Automated method of setting ideal sizes and positions of symbols or logos of various proportions, when put together (ignoring any text) I always spend too much time trying to scale symbols or logos that are supposed to look harmoniously next to each other, like below:    These seem to be acceptable to me, but I wonder if there is any formula or recipe that can be used to make a row of random proportions symbols look good and save time? I guess spacing also can be optimised, like in case of fonts. It probably depends on shapes of symbols, not only on their outer boundaries, but maybe there is some not too complicated solution?  It would be ideal to have a script that does it.  EDIT: Thanks to  and  for suggesting a similar question (), there are some great answers there. However they stress on importance of making the text look of similar size. At the moment I usually deal with symbols that rarely have text in it, so it is more a matter of balancing the geometry. Ideally I'm interested in solution that could be scriptable, semi-automatic or fully-automatic.
What methods can I use to create balance and consistency between a group of differing logos? A regular challenge that I face is balancing two (or more) logos. Whether they need to be equal or one needs to be given priority. Some logos however might be squares, others rectangles, circles, etc...   As a quick sample I snagged a nice high resolution photo from  and pretend its going to be an advertisement that needs to show some footwear brand logos on it. In this case I used Adidas and Saucony.  This is certainly not balanced even though they're height is the same:    Likewise this is not balanced even though they're width is the same:    So then the question becomes when are they in balance, is this balance:    Maybe a little more adjustment, is this balance:    And in these examples I'm only working with two Black Logos. Factor in color and it can get even more difficult to balance. Another issue being when there's tiny text as part of the logo.  So the question is, other than estimating / eye-balling it, what tips, methods or even tools are there to balance different sized logos?
How do I install the latest  on Ubuntu? I've been looking around, and I can't find anything. Is there a Ubuntu package for node.js, or do I have to compile it myself? I attended a business meeting in the Midwest and one of our clients took our management team and a few other business partners to dinner at an awesome Mexican restaurant. When the appetizers were served I commented that it was a wonderful presentation and that everything looked very fresh, including the avocado slices.   Speaking to the woman seated across from me I said that even though I use a good amount of lemon juice, whenever I prepare avocados they still turned dark pretty quickly. This happens whether they are sliced, used in guacamole, etc. She responded that the secret is to use lime juice. She proceeded to tell me that she was born and raised in Central America and that it is customary there to use fresh limes or juice rather than lemon.  I have tried it and lime seems to work much better than lemon, so it would stand to reason that they are more acidic. However, I never thought there was that much difference. So, on to the questions.  Are limes more acidic than lemons? Are there any other differences in their properties that could make a difference? Where do I find out how a command/environment is defined? Say I want to redefine the itemize environment, or make a modified version of it. I want to know how it is currently defined. Where do I find this information? If it's some particular package command, I can just look at the .sty file for that package, but if it's something more basic, I don't know where to look...  Is there a reference manual of where all this stuff is explained? Or is there a file in the depths of my texmf tree I should poke around in? Where will my bus be at the Port Authority Bus Terminal in New York? Proof for two sequences producing the maximum value when sorted I am trying to improve my discrete Math skills by doing some proof exercises. But I am struggling to understand how to start proving the following hypothesis:  $$ S = {x}_1{y}_1 + {x}_2{y}_2 + \ldots + {x}_n{y}_n $$ Where ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are ordering of two different sequences of positive real numbers, each containing n elements. S takes its maximum value when ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are sorted in non decreasing order.  I was thinking that I should maybe use a proof by contradiction. Where the negation of the hypothesis is: S takes it minimum value over all ordering of the two sequences when both sequences are sorted into non increasing order.  