Difference in meanings
"I couldn't but laugh" - correct or not?
When will L1 regularization work better than L2 and vice versa? It is easy to find the minimum of $\|Ax-b\|_2$, when $A$ has full column rank. But how is the case when we add the constraint $\|x\|_2=1$? Or, to be explicit,  $$\min_{\|x\|_2=1}\|Ax-b\|_2=?$$  My idea is to construct the corresponding Lagrange function  $$L(x,\lambda) = (Ax-b)^T(Ax-b) + \lambda(x^T x - 1)$$  Differentiate the function with respect to $x,\lambda$, we have  $$A^T A x - A^T b + \lambda x = 0$$  $$x^T x=1$$  However, I find it hard to move forward to get the answer. Could anyone help me? Thanks a lot! Anti-virus comparison for Mac OS X This is not a "I use OS X, do I need Anti-Virus?" question.    I am looking at comparison and user opinion of existing AV products. I know I can avoid most (if not all) threats by being careful on the sites I visit, and the emails I download. But I need an anti-virus, for a variety of reasons - mostly to prevent my Mac as a carrier for viruses. (Many friends' USB drives turn out to be infected).  I was looking for the "Best" of the anti virus software out there.  I am looking prominently at anti-virus. "Internet Security" and the like are not important, and would try to avoid them if it would save money or not make my mac slower.  By "Best" I mean the best combination of detect-rate (or whatever that is called) and performance.  I don't intend to run it always in the background. Maybe I would do a onetime scan of my system and hard drives, and then it would be mostly on a need basis, especially on USB drives/portable hard disks of friends. So primary objective: High Detect rate  I have used  and  (got this with one of those software bundles sometime before, not the latest version) and had problems with both. Both sometimes hog my CPU, and somehow "lock" my USB drives preventing me from Ejecting it (I had to force eject them or just pull them off from the port) (thought off late Norton seemed a little better)  Ok, thats a long one. But my question is simple: What anti-virus do you recommend for the Mac?  Thanks. Where can I get freely available audio, graphics, and other resources for games? The impression that I got from the  films was that if  was successful, most of the world was going to suffer greatly. Basically everyone would serve Voldemort as slaves or die. So what's the point of serving someone who's probably going to ultimately end up betraying and/or enslaving you? I know the  hated , but is that really enough to justify tearing down Wizard society? Why exactly do the Death Eaters serve Lord Voldemort? Fear? Is the post-Voldemort world not that bad? (I for one welcome our ) Captured variable in a loop in C# How do I choose grid and block dimensions for CUDA kernels? An excerpt from Introduction to Analytic Number Theory by Tom M. Apostol.      I have three main concerns regarding this proof:    What is the abscissa of convergence for $\frac{1}{F(s)}$ - why can we take the product of the two series. I only know this is true if the two series are absolutely convergent.  Why can we do term by term integration? I believe its suffices to show that the series converges locally uniformly - BUT is this true?  How does the proof show that $G(s)$ converges uniformly? How do I monitor network usage on a Windows server? Why and how can you hear explosions in space in Star Wars? Considering that sound can't travel through vacuum. How to subtract a day from a date? How to search inside files on Windows 7? In Windows XP we can search for files that contain a defined keyword (inside all files types).  Windows 7 can look inside files for a keyword, but only for text files. (*.doc, *.txt, *.inf, ...), not (*.conf, *.dat, *.*, ...).   don't contain any filter I can use for this.  How is this possible? How does password salt help against a rainbow table attack? I'm having some trouble understanding the purpose of a salt to a password.  It's my understanding that the primary use is to hamper a rainbow table attack.  However, the methods I've seen to implement this don't seem to really make the problem harder.  I've seen many tutorials suggesting that the salt be used as the following:  $hash =  md5($salt.$password)   The reasoning being that the hash now maps not to the original password, but a combination of the password and the salt.  But say $salt=foo and $password=bar and $hash=3858f62230ac3c915f300c664312c63f.  Now somebody with a rainbow table could reverse the hash and come up with the input "foobar".  They could then try all combinations of passwords (f, fo, foo, ... oobar, obar, bar, ar, ar).  It might take a few more milliseconds to get the password, but not much else.  The other use I've seen is on my linux system.  In the /etc/shadow the hashed passwords are actually stored with the salt.  For example, a salt of "foo" and password of "bar" would hash to this: $1$foo$te5SBM.7C25fFDu6bIRbX1.  If a hacker somehow were able to get his hands on this file, I don't see what purpose the salt serves, since the reverse hash of te5SBM.7C25fFDu6bIRbX is known to contain "foo".  Thanks for any light anybody can shed on this.  EDIT:  Thanks for the help.  To summarize what I understand, the salt makes the hashed password more complex, thus making it much less likely to exist in a precomputed rainbow table.  What I misunderstood before was that I was assuming a rainbow table existed for ALL hashes. For example how come $\zeta(2)=\sum_{n=1}^{\infty}n^{-2}=\frac{\pi^2}{6}$. It seems counter intuitive that you can add numbers in $\mathbb{Q}$ and get an irrational number. Does light pollution affect sleep quality while already asleep? Many articles on the internet write about melatonin and its effects, making you tired. A lot of articles also point out how the use of devices before going to bed in modern days likely decrease melatonin production. Therefore, making it harder to fall asleep. But this information is only about the process of getting to sleep, before we are actually sleeping.  A recent Harvard Medical article 1 states:     High exposure to bright, artificial outdoor lights during the night may result in sleepless nights for older adults.   Referring to a publication on Nov. 15, 2018, in the Journal of Clinical Sleep Medicine.  Considering that:    many people nowadays, use their mobile devices in bed prior to going to sleep; modern cities or houses have (street) lights that are always enabled at night; ignoring the phase of falling sleep; focusing only on the time we are asleep already, so during the actual sleep cycles.   Does a darker room with less or no (artificial) light pollution improve sleep quality, with all associated health benefits as a result? In other words: Does light pollution, while asleep decrease the sleep quality or does light pollution only negatively affect the phase of “falling asleep”?  I wasn't able to find any studies or information regarding sleep quality in relation to light pollution during sleep. Were such studies performed? Are there specific moments when light pollution affects sleep quality the most, for example during REM-sleep or in a specific sleeping phase?    1 Allow retracting a moderator flag if the post has been deleted and I don't have enough reputation to see deleted posts Currently, custom flags for moderator attention are not automatically invalidated (marked helpful) when a post gets deleted. Ordinarily, one can retract a moderator flag by going to the post, clicking &quot;flag&quot;, and then &quot;Retract Flag&quot;. This works even if the post has been deleted, provided they can see the post (they have 10,000+ rep, it's their own post, or they have answered it). However, it's not possible to self-remove a flag on a deleted post if they can't see the deleted post, because they can't get to the &quot;flag&quot; button. Is this intended? If not, can this ability please be implemented? As Aurora0001 commented, there is no server-side check, the button is just not visible. Can this please be implemented on the website, or is the fact that it's possible server-side a bug that will soon be fixed by removing it? Did Sidious know the secret of cheating death? Rectangle with cross on title bar I have installed Ubuntu 14.04 and I think that I have found a bug. When I open terminal and  go to edit profile preferences I get a rectangle with a cross on the title bar. It happened with other applications too. Here are the screen shots: Why won't vertical-align: middle work?  And yet, vertical-align: top does work.   span{   vertical-align: middle; } &lt;div&gt;   &lt;img src="https://via.placeholder.com/30" alt="small img" /&gt;   &lt;span&gt;Doesn't work.&lt;/span&gt; &lt;/div&gt; Can Cycles use multiple UV layers?