I'm writing with the LNCS template on Overleaf, but one of my figures keeps displaying somewhere way behind where I explain it. Is there a way to specify where I want it to display?  \begin{figure}[hbt!]     \centering     \includegraphics[width=12cm]{Replay.eps}     \caption{Buffer Size for Experience Replay}     \label{Replay} \end{figure}     The figure is inserted to where the red arrow points to, but shows up two pages later.
How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference
Do photons bend spacetime or not? I have read this question:     where Safesphere says in a comment:     Actually, photons themselves don't bend spacetime. Intuitively, this is because photons can't emit gravitons, because, as any massless particles not experiencing time, photons can't decay by emitting anything. The latest theoretical results show that the gravitational field of a photon is not static, but a gravitational wave emanating from the events of the emission and absorption of the photon. Thus the spacetime is bent by the charged particles emitting or absorbing photons, but not by the photons themselves.        where John Rennie says:     as far as I know there has been no experimental evidence that light curves spacetime. We know that if GR is correct it must do, and all the experiments we've done have (so far) confirmed the predictions made by GR, so it seems very likely that light does indeed curve spacetime.   Now this cannot be right. One of them says photons do bend spacetime, since they do have stress-energy, but it is hard to measure it since the energy they carry is little compared to astronomical body's stress-energy. So they do bend spacetime, it is just that it is hard to measure it with our currently available devices.  Now the other one says that photons do not bend spacetime at all. It is only the emitting charge (fermion) that bends spacetime.  Which one is right? Do photons bend spacetime themselves because they do have stress-energy or do they not? Why is plain-hash-then-encrypt not a secure MAC? I was working on a problem in group theory, which asks about the automorphism group of a direct product of groups.  Okay, so I know that if $G,H$ are two groups whose orders are relatively prime, then $\operatorname{Aut}(G\times H)\cong\operatorname{Aut}(G)\times \operatorname{Aut}(H)$.  I also know that if $G,H$ are abelian and simple and isomorphic, then $\operatorname{Aut}(G\times H)\cong \operatorname{GL}_2(\mathbf{Z}_p)$ where $p$ is the order of $G$.  What I don't know is the following: what if $G,H$ are simple, yet not abelian? Let us for now focus on a more restricted case where $G\cong H$, in particular, $G=H$. What can we say about the group $\operatorname{Aut}(G\times H)$? (I heard something about this group being related to what is called "wreath product", which I do not know...)  Thanks bunch in advance! Dumbed-down explanation how scientists know the number of atoms in the universe? It is often quoted that the number of atoms in the universe is 10$^{70}$ or 10$^{80}$.  How do scientists determine this number?   And how accurate is it (how strong is the supporting evidences for it)?  Is it more likely (logically >50% chance) that the numbers are right, or is it more likely that the numbers are wrong? How do you find the directory of a command? What happens if I use RAM of a faster speed than the CPU supports? Looking at the  CPU, under Memory types it says "DDR3-1333/1600". My question is, in what way does the CPU limit the RAM speed? What would happen if I put in a DDR3-2133 RAM chip together with the CPU, if the motherboard supports the faster RAM speed? Would it be better to get a RAM chip that is DDR3-1600 so it matches the CPU's listed frequency? If a function has a finite limit at infinity, does that imply its derivative goes to zero? I've been thinking about this problem: Let $f: (a, +\infty) \to \mathbb{R}$ be a differentiable function such that $\lim\limits_{x \to +\infty} f(x) = L &lt; \infty$. Then must it be the case that $\lim\limits_{x\to +\infty}f'(x) = 0$?  