Brier score loss and Log loss cut-offs
What is a "good fit" Brier score and Harrell's C Index
Let $H$ be a subgroup of $G$ with $[G:H]=n$ and $G$ finite.  Let $G$ act on left cosets of $H$ by left multiplication.  Let $N$ be the kernel of the action.  Show that $[G:N]$ divides $n!$.  Ok so I have a theorem that says that if $G$ is simple then it embeds into $S_n$.  So if $G$ is simple than I'm done because $G$ divides $n!$ and thus $N$ divides $n!$ and hence $[G:N]$ divides $n!$.  Now I also know that $N$ is the largest normal subgroup of $G$ contained in $H$.  Thus if $G$ isn't simple then it contains some non-trivial normal subgroup $K$ and thus $K\cap H$ is normal in $H$ and by the 2nd Iso Theorem $H/K\cap H\cong KH/H$...    As you can see I'm not sure where to go from here. I was hoping to prove that $K\cap H$ wasn't trivial and thus that $N$ couldn't be trivial since it must contain $K\cap H$, but I'm not sure I can, and even if I could I'm not sure that would help me in showing that $[G:N]$ is small enough to divide $n!$.  Can anyone give some guidance?  Thanks. The only things I've found so far are a cart method (which ceased working in 1.6), a dispenser method (utilizing the decay on dropped items, but this requires occasional feeding), and a binary counter (which won't work for a single input but rather a fluctuating one).  I want to have a circuit that when I apply an input signal, the output signal doesn't change for 2 to 5 minutes.  When the input turns off, I again want a 2 to 5 minute delay.  I could accomplish this with (roughly) 240 to 600 redstone repeaters, but this is far in excess of being useful.  The only method I can think of, but would require a XOR gate (on the button-input and final output) to start and stop a clock attached to a binary counter.  While I can make room for a device of this size, I was hoping for something simpler. Can a fired moderator be elected as a moderator? While this question is inspired by recent events, it is an independent question and not tied down to any specific moderator or situation.  There's precedent for a moderator who resigned their diamond to simply ask Stack Exchange for their diamond back, without having to stand for reelection. Obviously, this may not apply if the moderator did not resign, but was removed for cause by Stack Exchange.  If a moderator has been "fired" by Stack Exchange (has had their diamond removed involuntarily by corporate action), is the person eligible to pull a  and regain a diamond through the democratic process on one of our sites, or would any such attempt be blocked? I'm aware that there is a restriction on  from standing for election, but this is not the same thing as being stripped of a diamond (fired moderators, IME, aren't also given a full site suspension unless their behavior goes beyond "possibly not a very good moderator" into "supervillain" territory).  If there is no particular rule, what should that rule be?   Should fired moderators be immediately eligible to stand for election, subject only to community approval of them returning? Should fired moderators have to go through a separate re-vetting process with Stack Exchange to regain eligibility to stand for office? Should fired moderators have an ineligibility window in a similar way that suspended users have one (e.g. after X months or years after being fired, they may stand for election). Should fired moderators be forever banned from election?   In no way am I asking about the process for a fired moderator to seek restoration through corporate appeals, etc. I'm asking only about the community election process - if a site's community wants to elect a previously fired moderator, is this inherently objectionable to Stack Exchange? Efficiently reverse the order of the words (not characters) in an array of characters How do you end with a single quote followed by a double quote? Why do wheels appear to revolve opposite to the direction they are rotating? When viewing cars that are driving along side of us, sometimes their wheels appear to be turning backwards even though they are traveling in the same direction as our car. Why do they look that way? $\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite Start modal operator from a click in panel I want to start a modal operator by clicking a button in a panel in the properties region. It should then stop when I click somewhere in the 3D viewport. I want to execute some code when I start and finish the operator (see the code below). I tried modifiyng the modal operator template with an execute method to start the modal operator. But the now the context.space_data.type is always &quot;PROPERTIES&quot; because that's where the panel is located, I guess. Is this a bad way of doing what I want? class MY_OPERATOR_OT_click_on_3dview(bpy.types.Operator):          bl_idname = &quot;mesh.click_on_3dview&quot;     bl_label = &quot;Click on 3D&quot;      def modal(self, context, event):                  if context.space_data.type != 'VIEW_3D':             return {'PASS_THROUGH'}                  if event.type in {'MIDDLEMOUSE', 'WHEELUPMOUSE', 'WHEELDOWNMOUSE'}:             # allow navigation             return {'PASS_THROUGH'}         elif event.type == 'LEFTMOUSE':             # DO ALL THE POST-SELECT STUFF             return {'FINISHED'}         elif event.type in {'RIGHTMOUSE', 'ESC'}:             return {'CANCELLED'}          return {'RUNNING_MODAL'}      def execute(self, context):         # DO ALL THE SETUP STUFF           context.window_manager.modal_handler_add(self)              return {'RUNNING_MODAL'}            def cancel(self, context):         print(&quot;CANCEL???&quot;) Array versus List: When to use which? What is the fastest way to create a 90° joint? I often want to create joints like this:    Since I end up making these more than a little, I'd like a fast way to do it (i.e. on the order of &lt; 10 seconds)  I've found a couple tools which come close to being the ideal solution, but I've had some problems with them as listed below:   When using the spin tool I usually end up having to fiddle with the location for a while in order to to get a natural curve:    Are there any techniques to expedite this process of fiddling? The bridge tool is nice because I can precisely specify where both ends of the joint will be, however I often end up with subtly uneven joints, probably due to my initial mesh being not quite square.    