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    <updated>2007-03-21T22:59:04Z</updated>
<entry><title>software testing (thing)</title><link rel="alternate" type="text/html" href="http://everything2.com:80/user/flyingroc/writeups/software+testing"/><id>http://everything2.com:80/user/flyingroc/writeups/software+testing</id><author><name>flyingroc</name><uri>http://everything2.com:80/user/flyingroc</uri></author><published>2007-03-21T22:59:04Z</published><updated>2007-03-21T22:59:04Z</updated>
<content type="html">&lt;h3&gt;What is software testing&lt;/h3&gt;
&lt;p&gt;
Software testing is the act of comparing the behavior of &lt;a href=&quot;/title/software&quot;&gt;software&lt;/a&gt; against its formal or informal &lt;a href=&quot;/title/specification&quot;&gt;specification&lt;/a&gt;. That is, we are testing a piece of software when we compare what it &lt;em&gt;does&lt;/em&gt; against what it is &lt;em&gt;supposed&lt;/em&gt; to do. The aim of testing is twofold:
&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Find &lt;a href=&quot;/title/bug&quot;&gt;bugs&lt;/a&gt;
&lt;li&gt;Increase confidence in the quality of the software under test
&lt;/li&gt;&lt;/li&gt;&lt;/ul&gt;
&lt;h3&gt;The testing process&lt;/h3&gt;
&lt;p&gt;
Software testing can happen at any time in the development process, and is done in three stages. First, &lt;a href=&quot;/title/test+case&quot;&gt;test cases&lt;/a&gt; are &lt;em&gt;generated&lt;/em&gt;; this may be done by humans (e.g. a programmer writing a &lt;a href=&quot;/title/unit+test&quot;&gt;unit test&lt;/a&gt;), or automatically generated by software. Test cases are often grouped together in a &lt;a href=&quot;/title/test+suite&quot;&gt;test suite&lt;/a&gt;. Tests are then &lt;em&gt;executed&lt;/em&gt;, often using an automated test-runner, but also possibly manually by a user. Finally, an &lt;em&gt;evaluation&lt;/em&gt; is made both of the quality of the software under test, and the quality of the test cases themselves.
&lt;/p&gt;&amp;hellip;</content>
</entry><entry><title>Lorenzo Ruiz (person)</title><link rel="alternate" type="text/html" href="http://everything2.com:80/user/flyingroc/writeups/Lorenzo+Ruiz"/><id>http://everything2.com:80/user/flyingroc/writeups/Lorenzo+Ruiz</id><author><name>flyingroc</name><uri>http://everything2.com:80/user/flyingroc</uri></author><published>2004-03-05T07:39:33Z</published><updated>2004-03-05T07:39:33Z</updated>
<content type="html">&lt;p&gt;
St. &lt;a href=&quot;/title/Lorenzo+Ruiz&quot;&gt;Lorenzo Ruiz&lt;/a&gt; is the first &lt;a href=&quot;/title/Philippines&quot;&gt;Filipino&lt;/a&gt; to be canonized as a &lt;a href=&quot;/title/List+of+Saints&quot;&gt;Saint&lt;/a&gt;. 
&lt;/p&gt;
&lt;p&gt;
Not too much is known about the early life of Lorenzo Ruiz.
He was born sometime between 1600 and 1610, in &lt;a href=&quot;/title/Chinatown&quot;&gt;Chinatown&lt;/a&gt; -- &lt;a href=&quot;/title/Binondo&quot;&gt;Binondo&lt;/a&gt;, &lt;a href=&quot;/title/Manila&quot;&gt;Manila&lt;/a&gt;. His parents were both devout &lt;a href=&quot;/title/Catholic&quot;&gt;Catholic&lt;/a&gt;s. His father was &lt;a href=&quot;/title/Chinese&quot;&gt;Chinese&lt;/a&gt;, while his mother was a &lt;a href=&quot;/title/Filipina&quot;&gt;Filipina&lt;/a&gt;.
&lt;/p&gt;
&lt;p&gt;
St. Lorenzo Ruiz was educated by the &lt;a href=&quot;/title/Dominican&quot;&gt;Dominican&lt;/a&gt;s; he was a &lt;a href=&quot;/title/sacristan&quot;&gt;sacristan&lt;/a&gt; when he was a child, and as a young man worked as a &lt;a href=&quot;/title/scribe&quot;&gt;scribe&lt;/a&gt; for the Dominican priests. He was married, and had three kids, two boys and a girl.
