Gaussian Kernel and Feature Space
Can you explain Parzen window (kernel) density estimation in layman's terms?
Show that $\left | \sin a - \sin b \right | \leq \left | a-b \right |$ I am trying to copy multiple files named "F3.bam" two level of directories to up and then rename these files with the name of the sub-directory after copy.  For example:  /samples/mydata1/RUN1/ID_date/PCR2/TIME1/F3.bam /samples/mydata2/RUN1/ID2_date4/PCR2/TIME7/F3.bam /samples/mydataxxx/RUN1/IDxxx_datexxx/PCR2/TIMExxx/F3.bam   Expected results:  1. The files are first copied two directories level up:  /samples/mydata1/RUN1/ID_date/F3.bam /samples/mydata2/RUN1/ID2_date4/F3.bam /samples/mydataxxx/RUN1/IDxxx_datexxx/F3.bam   2. The files are renamed according to the name of the current sub-directory:  /samples/mydata1/RUN1/ID_date/ID_date_F3.bam /samples/mydata2/RUN1/ID2_date4/ID2_date4_F3.bam /samples/mydataxxx/RUN1/IDxxx_datexxx/IDxxx_datexxx_F3.bam   Ideally a bash loop would be great (working on a Mac). What is the Physical Meaning of Commutation of Two Operators? I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics?   E.g. an operator $A$ with the Hamiltonian $H$? Is it safe to cancel CHKDSK when it has been started without any parameters? I know that it is not a good idea to forcibly stop a chkdsk process that has been executed with parameters like /f and /r.   But is it safe to stop the process when it has been started simply by the chkdskcommand? Chkdsk prints out a lot of errors and is continuing very slowly.  I suppose it to should be safe to cancel the process since there should be only in read mode, correct? Neutrino project in Tamil-Nadu India In , the Indian government is going to start a neutrino project.  Questions:   Is it harmful for people who stay there?   Will this project affect any living beings? Does it cause any pollution? Motion tracked Video doesn't show up in the render or in the compositing tab I tried to add a 3D object to a clip by following a youtube video. But clip doesn't show up in the render or in the compositing tab. It show up even in the camera view. I didn't change any settings. please help. Thank you.    And the  rendered images has only the cube in it like in the picture above. How can I make Chrome open bookmarked pages in new tab by default? Current situation:  I am currently browsing a page (say, www.google.com). I want to open a bookmarked page (say, www.bing.com), but I want to keep the current page (Google) opened. I need to click on new tab, then click on the bookmark for Bing. Alternatively, I can right click and open Bing in new tab.  But I want none of those because why click twice when one is enough?    What I want:  I am currently on Google. I want to open Bing, so I click on the bookmark and Bing opens in a new tab. Google remains open.    I am aware of a duplicate question linked . However it didn't really provide a satisfactory answer. Changing every link to javascript breaks the icon and is a pain to do; middle clicking doesn't really work because I'm on a laptop and the touchpad does not support middle clicking. I hope there is an extension for Chrome that can redefine this behavior to the way I want. A hidden setting in Chrome would be even better but I doubt Chrome offers that. What are the consequences of "copying" a data set for OLS? What is the use of the Dot Product of two vectors? This one-liner removes duplicate lines from text input without pre-sorting.  For example:  $ cat &gt;f q w e w r $ awk '!a[$0]++' &lt;f q w e r $    The original code I have found on the internets read:  awk '!_[$0]++'  This was even more perplexing to me as I took _ to have a special meaning in awk, like in Perl, but it turned out to be just a name of an array.  Now, I understand the logic behind the one-liner:  each input line is used as a key in a hash array, thus, upon completion, the hash contains unique lines in the order of arrival.  What I would like to learn is how exactly this notation is interpreted by awk. E.g. what the bang sign (!) means and the other elements of this code snippet.  How does it work? OAuth 2.0 access token request failed with error "must use HTTP POST" OAuth 2.0 Auth token request failed with below error   { "error": "invalid_request", "error_description": "must use HTTP POST" }   What does this error mean?  I am using Postman. Have a connected app. I have used Post method, Url has https. Same request works for other Orgs. Did I missed any configuration/Permission check?  https://testOrg.lightning.force.com/services/oauth2/token?grant_type=password&amp;client_id={{CLIENT_ID}}&amp;client_secret={{CLIENT_SECRET}}&amp;username={{USER_ID}}&amp;password={{PASSWORD}} Multiplication in Permutation Groups Written in Cyclic Notation I have an Ubuntu 12.04 machine on which I have installed VirtualBox with Ubuntu 12.04 as the guest OS.  How can I share files between the host and guest?   I have installed the guest additions also but still it’s not able to mount the sf_shared folders if even it’s mounted. This means I'm unable to retrieve the file from the host. What exactly is weakly informative prior? Is there a precise definition of weakly informative prior?  How is it different from a subjective prior with broad support? Hibernate @Enumerated mapping $\LaTeX$ and Mathematica A potential customer wants to evaluate our storage system. They run Windows 2008R2 x64 with 4KB NTFS on a virtual test machine they've sent us. They did not seem to know this at hand, so I think it's reasonable to assume that environment was not tweaked. The tests are inserting, indexing, searching, deleting. Tool is not known to me.  Given that the windows NTFS block size is 4KB, and SQL write in 64KB chunks - is it safe to assume that a block size of 64k on the SAN is a good choice?  They run SQL Server 2008, perhaps standard. How to get the pid of the last executed command in shell script? I want to have a shell script like this:  my-app &amp; echo $my-app-pid   But I do not know how the get the pid of the just executed command.  I know I can just use the jobs -p my-app command to grep the pid. But if I want to execute the shell multiple times, this method will not work. Because the jobspec is ambiguous. Assume $R=(\mathcal{U}_n)_n$ is a sequence of distinct ultrafilters on some set $X$. Since every Hausdorff space has an infinite discrete subspace, there is a subsequence $R=(\mathcal{V}_n)_n$ of $R=(\mathcal{U}_n)_n$ such that $\{\mathcal{V}_n|n \in \mathbb{N} \}$ is a discrete subspace of $\beta X$. In particular, there is a sequence $(A_n)_n$ of sets with $A_n \in \mathcal{V}_m$ if and only if $m =n$. If we let $B_n=A_n - (A_0 \cup...\cup A_{n−1})$, then the sequence $(B_n)_n$ is pairwise disjoint and $B_n \in \mathcal{V}_m$  iff $m=n$. If we let $B =\cup_n B_{2n}$, then $B \in \mathcal{V}_m$ if and only if $m$ is even. In other words, if $B =\{ \mathcal{V} \in βX|B \in \mathcal{V}\}$, then $B$ is a clopen set with $\mathcal{V}_m \in B$ iff $m$ is even. Therefore, we conclude that the sequence $(\mathcal{V}_m)_m$ cannot converge to any point, so the sequence $(\mathcal{U}_n)_n$ cannot converge to any point either.     I would like to know that:      (1) Why "$B_n \in \mathcal{V}_m$  iff $m=n$"? And " $B =\cup_n B_{2n}$, then $B \in \mathcal{V}_m$ if and only if $m$ is even "?      (2)$B$ is a clopen set with $\mathcal{V}_m \in B$ iff $m$ is even Sudo is also user login password - why? how to change? When installing Ubuntu I can create a user with an encrypted folder, what I always do. Now after the installation the login password for this user is also the sudo password. Is that how it should be? I actually would like to have a different user login and sudo password, does is make sense? Should I do that, how?