It looks like it's true, but I haven't managed to work out a proof. I came up with this, but it's pretty sketchy:  $$ \begin{align} \lim_{x \to +\infty} f'(x) &amp;= \lim_{x \to +\infty} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \lim_{x \to +\infty} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \frac1{h} \lim_{x \to +\infty}[f(x+h)-f(x)] \\ &amp;= \lim_{h \to 0} \frac1{h}(L-L) \\ &amp;= \lim_{h \to 0} \frac{0}{h} \\ &amp;= 0 \end{align} $$  In particular, I don't think I can swap the order of the limits just like that. Is this correct, and if it isn't, how can we prove the statement? I know there is  already, but I think this is different in two aspects. First, that question assumes that $\lim\limits_{x \to +\infty}f'(x)$ exists, which I don't. Second, I also wanted to know if interchanging limits is a valid operation in this case. How do I start Nautilus as root? Read data from Excel file in Objective-C (iPhone) E:Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages I am not sure what caused this error, but here is what the whole error says, and also this is sitting as a notification, and preventing me from updating any software using Update Manager - Please provide some assistance or tell me how to figure out what to do to fix it.  Could not calculate the upgrade  An unresolvable problem occurred while calculating the upgrade.  Please report this bug against the 'update-manager' package and include the following error message: 'E:Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.' Is it supposed to be a HTML or an HTML I've seen many people who say:     This is a HTML page.   Yet I've also seen many people who say:     This is an HTML page.   Are both usages equally correct?  Or, which is the grammatically correct one?       Possible Duplicates: Here is my candidate for  the most elementary proof that $\lim_{n \to \infty}(1+1/n)^n $ exists. I would be interested in seeing others.  $***$ Added after some comments: I prove here by very elementary means that the limit exists. Calling the limit "$e$" names it. $***$  It only needs Bernoulli's inequality (BI) in the form $(1+x)^n \ge 1+nx$ for $x &gt; -1$ and $n$ a positive integer, with equality only if $x = 0$ or $n = 1$. This is easily proved by induction: It is true for $n=1$, and $(1+x)^{n+1} = (1+x)(1+x)^n \ge (1+x)(1+nx) = 1+(n+1)x+nx^2 \ge 1+(n+1)x $. (If $-1 &lt; x &lt; 0$, if $1+nx \ge 0$, the above proof goes through, and if $1+nx &lt; 0$, $1+mx &lt; 0$ for all $m \ge n$ so certainly $(1+x)^m &gt; 1+mx$.)  This proof originally appeared in N.S Mendelsohn, An application of a famous inequality, Amer. Math. Monthly 58 (1951), 563 and uses the arithmetic-geometric mean inequality (AGMI) in the form $\big(\sum_{i=1}^n v_i/n\big)^n \ge \prod_{i=1}^n v_i$  (all $v_i$ positive) with equality if and only if all the $v_i$ are equal.  Let $a_n = (1+1/n)^n$ and $b_n = (1+1/n)^{n+1}$.  We will prove that $a_n$ is an increasing sequence  and $b_n$ is an decreasing sequence.  Since $a_n &lt; b_n$, this implies,  for any positive integers $n$ and $m$ with $m &lt; n$  that $a_m &lt; a_n &lt; b_n &lt; b_m$.  For $a_n$, consider n values of $1+1/n$ and $1$ value of $1$.  Since their sum is $n+2$ and their product is $(1+1/n)^n$, by the AGMI,  $((n+2)/(n+1))^{n+1} &gt; (1+1/n)^n$,  or $(1+1/(n+1))^{n+1} &gt; (1+1/n)^n$,  or $a_{n+1} &gt; a_n$.  For $b_n$, consider $n$ values of $1-1/n$ and $1$ value of $1$.  Since their sum is $n$ and their product is $(1-1/n)^n$, by the AGMI,  $(n/(n+1))^{n+1} &gt; (1-1/n)^n$  or $(1+1/n)^{n+1} &lt; (1+1/(n-1))^n$,  or $b_n &gt; b_{n+1}$.  Since $b_n-a_n  = (1+1/n)^{n+1} - (1+1/n)^n = (1+1/n)^n(1/n) =a_n/n $ and every $a_n$ is less than any $b_n$ and $b_3 = (1+1/3)^4 = 256/81 &lt; 4$, $b_n-a_n &lt; 4/n$, so $b_n$ and $a_n$ converge to a common limit.  These proofs do not seem to be really elementary,  since they use the AGMI.  However, they use a special form of the AGMI,  where all but one of the values are the same,  and this will now be shown to be implied by BI,  and thus be truly elementary.   Suppose we have $n-1$ values of $u$ and $1$ value of $v$ with $u$ and $v$ positive.  The AGMI for these values is  $(((n-1)u+v)/n)^n \ge u^{n-1}v$  with equality if and only if $u = v$.  We will now show that this is implied by BI: $(((n-1)u+v)/n)^n \ge u^{n-1}v$  is the same as  $(u+(v-u)/n)^n \ge u^n(v/u)$.  Dividing by $u^n$,  this is equivalent to  $(1+(v/u-1)/n)^n \ge v/u$.  By BI,  since $(v/u-1)/n &gt; -1/n &gt; -1$, $(1+(v/u-1)/n)^n \ge 1+n((v/u-1)/n) = v/u$  with equality only if $n=1$ or $v/u-1 = 0$. Thus BI implies this version of the AGMI. In blender cycles render engine, how do I put a movie clip on a plane so it displays the video? I want the video to be on the plane if there is a way. I am trying to understand Maximum likelihood estimation but it looks like I am missing something rather elementary.          suppose we have an iid random sample $X_1, X_2,..., X_n$ for which the probability density function of each $X_i$ is $f(x_i; \theta)$ where $\theta$ is an unknown parameter. Then, the joint probability density function of $X_1, X_2,..., X_n$ is given by:          $f(X_1=x_1,X_2=x_2,\cdots,X_n=x_n)=\prod_{i=1}^{n} f(x_i, \theta)$      In Maximum Likelihood estimation, we try to maximize $f$ as a function of $\theta$.  