<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<meta name="Generator" content="Microsoft Word 14 (filtered medium)">
<!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:Consolas;
panose-1:2 11 6 9 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
pre
{mso-style-priority:99;
mso-style-link:"HTML Preformatted Char";
margin:0in;
margin-bottom:.0001pt;
font-size:10.0pt;
font-family:"Courier New";}
span.HTMLPreformattedChar
{mso-style-name:"HTML Preformatted Char";
mso-style-priority:99;
mso-style-link:"HTML Preformatted";
font-family:"Consolas","serif";}
span.EmailStyle19
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="EN-US" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Should there be a naming convention so that<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">nll_xxxx gives a negative log likelihood<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">lnl_xxxx gives a log likelihood<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">R names gives a likelihood or distribution<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">And it is up to the user to choose the nll for an objective function?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<div>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> users-bounces@admb-project.org [mailto:users-bounces@admb-project.org]
<b>On Behalf Of </b>Steve Martell<br>
<b>Sent:</b> Thursday, October 02, 2014 11:06 AM<br>
<b>To:</b> Aaron Greenberg<br>
<b>Cc:</b> users@admb-project.org; Carlos Martorell<br>
<b>Subject:</b> Re: [ADMB Users] Problem with negative log likelihoods?<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">All the functions in statsLib return the negative log likelihood. ADMB minimizes the negative loglikelihoods. It does not maximize a function. So for me it seemed obvious that the functions should return the negative loglikelihood. But
that was a choice I made. If someone wants to change it, the open source platform allows you to do just that. But if you do change it, please warn all others who use these functions to reverse the sign in their objective functions.
<o:p></o:p></p>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">There was a bug in the vectorized version of dpois, so I fixed it. I very much appreciate Carlos pointing the bug out. I guess this is how open source software is supposed to work.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Grumpy Steve<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<div>
<p class="MsoNormal">On Oct 2, 2014, at 10:56 AM, bigA <<a href="mailto:jaguar.smart@gmail.com">jaguar.smart@gmail.com</a>> wrote:<o:p></o:p></p>
</div>
<p class="MsoNormal"><br>
<br>
<o:p></o:p></p>
<div>
<p class="MsoNormal">If I am not mistaken, in Iceland, there was substantial discussion amongst developers about what functions returned log-likelihood and which functions returned negative log-likelihood.
<o:p></o:p></p>
<div>
<p class="MsoNormal">If I am not mistaken this hasn't been standardized; it is often different from R. <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">The difference between the two versions of <span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">00075 appears to simply be a negative sign?
</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">Is this a documentation failure or a bug?</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">Aaron</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB"><br>
<br>
</span><o:p></o:p></p>
</div>
<div>
<div>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">nll -= -k(i)*</span><span style="font-size:10.0pt;font-family:"Arial","sans-serif""><a href="http://admb-project.org/documentation/api/d3arr2a_8cpp.html#a921f553085254834ebbe598d5e9c0341" target="_blank" title="Description not yet available."><span style="font-size:9.0pt;font-family:"Courier New";color:#4665A2;text-decoration:none">log</span></a></span><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">(lambda(i))+lambda(i)+</span><span style="font-size:10.0pt;font-family:"Arial","sans-serif""><a href="http://admb-project.org/documentation/api/group__gammafunc.html#gae01374ddda83bc2216ba9df9c76d9995" target="_blank" title="Log gamma function."><span style="font-size:9.0pt;font-family:"Courier New";color:#4665A2;text-decoration:none">gammln</span></a></span><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">(k(i)+1.);</span><span style="font-size:10.0pt;font-family:"Arial","sans-serif""><o:p></o:p></span></p>
</div>
</div>
<div>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">vs</span><o:p></o:p></p>
</div>
<div>
<div style="mso-element:para-border-div;border:solid #D6E5C4 1.0pt;padding:3.0pt 5.0pt 3.0pt 5.0pt;background:#FCFDFB;margin-left:1.5pt;margin-right:6.0pt">
