How to prove the convexity of $\operatorname{Tr}(WLW^T)$, where $L$ is a Laplacian matrix?
Is the function $\mbox{tr}(XAX')$ convex?
How do you reindex an array in PHP but with indexes starting from 1? I have seen some comments and speculations about the robot having an off switch or whatever. But I want to know if there is any source material or comment from the author on how they managed to pass the exam.  I have only seen the actual author's comment on Mineta:     But I was wondering if there are author notes for the other characters. How can we get rid of misspelled and unused (or "zombie") tags? During the re-tagging of questions, tags sometimes become orphaned from existing questions.  Are these zombie tags ever removed from the ?  What if a tag is misspelled and needs to be removed? How do we get rid of it? "Print" and "ui.Label" return different strings in console and in the UI in Google Earth Engine I am working on a variable label in Google Earth Engine and noticed that the label as printed in the console is not the same as the label shown on the map. Why is that? Code below:  var aoi = ee.Geometry.Polygon([[[-106.75701284923326, 42.31332966408458],           [-106.75701284923326, 42.003856624775146],           [-106.31755972423326, 42.06913460511273]]]);  var chirpsSelect = ee.ImageCollection("UCSB-CHG/CHIRPS/DAILY")             .filterDate('1985-01-01','2018-01-01')             .filter(ee.Filter.dayOfYear(3,6))             .filterBounds(aoi)  var chirpsStartImage = ee.String(chirpsSelect.first().get('system:index')) var dateStartString = ((((chirpsStartImage.slice(6,8)).cat('/')).cat(chirpsStartImage.slice(4,6))).cat('/')).cat(chirpsStartImage.slice(2,4))   var sortChirpsSelect = chirpsSelect.sort('system:index',false)  var chirpsEndImage = ee.String(sortChirpsSelect.first().get('system:index')) var dateEndString = ((((chirpsEndImage.slice(6,8)).cat('/')).cat(chirpsEndImage.slice(4,6))).cat('/')).cat(chirpsEndImage.slice(2,4)) var dateTitle = ee.String((dateStartString.cat(' to ')).cat(dateEndString))  print(dateTitle)  var dateLabel = ui.Label({   value: dateTitle })  var panel = ui.Panel() panel.add(dateLabel) Map.add(panel) I have recently noticed that in chat when I type enough and the profile picture expands with my message, the hat stays the same size and it stays in the same place (I have the  app): What is the product of the empty set? Give:  $fn(S)=\prod_{x\in S}x$  what is:  $fn(\emptyset)$  I can see reason that it would be defined as 1 or 0.    Note: I thought about restricting the domain of $S$ but that would make the problem less general. If there is no general answer then answers for restricted domains would be valid. permission error when installing ttf-mscorefonts-installer/Can't drop privileges as file couldn't be accessed by user '_apt' In , it is established that Thieves' Cant is more of an encoding system built on top of a language than a language in its own right. According to the Basic Rules,  is:  ...a secret mix of dialect, jargon and code allows you to hide messages in seemingly normal conversation. Only another creature that knows thieves' cant understands such messages. It takes four times longer to convey such a message than it does to speak the same idea plainly. In addition, you understand a set of secret signs and symbols used to convey short, simple messages, such as whether an area is dangerous or the territory of a thieves' guild, whether loot is nearby, or whether the people in an area are easy marks or will provide a safe house for thieves on the run. (PBR, p. 27)  Can two creatures communicate using Thieves' Cant if they do not have a basic spoken language in common, or if they are speaking different basic languages? E.g. if one creature knows Orcish, Goblin, and Thieves' Cant, and another creature knows Elvish, Giant, Common, and Thieves' Cant, can they communicate with each other by embedding Thieves' Cant into their own languages? Hypothetically speaking, I can see how this could be possible in our own world, if we assume that Thieves' Cant depends on nuances of body language, emphasis, and tempo, e.g., one might say to a non-Spanish speaker:  Tenemos quEEEEEEE ir (wink) a la tieeeeenda de (shuffle left foot) armas para (twirl hair and giggle) comprar una espada (wink twice) para mi herMANO (wag right pinky and nod).  The literal message itself (&quot;We need to go to the weapon store to buy a sword for my brother.