Since upgrading to MacTeX 2016 the following example no longer compiles as expected:  \documentclass{article} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{breqn}  \begin{document} \begin{align}  x &amp;= y, &amp;&amp; \text{(foo)} \end{align} \end{document}   with the text (foo) appearing a total of four times in four different sizes. The problem is due to the inclusion of breqn.  Without using breqn, or if using a previous version of MacTeX, everything is as expected.
MWE needs to be compiled with LuaTeX to reproduce the problem:  \documentclass[11pt]{report}% \usepackage{amsmath,mathtools} \usepackage{breqn}                          \begin{document} $J^{\ast} = \text{JFK} \to \text{NO} \to \text{SFO}$ \[ J^{\ast} = \text{JFK} \to \text{NO} \to \text{SFO} \] \end{document}   Gives (no compile error or any warning) the following strange output    I have to use breqn package. If I remove it, then I get the expected output    Is there a way to work around this, so I can use breqn and get correct output?  TL 2015. filelist: (compiled with lualatex)  This is LuaTeX, Version beta-0.80.0.1 (TeX Live 2015) (rev 5863)   *File List*   report.cls    2014/09/29 v1.4h Standard LaTeX document class   size11.clo    2014/09/29 v1.4h Standard LaTeX file (size option)  amsmath.sty    2013/01/14 v2.14 AMS math features  amstext.sty    2000/06/29 v2.01   amsgen.sty    1999/11/30 v2.0   amsbsy.sty    1999/11/29 v1.2d   amsopn.sty    1999/12/14 v2.01 operator names mathtools.sty    2015/11/12 v1.18 mathematical typesetting tools   keyval.sty    2014/10/28 v1.15 key=value parser (DPC)     calc.sty    2014/10/28 v4.3 Infix arithmetic (KKT,FJ)  mhsetup.sty    2010/01/21 v1.2a programming setup (MH)    breqn.sty    2015/08/11 v0.98d Breaking equations    expl3.sty    2015/12/20 v6326 L3 programming layer (loader)  expl3-code.tex    2015/12/20 v6326 L3 programming layer  l3pdfmode.def    2015/11/11 v6250 L3 Experimental driver: PDF mode flexisym.sty    2015/08/11 v0.98d Make math characters macros   cmbase.sym    2007/12/19 v0.92 mathstyle.sty    2015/08/11 v0.98d Tracking mathstyle implicitly graphicx.sty    2014/10/28 v1.0g Enhanced LaTeX Graphics (DPC,SPQR) graphics.sty    2014/10/28 v1.0p Standard LaTeX Graphics (DPC,SPQR)     trig.sty    1999/03/16 v1.09 sin cos tan (DPC) graphics.cfg    2010/04/23 v1.9 graphics configuration of TeX Live   pdftex.def    2011/05/27 v0.06d Graphics/color for pdfTeX infwarerr.sty    2010/04/08 v1.3 Providing info/warning/error messages (HO)  ltxcmds.sty    2011/11/09 v1.22 LaTeX kernel commands for general use (HO) supp-pdf.mkii pdftexcmds.sty    2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO) ifluatex.sty    2010/03/01 v1.3 Provides the ifluatex switch (HO)    ifpdf.sty    2011/01/30 v2.3 Provides the ifpdf switch (HO) luatex-loader.sty    2010/03/09 v0.4 Lua module loader (HO) epstopdf-base.sty    2010/02/09 v2.5 Base part for package epstopdf   grfext.sty    2010/08/19 v1.1 Manage graphics extensions (HO) kvdefinekeys.sty    2011/04/07 v1.3 Define keys (HO) kvoptions.sty    2011/06/30 v3.11 Key value format for package options (HO) kvsetkeys.sty    2012/04/25 v1.16 Key value parser (HO) etexcmds.sty    2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO) epstopdf-sys.cfg    2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live  ***********   Update  I found another case of duplication when using breqn, which does not involve \text at all. But the solution provided below also fixes this issue. I am adding this second case here for reference just in case it might be useful. Here is MWE  \documentclass[11pt]{article} \usepackage[T1]{fontenc} \usepackage{amsmath,mathtools} \usepackage{breqn} \begin{document} \[ \underset{\mathbf{S}} {\operatorname{arg\,min}}      \sum_{i=1}^{k} \sum_{\mathbf x \in S_i}       \left\| \mathbf x - \boldsymbol\mu_i \right\|^2  \] \end{document}   The output is    After adding the patch in the answer below the correct output is now given, which is