&lt;/p&gt;
&lt;p&gt;
In 1636, Ruiz was implicated in a murder, and to escape a manhunt, he sought asylum in a ship that was leaving Manila (We do not know the circumstances of the murder, or Lorenzo's part in it, if any). Once the ship sailed, Lorenzo found out that it was bound for &lt;a href=&quot;/title/Japan&quot;&gt;Japan&lt;/a&gt;, carrying missionaries at a time of great persecution of &lt;a href=&quot;/title/Christian&quot;&gt;Christian&lt;/a&gt;s. The ship was making one stop in &lt;a href=&quot;/title/Formosa&quot;&gt;Formosa&lt;/a&gt; (now &lt;a href=&quot;/title/Taiwan&quot;&gt;Taiwan&lt;/a&gt;), but fearing the&amp;hellip;</content>
</entry><entry><title>Stations of the Cross (idea)</title><link rel="alternate" type="text/html" href="http://everything2.com:80/user/flyingroc/writeups/Stations+of+the+Cross"/><id>http://everything2.com:80/user/flyingroc/writeups/Stations+of+the+Cross</id><author><name>flyingroc</name><uri>http://everything2.com:80/user/flyingroc</uri></author><published>2004-03-02T00:23:33Z</published><updated>2004-03-02T00:23:33Z</updated>
<content type="html">&lt;p&gt;
The Stations of the Cross is also called &quot;&lt;a href=&quot;/title/Via+Dolorosa&quot;&gt;Via Dolorosa&lt;/a&gt;&quot;, &quot;&lt;a href=&quot;/title/Via+Crucis&quot;&gt;Via Crucis&lt;/a&gt;&quot;, or the &quot;&lt;a href=&quot;/title/Way+of+the+Cross&quot;&gt;Way of the Cross&lt;/a&gt;&quot;. 
The devotion can be traced as originally coming from pilgrimages in the &lt;a href=&quot;/title/Jerusalem&quot;&gt;Jerusalem&lt;/a&gt;, where people would travel the path of Christ's &lt;a href=&quot;/title/Passion&quot;&gt;Passion&lt;/a&gt;, starting from the house of &lt;a href=&quot;/title/Pontius+Pilate&quot;&gt;Pontius Pilate&lt;/a&gt;, to the &lt;a href=&quot;/title/crucifixion&quot;&gt;crucifixion&lt;/a&gt; site at &lt;a href=&quot;/title/Calvary&quot;&gt;Calvary&lt;/a&gt;, stopping at holy sites along the way. It is said that the &lt;a href=&quot;/title/Virgin+Mary&quot;&gt;Virgin Mary&lt;/a&gt; visited the path of &lt;a href=&quot;/title/Christ&quot;&gt;Christ&lt;/a&gt;'s passion daily. 
&lt;/p&gt;
&lt;p&gt;
Because of the difficulty of traveling to the &lt;a href=&quot;/title/Holy+Land&quot;&gt;Holy Land&lt;/a&gt;, clergymen in various locations around &lt;a href=&quot;/title/Europe&quot;&gt;Europe&lt;/a&gt; built shrines of certain holy places in Jerusalem, allowing people to make mini pilgrimages. By the 15th century, the devotion had evolved more or less to its modern form, where people pray at each &quot;station&quot; -- an artisitc depiction of an event in &lt;a href=&quot;/title/Jesus&quot;&gt;Jesus&lt;/a&gt;'s Passion.
&lt;/p&gt;
&lt;p&gt;
The number of stations have not always been the way it is now. It has varied widely throught the years, but in 1731 &lt;a href=&quot;/title/Pope+Clement+XII&quot;&gt;Pope Clement XII&lt;/a&gt; fixed the number of stations to&amp;hellip;</content>
</entry><entry><title>Soup number five (thing)</title><link rel="alternate" type="text/html" href="http://everything2.com:80/user/flyingroc/writeups/Soup+number+five"/><id>http://everything2.com:80/user/flyingroc/writeups/Soup+number+five</id><author><name>flyingroc</name><uri>http://everything2.com:80/user/flyingroc</uri></author><published>2004-02-28T02:22:14Z</published><updated>2004-02-28T02:22:14Z</updated>
<content type="html">&lt;p&gt;
Of all the &lt;a href=&quot;/title/Filipino&quot;&gt;Filipino&lt;/a&gt; foods, one of the strangest must be the mysteriously named &quot;soup number five&quot;. Soup number five is a soup made out of bull &lt;a href=&quot;/title/penis&quot;&gt;penis&lt;/a&gt;, and &lt;a href=&quot;/title/testicle&quot;&gt;testicle&lt;/a&gt;s. It's supposed to be an &lt;a href=&quot;/title/aphrodisiac&quot;&gt;aphrodisiac&lt;/a&gt;, though how chewing an animal's genitalia can help arouse anyone's libido, I cannot understand.
&lt;/p&gt;
&lt;p&gt;
For a long time, I thought the existence of this soup was just an urban legend. But then, I chanced upon a restaurant one day, and on its signage quite clearly was &quot;Soup # 5.&quot; I don't remember now where exactly this restaurant was, but I won't be surprised if it was in &lt;a href=&quot;/title/chinatown&quot;&gt;chinatown&lt;/a&gt;. 
&lt;/p&gt;
&lt;p&gt;
I didn't have the stomach to go in and try this exotic food, so I don't really know what it tastes like, or how it looks. However, I know this guy who claimed to have had soup number five in some local restaurant. Apparently, when you order the soup, in your bowl you get either one testicle, or the shaft of the penis.
