Binary Classification - One Hot Encoding preventing me using Test Set
Obtaining consistent one-hot encoding of train / production data
Sum of Cosine/Exponential I try to simplify to get rid of sum $$ \sum_{k=0}^{n-1}\cos(2 \pi fk)$$  I discover I shall use euler equation to form:  $$ \sum_{k=0}^{n-1}\frac{1}{2}(e^{2 \pi fki}+e^{-2 \pi fki})$$  but how to sum exponentials? I am planning a trip to Italy this coming January. My plan is to land by plane in Roma and then go to France by train/bus stopping in some Northern Italian cities on the way, enjoying the architecture, the atmosphere, the art and and the food.   I want to do it at my own pace, without heavy scheduling. Ideally, I would just decide which cities to visit, and take a train whenever I feel it. I often do this here in South Korea where I am living, taking advantage of the "standing seats" as it is called here, that is travelling (for a cheap price and no reservation) standing on the romm between two cars. From my experience, it is also doable in Taiwan (at least in some trains).  In France, regional trains usually does not need any reservation, so you can buy a ticket and take the train whenever you want.  Can I expect a similar system in Italy, that is a way to make short travels between close cities without reservation?   Example of "short travel": Pisa - Firenze. Writing basic systemd service files I have an ArrayList that I want to output completely as a String. Essentially I want to output it in order using the toString of each element separated by tabs. Is there any fast way to do this? You could loop through it (or remove each element) and concatenate it to a String but I think this will be very slow. If it was possible to dig a hole that went from one side of the Earth to the other... ...And you jumped in.  What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up? How To Delete This Red Box on My Screen? I was editing my mesh and I wanted to only see a part of my mesh, so I pressed alt+B to only show a selected area. However, I did ctrl+B and created a red rectangle on my screen (I don't know what it does). Does anybody know how to get it off? Why does $x$ divided by zero not equal $x$? Why does $x$ divided by zero not equal $x$? After all, $x$ is not being divided by anything. How to remove Home Folder icon from desktop in Ubuntu 20.04? When I start Ubuntu I had my &quot;home/user&quot; in my Desktop. test is my User.   How do I make the folder not be on the desktop? In an exercise in Atiyah-Macdonald it asks to prove that the prime spectrum $\operatorname{Spec}(A)$ of a commutative ring $A$ as a topological space $X$ (with the Zariski Topology) is compact.   Now because the basic open sets $X_f = \{\mathfrak{p} \in \operatorname{Spec} (A) : \{f\} \not\subseteq \mathfrak{p} \}$ form a basis for the Zariski Topology it suffices to consider the case when   $$X = \bigcup_{i \in I} X_{f_i}$$   where $I$ is some index set. Then taking the complement on both sides we get that   $$\emptyset = \bigcap_{i \in I} X_{f_i}^c$$  so there is no prime ideal $\mathfrak{p}$ of $A$ such that all the $f_i$'s are in $\mathfrak{p}$. Now from here I am able to show that the ideal generated by the $f_i$'s is the whole ring as follows. Since there is no prime ideal $\mathfrak{p}$ such that all the $f_i \in \mathfrak{p}$, it is clear that there is no $\mathfrak{p}$ such that $(f_i) \subseteq \mathfrak{p}$ for all $i \in I.$ Taking a sum over all the $i$ then gives $$\sum_{i \in I} (f_i) = (1).$$  Now here's the problem:          How do I show from here that there is an equation of the form $1 = \sum_{i \in J} f_ig_i,$ where $g_i \in A$ and $J$ some finite subset of $I$?       This part has been giving me a headache. I am not sure if the finiteness bit has to do with algebra, topology or the fact that we are dealing with prime ideals.  This is not a homework problem but rather for self-study.  $\textbf{Edit:}$ I have posted my answer below after the discussion with Dylan and Pierre. What's the difference between $\mathbb{R}^2$ and the complex plane? I haven't taken any complex analysis course yet, but now I have this question that relates to it.  Let's have a look at a very simple example. Suppose $x,y$ and $z$ are the Cartesian coordinates and we have a function $z=f(x,y)=\cos(x)+\sin(y)$. However, now I change the $\mathbb{R}^2$ plane $x,y$ to complex plane and make a new function, $z=\cos(t)+i\sin(t)$.  So, can anyone tell me some famous and fundamental differences between complex plane and $\mathbb{R}^2$ by this example, like some features $\mathbb{R}^2 $ has but complex plane doesn't or the other way around. (Actually I am trying to understand why electrical engineers always want to put signal into the complex numbers rather than $\mathbb{R}^2$, if a signal is affected by 2 components)   Thanks for help me out! What word (or how do you phrase things) do you use when the ostensible word for the class is the same as the word for a subset of the class?  