How to change the font size of verbatiminput to footnotesize?
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Mass and Newton's Second Law Typeset an = with an ! above I've seen an equals sign with a small exclamation mark on top being used to say "equals because of data that was given in the problem", for example for a boundary condition or initial value in a differential equation.  A rough picture of what I mean:       ! f(x) = 4   How do I typeset this in LaTeX? I've tried $=^!$ (which doesn't produce the desired result) and looked through the "relations" section of the  without success. Ratios in Regression, aka Questions on Kronmal Recently, randomly browsing questions triggered a memory of on off-hand comment from one of my professors a few years back warning about the usage of ratios in regression models. So I started reading up on this, leading eventually to Kronmal 1993.  I want to make sure that I'm correctly interpreting his suggestions on how to model these.   For a model with a ratio with the same denominator on both the dependent and independent side: $ Z^{-1}Y = Z^{-1}1_n\beta_0 + Z^{-1}X\beta_X + \beta_Z + Z^{-1}\epsilon $   Regress dependent ratio on the (inverse) denominator variable in addition to the other ratios Weight by the (inverse) denominator variable  For a model with dependent variable as a ratio: $ Y = \beta_0 + \beta_XX + Z1_n\alpha_0 + ZX\alpha_X + Z^{-1}\epsilon $   Regress numerator by original variables, denominator, and denominator times original variables [what about categorical variables?] Weight by (inverse) denominator  For model with only independent variable ratios: $ Y = \beta_0 + X\beta_X + Z^{-1}1_n\beta_{Z^{-1}} + W\beta_W  + Z^{-1}W\beta_{Z^{-1}W} + \epsilon $   Include numerator and (inverse) denominator as main effects, ratio as interaction term.    Are my interpretations here correct? Are there philosophers who examined the reasons for believing in the existence of other people? While I am familiar with Descartes and the oft-quoted idea, I think therefore I am, I am not familiar with any philosophy that actively sought to rationalize that anybody else exists.  Are there philosophers who analyzed this question? Or is it taken for granted that it is (im)possible for anybody to validate their own existence to somebody else? Scenario  I created a journey with a Contact Data entry event that is triggered via the API. A subscriber should be able to be injected multiple times and the values in the data extension are updated while the subscriber is in the journey. The updated values should determine the path the subscriber follows.  Setup  As changed data needs to be evaluated and the contactkey cannot be used as primary key, I added a random id as primary key and created an attribute group for the data extension in Data Designer. The data extension is linked to the contact's contactkey using a one-to-many relationship as a contact should be able to enter the journey multiple times.  In the journey I'm using a decision split that is configured to use contact data from the created attribute group and has two branches (as it checks a boolean value).  Problem  For multiple entries the decision split doesn't evaluate correctly and always leads to same branch (value equals false). I suppose the problem is that journey builder doesn't use the primary key to identify the correct row in the data extension. Is there any way to make sure the row is matched using this id and not the contactkey as this leads to some strange behaviour as described here: Data from multiple lists using single REST API call Does a wing in a potential flow have lift? How do I test for an empty JavaScript object? How do I copy a string to the clipboard? If $a \cdot a = 1$ then $a = 1$ or $a = -1$ When a user who approved an edit is removed, an incorrect "-2 reverted" event appears in reputation history I am aware that . But now there is an extraneous "reverted" event to go along with user removal:     Source: .   The edit was not reverted, it's . In any case, I should not lose 2 points twice for the total of -4. And indeed, my reputation only dropped from 131 to 129 despite what the history suggests.   So the line with "-2 reverted" is a bug.     A more extreme example:  got 21 "reverted" events on 2017-06-30, none of which should be there. His rep loss is 42, not 84 as the reputation history says. After plain installation of Ubuntu 16.04 LTS gnome-software doesn't work. It has opened once with GUI, but installation of Unity Tweak Tool didn't finish.  When starting again, GUI doesn't come up. When opening from terminal, a warning appears, but the application GUI doesn't open.  $ gnome-software (gnome-software:7052): Gs-WARNING: failed to open plugin /usr/lib/gs-plugins-9/libgs_plugin_xdg_app_reviews.so: /usr/lib/gs-plugins-9/libgs_plugin_xdg_app_reviews.so: cannot open shared object file: No such file or directory   Does anybody have same experience, and eventually, a solution?    According to the recommendation:  $ dpkg-query -S /usr/lib/gs-plugins-9/libgs_plugin_xdg_app_reviews.so gnome-software: /usr/lib/gs-plugins-9/libgs_plugin_xdg_app_reviews.so   Proposed reinstall of gnome-software did not help.    As workaround, use Synaptic Package manager and command line. Selenium 2: Open link in new tab and close tabs What is the purpose of  in Python — especially with respect to when I would want to use it, and when not? I've been wondering about this one for a while; I find it a little weird how abruptly it happens. Basically, why do we need just three uniforms for $Z_n$ to smooth out like it does? And why does the smoothing-out happen so relatively quickly?  $Z_2$:     $Z_3$:    (images shamelessly stolen from John D. Cook's blog: )  Why doesn't it take, say, four uniforms? Or five? Or...? EDIT:  It seems that I've also had edits that stacked well, so I'm not sure if I had a timing problem, or was just delusional.  The one thing that can be fixed, that I'll turn this question into, is a feature request so that when I go to re-edit (either within the 5-minute grace period, or before a suggested edit is approved), it brings up the old edit summary text.  Right now, it brings up a blank edit summary, and this replaced the first one I did.  This isn't really intuitive, and even knowing that's what it's doing, I still forget to put everything in.  Original Question:  It has happened a few times now, when on a site where I don't have edit privileges, that I make an edit.  I then see that the edit didn't work quite right, so I go back in to re-edit it.  This creates a brand new edit review, with an additional useless summary. How about we have the same grace period to re-edit your up-for-review edit, as there is for a normal edit? Of course, it wouldn't be possible once it's been approved. Under what conditions is the exponential map on a Lie algebra injective? Let $G$ be a Lie group with Lie algebra $\mathfrak{g}$ and let $\exp :\mathfrak{g}\rightarrow G$ be the exponential map.  In his blog,  that if a Lie group is not simply-connected, then $\exp$ will not be injective.  Conversely, is it true that if a Lie group is simply-connected, then $\exp$ is injective?  If not, what is a counter-example? Will using 'var' affect performance? Earlier I asked a question about  and got the answer that while it is only necessary for anonymous types, that it is used nonetheless to make writing code 'quicker'/easier and 'just because'.  Following  I saw that var gets compiled down to the correct type in the IL (you will see it about midway down article).  My question is how much more, if any, IL code does using the var keyword take, and would it be even close to having a measurable level on the performance of the code if it was used everywhere? Why would you not want to rollover a previous employer's 401(k) when changing jobs? Are there any valid reasons to not rollover a former 401(k) when changing jobs?  I have several little ones that I never quite got around to rolling together - with an upcoming job change, should they all be combined into my new employer's retirement plan?  If not, what else might be considered? Ways of getting three of a kind in a 52 card deck This question has probably been asked before, but just to be clear here, I am NOT asking for the answer, I know the answer.  What i want to know is why my solution is not equivalent to the actual solution.  Three of a kind in a deck means you draw 3 cards of the same rank, and 2 other cards each of different ranks.  So. The solution in my book is the following: (13 C 1)(4 C 3) * (12 C 2)(4 C 1)(4 C 1)  The logic is the following:  1) Choose 1 out of the 13 ranks, then for the 4 cards in the chosen rank, pick 3.  2) Choose a combination of 2 ranks from the remaining 12, then for the 4 cards in each rank, choose 1.  Total combinations: 54912  My solution is the following:  ((13 C 1)(4 C 3)) * ((12 C 1)(4 C 1)) * ((11 C 1)(4 C 1))  1) My logic for the 3 of a kind is the same as the solution.   2) Choose 1 of the remaining 12 ranks, and 1 card from the 4 cards in the rank.  3) Choose 1 of the remaining 11 ranks, and 1 card from the 4 cards in the rank.  Total combinations: 109824  My solution says that the combinations are exactly double of the book's solution.  I'm just very confused as to why this is. If anyone could explain this to me I would be very appreciative, thank you.