Like in the question, how can I align underbraces in LaTeX? For example, the code \begin{align*} {\underbrace{Y \cdot \dfrac{\sum_{i=1}^t x_i}{D}}_{\text{abc} } } + {\underbrace{\sum_{j=t+1}^n K_j }_{\text{abc } } } \end{align*}  unfortunately yields an output where the text under the corresponding equations doesn't align.
I am trying to balance underbraces in the equation below, how can I ensure that both underbraces at the same depth?  \begin{equation} y = \underbrace{ \left [ x^2 + r^2 (a^2+\frac{a^{0.3}}{b}) \right]}_\text{growth rate} \times  \underbrace{ C_0}_\text{initial} \end{equation}
I just checked my server's /var/log/auth.log and found that I'm getting over 500 failed password/break-in attempt notifications per day! My site is small, and its URL is obscure. Is this normal? Should I be taking any measures? Calculating Latitude/Longitude X miles from point? I am wanting to find a latitude and longitude point given a bearing, a distance, and a starting latitude and longitude.  This appears to be the opposite of this question ().  I have already looked into the haversine formula and think it's approximation of the world is probably close enough.  I am assuming that I need to solve the haversine formula for my unknown lat/long, is this correct? Are there any good websites that talk about this sort of thing? It seems like it would be common, but my googling has only turned up questions similar to the one above.  What I am really looking for is just a formula for this. I'd like to give it a starting lat/lng, a bearing, and a distance (miles or kilometers) and I would like to get out of it a lat/lng pair that represent where one would have ended up had they traveled along that route. Appending to an ObjectOutputStream Minecraft item right/left click detection Every open set in $\mathbb{R}$ is a countable union of closed sets Interpreting coefficient in a linear regression model with categorical variables I will give my examples with R calls. First a simple example of a linear regression with a dependent variable 'lifespan', and two continuous explanatory variables.  data.frame(height=runif(4000,160,200))-&gt;human.life human.life$weight=runif(4000,50,120) human.life$lifespan=sample(45:90,4000,replace=TRUE) summary(lm(lifespan~1+height+weight,data=human.life))  Call: lm(formula = lifespan ~ 1 + height + weight, data = human.life)  Residuals: Min       1Q   Median       3Q      Max  -23.0257 -11.9124  -0.0565  11.3755  23.8591   Coefficients:              Estimate Std. Error t value Pr(&gt;|t|)     (Intercept) 63.635709   3.486426  18.252   &lt;2e-16 *** height       0.007485   0.018665   0.401   0.6884     weight       0.024544   0.010428   2.354   0.0186 *   --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   Residual standard error: 13.41 on 3997 degrees of freedom Multiple R-squared: 0.001425,   Adjusted R-squared: 0.0009257  F-statistic: 2.853 on 2 and 3997 DF,  p-value: 0.05781   In order to find the estimate of 'lifespan' when the value of 'weight' is 1, I add (Intercept)+height=63.64319  Now what if I have a similar data frame, but one where one of the explanatory variables is categorical?  data.frame(animal=rep(c("dog","fox","pig","wolf"),1000))-&gt;animal.life animal.life$weight=runif(4000,8,50) animal.life$lifespan=sample(1:10,replace=TRUE) summary(lm(lifespan~1+animal+weight,data=animal.life))  Call: lm(formula = lifespan ~ 1 + animal + weight, data = animal.life)  Residuals: Min      1Q  Median      3Q     Max  -4.7677 -2.7796 -0.1025  3.1972  4.3691   Coefficients:             Estimate Std. Error t value Pr(&gt;|t|)     (Intercept) 5.565556   0.145851  38.159  &lt; 2e-16 *** animalfox   0.806634   0.131198   6.148  8.6e-10 *** animalpig   0.010635   0.131259   0.081   0.9354     animalwolf  0.806650   0.131198   6.148  8.6e-10 *** weight      0.007946   0.003815   2.083   0.0373 *   --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   Residual standard error: 2.933 on 3995 degrees of freedom Multiple R-squared: 0.01933,    Adjusted R-squared: 0.01835  F-statistic: 19.69 on 4 and 3995 DF,  p-value: 4.625e-16   In this case, to find the estimate of 'lifespan' when the value of 'weight' is 1, should I add each of the coefficients for 'animal' to the intercept: (Intercept)+animalfox+animalpig+animalwolf? Or what is the proper way to do this?  Thanks Sverre Can we have threaded comments? The conversation often continues in the Comments and important information is held in the comments. I'd like to have threaded comments there. What regression model is the most appropriate to use with count data? I am trying to get a little into statistics, but I am stuck with something.  My data are as follows:  Year   Number_of_genes 1990          1 1991          1 1993          3 1995          4   I now want to build a regression model to be able to predict the number of genes for any given year based on the data. I did it with linear regression until now, but I have done some reading and it does not seem to be the best choice for this kind of data. I have read that Poisson regression might be useful, but I am unsure what to use. So my question is:  Is there a general regression model for this kind of data? If no, what do I have to do to find out which method is the most  appropriate to use ( in terms of what I have to find out about the data)? xcode app crashing on launch with breakpoint How does quantum trapping with diamagnets work? I just saw  demonstration by someone from a Tel Aviv University lab.  