+
+V následující kapitole se budeme zabývat konkrétním využitím
+rekursivních modelovacích metod v kombinaci s bayesovským učením
+v decentralizovaném řízení dopravy pomocí multiagentních systémů.
+Tento koncept byl testován a výsledky zveřejněny v článku \cite{1_rmm_bayes_learning}.\\
+
+Testy byly prováděny na modelu dvou křižovatek klasického typu, kde každý agent $R_1, R_2$
+ovládal jednu z nich. K modelování chování druhého agenta bylo použito třísyupňové RMM
+zakončené neinformovaným modelem. Obrázek \ref{fig:rmm_structure} z článku \cite{1_rmm_bayes_learning}
+znázorňuje RMM agenta $R_1$, kde se na každé úrovni agent rozhoduje mezi dvěma modely, informovaným a
+neinformovaným. Z počátku simulace jsou těmto modelům přiřazeny pravděpodobnosti po řadě 0,8 a 0,2.
+Tyto pravděpodobnosti jsou upravovány metodou bayesovskeho učení podle akcí provedených druhým agentem.
+Pro řešení tohoto modelu je použit algoritmus z \cite{4_rmm_formalization} popsaný v předchozí kapitole.\\
+
+Určujícím faktorem pro sestavení matice zisků je délka fronty čekajících aut. Tento údaj byl také
+použit jako klíčový pro srovnání s ostatními metodami při testování. Metoda byla testována
+za použití simulace psané v jazyce VC++ a porovnávána s dvěma dalšími, a to pevně dané sekvence
+stanovené dopravními experty a stochastická metoda "Hill-climbing process". Z tohoto srovnání
+vychází tato metoda podle výsledků prezentovaných v \cite{1_rmm_bayes_learning} nejlépe, jak můžeme vidět v
+\cite{fig:rmm_results}.
+
+\begin{figure}[H]
+\begin{center}
+    \includegraphics[width=70mm]{\cesta/rmm_structure.eps}
+    \caption{Tříúrovňová rekurzivní modelová struktura agenta $R_1$}\label{fig:rmm_structure}
+\end{center}
+\end{figure}
+
+\begin{figure}[H]
+\begin{center}
+    \includegraphics[width=70mm]{\cesta/rmm_results.eps}
+    \caption{Výsledky měření. M1 - RMM, M2 - pevné cykly, M3 - "Hill-climbing" }\label{fig:rmm_results}
+\end{center}
+\end{figure}
+
+
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Acknow.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Acknow.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Acknow.tex (revision 1419)
@@ -0,0 +1,2 @@
+  Rád bych poděkoval vedoucímu práce Ing. Janu Přikrylovi, Ph.D. a odbornému konzultantovi Ing. Václavu Šmídlovi, Ph.D. za odborné vedení a úsilí
+vynaložené při tvorbě této práce.
Index: /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Abstract.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Abstract.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Abstract.tex (revision 1419)
@@ -0,0 +1,42 @@
+\newbox\odstavecbox
+\newlength\vyskaodstavce
+\newcommand\odstavec[2]{%
+    \setbox\odstavecbox=\hbox{%
+         \parbox[t]{#1}{#2\vrule width 0pt depth 4pt}}%
+    \global\vyskaodstavce=\dp\odstavecbox
+    \box\odstavecbox}
+\newcommand{\delka}{120mm} % šířka textů ve 2. sloupci tabulky
+\def \abstrCZ {
+V této práci je ...
+}
+
+\def \abstrEN {
+This work represents ...
+}
+
+\begin{tabular}{l l}
+  {Název práce:} & \\
+  \multicolumn{2}{l}{\bf \Bookname} \\[5mm]
+  {Autor:} & \autor \\[5mm] 
+  {Obor:} & \obor \\
+  {Zaměření:} & \zamereni \\
+  {Druh práce:} & Výzkumný ůkol \\[5mm]
+  {Vedoucí práce:} & {\vedouci } \\[5mm]
+  % {Konzultant:} & {\konzultant } \\[5mm]
+  Abstrakt: & \\ 
+  \multicolumn{2}{l}{\odstavec{\textwidth}{\abstrCZ }} \\[5mm]
+  & \\
+  {Klíčová slova:} & \\ 
+  \multicolumn{2}{l}{multiagentní systémy, decentralizované řízení, řízení dopravy} \\[20mm]
+\end{tabular} 
+
+\begin{tabular}{l l}
+  {Title:} & \\
+  \multicolumn{2}{l}{\bf \BooknameEN}\\[5mm]
+  {Author:} & \autor \\[5mm]
+  Abstract: & \\ 
+  \multicolumn{2}{l}{\odstavec{\textwidth}{\abstrEN} } \\[5mm]
+  & \\
+  {Key words:} & \\ 
+  \multicolumn{2}{l}{multiagent systems, decentralized control, control of traffic lights} \\[20mm]
+\end{tabular} 
Index: /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Figures/lev.eps
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Figures/lev.eps (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Figures/lev.eps (revision 1419)
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Index: /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Declar.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Declar.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/00_Chapters/Declar.tex (revision 1419)
@@ -0,0 +1,11 @@
+\thispagestyle{empty}
+
+
+~\vfill
+\vspace{0.5cm}
+Prohlašuji, že jsem předloženou práci vypracoval samostatně, a že jsem uvedl veškerou
+použitou literaturu.
