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How can I set the drawableRight resource via code? drawing different parts of a line in different colours How to draw different parts of a line in different colours. In the following code can each part of the line be drawn in different colour      \documentclass{beamer} \beamertemplatenavigationsymbolsempty \usepackage{tikz} \usepackage{pgfplots} \begin{document} \begin{frame}[fragile,t] \frametitle{} { \begin{tikzpicture} \draw [thick, green] (2.3,1.4) +(-27:2.2cm)-- +(153:2.2cm) +(42:1.88cm) -- +(-138:1.88cm); \end{tikzpicture} } \end{frame} \end{document} I'm running macOS 10.15 Catalina Beta.  When I try to install Spotify I see the following error:    Is this a Spotify issue or a Catalina issue?  Thanks. How can I download this flash game for offline play? is one of the best flash games ever.    Is there some way to download it, so that I can play it offline? What should children call a step-grandparent? My mom remarried to a great guy who has been absolutely wonderful to my kids. Ever since my mom and he were dating my kids have called him Mr. Joe. Lately my mom has been bugging me to get the kids to call him Grampa.  I agree that he deserves more respect than Mr.  The problem is that he isn't their real grampa so I don't really want them calling him that. Does anybody have any suggestions on what we should have the kids call him? They are 9 and 12 years old.  EDIT: I appreciate the comments regarding different variations of grampa and hearing how others have no issues with calling their step-granddad grampa. But I was hoping maybe someone has some suggestions for names that show the importance of the step-granddad without calling him some variation of the grampa name but still has a feeling of warmth and family in the name (I hope that makes sense). Is there a statement whose undecidability is undecidable? We know there are statements that are undecidable/independent of ZFC. Can there be a statement S, such that (ZFC $\not\vdash$ S and ZFC $\not\vdash$ ~S) is undecidable? Are battery packs allowed in hand luggage? When flying, are you allowed to bring battery packs / power banks? I'd like to bring my ACC 10400mAh Power Bank on several flights. Decision Tree in LaTeX with TikZ Grid line doesn't have to be included     \documentclass[10pt]{beamer}  \usetheme{default}  \usepackage{graphicx}  \usepackage{amssymb,amsmath}  \usepackage{tikz}  \usetikzlibrary{matrix}  \usepackage{adjustbox}  \usepackage{caption} \ usepackage{subcaption}   \setbeamercolor{title}{fg=black}  \setbeamercolor{subtitle}{fg=gray}  \setbeamercolor{footlinecolor}{fg=white,bg=green}  \setbeamertemplate{footline}[text line]{% \parbox{\linewidth}{\vspace*{-10pt} \textit{Where Wall Street Goes to School} \hfill \insertpagenumber} } \setbeamertemplate{navigation symbols}{} –  \begin{tikzpicture}[&gt;=stealth,sloped][scale=0.8]  \matrix (tree) [matrix of nodes, minimum size=0.25cm, column sep=2cm, row sep=1cm, ]  { &amp; $C_{i+1,j+1}$ \\ $C_{i,j}$ &amp;$C_{i+1,j}$ \\  &amp; $C_{i+1,j-1}$ \\   };  \draw[-&gt;] (tree-3-1) -- (tree-1-3) node [midway,above] {};  \draw[-&gt;] (tree-3-1) -- (tree-3-3) node [midway,above] {};  \draw[-&gt;] (tree-3-1) -- (tree-5-3) node [midway,below] {};  \end{tikzpicture}  \end{adjustbox} – I have a edge loop that has vertices on it. Is there a way I can separate the vertices on the the edge evenly without moving the end points? I would also like for the vertices to maintain the current shape. I'd like to have Ubuntu installed on a USB stick, that I could plug in (almost) any computer and boot from it, and that I could use (almost) normally, as if it was installed on that computer. I'd also like to have a data partition on it that could be used by (almost) any computer, mostly to store some portable apps, just in case.    I've been told that if I installed Ubuntu in BIOS mode, I wouldn't be able to boot from a computer in UEFI mode, and vice versa.  Since I'd like to be able to boot on any computer, it's a big problem.  What can I do to be able to boot on computers in BIOS or UEFI modes in my case?  I've been searching for solutions but most of them are for specific needs that are different than mine, so it's difficult to extract the minimum requirements from those solutions to apply them to my problem.  Is there a simple, "clean" and quite generic solution to this problem?  I'd appreciate some explainations about the reasons why a specific solution is good or a specific step is needed.    