I have read  but it doesn't have any well-explained answer for this case: I understand the ROC curve in overall, but I'm looking for a step-to-step explanation in order to understand how the curve changes when one true-positive becomes false-positive (and so on). For example, how can I draw a ROC curve with this set?. Does the score means the "certainty" for the value given? (for example: for the id == A the is a 0.03 of certainty that the value is active/decoy == a?)  id  score   active/decoy  A   0.03    a B   0.08    a C   0.10    d C   0.11    a D   0.22    d E   0.32    a F   0.35    a G   0.43    a H   0.57    a I   0.61    d J   0.68    a
I am interested in calculating area under the curve (AUC), or the c-statistic, by hand for a binary logistic regression model.  For example, in the validation dataset, I have the true value for the dependent variable, retention (1 = retained; 0 = not retained), as well as a predicted retention status for each observation generated by my regression analysis using a model that was built using the training set (this will range from 0 to 1).  My initial thoughts were to identify the "correct" number of model classifications and simply divide the number of "correct" observations by the number of total observations to calculate the c-statistic. By "correct", if the true retention status of an observation = 1 and the predicted retention status is > 0.5 then that is a "correct" classification. Additionally, if the true retention status of an observation = 0 and the predicted retention status is &lt; 0.5 then that is also a "correct" classification. I assume a "tie" would occur when the predicted value = 0.5, but that phenomenon does not occur in my validation dataset. On the other hand, "incorrect" classifications would be if the true retention status of an observation = 1 and the predicted retention status is &lt; 0.5 or if the true retention status for an outcome = 0 and the predicted retention status is > 0.5. I am aware of TP, FP, FN, TN, but not aware of how to calculate the c-statistic given this information.
Suppose that G is a group and N &lt; G a normal subgroup. Assume that there is no normal subgroup M &lt; G with N &lt; M. Prove that G/N is simple.  This problem is really throwing me for a loop. The concept of quotient groups and how they relate to simple subgroups is confusing me, and so I am not really sure how to begin. If a simple subgroup's only normal subgroup is itself (and the trivial group), then G/N being simple would be proving that when multiplying the entire subgroup N by an element g for all g in G, that the collection of those sets cannot be broken into smaller normal subgroups? I have too many sections in my presentation such that the left-hand-side navigation bar is full and only shows the first sections in Fig. 2, initial situation in Fig. 1.  Pseudocode    clean the left-hand-hand side navigation bar when exceed the threshold and start a new one there when on sufficient page  this feature occurs with Beamer Berkeley appendix so it is possible also with the main document   Code which problem shown in Fig. 2   \documentclass{beamer} \usetheme{Berkeley}  \logo{\includegraphics{logo.png}} \usepackage{hyperref} % https://tex.stackexchange.com/a/346486/13173 \newenvironment{slide}[1] {\begin{frame}[environment=slide,allowframebreaks] \frametitle{\insertsection-#1} } {\end{frame}} % fragile only if code % allowframebreaks not by default   \begin{document}  \title{Sensory system. Primary sensory modalities. Cortical modalities. Kinds of sensory disturbances. Spinal cord disorders. Spinal cord transverse and partial lesion. Cauda equina damage.} \author{Leo}  \section{Cortical modalities} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \section{Cortical modalities} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \section{Cortical modalities 2} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \section{Cortical modalities 3} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \section{Cortical modalities 4} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \end{document}   Fig. 1 Situation at the first page,  Fig. 2 Situation at Section 6 wheere the navbar has not changed,  Fig. 3 Samcarter's answer output + one slide addition but without \part{} - fails on sufficient page count       Output: the left-hand-side navigation bar is not refreshed when the amount of sections exceed its capacity on suffcient enough page     Testing Samcarter's proposal  I include one slide before Samcarter's body so I get the wrong output in Fig. 3.  Solution: Eventually correct output by just adding \part{} in the place where the new navbar is wanted.   