Imputing Missing Values
Methods to work around the problem of missing data in machine learning
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$ Accepted way to abbreviate cities that have "Saint" in their name My first question here, so I'm not sure if this OT or not, so please bare with me.  Background: I don't live in US. I'm working with some data that I'm pulling from . Sometimes, I'm getting a city name as St. John and sometimes as Saint Ann.   So my question is, is there an accepted way on how people write a US city names which starts with Saint or is this just some random thing (or just specific to AdWords maybe)?  I'm asking this, because if for example I'll get both St. John and Saint John in the same file, should I consider them the same or should I be suspicious? How to automatically resize the vertical bar in a set comprehension? I have a simple command which I use to write set comprehensions so that the braces automatically resize with respect to size of the enclosed arguments, e.g.  \usepackage{amsmath} \newcommand{\set}[1]{\left\lbrace #1\right\rbrace}  \begin{equation*} \set{x \in X \mid x &gt; \frac{1}{2}}   \end{equation*} % Produces something like: { x : X | x &gt; 1/2 }   However, the \mid vertical bar wont resize like the braces { .. } do. How can I get the \mid to resize as well? I have this table but check constraint is throwing me an error:     Column CHECK constraint for column 'MedicamentRegulated' references another column, table 'Medicaments'.   I've seen this as allowed in SQL Server but I don't know why it doesn't work :/  CREATE TABLE Medicaments ( MedicamentID INT NOT NULL IDENTITY(1,1) PRIMARY KEY, Name VARCHAR(50), DateValidity DATE, MedicamentRegulated BIT CHECK((MedicamentRegulated = 1 AND DateValidity IS NOT NULL)    OR MedicamentRegulated = 0) ) What are the consequences of using a low-wattage USB-C power supply with a MacBook Pro? Should I upgrade my body or lens first? Mclaurins with $e^{\sin(x)}$ To evaluate $e^{\sin(x)}$ I use the standard series $e^t$ and $\sin(t)$, combining them gives me:  $e^t = 1+t+\dfrac{t^2}{2!}+\dfrac{t^3}{3!}+\dfrac{t^4}{4!}+O(t^5)$  $\sin(t) = t-\dfrac{t^3}{3!}+O(t^5)$  $\therefore e^{\sin(x)} = 1+\sin(x)+\dfrac{\sin^2(x)}{2!}+\cdots+O(x^5)$  $\iff e^{\sin(x)}=1+\left(x-\dfrac{x^3}{6}\right)+\dfrac{\left(x-\frac{x^3}{6}\right)^2}{2}+\dfrac{x^3}{6}+O(x^5) = 1+x +\dfrac{x^2}{2}-\dfrac{x^4}{6} + O(x^5)$  In the last step, I only evaluate up to $\sin^3x$ term, everything above has a grade equal to or greater than $x^5$  However, I'm wrong. According to Wolfram, the series expansion for $e^{\sin x} = 1+x+\dfrac{x^2}{2}-\dfrac{x^4}{8}+O(x^5)$.  What did I do wrong? I can't seem to find what or where. Was Tracy Mills a part of John Doe's plan from the beginning? In , John Doe is shown as being extremely meticulous and patient while carrying out his plan of murdering and/or torturing people in accordance with the seven deadly sins.  At the end of the film, it is revealed that John Doe had killed and decapitated Tracy Mills, the wife of Detective David Mills.  Was Tracy Mills his intended target from the beginning?  Did John Doe decide to kill Tracy only after Detective Mills and Somerset discovered his residence? Is there geometric or visual (but rigorous) proof for the equation of hyperbola whose foci are on the $x$-axis using only the traditional definition of hyperbola: a hyperbola is a set of points such that the difference of distances from each point to focus is constant $(|r_1 - r_2| = 2a)$?  Also, can you maybe geometrically explain asymptotes of hyperbola (why do they exist)? what is a thyristor As part of my 2330 lv3 am required to know about thyristors. I just want to confirm my understanding is correct. A thyristor is basically similar to a transistor, only it stays switched on when it's trigged for as long as there isn't a break in the circuit it's switching. Am I correct? How to print original variable's name in Python after it was returned from a function? I have enum and use the variables like myEnum.SomeNameA, myEnum.SomeNameB, etc.  When I return one of these variables from a function, can I print their names (such as myEnum.SomeNameA) instead of the value they returned? Infinite DeMorgan laws Let $X$ be a set and $\{Y_\alpha\}$ is infinite system of some subsets of $X$. Is it true that: $$\bigcup_\alpha(X\setminus Y_\alpha)=X\setminus\bigcap_\alpha Y_\alpha,$$ $$\bigcap_\alpha(X\setminus Y_\alpha)=X\setminus\bigcup_\alpha Y_\alpha.$$ (infinite DeMorgan laws)  Thanks a lot! $n$ balls are thrown randomly into $k$ bins - how many are empty? A large number of variants of this question were already asked here, including these - , , which are close, but none seem to answer my question. Assume that $n$ balls are thrown randomly and independently into $k$ bins.  What is the probability of finding $x$ empty bins? What is the expectation of the number of empty bins? How to change the href for a hyperlink using jQuery How can you change the href for a hyperlink using jQuery? Software needed to scrape data from graph Anybody have any experience with software (preferably free, preferably open source) that will take an image of data plotted on cartesian coordinates (a standard, everyday plot) and extract the coordinates of the points plotted on the graph?  Essentially, this is a data-mining problem and a reverse data-visualization problem. $N(ab) \geq N(a)$ is not necessary for the ring to be euclidean The definition of euclidean ring in my textbook is 1) $N(ab) \geq N(a)$ 2) Euclidean algorithm works. However there is a note that the first condition is not necessary. There is a hint that we can choose a following norm: $N'(a) = \min_{b\sim a} N(b)$. I do not understand why it works. We need to check that euclidean algorithm still works with this norm.   I tried to do the following. If $a \sim b$, then $a = bx, x \in K^*$. Let $N'(a)$ be $N(ax)$. Let us divide $ax$ by $bx$ instead of $b$. We get $ax = bxq + rx$, $N(rx) \leq N(bx)$. Here I am stuck and have no idea how to continue. Is the latest version of Ubuntu 100% FREE Enum ToString with user friendly strings My enum consists of the following values:  private enum PublishStatusses{     NotCompleted,     Completed,     Error };   I want to be able to output these values in a user friendly way though. I don't need to be able to go from string to value again. Which process scheduler is my linux system using? I'm not quite sure if stackoverflow or serverfault is the forum to use for this question, but ill try here.  Is there some command I can use or a file I can check in order to find out which process scheduler I'm using on my Linux system? I am not looking for the I/O scheduler, but the process scheduler, and please, do not refer to guides or howtos for what a scheduler is, what I'm simply asking is if there is a command or file I can run/check to see this. I could check the doc for my kernel but again I'm just wondering if there is a command or file i can check.  I might have been a little redundant above but that's because the posts I've seen people seem to confuse process scheduler with the i/o scheduler, and they don't seem to answer the actual question, just provide links to what a scheduler is which is not what I'm after here, so apologies if the above comments sounded rude. How to hide the .html extension with Apache mod_rewrite