Due to  I will have to revert back to Ubuntu 12.04 LTS when . I see that , LibreOffice 3.5, and other outdated (functionality-wise) software.  Though I have no problem compiling Firefox, LibreOffice, and other apps, I would like to know how could I find out what the currently available software versions are. How could I check this before installing Ubuntu 12.04? I suppose that at least Firefox would have been updated (due to Mozilla update policy), but I would like to check first before I install.  Is there some way to query the Canonical repos for the latest software versions available for 12.04 from my current 12.10 system? Would it be easier to check from some web interface on Launchpad? I'm looking for something similar to aptitude show foobar, but for which I could specify the distro version that the results would be returned for.  I could install a virtual machine to check, but I find that cumbersome and not really practical as a day-to-day solution should I ever need to do a similar check in the future.
How can I check the version of the available package in the Ubuntu repositories without installing it?
Validity of maximising log-likelihood for maximum likelihood estimation For reasons owing to mathematical convenience, when finding MLEs (maximum likelihood estimates), it is often the log-likelihood function---as opposed to the standard likelihood function---which is maximised.  From what I've gathered, this approach is deemed valid as a result of the monotonically increasing nature of the (natural) logarithm function.  My understanding of a monotonically increasing function is: for all $x$ and $y$ (defined on a subset of the reals), if $x \leq y$ then $f(x) \leq f(y)$.  This, however, does not appear to be the case for all log-likelihood functions; for example: for the log-likelihood $\text{Gamma}(3, 5)$ function, if $x = 0.15$ and $y = 0.46$, then $f(x) = -0.59$ and $f(y) = -1.19$.  Clearly, I've misunderstood this concept. Fundamentally, I guess I'm asking can somebody (preferably mathematically) demonstrate why:  $$ \hat{\theta} = \text{argmax} \text{ } L(\theta) = \text{argmax} \text{ } \text{log} \text{ } L(\theta) $$  where $\hat{\theta}$ is the MLE for a given likelihood function. custom button visibility list view I need a robust and simple way to remove illegal path and file characters from a simple string. I've used the below code but it doesn't seem to do anything, what am I missing?  using System; using System.IO;  namespace ConsoleApplication1 {     class Program     {         static void Main(string[] args)         {             string illegal = "\"M&lt;&gt;\"\\a/ry/ h**ad:&gt;&gt; a\\/:*?\"&lt;&gt;| li*tt|le|| la\"mb.?";              illegal = illegal.Trim(Path.GetInvalidFileNameChars());             illegal = illegal.Trim(Path.GetInvalidPathChars());              Console.WriteLine(illegal);             Console.ReadLine();         }     } } I've been reading , and I would like to know why the Lasso provides variable selection and ridge regression doesn't.  Both methods minimize the residual sum of squares and have a constraint on the possible values of the parameters $\beta$. For the Lasso, the constraint is $||\beta||_1 \le t$, whereas for ridge it is $||\beta||_2 \le t$, for some $t$.  I've seen the diamond vs ellipse picture in the book and I have some intuition as for why the Lasso can hit the corners of the constrained region, which implies that one of the coefficients is set to zero. However, my intuition is rather weak, and I'm not convinced. It should be easy to see, but I don't know why this is true.  So I guess I'm looking for a mathematical justification, or an intuitive explanation of why the contours of the residual sum of squares are likely to hit the corners of the  $||\beta||_1$ constrained region (whereas this situation is unlikely if the constraint is $||\beta||_2$). This is irritating me. I seen several suggestions (all using different files and syntax) and none of them worked.  How do I set an environment variable for a specific user? I am on debian squeeze. What is the exact syntax I should put in the file to make ABC = "123"? I installed Blender from official Ubuntu repository but its version is always behind the version available from the official Blender website.  I'm aware that I can launch the program within the downloaded folder, but i want to replace the install version with a new version downloaded from the website?   It must be present in the unity launcher.  I'm also aware of the available PPA's that are available, however I just want to install Blender manually.  Thanks in advance Is it OK to reduce the charging current for a Li-ion 18650 battery? I am using NCR18650 batteries with the tp4056 charging module.  When I connect the charger at 2.8&nbsp;V (fully discharged), the tp4056 IC is getting hot at a 1&nbsp;A charge current. Is it OK to reduce this charge current by changing the charge current selecting resistor? So the tp4056 IC heat would be reduced, wouldn't it?  