I create a chart with many (actually 10) lines in different colors (see example). I want to make it as easy as possible to differentiate the different lines.    Some possibilities I have in mind:   Take most different colors Avoid light colors (e.g. yellow - on prints the line are hard to see) Use patterns (dashed, dotted, different dash pattern)  Use different thickness (I don't believe this is a good idea)   Are there best practices, rules or guides for this task?  My example code:  \documentclass[border=5mm] {standalone} \usepackage{pgfplots, pgfplotstable} \begin{document} \pgfplotstableread[col sep=&amp;, header=true]{ description&amp;A&amp;B&amp;C&amp;D&amp;E&amp;F&amp;G&amp;H&amp;I&amp;K 2009&amp;46&amp;0&amp;33&amp;3&amp;0&amp;74&amp;3&amp;7&amp;2&amp;7 2010&amp;35&amp;0&amp;22&amp;1&amp;0&amp;90&amp;2&amp;5&amp;3&amp;3 2011&amp;38&amp;0&amp;33&amp;3&amp;1&amp;77&amp;1&amp;9&amp;2&amp;8 2012&amp;25&amp;0&amp;15&amp;0&amp;4&amp;55&amp;4&amp;5&amp;0&amp;1 2013&amp;18&amp;0&amp;8&amp;0&amp;0&amp;46&amp;5&amp;4&amp;0&amp;3 2014&amp;37&amp;0&amp;54&amp;1&amp;3&amp;54&amp;5&amp;12&amp;10&amp;2 2015&amp;29&amp;0&amp;63&amp;8&amp;1&amp;77&amp;0&amp;8&amp;7&amp;5 }\datatableentry \begin{tikzpicture} \begin{axis}[   title={My Chart},   enlarge y limits ={value=0.2,upper},   xtick=data,   xticklabels ={2009,2010,2011,2012,2013,2014,2015},     x tick label style={rotate=-45,anchor=west,font=\tiny},   legend style={font=\tiny,legend pos=north west,legend cell align=left}, ] \addlegendentry{A}; \addplot [color=blue] table [y=A, x expr=\coordindex] {\datatableentry}; \addlegendentry{B}; \addplot [color=cyan] table [y=B, x expr=\coordindex] {\datatableentry}; \addlegendentry{C}; \addplot [color=gray] table [y=C, x expr=\coordindex] {\datatableentry}; \addlegendentry{D}; \addplot [color=yellow] table [y=D, x expr=\coordindex] {\datatableentry}; \addlegendentry{E}; \addplot [color=green] table [y=E, x expr=\coordindex] {\datatableentry}; \addlegendentry{F}; \addplot [color=lime] table [y=F, x expr=\coordindex] {\datatableentry}; \addlegendentry{G}; \addplot [color=black,loosely dashed] table [y=G, x expr=\coordindex] {\datatableentry}; \addlegendentry{H}; \addplot [color=red,densely dashed] table [y=H, x expr=\coordindex] {\datatableentry}; \addlegendentry{I}; \addplot [color=blue,dotted] table [y=I, x expr=\coordindex] {\datatableentry}; \addlegendentry{K}; \addplot [color=cyan,dashed] table [y=K, x expr=\coordindex] {\datatableentry}; \end{axis} \end{tikzpicture} \end{document}   Disclaimer: I'm not sure if this question belongs to . The main problem is a design question, but the solution is needed in Tikz.
Tufte advocates to "minimize the ink-to-data ratio" for charts. I am trying to style a multi data series bar chart, that can have a grid and axes as shown below (chart at the left is from the Economist and on the right my attempt).      Here is the code:  \documentclass[justified]{tufte-book} \usepackage{pgfplots,lipsum} \pgfplotsset{compat=newest} \begin{document} \section{Bar Charts}  \lipsum[1-2]\vfill   \begin{figure*}[htbp]   \fbox{  \begin{tikzpicture}   \centering   \begin{axis}[         ybar,           title={Cumulative Progress of Works},         height=8cm,         width=15.5cm,         bar width=0.4cm,         ymajorgrids, tick align=inside,         enlarge  y limits={value=.2,auto}, % see the upper          ymin=0,         ymax=100,         axis x line=bottom,          axis y line=right,         %enlarge x limits =e,         legend style={at={(0.5,-0.2)},         anchor=north,legend columns=-1},         ylabel={Percentage (\%)},         symbolic x coords={            Sep-11,Oct-11,Nov-11,Dec-11,            Jan-12,Feb-12,            Mar-12,           Apr-12},        xtick=data,        nodes near coords,        every node near coord/.append style={         anchor=mid west,         rotate=70       }     ]     \addplot coordinates {       (Sep-11,75.4064)       (Oct-11, 72.7961)        (Nov-11,94.4597)       (Dec-11,66.6786)        (Jan-12,67.5600)        (Feb-12,88.2339)       (Mar-12,78.6138)        (Apr-12,58.9129) };    \addplot coordinates {       (Sep-11,75.4064)       (Oct-11, 89.7961)        (Nov-11,94.4597)       (Dec-11,76.6786)        (Jan-12,77.5600)        (Feb-12,78.2339)       (Mar-12,88.6138)        (Apr-12,78.9129) };    \addplot coordinates {       (Sep-11,75.4064)       (Oct-11, 89.7961)        (Nov-11,94.4597)       (Dec-11,76.6786)        (Jan-12,77.5600)        (Feb-12,78.2339)       (Mar-12,88.6138)        (Apr-12,78.9129) };      \legend{First Fix,Second Fix,Third Fix}   \end{axis}   \end{tikzpicture} }  \caption{\protect\raggedright Cumulative progress for all MEP works. Notice the slower rate of production during the last three months.} \end{figure*}  \lipsum[1-3] \end{document}   I have moved the y-axis to the right, but cannot get rid of the axis line. The plot is also not fitting within the plot width, despite using \enlarge.   Edit  And thanks to Jake the ugly duckling has been transformed to the following, with minor variations to the code as suggested by Jake. I have only added a stronger color for one of the bars in order to highlight it:
Setup or "set up"? The word setup (as a noun), I feel, has become an acceptable part of the English language, at least insofar as technical manuals or computer textbooks are concerned. However I find that the word is used very often in verb form like so:     "You can setup the program quite easily ..."   when in fact my understanding is that the actual sentence should be:     "You can set up the program quite easily ..."   I would like to know if setup can be used as a verb. The situation seems be very similar to the word output (as a noun). Output is a purely technical word and its use is restricted solely to technical texts or at least in a technical context within non-technical books. However it is also used in verb form now like so:     "The system will output the signal ..."   I would be very grateful if this question is answered. Thank you Mathematical notation around the world Something special about energy eigenstates when it comes to time evolution? A particle is subject to an infinite square well potential with  $$V(x)= \begin{cases}  0  &amp;   −a \lt x \lt a\\   \infty &amp;  \,\,\,\,\text{otherwise} \end{cases}$$  At a time $t=0$ its wavefunction is given by $$\psi(x, t=0)=\frac{1}{\sqrt{5a}}\cos\left(\frac{\pi x}{2a}\right)+\frac{2}{\sqrt{5a}}\sin\left(\frac{\pi x}{a}\right)$$       (a) What are the possible results of an energy measurement at $t = 0$, and with what probabilities?     Re-writing the terms in $\psi(x,t=0)$ as $$u_1(x)=a^{-1/2}\cos\left(\frac{\pi x}{2a}\right)\qquad \text{&amp;} \qquad u_2(x)=a^{-1/2}\sin\left(\frac{\pi x}{a}\right)$$ such that $$\psi(x,t=0)= \frac{1}{\sqrt{5}}u_1(x)+\frac{2}{\sqrt{5}}u_2(x)$$ with energies $$E_1=\frac{\hbar^2 \pi^2}{8ma^2}\qquad \text{&amp;} \qquad E_2=\frac{\hbar^2 \pi^2}{2ma^2}$$ and probabilities $$P(E_1)=\frac15 \qquad \text{&amp;} \qquad P(E_2)=\frac45$$       (b) If no measurement is performed, what is the wavefunction $\psi(x, t)$ at all times $t$? What are the possible energies and their probabilities if a measurement is first performed at time $t$?     At a time $t$ the wavefunction is given by $$\psi(x, t=0)=\frac{1}{\sqrt{5a}}\cos\left(\frac{\pi x}{2a}\right)\exp\left(\frac{-i E_1 t}{\hbar}\right)+\frac{2}{\sqrt{5a}}\sin\left(\frac{\pi x}{a}\right)\exp\left(\frac{-i E_2 t}{\hbar}\right)$$    The problem is that I cannot answer the second part of the question (b).    The answer states that:      Because the two terms are energy eigenstates, the relative probabilities do not change and are as in the previous part.     I have some questions about the above statement: why does an "energy eigenstate" mean that the probablities don't change with time? Or, put in another way, does a "momentum eigenstate" (for example) have constant relative probabilities when measured at any time?   