How to make player rotate towards mouse
How do I make an object face the mouse position, but only on one plane?
Fit mixture of distributions to your time-series data in R I have time-series data containing 1440 observations and the plot of the data is   I want to fit the Gaussian Mixture Models (GMM) to the above plot, and for the same I am using Mclust function of  package. Finally, I want a fit somewhat like this:   On using Mclust function, I do get following statistics     mclus_data &lt;- Mclust(givendataseries)    &gt; summary(mclus_data) ---------------------------------------------------- Gaussian finite mixture model fitted by EM algorithm  ----------------------------------------------------  Mclust E (univariate, equal variance) model with 8 components:   log.likelihood    n df      BIC      ICL        9525.438 1440 16 18934.52 18183.67  Clustering table:    1    2    3    4    5    6    7    8  1262    0    0    0    0   13  114   51    In the above statistic, I can not understand following:   Significance of log.likelihood, BIC and ICL. I can understand what each of them is, but what their magnitude/value refers to? It shows there are 8 clusters, but why cluster no. 2,3,4,5 has 0 values? What does this mean? From the plot it is clear that there must be two Guassians, but why Mclust function shows there are 8 Guassians?   Update: Actually, I want to do model based clustering of time series data. But currently  I want to fit the distribution to my raw data, as shown in Figure 1 on page no. 3 of  paper. For your quick reference, mentioned figure in said paper is How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$? Show that $\,\displaystyle\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$.   I'm thinking right now (though not getting anywhere with it) that I want to expand out the summation portion to $i!/2!(i-2)!$ and simplify from there? Not sure if that will help, not to mention if I put $1$ in for $i$ I get $1/-2$ which I don't think is right.   Anyone care to shed some light on the subject?   Thanks. When umpire change the cricket ball, was the old ball thrown as waste or keep for reuse? I've been modeling an F-15, but when I rotate the flaps on Y-Axis the Flaps offset from the wing and they look like they are about to fall out, so I end up correcting it by rotating in the X and Z-axis to align them correctly.  However when I rotate them back from the Y-Axis they look distorted again because I did rotations on the X and Z axis. I tried riding it, no help. I saw something about custom orientation to fix it but that was not clearly explained and it was done on an ideal plane that was (0,0,0); mine is pre-rotated on all axis.   I'll take scripts if needed and I'm using Blender 2.8.  When I rotate it on the Y-Axis:    Fixing it using X and Z rotation:    Rotating it back on the Y distorted it again:    Here's the wing with ailerons and flaps: Which one is correct?   Neither my friend nor I feel my best in the morning. Neither my friend nor I feel her best in the morning. Neither my friend nor I feel our best in the morning.    I already know that the verb agrees with the subject closer to the verb:   Neither my friends nor my brother understands me. (correct) Neither my friends nor my brother understand me. (wrong)   AND   Neither my brother nor my friends understand me. (correct) Neither my brother nor my friends understands me. (wrong) So I am in an introductory linear algebra(with proofs) class, and I came across the following theorem:  If $S$ is a subspace of a vector space $V(F)$ and is generated by $\{a_1,...,a_n\}$ then any subset $\{b_1,...,b_m\}$ of $S$ with $m&gt;n$ is linearly dependent.   The proof in the textbook is done through induction (as most proofs regarding finite sets are) but I really do not follow it and I feel there is a simpler way of doing it. A hint would be appreciated. I have a friend who has got a computer that is not connected to the Internet. Is there any way to install software offline easily? I'm from Western Pennsylvania. Until I moved away, I never realized that when I omitted the to be from phrases like needs to be cleaned, my usage was different than what most English speakers are accustomed to. Is it wrong? See all my questions across all Stack Exchange sites? A dollar amount $\${-}67.9{-}$ is divisible by 72. What is this number? A client buys 72 turkeys. On the receipt, 2 digits are missing, the first and the last. So, the total price is $\${-}67.9{-}$. Find a way to make the price of each turkey round at the second digit without trial-and-error method.  So, the answer is obviously $\$5.11$/turkey, so $\$367.92$ total. I found that with with 2-3 trial-and-error.  I bypassed his problem by using python and made a script that tries every combination and assures it is divisible by 0.01.   Please help me find a mathematical way of solving this problem. Fix terminal after displaying a binary file Factorial of 0 - a convenience? Where can I find examples of good Mathematica programming practice? TimedRotatingFileHandler Changing File Name? Unsung hero dilemma This is partly related to  question.  