Backup with duplicity on Google Cloud Storage I have already set a backup routine that backups all my files to Amazon S3 using duplicity. I would like to create a similar backup routine with Google Cloud Storage. Is it possible to get duplicity to work with GCS? Show that $\ker \hat{T} = \text{ann}(\text{range } T)$ This is an old exam problem: Let $V$ and $W$ be finite dimensional vector spaces over a field $F$ and let $T: V \to W$ be a linear transformation. Define $\hat{T}: W^* \to V^*$ by $(\hat{T}(f))(v)=f(T(v))$. Here, $U^*$ denotes the dual vector space $U$. Since $\hat{T}$ is a linear transformation prove $\ker \hat{T} = \text{ann}(\text{range } T)$ where $\text{ann}(Y) = \{g \in U^* : g(y)=0 \text{ for all } y \in Y \}$ for a subspace $Y$ of vector space $U$.  I'm really not sure how to start this problem. Any advice would be great! Punctuations with relative pronouns Sogou is a Chinese search engine, which can search text, images, music and maps.  Is a comma required before "which" in the above sentence? Variance of Normal Order Statistics Suppose we have $X_1, \cdots, X_n \overset{\textrm{i.i.d.}}{\sim} \mathcal{N}(0, 1)$ with $n &gt; 50$, and let $X_{(1)}, \cdots, X_{(n)}$ be the associated order statistics. Are there any references pointing to formulas that specify (or estimate) the variance of the $k^{\textrm{th}}$ order statistic, i.e. $\textrm{Var}(X_{(k)})$, for $1 \leq k \leq n$? I am looking for formulas can be explicitly evaluated without resorting back to numerical integration.  I have seen this question: , which attracted a number of answers on approximate formula for the mean of the $k^{\textrm{th}}$ order statistic, e.g. Blom (1958) (and modifications based on work by Harter (1961) and Elfving (1947)). Searching on Google also yields a number of work on the variance / standard deviation for the $k^\textrm{th}$ order statistics for small $n$, all of them opting for a computation/tabulation route. They are: Godwin(1949), Teichroew (1956), and Parrish (1992). I have also attempted to derive something myself following the method sketched by @probabilityislogic in , along the lines of: $$\textrm{Var}(X_{(k)}) = \int_{-\infty}^{\infty} \left(x-\mathbb{E}(X)\right)^2 \frac{n!}{(k-1)!(n-k)!} f_X(x)[1-F_X(x)]^{n-k}[F_X(x)]^{k-1}\;\textrm{d}x,$$ with lower case $f$ denoting the PDF of a r.v. $X$, and upper case $F$ denoting the CDF. Noting $x = F^{-1}(F_X(x))$ and using the substitution $u = F_X(x)$ (with corresponding r.v. in upper case $U$), we have: $$\textrm{Var}(X_{(k)}) = \int_{0}^{1} \left(F_X^{-1}(u) - \mathbb{E}\left(F_X^{-1}(U)\right)\right)^2\,\mathcal{B}(u | k, n-k+1) \; \textrm{d}u,$$ where $\mathcal{B}$ denotes the PDF of a beta distribution (not the beta function). This can be rewritten as the variance based on the beta distribution: $$\textrm{Var}(X_{(k)}) = \textrm{Var}_{\mathcal{B}(u | k, n-k+1)}\left(F_X^{-1}(u)\right).$$ Approximating the RHS using (the variance bit of the) delta method, we get: $$\textrm{Var}_{\mathcal{B}(u | k, n-k+1)}\left(F_X^{-1}(u)\right) \approx \textrm{Var}_{\mathcal{B}(u | k, n-k+1)}(U) \cdot \left[(F_X^{-1})'\left(\mathbb{E}_{\mathcal{B}(u | k, n-k+1)}(U)\right)\right]^2,$$ where the prime denotes the derivative. The first term of the product is standard result. For the second part, given $(F^{-1})'(\cdot)=\frac{1}{f(F^{-1})(\cdot)}$ (see e.g. ), we then have: $$\textrm{Var}_{\mathcal{B}(u | k, n-k+1)}\left(F_X^{-1}(u)\right) \approx \frac{k(n-k+1)}{(n+1)^2(n+2)} \frac{1}{\left(f\left(F^{-1}\left(\frac{k}{n+1}\right)\right)\right)^2}.