materials not being rendered
Object renders black
How to select a clustering method? How to validate a cluster solution (to warrant the method choice)? One of the biggest issue with cluster analysis is that we may happen to have to derive different conclusion when base on different clustering methods used  (including different linkage methods in hierarchical clustering).  I would like to know your opinion on this - which method will you select, and how. One might say "the best method of clustering is which gives you the right answer"; but I may question in response that cluster analysis is supposed to be an unsupervised technique - so how do I know which method or linkage is the right answer?  In general: is a clustering alone robust enough to rely on? Or we need a second method and get a shared result to be based on both?  My question is not only about possible ways to validate / evaluate clustering performance, but is broader - on what basis do we select/prefer one clustering method/algorithm over another one. Also, is there common warnings that we should look around when we are selecting a method to cluster our data?  I know that it is very general question and very difficult to answer. I only would like to know if you have any comment or any advise or any suggestion for me to learn more about this. Plotting discontinuous functions without spurious vertical segments I have a directory full of images:  image0001.png image0002.png image0003.png ...   And I would like a one-liner to rename them to (say).  0001.png 0002.png 0003.png ...   How do I do this? Schema for a multilanguage database I'm developing a multilanguage software. As far as the application code goes, localizability is not an issue. We can use language specific resources and have all kinds of tools that work well with them.  But what is the best approach in defining a multilanguage database schema? Let's say we have a lot of tables (100 or more), and each table can have multiple columns that can be localized (most of nvarchar columns should be localizable). For instance one of the tables might hold product information:  CREATE TABLE T_PRODUCT (   NAME        NVARCHAR(50),   DESCRIPTION NTEXT,   PRICE       NUMBER(18, 2) )   I can think of three approaches to support multilingual text in NAME and DESCRIPTION columns:   Separate column for each language  When we add a new language to the system, we must create additional columns to store the translated text, like this:  CREATE TABLE T_PRODUCT (   NAME_EN        NVARCHAR(50),   NAME_DE        NVARCHAR(50),   NAME_SP        NVARCHAR(50),   DESCRIPTION_EN NTEXT,   DESCRIPTION_DE NTEXT,   DESCRIPTION_SP NTEXT,   PRICE          NUMBER(18,2) )  Translation table with columns for each language  Instead of storing translated text, only a foreign key to the translations table is stored. The translations table contains a column for each language.  CREATE TABLE T_PRODUCT (   NAME_FK        int,   DESCRIPTION_FK int,   PRICE          NUMBER(18, 2) )  CREATE TABLE T_TRANSLATION (   TRANSLATION_ID,   TEXT_EN NTEXT,   TEXT_DE NTEXT,   TEXT_SP NTEXT )  Translation tables with rows for each language  Instead of storing translated text, only a foreign key to the translations table is stored. The translations table contains only a key, and a separate table contains a row for each translation to a language.  CREATE TABLE T_PRODUCT (   NAME_FK        int,   DESCRIPTION_FK int,   PRICE          NUMBER(18, 2) )  CREATE TABLE T_TRANSLATION (   TRANSLATION_ID )  CREATE TABLE T_TRANSLATION_ENTRY (   TRANSLATION_FK,   LANGUAGE_FK,   TRANSLATED_TEXT NTEXT )  CREATE TABLE T_TRANSLATION_LANGUAGE (   LANGUAGE_ID,   LANGUAGE_CODE CHAR(2) )    There are pros and cons to each solution, and I would like to know what are your experiences with these approaches, what do you recommend and how would you go about designing a multilanguage database schema. For an existing set of line features, I would like to generate a perpendicular line, of say 1km, at the midpoint of each existing line feature in ArcGIS.  I imagine that The methodology would be to:   create a tangent line at the midpoint of each existing line feature calculate the angle of the tangent line based on the angle of the tangent line, calculate the location of the endpoint of the new line create the new line with the calculated endpoint of the new line and the existing midpoint of the old line   Let's assume that we are in a UTM projection and can use coordinates to calculate distance and direction.  How would I do this with ArcGIS tools or with ArcPy? Finite multiplicative group of matrices with sum of traces equal to zero. Let  $G=\{M_1,M_2,...,M_k\}$ be a finite set such that $ M_i\in M_n(\mathbb R)$ and $(G,\;\cdot\:)$ is a group with matrix multiplication. If $\sum _{i=1}^k \operatorname{tr} (M_i)=0$ then how to prove $\sum _{i=1}^k M_i=0$ ? Is there a standard pronunciation for gender-neutral -@ or -x More and more I see, especially in activist communities, Spanish-derived words ending in x or @ in order to neuter the gendering inherent in the original language. For example: latinx (or latin@) as opposed to latina and latino. How, though, are these endings pronounced? Please provide evidence of how this orthography is most commonly pronounced. Note 1: I recognize this is in an English Language site, rather than a Spanish language site, but this phenomenon is very much happening in English, albeit with Spanish loan words. Therefore the question is relevant to non-Spanish-speaking English speakers. Note 2: A question like this can lead to politically charged or, at least, sarcastic comments. Please refrain from bringing in your biases for or against. Note 3: This question is not seeking opinions as to how some people pronounce the suffixes. Answers should address evidence of a developing orthodoxy in pronunciation. How can I take shallow depth of field photos with a point-and-shoot camera? Which parts are from Eminems real life? In "" we saw how Bunny Rabbit got into the rapping gang and won the heart of millions of rap lovers. Now in Eminem's original life too similar thing happened. We know how Dr. Dre helped him getting into an industry which is dominated by mainly black people in USA. In fact,  called the film semi-autobiographical. So I want to know which parts are direct picturisations of his real life? Squeezing all the SEO out of a URL as possible I am working on an ecommerce site, I told our SEO consultant that I plan to make the URL scheme: /products/&lt;id&gt;/&lt;name&gt;. This is similar to Stackoverflow's URLs which are /questions/&lt;id&gt;/&lt;title&gt;.  