&lt;/p&gt;
&lt;p&gt;
&quot;Well, what does it taste like?&quot; I asked the guy. &lt;br&gt;
&quot;Oh,&quot; he said nonchalantly, &quot;it tastes like soup.&quot; 
&lt;/p&gt;
&lt;p&gt;We left the conversation at that.&lt;/p&gt;</content>
</entry><entry><title>complete graph (thing)</title><link rel="alternate" type="text/html" href="http://everything2.com:80/user/flyingroc/writeups/complete+graph"/><id>http://everything2.com:80/user/flyingroc/writeups/complete+graph</id><author><name>flyingroc</name><uri>http://everything2.com:80/user/flyingroc</uri></author><published>2004-02-27T15:38:37Z</published><updated>2004-02-27T15:38:37Z</updated>
<content type="html">&lt;p&gt;(&lt;a href=&quot;/title/graph+theory&quot;&gt;graph theory&lt;/a&gt;)&lt;/p&gt;
&lt;p&gt;
A &lt;strong&gt;complete graph&lt;/strong&gt; is a &lt;a href=&quot;/title/simple+graph&quot;&gt;simple graph&lt;/a&gt; whose vertices are pairwise &lt;a href=&quot;/title/adjacent&quot;&gt;adjacent&lt;/a&gt;. In other words, there is an &lt;a href=&quot;/title/edge&quot;&gt;edge&lt;/a&gt; between every two &lt;a href=&quot;/title/vertex&quot;&gt;vertices&lt;/a&gt; in the graph. In other words (version 2), every vertex in a complete graph has an edge to every other vertex in  the graph.
&lt;p&gt;
&lt;/p&gt;
A complete &lt;a href=&quot;/title/graph&quot;&gt;graph&lt;/a&gt; with &lt;em&gt;n&lt;/em&gt; vertices is usually denoted as &lt;em&gt;K&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;. A complete graph is also sometimes called a &lt;a href=&quot;/title/clique&quot;&gt;clique&lt;/a&gt;.
&lt;/p&gt;
&lt;p&gt;
There are several variants of what is called a complete graph. There is the complete graph with &lt;a href=&quot;/title/loop&quot;&gt;loop&lt;/a&gt;s where every vertex also has an edge going back to itself; and the complete &lt;a href=&quot;/title/directed+graph&quot;&gt;directed graph&lt;/a&gt; where between every pair of vertices u and v there are two edges: one going from u to v, another going from v to u.
&lt;/p&gt;
&lt;p&gt;Another type of graph that is often discussed along with complete graphs is the &lt;a href=&quot;/title/complete+bipartite+graph&quot;&gt;complete bipartite graph&lt;/a&gt;. A complete bipartite graph is a &lt;a href=&quot;/title/bipartite+graph&quot;&gt;bipartite graph&lt;/a&gt; such that for every vertex in one &lt;a href=&quot;/title/partite+set&quot;&gt;partite set&lt;/a&gt;, there&amp;hellip;</content>
</entry><entry><title>Cayley's formula (thing)</title><link rel="alternate" type="text/html" href="http://everything2.com:80/user/flyingroc/writeups/Cayley%2527s+formula"/><id>http://everything2.com:80/user/flyingroc/writeups/Cayley%2527s+formula</id><author><name>flyingroc</name><uri>http://everything2.com:80/user/flyingroc</uri></author><published>2004-02-27T07:25:27Z</published><updated>2004-02-27T07:25:27Z</updated>
<content type="html">&lt;p&gt;
Named after &lt;a href=&quot;/title/Arthur+Cayley&quot;&gt;Arthur Cayley&lt;/a&gt;, the formula says that the number of labeled &lt;a href=&quot;/title/spanning+tree&quot;&gt;spanning trees&lt;/a&gt; of a &lt;a href=&quot;/title/complete+graph&quot;&gt;complete simple graph&lt;/a&gt; with &lt;em&gt;n&lt;/em&gt; &lt;a href=&quot;/title/vertex&quot;&gt;vertices&lt;/a&gt; is &lt;strong&gt;n&lt;sup&gt;n-2&lt;/sup&gt;&lt;/strong&gt;
&lt;/p&gt;
&lt;p&gt;
The interesting thing about Cayley's formula is that there are numerous different proofs for it, and new ones come out often, even to this day. Many textbooks use the proof by Prüfer (perhaps because professors like the phrase &quot;Prüfer's proof&quot;). Prüfer links the fact that n&lt;sup&gt;n-2&lt;/sup&gt; is the number of ways to write down a &lt;a href=&quot;/title/string&quot;&gt;string&lt;/a&gt; of length n-2 from a &lt;a href=&quot;/title/set&quot;&gt;set&lt;/a&gt; S of n numbers. 
&lt;/p&gt;
&lt;p&gt;
The proof sets up a code (called Prüfer's code) that maps such strings to labeled spanning trees in a one-to-one correspondence. The actual proof, however, is left to a better noder than I to explain, as it requires some drawing and a lot of hand-waving. 
&lt;/p&gt;</content>
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