For my application I don't need a quick charge. With a low current, charging time will be increased, but it does not matter for my application.  Will reducing the charge current affect the battery's lifetime? Or will it damage the battery?  I am trying to reduce the heat of the tp4056 IC by reducing the charging current, maybe from 1&nbsp;A to 500&nbsp;mA or less. The 18650 battery never heats for a 1&nbsp;A charge current. Primes congruent to 1 mod 6 I came across a claim that I found interesting, but can't seem to prove for some reason. I have the feeling it should be easy  a prime $p$ can be written in the form $p = a^2 -ab +b^2$ for some $a,b\in\mathbb{Z}$ if and only if $p\equiv 1\bmod{6}$ How to translate coordinates on the earth I'm looking to install 32-bit windows with IIS to dual-boot with my 64-bit edition of windows on a laptop. I have a ten gig partition on my harddrive - is this large enough for a simple Windows install and a few programs?   I've never dual booted before, so I'm not quite sure how easy it is to mess up the process. Can you recommend any tutorials on how to set up a dual-boot configuration on Windows? Any way to add CSS for a single page/node? I'm cleaning up my big crazy style sheets (possibly pertinent to a future question) and I'm wondering the best way to add custom CSS to a specific node or page. In particular, my work site's home page is a Panel Page and it has a bunch of different styling. Right now the CSS is just included with the main theme style sheet. Is there a way to say, &quot;if this is node Foo, then add foo.css&quot;? Is  what I'm looking for? I might be interested in generalizing this to other nodes/sections/etc, but at the moment I just want to handle this one item. How do I enforce a password complexity policy? Rectifiability of a curve Let $f$ be a function defined on $[0,1]$ by   $$f(x) = { 0, \text{ if } x = 0} $$ $$f(x) = { x \sin \frac 1 x , \text{ if } 0 &lt; x \leq 1} $$  Prove that the curve $\{(x, f(x)) : x \in [0,1]\}$ is not rectifiable.   I'm not sure how to approach this. The general idea seems logical, we're proving that the length of the curve is infinite, but the method seems difficult to find. How are House points tabulated/tracked? Publishing a conference version of a journal paper at the same time ? (copyright issues) How to assign a SSL Certificate to IIS7 Site from Command Prompt Can you advise me whether it is possible or not to assign a SSL Certificate to a website in IIS7 using the APPCMD application?  I am familiar with the command to set the HTTPS Binding  appcmd set site /site.name:"A Site" /+bindings.[protocol='https',bindingInformation='*:443:www.mysite.com']   and how to obtain current mappings   %windir%\system32\inetsrv\Appcmd   but can not seem to find any way to map a site to a certificate (say the certificates hash for example) Fibonacci numbers and proof by induction Consider the Fibonacci numbers $F(0) = 0; F(1)=1; F(n) = F(n-1) + F(n-2)$.  Prove by induction that for all $n&gt;0$,  $$F(n-1)\cdot F(n+1)- F(n)^2 = (-1)^n$$  I assume $P(n)$ is true and try to show $P(n+1)$ is true, but I got stuck with the algebra. How do we reach $P(n+1)$ from $P(n)$? Also, strong induction may be used instead. Subgroups of finitely generated groups are not necessarily finitely generated I was wondering this today, and my algebra professor didn't know the answer.      Are subgroups of finitely generated groups also finitely generated?    I suppose it is necessarily true for finitely generated abelian groups, but is it true in general?  And if not, is there a simple example of a finitely generated group with a non-finitely generated subgroup?  NOTE:  This question has been merged with another question, asked by an undergraduate.  For an example not involving free groups, please see Andreas Caranti's answer, which was the accepted answer on the merged question. Comparing negatives: "she seems not to know" vs. "she doesn't seem to know" What is the difference in style and meaning between the following two:        She seems not to know.   She doesn't seem to know.      Is there a name to this type of construction? Calculating determinant with different numbers on diagonal and x everywhere else I'm having troubles solving the following determinant:  $$\left|   \begin{array}{cccc}     a_1 &amp; x &amp; \ldots &amp; x \\    x &amp; a_2 &amp; \ldots &amp; \vdots \\     \vdots &amp; \ldots &amp; \ddots &amp; x \\     x &amp; \ldots &amp; x &amp; a_n \\   \end{array} \right|$$  I have tried coming up with recurrent formula, but there's always one lingering row and column. I also tried finding values of x for which determinant is 0, hoping I could get a nice polynomial solution, with no luck.  By subtracting first row from every other I get somewhat nicer result, but there's still that one row/column which I can't solve. If all other columns are added to the first one and then I subtract the first row, then the column doesn't depend on x anymore, but I haven't found 1..n much more useful.