The answer seems to be implying there is something special about energy eigenstates when it comes to time evolution. The eigenvalues of energy measurements don't seem to change regardless of how many times you measure them, and no matter how long you wait until you measure them. I'm not sure if this is the case, but could someone please explain why all quantum operators (except Hamiltonian) do not exhibit this behaviour. find a $\int_{x}^{g(x)} f(t)\,dt = 1$ Let $f : [0, 2] → \mathbb{R}$ be a continuous, positive function and  $$\int_{0}^1 f(x)\,dx = \int_{1}^2 f(x)\,dx= 1$$ For each $x \in [0, 1]$, prove that there exists a unique function $g(x) \in [1, 2]$ such that $$\int_{x}^{g(x)} f(t)\,dt = 1$$ and $g \in C^1$. Well, I think in $g(x) = x +1$, but I'm not sure. Any hint is appreciated.  Thank you. 'POCO' definition Can someone define what exactly 'POCO' means? I am encountering the term more and more often, and I'm wondering if it is only about plain classes or it means something more? A situation when two or more people speak at the same time The word or phrase I am looking for is quite opposite to that of the situation when people, such as students or sports players, sing their national anthem with the same tone and words.  I want a single word or even phrase that can describe the situation when two or more people speak at the same time with different tone and words . . . and at the end, the listener cannot get what they are saying. This situation can be found while debating, telling a news about any incident or even while complaining.     Due to _____ , the teacher could not get what they are saying.   If it's not feasible to find a noun or phrase for such situation, then here I request to have an adverb standing alone to describe how they are speaking, for instance, what is the adverb for "at the same time"?.  Here is how, I want to convert sentence 1 into sentence 2.        They spoke at the same time, and the teacher could not get what they are saying.   They spoke _____ , and the teacher could not get what they are saying. An excerpt from Introduction to Analytic Number Theory by Tom M. Apostol.      I have three main concerns regarding this proof:    What is the abscissa of convergence for $\frac{1}{F(s)}$ - why can we take the product of the two series. I only know this is true if the two series are absolutely convergent.  Why can we do term by term integration? I believe its suffices to show that the series converges locally uniformly - BUT is this true?  How does the proof show that $G(s)$ converges uniformly? Error: the question could not be loaded When I was trying to open  I just added using the iOS app I received this error:     Error The question could not be loaded   Reproduction scenario:   add a question; in my case it didn't open it directly; it doesn't show up in the list yet; I opened my profile and clicked the question; bang! Where can I buy an Ubuntu Phone? I need to buy an Ubuntu phone, where can I buy it? It is unavailable everywhere. In Elias Stein and Rami Shakarchi's Complex Analysis textbook, we have the following exercise:     Show that if $\{a_n\}_{n=0}^\infty$ is a sequence of complex numbers such that $$\lim_{n\to\infty}\frac{|a_{n+1}|}{|a_n|}=L,$$ then $$\lim_{n\to\infty}|a_n|^{1/n}=L.$$    I've been trying to prove this with no luck. The only thing I've thought of doing is $$\lim_{n\to\infty}\left(\frac{|a_{n+1}|^n}{|a_n|^n}\right)^{1/n},$$but this hasn't lead me anywhere except dead ends. Will someone provide a hint for me about how to proceed? Thanks!  Minor update: I don't know if it's helpful yet, but I know we can write the limit as $$\lim_{n\to\infty}\left(\frac{|a_{n+1}a_n\cdots a_0|}{|a_n\cdots a_0|}\cdot\frac{1}{|a_n|}\right).$$This reminds me a lot of the geometric mean, which even has the exponents I'm trying to get... Inverse of sum of exponential random variables (mean and variance) Assume $X_1,X_2, \dots , X_n$ following the exponential distribution with mean $\theta &gt; 0 $ and the statistic: $$ T = \sum\limits_{i = 1}^n X_i $$  I know that the sum of exponential random variables follows the Gamma distribution, but I cannot infer anything about the inverse of the sum $\frac{1}{T}$. My guess would be that: $$ E\left[\frac{1}{T}\right] = \frac{1}{\theta} \quad \text{and} \quad V\left[ \frac{1}{T} \right] = \frac{1}{\theta^2} $$ but why? How is well-ordering in real line possible?  