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<head>
<title>Alexey Spiridonov: Links to elsewhere</title>
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<body onclick="initWave();" onload="initPage();">
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<!-- XXX: judicious use of colors for section headings? -->
<!-- XXX: deprecate 'a name' for subsections if there are no old-browser
visitors -->
<!-- list of browser bugs i don't get:
- ems & pts in ff are not consistently sized. 2pt in this element is more
pixels than 2pt in that element.
- iewin fade doesn't work if the 'a name' is above the 'div id'
- why do i need the iewin hacks for the various 'a' tags above?
- the stuff with the date floats wrapping (see iewin near date p) is
just weird
- ems in iewin don't scale at all.
-->
<script src="common.js" type="text/javascript"></script>
<script src="wave-borders.js" type="text/javascript"></script>
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<div id="content">
<div id="header">
<hr class="hfdiv divider" style="margin-bottom: 0; margin-top: 1em;"/>
<!-- smiling bat by yours truly -->
<table><tr>
<td>
<pre title="A smiling, text-only bat welcomes you!">
)\./(
_V ( o o ) V_
)`-,)`-'(,-'(
),'; /^\ :`.(
)/ | . | \(
`).\_/.('
' m m `
</pre>
</td>
<td>
<!-- this pre is a vertical bar of the same height as the drawing,
so it should have the same number of lines. -->
<pre class="divider" style="width: 2px;">
</pre>
</td>
<td>
<!-- the fade is easy to do dynamically, but i'm going for
compatibility, so I use a local script instead -->
<!-- this is a lightness-based fade, as opposed to a
componentwise rgb fade -->
<p>
<span style="color: #000000;">A</span><span
style="color: #00000d;">l</span><span
style="color: #00001a;">e</span><span
style="color: #000026;">x</span><span
style="color: #000033;">e</span><span
style="color: #000040;">y</span><span
style="color: #00004d;"> </span><span
style="color: #000059;">S</span><span
style="color: #000066;">p</span><span
style="color: #000073;">i</span><span
style="color: #000080;">r</span><span
style="color: #00008c;">i</span><span
style="color: #000099;">d</span><span
style="color: #0000a6;">o</span><span
style="color: #0000b3;">n</span><span
style="color: #0000bf;">o</span><span
style="color: #0000cc;">v</span><span
style="color: #0000d9;">:</span><span
style="color: #0000e6;"> </span><a
href="http://en.wikipedia.org/wiki/Transitional_fossil"><span
style="color: #0000f2;">L</span><span
style="color: #0000ff;">i</span><span
style="color: #0d0dff;">n</span><span
style="color: #1a1aff;">k</span><span
style="color: #2626ff;">s</span></a><span
style="color: #3333ff;"> </span><span
style="color: #4040ff;">t</span><span
style="color: #4d4dff;">o</span><span
style="color: #5959ff;"> </span><span
style="color: #6666ff;">e</span><span
style="color: #7373ff;">l</span><span
style="color: #8080ff;">s</span><span
style="color: #8c8cff;">e</span><span
style="color: #9999ff;">w</span><span
style="color: #a6a6ff;">h</span><span
style="color: #b3b3ff;">e</span><span
style="color: #bfbfff;">r</span><span
style="color: #ccccff;">e</span><span
style="color: #ddddff;">.</span><span
style="color: #e5e5ff;">.</span><span
style="color: #eeeeff;">.</span><span
style="color: #ffffff;"> </span><span
style="color: #ffffff;">=</span><span
style="color: #ffffff;">)</span>
</p>
</td>
</tr></table>
<hr class="hfdiv divider" style="margin-top: 0;"/>
</div> <!-- end of header -->
<div id="navbar">
<ul>
<li><a href="#papers">Papers</a></li>
<li><a href="#software">Software</a></li>
<li><a href="#notes">Notes and Homework</a></li>
<li><a href="#changelog">Changelog</a></li>
</ul>
</div>
<!-- page introduction -->
<div id="intro">
<p>
This page collects links to various things that I put on the Web at
various times.
</p>
<p>
I have a (rather dated) <a href="papers/cv.pdf">curriculum vitæ</a>
and a <a href="papers/industry-resume.pdf">résumé</a>.