However I am not sure my negation of the hypothesis is correct or how proceed from there. I do not want the complete proof because I am trying to learn how to do it myself but if some one can tell me how to make a start on this I would be grateful. How can timelapse sequences be shot without in-camera support? How can timelapse sequences be shot without having in-camera support for it?  Which third-party tools are recommended? Setting "checked" for a checkbox with jQuery RegEx: Grabbing values between quotation marks How to vote on friends / colleagues ' questions (or answers) In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calculator?  Sometimes I don't feel right when I can't do things out myself and let a machine do it when I can't.  Or, if you could redirect me to a place that explains how to do it, please do so.  My dad said there isn't, but I just had to make sure.  Thanks. Highlight the difference between two strings in PHP What is the easiest way to highlight the difference between two strings in PHP?  I'm thinking along the lines of the Stack Overflow edit history page, where new text is in green and removed text is in red. If there are any pre-written functions or classes available, that would be ideal. Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space? I have a non homework related question from a text and require a nice clear proof/disproof please  Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?  my ideas:  if $H$ is the subset of the topological space $X$  if the subset is closed in the closed subspace, the complement is open in the subspace, which means the complement is of form $U\cap H$ for some $U$ open in $X$  if the subspace is closed the complement is open which means complement of $H=U$ for some open $U$ in $X$  kind thanks dpkg -V , What does the output mean? I ran DPKG Verify on all packges and got this output and I don't know what it means :  ??5?????? c /etc/lightdm/lightdm-gtk-greeter.conf ??5?????? c /etc/default/chromium-browser ??5??????   /usr/local/etc/no-ip2.conf ??5??????   /var/lib/dokuwiki/data/cache/_dummy ??5?????? c /etc/xdg/menus/mate-settings.menu ??5?????? c /etc/apache2/apache2.conf ??5?????? c /etc/apt/apt.conf.d/10periodic ??5?????? c /etc/sysctl.conf ??5??????   /var/lib/xine/xine.desktop ??5??????   /boot/vmlinuz-4.4.0-21-generic ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/cupshelpers.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/xmldriverprefs.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/config.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/openprinting.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/__init__.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/ppds.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/installdriver.cpython-35.pyc ??5?????? c /etc/xdg/autostart/mate-volume-control-applet.desktop ??5?????? c /etc/libvirt/qemu/networks/default.xml JavaScript open in a new window, not tab I have a select box that calls window.open(url) when an item is selected.  Firefox will open the page in a new tab by default.  However, I would like the page to open in a new window, not a new tab.    How can I accomplish this? Fullscreen Vista's Command Prompt, or Replacement Complex numbers equation: $z^4 = -16$ A proof that $1=2$. May I know why it’s false? Moment generating function of the natural sufficient statistics of Gamma distribution I have $X_1,X_2 ... X_n$ Gamma-distributed r.v with density:    First of all I showed, that Gamma distribution belongs to exponential family and can be represented in form     I found, that for Gamma distribution $B(\theta) = log(\theta)$ where $\theta$ is $\alpha/\beta$  Then we know, that moment generating function of the random variable $T(X)$ is given by $$M(t)=\exp\{B(\theta+t)-B(\theta)\}$$  Natural sufficient statistics for Gamma distribution is:    But I didn't understand what should I do next? Because Natural sufficient statistics is two dimensional it confuses me:  $M(T) = exp[log(\theta + T) - log(\theta)]$  and $T = [s,t]^\intercal$ Estimating partial sums $\sum_{n = 1}^m \frac{1}{\sqrt{n}}$ Apostol's Calculus, exercise number I 4.7 13.     Prove that if $n \geq 1$, then   $$ 2(\sqrt{n+1} - \sqrt{n}) &lt; \frac{1}{\sqrt{n}} &lt; 2(\sqrt{n} - \sqrt{n-1}) $$   and use this to prove that if $m \geq 2$, then   $$ 2 \sqrt{m} - 2 &lt; \sum_{n = 1}^m \frac{1}{\sqrt{n}} &lt; 2\sqrt{m} - 1 $$   In particular, when $m = 10^6$ the sum lies between $1998$ and $1999$.   After establishing the trivial case, for $n=1$, I can't think of a way to perform the inductive step:  assuming $2(\sqrt{n+1} - \sqrt{n}) &lt; \frac{1}{\sqrt{n}} &lt; 2(\sqrt{n} - \sqrt{n-1})$ and using this, deducing the same for $n+1$ is true as well:  $2(\sqrt{n+2} - \sqrt{n+1}) &lt; \frac{1}{\sqrt{n+1}} &lt; 2(\sqrt{n+1} - \sqrt{n})$  Any help is very appreciated, thanks How to make an international emergency call?