I know that the axiom of choice provides possible well-ordering, but intuitively, this does not seem to make sense.  How can you compare 1.111111.... and 1.111111... when we can never know the full digits of each number? How to calculate $\int \frac{x^2 }{(x^2+1)^2} dx$? I'm trying  to calculate $\int \frac{x^2 }{(x^2+1)^2} dx$ by using the formula: $$ \int udv = uv -\int vdu $$  I supposed that $u=x$ s.t $du=dx$, and also that $dv=\frac{x}{(x^2+1)^2}dx$, but I couldn't calculate the last integral. what is the tick here?           the answer must be: $ \frac{1}{2}arctan\ x - \frac{x}{2(1+x^2)} $ + C I often need to view on the canvas the (selected or not) features from the current active vector layer.  In this situation, I only need to view something on the canvas, without doing anything on the canvas itself (so, the active window is always the Attribute Table).  This is what I usually do:   Open the Attribute Table for the current active layer; Select the first feature; Press Ctrl+P button (i.e. the "Pan map to the selected row" button); Minimize the Attribute Table; View something on the canvas for the current feature; Go to the first step until needed.   Is there a way (a method, a shortcut) for directly browsing every feature on the canvas without the needing of going backwards and forwards with the Attribute Table? I mean, something like a "next" button?  (I may use the workaround of splitting the windows of the Attribute Table and of the canvas within the monitor, or also docking the Atrribute Table, but I would like to work on the full QGIS window).    EDIT I saw that my question was casted as a duplicate of  question. The two questions are very similiar, but I think it should be left as open for two reasons:   the related duplicated question doesn't have an accepted answer; my question is slightly different because I'm looking for the possibility of displaying only the selected features (and the @Joseph's , that I marked as accepted, answers well to my request). $SU(3)$ irreducible representations with tensor method Auto-run scripts security options You'd think that as soon as Harry met someone who was friends with his dad, he'd have asked about his family.  Certainly Lupin or Sirius could have told him something of his family, given that they were James' closest friends, and Sirius was "always welcome at the Potters".  Obviously there's nothing in the books, but did J.K. Rowling ever explain why there was no mention of any living relative other than Aunt Petunia, or even what happened to Harry's grandparents? Why are there gaps in my IDENTITY column values? Setting PATH variable in /etc/environment vs .profile Where is the preferred place to set the PATH envvar?  ~/.profile or /etc/environment?  What is the case when PATH is set in both places? Is the end result a concatenation of both values set in those two places? Saving an Adobe illustrator file as a pdf - are fonts embedded? If so, why does Adobe illustrator say I don't have the font when I open it? If I have an Adobe Illustrator file, and I save it as a .pdf - it looks like the fonts are included in that .pdf file. (I think this because when I open the .pdf file in Reader it looks the way I expect it to.) However, when I open this same .pdf file on a different computer (or workstation) with Adobe Illustrator - Illustrator says I 'don't have the font I need'. This doesn't make sense to me because - If I can see the document correctly in reader, I would expect it to be there for Illustrator as well. Can someone explain why this is? I am asking because saving a file as a .pdf for print seems to handle most font troubles that come up - but sometimes I need to change the text in a file before I print it... I am hoping there is a way to open a .pdf so that .ai recognizes that the font is in there.  But I am unsure on the details of saving as a .pdf in Illustrator, how fonts are handled, and what is possible.