</p>
<p>
Contact me on <a href="http://fb.me/lesha">Facebook</a>.
</p>
<p id="plus_sidenote" class="sidenote" style="display: none;">
<!-- this is hidden by default so that if JS is disabled,
we won't confuse the user with wrong information.
XXX: this should probably be written *by* javascript -->
A plus
<span style="font-style: normal; font-weight: bold; color: #ccf;">
|<span style="color:blue; font-size: small; ">+</span>|</span>
next to a sub-section heading is a link to that very sub-section, useful
for bookmarking a specific place on this page.
</p>
</div>
<hr class="secdiv divider"/>
<div class="section">
<div>
<div class="trileft triangle"></div>
<div id="papers" class="sectitle">Papers</div>
<div class="triright triangle"></div>
<a name="papers"></a>
</div>
<p>
This section is an annotated list of files from <a
href="papers/index.html">papers/</a>. It does not cover my <a
href="http://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed&cmd=DetailsSearch&term=spiridonov+an">
computational biology work</a> — 4 more submitted or in
preparation as of December 2008. It also omits an old <a
href="http://portal.acm.org/citation.cfm?id=977677">memory profiling
paper</a> (<a href="papers/cgo-memory-profiling.pdf">pdf</a>).
</p>
<p class="sidenote">
The dates in this section denote when the paper was finished; I may have
made minor corrections after the date.
</p>
<div id="fpsac-pattern-avoidance-sec">
<div id="fpsac-pattern-avoidance" class="subsectitle">
<a href="papers/pattern-pair-avoidance-extended-abstract.pdf">
Pattern-pair avoidance in binary fillings of grid shapes (extended abstract) <tt>(pdf)</tt>
</a></div>
<a name="fpsac-pattern-avoidance"></a>
<p class="date">April, 2008 (to appear)</p>
<p>
This is a 14-page overview of a part of my Ph. D. thesis-to-be. I
presented a <a href="papers/fpsac-2008-poster.pdf">poster</a> of
this at <a href="http://inst-mat.utalca.cl/fpsac2008">FPSAC
2008</a>; it will be published in the proceedings.
</p>
<p>
My patterns are pairs of 2x2 matrices, with all entries equal to 0
or 1. Grid shapes are arbitrary subsets of boxes on graph paper
— Young diagrams are a very particular case. Choose a
particular grid shape <i>S</i>, and some two patterns <i>a</i> and
<i>b</i> (each is a pair of matrices). For <em>some</em> such choices,
the number of ways of filling <i>S</i> with 0s and 1s so that it
avoids <i>a</i> is equal to the number of fillings avoiding
<i>b</i>. Then, we say <i>a</i> is <em>equivalent</em> to <i>b</i> in
<i>S</i> — a close relative of Wilf-equivalence. This paper
makes the "some" precise, systematically describing which
equivalences hold in what classes of shapes.
</p>
</div>
<div id="graph-rigidity-paper-sec">
<div id="graph-rigidity-paper" class="subsectitle">
<a href="papers/graph-rigidity-preprint.pdf">
The Parallel Rigidity Index of a Graph <tt>(pdf)</tt>
</a></div>
<a name="graph-rigidity-paper"></a>
<p class="date">April, 2007 (preprint)</p>
<p>
This is joint work with <a href="http://math.mit.edu/~apost">Alex Postnikov</a>, my Ph. D.
thesis advisor.
</p>
<p>
Imagine that you are to build a system of space stations (graph
vertices), which communicate via laser beams (edges). The edge
directions were already chosen, but you must place the stations so that
none of the beams miss their targets. In this paper, we let the edge
directions be generic and independent, a choice that constrains
vertex placement the most. We then give an elegant combinatorial
characterization of the number of degrees of freedom in this system,
and prove some other related results.
</p>
</div>
<div id="srg-near-zero-sec">
<div id="srg-near-zero" class="subsectitle">
<a href="papers/sparse-random-graphs-near-zero-final-project-S06-18.318.pdf">
Sparse Random Graphs Near Zero <tt>(pdf)</tt>
</a></div>
<a name="srg-near-zero"></a>
<p class="date">May, 2006</p>
<p>
The first few pages of this paper give a quick overview of the
results of my <a href="#srg-thesis">senior thesis</a>. The remainder
has some additional results about the decay of the spectrum near
zero. Due to time constraints, I did not prove one key conjecture
-- which later turned out to be known (see below). This was my
final project for 18.318 in Spring 2006.
