Mth position of the Nth Ordered permutation of an ordrered set all elements taken at once
Elementary formula for permutations?
Confidence interval around binomial estimate of 0 or 1 What is the best technique to calculate a confidence interval of a binomial experiment, if your estimate is that $p=0$ (or similarly $p=1$) and sample size is relatively small, for example $n=25$? Two ethernet ports on motherboard. How can I get double the bandwidth? Direct Question:  My evga classified motherboard has two ethernet ports.  I want to use them simultaneously to improve the speed of a remote connection.  (Yay for programming remotely).  How do I do this?  At present /etc/network/interfaces:  auto lo eth0 eth1  iface lo inet loopback  iface eth0 inet static address 192.168.1.202 netmask 255.255.255.0 gateway 192.168.1.2  ifrace eth1 inet static address 192.168.1.201 netmask 255.255.255.0   What should I change? Is there a package I need to install to bond the two channels.  Background: I do a lot of remote computing both from home to office and office to home.  But (to take my ISP out of the equation), let's frame the question as if I'm really just interested in maximizing the file transfer rate between two computers on the same (local) network.  Both boxes have dual ethernet motherboards.  Using a simple Linksys WRT54GS as a 5 port switch (ignore wireless and isp) -- how do I maximize the transfer rates between the computers?  Please Note: I'm not interested in load balancing -- Correct me if I'm wrong, but I want to bond the two channels together so that the box appears as if it has one connection that's twice as fast. How many connected components does $\mathrm{GL}_n(\mathbb R)$ have? I've noticed that $\mathrm{GL}_n(\mathbb R)$ is not a connected space, because if it were $\det(\mathrm{GL}_n(\mathbb R))$ (where $\det$ is the function ascribing to each $n\times n$ matrix its determinant) would be a connected space too, since $\det$ is a continuous function. But $\det(\mathrm{GL}_n(\mathbb R))=\mathbb R\setminus\{0\},$ so not connected.  I started thinking if I could prove that $\det^{-1}((-\infty,0))$ and $\det^{-1}((0,\infty))$ are connected. But I don't know how to prove that. I'm reading my notes from the topology course I took last year and I see nothing about proving connectedness... How to interpret autocorrelation plot in MCMC I am getting familiar with Bayesian statistics by reading the book Doing Bayesian Data Analysis, by John K. Kruschke also known as the "puppy book". In chapter 9, hierarchical models are introduced with this simple example: \begin{align} y_{ji}   &amp;\sim {\rm Bernoulli}(\theta_j)  \\ \theta_j &amp;\sim {\rm Beta}(\mu\kappa, (1-\mu)\kappa)  \\ \mu      &amp;\sim {\rm Beta}(A_\mu, B_\mu)   \\ \kappa   &amp;\sim {\rm Gamma}(S_\kappa, R_\kappa) \end{align} and the Bernoulli observations are 3 coins, each 10 flips. One shows 9 heads, the other 5 heads and the other 1 head.  I have used pymc to infer the hyperparamteres.  with pm.Model() as model: # define the          mu = pm.Beta('mu', 2, 2)     kappa = pm.Gamma('kappa', 1, 0.1)     # define the prior     theta = pm.Beta('theta', mu * kappa, (1 - mu) * kappa, shape=len(N))     # define the likelihood     y = pm.Bernoulli('y', p=theta[coin], observed=y)      # Generate a MCMC chain     step = pm.Metropolis()     trace = pm.sample(5000, step, progressbar=True)     trace = pm.sample(5000, step, progressbar=True)   burnin = 2000  # posterior samples to discard thin = 10  # thinning  pm.autocorrplot(trace[burnin::thin], vars =[mu, kappa])   My question is regarding the autocorrelation. How shall I interpret autocorrelation? Could you please help me to interpret the autocorrelation plot?    It says as the samples gets further from each other the correlation between them reduces. right? Can we use this to plot to find the optimum thinning? Does the thinning affect the posterior samples? after all, what is the use of this plot? When ssh'ing, how can I set an environment variable on the server that changes from session to session? How to make a good glow effect around a sun? Explicit space character? I'm wondering about the best way to do an explicit space character (I don't even know what it's properly called), like the ones you get in the \begin{verbatim*} environment. The closest I've found is  \sqcup   in math mode, but it seems like a bit of a hack to me. Is there any text symbol for what I'm looking for? Why is a subgroup with the index of 2 normal to the group?  