Question: Why do we maximize probability density instead of probability? In what way does it make sense?  Edit: As explained in the answers, the probability of choosing a finite number of sample points from a continuous probability distribution is zero, so maximizing probability doesn't make sense, but how does maximizing probability density make sense? Execute Java from command line Completing a 3x3 correlation matrix: two coefficients of the three given I was asked this question in an interview.  Lets say we have a correlation matrix of the form \begin{bmatrix}1&amp;0.6&amp;0.8\\0.6&amp;1&amp;\gamma\\0.8&amp;\gamma&amp;1\end{bmatrix}  I was asked to find the value of gamma, given this correlation matrix. I thought I could do something with the eigenvalues, since they should be all greater than or equal to 0.(Matrix should be positive semidefinite) - but I don't think this approach will yield the answer. I am missing a trick.  Could you please provide a hint to solve for the same? I have two examples of different scenarios that are confusing to me.  First, if I have a 1/1 creature with first strike and deathtouch, and my opponent blocks it with a 2/2 creature, will my creature die? I can see two alternative ways this could play out and I'm not sure which is correct.   My creature deals his first strike damage, immediately killing the opponent's creature before he is able to deal combat damage as a state-based effect. My creature deals his first strike damage, which would normally be lethal due to deathtouch, but state-based effects are not checked, and thus the opposing creature deals his damage and both die.   I'm almost positive in this case that it's the first option above.  What gets trickier is, for example, if a creature has first strike and a triggered ability "Whenever this creature deals combat damage to a creature, return that creature to its owner's hand."  This is not a state-based effect, but rather uses the stack. Similar to above, there are two possibilities.   My creature deals his first strike damage, and his triggered ability is placed on the stack. The stack waits to resolve until after all combat damage is dealt, so the opposing creature still kills mine. My creature deals his first strike damage, and his triggered ability is placed on the stack. Both players now gain priority between first strike and combat damage (which I don't think normally happens, thus my confusion). The stack finishes resolving, and the opponent's creature doesn't have a chance to deal damage.   Can someone clarify this area of the rules? I have noticed that some browsers (in particular, Firefox and ) are very zealous in using cached copies of .css and .js files, even between browser sessions. This leads to a problem when you update one of these files, but the user's browser keeps on using the cached copy. What is the most elegant way of forcing the user's browser to reload the file when it has changed? Ideally, the solution would not force the browser to reload the file on every visit to the page.  I have found  and  suggestion to be useful. It turns out there is a term for this: auto-versioning. I have posted a new answer below which is a combination of my original solution and John's suggestion. Another idea that was suggested by SCdF would be to append a bogus query string to the file. (Some Python code, to automatically use the timestamp as a bogus query string, was .) However, there is some discussion as to whether or not the browser would cache a file with a query string. (Remember, we want the browser to cache the file and use it on future visits. We only want it to fetch the file again when it has changed.) We hold an L1 visa (Citizens of India) and are planning a cruise to the Bahamas this summer. Are there any Visa requirements to enter Bahamas. Asking users to accept answer when they comment that it answers their question I've had a couple of answers today where the OP indicated via a comment that I solved their problem, but the question wasn't upvoted or accepted.  In both cases the person probably wasn't able to upvote since they were new, but they could have accepted my answer. I felt a little guilty asking them to accept the answer, but since it solved their problem I felt that it would help others who stumbled on the question trying to solve their own problem to know that my solution really was the answer. Is asking the OP to accept your answer when they've said that it solved their problem a reasonable thing to do or does that feel like nagging for reputation?