</p>
<p>
<em>Update:</em> In 2007, I repeated my regular search for "least
positive tree eigenvalue", and discovered <a
href="http://www.springerlink.com/content/m58168l847t23125/">this
paper</a>, which completes my result on near-zero asymptotics:
</p>
<p>
C. D. Godsil, "Inverses of trees", Combinatorica <b>5</b> (1985), No. 1, 33-9
</p>
<p>
It proves that the least positive eigenvalue on even trees occurs on
a path. As far as I know, the case of odd trees (conjectured to be a
"forked path" — a <i>2n</i>-path with an extra edge added to
the second vertex), is still open.
</p>
</div>
<div id="srg-thesis-sec">
<div id="srg-thesis" class="subsectitle">
<a href="papers/sparse-random-graphs-senior-thesis.pdf">
Spectra of Sparse Random Graphs and Matrices <tt>(pdf)</tt>
</a></div>
<a name="srg-thesis"></a>
<p class="date">May, 2004</p>
<p>
This was my Princeton undergraduate senior thesis, written under
Professor <a href="http://en.wikipedia.org/wiki/Yakov_G._Sinai">
Yakov G. Sinai</a>. It concerns studied the <em>adjacency</em> spectra
of sparse random matrices. I established that the spectra are
well-defined, gave some bounds on the tail asymptotics, provided a
numerical overview of the various regimes, and made some steps
towards quantifying the spectrum in the neighborhood of zero (see
more on this <a href="#srg-near-zero">here</a>). Here are the
relevant computer programs:
</p>
<ul style="list-style-type: none;">
<li style="margin-bottom: 0.5em;">
<a href="papers/moment_progs.tar.gz">
Calculating moments <tt>(tgz)</tt>:
</a>
Includes a program to calculate the moments of the limiting
adjacency spectrum of a sparse graph, and one for a
gaussian-weight sparse graph.
</li>
<li>
<a href="papers/tree_progs.tar.gz">
Tree enumeration <tt>(tgz)</tt>:
</a>
This is an implementation of my <i>O(n)</i> cpu, <i>O(sqrt(n))</i>
memory algorithm for enumerating free trees. It uses more memory
than the <i>O(1)</i> of the
<a href="http://theory.cs.uvic.ca/inf/tree/FreeTrees.html">
Li-Ruskey algorithm</a>,
but provides every tree's automorphism group size at no cost.
The implementation also computes tree adjacency spectra, and
characteristic polynomials.
</li>
</ul>
</div>
<div>
<div id="srg-numerics" class="subsectitle">
<a href="papers/sparse-random-graphs-jp-for-sinai.pdf">
Sparse Random Graph Numerics <tt>(pdf)</tt>
</a></div>
<a name="srg-numerics"></a>
<p class="date">May, 2003</p>
<p>
This was a small numerical investigation that I did during my junior
year. It has some spectrum pictures that are not in the <a
href="#srg-thesis">senior thesis</a>, but is otherwise obsolete.
</p>
</div>
<div>
<div id="moore-and-self-dual" class="subsectitle">
<a href="papers/moore-and-self-complementary-dual-graphs-for-seymour.pdf">
Moore Graphs as Maximal-Girth Graphs, and Self-Dual,
Self-Complementary Graphs on the Plane and Torus <tt>(pdf)</tt>
</a></div>
<a name="moore-and-self-dual"></a>
<p class="date">January, 2003 </p><!-- space needed for iewin -->
<p>
A pair of graph theory exercises that I solved in 2002
(they were suggested by Professor
<a href="http://www.math.princeton.edu/~pds/">Paul Seymour</a>
for my junior paper). There are probably no new results;
I'm not 100% certain that anybody else worked out at the torus case,
but the rest is known.
