Just got a notice on StackOverflow that I can now "protect questions" .... I've seen diamond moderators do this a few times before, but for the most part I haven't seen it used too often. Therefore I have little body-of-knowledge on when/if questions should be protected.  Any tips on when/if questions should be protected?
Questions can be protected (i.e. marked "highly active").   What does it mean for a question to be protected? Why are some questions protected? Who can protect and unprotect questions? Who can answer a protected question? How are protected questions displayed? When should I protect or unprotect a question? When does the Community user protect a question?
Can I change the ordering for grouped dock items to be static? In the Ubuntu dock on Ubuntu 18.04, multiple windows of the same application are grouped and orange dots are shown to tell you how many windows of the application are opened. When you click on the icon, a small screen capture of each of the windows is shown.  However, these screen captures are shown in an order that's based on which window was last active on the desktop. This is something that clashes with the way I use the dock. I'm used to mentally mapping the windows to their dock positions. As such, I will often be trying to get to "the top one" and then I end up needing several clicks before I actually get to the terminal (or some other application) that I was looking for.  Is there some way to make sure that the order of these screen captures does not change whenever a window becomes active? How does light speed up after coming out of a glass slab? As I learned today in school, my teacher told me that when light enters a glass slab it slows down due to the change in density and it speeds up as it goes out of the glass slab. This causes a lateral shift and the light emerges out from the point different than that from where it should have actually emerged from.  Okay so what I mean to ask is, when light enters point A on glass slab and emerges from point C why does the light speed up? Where does it get the energy it has lost when it entered the glass slab?  P.S.: Also, if I place a very very very large glass slab and make a beam of light pass through it will the light never come out as all the energy was lost in place of heat? I want to burn Ubuntu Minimal CD ISO to an old, 1 GB USB thumbdrive. Regular ISO doesn't fit. I already tried Startup Disk Creator and Unetbootin but both failed. I tried installing GRUB and pointing it to boot like this:  insmod part_msdos linux /linux initrd /initrd.gz   but it doesn't work. I also tried dd but I ended up with not bootable drive.  Rufus worked on Windows with the same thumbdrive but I no longer use Windows.  What else can I do? Apparently ;-) the standard containers provide some form of guarantees.  What type of guarantees and what exactly are the differences between the different types of container?  Working from  (about ) I have come up with this:  Container Types: ================ Container:     Forward Container         Reverse Container             Random Access Container     Sequence         Front Insert Sequence         Back  Insert Sequence     Associative Container         Simple   Associative Container         Pair     Associative Container         Sorted   Associative Container         Multiple Associative Container  Container Types mapped to Standard Containers =============================================  std::vector:    Sequence    Back        Sequence                    Forward/Reverse/Random Container std::deque:     Sequence    Front/Back  Sequence                    Forward/Reverse/Random Container std::list:      Sequence    Front/Back  Sequence                    Forward/Reverse Container std::set:       Sorted/Simple/Unique    Associative Container       Forward Container std::map:       Sorted/Pair/Unique      Associative Container       Forward Container std::multiset:  Sorted/Simple/Multiple  Associative Container       Forward Container std::multimap:  Sorted/Pair/Multiple    Associative Container       Forward Container   Container Guarantees: =====================                                                                                    Simp                                                                                   or                           For   Rev  Rand        Front  Back  Assoc        Sort   Mult                     Cont: Cont: Cont Cont: Sequ: Sequ:  Sequ: Cont:        Cont:  Cont: Copy    Const:      O(n) Fill    Const:                             O(n) begin()             O(1) end()               O(1) rbegin()                        O(1) rend()                          O(1) front()                                    O(1) push_front()                                     O(1) pop_front()                                      O(1) push_back()                                             O(1) pop_back()                                              O(1) Insert()                                                                          