How to compute F-statistics for each features of regression models in glmnet?
Lasso and statistical signficance of selected variables
I’ve always understood that the phrase two weeks usually turns into two weeks’ when used as a modifier as in   I’m giving my two weeks’ notice.  I get two weeks’ vacation. (“two weeks’ holiday” for Brits)   with an apostrophe on the word weeks’, indicating that the vacation “belongs” to the weeks.   One way to explain this is the phrase “two weeks of vacation” being contracted to “two weeks’ vacation” – the vacation is “of” the weeks; that is, it is possessed by them.  But I’ve seen a lot of people omit the apostrophe in casual writing, and thinking about it, it seems plausible that the noun vacation would be plainly modified by the adjectival phrase two weeks.  But on the other hand, shouldn’t adjectival phrases be hypenated, namely two-weeks vacation?  Yet that seems wrong, too: the hyphenate should be singular, two-week vacation (like two-tone shoes) because .   touches on this (and references a good ) but doesn’t explain why the plural must be possessive in this case.   suggests that two weeks might be adverbial rather than adjectival, and thus resists being used attributively. But that still doesn’t quite explain this particular muddle of pluralization, possession, and attribution.  Given all this, why should “two weeks vacation” be written “two weeks’ vacation” with a possessive apostrophe? What is the best way to remove texture from a scanned textured photo paper? I have a bunch of scanned old family photos where the photo paper has a texture. Unfortunately, the texture of the photo scans quite well. What is the best way to remove the texture?  (Photoshop CS5) Stripping seasoning from cast iron After reading , I want to try to re-season a skillet with flaxseed oil; I'm fairly certain I did a terrible job when I seasoned the skillet several years ago. Is it possible to do this with steel wool or vinegar? (I don't have a self-cleaning oven, so that method is out.) Documents with typical LaTeX errors I am giving a LaTeX course and have the idea to let the students find and solve problems within a few documents. Basically they shall learn how to create minimal examples and read error messages.  However, currently I have no document with 'typical' errors around.  If someone has such examples from him- or herself or within this forum I would like to have the code or link. It does not matter if its short or long. It should just be enough to let the students play with it for some minutes. I stumbled across this relationship while I was messing around. What's the proof, and how do I understand it intuitively? It doesn't really make sense to me that the sum of odd numbers up to $2x + 1$ should equal $x^2$. How to find correct size inner tube I have 3 accounts that I am deleting - however, several hours after the 24 hour (+ grace period - end about 4-5 hours ago), the countdown completed, but disappeared and the accounts are still there.   I would rather not go through another 24 hours, and would like to have these accounts deleted (and yes, I have thought about it and this decision is not up for discussion).  Currently, the accounts are still there.  Could this please be seen to? tikz declare function and babel french option In the Wikipedia article , it says     After Newtonian gravitation was found to be inconsistent with special relativity, . . .   I don't see how Newtonian gravitation itself is inconsistent with special relativity.  After all, Newton's Universal Law of Gravitation is completley analogous to Coulomb's Law, so it would seem that, if there were an analogous "gravitational magnetic field", one could formulate a theory of gravitation in exact analogy with Maxwell's Theory of Electromagnetism, and of course, this would automatically be consistent with Special Relativity.  What about this approach to gravitation does not work?  The only problem I could see with this is the lack of evidence for a "gravitational magnetic field".  That being said, gravity is "weak" as it is, and my guess is that it would be extremely difficult to set up an experiment in which a massive body were moving fast enough for this "magnetic field effect" to be obsevable.  EDIT:  As has been pointed out to me in the answers, Newton itself is inconsistent with SR.  Similarly, however, so is Coulomb's Law, yet, electromagnetism is still consistent with SR.  Thus, how do we know that it is not the case that Newton's Law is the special "static" case of a more general gravitomagnetic theory exactly analogous to Maxwell's Theory:  Let $\mathbf{G}$ be the gravitation field, let $\rho$ be the mass density, and $\mathbf{J}$ be the mass current density, let $\gamma _0$ be defined so that $\frac{1}{4\pi \gamma _0}=G$, the Universal Gravitation Constant, let $\nu _0$ be defined so that $\frac{1}{\sqrt{\gamma _0\nu _0}}=c$, and suppose there exists a field $\mathbf{M}$, the gravitomagnetic field, so that the following equations hold: $$ \vec{\nabla}\cdot \mathbf{G}=-\frac{\rho}{\gamma _0} $$ $$ \vec{\nabla}\cdot \mathbf{M}=0 $$ $$ \vec{\nabla}\times \mathbf{G}=-\frac{\partial \mathbf{M}}{\partial t} $$ $$ \vec{\nabla}\times \mathbf{M}=\nu _0\mathbf{J}+\gamma _0\nu _0\frac{\partial \mathbf{G}}{\partial t} $$ where theses fields would produce on a mass $m$ moving with velocity $\mathbf{v}$ in our inertial frame the Lorentz force $\mathbf{F}=m\left( \mathbf{G}+\mathbf{v}\times \mathbf{M}\right)$.  This theory would automatically be consistent with SR and would reduce to Newton's Law of Gravitation for the case of gravitostatics:  $\frac{\partial \mathbf{G}}{\partial t}=\frac{\partial \mathbf{M}}{\partial t}=\mathbf{J}=0$.  (To be clear, you can't just set the time derivatives equal to $\mathbf{0}$ as it seems I have done.  