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in;white-space:pre-wrap;word-wrap:break-word;overflow:auto"><span style="font-size:9.0pt"> nll -= k(i)*<a href="http://admb-project.org/documentation/api/d3arr2a_8cpp.html#a921f553085254834ebbe598d5e9c0341" target="_blank" title="Description not yet available."><span style="color:#4665A2;text-decoration:none">log</span></a>(lambda(i))+lambda(i)+<a href="http://admb-project.org/documentation/api/group__gammafunc.html#gae01374ddda83bc2216ba9df9c76d9995" target="_blank" title="Log gamma function."><span style="color:#4665A2;text-decoration:none">gammln</span></a>(k(i)+1.);<o:p></o:p></span></pre>
</div>
</div>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p class="MsoNormal">On Tue, Sep 30, 2014 at 6:57 PM, Carlos Martorell <<a href="mailto:martorell@ciencias.unam.mx" target="_blank">martorell@ciencias.unam.mx</a>> wrote:<o:p></o:p></p>
<div>
<p class="MsoNormal">Hi, <o:p></o:p></p>
<div>
<p class="MsoNormal">After checking the output of an ADMB run I believe that I have found a problem in (at least) a couple of the functions used to calculate the negative log-likelihoods in dpois and dnbinom functions in the statsLib.h library. When a vector
of parameters (lambdas in the Poisson case) is provided, the code for the log-likelihood is<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<div style="mso-element:para-border-div;border:solid #D6E5C4 1.0pt;padding:3.0pt 5.0pt 3.0pt 5.0pt;background:#FCFDFB;margin-left:1.5pt;margin-right:6.0pt">
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in;word-wrap:break-word;overflow:auto"><span style="font-size:9.0pt">00067 <a href="http://admb-project.org/documentation/api/classdvariable.html" target="_blank" title="Fundamental data type for reverse mode automatic differentiation."><span style="color:#4665A2;text-decoration:none">dvariable</span></a> <a href="http://admb-project.org/documentation/api/dpois_8cpp.html#a64d2001c40c90f8295bd86ea88ff6979" target="_blank"><span style="color:#4665A2;text-decoration:none">dpois</span></a>(<span style="color:green">const</span> <a href="http://admb-project.org/documentation/api/classdvector.html" target="_blank" title="Vector of double precision numbers."><span style="color:#4665A2;text-decoration:none">dvector</span></a>& k, <span style="color:green">const</span> <a href="http://admb-project.org/documentation/api/classdvar__vector.html" target="_blank" title="Description not yet available."><span style="color:#4665A2;text-decoration:none">dvar_vector</span></a>& lambda)<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00068"></a><span style="font-size:9.0pt">00068 {<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00069"></a><span style="font-size:9.0pt">00069 <a href="http://admb-project.org/documentation/api/group__RA.html#ga9616d0c80845da3942a30acbb1dbbfa9" target="_blank" title="Increments gradient_structure::RETURN_ARRAYS_PTR."><span style="color:#4665A2;text-decoration:none">RETURN_ARRAYS_INCREMENT</span></a>();<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00070"></a><span style="font-size:9.0pt">00070 <span style="color:#604020">int</span> i;<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00071"></a><span style="font-size:9.0pt">00071 <span style="color:#604020">int</span> n = <a href="http://admb-project.org/documentation/api/dsize_8cpp.html#aa42ba747b253f027435b478a7d747f52" target="_blank" title="Description not yet available."><span style="color:#4665A2;text-decoration:none">size_count</span></a>(k);<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00072"></a><span style="font-size:9.0pt">00072 <a href="http://admb-project.org/documentation/api/classdvariable.html" target="_blank" title="Fundamental data type for reverse mode automatic differentiation."><span style="color:#4665A2;text-decoration:none">dvariable</span></a> nll=0;<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00073"></a><span style="font-size:9.0pt">00073 <span style="color:#E08000">for</span>(i = 1; i <= n; i++)<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00074"></a><span style="font-size:9.0pt">00074 {<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00075"></a><span style="font-size:9.0pt">00075 nll -= k(i)*<a href="http://admb-project.org/documentation/api/d3arr2a_8cpp.html#a921f553085254834ebbe598d5e9c0341" target="_blank" title="Description not yet available."><span style="color:#4665A2;text-decoration:none">log</span></a>(lambda(i))+lambda(i)+<a href="http://admb-project.org/documentation/api/group__gammafunc.html#gae01374ddda83bc2216ba9df9c76d9995" target="_blank" title="Log gamma function."><span style="color:#4665A2;text-decoration:none">gammln</span></a>(k(i)+1.);<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00076"></a><span style="font-size:9.0pt">00076 }<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00077"></a><span style="font-size:9.0pt">00077 <a href="http://admb-project.org/documentation/api/group__RA.html#ga780ea9f1c9038a5116c28140166d6e7e" target="_blank" title="Decrements gradient_structure::RETURN_ARRAYS_PTR."><span style="color:#4665A2;text-decoration:none">RETURN_ARRAYS_DECREMENT</span></a>();<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00078"></a><span style="font-size:9.0pt">00078 <span style="color:#E08000">return</span> nll;<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00079"></a><span style="font-size:9.0pt">00079 }<o:p></o:p></span></pre>