He asked me if I could change the URL scheme to /p/&lt;id&gt;/&lt;name&gt; instead. I know why he wants this change, the word "products" isn't needed to find the correct product, and it doesn't offer any SEO, so shortening it to just p would make the relevant keywords in the &lt;name&gt; weigh more.  His main priority is maximizing SEO, but the part that I don't think he is considering is how this effects the semantics of the site. Also having the word "products" looks like it has meaning and a reason for being there, just having a p looks chaotic and ugly to me. I also don't think it makes that much of a difference does it? Stackoverflow doesn't use /q/&lt;id&gt;/&lt;title&gt; and they do just fine, I do realize that theres many factors at play here though, not just the URL.  So I want some outside opinions on which is the better way and why? Did your team win the football match yesterday?         The weather was very bad, so we weren't playing.   vs     The weather was very bad, so we didn't play.   Is the first one not correct? Why is it? How can I put two figures side-by-side? Not two sub-figures, but two actual figures with separate "Fig.: bla bla" captions.  A figure is supposed to spread over the entire text width, but I have two figures which are narrow and long, and I need to save the space in order to withstand the pages limit. How do I post code in chat? I would like to be able to post code in chat. I know that I can post inline snippets of code by using backticks, but I don't know how to post blocks of code, with the entire chat message formatted as code, and indentation respected. I am aware of . After reading the comments, I found out that I could format in "fixed width", but I can't see a "fixed width" button anywhere. What should I do? Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function In Walter Rudin's Principles of mathematical analysis Exercise 5.21, it is proved that for any closed subset $E\subseteq \mathbb{R}$, there exists a smooth function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$.   Since $E^c$ is open in $\mathbb{R}$, $E^c$ is a countable disjoint union of open intervals $(a_i,b_i)$. On an interval $(a,b)$, if we let $f(x)=\exp(\frac{1}{(x-a)(x-b)})$, $x\in(a,b)$; $f(x)=0$, $x\notin(a,b)$, ($f(x)=\exp(\frac{1}{(x-a)})$ or $f(x)=\exp(\frac{1}{(x-b)})$ on $(a,\infty)$ and $(-\infty,b)$ resp.), then $f$ is smooth. Hence we can get a smooth function on $\mathbb{R}$ such that $E$ is the zero point sets of $f$.  (1). How about a closed subset $E$ of $\mathbb{R}^n$? is it true that for any closed subset $E\subseteq \mathbb{R}^n$, there exists a smooth function $f$ on $\mathbb{R}^n$ such that $E=\{x\in \mathbb{R}^n\mid f(x)=0\}$?  An open set in $\mathbb{R}^n$ cannot be written as a disjoint union of countable open balls hence the proof above is not valid. The partition of unity only claims that for an  open set $U$, there exists open $V$ in $U$ such that $\bar V\subseteq U$ and a smooth function $f$ on $\mathbb{R}^n$ such that $supp f\subseteq U$, $f|_V=1$.   (2). The taylor series of $f(x)=\exp(\frac{1}{(x-a)(x-b)})$ does not converge around points $a,b$ hence $f$ is not analytic at $a,b$. Is it true that for any closed subset $E\subseteq \mathbb{R}$, there exists an analytic function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$? I will go to France from 17/12/13 – 19/12/13, then I will come back to London. And again I will go back to Portugal and Spain from 26/12/13 to 03/01/14 which I will stay in Spain for the longest period. However, the Spanish consulate told me that I have to request for the visa from the French consulate.  The point is: Do I need to apply for a visa for a single trip two times (from French and Spanish consulate) or a single visa for multiple time (from French consulate). How can I do traffic shaping in Linux by IP? We have a transparent proxy setup. I tried looking for traffic shaping in Linux, and all I could find online was to limit traffic by interface (eth0/eth1...).  I need to limit the bandwidth (never exceeding a specific limit) by IP address or IP ranges and I can't find a way to do that.  Is there any way to do that? I am aware that there are plenty of threads on intensifiers(very, rather, pretty, quite, fairly, etc.), both on this site and on the web, because of their ambiguity in terms of meaning. What I have learned is that their meaning can change depending on which country you are from, which context they are used, or your intonation. So instead of comparing all intensifiers, I decided to make my question more specific. I chose to focus on the word pretty because of its "common" usage.  So as we can see, the word pretty has two meanings and unfortunately they are "pretty" opposite. My question is can you tell me, just by taking into account  the example sentences below, in which sentences "pretty" means "fairly,", and in which it means "very?"  Does "Tom looks pretty tired" always mean "Tom looks a little/fairly tired" ? Generate three correlated uniformly-distributed random variables Product of two cyclic groups is cyclic iff their orders are co-prime Say you have two groups $G = \langle g \rangle$ with order $n$ and $H = \langle h \rangle$ with order $m$. Then the product $G \times H$ is a cyclic group if and only if $\gcd(n,m)=1$.  I can't seem to figure out how to start proving this. I have tried with some examples, where I pick $(g,h)$ as a candidate generator of $G \times H$. I see that what we want is for the cycles of $g$ and $h$, as we take powers of $(g,h)$, to interleave such that we do not get $(1,1)$ until the $(mn)$-th power. However, I am having a hard time formalizing this and relating it to the greatest common divisor.  Any hints are much appreciated! Mathematical notation around the world