TeXLive: 2016 OS: Debian 8.7 ZF: Difference between POW and SEP? How to compute azimuth between QgsPointV2s? The  class has an azimuth() method but the new  class does not. What's the best way to compute the azimuth between QgsPointV2s? I couldn't find a convenient way to convert V2 to the old version, so my fallback is to construct a QgsPoint from the V2's x and y:   self.traj = QgsLineStringV2(...)     p_i = self.traj.pointN(self.i) # this returns a QgsPointV2 p_j = self.traj.pointN(self.j) a = QgsPoint(p_i.x(),p_i.y()).azimuth(QgsPoint(p_j.x(),p_j.y()))   Is there a better way? Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite? Let $E/K$ be an algebraic extension of fields and denote by $E_s$ the separable closure of $K$ in $E$, i.e. the set of all elements of $E$ that are separable over $K$ (which can be shown is a (separable) subfield of $E$).  I would like to show that the implication     $\left[E:K\right]_s &lt; \infty \implies \left[E_s:K\right] &lt; \infty$   holds, where $\left[E:K\right]_s$ denotes the separable degree of $E/K$ and $\left[E_s:K\right]$ the 'ordinary' degree of $E_s/K$.  In the textbook I am learning with, it is said that one could use the Primitive Element Theorem to do this, but I would also be fine with any other approach, as long as it's not getting too fancy and staying in the realm of 'common' textbook theorems known when dealing with separable extensions (and I didn't see how the Primitive Element Theorem would help).  This is not my focus (I want to write a Bachelor's thesis about polynomial factorizing elements of $\mathbb{Z}[X]$), but I'm in the process of reading into commutative algebra after about 1.5 years break from it.  My idea was something like assuming $\left[E_s:K\right] &lt; \infty$ and $\left[E_s:K\right] = \infty$ to construct infinitely many $K$-homomorphisms $E_s/K \longrightarrow C/K$, where $C$ is some algebraic closure of $E_s$, which would then contradict $\left[E_s:K\right]_s = \left[E_s:K\right] &lt; \infty$. Of course, an infinite basis would yield infinitely many $K$-vector space homomorphisms, but getting (infinitely many) ring morphisms seems to by an entirely different ting (unsurprisingly so...). Thought of using something like     Given two roots of the minimal polynomial of one of the infinitely many elements of a $K$-basis of $E_s/K$, there is a $K$-morphism $E_s/K \longrightarrow C/K$ that sends one to the other.   but this didn't seem very fruitful. I admit I haven't spent hours on this, I just didn't get very far and should focus on moving on, while still getting an answer on the 'howto' along the road would be really nice. "Accountsd wants to use the 'iCloud' keychain" I, too, am suddenly getting this message.  I don't see a Keychain First Aid option in Keychain, and the two Login Keychain Settings were already unlocked.  Any other ideas for what the error message is all about, and what I should do about it? Alpha and Omega limit sets (dynamical systems) What are all the possible $α$- and $ω$-limit sets of points for the linear system of equations $x'=Ax$ given by the following matrices $A$:  I guess I don't really know how to get started, Could I have some guidance? So I was told to calculate the eigenvalues (fine) and eigenvectors (I kind of forgot how to do that...)  I know that the $ω$-limit sets of points are the set of points that the system of equation approach as time goes to infinity, and the $α$-limit sets of points are the points approached as t goes to negative infinity.   $    A=   \left[ {\begin{array}{cc}    -4 &amp; -2 \\    3 &amp; 11 \\   \end{array} } \right] $   $λ_1=-10$ $λ_2=-5$  Since both eigenvalue are negative, this is a stable node, and the $ω$-limit set=0.  for $λ_1=-10$:  eigenvector $    =   \left[ {\begin{array}{cc}   1 \\    3 \\   \end{array} } \right] $  for $λ_2=-5$:  eigenvector $    =   \left[ {\begin{array}{cc}   2 \\    1 \\   \end{array} } \right] $   $    A=   \left[ {\begin{array}{cc}    1 &amp; 1 \\    3 &amp; 1 \\   \end{array} } \right] $   $λ_1=4$ $λ_2=-2$  Since one eigenvalue is positive and one is negative, it is not stable, so I can't use the same reasoning that I used above to find the $ω$-limit set... so I am not sure how to continue  for $λ_1=4$:  eigenvector $    =   \left[ {\begin{array}{cc}   1 \\    1 \\   \end{array} } \right] $  for $λ_2=-2$:  eigenvector $    =   \left[ {\begin{array}{cc}   -1 \\    1 \\   \end{array} } \right] $   $    A=   \left[ {\begin{array}{cc}    4 &amp; 5 \\    -5 &amp; -2 \\   \end{array} } \right] $   $λ_1=1+4i$ $λ_2=1-4i$  for $λ_1=1+4i$:  eigenvector $    =   \left[ {\begin{array}{cc}   -3/5-(4i)/5 \\    1 \\   \end{array} } \right] $  for $λ_1=1-4i$:  eigenvector $    =   \left[ {\begin{array}{cc}   -3/5+(4i)/5 \\    1 \\   \end{array} } \right]$ How to set edge bevel weights from a python script I need to set weights for some edges from a python script. I have tried looping through object.data.edges and setting bevel_weight values but I can't get it right. It only works if I have first edited some edge's bevel weight by hand from the 3d-view's transform window. But I would like to get it work from my script without any manual hacking.  