How can I use an attribute value from a mesh's material in another material?
How to link a variable of a material to another material?
Inserting an image in plain TeX I used the OzTeX implementation of TeX, also I used to typeset my docs in plain TeX, not LaTeX for me, so I had no problem to insert an image using the OzTeX, now I'm back to TeX docs, am using the TeXWorks frontend, but I can't insert an .eps image file, it seems the \includegraphics macro its only for LaTeX, so I can't use it, any idea on how to insert an image when using plain TeX? This question is about an efficient way to compute principal components.   Many texts on linear PCA advocate using singular-value decomposition of the casewise data. That is, if we have data $\bf X$ and want to replace the variables (its columns) by principal components, we do SVD: $\bf X=USV'$, singular values (sq. roots of the eigenvalues) occupying the main diagonal of $\bf S$, right eigenvectors $\bf V$ are the orthogonal rotation matrix of axes-variables into axes-components, left eigenvectors $\bf U$ are like $\bf V$, only for cases. We can then compute component values as $ \bf C=XV=US$. Another way to do PCA of variables is via decomposition of $\bf R=X'X$ square matrix (i.e. $\bf R$  correlations or covariances etc., between the variables ). The decomposition may be eigen-decomposition or singular-value decomposition: with square symmetric positive semidefinite matrix, they will give the same result $\bf R=VLV'$ with eigenvalues as the diagonal of $\bf L$, and $\bf V$ as described earlier. Component values will be $\bf C=XV$.   Now, my question: if data $\bf X$ is a big matrix, and number of cases is (which is often a case) much greater than the number of variables, then way (1) is expected to be much slower than way (2), because way (1) applies a quite expensive algorithm (such as SVD) to a big matrix; it computes and stores huge matrix $\bf U$ which we really doesn't need in our case (the PCA of variables). If so, then why so many texbooks seem to advocate or just mention only way (1)? Maybe it is efficient and I'm missing something? Mismatch Reputation in the thumbnail and the actual Reputation Actually this was quite surprising. A casual troll in the Users Page revealed few users with negative vote. One example is here    Then trying to see what could have causes such a low reputation, I peeked inside the Profile Page of this particular User and was surprised to see a decent positive score.    Can someone explain to me how this can be possible? If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$ Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$ I'm trying to write a blog post which includes a code segment inside a &lt;pre&gt; tag. The code segment includes a generic type and uses &lt;&gt; to define that type. This is what the segment looks like:  &lt;pre&gt;     PrimeCalc calc = new PrimeCalc();     Func&lt;int, int&gt; del = calc.GetNextPrime; &lt;/pre&gt;   The resulting HTML removes the &lt;&gt; and ends up like this:  PrimeCalc calc = new PrimeCalc(); Func del = calc.GetNextPrime;   How do I escape the &lt;&gt; so they show up in the HTML? I am trying to create buffers around the Hurricane Sandy path I created in QGIS (points are lat/long).   I have both points from each day she was tracted and the line I created from it with Points2One.   When I go to make buffers around either the line or the points, the buffer takes up the whole screen. Its all just one color.   I have made buffers before but from data I did not create.   Right now all of my projections are set to WGS 84 EPSG 4326. Why this javascript regex doesn't work? How to split strings into text and number? how to shuffle characters of strings in bash? i have this script where it generates random password but it needs to be shuffled. I couldnt find a way to do it. Please Help me.  num=("0" "1" "2" "3" "4" "5" "7" "8" "9") special=("@" "#" "$" "%" "*" "-" "+") upper=(A B C D E F G H I J K L M N O P Q R S T U V W X Y Z) lower=(a b c d e f g h i j k l m n o p q r s t u v w x y z) lower2=${#lower[*]}   #${lower[$((RANDOM%lower2))]} upper2=${#upper[*]}   #${upper[$((RANDOM%upper2))]} num2=${#num[*]}     #${num[$((RANDOM%num2))]} special2=${#special[*]} #${special[$((RANDOM%special2))]} echo "${special[$((RANDOM%special2))]}${num[$((RANDOM%num2))]}${lower[$((RANDOM%lower2))]}${upper[$((RANDOM%upper2))]}${lower[$((RANDOM%lower2))]}${upper[$((RANDOM%upper2))]}${lower[$((RANDOM%lower2))]}${upper[$((RANDOM%upper2))]}"   this is the output: @7nOyIaJ  how do I randomize this? Can we calculate the standard error of prediction just based on simple linear regression output? The standard error of prediction in simple linear regression is $\hat\sigma\sqrt{1/n+(x_j-\bar{x})^2/\Sigma{(x_i-\bar{x})^2}}$.  