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Using mask as a garbage matte to hide an object Variation of Pythagorean triplets: $x^2+y^2 = z^3$ Explanation of seasons in "A Song of Ice and Fire" Which textbook is good for introductory group theory? How do I pipe colored diff output to less? How can I set CSS only for specific IE browsers? Is it possible to reconstruct the Hamiltonian from knowledge of its ground state wave function? Is it possible to "construct" the Hamiltonian of a system if its ground state wave function (or functional) is known? I understand one should not expect this to be generically true since the Hamiltonian contains more information (the full spectrum) than a single state vector. But are there any special cases where it's possible to obtain the Hamiltonian? Some examples would be really helpful. How do I make Units efficiently? I just blew almost all my money on a really cool lookin' ship. How do I regain solvency without spending a lot of time fiddling around in my inventory?  At the moment I've found a sequence of steps that'll turn 50 carbon and 100 Plutonium into ~5000 Units (by creating Suspension Fluid and then turning it into Electron Vapor). Are there better recipes or sequences of recipes I should look for? Or should I just drop the whole thing and go mine a particular mineral? How is it possible in Eclipse JDT to convert a multiline selection to String. Like the following  From:  xxxx yyyy zzz   To:  "xxxx " + "yyyy " + "zzz"   I tried the following template   "${line_selection}${cursor}"+   but that way I only get the whole block surrounded not each line separately. How can I achieve a multiline processing like commenting the selected block? Execute command from file in current shell I want to executed command from file (which is script) in current shell in terminal.  Example: I have file ch_dir contains following:  #!/bin/bash cd /usr   Now if I execute file usually as following then it executes commands in different shell:  pandya@pandya-desktop:~$ ./ch_dir pandya@pandya-desktop:~$   Here cd /user is executed in different shell.  But I want to execute in Current shell. How do I do that?  Note: Here cd is only used to explain. Question's aim is to execute any command in current shell How to properly typeset multiletter quantities, e.g. Re or Nu (Reynolds, Nusselt numbers) If we look at light as a collection of little particles, we can say that dimmer light has its photons more spread out.  But if we look at light as a wave, then there no gaps unless specifically placed there on purpose.  So how can one interpret the formation of gaps between the photons? Axiom of Choice: Family of non-empty sets mutually disjoint or not? In a topological space, why the intersection only has to be finite? I was wondering if there is a reason why in the definition of a topologic space, the reunion of any collection of open sets is also an open set but the intersection has to be finite to be a set.  Is there because of the definition of an open set itself ? I have always seen it as a definition, but now I want to know why.  Thanks for your help. 3D arrows with TikZ Asymptote does give 3D arrows when drawing three dimensional figures (they even have shade!). Could we fake it with TikZ? Here's an example, manually written, with just one arrow worked:  \documentclass{scrartcl} \usepackage{tikz} \usetikzlibrary{arrows.meta} \begin{document} \begin{tikzpicture}[-&gt;,scale=2]   \draw[&gt;={Triangle[width=3pt,length=5pt]}] (0,0,0) -- (1,0,0);   \draw[&gt;={Triangle[width=3pt,length=5pt]}] (0,0,0) -- (0,1,0);   \draw[&gt;={Circle[sep=-.9pt,width=3.08pt,length=2pt]Triangle[width=3pt,length=5pt]}] (0,0,0) -- (0,0,1); \end{tikzpicture} \end{document}     But that's (wrongly) manually calculated by trial and error (apart from the fact that it's not perfect, seeing how the other two axis —x and y— are oriented, it should have certain slant). It would be nice to have an interface like the other arrows  &gt;={3D[length=⟨real length⟩,width=⟨real width of the base⟩]}   Which would then calculate