I'm under Windows 7, and I'd like to know if it's possible to create a virtual folder that points to many other folders, effectively listing all their contents as if being in a  single directory.  I'll try to be more precise with an example.  Let's suppose that I have many files in a directory structure to better categorize them, like this:    Main_dir |-&gt; Subfolder1 |   |-&gt; File1A.zip |   |-&gt; File1B.zip |-&gt; Subfolder2 |   |-&gt; File2A.zip |   |-&gt; File2B.zip |-&gt; Subfolder3     |-&gt; File3A.zip     |-&gt; File3B.zip   And so on. I need to keep those files inside this hierarchical structure, like I said to have them categorized; but I also need to have all of them listed as being inside a single directory, like this:  Virtual_dir |-&gt; File1A.zip |-&gt; File1B.zip |-&gt; File2A.zip |-&gt; File2B.zip |-&gt; File3A.zip |-&gt; File3B.zip   Basically, I want to create a link named Virtual_dir that points to Main_dir\Subfolder1 AND Main_dir\Subfolder2 AND Main_dir\Subfolder3.  Is it possible to do so? Linking any single file inside the Virtual_dir is not what I'm trying to do. I want to use a feature similar to , with folder containing any kind of files (not just music, videos and documents) in a way that can be understood not just by Windows itsefl but also by any other arbitrary piece of software.
I have 3 folders with large amount of data in each which has to be maintained seperately. Can I create a sym link or shortcut.in windows which should show me the merged contents of the 3 folders. I am not looking for library conf in Win7.   Any suggestion is highly appreciated.
Resetting crontab file to default Programmatically combining images in PHP I'm a big fan of Yahoo's  for speeding up websites. One of the recommendations is to combine images where possible to cut down on size and the number of requests. However, I've noticed that while it can be easy to use CSS sprites for layouts, other image uses aren't as easily combined. The primary example I'm thinking of is a blog or article list, where each blog or article also has an image associated with it. Those images can greatly affect load time and page size, especially if they aren't optimized. What I'm looking for, in concept or in practice, is a way to dynamically combine those images while running them through a loss-less compression using PHP.   A few added thoughts or concerns:   Combining the images and generating a dynamic CSS stylesheet to position the backgrounds of the images might be one way to go about it, but I also worry about accessibility and semantics. As far as I understand, CSS images should be used for layout elements and the img tag (with the alt attribute) should be used for images that are meant to convey information. I could set the image as a background to a div element and substitute a title attribute for the alt attribute, but I'm unsure about the accessibility and semantic implications of doing so. Might the GD library be a good candidate for something like this? Can you recommend other options? I think some good words would be conflicted, or confused. As an example of context, think of someone who believes in freedom of speech, but, at the same time, they would support banning comedians who make jokes about certain issues that person cares about. Error entering equation in DSolve A question about E12 series resistors I'm trying to calculate E12 resistor series myself.  Above is an illustration of the idea where such equation can be written:  x = r3 + r3 * %tol = r4 - r4 * %tol  form that we can derive:  r4 = r3* [(1 + %tol)/(1 - %tol)]  hence in generalized form we can write (%tol = 0.1 for E12 series);   r(i+1) = ri* [(1 + %tol)/(1 - %tol)]  But when I iterate the above formula in a for loop I obtain the following results for the first resistor values:  1.0000    1.2222    1.4938    1.8258    2.2315    2.7274    3.3335    4.0743    4.9797    6.0863    7.4388  Then I take [(1 + %tol)/(1 - %tol)] = 1.2 rounded value instead of 1.222222 and write the formula as:  r(i+1) = r(i)*1.2  But again when I iterate the above formula in a for loop I obtain the following results for the first resistor values:  1.0000    1.2000    1.4400    1.7280    2.0736    2.4883    2.9860    3.5832    4.2998    5.1598    6.1917  But the real values for E12 should be as:  1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8  What am I doing wrong here? Fingerprint GUI not installing in Ubuntu 20.04 I'm trying to install fingerprint-gui on my Lenovo Ideapad 520 having Ubuntu 20.04 on which fingerprint isn't working for now. I tried going directly to Settings → Users → Automatic login and enabled the fingerprint login, but the error is:  Could not access any fingerprint readers Please contact your system administrator for help!  I also tried to install Fingerprint GUI: sudo apt-add-repository ppa:fingerprint/fingerprint-gui &amp;&amp; sudo apt-get update  sudo apt-get install libbsapi policykit-1-fingerprint-gui fingerprint-gui  but encountered this error: E: Package 'policykit-1-fingerprint-gui' has no installation candidate E: Package 'fingerprint-gui' has no installation candidate  What could be the problem here? Acro package provides "! Missing number, treated as zero." after update to acro-v2.7b A finite summation of double binomial coefficients I find the following identity and have checked on Mathematica, while I have no idea how to prove it:  $$\sum_{j=0}^n(-1)^{n-j}\binom{p+j}{j}\binom{n+\beta}{n-j}=\binom{p-\beta}{n}, \quad \beta&gt;-1, \quad p&gt;\beta-1.