I believe it has something to do with it being half and having nowhere to go. I would like to work out the Fourier transform of the Gaussian function   $$f(x) = \exp \left(-n^2(x-m)^2 \right)$$  It seems likely that I will need to use differentiation and the shift rule at some point, but I can't seem to get the calculation to work. Does anyone have any advice?  By the way, I am using   $$\mbox{FT}(f)(k)=\int_{-\infty}^\infty f(x)e^{-ikx}\,\mathrm d x$$  as my definition of a Fourier transform. Many thanks. How to delete column/field in PyQGIS? What does the "RW" logo mean in a DVD+R? If you look at this product:    you can clearly see that it is a DVD+R, i.e. once it is written, it cannot be erased/rewritten.  Then what does the "RW" logo (in the lower right corner) mean? I thought it stood for ReWritable, but experimenting with the medium shows that it is not. Rights if we possess Carta di Soggiorno? I have searched the internet but could not find specific information so if we have got the following document "Carta di Soggiorno di Familiare di Un Cittadino Dell'Unione" (Residence Card of a family member of a Union Citizen, Italy) issued by the Italian authority, what rights do we possess of working inside Italy and EU? What about travelling? Will we be requiring visas for the states which are are not in Schengen? I had a tin of golden syrup for a long time - longer than I care to admit. When I opened it up yesterday (to sweeten up some mulled wine), it was granular (a bit like honey can be), and black around the edges.   Is this 'bad', or just different?   Is the blackness the result of some chemical reaction with the tin?  And in general, does it eventually go off, or does it last indefinitely? Flagging summary improvement: filters Here is my flagging summary on SU:   Your flagging history   32 posts flagged as requiring moderator attention    2 are waiting for review   3 were marked valid   1 were marked invalid   (older flags were not recorded valid/invalid)    2 posts marked as spam    It is too complicated to look for invalid flags. Would it be possible to make filters on the top of the page (like on favorites for example) with:  By date, By type (off-topic, spam, dupes), By status (accepted, pending, rejected)  It would make it easier for reviewers to check their flagging and eventually know what to improve on.  Or is there another easy way to audit this? I am currently using Sheep It! to render my blend (built on v2.68c) on multiple computers, and I noticed something rather strange. According to the log on-site, the frames rendered from other people's blends were completing in 3 to 4 minutes. This was on an 4 core i5. My main rig (with an 8 core i7) was completing frames in no less than half an hour. How is this possible?  To clarify, these people's frames are very complex, often with very detailed textures. I have 2 objects in my blend. Below are the options I changed for my blend:   Aspect Ratio: 1000px x 1000px Output: PNG Clamp Indirect: 0.98 Render Sampling: 128 Min Light Bounces: 0 Max Light Bounces: 4 Cycles Render   Is there something in there that I should change to make it go faster? I can't really comprehend how it's going to quickly.  EDIT: To answer what @Duarte asked...   System Specs: i7-920, 3GB DDR3, GT 630, Windows 10 I have two circles, extended to form a sort of coin with a star on it. It is not complex at all. I have Firefox and Steam running in the background, but not actively. I've been away from the computer for 8 hours and noticed this behavior. (I am running Blender from Steam.) I made sure when I began rendering that the blend was set for CPU rendering.          And to answer what @pycoder asked, yes, I am using Cycles Render. Compute $\frac{1}{e}\sum\limits_{n=0}^{\infty}\frac{n^{k}}{n!}$ for $k=0, 1, 2 ... $ Using some matlab (I know it's cheating) I found that: $$k=0 =&gt; Result=1$$ $$k=1 =&gt; Result=1$$ $$k=2 =&gt; Result=2$$ $$k=3 =&gt; Result=5$$ $$k=4 =&gt; Result=15$$ $$k=5 =&gt; Result=52$$ $$k=6 =&gt; Result=203$$  This sequence is puzzling... Implementing a PIVOT query If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field. New Google SEO benefit with SSL - with only a few sections in SSL, or always on? Why was the previous Code of Conduct FAQ (and all answers) removed? I noticed that the  was deleted.   When the  came out, I tried to look for my old answer as well as others for comparison.  Why not just mark the old one superseded by [insert link]?  Note: I don't care about lost rep. There were a lot of useful links in answers and comments there (and some less-than-useful ones too).     Old CoC FAQ may be available  and . Source: (, ).