Reinhardt's shield blocks most enemy projectiles and bullets but there are certain attacks which can go right through it. Which attacks ignore Reinhardt's shield?
Reinhardt's main strength is his shielding abilities and the protection he provides for his team, but Are there any abilities that cannot be blocked by Reinhardt's barrier field?
I'm having some difficulty understanding how to interpret variable importance output from the Random Forest package. Mean decrease in accuracy is usually described as "the decrease in model accuracy from permuting the values in each feature".   Is this a statement about the feature as a whole or about specific values within the feature? In either case, is the Mean Decrease in Accuracy the number or proportion of observations that are incorrectly classified by removing the feature (or values from the feature) in question from the model?   Say we have the following model:  require(randomForest) data(iris) set.seed(1) dat &lt;- iris dat$Species &lt;- factor(ifelse(dat$Species=='virginica','virginica','other')) model.rf &lt;- randomForest(Species~., dat, ntree=25, importance=TRUE, nodesize=5) model.rf varImpPlot(model.rf)     Call:  randomForest(formula = Species ~ ., data = dat, ntree = 25,  proximity = TRUE, importance = TRUE, nodesize = 5)  Type of random forest: classification Number of trees: 25 No. of variables tried at each split: 2          OOB estimate of  error rate: 3.33% Confusion matrix:           other virginica class.error other        97         3        0.03 virginica     2        48        0.04     In this model, the OOB rate is rather low (around 5%). Yet, the Mean Decrease in Accuracy for the predictor (Petal.Length) with the highest value in this measure is only around 8.   Does this mean that removing Petal.Length from the model would only result in an additional misclassification of 8 or so observations on average?   How could the Mean Decrease in Accuracy for Petal.Length be so low, given that it's the highest in this measure, and thus the other variables have even lower values on this measure? Measures: Atom Definitions Let $\Omega$ be a measure space with measure $\mu$. (Here, a measure is only meant to be countable additive!)  Consider a subset $A\in\Sigma$.  Then according to the  it is an atom if: $$(1)\quad\forall E\subseteq A:\quad\mu(E)&lt;\mu(A)\implies\mu(E)=0\quad(\mu(A)&gt;0)$$ and according to the  it is an atom if: $$(2)\quad\forall E\in\Sigma:\quad\mu(E\cap A)=0\lor\mu(E^c\cap A)=0\quad(\mu(A)&gt;0)$$  Now, these definitions agree for the really trivial cases: $$\mu\equiv0$$ $$\mu\equiv\infty$$ but they differ for the less trivial case: $$\quad\mu(E\neq\varnothing):=\infty,\,\mu(\varnothing):=0$$ namely the atoms are w.r.t. (1) all nonempty subsets whereas w.r.t. (2) only the singletons.  Excluding this pathological case, are the definitions equivalent? (More precisely, assume there exists a measurable subset $0&lt;\mu(F)&lt;\infty$.)  So far I checked that: $$(2)\implies(1):\quad\mu(E)&lt;\mu(A)\implies\mu(A\setminus E)&gt;0\implies\mu(E)=0$$ but what about the other direction? Finitely generated group which is not finitely presented Is there any easy group theoretical way of showing that the wreath product $G$ of two infinite cyclic groups is not finitely presented?  I was looking for a finitely presented group with a central subgroup isomorphic to the free group of countable rank and whose factor group is isomorphic to $G$; in this way assuming that $G$ is finitely presented we get a contradiction.   Any ideas? How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$? I was trying to install minted package in TeXLive. I installed it and then run sudo tlmgr update --all. It was running slow so I stopped it using Ctrl+Z in an ubuntu terminal and then I run sudo tlmgr update --list. After that I installed texlive-latex-extra and python-pygments. Later on I run sudo tlmgr update --all again and let it finish.  After that I am trying to run a simple code using listings and greek but I get an error     Bad Character code (256)   A MWE that illustrated the problem is the following  \documentclass{book}  \usepackage[english,greek]{babel} \usepackage[iso-8859-7]{inputenc} % %\usepackage[utf8]{inputenc} \usepackage{kerkis} \usepackage{pifont} % %  \newcommand{\sw}{\selectlanguage{english}} \newcommand{\sq}{\selectlanguage{greek}} \newcommand{\eng}[1]{\latintext#1\greektext} \newcommand{\gre}[1]{\greektext#1\latintext}  \usepackage{xcolor} \usepackage{listings} \usepackage{textcomp}  \definecolor{listinggray}{gray}{0.9} \definecolor{lbcolor}{rgb}{0.9,0.9,0.9}  \lstdefinestyle{JavaStyle}{         backgroundcolor=\color{lbcolor},     tabsize=4, %   rulecolor=,     language=Java,      % choose the language of the code         basicstyle=\scriptsize,     % the size of the fonts that are used for the code         upquote=true,         aboveskip={1.5\baselineskip},         columns=fixed,         showstringspaces=false,         extendedchars=false,         breaklines=true,         prebreak = \raisebox{0ex}[0ex][0ex]{\ensuremath{\hookleftarrow}},         frame=single,         numbers=left,         showtabs=false,         showspaces=false,         showstringspaces=false,         identifierstyle=\ttfamily,         keywordstyle=\color[rgb]{0,0,1},         %commentstyle=\color[rgb]{0.026,0.112,0.095},         commentstyle=\itshape\color{green!40!black},         stringstyle=\itshape\color{red!90!black},         numberstyle=\itshape\color{yellow!50!black} }  \lstdefinestyle{CppStyle}{         backgroundcolor=\color{lbcolor},     tabsize=4, %   rulecolor=,     language=C++,       % choose the language of the code         basicstyle=\scriptsize,     % the size of the fonts