Upon doing so, you obtain the corresponding static theory, which is technically incorrect (as you can easily see because it won't be relativistically invariant), but is nevertheless often a useful approximation.)  My question can thus be phrased as:  without appealing directly to GR, what is wrong with this theory? How to blacklist kernel modules? What is the result of $\infty - \infty$? I would say $\infty - \infty=0$ because even though $\infty$ is an undetermined number, $\infty = \infty$. So $\infty-\infty=0$. I have a table similar to this:  CREATE TABLE example (   id integer primary key,   name char(200),   parentid integer,   value integer);   I can use the parentid field to arrange data into a tree structure.  Now here's the bit I can't work out. Given a parentid, is it possible to write an SQL statement to add up all the value fields under that parentid and recurse down the branch of the tree ?  UPDATE: I'm using posgreSQL so the fancy MS-SQL features are not available to me. In any case, I'd like this to be treated as a generic SQL question.  BTW, I'm very impressed to have 6 answers within 15 minutes of asking the question! Go stack overflow! I've switched from Drupal 7.14 to 7.15 three weeks ago and therefore, I'm encountering a series of very sophisticated (for me) memory limit errors.  Those errors occur any time I'm trying to clear cache in performance or to run update scripts.  My hosting company has increased my memory limit in php.ini up to 126 M, 256 M, 512 M, and even 1024 M. But the errors still occur. I've migrated my site from shared to VPS, But the error incredibly still occurs. I have no way and no idea how to move forward.   Here are the errors:   Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 30 bytes) in /home/example/public_html/sites/all/modules/views/views.module on line 416 Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 108 bytes) in /home/example/public_html/includes/menu.inc on line 2736 Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 71 bytes) in /home/example/public_html/sites/all/modules/chain_menu_access/chain_menu_access.module on line 59 allocate 64 bytes) in /home/example/public_html/sites/all/modules/views/includes/base.inc on line 93 How do I kill background processes / jobs when my shell script exits? I am looking for a way to clean up the mess when my top-level script exits.  Especially if I want to use set -e, I wish the background process would die when the script exits. Find Nearby Accounts migration to Google Maps API v3 we have been using the Find Nearby Accounts app from appexchange for a while now. The app uses the Google Maps API vs 2 which is now deprecated and hence has rendered the app ineffective. I have tried migrating the Google maps API version for the app from v2 to v3 by generating a v3 API key. The URL for my salesforce instance was included in the creation of the Client ID under API Access. After all these steps, I still get the error "Problem with Address. I know the address is right.   Has anyone been able to get this working? Thanks. For which $f,g \in k[t]$, $k[f,g]$ is integrally closed? Let $f,g \in k[t]$, $k$ is a field of characteristic zero, $\deg(f)=n \geq 2$, $\deg(g)=m \geq 2$.     Is it possible to characterize all such $f$ and $g$ for which $k[f,g]$ is integrally closed in its field of fractions $k(f,g)$?   I do not mind to further assume that $k(f,g)=k(t)$ (but I do not want to assume that $k[f,g]=k[t]$, which makes my question trivial).  Thank you very much!  Edit: (i)  is relevant.  (ii) If also $k(f,g)=k(t)$, then being integrally closed is equivalent to $k[f,g]=k[t]$. Indeed: (a) If $k[f,g]=k[t]$ then $k[f,g]$ is integrally closed (since $k[t]$ is). (b) If $k[f,g]$ is integrally closed then, in particular, since $t \in k(t)=k(f,g)$ (= the field of fractions of $k[f,g]$) and obviously $t$ is integral over $k[f,g]$ (for example, $t$ is a root of $f(T)-f \in k[f,g][T]$) hence $t \in k[f,g]$, so $k[f,g]=k[t]$.  For example: $f(t)=t^2+1$, $g(t)=t^3-4t$. We have, $t= \frac{t(t^2-4)}{t^2+1-5}=\frac{g}{f-5}$, so $k(f,g)=k(t)$. By Abhyankar-Moh-Suzuki theorem, $k[f,g] \neq k[t]$, so $k[f,g]$ is not integrally closed. Similarly, for every $f,g$ such that $k(f,g)=k(t)$ and one of the degrees does not divides the other, then $k[f,g]$ is not integrally closed.  (iii) If also $k(f,g)=k(t)$ and $k$ is algebraically closed, then being integrally closed is equivalent to $H(t)=(f(t),g(t))$ is injective and $H'(t)=(f'(t),g'(t)) \neq (0,0)$ for every $t \in k$. Indeed, $k[f,g]=k[t]$ is equivalent to the new conditions (it is important that $k$ is algebraically closed!!).  Edit: What if we replace $k$ by an integral domain $D$ (which is a $k$-algebra)? See also  question. Why is Python running my module when I import it, and how do I stop it? continuity, discontinuity derivative and relation to being derivative but its partials are not continuous is $$f(x) =\begin{cases} x^2\sin(\frac{1}{x}) \mbox{ for } x\neq 0 \\ 0  \mbox{ for } x= 0\end{cases}$$ a continuous function specially at point x=0?  And why being derivable its derivative is not continuous at x=0 since  $$f`(x) =\begin{cases} 2x\sin\frac{1}{x}-\cos\frac{1}{x} \mbox{ for } x\neq 0 \\ 0  \mbox{ for } x= 0\end{cases}$$?  I suspect this as to do with being derivable a function f $\mathbb{R}^n\rightarrow\mathbb{R}^m$ that don't imply its partial derivatives are continuous .this I don't get it so far.however partials derivatives if continuous is derivable.  Can you provide me a more general case than just one variable where f is derivable but its partials are not continuous? Order of finite fields is $p^n$ Let $F$ be a finite field. How do I prove that the order of $F$ is always of order $p^n$ where $p$ is prime? Integral of the square of the normal distribution. Does someone know what the integral of the square of the normal distribution with standard deviation sigma over the range $-\infty$ to $+\infty$ is?  Thanks!