Template:Team:Amsterdam/testpage

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$ S(t) = \begin{array}
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<html>
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i-1 & 897 \\
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i-1 & 897
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<!-- STYLESHEET -->
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\end{array}
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<!-- *********** -->
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$
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<link rel="stylesheet" href="https://2012.igem.org/Team:Amsterdam/mstylesheet?action=raw&ctype=text/css" type="text/css" />
 +
 
 +
<!-- JAVASCRIPTS -->
 +
<!-- *********** -->
 +
 
 +
    <!-- ie9.js (fixes all Internet Explorer browsers older than ie9) -->
 +
    <!--[if lt IE 9]>
 +
    <script src="http://ie7-js.googlecode.com/svn/version/2.1(beta4)/IE9.js"></script>
 +
    <![endif]-->
 +
 
 +
    <!-- jQuery Tools (slider) -->
 +
    <script src="http://cdn.jquerytools.org/1.2.5/full/jquery.tools.min.js"></script>
 +
    <script>
 +
        $(function() {
 +
    // initialize scrollable
 +
    $(".scrollable").scrollable().navigator();
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        });
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    </script>
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 +
    <!-- Navigation scroll follow -->
 +
    <script type="text/javascript">
 +
        $(window).scroll(function () {
 +
            var scrollPos = $(window).scrollTop();
 +
            if (scrollPos > 110) {
 +
                $(".navigation").addClass("stickToTop");
 +
            } else {
 +
                $(".navigation").removeClass("stickToTop");
 +
            }
 +
            if (scrollPos > 180) {
 +
                $(".toc").addClass("stickBelowNavigation");
 +
            } else {
 +
                $(".toc").removeClass("stickBelowNavigation");
 +
            }
 +
        });
 +
    </script>
 +
 
 +
    <!-- MathJax (LaTeX for the web) -->
 +
    <script type="text/x-mathjax-config">
 +
        MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
 +
        MathJax.Hub.Config({
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            TeX: {
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                equationNumbers: {  autoNumber: "AMS"  }
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            }
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        });
 +
    </script>
 +
    <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
 +
 
 +
    <!-- Sexy Drop Down (drop down navigation) -->
 +
    <script type="text/javascript">
 +
        $(document).ready(
 +
            function(){
 +
                $("ul.subnav").parent().find("> a").append("<span> ▼</span>");
 +
                $("ul.topnav li").hover(
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                    function() {
 +
                        // Hover over
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                        $(this).parent().find("ul.subnav").hide();
 +
                        $(this).find("ul.subnav").show();
 +
                        // Hover out
 +
                        $(this).hover(
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                            function() {
 +
                            },
 +
                            function(){
 +
                                $(this).find("ul.subnav").hide();
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                            }
 +
                        );
 +
                    },
 +
                    function(){
 +
                        $(this).find("ul.subnav").hide();
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                    }
 +
 
 +
                );
 +
            }
 +
        );
 +
    </script>
 +
 
 +
    <!-- iGem wiki hacks -->
 +
        <!-- Remove all empty <p> tags -->
 +
        <script type="text/javascript">
 +
            $(document).ready(function() {
 +
                $("p").filter( function() {
 +
                    return $.trim($(this).html()) == '';
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                }).remove();
 +
            });
 +
        </script>
 +
 
 +
        <!-- Remove "team" from the menubar -->
 +
        <script type="text/javascript">
 +
            $(document).ready(function() {
 +
                $("menubar > ul > li:last-child").remove();
 +
            });
 +
        </script>
 +
 
 +
        <!-- Empty heading? - Then remove it.. -->
 +
        <script type="text/javascript">
 +
            $(document).ready(function() {
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                if ("" == "</html>{{{1}}}<html>") {
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                    $("#heading").remove();
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                }
 +
            });
 +
        </script>
 +
 
 +
 
 +
<!-- HTML CONTENT -->
 +
<!-- ************ -->
 +
 
 +
    <!-- Header image -->
 +
    <div id="header">
 +
        <div class="centering">
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        </div>
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    </div>
 +
 
 +
    <!-- Navigation bar -->
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    </html>{{MaartenNavigationbar}}<html>
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 +
    <!-- Page heading -->
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    <div id="heading">
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        <div class="centering">
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            <h1>
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</html>
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{{{1}}}
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<html>
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            </h1>
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        </div>
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    </div>
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 +
    <!-- Prepare for content -->
 +
    <div id="innercontent">
 +
        <div class="centering">
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            <div class="whitebox article">
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</html>
 +
== Simplification and construction of ODEs ==
 +
The general reaction scheme is
 +
\begin{align}
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\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
 +
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
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\end{align}
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 +
\begin{align}
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\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
 +
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
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\end{align}
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 +
 
 +
\begin{align}
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\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
 +
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
 +
\end{align}
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 +
 
 +
\begin{align}
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\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
 +
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
 +
\end{align}
 +
 
 +
 
 +
\begin{align}
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\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
 +
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
 +
\end{align}
 +
 
 +
 
 +
\begin{align}
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\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
 +
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
 +
\end{align}

Latest revision as of 16:27, 24 September 2012

{{{1}}}

Simplification and construction of ODEs

The general reaction scheme is \begin{align} \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r \end{align}

\begin{align} \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r \end{align}


\begin{align} \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r \end{align}


\begin{align} \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r \end{align}


\begin{align} \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r \end{align}


\begin{align} \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r \end{align}

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