Is there a fast way to correctly line up the initial edge loops in a way that will result in an even joint? Viruses: Adaptation to a new host through repeated host jumps Can I do it with reflection or something like that? Frequency count of two column in R How can I specify the default save directory for gnome-screenshot? Are there any sort of configuration options for specifying the default save location for gnome-screenshot, or is this hard-coded into the source code? It used to be ~/Desktop, which seems to have changed to ~/Pictures (in 12.04). The only possible solution I've seen is about  (as it includes time stamp information now instead of simply 'Screenshot#'), but that solution doesn't really seem ideal to me. Also,  post suggested that the last save location is remembered the next time you take a screenshot, but in my experience, this doesn't seem to be the case. And in any case, following on from that, that entry in gconf-editor doesn't even seem to accurately reflect the last location, so more than likely an entry related to an older version of gnome-screenshot. Table of contents: Well, luckily I got this error on my test environment. I'm so scared about this error that I disabled all logon triggers I was using on production environment.   I created the famous logon trigger, and I put a database in offline mode just to mess with something else. Then I discover that because the trigger can't find the table, I can't access the instance anymore. There are plenty of questions related to this, but even doing everything I could find, I still can't acces the instance, not even with SQLCMD.  I'm doing this:  sqlcmd -S server\instance -U sa -P &lt;pass&gt;  -A   If I don't use -A I receive the famous error:  logon failed for sa due trigger execution.   If I use -A:     Sqlcmd: Error: Microsoft ODBC Driver 11 for SQL Server : SQL Server   Network Interfaces: An error occurred while obtaining the dedicated   administrator connection (DAC) port. Make sure that SQL Browser is   running, or check the error log for the port number [xFFFFFFFF]. .   Sqlcmd: Error: Microsoft ODBC Driver 11 for SQL Server : Login timeout   expired. Sqlcmd: Error: Microsoft ODBC Driver 11 for SQL Server : A   network-related or instance-specific error has occurred while   establishing a connection to SQL Server. Server is not found or not   accessible. Check if instance name is correct and if SQL Server is   configured to allow remote connections. For more information see SQL   Server Books Online..   Why i'm not able to connect to the sql server    sql server express here.  I could enable SQL Browser, but I still can't access it.  I don't think this question is duplicated because is not about the trigger, is about Why I can't access the server with SQLCMD. I pretty much know how to fix this. I just don't know how can I acces sql server without triggering the trigger. Say I am logged into a remote system, how can I know what it's running? On most modern Linuxes (Linuces?), you have the lsb_release command:  $ lsb_release -ic     Distributor ID: LinuxMint Codename:       debian   Which as far as I can tell just gives the same info as /etc/lsb-release. What if that file is not present? I seem to recall that the lsb_release command is relatively new so what if I have to get the OS of an older system?  In any case, lsb stands for Linux Standard Base so I am assuming it won't work on non-Linux Unices. As far as I know, there is no way of getting this information from uname so how can I get this on systems that do not use lsb_release? The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$ Wild Magic Surge - What does "You cast ..." mean for your spell slots? In response to  question, I started to think about what it means when a Wild Magic Surge results in a "You cast spell-X".  So, "specific beats general" gives:   You can cast a second spell when you would not normally be allowed to You can cast a spell you don't know If the surge forces you to cast a concentration spell you would lose any concentration spell that you currently had active Subject to what the specific entry says you can target it how you like Unless the specific entry prohibits it you could use metamagic on the spell   I am pretty confident in all of the above but if anyone disagrees please address in an answer.  Here comes the question.  How does this impact on your available spell slots?  "You cast ..." to me suggests that if you have an applicable slot available then you have to use it to cast the spell because that is the general rule for casting spells but if you don't then "specific beats general" and it is cast anyway.  Specific examples:     You cast fireball as a 3rd-level spell centered on   yourself   This must be a 3rd level spell:   if you have a 3rd level slot available you have to use it? if you don't, if you have 5 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?      You cast confusion centered on yourself.   No level specified and confusion is a 4th level spell:   if you have a 4th level slot available you have to use it? if you have a 4th, a 6th and an 8th level slot you can choose which one to use? if you have only a 5th level slot but also 6 sorcery points and a bonus action, you could choose to use the 5th level slot or use the points to create a 4th level slot? if you don't have any 4th level or higher slots but you have 6 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?   And so on ... How to sort this JSON I received an undesirable status for overstaying a SA visa while hospitalized for injuries sustained in Lesotho. I had to cross into SA from Lesotho. Now I am banned entry into SA until Feb 2016 and though I have submitted a waiver request to remove the undesirable status, I hear from some the waiver request may take 4-5 months or even take longer than the time of banishment.  I have a pre-paid safari planned in October in which I need to fly through Johannesburg to get to Botswana. The Jburg border control requires tourists to pass through SA immigration even when simply changing planes.  1) Will SA grant me "transit" access if I don't leave the airport?  2) Will SA allow me to spend a night in the airport as the layover is 12 hours>  Thanks for passing on any info.