How to line up the "&" to make tables readable in code
Aligning table within latex editor
sed : Ignore line starting whitespace for match What are the advantages of stacking multiple LSTMs? What are the advantages, why would one use multiple LSTMs, stacked one side-by-side, in a deep-network? I am using a LSTM to represent a sequence of inputs as a single input. So once I have that single representation— why would I pass it through again?  I am asking this because I saw this in a natural-language generation program. Below is experimental data for the ratio $$R=\frac{\sigma(e^+e^-\rightarrow hadrons)}{\sigma(e^+e^-\rightarrow\mu^+\mu^-)}$$ as a function of the centre of mass energy $\sqrt s$. I am interested in the peak at around $100GeV$ which corresponds to the resonance of the $Z^0$ boson. There are two ways of looking at this that I have in mind:  We can effectively ignore the electromagnetic process around this energy, and so each process should have it's own Breit-Wigner peak centred on the mass energy of the $Z^0$. The ratio of these is just a constant. Thinking in terms of Feynman rules and again ignoring the electromagnetic process around this region, each process has the same propagator and vertex factors (roughly - ignore quark mixing) and there are some extra factors due to different quarks being possible and colour degeneracy, but still the ratio should be a constant (one possible issue here is interference between Feynman diagrams which I have neglected?).  So my question is why does the peak exist in the data? Why can "trans" be replaced with an x? I can't think of an example, so I may be wrong about this, but I think I've seen people replace the prefix "trans" as in transport with an x. "Cross" makes sense, as in "railroad crossing", and I guess "chris" is sort of a punny extension, the extension being like "chris cross" and the example being "xmas", but why trans? Allow horizontal scrolling of long math expressions Stack Exchange formats math, but often the formatted math is wider than the screen. It would be nice if formatted math were scrollable the same way that formatted code wider than the screen is scrollable. Does Google use the Meta Description Tag for Description of Page? The  feat (PHB, p. 168) says:     While you are wielding a glaive, halberd, pike, or quarterstaff, other creatures provoke an opportunity attack from you when they enter your reach.   The  feat (PHB, p. 170) says:     When a hostile creature's movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, rather than making an opportunity attack. The spell must have a casting time of 1 action and must target only that creature.   On this very topic, Mearls has :     Q: Do Polearm Master and War Caster combine to allow a magic user to make a spell opportunity attack when they enter reach?   A: No - polearm master applies only if you use the weapons it lists to make the attack     Another question on this very topic:   But since then, we now have spells like  (SCAG, p. 142):     As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails. On a hit, the target suffers the attack’s normal effects, and it becomes sheathed in booming energy until the start of your next turn. If the target willingly moves before then, it immediately takes 1d8 thunder damage, and the spell ends.    So, with the addition of booming blade, if I have a quarterstaff + War Caster + Polearm Master, could I use my reaction to cast booming blade if someone steps into my reach? How to solve "sudo: /etc/sudoers.d is world writable" R: loading a table with number as the column heading all were wrongly added a X, how to solve it? How can I create an AddIn to ArcGIS Pro and where can I find it from ArcGIS Pro application? Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$ Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$   I can not understand how to prove it. Please help me. Find coefficient of $x^{50}$ in $(\sum_{i=1}^{\infty}x^n)^3$ What's the best order to read HP Lovecraft's novels? I've always been interested in the Cthulhu mythos and I wanted to get into HP Lovecraft's books. What is the best book to start with? I know that Cthulhu was first mentioned in Lovecraft's Call of Cthulhu in 1928. Is that the best book to start with? Should I just start reading Lovecraft's books from his first publication onward? Understanding a particular evaluation of $\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right)$ I'm having a hard time understanding the following evaluation of the infinite product  $$ \prod_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right).