My current setup:   USB stick:  OS: Xubuntu 16.04 i386 installation: full install (from a Live USB built with Rufus) drivers: none proprietary file systems:    partition table:    2: , /boot/efi, 128 Mio, FAT32, [boot,esp] 3: , 128 Mio, HFS+ 4: , 2 Mio, [bios_grub] 5: swap, 512 Mio 6: , /, 24 Gio, ext4, defaults,errors=remount-ro,lazytime,commit=60 1: , /media/data, ~3.6 Gio, FAT32, defaults,lazytime,check=strict  RAM:   /tmp, tmpfs, defaults,nosuid,nodev,noexec,mode=1777   swap:    vm.swappiness=5 swap partition: 512 Mio, for emergency zRAM swap files:    /var/swap/hib.swp: same size as RAM, for hibernation, generated by a script at startup /var/swap/opt.swp: if needed, generated by a script   overprovisioning: ~5.6%   built-in: ~1.2 Gio (apparently) added: 512 Mio  scheduler: deadline How to understand the drawbacks of K-means K-means is a widely used method in cluster analysis. In my understanding, this method does NOT require ANY assumptions, i.e., give me a dataset and a pre-specified number of clusters, k, and I just apply this algorithm which minimizes the sum of squared errors (SSE), the within cluster squared error.  So k-means is essentially an optimization problem.  I read some material about the drawbacks of k-means.  Most of them say that:   k-means assumes the variance of the distribution of each attribute (variable) is spherical;  all variables have the same variance; the prior probability for all k clusters is the same, i.e., each cluster has roughly equal number of observations;   If any one of these 3 assumptions are violated, then k-means will fail.  I could not understand the logic behind this statement. I think the k-means method makes essentially no assumptions, it just minimizes the SSE, so I cannot see the link between minimizing the SSE and those 3 "assumptions". I am trying to show that if for a group $G$ we have $Z(G)=1$, then $Z(\operatorname{Aut}(G))=1$.  I have tried everything I can think of, but to no avail.  The first part of the problem was to show that $\operatorname{Inn}(G) \triangleleft  \operatorname{Aut}(G)$ - does this have any connection?  I couldn't find one.  I know that $\operatorname{Inn}(G) \cong G/Z(G)$, so in this case $\operatorname{Inn}(G) \cong G$ and $Z(\operatorname{Inn}(G))=1$.  Is there any way to get from this to $Z(\operatorname{Aut}(G))=1$?  How do we go about showing this?  Thanks. How do you attach a debugger to a Web service? I am using a Web service. Can anybody tell me how to debug through it? How many connected components does $\mathrm{GL}_n(\mathbb R)$ have? I've noticed that $\mathrm{GL}_n(\mathbb R)$ is not a connected space, because if it were $\det(\mathrm{GL}_n(\mathbb R))$ (where $\det$ is the function ascribing to each $n\times n$ matrix its determinant) would be a connected space too, since $\det$ is a continuous function. But $\det(\mathrm{GL}_n(\mathbb R))=\mathbb R\setminus\{0\},$ so not connected.  I started thinking if I could prove that $\det^{-1}((-\infty,0))$ and $\det^{-1}((0,\infty))$ are connected. But I don't know how to prove that. I'm reading my notes from the topology course I took last year and I see nothing about proving connectedness... Do any queries exist that require RIGHT JOIN, or can they always be re-written with LEFT JOIN?  And more specifically, how do you re-write this one without the right join (and I guess implicitly without any subqueries or other fanciness):   SELECT * FROM t1 LEFT JOIN t2 ON t1.k2 = t2.k2 RIGHT JOIN t3 ON t3.k3 = t2.k3 What are neutral density filters and how do I use them to create long exposures in daylight? I've seen a few related posts on the site but nothing specifically on this point:  I'd like to be able to take long exposure photos during daylight (like the examples in ). I'm told that you can do this by using a neutral density filter. So my question is: what is a neutral density filter exactly, and how is it used to achieve that smooth long exposure effect? Find all rings $R$ satisfying $\mathbb Z \subset R \subset \mathbb Z[\frac {1}{2}]$ Best File Management Practices when you have thousands of Files Can I mix different RAM modules in PC? I have 4 RAM slots on the motherboard P5K. At the moment I have two 1GB RAM modules and two 2GB RAM modules. Everything is working fine.   Can I buy one 4GB module and put it instead of the 1GB module?  Another question, can I mix MHz values, like that I have two 667MHz modules and two 1066MHz modules? Is this dangerous for the comp? Are there any programs that will let me dictate (speech-to-text) to any program? Or at least to a text editor and text fields in Firefox.  I’m not interested in anything that uses an online service, it has to be on-device. It may be a commercial product.