Function to add two matrices mod 2
What are the most common pitfalls awaiting new users?
Cell identification by Body Cells How do the B-cells and T-cells recognize or distinguish a body cell from a foreign particle?  I suspect something to do with this causes Auto Immune Disorders. If $A^2\succ B^2$, then necessarily $A\succ B$ I remember reading somewhere about the following properties of non-negative definite matrix. But I don't know how to prove it now.  Let $A$ and $B$ be two non-negative definite matrices. If $A^2\succ B^2$, then it necessarily follows that $A\succ B$, but $A\succ B$ doesn't necessarily leads to $A^2\succ B^2$.  How can you prove it? Thanks! Let $X$ be a random variable and let $g,f$ be real-valued, nondecreasing, and bounded.   Show that $\mathbb{E}[f(X)g(X)]\geq \mathbb{E}[f(X)]\mathbb{E}[g(X)]$  Having a hard time seeing where to start for some reasons, any hints?  I managed to write:  $\mathbb{E}[f(X)g(X)] = \frac{1}{4}\mathbb{E}[(f(X)+g(X))^2 - (f(X)-g(X))^2]$  But I'm not sure if this is in the right direction or not. are used by the Empire in a manner that is tactically identical to how a modern day army would use a tank, in that they are used as shock armour with powerful main guns which will punch through entrenched positions. (No combined arms tactics were used in the Battle of Hoth, but that's a different question altogether)  However, AT-AT walkers have a number of (rather lethal) drawbacks and no advantages that I can see compared to tanks.    They have footpads in place of treads, which greatly increase their ground pressure, and which will cause them to easily sink as compared to treads They have a high center of gravity and can be easily tripped, which was exploited in the Battle of Hoth. (granted that this was canonically presented as an oversight, albeit a rather stupid one, since most martial arts strongly emphasise lowering your CG.) They are slower than a modern main battle tank despite their long legs, which one would normally expect to grant additional mobility (max speed 60km/h on flat terrain, compared to 72km/h on flat terrain for the ). This is exacerbated by the fact that AT-AT walkers are using fusion power cells as compared to diesel engines.   It would seem that it would make far more sense for the Empire to remove the legs and mount the main chassis on treads, which would make the vehicle far more effective. Why then, did they not do this? It clearly was not the case that imperial Engineers lacked imagination, as they did produce .   Possible answers which I find implausible as advantages:  1: AT-AT walkers are tall, and therefore have a surveying advantage over the battlefield / have a better vantage point to fire from  Orbital satellites can provide the observation, and in any case air/orbital support should always be called in, especially if fire support from above is required. Recovering data off of a dead hard drive My hard drive died in my macbook and it no longer will start up. It will not mount in an external enclosure but disk utility is still reading that the hard drive is there, and I tried to repair disk and I am getting this error: (Disk Utility can’t repair this disk. Back up as many of your files as possible, reformat the disk, and restore your backed-up files.) So my question is how do I backup my files if the hard drive won't mount? The only way that I have been able to see the hard drive is through disk utility. I just want to be clear that I am using mac os x snow leapard. they were question banned; it turned out it (in part) it was because of deleted questions.   was deleted by the Community user.  I'm aware it will delete old posts that have a negative score, but for a minute or two, I was really puzzled as to why it was unilaterally deleted without some notation left.  Can we have the Community user leave a notation in a post's history as to why the post was deleted?    Something like the following would suffice:     Post deleted automatically due to having negative votes and no activity for three months I work in D8, I create a custom module first_module. By modules create a url and display all nodes by *.html.twig file.  Write code in controller.php  public function contentthree() {    $connection = Database::getConnection();    $query = $connection-&gt;select('node', 'n');   $query-&gt;fields('n', ['nid', 'type']);    $groups = $query-&gt;execute()-&gt;fetchAll();    foreach ($groups as $group) {     $events[] = [$group-&gt;nid, $group-&gt;type];   }    return [     '#theme'  =&gt; 'first_module_display',     '#events' =&gt; $events,   ]; }   In *.module  function first_module_theme($existing, $type, $theme, $path) {    return [     'first_module_display' =&gt; [       'variables' =&gt; ['events' =&gt; NULL],       'template'  =&gt; 'first-module-list',     ],   ]; }  function _get_node_details() {    $output = 'Welcome D8';    $output .