Steps to reproduce:  Start Blender with default cube and switch to Scripting view.  Try to set weights for all edges:  for edge in C.object.data.edges:     edge.bevel_weight = 1.0   Verify that values changed:  for edge in C.object.data.edges:     edge.bevel_weight   Switch into edit mode in 3d-view and open up transform window by pressing n. Select edges to see that the change did not work (bevel weights are all zero). Switch back to object mode and read values again in scripting console to see that they were reset to zero:  for edge in C.object.data.edges:     edge.bevel_weight   Go back to edit mode and change some edge bevel weight straight from the transform window by hand. Go back to object mode and change values again from the scripting console:  for edge in C.object.data.edges:     edge.bevel_weight = 1.0   This time it works, bevel weights are 1.0 when you go back to edit mode and look from the transform window.   Any ideas? My final need is to apply a bevel modifier to only some set of edges and that's why I'm trying to mark them by using weights. Using vertex group for bevel modifier does not work in my situation, since I need to specify edges, not vertices, which to bevel.   I'm using Blender v2.71. "It's cold today" -- what term do linguists use to call "it" when it's used as the subject of a sentence, but has no real antecedent? Correct usage of "persons" (vs. "people") I had a little fight about persons vs. people.  Could you advise if both of the following are correct, if possible with reference to a dictionary?        A table for two people please.   A table for two persons please.      Besides that, how would you ask for a table in a restaurant?  I read  and , but they didn't really solve the question if both are correct.  I also found the last paragraph of , which suggests that (1) is "more correct", but doesn't say (2) is wrong. Background  Recently  was implemented. With this feature the amount of questions with new activity is shown in parenthesis at the beginning of the page title, e.g.     (2) Meta Stack Overflow   means that MSO has two questions with new activity since the user last viewed it.   this feature is unrelated to inbox updates. Here is an example to illustrate this:    Even though there are two inbox messages in this screenshot this is not reflected by the page title. The page title is currently only sensitive to questions with new activity.  Suggestion  I suggest that the page title also reflects inbox updates. For the screenshot above this would mean that the page title shows that there are two inbox updates and two questions with new activity.  I am not sure what format is best for showing this. For chat * in the page title is used to show that there are messages directed at you which is similar in meaning to inbox updates. However, * if is placed after the number in parenthesis to denote inbox updates there might be confusion as there is no connection between the number in parenthesis and * like in chat. Thus, one might prefer another format such as one of the following (all are meant to reflect the status of the screenshot above):      * (2) Meta Stack Overflow     2* (2) Meta Stack Overflow     [2] (2) Meta Stack Overflow     2i 2q  Meta Stack Overflow     (2/2)  Meta Stack Overflow     (2|2)  Meta Stack Overflow    For the alternatives without an explicit hint of which number refers to what it might be best to place the number for questions with new activity first as it will in most cases be greater. This will to a greater degree avoid combinations such as "(0/2)" which may be confused zero of two.  An advantage of the suggested feature is that if the user has a browser tab with a Stack Exchange site then they will be instantly notified of inbox updates. They do not need to focus a tab with a Stack Exchange site to know if there are inbox updates, they merely have to check the relevant page titles among their tabs.  A disadvantage of the suggested feature is that it might be experienced as verbose. I suggest that it is implemented such that it is as unobtrusive as possible while still being informative. Think of a situation where a user has   one Meta Stack Overflow tab with two inbox updates relating to Meta Stack Overflow and two questions with new activity, and one Super User tab with one inbox updates relating to Super User and three questions with new activity.   