Missing values are very common in large time series data. How should the missing values of a time series be estimated? Is interpolation useful or I need to forecast them from the past values?
Suppose I have a dataframe consisting of six time series. In this dataframe, some observations are missing, meaning at some timepoints all time series contain a NA-value. In R, one possible imputation package that can be used to impute time series data is Amelia. However, this package does not work for observations that are completely missing. Are there other ways to impute my data? For what it's worth, the amount of missing observations is less than 20% of all observations.
$(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$ Let $\sim$ be the equivalence relation on $S_1 \times I$ given by $(x,t)\sim(y,s)$ if and only if $xt=ys$ where $I=[0,1]$  How do I prove that $(S_1 \times I)/\sim$ is homeomorphic to the unit disk $D^2$ with the induced topology? Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$ Find the maximum value of $f(x)$ when $0 \leq x \leq 1$ and $$ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$$   I'm guessing that the Fundamental Theorem of Calculus can't be used because the integrand is a function of $x$.  Any help would be greatly appreciated. Close vote review audit flawed - fails without casting vote Having just  from any of the queues, it was reviewing close votes; however, this audit was flawed in that I didn't even cast a close vote.  Often I press the Close button to preview greater detail and sentiment of the closure, spawning the Why should this question be closed dialog box:    Especially for duplicates, where functionality is solely dependent on spawning this dialog.  From Closing > Duplicate, I can search or view selected duplicates:    Although, I realize general closure reasons are summarized on the page:    This question had 6-upvotes, but seemed very localized referencing subjective query is "taking too long" and even had a sqlfiddle link.  Maybe overly broad regarding performance tuning, the OP was posting like a forum with two answer posts to his own question  and  with one of those answers asking follow-up questions.    Wanting to gauge community response, current closure totals struck my curiosity.  So, I pressed the Close button and boom - oh, the humanity!  I failed, and didn't even cast a close vote.    Votes are not cast until a reason for closure is selected and Vote to Close is pressed.  Taking any review very seriously on this site, it only seems fair that my review quality is tested through actionable steps instead of clicking for more detailed information, leveraging the functional design of the close vote user interface.  Sure, it's complex to seed fake vote totals, and then there's controversy of mindless voting in the majority or people who simply cherry pick 4-vote questions.  Still though, it seems unfair I should hesitate to review further information of vote totals and duplicates before skipping due to the implementation of this audit. Uniform Scattering with vector I'm attempting to create a random spread of dots to create a gradient look. I'm getting really close to the effect I want by blending two scatter brushes. The issue I'm having is that the blended brushes creates unwanted lines, and the dots run into each other. I keep adjusting the settings with no luck.  Here's the effect I'm wanting to achieved.    Smooth transition  On Circular path Dots don't converge Scattered at random-ish     Here's how close I'm able to get:   Blended scatters create unwanted lines Dots converge Spacing isn't gradual from edge to center 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? How to pass parameters to query? I'm a physics teacher and I would like to find a simulation software that could be used to give exact numerical answers to high school level problems in Newtonian mechanics.  I want the students to first calcultate a numerical answer to a physics problem and then use the simulator to visualize the problem in order to understand it better and verify that the simlator gives the same answer that they got when doing the calculation themselves.  Here are some examples of what kind of problems I want the students to be able to solve with the simulator:   A slope with a specific angle of inclination and a ball starts rolling at a certain point. Determine the speed, angular momentum and total mechanical energy of the ball after a specific time t. A ladder of known mass and length is leaning against the wall at a specific angle. The contact between the ladder and the wall is frictionless. Calcultate the x and y components of the force between the floor and the ladder.   I would like the software to have the following features:  - Simulation in 2D. No 3D simulations are necessary and the software should at least have the option of doing simulations only in 2D.  - Position all objects exactly by writing numbers (just positioning the objects using the mouse is not precise enough).  - Show animations of the time evolution of the system.  - Show forces, velocities and accelerations as arrows.  - Give exact numerical results so that the students can use the software to verify their calculation.  