+\vspace{10mm}
+
+Praha, 8. července 2010 \hfill \autor \qquad
+\vspace{5mm}
Index: /applications/doprava/texty/novotny_vyzk_LQ/Appendix/01.tex
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Appendix/01.tex (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Appendix/01.tex (revision 1419)
@@ -0,0 +1,2 @@
+
+\chapter{Příloha 1}
Index: /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib.bak
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib.bak (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib.bak (revision 1419)
@@ -0,0 +1,111 @@
+% This file was created with JabRef 2.7b.
+% Encoding: UTF-8
+
+@ARTICLE{7_lq_methods,
+  author = {Anderson, B.D.O., Moore, J.B.},
+  title = {Optimal Control - Linear Quadratic Methods},
+  journal = {Prentice Hall, Englewood Cliffs, NJ},
+  year = {1990},
+  owner = {jabu},
+  timestamp = {2011.11.24}
+}
+
+@ARTICLE{dynamic_programming,
+  author = {R. Bellman},
+  title = {Dynamic programming},
+  journal = {Princeton University Press},
+  year = {1957}
+}
+
+@ARTICLE{2_int_a_in_dec,
+  author = {E.D. Ferreira and E. Subrahmanian and D. Manstetten},
+  title = {Intelligent agents in decentralized traffic control},
+  journal = {Intelligent Transportation Systems},
+  year = {2001}
+}
+
+@ARTICLE{4_rmm_formalization,
+  author = {P. J. Gmytrasiewicz and E. H. Durfee},
+  title = {A rigorous, operational formalization of recursive modeling},
+  journal = { First International Conference on Multiagent Systems},
+  year = {1995}
+}
+
+@ARTICLE{5_bayes_learn,
+  author = {I. Nagy and P. Nedoma and P. Ettler and L. Pavelkov{\'a} and NewAuthor2},
+  title = {O bayesovsk{\'e}m u\v{c}en{\'i}},
+  journal = {Automa},
+  year = {2002}
+}
+
+@ARTICLE{1_rmm_bayes_learning,
+  author = {H. Ou and W. Zhang and X. Xu},
+  title = {Urban traffic multi-agent system based on RMM and Bayesian learning},
+  journal = {American Control Conference},
+  year = {2002}
+}
+
+@ARTICLE{17_fronta,
+  author = {Pecherková P.,Duník J., Flídr M.},
+  title = {Modelling and Simultaneous Estimation of State
+	
+	and Parameters of Traffic System},
+  journal = {Robotics, Automation and Control},
+  year = {2008},
+  owner = {jabu},
+  timestamp = {2011.12.31}
+}
+
+@ARTICLE{learning_to_predict,
+  author = {R. S. Sutton},
+  title = {Learning to predict by the methods of temporal didffrences},
+  journal = {Machine Learning},
+  year = {1988}
+}
+
+@ARTICLE{tlc_using_sarsa,
+  author = {T. Thorpe},
+  title = {Vehicle traffic light controlusing sarsa},
+  journal = {Master’s thesis, Department of Computer Science, Colorado State University},
+  year = {1997}
+}
+
+@ARTICLE{6_tuc_lq,
+  author = {Vaya Dinopoulou, Christina Diakaki, Markos Papageorgiou},
+  title = {Applications of the urban traffic control strategy TUC},
+  journal = {European Journal of Operational Research},
+  year = {2005},
+  owner = {jabu},
+  timestamp = {2011.11.24}
+}
+
+@ARTICLE{leraning_from_delayed_rewards,
+  author = {C. J. C. H. Watkins},
+  title = {Leraning from Delayed Rewards},
+  journal = {PhD thesis, King's College, Cambridge, England},
+  year = {1989}
+}
+
+@ARTICLE{q_learning,