Then the sum of the inbox notification in the page titles should be local to sites and not global. The page titles for the tabs above should be something like the following pair:      2i 2q  Meta Stack Overflow     1i 3q  Super User I would like to declare functions in tikz for multiple uses of the same function within the code.  Sadly, it seems that the tikz "declare function" is not compatible with the french option in babel. Indeed, the following code (that I simplifed on purpose) runs fine :  \documentclass[english]{article} \usepackage{babel}                       \usepackage{tikz}  \begin{document} \begin{tikzpicture}     \tikzset{declare function={Carre(\t)=\t*\t;}}     \draw plot [domain=-1:1] (\x,{Carre(\x)}); \end{tikzpicture} \end{document}   But when I replace   \documentclass[english]{article}   with   \documentclass[english,french]{article}   compilation generates an error. This is what the log file says :     Missing character: There is no = in font nullfont!   Missing character: There is no @ in font nullfont!   Missing character: There is no @ in font nullfont!      Runaway argument?   -1:1] (\x ,{Carre(\x )}); \end {tikzpicture} \end {document}    ! Paragraph ended before \pgfmath@local@@functions was complete.                          \par    l.18       I suspect you've forgotten a `}', causing me to apply this   control sequence to too much text. How can we recover?   My plan is to forget the whole thing and hope for the best.   Before posting this, I updated all packages without success.  Any help welcome! Say person A and person B are having a discussion/argument.   Person A tells person B that his views are arrogant, or closed-minded, or some other derogatory adjective. But in fact it is person A's views that are arrogant, closed-minded, etc. Person B's views are usually the exact opposite of what person A is accusing him of.  This sort of situation happens a lot when discussing politics or religion, for example.  What do you call person A, for calling person B something that he himself is?  I guess, for the most part, person A doesn't actually realize that he is the one that the adjective applies to, and not person B. Maybe there is a different name if person A knows the adjective also applies to him. How to determine the encoding of text? I received some text that is encoded, but I don't know what charset was used. Is there a way to determine the encoding of a text file using Python?  deals with C#. Can someone explain collection_select to me in clear, simple terms? Remote desktop without a password I have an HTPC with a user that has no password and autologin.  I want to be able to connect to it via Remote Desktop without a password, so I can login with the original user. (I don't want to add another user just for the mstsc)  Is there a way of doing that?  The OS is Windows 7, 32bit. How do I detect orientation on app launch for splash screen animation on iPad! I have the need to synchronize the data in certain Salesforce tables (user, account, opportunity, lead, task, contact, etc.) to a local database. For reasons that I won't go into here, I can't use the streaming API. I want to kick off a local process every X minutes that will:   Go through each of the tables on my list Insert any new records Update any existing records that were updated Delete any records locally that were deleted on the server (either deleted directly or indirectly (e.g. through a foreign key relationship, like when an account is deleted its associated tasks are deleted as well).   Can you please offer advice on what API's might be good to use here, and whether one stands out more than the others? Are there any specific design recommendations that might be useful for achieving this goal? Or is there really no practical difference between what REST vs SOAP can do?  It comes down to what is the easiest to maintain/implement? Is there some other route that might be beneficial to use (example: bulk data load to start out followed by outbound messaging tied to all of the objects in question to get updates/inserts/deletes)?   I am using C#/.net. How to get method parameter names? Given the Python function:  def a_method(arg1, arg2):     pass   How can I extract the number and names of the arguments. I.e., given that I have a reference to func, I want the func.[something] to return ("arg1", "arg2").  The usage scenario for this is that I have a decorator, and I wish to use the method arguments in the same order that they appear for the actual function as a key. I.e., how would the decorator look that printed "a,b" when I call a_method("a", "b")? Concatenate multiple rows