For example, in the United States, there are many brands of sugared, carbonated soft drink that one can buy: Coca-Cola (or Coke), Pepsi, RC Cola, Sprite, 7-Up, A&amp;W or Mug Root Beer, etc). The first two are kinds of 'coke' or 'cola' (but no one says 'cola').  , one asks for any type of such drink as 'coke'. How does one then ask for the particular kind of 'coke' that is 'Coke' (pronounced the same)? Does one reduplicate and say a 'Coke coke', does one repeat with emphasis (or without), does one use a different word like 'coca-cola' (co-cola), or what?  The (perceived) difficulty (surely those in the South are able to get the drink they want somehow) isn't limited to there. Where the drink is called 'soda', if you ask for a 'coke', you'll still sometimes have the choice among Coca-Cola, Pepsi, etc. "Can I have a Coke?" the response might be "Is Pepsi OK?". "Sure, Pepsi, Coke, whatever." You don't use 'cola', you just ask for the particular kind and hope the listener will help differentiate.   Given these multiple strategies for disambiguating, what do you do say to get a 'Coke' in the southern US? are there any other examples of a hypernym being the same as the hyponym, and so creating a disambiguation problem? Well, the original task was to figure out what the following expression evaluates to for any $n$.  $$\begin{pmatrix} 1 &amp; 1 \\ 0 &amp; 1\end{pmatrix}^{\large n}$$  By trying out different values of $n$, I found the pattern: $$\begin{pmatrix} 1 &amp; 1 \\ 0 &amp; 1\end{pmatrix}^{\large n} = \begin{pmatrix} 1 &amp; n \\ 0 &amp; 1\end{pmatrix}$$  But I have yet to figure out how to prove it algebraically.   Suggestions? ArcPy importing error after setting path? This questions has been asked before too and I did go through most of the suggestions. Things I have tried so far: setting up correct  path variable environment, installing anaconda 32 bits, python 2.7, or even switching to python 2.7 in cmd while initially using Anaconda 3 , adding Desktop 10.4.pth file with  following path.  C:\Program Files (x86)\ArcGIS\Desktop10.4\bin C:\Program Files (x86)\ArcGIS\Desktop10.4\ArcPy C:\Program Files (x86)\ArcGIS\Desktop10.4\ArcToolBox\Scripts   I also added those paths in environment variable   These suggestions help me to reduce the error. But Now I am getting a different error. Looks like python can find arcpy but missing another package.  Getting this error while trying to import arcpy in python 3.6.   File "C:\Program Files (x86)\ArcGIS\Desktop10.4\ArcPy\arcpy\__init__.py", line 22, in &lt;module&gt;     from arcpy.geoprocessing import gp    File "C:\Program Files (x86)\ArcGIS\Desktop10.4\ArcPy\arcpy\geoprocessing\__init__.py", line 14, in &lt;module&gt;     from _base import *  ModuleNotFoundError: No module named '_base'   Any suggestions? How to show setCustomValidity message/tooltip without submit event Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods? I have seen the Fresnel integral  $$\int_0^\infty \sin x^2\, dx = \sqrt{\frac{\pi}{8}}$$  evaluated by contour integration and other complex analysis methods, and I have found these methods to be the standard way to evaluate this integral.  I was wondering, however, does anyone know a real analysis method to evaluate this integral? Windows says RAM ran out while there is still 4 GB of physical memory available This equation is directly given in my book and I am don't know anything about its proof.I tried L'Hospital rule by differentiating the both numerator as well as denominator(division rule), but the result is still coming in indeterminate forms.I am a beginner , and haven't practiced limits that much. This formula is really confusing me. Story about a trip to a Valley of Sound Maven plugin executing another plugin I'm trying to create a new plugin to package my latest project.  I'm trying to have this plugin depend on the maven-dependency-plugin to copy all my projects dependencies.  I've added this dependency to my plugin's pom, but I can't get it to execute.  I have this annotation in my plugins main Mojo:  @execute goal="org.apache.maven.plugins:maven-dependency-plugin:copy"   I've tried a few other names for the goal, like dependency:copy and just copy but they all end with a message saying that the required goal was not found in my plugin.  What am I doing wrong?  Secondary to this is where to I provide configuration info for the dependency plugin? When I have .txt files or .py files, I can Quick Look those files in Finder. I have .jl files that are codes written in the Julia Language. Of course they are text files. They will open in a text editor like Sublime Text. How can I Quick Look these .jl files in Finder?