that are used for the code         upquote=true,         aboveskip={1.5\baselineskip},         columns=fixed,         showstringspaces=false,         extendedchars=false,         breaklines=true,         prebreak = \raisebox{0ex}[0ex][0ex]{\ensuremath{\hookleftarrow}},         frame=single,         numbers=left,         showtabs=false,         showspaces=false,         showstringspaces=false,         identifierstyle=\ttfamily,         keywordstyle=\color[rgb]{0,0,1},         %commentstyle=\color[rgb]{0.026,0.112,0.095},         commentstyle=\itshape\color{green!40!black},         stringstyle=\itshape\color{red!90!black},         numberstyle=\itshape\color{yellow!50!black} } \begin{document}  This is a dummy text. kjhbki \end{document}   The .aux file says  \relax  \select@language{greek} \@writefile{toc}{\select@language{greek}} \@writefile{lof}{\select@language{greek}} \@writefile{lot}{\select@language{greek}}   while the .log file can be found   Any idea why is this happening and how to fix this? Note that if I remove the listings preamble, delete all produced files and build the document, everything works fine. Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$ $T(0)=1 \\ T(n) = 1 + \sum_{j=0}^{n-1}T(j) \\ $  Show that $T(n) = 2^n$.  I know how to prove this by induction, but I would like to know how to show this using first principles.  Edit: The way I want to solve this problem is manipulate $T(n)$ in such a way that it ends up as $2^n$. Finding the limit of $(1-\cos(x))/x$ as $x\to 0$ with squeeze theorem How do I find:  $$ \lim_{x\to0}\frac{1-\cos(x)}{x} $$  Using the squeeze theorem.  Particularly, how would I arrive at its bounding functions?   If possible, please try not to use derivatives. Where to find the Mac OS X Lion security configuration guide? What is IEEE 802.3 Ethernet's communication type: Synchronous or Asynchronous? In the IEEE 802.3 frame structure there is a 7 byte preamble section for synchronization. If it is really for synchronization does that mean Ethernet is synchronous and not asynchronous?    Ethernet structure for reference: If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely Assume that $X$ and $Y$ are two random variables such that $Y=E[X|Y]$ almost surely and $X= E[Y|X]$ almost surely. Prove that $X=Y$ almost surely.   The hint I was given is to evaluate: $$E[X-Y;X&gt;a,Y\leq a] + E[X-Y;X\leq a,Y\leq a]$$  which I can write as: $$\int_A(X-Y)dP +\int_B(X-Y)dP$$ where $A=\{X&gt;a, Y\leq a\}$ and $B=\{X\leq a,Y\leq a\}$.  But I need some more hints. I am trying to print a simple value for $AR1_p1 but the variable $i is not evaluating. for i in 1 2 3 4 do     AR1_p1=22     AR1_p2=23     AR1_p3=24     AR1_p3=25     echo $AR1_p$i done   It's like concatenating dynamically. Any suggestions on how to fix this?. How are the AES S-Boxes calculated? I'm trying to understand how the AES S-Boxes are calculated. I understand how the multiplicative inverse is calculated over $GF(2^8)$, but I'm confused by the description of the affine transformation. I haven't been able to Google a good explanation of how the S-Box values are calculated. Can someone explain how this works, starting after the calculation of the multiplicative inverse? Why is every Noetherian zero-dimensional scheme finite discrete? Adding HTML entities using CSS content How do you use the CSS content property to add HTML entities?  Using something like this just prints &amp;nbsp; to the screen instead of the non-breaking space:  .breadcrumbs a:before {     content: '&amp;nbsp;'; } I cannot remember anyone writing the letter epsilon in any other way than \varepsilon in any math class; but in LaTeX \epsilon and \varepsilon are different symbols. Do any of you know why there are two different symbols? (I.e. if \epsilon is the correct way to write the letter epsilon, why aren't mathematicians using it, and when is, according to the standards today, the correct situation to use each of the symbols?) So I have a generic list, and an oldIndex and a newIndex value.  I want to move the item at oldIndex, to newIndex...as simply as possible.  Any suggestions?  Note  The item should be end up between the items at (newIndex - 1) and newIndex before it was removed. Let $R \simeq S$ be isomorphic commutative rings with unity. Prove the following:  a). If $R$ is an integral domain then $S$ is an integral domain.  For this, I said that If I let $f: R \to S$ be an isomorphism and $(R, + , \circ), (S, \oplus, \ast)$, then let $x, y\in R$,  such that $x \circ y = 0_R$, because $f$ is an isomorphism, $f(x \circ y) = f(x) \ast f(y) = f(0_R)$. If I let $R$ be an integral domain then, as per the definition $R$ is commutative, has unity, and no zero divisors.   So $f(x \circ y) = f(x) \ast f(y) = f(0_R)$ where we have either $f(x \circ y) = f(0_R) \ast f(y) = f(0_R)$ or $f(x \circ y) = f(x) \ast f(0_R) = f(0_R)$.   Since $f$ is an isomomorphism, let $s = f(x), t = f(y)| s,t \in S$. Then $s \ast t = f(0_R)$. By definition, $S$ also has unity so $0_S$ exists. If we map $0_R \to 0_S$. Then either $s = 0_S$ or $t = 0_S$.   So then, since $S$ has unity, is commutative, and has a no zero divisors as we showed above, it is also an Integral domain.  I'm not sure I have this correctly.  b). If $R$ is a field then $S$ is a field. I don't really understand how to do this one. Since $S$ is an integral domain, it has a $0_S$. So I need to show that $S$ distributes $\ast$ over $\oplus$.  Any help with these is appreciated \varepsilon vs. \epsilon Define functions in structs Is is possible to convert a .vdi file into a .iso that can be burned to a cd or dvd and make it like an installer. Or Is it possible to convert virtual machines to physical environments?