What they achieved there is mind blowing. I myself own a levitron that uses the Hall effect to levitate a magnet, the problem with that is the magnet must always be flat facing the Hall effect base, any unbalance will wreck the levitation. But in the case of the video you can see that he isn't constrained by such things, the disk can levitate and stay still at whatever angle and orientation. Instead of being levitated, the disk is simply being held still.   How does this happen? He referred to this as quantum trapping, but I've little idea about what that is....  Also, what material is the base in these demos? Is the circular track in the demonstration magnetic? I assume this is so. Is there any conceivable way for this technology to make objects levitate on any surface? Does D&D 5e have a rule for character knowledge about monsters? In the 3rd and 4th editions of D&amp;D, there were explicit rules for determining if a character knew anything about a monster before them.  In 3rd edition, for example, use of the  skill with a general DC of 10 + the monster's HD allowed for determining one fact, plus one fact per 5 points over the check.  Looking at the Intelligence section of the 5e PHB, I don't see any similar notation.  Does 5e provide any guidance as to when a player could use their out-of-game knowledge about a monster, or when the player might be told things their character would probably know in-game? Image in a cell with a hyperlink the numer of partial function between two sets in combinatoric way $A$ and $B$ two sets. $|A|=k, |B|=n.$ I need to prove in a combinatoric way that the number of partial function from $A$ to $B$ is $(n+1)^k.$ I thing the number is $Σ(n^i),$ for $i=0$ to $k.$ but I have no idea how to show equality, and how to prove it in a combinatoric way.  If someone can show me the way or guide me that will be great!  thanks for helpers. Which are the spec bits in this cache? I have a direct mapped cache of size S with the line size L. The cache is physically indexed and tagged. The physical address is 50 bits, numbered from 0 to 49 (with 0 being the least significant bit). The machine has a word size of 4 bits and the memory is byte-addressable. Which bits of the 50 bits are compared with the address tag? Extracting numbers from string field using Python Parser of ArcMap Field Calculator? I am trying to calculate field test2 with only the numeric values from a string field test. The entire script is like:    def makestr(test)      list=[]      for s in test:          if s.isdigit():              list.append(s)      for a in list:          str=''.join(list)     But I keep getting an error:    Any ideas? "In a party people shake hands with one another" I know that to better balance paragon and epic level players against similar level monsters, WotC changed the math used for monsters for MM3, and I believe that they changed some of the types of powers they gave monsters.   If I want to update monsters from MM1 or MM2 to be in line with MM3 era monsters, what changes should I make? In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to infinity. What does the $\Delta t$ mean, since $t$ is not even an observable? Vertical component of moving weight at a 45 degree angle Here's an easier one. I use the leg press machine at the gym so I don't have to worrying about hurting myself while lifting heavier weight.  The weight glides on a track that looks to be 45 degrees.  What's the equation to figure out how much weight I would be able to squat normally.  IE the vertical component of moving 400lbs at a 45 degree angle. \AtEveryBibitem{\clearfield{Title}} in beamer? In my beamer presentation, I want to cite the reference without title. So, I tried:  \documentclass{beamer} \usepackage[   backend=bibtex8,   defernumbers=true,   sorting=none,   firstinits=true,   uniquename=init,   uniquelist=false,   refsegment=section,   citestyle=numeric ]{biblatex} \addbibresource{mini.bib} \AtEveryBibitem{\clearfield{Title}} \begin{document} \section{Start} \begin{frame}   first cite\footfullcite{Julie2006}   %\printbibliography \end{frame} \section{2nd} \begin{frame}   Second cite\footfullcite{gyof} \end{frame} \end{document}   with the mini.bib :  @article{gyof,   Author={BLJ},   Title={Some Title},   Journal={joural1},   volume={15},   pages={1337},   Year={1985} } @article{Julie2006,   Author={JBS},   Title={Some Other Title},   Journal={journal2},   volume={74},   pages={144411},   Year={2006} }   with \AtEveryBibitem{\clearfield{Title}} I was expecting no title will be produced, but thats not the case:   Is there any incompatibility between clearfield and footfullcite? Or I am just missing something?