</p>
</div>
<div>
<div id="hoffman-puzzle" class="subsectitle">
<a href="papers/hoffman-puzzle-for-conway.pdf">
Hoffman's Packing Puzzle in 3 and 4 Dimensions <tt>(pdf)</tt>
</a></div>
<a name="hoffman-puzzle"></a>
<p class="date">May, 2003</p>
<p>
Professor <a href="http://en.wikipedia.org/wiki/John_Horton_Conway">
John H. Conway</a> introduced me to this neat puzzle. Take 27 <i>a</i>
by <i>b</i> by <i>c</i> blocks, and try to assemble them into an
(<i>a + b + c</i>)<sup>3</sup> cube. It's hard, but certainly doable.
This paper shows how. If you think about it, this proves the
arithmetic-geometric mean inequality for 3 variables! :)
</p>
<p>
I also tried to tackle the 4D case, but ran out of time. There was
some progress made; it might be doable as well. The paper refers to
this <a href="papers/hoffman-puzzle.tgz">puzzle-solving code
<tt>(tgz)</tt></a>.
</p>
<p>
You can make your own copy of the puzzle! Take a 68-inch <a
href="http://en.wikipedia.org/wiki/Dimensional_lumber">2" x 4"</a>,
and saw it into 27 2.5-inch bricks (half-an-inch to spare). Sand them
a bit, and go impress your friends! Note: you're probably better off
with a circular saw, not a hand saw, since the cuts should be rather
straight.
</p>
</div>
<div>
<div id="waring-problem" class="subsectitle">
<a href="papers/waring's-problem-final-project-mat403.pdf">
Waring's Problem <tt>(pdf)</tt>
</a></div>
<a name="waring-problem"></a>
<p class="date">May, 2004</p>
<p>
This is a re-telling of a book (see reference in paper) chapter on
solving <a href="http://mathworld.wolfram.com/WaringsProblem.html">
Waring's problem</a> with Linnik's approach, using Shnirel'man
density. Written rather hastily (class final project), and not
certainly not cribbed. Thus, it is probably less readable than the
book. But, it is written from a different angle, so who knows, you
might find it helpful.
</p>
</div>
<div>
<div id="alexandrov-n-dim-frame" class="subsectitle">
<a href="papers/rigidity-n-dimensional-frame-final-project-S05-18.318.pdf">
Rigidity of the <i>n</i>-Dimensional Frame <tt>(pdf)</tt>
</a></div>
<a name="alexandrov-n-dim-frame"></a>
<p class="date">May, 2005 (unfinished)</p>
<p>
The paper is <em>very</em> sloppily written, the work is unfinished, and
the proofs may be wrong. I'm putting it out here in the hope that it
will be useful to somebody working on the same problem — I do not
plan to come back to this soon.
</p>
<p>
I wrote this after Professor <a href="http://www.math.umn.edu/~pak/">
Igor Pak</a> suggested I look at the paper
<a href="http://math.nsc.ru/~vaalex/pub.html">
"A new example of a flexible polyhedron"</a> by
<a href="http://math.nsc.ru/~vaalex/">Victor Alexandrov</a>.
The original paper uses some fairly tricky trigonometry to prove
that the described 3D polyhedron is flexible, and has zero volume.
</p>
<p>
I constructs a generalization of Alexandrov's polyhedron in <i>n</i>
dimensions, and sketches what might be a nicer proof (if correct :) of
Alexandrov's result for dimension 3. It also argues that the
construction in 4 or more dimensions would be rigid.
</p>
</div>
</div>
<hr class="secdiv divider"/>
<div class="section">
<div>
<div class="trileft triangle"></div>
<div id="software" class="sectitle">Software</div>
<div class="triright triangle"></div>
<a name="software"></a>
</div>
<p>
Here is the small fraction of my hacks that I bothered to clean up and
package. Let me know if you find something useful — I might improve it
:)
</p>
<p class="sidenote">
The dates in this section denote first release. Software evolves a lot
more than papers do. I've usually use a program for a while before
releasing it, and change it substantially post-release.
</p>
<div>
<div id="dynkin-diagrams" class="subsectitle">
<a href="dynkin-diagrams.html">Dynkin Diagrams</a>
</div>
<a name="dynkin-diagrams"></a>
<p class="date">December 2006</p>
<p>
This is a program that I wrote at Professor
<a href="http://www.math.cornell.edu/~ebd/">Eugene B. Dynkin</a>'s
suggestion. It draws nice diagrams in HTML and EPS (for use in
LaTeX). It lets you choose labels for the vertices of Dynkin diagrams.
