Load Graphics as Empty Boxes for Positioning and Quick Compiling
Draft mode for pgfplots
Which pronoun to refer to "person"? It? He or She? They? "When he found his seat on the plane, Sam recognized the person who was sitting in the seat next to his. It? She? was a woman he knew."  Which is more common/natural? Isn't 'it' more correct – grammatically speaking – than 'she', since 'a person' can be a 'he' or a 'she', and obviously you cannot use the singular 'they' here? Understanding English (Listening skills) What is the difference between the command  $ env FOO=bar baz   and  $ FOO=bar baz   What effect does env have? Meridian convergence. True north, magnetic north and grid north I'm having difficulty wrapping my mind around meridian convergence, the horizontal angular distance between true north and grid north.   Say I want to determine if a feature lies to the east or west of the central meridian (CM) by using true north and grid north designations on a topo map.   I realize grid north is parallel to the CM, while true north points to the poles, and magnetic north is the direction a compass points and constantly changing.   Looking at the figure below, I see grid north points to the east of true north. So does this fact alone mean everything on the grid is to the east of the true north, and therefore the CM? Does this simple fact mean that features in this grid lie to the east of the CM, or am I missing something.   Also, I realize I can just look at the tick marks and and see that this this grid in particular covers -80°22’ to -80°15, and the CM for zone 17R lies at 81°. But had I not known that and wanted to use the north arrows. Please explain. Preview on the right please, optionally? windows bat file error How to do volumetric lighting for a forest scene? I have scene that looks like this:   And I want to add volumetric lighting to it so that light forms a rays of light when it go through the trees like on this example that I found in youtube:   But the problem is that all of these tutorials show how to make this lighting coming from windows, but when I try to replicate it in my forest scene it looks like big ugly fog with cubical shape. Also the light is coming from the back of the camera (as you can see) and there are some spots that needs this special lighting (like places where light goes through trees) and some that don't (like big bright are on the bottom left corner) so I can't just add a giant cube to all of the scene. Assume that $Y_0,\ldots , Y_n$ are independent random variables with the following identical distribution: $Y_i=1$ with propability $p$ and $Y_i=0$ with propability $1-p$. Also set $S_0=0$ and $S_n=Y_0+\ldots + Y_n$.  It's quite trivial that $(Y_n)_{n\geq 0}$ is a Markov chain, and I managed to show that $(X_n)=(S_n)_{n\geq 0}$ is also a Markov chain, by showing that  $\mathbb{P}(X_{n+1}=i_{n+1}\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(X_{n+1}-X_n=i_{n+1}-X_n\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(Y_{n+1}=i_{n+1}-X_n\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(Y_{n+1}=i_{n+1}-i_n)=\mathbb{P}(Y_{n+1}+i_n=i_{n+1})=\mathbb{P}(X_{n+1}=i_{n+1}\,|\,X_n=i_n)$  However I am now running into the problem that I have to find whether or not $(X_n)=(S_0+\ldots + S_n)_{n\geq 0}$ is a Markov chain. I suspect that it isn't, but i'm having trouble finding a counterexample. I also need to find if $(X_n)=(S_n, S_0+\ldots+S_n)$ is a Markov chain, but I think this actually might be one, since $X_n$ gives "more information" (so to speak) to $X_(n+1)$. Again, having trouble actually proving that.  I appreciate any help, tips etc you can give me. Why Faddeev-Popov ghost cannot exist in external line? If $k=1$, we have \begin{align} \sum_{n\ge1}\frac{1}{\binom{2n}{n}}&amp;=\frac12\sum_{n\ge1}n\mathrm{B}(n,n)\\ &amp;=\frac12\int _{0}^{1}\sum_{n\ge1}n(t-t^2)^{{n-1}}{\mathrm  d}t\\ &amp;=\frac12\int _{0}^{1}\frac{1}{(t-t^2-1)^2}{\mathrm  d}t\\ &amp;=\frac13+\frac{2\sqrt3\pi}{27} \end{align} I wonder if there exists a general formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$ with $k\in\Bbb N^*$. This may involve some ${}_pF_q$ functions. 