</div>
<div>
<p class="MsoNormal">I believe that the correct code for line 00075 should be<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">nll -= -k(i)*</span><a href="http://admb-project.org/documentation/api/d3arr2a_8cpp.html#a921f553085254834ebbe598d5e9c0341" target="_blank" title="Description not yet available."><span style="font-size:9.0pt;font-family:"Courier New";color:#4665A2;text-decoration:none">log</span></a><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">(lambda(i))+lambda(i)+</span><a href="http://admb-project.org/documentation/api/group__gammafunc.html#gae01374ddda83bc2216ba9df9c76d9995" target="_blank" title="Log gamma function."><span style="font-size:9.0pt;font-family:"Courier New";color:#4665A2;text-decoration:none">gammln</span></a><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">(k(i)+1.);</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Courier New";background:#FCFDFB">This is evident in the same function when lambda is constant, e.g., </span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<div style="mso-element:para-border-div;border:solid #D6E5C4 1.0pt;padding:3.0pt 5.0pt 3.0pt 5.0pt;background:#FCFDFB;margin-left:1.5pt;margin-right:6.0pt">
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in;word-wrap:break-word;overflow:auto"><span style="font-size:9.0pt"><a href="http://admb-project.org/documentation/api/statsLib_8h.html#a64d2001c40c90f8295bd86ea88ff6979" target="_blank"><span style="color:#4665A2;text-decoration:none">00035</span></a> <a href="http://admb-project.org/documentation/api/classdvariable.html" target="_blank" title="Fundamental data type for reverse mode automatic differentiation."><span style="color:#4665A2;text-decoration:none">dvariable</span></a> <a href="http://admb-project.org/documentation/api/dpois_8cpp.html#a64d2001c40c90f8295bd86ea88ff6979" target="_blank"><span style="color:#4665A2;text-decoration:none">dpois</span></a>(<span style="color:green">const</span> <span style="color:#604020">double</span>& k, <span style="color:green">const</span> <a href="http://admb-project.org/documentation/api/classprevariable.html" target="_blank" title="Base class for dvariable."><span style="color:#4665A2;text-decoration:none">prevariable</span></a>& lambda)<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00036"></a><span style="font-size:9.0pt">00036 {<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00037"></a><span style="font-size:9.0pt">00037 <a href="http://admb-project.org/documentation/api/group__RA.html#ga9616d0c80845da3942a30acbb1dbbfa9" target="_blank" title="Increments gradient_structure::RETURN_ARRAYS_PTR."><span style="color:#4665A2;text-decoration:none">RETURN_ARRAYS_INCREMENT</span></a>();<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00038"></a><span style="font-size:9.0pt">00038 <a href="http://admb-project.org/documentation/api/classdvariable.html" target="_blank" title="Fundamental data type for reverse mode automatic differentiation."><span style="color:#4665A2;text-decoration:none">dvariable</span></a> tmp = -k*<a href="http://admb-project.org/documentation/api/d3arr2a_8cpp.html#a921f553085254834ebbe598d5e9c0341" target="_blank" title="Description not yet available."><span style="color:#4665A2;text-decoration:none">log</span></a>(lambda)+lambda + <a href="http://admb-project.org/documentation/api/group__gammafunc.html#gae01374ddda83bc2216ba9df9c76d9995" target="_blank" title="Log gamma function."><span style="color:#4665A2;text-decoration:none">gammln</span></a>(k+1.);<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00039"></a><span style="font-size:9.0pt">00039 <a href="http://admb-project.org/documentation/api/group__RA.html#ga780ea9f1c9038a5116c28140166d6e7e" target="_blank" title="Decrements gradient_structure::RETURN_ARRAYS_PTR."><span style="color:#4665A2;text-decoration:none">RETURN_ARRAYS_DECREMENT</span></a>();<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00040"></a><span style="font-size:9.0pt">00040 <span style="color:#E08000">return</span> tmp;<o:p></o:p></span></pre>
<pre style="mso-margin-top-alt:3.0pt;margin-right:0in;margin-bottom:3.0pt;margin-left:0in;line-height:11.25pt;background:#FCFDFB;border:none;padding:0in"><a name="148ccdcf03885333_l00041"></a><span style="font-size:9.0pt">00041 }<o:p></o:p></span></pre>
</div>
</div>
<div>
<p class="MsoNormal">I found these codes both in the ADMB version that I downloaded and in the package documentation (<a href="http://admb-project.org/documentation/api/dpois_8cpp_source.html" target="_blank">http://admb-project.org/documentation/api/dpois_8cpp_source.html</a>).