= 'Node Details';    return $output; }   and create templates first-module-list.html.twig and display data  {%for key, data in events %}  {%for key1, data1 in data %}     {{ data1 }}  {% endfor %}  {% endfor %}   work fine and showing data correct. But, my question is how to call function _get_node_details() and how to render node details in first-module-list.html.twig files? How do I connect to a MySQL Database in Python? How do I connect to a MySQL database using a python program? How to intuitively understand eigenvalue and eigenvector? I'm learning multivariate analysis and I have learnt linear algebra for two semester when I was a freshman.  Eigenvalue and eigenvector is easy to calculate and the concept is not difficult to understand.I found that there are many application of eigenvalue and eigenvector in multivariate analysis. For example     In principal components, proportion of total population variance due   to kth principal component equal    $$\frac{\lambda_k}{\lambda_1+\lambda_2+...\lambda_k}$$   I think eigenvalue product corresponding eigenvector has same effect as the matrix product eigenvector geometrically.   I think my former understanding may be too naive so that I cannot find the link between eigenvalue and its application in principal components and others.   I know how to induce almost every step form the assumption to the result mathematically. I'd like to know how to intuitively or geometrically understand eigenvalue and eigenvector in the context of multivariate analysis(in linear algebra is also good).  Thank you! "Economic" vs. "economical" Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$ What is crop factor and how does it relate to focal length? I'm reading that a 50mm lens is recommended as a first prime lens for DSLR owners as it's supposed to give a 'natural' perspective, but when used on (most) DSLRs, the view is cropped, as if you were zoomed in by 1.5-1.6x, so it's more of a telephoto lens when used on a DSLR. I've also read however that the 50mm lens gives the same perspective on a DSLR and a 35mm, and shouldn't really be considered to be 'equivalent' to an 80mm lens as the crop factor isn't really a magic focal length changer.  Can someone explain how the image is different from (for example) a 50mm lens on a DSLR and an 80mm lens (assuming 1.6x crop factor) on a 35mm camera? Allow [tag:tag-name] syntax to link to any site User group (company) page that shows summary of all user accounts belonging to the same company/user group What is the difference between "INNER JOIN" and "OUTER JOIN"? $f$ differentiable except in $1$ point How did Enrico Fermi calculate the classical Fermi Problem? From Wikipedia: Fermi was known for his ability to make good approximate calculations with little or no actual data, hence the name. One example is his estimate of the strength of the atomic bomb detonated at the Trinity test, based on the distance travelled by pieces of paper dropped from his hand during the blast. Fermi's estimate of 10 kilotons of TNT was remarkably close to the now-accepted value of around 20 kilotons, a difference of less than one order of magnitude.  I have not been able to find any references explaining how he made this calculation. Please provide a reference or an example calculation.  See also: What "exactly" happens when someone turns to the Dark Side? When I saw the original Star Wars saga as a kid, the concept of the Dark Side imprinted in me was quite simple. You did a bad thing, so you're a bad person so you go to the Dark Side and keep doing bad things.  Now, obviously this doesn't hold true in reality. In my mind it is perfectly reasonable for Luke to kill the Emperor and Vader and then just flee the Death Star and rejoin the Alliance. After all they are at war, those are enemy officers that have captured him and are taunting him by threatening with death of all loved ones and the whole operation was intended to kill the Emperor anyway.   The same would hold true for Anakin. He could have killed Mace Windu to save the Chancellor and Padme but that doesn't mean he's going to then go mad and kill all Jedis including children. It doesn't add up from a merely psychological point of view. He had a set of objectives and that made him want to keep the Chancellor alive (quite valid by the way, Mace Windu is quite clumsy on that) but just after killing him he goes into "Yes master I'll do whatever you say" which from a normal point of view will NEVER ever make sense.  In both cases it seems like the assumption is once you use the Dark Side you completely turn to the Dark Side and become a different person that you were before. That would be coherent with Anakin "dying" and Vader being born.  Is that the way the Dark Side works? Is there any canon information about what happens when someone turns to the Dark Side? Specifically to whether they become a different person or how he or she actually changes?  Note: Vader is angry after he finds out Padme is dead, even though he's already turned.  Example of what I mean. In Buffy they explain how people that turn into Vampires lose their soul and it's taken over by a demon, and thus they are, in all effects, a different person with their memories. Prove no existing a smooth function satisfying ... related to Morse Theory Why can't the end code of an environment contain an argument?