O(ln(n)) Insert: fill                               O(n) Insert: range                              O(n)                                   O(kln(n)+n) size()              O(n) swap()              O(1) erase key                                                     O(ln(n)) erase element                                                 O(1) erase range                                                   O(ln(n)+S) count()                                                       O(log(n)+k) find()                                                        O(ln(n)) equal range                                                   O(ln(n)) Lower Bound/Upper Bound                                                    O(ln(n)) Equality                  O(n) InEquality                O(n) Element Access                       O(1) Finding maximal sublist of linearly independent vectors Double dual mappings $\newcommand{\Hom}{\operatorname{Hom}}$Let $U,V$ be vector spaces. Denote the dual space of $U$ with $U^\intercal$ and the dual mapping of a linear map $\Phi$ be $\Phi^\intercal$. Define the double dual embedding on $U$ to be $\iota_U:U \to U^{\intercal\intercal}$. ($u \in U, f \in U^\intercal$) $$ \iota_U(u)(f) = f(u) $$     If $\Phi \in \Hom(V,U)$, then $\Phi^{\intercal\intercal} \circ \iota_V = \iota_U \circ \Phi:V \to U^{\intercal\intercal}$   Proof: Let $v \in V, f \in U^\intercal$. Then $$ \iota_U \circ \Phi(v)(f) = f(\Phi(v)) $$ but how do I show that $$ \Phi^{\intercal\intercal} \circ \iota_V(v)(f) = f(\Phi(v)) $$ ? Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$ I want to prove the assertion:      The unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ when $p \equiv 1 \pmod{4}$, respectively $\mathbb{Q}(\sqrt{-p})$ when $p \equiv 3 \pmod{4}$.   My first attempt is this. In $\mathbb{Z}[\zeta_p]$, $1-\zeta_p$ is prime and $$ p = \epsilon^{-1} (1-\zeta_p)^{p-1} $$ where $\epsilon$ is a unit.  Since $p$ is an odd prime, $(p-1)/2$ is an integer and  $$ \sqrt{\epsilon p } = (1-\zeta_p)^{(p-1)/2} $$ makes sense and belongs to $\mathbb{Z}[\zeta_p]$.    How do I deal with the $\epsilon$ under the square root?  I guess the condition on the congruence class of $p$ comes from that.  Is this even the right way to proceed?  Uniqueness is not clear to me either.  I thought about looking at the valuation $v_p$ on $\mathbb{Q}$, extending it to two possible quadratic extensions beneath $\mathbb{Q}(\zeta_p)$, then seeing how those have to extend to common valuations on $\mathbb{Q}(\zeta_p)$, but I didn't see how to make it work.  I would appreciate some help. The set that only contains itself SEDE logs me out more often than it used to do I'm pretty sure that since a month or so,  seems much more eager to get rid of my session and log me out in that process. I don't mind logging in a couple of times per day, if that helps to reduce resource consumption, but the user experience isn't all that great when it happens. Here is why: I'm most often in the middle of writing a query for an MSE question, for example . So I have the edit window open and am creating a new revision of my query. When I click &quot;run,&quot; I do notice the button gets grayed-out, as it normally does, but I never get any result back. There is also no error message. To recover from this I have to copy the SQL text I have typed, open a new tab and load SEDE, log in, switch back to the stalled tab, refresh, paste the SQL text, run query. Repeat the process after 10 minutes. If the intended behavior is to log users out of their session on such short notice (I recall sessions lived for 24 hours), can there then be a slightly better handling in the browser of that state, so it is clear you're logged out once you click the run button? I prefer, however, to have the longer allowed sessions back. I'm experiencing this behavior mostly in Chrome on Win 10. I tried this:  find . -type f -size 128 -exec mv {} new_dir/  \;   Which didn't work, and it didn't give me an error. Here is an example of what the file looks like, when using stat -x  $ stat -x ./testfile | grep Size    Size: 128          FileType: Regular File How can I account for a nonlinear variable in a logistic regression? How can I account for a nonlinear independent variable in a logistic regression?  For example, consider this data set:  b1  b2  b3  b4  b5 1   1   0   0   20 0   1   0   0   20 1   0   0   0   13 1   1   1   0   8 1   1   0   1   5 0   1   0   1   4 1   1   0   1   5 0   0   0   0   8 0   0   1   0   13 1   0   0   1   20 1   0   0   0   29 1   1   0   1   40 1   0   0   0   53 0   1   1   0   68   Suppose I gathered some data like the above (suppose I had 10,000 rows) and I want to use them to predict future sets of similar data with an equation generated by a logistic regression. I get the above data. My independent variables are b1 through b5. By looking at the data, I can clearly see that independent variables b1 through b4 are binary (maybe they are male/female, rent/own, etc).   