3.8 GPA, but 3 Fs and 1 D on transcript So here's a funny thing: I have 3 Fs and 1 D on my transcript, but my GPA is ~3.8, which is "high" because I double majored in math and computer science. The reason for those 4 bad grades is that I had 2 bad semesters where I suffered from depression; I didn't drop the classes before the deadline so I ended up failing the classes. However I retook the classes and got As in them (hence my GPA), and in fact got A/A-s in all subsequent classes (quite an improvement). I plan to apply to a master's for computer science, and eventually a phd. However I know the admission officers eyes will bleed when they see my transcript, despite my GPA, because my school keeps ALL grades on transcripts, even if the grades were replaced by retaking classes. Do I still have a chance at top-10 graduate school for computer science even with these grades (which were retaken and then aced)? Detect browser language in Rails The Node Editor won't work for the object selected At what age is the Force detectable in children? Graph of a continuous function is closed Hilbert, Gödel, and "God equations" - a 19th century lesson for 21st century physicists? It seems there are a lot of respected physicists appearing on pop-sci programs (discovery channel, science channel, etc.) these days spreading the gospel of   Three examples, quickly: 1) Many programs feature Michio Kaku saying that he is on a quest to find an equation, "perhaps just one inch long," which will "describe the whole universe."  2) Max Tegmark has come out with  in which he expresses the gut feeling that "nothing is off-limits" to science.  The subtitle of this book is My Quest for the Ultimate Nature of Reality.  3) In the series  there is talk about a search for the "God equation."  (A good counter-example would be Feynman, but his self-described "non-axiomatic" or "Babylonian" approach does not seem popular with physicists today.)  Is there any sense among physicists that it might be impossible to articulate the "ultimate nature of reality" in equations and formal logic?  It seems to me that physicists are following in the footsteps of the 19th century mathematicians (led by Hilbert) who were on a similar quest which was put to rest by Gödel's incompleteness theorems in 1931.  Is there any appreciation for how the Incompleteness Theorems might apply to physics?  Has any progress been made on  for the 20th century?  Shouldn't this be addressed before getting all worked up about a "God equation?" Book series with college students finding a way to open portals to other planets I got the storyline of this book series (I believe it was a series) told to me by a colleague at a former workplace but I can't remember the name of the author or of any of the books in the series. The first book is about a couple of college students who find a way to relatively easily open portals to pretty much wherever they want to go. One day, NASA(?) finally succeeds in sending astronauts to Mars(?). When they have just left the spaceship, one of them suddenly gets a tap on the shoulder, and when he/she turns around, these college students stand there in their homemade space suits, chuckling. I believe these students later also start a company that helps other organizations establish themselves on other planets, or perhaps even &quot;conquers&quot; and sells planets to other organizations. A later book in the series also describes a system that lets people upload their minds to the cloud. Some people choose to live solely in the cloud as virtual creatures, only deciding to &quot;descend&quot; into a &quot;flesh&quot; body when they need to perform some task that requires them to be in physical form. Some people also choose to live in physical form but as several entities, or clones, and sync their mind between the clones through this system, basically allowing them to, for example, run a one-man company with several &quot;instances&quot; of the same human who all share their knowledge and all know exactly what all other clones know in the same moment, effectively creating a super-efficient team of workers. Windows update doesn't progress beyond 0 KB 0% What happens to the semiconductor in an LED when it is given voltage that it cannot handle? Intraclass correlation coefficient vs. F-test (one-way ANOVA)? I'm a little confused regarding the intraclass correlation coefficient and one-way ANOVA.  As I understand it, both tell you how similar observations within a group are, relative to observations in other groups.  Could someone explain this a little better, and perhaps explain the situation(s) in which each method is more advantageous?