+  author = {C. J. C. H. Watkins and P. Dayan},
+  title = {Q-leraning},
+  journal = {Machine Learning},
+  year = {1992}
+}
+
+@ARTICLE{3_i_traff_light_c,
+  author = {M. Wiering and J. {Van Veenen} and J. Vreeken and A. Koopman},
+  title = {Intelligent traffic light control},
+  journal = {European Research Consortium for Informatics and Mathematics},
+  year = {2003}
+}
+
+@BOOK{wooldridge,
+  title = {Multi Agent Systems},
+  publisher = {MIT Press},
+  year = {2005},
+  author = {Michael Wooldridge},
+  month = mar,
+  key = {wooldridge}
+}
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib.bckp
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib.bckp (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib.bckp (revision 1419)
@@ -0,0 +1,79 @@
+@Book{ wooldridge,
+	title = "Multi Agent Systems",
+	author = "Michael Wooldridge",
+	month = mar,
+	year = "2005",
+	key = "wooldridge",
+	publisher = "MIT Press"
+}
+
+@Article{ 1_rmm_bayes_learning,
+	title = "Urban traffic multi-agent system based on RMM and Bayesian learning",
+	author = "H. Ou and W. Zhang and X. Xu",
+	journal = "American Control Conference",
+	year = "2002"
+}
+
+@Article{ 2_int_a_in_dec,
+	title = "Intelligent agents in decentralized traffic control",
+	author = "E.D. Ferreira and E. Subrahmanian and D. Manstetten",
+	journal = "Intelligent Transportation Systems",
+	year = "2001"
+}
+
+@Article{ 3_i_traff_light_c,
+	title = "Intelligent traffic light control",
+	author = "M. Wiering and J. {Van Veenen} and J. Vreeken and A. Koopman",
+	journal = "European Research Consortium for Informatics and Mathematics",
+	year = "2003"
+}
+
+@Article{ 4_rmm_formalization,
+	title = "A rigorous, operational formalization of recursive modeling",
+	author = "P. J. Gmytrasiewicz and E. H. Durfee",
+	journal = " First International Conference on Multiagent Systems",
+	year = "1995"
+}
+
+@Article{ 5_bayes_learn,
+	title = "O bayesovsk{\'e}m u\v{c}en{\'i}",
+	author = "I. Nagy and P. Nedoma and P. Ettler and L. Pavelkov{\'a} and NewAuthor2",
+	journal = "Automa",
+	year = "2002"
+}
+
+@Article{ learning_to_predict,
+	author = "R. S. Sutton",
+	journal = "Machine Learning",
+	year = "1988",
+	title = "Learning to predict by the methods of temporal didffrences"
+}
+
+@Article{ dynamic_programming,
+	title = "Dynamic programming",
+	author = "R. Bellman",
+	journal = "Princeton University Press",
+	year = "1957"
+}
+
+@Article{ tlc_using_sarsa,
+	title = "Vehicle traffic light controlusing sarsa",
+	author = "T. Thorpe",
+	journal = "Master’s thesis, Department of Computer Science, Colorado State University",
+	year = "1997"
+}
+
+@Article{ leraning_from_delayed_rewards,
+	title = "Leraning from Delayed Rewards",
+	author = "C. J. C. H. Watkins",
+	journal = "PhD thesis, King's College, Cambridge, England",
+	year = "1989"
+}
+
+@Article{ q_learning,
+	title = "Q-leraning",
+	author = "C. J. C. H. Watkins and P. Dayan",
+	journal = "Machine Learning",
+	year = "1992"
+}
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/Bibl/bibl.bib (revision 1419)
@@ -0,0 +1,111 @@
+% This file was created with JabRef 2.7b.