It has a catalog of all Dynkin diagrams (up to size 8), and of all
extended and affine Dynkin diagrams (up to size 9). It can be used
offline. It's written using a combination of JavaScript / XHTML / CSS,
and runs in the major browsers (but works/looks best in Firefox).
</p>
<p>
You may also be interested in the <a href="http://dynkincollection.library.cornell.edu/">Eugene B. Dynkin Collection of Mathematics Interviews</a>.
</p>
</div>
<div>
<div id="audio-coding" class="subsectitle">
<a href="audio-coding/index.html">Lossless, Peelable Audio Coding</a>
</div>
<a name="audio-coding"></a>
<p class="date">April 2006</p>
<p>
Well, I had this crazy idea, and this is the result of my 30-minute
feasibility study. It turned out to work pretty well, in my opinion.
</p>
</div>
<div>
<div id="xwmconsole" class="subsectitle">
<a href="software/xwmconsole.tar.bz2">xwmconsole <tt>(tbz2)</tt></a>
</div>
<a name="xwmconsole"></a>
<p class="date">November 2003</p>
<p>
A couple of scripts to replace XDM/GDM. Allows you to run many X
sessions with ease, log directly into X from the console, and
makes you impervious to window manager crashes.
</p>
<p class="sidenote">
Some assembly required — you should be at ease editing shell
configuration files.
</p>
</div>
<div>
<div id="xv-package" class="subsectitle">
<a href="software/xv-package.tar.bz2">
xv custom keys / lossless rotation / annotation patch
<tt>(tbz2)</tt>
</a>
</div>
<a name="xv-package"></a>
<p class="date">November 2003</p>
<p>
This small patch for XV, the image viewer, which allows you to run
scripts by pressing a key from F1 through F12. Included are scripts to
losslessly rotate JPEGs, to edit JPEG comments, to run batch
rotations, and to perform <em>reversible</em> crops. Another easy
application of this patch is a script for face annotation (see
README). If you don't know how, and ask nicely, I can write it for
you. If you write one, let me know, and I'll include it.
</p>
<p class="sidenote">
Some assembly required, but detailed instructions are provided.
</p>
</div>
<!-- XXX: more code (e.g. timed-cat, plottool) -->
</div>
<hr class="secdiv divider"/>
<div class="section">
<div>
<div class="trileft triangle"></div>
<div id="notes" class="sectitle">Notes and Homework</div>
<div class="triright triangle"></div>
<a name="notes"></a>
</div>
<p>
I habitually typed homework solutions in <a href="http://www.lyx.org">
LyX</a>, and, on occasion also typed up or scanned (the latter are
typically by some friendly person with nicer handwriting) lecture
notes. If you are studying one of the topics below, I hope that these
materials will help you learn.
</p>
<p>
<em>Concerning homeworks:</em> I don't recommend that anyone crib
solutions. Even if your professor allows the use of outside sources
(if not, go away!), or you're studying on your own, the point is still
to try to do the problems. On the other hand, there's not much
learning happening while you're out of ideas and running in circles.
So, the recommended use is:
</p>
<ol>
<li>
Think about a problem until you're seriously stuck. (Hey, you
might not even get there!)
</li>
<li>
Look at a solution line-by-line up to the point when you become
less stuck. Odds are it won't be easy to read anyway :)
</li>
<li>
Repeat until you're done.
</li>
</ol>
<p class="sidenote">
The dates here denote when the body of notes/lectures for the course
was completed.
</p>
<!-- XXX - notes for benny's class. also, what else might I have
in scanned form? -->
<div>
<div id="lyx-spams-notes" class="subsectitle">
<a href="lyx/index.html">LyX SPAMS Talk Notes</a>
</div>
<a name="lyx-spams-notes"></a>
<p class="date">February 2008</p>
<p>
During the semester's first installment of the <a
href="http://math.mit.edu/spams/"> Simple Person's Applied Math
Seminar</a>, I tried to convince attendees that <a
href="http://www.lyx.org">LyX</a> is a great way to create LaTeX
documents. This page lists some caveats and "how to" ideas.