$$ Substituting in the standard normal distribution ($\phi$ for PDF, $\Phi$ for CDF) and scaling it to the desired variance $\sigma^2$ we arrive at: $$\textrm{Var}(X_{(k)}) \approx \frac{k(n-k+1)}{(n+1)^2(n+2)} \frac{1}{\left(\phi\left(\Phi^{-1}\left(\frac{k}{n+1}\right)\right)\right)^2},$$ which we can throw in a $\sigma^2$ term in front if it is not a standard normal. But surely someone must have derived that somewhere (again I am looking for some references), and there is a high chance that I have gone off track somewhere above. What is the formula for percent of frame filled at a specific distance and focal length? I am thinking about buying a new lens specifically to take photos of distant targets (birds, bears, etc). I currently own the Canon 70-300 IS USM, which is a nice lens, but I find that if I want to take a photo of anything further away than about 10 meters, the target does not fill a large amount of the frame (meaning I have to significantly crop in post production).  I am currently looking at the Canon prime 400mm, however I would like to determine at what distance an object will fill a reasonable proportion of the frame.  Is there a formula or rule of thumb I can apply that will help me in this situation? I realise the size of the target I am shooting will play a role here, so if we need to make an assumption about the size of the target please let me know. Converting string of 1s and 0s into binary value I'm trying to convert an incoming sting of 1s and 0s from stdin into their respective binary values (where a string such as "11110111" would be converted to 0xF7). This seems pretty trivial but I don't want to reinvent the wheel so I'm wondering if there's anything in the C/C++ standard libs that can already perform such an operation? This was a question my friend found in a book.  A block attached to a spring pulled by a constant horizontal force is kept on a smooth horizontal surface. Initially the spring is in its natural state. Then the maximum work that the applied force F can do is:  (a) $F^2/k$ (b) $2F^2/k$ (c) $4F^2/k$ (d) $F^2/2k$  My friend thought that the answer is (a) since the maximum displacement is $x=F/k$ and $W=Fx=F^2/k$. But he saw that the book's answer is different and he asked this question to me. I at first thought that the answer will be (a), but then I realised that this situation is somewhat similar to a charging capacitor. The final energy of the spring is actually $\frac12kx^2=F^2/2k$. So probably the answer is (d)? But the work done is still (a)? But the book says neither. It's (b). This is the logic in the book:  Method 1: in the book:  $$Fx=\frac12kx^2$$  $$x=2F/k$$  $$W=\frac12kx^2=2F^2/k$$  (since the book is an objective questions book it did not have detailed explanations)  What is wrong in the following methods?  Method 2: by calculating the maximum displacement  $$x=F/k$$  $$W=Fx=F^2/k.$$ Method 3: by calculating the final energy  $$x=F/k$$  $$\frac12kx^2=F^2/2k$$  PS: We both know calculus so don't hesitate to use it in the answers. Show us who submitted offensive and comment flags Chocolate and oil mixed When I melt 16 oz of chocolate I add 4 oz of oil how long can I keep this and how should it be stored. Someone said something about botulism ?? How do I get adequate depth of field in macro photography? I have been messing around with some Macro Photography using the techniques (and a reversal ring) described in a  by @ My main issue is that I am having a hard time getting the subject into focus. There are times when the center is blurred and the outside is in focus or the center in focus and the outside out of focus. What are ways to get as much of the subject in focus?   