+% Encoding: UTF-8
+
+@ARTICLE{7_lq_methods,
+  author = {Anderson, B.D.O., Moore, J.B.},
+  title = {Optimal Control - Linear Quadratic Methods},
+  journal = {Prentice Hall, Englewood Cliffs, NJ},
+  year = {1990},
+  owner = {jabu},
+  timestamp = {2011.11.24}
+}
+
+@ARTICLE{dynamic_programming,
+  author = {R. Bellman},
+  title = {Dynamic programming},
+  journal = {Princeton University Press},
+  year = {1957}
+}
+
+@ARTICLE{2_int_a_in_dec,
+  author = {E.D. Ferreira and E. Subrahmanian and D. Manstetten},
+  title = {Intelligent agents in decentralized traffic control},
+  journal = {Intelligent Transportation Systems},
+  year = {2001}
+}
+
+@ARTICLE{4_rmm_formalization,
+  author = {P. J. Gmytrasiewicz and E. H. Durfee},
+  title = {A rigorous, operational formalization of recursive modeling},
+  journal = { First International Conference on Multiagent Systems},
+  year = {1995}
+}
+
+@ARTICLE{5_bayes_learn,
+  author = {I. Nagy and P. Nedoma and P. Ettler and L. Pavelkov{\'a} and NewAuthor2},
+  title = {O bayesovsk{\'e}m u\v{c}en{\'i}},
+  journal = {Automa},
+  year = {2002}
+}
+
+@ARTICLE{1_rmm_bayes_learning,
+  author = {H. Ou and W. Zhang and X. Xu},
+  title = {Urban traffic multi-agent system based on RMM and Bayesian learning},
+  journal = {American Control Conference},
+  year = {2002}
+}
+
+@ARTICLE{17_fronta,
+  author = {Pecherkov{\'a} P. and Dun{\'i}k J. and Fl{\'i}dr},
+  title = {Modelling and Simultaneous Estimation of State
+	
+	and Parameters of Traffic System},
+  journal = {Robotics, Automation and Control},
+  year = {2008},
+  owner = {jabu},
+  timestamp = {2011.12.31}
+}
+
+@ARTICLE{learning_to_predict,
+  author = {R. S. Sutton},
+  title = {Learning to predict by the methods of temporal didffrences},
+  journal = {Machine Learning},
+  year = {1988}
+}
+
+@ARTICLE{tlc_using_sarsa,
+  author = {T. Thorpe},
+  title = {Vehicle traffic light controlusing sarsa},
+  journal = {Master’s thesis, Department of Computer Science, Colorado State University},
+  year = {1997}
+}
+
+@ARTICLE{6_tuc_lq,
+  author = {Vaya Dinopoulou, Christina Diakaki, Markos Papageorgiou},
+  title = {Applications of the urban traffic control strategy TUC},
+  journal = {European Journal of Operational Research},
+  year = {2005},
+  owner = {jabu},
+  timestamp = {2011.11.24}
+}
+
+@ARTICLE{leraning_from_delayed_rewards,
+  author = {C. J. C. H. Watkins},
+  title = {Leraning from Delayed Rewards},
+  journal = {PhD thesis, King's College, Cambridge, England},
+  year = {1989}
+}
+
+@ARTICLE{q_learning,
+  author = {C. J. C. H. Watkins and P. Dayan},
+  title = {Q-leraning},
+  journal = {Machine Learning},
+  year = {1992}
+}
+
+@ARTICLE{3_i_traff_light_c,
+  author = {M. Wiering and J. {Van Veenen} and J. Vreeken and A. Koopman},
+  title = {Intelligent traffic light control},
+  journal = {European Research Consortium for Informatics and Mathematics},
+  year = {2003}
+}
+
+@BOOK{wooldridge,
+  title = {Multi Agent Systems},
+  publisher = {MIT Press},
+  year = {2005},
+  author = {Michael Wooldridge},
+  month = mar,
+  key = {wooldridge}
+}
+
Index: /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.log
===================================================================
--- /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.log (revision 1419)
+++ /applications/doprava/texty/novotny_vyzk_LQ/LQ_rizeni.log (revision 1419)
@@ -0,0 +1,27 @@
+This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2011.10.24)  5 NOV 2011 17:02
+entering extended mode
+ %&-line parsing enabled.
+**LQ_rizeni.tex
+(./LQ_rizeni.tex
+LaTeX2e <2009/09/24>
+Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
+yphenation, loaded.
+! Undefined control sequence.
+l.1 \section
+            {LQ řízení}
+? 
+! Emergency stop.
+l.1 \section
+            {LQ řízení}
+End of file on the terminal!
+
+ 
+Here is how much of TeX's memory you used:
+ 5 strings out of 495061
+ 141 string characters out of 1182620
+ 45108 words of memory out of 3000000
+ 3282 multiletter control sequences out of 15000+50000
+ 3640 words of font info for 14 fonts, out of 3000000 for 9000
+ 28 hyphenation exceptions out of 8191
+ 5i,0n,1p,38b,8s stack positions out of 5000i,500n,10000p,200000b,50000s
+!  ==> Fatal error occurred, no output PDF file produced!