My question is to calculate the standard error of prediction for $pop=1029$ just based on the following regression output. I can get all except $\bar{x}$. And I also know how to calculate the approximate standard error of prediction based on the standard errors of intercept and coefficient of $pop$, ignoring their correlation. What makes a good jump scare? I am working on a game and would like to include a few jump scares. So here is a rather simple question — What makes a good jump scare and when and how should they happen? Sentence vs proposition So, I have proven already that every open set in $\mathbb{R}$ can be written as a countable union of disjoint open intervals; i.e., that $\mathcal{O} = \bigcup_{i=1}^\infty (a_{x_i}, b_{x_i})$.  Now, consider the closed interval $\left [ a + \frac{1}{n}, b - \frac{1}{n}\right ] \subset (a, b)$.  Since the midpoint of $(a,b)$ is $\frac{b-a}{2}$, we need $\displaystyle n &gt; \frac{2}{b-a}$.  Otherwise, $\displaystyle a + \frac{b-a}{2} = a + \frac{1}{ \frac{2}{b-a}} = b - \frac{1}{ \frac{2}{b-a}} = b - \frac{b-a}{2}$, and our interval will be degenerate.  Note that $\forall (a,b) \in \mathcal{O}$,   $\displaystyle \bigcup_{n = \frac{b-a}{2}+1}^{\infty} \left[ a + \frac{1}{n}, b - \frac{1}{n} \right] = (a,b)$.  So, we have $\displaystyle \mathcal{O} = \bigcup_{i=1}^\infty \left ( \bigcup_{n = \frac{b-a}{2} + 1}^\infty \left[ a_{x_i}+\frac{1}{n}, b_{x_i}-\frac{1}{n} \right] \right)$.  But, I don't like this. It looks like I'm still just taking a union of open sets.  Please help me get this to look like the union of closed sets.  (For unbounded intervals, I know what to do - it should follow from this relatively easily). What makes a Feynman diagram real or virtual? Simple question: as the title says, what makes a real Feynman diagram real, and what makes a virtual diagram virtual? Or in other words, how do I tell whether any given diagram is real or virtual? I've never gotten a really satisfying explanation of this. I would imagine it has something to do with virtual particles, but all internal propagators are virtual particles and I know for a fact that having internal lines doesn't make a diagram virtual. In my lecture, the lecturer said:      Let $K$ be the key generation algorithm. Given a security parameter represented in unary, $1^k$, $K(1^k)$ will output a keypair $(pk; sk)$, known as the public key and the private (or secret) key, respectively.    My question is: When I want to implement the cryptosystem, how should I represent this $1^k$?  When I implement the key generation procedure, do I literally require callers to pass me a string of $k$ one-bits that the procedure will never use?  And, if so, why is it there in the first place? Let $A$ be a $m \times n$ matrix with entries from some field $F$. Define the determinant rank of $A$ to be the largest possible size of a nonzero minor, i.e. the size of the largest invertible square submatrix of $A$. It is true that the determinant rank is equal to the rank of a matrix, which we define to be the dimension of the row/column space.  It's not difficult to see that $\text{rank} \geq \text{determinant rank}$. If some submatrix of $A$ is invertible, then its columns/rows are linearly indepedent, which implies that the corresponding rows/columns of $A$ are also linearly indepedent.  Is there a nice proof for the converse? "FTL" Communication with Quantum Entanglement? Can quantum entanglement make sending a message, whether audio, video, or even Morse code, instantaneous between two points (faster than it could travel normally at the speed of light)?  Let me first be clear, my question is not whether a message can travel faster than light. I simply mean whether a message can be generated here and then a copy of that message heard over there sooner than the message would normally be received.  Say a large number of entangled pairs are generated. One half the particles are given to Jack and the opposite ones to Sally. Jack then hops on a ship and travels 8 months to Mars. Sally then manipulates her particles in the form of a message. Do the corresponding opposite particles get manipulated simultaneously so that Jack receives the message instantly instead of the 16 light-minutes for a classically transmitted message? How do I get the browser to reask me to integrate with a website? I'm using  and I accidentally clicked "No" when asked if I want to integrate with the website.  How can I have Firefox or Chrome reask me to integrate the site with Ubuntu? Word or expression for a constituent that perfectly exemplifies the whole Suppose that  (1990) is considered appalling, but you can't put your finger on exactly why, mainly because there are a plethora of reasons, most of which you lack the training/education/expertise to comment in-depth on (e.g. the writing, directing, editing etc.), so you use what you consider to be a disastrous moment/scene as an example, and think "this pretty much sums it up", for example , what would you call a scene like that? A single word or expression is satisfactory.  As an example:     "The Godfather 3 is so bad, for so many reasons, but here is a ______ that perfectly represents everything wrong with the movie."   An expression is also acceptable, and the example I gave is flexible (doesn't have to be structured as it is in the example).