</p>
</div>
<div>
<div id="lie-algebra-notes" class="subsectitle">
<a href="745lec/index.html">18.745 Lie Algebras Notes</a>
</div>
<a name="lie-algebra-notes"></a>
<p class="date">January 2005</p>
<p>
The class was taught by Professor
<a href="http://math.mit.edu/~kac/index.html">Victor Kac</a>.
This compilation of lecture notes was typed by the students.
Exercises are stated and solved in every lecture
write-up. PDFs are available for every lecture, with LaTeX
source for most.
</p>
</div>
</div>
<hr class="secdiv divider"/>
<div class="section">
<div>
<div class="trileft triangle"></div>
<div id="changelog" class="sectitle">Changelog</div>
<div class="triright triangle"></div>
<a name="changelog"></a>
</div>
<p>
This section lists substantial page updates, just so you know when
this site kicks the bucket.
</p>
<div>
<div id="cl-20150510" class="subsectitle">
Moved hosting
</div>
<a name="cl-20150510"></a>
<p class="date">May 10, 2015</p>
<p>
Trying to be a grown-up and have my own domain. Thanks for all the
bits, <a href="http://andreygoder.com/">Andrey</a>!
</p>
</div>
<div>
<div id="cl-20110601" class="subsectitle">
Moved hosting
</div>
<a name="cl-20110601"></a>
<p class="date">June 1, 2011</p>
<p>
The MIT math department doesn't host pages indefinitely, so I moved
to the domain of my awesome friend
<a href="http://andreygoder.com/">Andrey Goder</a>.
</p>
</div>
<div>
<div id="cl-20081215" class="subsectitle">
The job hunt is on
</div>
<a name="cl-20081215"></a>
<p class="date">December 15, 2008</p>
<p>
Added a resume, CV, some more papers, fixed some typos, improved
writing and visual consistency.
</p>
</div>
<div>
<div id="cl-20080208" class="subsectitle">
Not dead yet!
</div>
<a name="cl-20080208"></a>
<p class="date">February 8, 2008</p>
<p>
Added a LyX notes link, hope to find time to add more material.
</p>
</div>
<div>
<div id="cl-20070115" class="subsectitle">
Initial Release
</div>
<a name="cl-20070115"></a>
<p class="date">January 15, 2007</p>
<p>
Things I hope to add in the future: some art/photos, more code and
lecture notes, lots of math homeworks.
</p>
</div>
<div>
<div id="history" class="subsectitle"> History</div>
<a name="history"></a>
<p class="date">wasting your bandwidth since 1999</p>
<p>
Before Facebook obviated the need for self-description, I made a
couple of personal homepages. The current one, I hope, is more of a
"here's some interesting stuff" homepage. Here are the links to the
previous iterations:
</p>
<p>
<a href="old-page/index.html">Princeton era (2003-2005)</a>
</p>
<p>
<a href="http://ahel.freehostia.com">
Ithaca High era (1999-present)</a>
<span style="color: red;">[warning :) ugly]</span>
</p>
</div>
</div>
<!-- XXX: don't forget art & music -->
<!-- footer with validation and licensing -->
<hr class="hfdiv divider"/>
<div id="license">
<p>
Text, papers, XHTML / CSS markup, and homeworks are licensed under the
<a href="#mit_x_license">MIT X License</a>. JavaScript code, software,
and lecture notes are licensed on separate terms, listed in each item's
documentation.
</p>
<div id="mit_x_license_sec" class="hide-by-default add-hiding-link">
<h3 id="mit_x_license">
<a name="mit_x_license"></a>
The MIT X License
</h3>
<p>
<span style="font-style: italic; font-size: smaller">The
license text comes from
<a href="http://www.opensource.org/licenses/mit-license.php">here</a>.
It is only being applied to the text and XHTML / CSS markup on this
page.</span>
</p>
<p>
Copyright (c) 2007 Alexey Spiridonov
</p>
<p>
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
</p>
<p>
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
</p>
<p>
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
</p>
</div>
</div>
<p id="validated">
[<a href="http://validator.w3.org/check?uri=referer">valid XHTML</a>]
[<a href="http://jigsaw.w3.org/css-validator/check/referer">valid
CSS</a>]
[JavaScript checked by <a href="http://www.jslint.com">JSLint</a>.]
</p>
</div><!-- end of content div -->