Ideally the software would have a graphical user interface, but if no suitable software with graphical interface exixts, I could also consider a software with text-based inputs. I would consider both free and commercial software.  My question is: Is there any software that would meet these requirements and if there is, where could I get it? Split Java String by New Line I'm trying to split text in a JTextArea using a regex to split the String by \n However, this does not work and I also tried by \r\n|\r|n and many other combination of regexes. Code:  public void insertUpdate(DocumentEvent e) {     String split[], docStr = null;     Document textAreaDoc = (Document)e.getDocument();      try {         docStr = textAreaDoc.getText(textAreaDoc.getStartPosition().getOffset(), textAreaDoc.getEndPosition().getOffset());     } catch (BadLocationException e1) {         // TODO Auto-generated catch block         e1.printStackTrace();     }      split = docStr.split("\\n"); } How to use WPF Background Worker Why does light in a room not form constructive and destructive interference patterns? Known proofs of Wirtinger's Inequality? In theory, is it possible that the loss on the train set will increase together with the train set accuracy? (in the normal case the train set loss should go down) And vice versa, can the train loss decrease along with the accuracy?   Note: This is obviously different than the classic underfit / overfit cases which are easier to grasp. This question attempts to collect the few pearls among the dozens of bad C++ books that are published every year. Unlike many other programming languages, which are often picked up on the go from tutorials found on the Internet, few are able to quickly pick up C++ without studying a well-written C++ book. It is way too big and complex for doing this. In fact, it is so big and complex, that there are very many very bad C++ books out there. And we are not talking about bad style, but things like sporting glaringly obvious factual errors and promoting abysmally bad programming styles. Please edit the accepted answer to provide quality books and an approximate skill level — preferably after discussing your addition in . (The regulars might mercilessly undo your work if they disagree with a recommendation.) Add a short blurb/description about each book that you have personally read/benefited from. Feel free to debate quality, headings, etc. Books that meet the criteria will be added to the list.  Books that have reviews by the Association of C and C++ Users (ACCU) have links to the review. *Note: FAQs and other resources can be found in the  and under . I have a really strange situation here. My PC works fine, at least in most cases, but there's one thing that I can't deal with. When I try to copy a file from my pendrive, everything is ok -- I got 16-19M/s , it works pretty well. But when I try to copy something to the same pendrive, my PC freezes. The mouse pointer stops moving for a sec or two, then it moves a little bit and it stops again. When something is playing, for example, in Amarok, the sound acts like a machine gun. The speed jumps from 500K/s to 15M/s, average 8M/s. This occurs only when I'm copying something to a pendrive. When the process of copying is done, everything backs to normal.   I tried everything -- other pendrive, a different USB port on front panel or those ports from back, I even changed the USB pins on motherboard (front panel), but no matter where I put my USB stick, it's always the same. I tried different filesystem -- fat32, ext4. I have no problem with the device on Windows, on my laptop. It has to be my PC or something in my system. I have no idea what to look for. I'm using Debian testing with standalone Openbox. My PC is kind of old -- Pentium D 3GHz, 1GiB of RAM, 1,5TB WD Green disk. If you have something that would help me to solve this issue, I'd be glad to hear that.  I don't know what else info I should provide, but if you need something, just ask, I'll update this post as soon as possible.  I tried to reproduce this problem on ubuntu 13.04 live cd. I mounted my encrypted partition + encrypted swap and connected my pendrive to a usb port. Next I tried to start some apps, and now I have ~820MiB in RAM and about 400MiB in SWAP. There's no problem with copying, no freezing at all, everything is as it should be. So, it looks like it's a fault of the system, but where exactly? What would cause such a weird behavior? I want to convert a std::string to lowercase. I am aware of the function tolower(). However, in the past I have had issues with this function and it is hardly ideal anyway as using it with a std::string would require iterating over each character. Is there an alternative which works 100% of the time? Is it possible to create a counter just with wiring? With the new logic gates in the 1.3.1 update, is it possible to create some wiring circuit that counts how many times a trigger was activated? In other words, is it possible to make a circuit that outputs a trigger every two input triggers?  I've done some experimenting but the nature of wires and there being no intrinsic on/off state in Terraria makes it pretty counter-intuitive compared to real world logic circuits. Confirmation that (inner) classes are still not fully supported in @AuraEnabled methods? Is "You are correct" correct? How do we know that certain quantum effects are random? Linux - Help, I'm running out of inodes!