&quot;) would just be a carrier - the real message might be hidden within the gestures and the accented and extended syllables. Perhaps the drawn-out &quot;E&quot; vowel means &quot;robbery planned&quot;, the wink means &quot;bank&quot;, shuffling the left foot means &quot;be there at sunset&quot;, etc., and these are things that you wouldn't necessarily need to know Spanish to extract. Is this how Thieves' Cant actually works, or does it require actual comprehension of the literal message transmitted before the &quot;secret&quot; message can be extracted from it? Why isn't the symmetric twin paradox a paradox? Two twin sisters synchronize their watches and simultaneously (from the earth frame) depart earth in different directions. Following a predetermined flight plan, each sister accelerates identically to 99.9%c and then returns home at the same time (again in the earth frame). The observers on earth see each twin as having aged identically, as the symmetry of the problem dictates. Each twin however should see the other as having aged... What gives? Flagging summary improvement: filters Are there attacks that break collision resistance but not preimage resistance? Are there any examples of attacks on hash functions which:   break collision resistance and second preimage resistant, or break collision resistance and preimage resistant?   I have looked at Rogaway's paper1, but it seems complicated, hence was wondering if a succinct example exists.  1)  Phillip Rogaway and Tom Shrimpton. Fast Software Encryption (FSE) 2004, LNCS vol. 3017, pp. 371&ndash;388, Springer, 2004. Find equation of a plane that passes through point and contains the intersection line of 2 other planes Find equation of a plane that passes through point P $(-1,4,2)$ that contains the intersection line of the planes  $$\begin{align*} 4x-y+z-2&amp;=0\\ 2x+y-2z-3&amp;=0 \end{align*}$$  Attempt: I found the the direction vector of the intersection line by taking the cross product of vectors normal to the known planes. I got $\langle 1,10,6\rangle$. Now, I need to find a vector normal to the plane I am looking for. To do that I need one more point on that plane. So how do I proceed? New global preferences: keyboard shortcuts and sticky topbar Q&A blank in Stack Exchange Android app v1.0.95 - S10e/Android 10 Recently upgraded to a Samsung S10e and Android 10, but all Q&amp;A in the Stack Exchange app v1.0.95 are blank.  The title and comments are visible, but question/answer posts are just white space. Accessing the About page in the app is also blank.  I tried clearing data, cache and re-installing the app, but I still get the same behaviour. After I deleted my Ubuntu partition, I rebooted my computer and I only get a prompt:   grub rescue &gt;   The command ls lists   (hd0) (hd0,msdos5) (hd0,msdos3) (hd0,msdos2) (hd0,msdos1) (hd1) (hd1,msdos1)   I check them one by one:  ls (hd0,msdos5)/ ls (hd0,msdos1)/   But I cannot find the right partition. Regex for quoted string with escaping quotes Is there any way I can use  partitions on Windows&nbsp;7?  I have tried to install , but it doesn't seems to run on Windows&nbsp;7. I'm sure its a simple question and I suppose it was asked many times, but I just can't figure it out from other answers, sorry.  I use recent versions of PostgreSQL and MySQL. I have 2 tables:  CREATE TABLE authors (     id INT,     name VARCHAR )  CREATE TABLE posts (     id INT,     author_id INT,     text VARCHAR,     date DATE )   I need to select one most recent post for each author. Thanks!  UPDATE  Thanks, both links provide answers to my question with some exception. All the following queries give the same result (which one is the most efficient btw?) The issue is when there is more than one post from the same author with the same date. Then the returned result set contains all such posts. How should I modify these queries to return exactly one post per author?  SELECT p1.* FROM posts p1 LEFT JOIN posts p2 ON p1.author_id = p2.author_id AND p1.date &lt; p2.date WHERE p2.author_id IS NULL ORDER BY p1.author_id;  SELECT p1.*  FROM posts p1 INNER JOIN (   SELECT author_id, MAX(date) AS max_date   FROM posts   GROUP BY author_id) p2   ON p1.author_id = p2.author_id AND p1.date = p2.max_date ORDER BY p1.author_id;  SELECT * FROM posts p1 WHERE date = (SELECT MAX(p2.date)               FROM posts p2               WHERE p1.author_id = p2.author_id) ORDER BY author_id;  SELECT * FROM (     SELECT author_id, MAX(date) date     FROM posts GROUP BY author_id ) p1 INNER JOIN posts p2 USING (author_id, date) ORDER BY author_id; How to add an image to a JPanel? I have a  to which I'd like to add JPEG and PNG images that I generate on the fly.  All the examples I've seen so far in the , specially in the  use ImageIcons.  I'm generating these images as byte arrays, and they are usually larger than the common icon they use in the examples, at 640x480.   Is there any (performance or other) problem in using the ImageIcon class to display an image that size in a JPanel? What's the usual way of doing it? How to add an image to a JPanel without using the ImageIcon class?   Edit: A more careful examination of the tutorials and the API shows that you cannot add an ImageIcon directly to a JPanel. Instead, they achieve the same effect by setting the image as an icon of a JLabel. This just doesn't feel right... Unmarshal a single element list fails