I ran some queries on odata for my work on Stack Overflow, and I have found that my statistics are the following ones:  Accepted answers: 148 Zero score accepted answers: 36 Percentage of total: 24,3%  I probably fit the idea of the Unsong hero badge, as I've mostly been active in  questions, from when it only had around 200 Questions until now.  To get the badge I could either try to get one of my accepted answers downvoted once, that would give me a 25% accept rate; I could also delete 4 of my accepted answers with 1 or more score. That would also give me the badge, but this just seems wrong: You are actually encouraging me to either try to get a down-vote on a good answer, or delete good answers.  So, should I delete good answers to receive a gold badge?  Update: It's not that I care much if I get a badge or not, it's only a badge after all and not why I spend time on Stackoverflow anyways. But it's not ideal [read: problem] that I'm encouraged to delete accepted answers or try to get downvotes to achieve a badge. Computing $\lim_{n\rightarrow \infty} \frac{1+\sqrt{2}+\sqrt[3]{3}+\cdots+\sqrt[n]{n}}{n}$. I have a problem with the calculation of the following limit. \begin{equation} \lim_{n\rightarrow \infty} \frac{1+\sqrt{2}+\sqrt[3]{3}+\cdots+\sqrt[n]{n}}{n} \end{equation} I do not know where to start! Thank you very much I'm bugged by the following that's summarized on p. 109 of .     False theorem: All horses are the same color.      Proof by induction:      $\fbox{$P(n)$ is the statement: In every set of horses of size $n$, all $n$ horses are the same color.}$   $\fbox{Base Case or $P(1)$:}$ One horse is the same color as itself. This is true by inspection.   $\fbox{Induction Step:}$ Assume $P(k)$ for some $k \geq 1$.   $\fbox{Proof of $P(k + 1) :$}$   Since $\{H_1, H_2, ... , H_n\}$ is a set of $n$ horses, the induction hypothesis applies to this set. Thus, all the horses in this set are the same color.   Since $\{H_2, H_3, ... , H_{n+1}\}$ is also a set of $n$ horses, the induction step likewise holds for this set. Thus, all the horses in this set are the same color too.         Therefore, all $n +1$ horses in $\{H_1, H_2, H_3, ... , H_n , H_{n+1}\}$ are the same color. QED.   The issue the instructor was trying to point out is clearly valid. For the case $n = 1$, there is only ${H_1}$. So this case says nothing about possible overlapping elements of each set of $(n + 1)$, for instance $H_2$ in the above proof.    But it was proposed in the class discussion that this was the only problem. Had you been able to prove $P(2)$ true, then a proof of the above format would have been fine.    My interpretation is that yes, you could prove all horses are the same color, if you can prove that any set of two horses will be the same color. But this format would not work.  Why not? The problem I see is that the above proof is for the existence of at least one particular pair of sets of horses of sizes $n$ and $n + 1$, such that in each set, all horses are the same color.  Particularly when the set of size $n$ is a subset of the set of size $n + 1$.  In order to prove the induction step, don't you need to prove that sets of sizes $n$ and $n + 1$, do not necessarily contain the same, overlapping elements?  You could prove that any horse can be added to a set of 2 horses.  Take the last two, and they must be the same color, and so on.  Wwhatever color the first two happen to be, all other horses must thus be the same color.    Am I misinterpreting the example, or am I making a logical error? Thanks in advance. PythonTEX not working on current Overleaf compiler Is there a way to make PythonTEX compile as of today in Overleaf V2 ?  \documentclass[]{article} \usepackage[utf8]{inputenc} \usepackage{pythontex}  \begin{document} \begin{pyverbatim} def calc_ellipticity(theta, delta):     theta = np.deg2rad(theta)     psi = np.arcsin(np.sin(2*theta) * np.sin(delta))/2     return np.tan(psi) \end{pyverbatim} \end{document}   Compiling gives : ? PythonTEX ? Whenever I want to use the pipe operator in the terminal, I get a weird kind of "bug":    As is shown in the image above, I can type the exact same command twice and it will sometimes register it or sometimes include some spacing in the command, as can be seen in the error message. The only difference between the two commands was the speed I typed them, with fast typing the char sequence "| " (without the "") leading to the error. I've checked in the terminal settings if this sequence somehow triggers a shortcut, but I did not find anything.   In case it matters, I'm using a swiss keyboard. The layout is as follows:    To produce the "|" character, I press "alt + 7". Does anybody know what the cause of this problem is? I tried to learn Dvorak keyboard layout a few years ago, and got reasonably good at it, but I couldn't get past the fact that command-key shortcuts were no longer in the right place.  In particular, Ctrl+Z (undo), Ctrl+X (cut), Ctrl+C (copy), and Ctrl+V (paste) are all chosen specifically because of the location of those keys on a Qwerty keyboard (well, maybe Ctrl+C makes sense).  Ctrl+A (select all) and Ctrl+S (save) are also very convenient because of their Qwerty keyboard location.  Is there any way (on Windows XP) to use Dvorak except when a control key (Ctrl, Alt, and/or WinLogo) is pressed?  (Preferably without having to install any third party app.)