I am using a Nikon D5100, I have a 18-55mm kit lens but I find the 55-200mm lens easier to use for shooting. How to snap and align 2 objects Hi! I'm a beginner learner and I'd like to know how to snap these three objects. I'd like to snap the two cylinders with the different faces of the cube. The short one on the left and the highest cylinder on the top of the cube. I'd like to have the center of the cylinder aligned with the center of the cube (the base of the cylinder inscribed into the face of the cube)  I'm sorry for bad explanation I hope someone can help me  Thanks!   I add a screenshoot in which you can see what I have to do   Thanks again if someone can help me with this! $A^A$ in category of graphs (reference is Lawvere/Schanuel, Session 31, Ex. 1)  I'm trying to calculate the exponential object $A^A$ and its evalution map $e \colon A \times A^A \to A$ in the category of graphs, where $A$ is the "arrow graph" (ie. one arrow and two dots).  In the following, $D$ is the graph with one dot and no arrows, $1$ is the terminal object in this category (graph with one dot and one arrow, the loop).  So far I have:   The points of $\mathbf{1}\to A^A$ correspond to the maps $A\to A$ (via two standard isomorphisms), and since $\mathbf{1}$ is the loop, and there is one map of graphs $A \to A$, there is one loop in $A^A$. The dots $D\to A^A$ correspond to the maps $A \times D \to A$, of which there are four, hence four dots in $A^A$. The arrows $A \to A^A$ correspond to the maps $A \times A \to A$, of which there are four, hence four arrows in $A^A$.   But I'm stuck on how to put these together to constitute $A^A$ and its evaluation map. Can "Wow!" be a sentence? The question is clear. Can "Wow!" be a sentence?  Imagine a hypothetical context where I'd utter something like this:     Wow! What an amazing idea! I should think about a way to push this fix.   We see "wow" in casual speech often. It bears punctuation marks (typically an exclamation mark, denoting the rising intonation) and a capital letter &mdash; just like all "regular" sentences.  On the other hand, neither Wow! nor What an amazing idea! contain any verbs. These certainly don't have any parts of speech in the other sentence, so what are they? Are they sentences or clauses? In other words, can "Wow!" be a sentence despite its lack of [any implied] verbs, and subsequently lack of any distinguishable predicates?  Please back up your answers with references. Prime ideal and nilpotent elements "Much more easy" versus "much easier" Is  (i.e. repulsive gravity) possible in string theory?  I have read some articles about scientists making assumptions about the existence of anti-gravity, but is it possible in string theory? $X_n\leq Y_n$ implies $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$ Can anyone prove this question? I tried but I didn't get any I idea, so I hope someone can solve it.     Let $X_n\leq Y_n$ for each $n\in \Bbb N$. Show that $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$.   Please prove this question - thanks.  The definition I have:     Let $X_n$ be a sequence in real number and let $$E=\{x\in \Bbb R^\sharp:(X_{n_k}) \rightarrow x \text{ for some subsequence }(X_{n_k})\text{ of }(X_n)\}$$ for all $n \in \Bbb N$ and $k$ from $1$ to $\infty$. Then by definition $\lim\sup X_n = \sup E$ and $\lim\inf X_n = \inf E$. Am I going to have trouble flying without my full name on the ticket? Which is the rarest badge awarded/the least popular one/the one hardest to get? How does an accelerating charge radiate electromagnetic waves?