$$ In particular, I don't understand how you go from line 2 to line 3. Here $\omega = -\frac{1}{2}+ i \frac{\sqrt{3}}{2}$, which is a primitive third root of unity.  $$\begin{align}\prod_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right)  &amp;=\prod_{n=2}^{\infty}\frac{(n-1)(n^2+n+1)}{n^3} \\  &amp;=\lim_{m\to\infty}\frac{1}{m}\prod_{n=2}^m\frac{(n-\omega)(n-\omega^2)}{n^2} \\  &amp;=\lim_{m\to\infty}\frac{\Gamma(m+1-\omega)\Gamma(m+1-\omega^2)}{m(m!)^2\Gamma(-\omega)\Gamma(-\omega^2)(1-\omega)(1-\omega^2)(-\omega)(-\omega^2)} \\  &amp;=\frac{1}{3\Gamma(-\omega)\Gamma(-\omega^2)} \\ &amp;=\frac{\sin{\pi(-\omega)}}{3\pi} \\  &amp;=\frac{\cosh (\frac{\sqrt{3}\pi}{2})}{3\pi } \end{align}$$ EDIT: I think I'm starting to make sense out of this by writing out the terms. $$ \begin{align} \prod_{n=2}^{m} \frac{(n- \omega)(n-\omega^{2})}{n^{2}} &amp;= \frac{(2-\omega)(3-\omega) \cdots (m- \omega)(2-\omega^{2})(3-\omega^{2})\cdots (m- \omega^{2})}{2^{2} \cdot 3^{2} \cdot \cdots  \cdot m^{2}}  \\ &amp;= \frac{1}{(m!)^{2}} \frac{\Gamma(m+1-\omega)}{(1-\omega)(-\omega)\Gamma(-\omega)} \frac{\Gamma(m+1-\omega^{2})}{(1-\omega^{2})(-\omega^{2})\Gamma(-\omega^{2})} \end{align}$$ Now I have to figure out how to take the limit as $m \to \infty$. How exactly to compute the ridge regression penalty parameter given the constraint? The accepted answer in  does a great job of showing that there is a one-to-one correspondence between $c$ and $\lambda$ in the two formulations of the ridge regression: $$ \underset{\beta}{min}(y-X\beta)^T(y-X\beta) + \lambda\beta^T\beta $$ and  $$ \underset{\beta}{min}(y-X\beta)^T(y-X\beta) \text{ s.t. }\beta^T\beta\leq{c} $$  The linked answer shows this in the orthogonal case.    In a general (non-orthogonal case), how can I compute $\lambda$ from $c$?  Update Here is an answer for going from $\lambda$ to $c$:   Assuming that the coefs are constrained by the penalty, $$ \beta^T\beta = c $$ and  $$ \beta = (X^TX + \lambda I)^{-1}X^Ty\\ \beta^T\beta = c = \beta^T(X^TX + \lambda I)^{-1}X^Ty $$  Still working on going the other way find an approximate solution, up to the order of epsilon The question is to find an approximate solution, up to the order of epsilon of following problem.  $$y'' + y+\epsilon y^3 = 0$$ $$y(0) = a$$ $$y'(0) = 0$$  I tried to solve the given problem using perturbation theory.  $$y(t) = y_0(t) + \epsilon y_1(t) + \epsilon^2 y_2(t) + \cdots$$ $$t = w(\epsilon)t = (1 + \epsilon w_1 + \epsilon^2 w_2 + \cdots )t$$  However, i failed to find an appropriate approximate solution... help me!! Setting a fill and border is pretty easy in apps like Illustrator and Gravit Designer but in Blender. I've found it to be more tedious as I can't find anything online to solve this problem.  The picture above is a simple 2d mouth with lips. I would like to be able to move the lips and still have a fill but in Blender I needed to add another path for the mouth. Is there anyway I can move my lips path while having it also take the exact same shape (but not material) as my mouth's path?    (454.2 KB)  I work in Blender 2.79 cause 2.8 doesn’t run well on my laptop at all. ResultSet: Retrieving column values by index versus retrieving by label When using JDBC, I often come across constructs like    ResultSet rs = ps.executeQuery(); while (rs.next()) {     int id = rs.getInt(1);     // Some other actions }   I asked myself (and authors of code too) why not to use labels for retrieving column values:    int id = rs.getInt("CUSTOMER_ID");   The best explanation I've heard is something concerning performance. But actually, does it make processing extremely fast? I don't believe so, though I have never performed measurements. Even if retrieving by label would be a bit slower, nevertheless, it provide better readability and flexibility, in my opinion. So could someone give me good explanation of avoiding to retrieve column values by column index instead of column label? What are pros and cons of both approaches (maybe, concerning certain DBMS)? How can I make two columns in two columns How can I make two columns in two columns same as in the picture? Completing a 3x3 correlation matrix: two coefficients of the three given I was asked this question in an interview.  Lets say we have a correlation matrix of the form \begin{bmatrix}1&amp;0.6&amp;0.8\\0.6&amp;1&amp;\gamma\\0.8&amp;\gamma&amp;1\end{bmatrix}  I was asked to find the value of gamma, given this correlation matrix. I thought I could do something with the eigenvalues, since they should be all greater than or equal to 0.(Matrix should be positive semidefinite) - but I don't think this approach will yield the answer. I am missing a trick.  Could you please provide a hint to solve for the same?