from those values (and, of course, also taking into account x=⟨x vect⟩,y=⟨y vect⟩,z=⟨z vect⟩)  Circle[sep=⟨value⟩,width=⟨value⟩,length=⟨value⟩,slant=⟨value⟩] Triangle[width=⟨value⟩,length=⟨value⟩] % And I'm not sure if `slant=⟨value⟩`                                        % is necessary in this Triangle case   Example  Using the code from the answer (thanks to Symbol1), for instance, this code (taking the idea from another question, link in the comments)  \begin{tikzpicture}[x={(0cm,1cm)},                     y={({cos(30)*1cm},{sin(30)*-1cm})},                     z={({cos(20)*1cm},{sin(20)*1cm})},                     thick,                     scale=3]   \pgfmathsetmacro{\ax}{.4}   \pgfmathsetmacro{\ay}{.6}   \pgfmathsetmacro{\az}{-.6}   \pgfmathsetmacro{\bx}{.4}   \pgfmathsetmacro{\by}{-.7}   \pgfmathsetmacro{\bz}{-.8}   \draw[densely dotted,thin] (\ax,\ay,\az) -- (\ax,0,\az);   \draw[densely dotted,thin] (\ax,\ay,\az) -- (0,\ay,\az);   \draw[densely dotted,thin] (\ax,0,0) -- (\ax,0,\az) -- (0,0,\az);   \draw[densely dotted,thin] (0,0,\az) -- (0,\ay,\az) -- (0,\ay,0);   \draw[densely dotted,thin] (\bx,\by,\bz) -- (\bx,0,\bz);   \draw[densely dotted,thin] (\bx,\by,\bz) -- (0,\by,\bz);   \draw[densely dotted,thin] (\bx,0,0) -- (\bx,0,\bz) -- (0,0,\bz);   \draw[densely dotted,thin] (0,0,\bz) -- (0,\by,\bz) -- (0,\by,0);   \draw[-{Cone3}] (0,0,0) -- (1,0,0) node[right] {$x$};   \draw[-{Cone3}] (0,0,0) -- (0,1,0) node[above right] {$y$};   \draw[-{Cone3}] (0,0,0) -- (0,0,1) node[below right] {$z$};   \draw[-{Cone3}] (0,0,0) -- (0,0,-1) node[above left] {$-z$};   \draw[thin] (0,0,0) -- (0,-.9,0);   \draw[-{Cone3}] (0,0,0) -- (\ax,\ay,\az) node[below left] {source};   \draw[-{Cone3}] (0,0,0) -- (\bx,\by,\bz) node[above right] {sim}; \end{tikzpicture}   gives this figure Determine if Type is a pointer in a template function A 10th level Drow warlock (for instance) has the following Drow Magic racial trait (PHB p. 24), in addition to its warlock spellcasting abilities:  You know the dancing lights cantrip. When you reach 3rd level, you can cast the faerie fire spell once per day. When you reach 5th level, you can also cast the darkness spell once per day. Charisma is your spellcasting ability for these spells.  Can the Drow warlock cast faerie fire (which is not on the warlock spell list) using a warlock spell slot? Can it cast darkness (which is on the warlock spell list) using a warlock spell slot?  The  says this about the Magic Initiate feat:  If you’re a spellcaster, can you pick your own class when you gain the Magic Initiate feat? Yes, the feat doesn’t say you can’t. For example, if you’re a wizard and gain the Magic Initiate feat, you can choose wizard and thereby learn two more wizard cantrips and another 1st-level wizard spell. If you have spell slots, can you use them to cast the 1st-level spell you learn with the Magic Initiate feat? Yes, but only if the class you pick for the feat is one of your classes. For example, if you pick sorcerer and you are a sorcerer, the Spellcasting feature for that class tells you that you can use your spell slots to cast the sorcerer spells you know, so you can use your spell slots to cast the 1st-level sorcerer spell you learn from Magic Initiate. Similarly, if you are a wizard and pick that class for the feat, you learn a 1st-level wizard spell, which you could add to your spellbook and subsequently prepare.  But this specifically requires you to pick the feat for one of your classes to be able to cast the spell learnt using your class spell slots, and does not seem directly applicable. A Warlock can use warlock Pact Magic spell slots to cast spells learnt from levels of another spellcasting class, per the multiclass spellcasting rules (PHB p. 164):  If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.  Similarly, if the warlock has learnt the invocation Mask of Many Faces (PHB p. 112)...  You can cast disguise self at will, without expending a spell slot.  ...Can the warlock cast disguise self using a spell slot, e.g. to decrease the chance it can be dispelled? In statistical learning, implicitly or explicitly, one always assumes that the training set $\mathcal{D} = \{ \bf {X}, \bf{y} \}$ is composed of $N$ input/response tuples $({\bf{X}}_i,y_i)$ that are independently drawn from the same joint distribution $\mathbb{P}({\bf{X}},y)$ with  $$ p({\bf{X}},y) = p( y \vert {\bf{X}}) p({\bf{X}}) $$  and $p( y \vert {\bf{X}})$ the relationship we are trying to capture through a particular learning algorithm. Mathematically, this i.i.d. assumption writes:  \begin{gather} ({\bf{X}}_i,y_i) \sim \mathbb{P}({\bf{X}},y), \forall i=1,...,N \\ ({\bf{X}}_i,y_i) \text{ independent of } ({\bf{X}}_j,y_j), \forall i \ne j \in \{1,...,N\} \end{gather}  I think we can all agree that this assumption is rarely satisfied in practice, see this related  and the wise comments of @Glen_b and @Luca.  My question is therefore:      Where exactly does the i.i.d. assumption becomes critical in practice?    [Context]   I'm asking this because I can think of many situations where such a stringent assumption is not needed to train a certain model (e.g. linear regression methods), or at least one can work around the i.i.d. assumption and obtain robust results. Actually the results will usually stay the same, it is rather the inferences that one can draw that will change (e.g. heteroskedasticity and autocorrelation consistent HAC estimators in linear regression: the idea is to re-use the good old OLS regression weights but to adapt the finite-sample behaviour of the OLS estimator to account for the violation of the Gauss-Markov assumptions).   My guess is therefore that the i.i.d. assumption is required not to be able to train a particular learning algorithm, but rather to guarantee that techniques such as cross-validation can indeed be used to infer a reliable measure of the model's capability of generalising well, which is the only thing we are interested in at the end of the day in statistical learning because it shows that we can indeed learn from the data. Intuitively, I can indeed understand that using cross-validation on dependent data could be optimistically biased (as illustrated/explained in ).   For me i.i.d. has thus nothing to do with training a particular model but everything to do with that model's generalisability. This seems to agree with a paper I found by Huan Xu et al, see "Robustness and Generalizability for Markovian Samples" .   Would you agree with that?  [Example]   If this can help the discussion, consider the problem of using the LASSO algorithm to perform a smart selection amongst $P$ features given $N$ training samples $({\bf{X}}_i,y_i)$ with $\forall i=1,...,N$ $$ {\bf{X}}_i=[X_{i1},...,X_{iP}] $$ We can further assume that:   The inputs ${\bf{X}}_i$ are dependent hence leading to a violation of the i.i.d. assumption (e.g. for each feature $j=1,..,P$ we observe a $N$ point time series, hence introducing temporal auto-correlation) The conditional responses $y_i \vert {\bf{X}}_i$ are independent. We have $P \gg N$.    In what way(s) does the violation of the i.i.d. assumption can pose problem in that case assuming we plan to determine the LASSO penalisation coefficient $\lambda$ using a cross-validation approach (on the full data set) + use a nested cross-validation to get a feel for the generalisation error of this learning strategy (we can leave the discussion concerning the inherent pros/cons of the LASSO aside, except if it is useful). Given fields $K\subseteq L$, why does $f,g$ relatively prime in $K[x]$ imply relatively prime in $L[x]$? What item bonuses apply to my follower? There are a lot of different side effects an item can have, and I assume that things like magic find have no influence on any of "our" found items at all.  However, I'm not sure about other things. For example:   Do followers get life-steal on weapons, too? Does increased orb healing make any difference? What about +experience after kills? Will my follower level up faster?   and probably a lot more.  Is there some general rule as to what effects of an item apply to followers, and which don't?