The Proximal Operator of the $ {L}_{1} $ Norm Function
$ {L}_{1} $ Regularized Unconstrained Optimization Problem
Animagi (Sirus specifically) and wands? I have 3 questions about animagus transformation and wands      Does animagus transformation require the use of a wand?   If yes, where does the wand go after the wizard transforms?   Again, if 1 is yes, how did Sirius transform into a dog in Azkaban?     Note that 2 and 3 are invalidated if the answer to 1 is no. If so, is it mentioned anywhere in the books, or can be implied by something in the books, that wand use is not required? I don't think Sirius managing to do it in Azkaban can be used as a proof here, as in Book 3 Wormtail needs a wand to change back into a rat When computing the covariance matrix of a sample, is one then guaranteed to get a symmetric and positive-definite matrix?  Currently my problem has a sample of 4600 observation vectors and 24 dimensions. rake db:migrate doesn't seem to work in production Colored item names in Minecraft? I came across a map and when I was playing I found some coloured and bolded item names. I thought it isn't possible as at most you can only use the custom name tag to rename things! Is there a way to colour and bold item names in vanilla Minecraft? External programs are OK. Oh, and the wiki page of formatting codes doesn't really do much. When your 10-year old boy says “It’s meta,” what does it mean? In what situation and of what sort of object they use this phrase? I asked about  a few days ago, quoting Maureen Dowd’s review of the movie, “J. Edgar” in New York Times.   I received six answers. But I still don’t get a clear idea of what “It’s meta” means because I don't understand (or have a total inability to comprehend) the concept of “self-referential.”   An answerer : “Meta in this fairly recent, casual context is supposed to mean self-referential, or recursive in some way. This is the sense in which my teenagers would use this term.”  So let me resubmit the question on “meta” in simpler format. When your teenager boy says “It’s (or this is) meta,” what does it mean? In what situation and of what sort of object they use this phrase?  I’m sorry for many users who lent me kind answers to my previous question. But I would like to get it fully on the meaning and usage of “it’s meta,” as a colloquial expression, not the meaning of meta as a prefix. How to install Ubuntu on portable external Hard Drive? OS: Windows 7. I want install Linux Ubuntu on portable external Hard Drive USB 2.0. I read a variety of methods, but I'm confused by contradictory advices and methods. Actually, installing Ubuntu on anything other than clean PC looks much more complicated than installing Windows. I need to have Ubuntu package + Python 2.7 + C compiler installed. My external hard drive is partially filled, I need to keep all files.   Will Ubuntu run entirely on external hardrive, without writing anythinhg to Windows system folders and to registry?  Can anyone post detailed guide how install Ubuntu on external hard drive? How much can a grappler with reach move a grappled creature inside its reach? I can't use the terminal while gedit command is running I know Americans commonly use &quot;damn&quot; or &quot;damned&quot; to describe things. Sometimes, more appropriately, it's even &quot;darn&quot; or &quot;darned&quot;. For example,  This damn/damned computer is too slow.  However, I can't wrap my head around when to use &quot;damn&quot; and when to use &quot;damned&quot;. Or is only one of them correct? What was the galaxy formation Rust saw before confronting Erol Childress? What was the galaxy formation Rust saw before confronting Erol Childress in  S01E08?  It was weird like out of the series. I guess it was some sort of hallucination, a product of Rust's madness or addiction. Are there any Combinatoric proofs of Bertrand's postulate? I feel like there must exist a combinatoric proof of a theorem like: There is a prime between $n$ and $2n$, or $p$ and $p^2$ or anything similar to this stronger than there is a prime between $p$ and $(\prod_p p) + 1$ (Euclid's theorem).  I was trying to prove one by the Sieve on this grid      1     2     3     4 ... p   p+1   p+2   p+3   p+4 ... 2p  2p+1  2p+2  2p+3  2p+4 ... 3p ........................... ........................... ........................... p^2 p^2+1 p^2+2 p^2+3 p^2+4 ...   but it did not work.  Do any good arguments like this exist? I don't expect anything as strong as Prime Number Theorem or even Bertrand, but surely a direct combination proof can prove that there are lots of primes? What will be the trajectory of the given motion If it is given that component of acceleration perpendicular to the velocity of a body has a constant, non-zero magnitude, how can we mathematically prove that the trajectory of the body will be circular?   I have basic knowledge of calculus, vectors and co-ordinate geometry. I can prove that the trajectory of a body in projectile motion is parabolic. I tried to follow a similar method to get an equation of circle but couldn't succeed. I tried forming parametric equations of x and y in terms of time t (the way we proceed when proving the parabolic path of a projectile) but could not reach the conclusion.  Edit: I have edited the question in order to improve it. However I still can not share my work on this question as I had asked the question almost 6 months ago and now I can not find where I tried solving it. Sincerely sorry for that. Let $G$ be a finite group. For each positive integer $m$, if $x^{m}=e$ has at most $m$ solutions in $G$, $G$ is cyclic.   What I have thought is that $n=\sum_{d\mid n}\phi(d)$ can be used to solve this and showing that $|G|$ order element in $G$ exists is enough. rsync a file from serverC to serverA through serverB Does $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}=1$ imply that $a_n$ convergent? Does the condition $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}=1$ imply that $a_n$ convergent?  When I say convergent I mean to $L\in \mathbb{R}$ or to $\infty$ or to $-\infty$  I have a gut feeling this statement is false, just can't find a series which contradicts it.  Thanks a lot 1970s or 80s kids book: girl's life taken over by a robot doppelganger version of herself I read this book between 1980-82 but it could have been written earlier.  It's about a girl who is dissatisfied with her life, as her parents have her on a diet and she wants to be able to eat what she wants. Someone offers her a solution: to come live in this large building where she can eat all the chocolate eclairs and other junkfood she wants, while a robot doppelganger android version of herself will take her place at home and at school.  The girl agrees, but finds that after week of eating mainly eclairs, she is sick and wants to eat a decent meal. But she is not allowed to eat anything else and has found herself to be a prisoner, so she sets out to get rid of the android and get her life back.   I don't recall the ending but it seemed the 'people' behind it all might have been aliens and the building might have been a kind of ship that then disappears. What Is the Real Name of the #? I used to say "sharp sign" to refer to the # sign.   Today a friend told me that the correct term is number sign or hash sign or even just hash.  What is the difference between these options and what's the correct usage of the names for this sign? "Dare speak" vs. "dare to speak" vs "dares to speak" Which is the most appropriate improvement in the following     I am surprised that he dares speak in such a tone to his father.     a) he dares to speak b) he dare to speak c) he dare speak    I think the answer should be 'c' but the book says 'a'. I have recently installed lubuntu 11.10 on my old laptop (acer aspire 5315 celeron) and observed that fan is not working properly on lubuntu side.I find it strange that it is working perfectly under window vista.   How could I solve this problem? The collection of all subsets of $\mathbb{Z}$ is uncountable, due to   But how can I prove that the collection of all finite subsets of $\mathbb{Z}$ is countable?