After making the correction that I propose above and re-running ADMB, the program reports the correct log-likelihoods. The same problem can be found in dnbinom and maybe in other functions.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">Given that the functions provided for the estimation of negative log-likelihoods are widely used, it would be important to check that their outputs are correct.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">Best,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<p class="MsoNormal">-- <br>
<span style="font-size:10.0pt;font-family:"Arial","sans-serif""> I think [the island's] unusually sterile character gives it a grandeur <br>
which more vegetation might have spoiled. </span> <o:p></o:p></p>
<div>
<p class="MsoNormal"><span style="font-family:"Arial","sans-serif""> ----Ch. Darwin. El diario del Beagle </span><br>
<span style="font-family:"Arial","sans-serif""> </span><br>
<span style="font-family:"Arial","sans-serif"">Dr. Carlos Martorell </span><br>
<span style="font-family:"Arial","sans-serif""> </span><br>
<span style="font-family:"Arial","sans-serif"">Departamento de Ecología y Recursos Naturales </span><br>
<span style="font-family:"Arial","sans-serif"">Facultad de Ciencias-UNAM </span><br>
<span style="font-family:"Arial","sans-serif"">Circuito Exterior S/N, Cd. Universitaria </span><br>
<span style="font-family:"Arial","sans-serif"">04510 México D.F. </span><br>
<span style="font-family:"Arial","sans-serif"">Tel. (55) 5622 4835 Fax (55) 5622 4828 </span><br>
<span style="font-family:"Arial","sans-serif";color:blue"><a href="http://www.fciencias.unam.mx/investigacion/grupos/biologia/ecologia/ambientesl" target="_blank">http://www.fciencias.unam.mx/investigacion/grupos/biologia/ecologia/ambientesl</a></span><o:p></o:p></p>
</div>
</div>
</div>
<p class="MsoNormal" style="margin-bottom:12.0pt"><br>
_______________________________________________<br>
Users mailing list<br>
<a href="mailto:Users@admb-project.org">Users@admb-project.org</a><br>
<a href="http://lists.admb-project.org/mailman/listinfo/users" target="_blank">http://lists.admb-project.org/mailman/listinfo/users</a><o:p></o:p></p>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<p class="MsoNormal">_______________________________________________<br>
Users mailing list<br>
<a href="mailto:Users@admb-project.org">Users@admb-project.org</a><br>
<a href="http://lists.admb-project.org/mailman/listinfo/users">http://lists.admb-project.org/mailman/listinfo/users</a><o:p></o:p></p>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div class="MsoNormal" align="center" style="text-align:center">
<hr size="3" width="100%" align="center">
</div>
<p class="MsoNormal"><span style="font-size:7.5pt;font-family:"Arial","sans-serif";color:gray"><br>
This internet e-mail message, and any files transmitted with it, contains confidential, privileged information that is intended only for the addressee. If you have received this e-mail message in error, please call us at (206) 634-1838 collect if necessary)
and ask to speak to the message sender. Nothing in this e-mail or the act of transmitting it, is to be construed as a waiver of any rights or privileges enjoyed by the sender or the International Pacific Halibut Commission pursuant to the International Organizations
Immunities Act, 22 U.S.C. Sec. 288 et seq.</span><o:p></o:p></p>
</div>
</body>
</html>