However I see that b5 is clearly not binary. Upon graphing it and looking at the numbers I determine that the b5 variable has a bathtub shaped U curve with an equation of b5=(x-4)^2+4.   I understand that using the b5 variable as it is would screw up my logistic regression - since any interval independent variables must have a linear relationship with the dependent variable.   Yet, I must account for the variable b5 in my data set while doing a logistic regression for it to be accurate and predict well (right?).  Given the above data, how would I go about making a predictive model with a logistic regression? Any references online or in books would greatly be appreciated as I am having trouble finding a good explanation of the above.  Cheers =)  EDIT:  Sorry if my question is unclear.  Consider this: Suppose we had the following data on many people:  Y: Whether they had a stroke before the age of 50 or not 1. Whether they own a pet or not. 2. Whether they graduated college or not. 3. Whether they are male or female. 4. The number of hours they exercise every week.  We want to train a logistic regression model based on historical data to predict if someone in the future with the same data will be more apt or not to have a stroke before the age of 50.  The problem I am having is with the last variable. A continuous ratio variable like "number of hours exercised each week."  Exercising more each week may have diminishing returns on health and thus having a stroke. For example decreasing an increasing rate. Or maybe (totally made up) exercising a little bit is really good for you, exercising a moderate amount is really bad for you, and exercising a lot is really good for you again. We might have a U shaped curve like (x-4)^2+4 for example when plotting health to exercise.   I would image that having a curved, non-linear independent variable in a logistic regression like the one I described above would cause problems. Am I right? And if so, what kinds of things can you do to still include the variable in the logistic regression. Perhaps a transformation? Is that all? Is it possible to use the fact that $\sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90}$ to compute $\sum_{n=1}^\infty \frac{(-1)^n}{n^4}$? VMware Linux Server -- how can you tell if you are a vm or real hardware? An interesting question.  I have logged into a Linux (most likely SuSE) host.  Is there some way that I can tell programmatically that I am a VM host or not?    Also assume that the vmtools are not installed. How to prove this sequent using natural deduction? I just try to visualize some points using GeoServer to publish them as WMS and bind this WMS to my Openlayers website using the GeoServer internal Heatmap process to visualize it. I don't want to use the Openlayers Heatmap function.   But there seem to be some problems, look here:    I'm using this Openlayers implementation to bind my WMS URL:    Changing the params to:  params: {'LAYERS': 'test:points','TILED': true,'STYLES': 'heatmap'},   And using this as SLD to define the Heatmap:    Any ideas why this happens? Why I cannot use universal instantiation rule here? I have the following premise:      $$\forall x (Fx \vee \neg Fx) \rightarrow Ga$$   Why I cannot use UI and get: $(Fa \vee \neg Fa) \rightarrow Ga$ And what is the difference between the first premise and the below premise:     $$\forall x ((Fx \vee \neg Fx) \rightarrow Ga)$$   Thanks in advance. Rep graph overview thing™ is white (only in latest Chrome) As you can see, if you go to the reputation graph on your profile on Stack Overflow, the bars in the bottom overview will be white. This makes them invisible unless they are selected.  Eeek!  This does not happen on meta or any other site. Also, I cannot seem to reproduce it on others' profile. Possibly a bug only on your own profile? EDIT: I think I've existed for too long. If I change the CSS on one of the bars to stroke: none, then it becomes green. I think the outline is covering the fill because the bars are too skinny. EDIT2: Confirmed hypothesis by reproducing on Jon Skeet's graph. Proposed solution: enforce minimum bar width and add horizontal scrollbar. EDIT3: Can only repro on Chrome 29.0.1547.57 (Official Build 217859) m (the latest version). Norepro on older versions of Chrome, IE9 (winces), all versions of FF, and all versions of Safari. EDIT4: Can be fixed simply by running the JavaScript $('rect').css('stroke-width', '0') or a userstyle rect { stroke: none }. I may make a user[style|script] to fix this. Consider there is a box of mass $m$ at rest on the floor. Most books give an example that we need to do a work of $mgh$ to lift the box $h$ upward.  If we analyze this work done, the external force acting on the box by us should be equal to the weight of the box. Therefore the net force is zero which in turn there is no acceleration. If there is no acceleration and the initial velocity of the box is also zero, how can the box move upward? Why does shell ignore quoting characters in arguments passed to it through variables? Can I list-initialize a vector of move-only type?