$$  It seems that proof by induction does not work and because of the gamma function, the transform technique does not work either. How do I prompt for Yes/No/Cancel input in a Linux shell script? I want to pause input in a shell script, and prompt the user for choices. The standard Yes, No, or Cancel type question. How do I accomplish this in a typical bash prompt? It is a common practice to apply PCA (principal component analysis) before a clustering algorithm (such as k-means). It is believed that it improves the clustering results in practice (noise reduction).   However I am interested in a comparative and in-depth study of the relationship between PCA and k-means. For example, Chris Ding and Xiaofeng He, 2004,  showed that "principal components are the continuous solutions to the discrete cluster membership indicators for K-means clustering". However, I have hard time understanding this paper, and Wikipedia actually .  Also, the results of the two methods are somewhat different in the sense that PCA helps to reduce the number of "features" while preserving the variance, whereas clustering reduces the number of "data-points" by summarizing several points by their expectations/means (in the case of k-means). So if the dataset consists in $N$ points with $T$ features each, PCA aims at compressing the $T$ features whereas clustering aims at compressing the $N$ data-points.  I am looking for a layman explanation of the relations between these two techniques + some more technical papers relating the two techniques. Does opacity:0 have exactly the same effect as visibility:hidden If so, does it effectively deprecate the visibility property?  (I realize that Internet Explorer does not yet support this CSS2 property.) What does the notation like 8.6e-28 mean? What is the 'e' for? I have a problem with the interpretation of a test result in which the p-value is 8.6e-28. How should it be interpreted? What is the e for?  Specifically, I used White's Test for the homoscedasticity assumption of a linear regression:  White's general test statistic :  150.0535  Chi-sq( 9)  P-value =  8.6e-28 Please bring back the oldest sort order for answers, I think we can deal with four different types of sort order.  It's helpful if you don't want to have to tool-tip every post to see which got posted first, so that you can upvote the oldest answer when answers duplicate each other.  Edit:  Also, trying to read newest backwards doesn't work well for questions with multiple pages of answers. How to minimize $|z_1 - z_2|^2 + |z_1 - z_4|^2 + |z_2 - z_3|^2 + |z_3 - z_4|^2$? If $z_1,z_2,z_3,z_4 \in \mathbb{C}$ satisfy $z_1 + z_2 + z_3 + z_4  =  0$ and $|z_1|^2 + |z_2|^2 + |z_3|^2 + |z_4|^2 = 1$, then the least value of $|z_1 - z_2|^2 + |z_1 - z_4|^2 + |z_2 - z_3|^2 + |z_3 -  z_4|^2$ is $2$.   I solved this by taking two of the values to be $\frac{1}{2}$ and other two as $-\frac{1}{2}$. But I couldn't prove this in an efficient manner. In some papers or documents, "linear times series" seems to refer to a time series that can be modeled as a linear AR (auto-regressive) model.   In other places, "linear time series" seems to refer to a time series with a linear trend.   When someone just drops "linear time series" out of the blue without any context, what do they mean usually? I am a graduate student of math right now but I was not able to get a topology subject in my undergrad... I just would like to know if you guys know the best one.. Solving linear congruence (modular inverse or fraction) via gcd Bezout equation Isn't finding the inverse of $a$, that is, $a'$ in $aa'\equiv1\pmod{m}$ equivalent to solving the diophantine equation $aa'-mb=1$, where the unknowns are $a'$ and $b$? I have seem some answers on this site (where the extended Euclidean Algorithm is mentioned mainly) as well as looked up some books but there is no mention of this. Am I going wrong somewhere or is this a correct method of finding modular inverses? Also can't we find the Bézout's coefficients by solving the corresponding diophantine equation instead of using the extended Euclidean Algorithm? Why is it called Area 51? According to : "We like the little aliens."  This seems well targeted to appeal to the Stack Overflow / Server Fault / Super User audience, but way off the mark if the goal is to "make the Internet a better place to get expert answers to your questions."    There are experts who aren't interested in or focused on technology oriented topics.  Little aliens are unlikely to be something that someone interested in organizing a site on gardening would gravitate too.  No, I'm not suggesting that no one interested in gardening would be bother to look at a site with little aliens, but won't it be likely that the sort of mass appeal to to a very broad cross section of the internet will be lacking? Placement of images in row using subfigure I want to put four figures in a single row. The code I am trying to use is taken from .  This puts three figures in a row. When I add a fourth one, I get three images in row and the last one appears in the second row. But I want all of them in one row. Here is my code.  \documentclass[12pt,twoside]{report}% Use this line for the print version of the thesis   \usepackage{graphicx} \usepackage{caption} \usepackage{subcaption} \begin{document}  \begin{figure}         \centering         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{gull}                 \caption{A gull}                 \label{fig:gull}         \end{subfigure}%           \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{gull}                 \caption{A gull2}                 \label{fig:gull2}         \end{subfigure}%          ~ %add desired spacing between images, e. g. ~, \quad, \qquad etc.           %(or a blank line to force the subfigure onto a new line)         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{tiger}                 \caption{A tiger}                 \label{fig:tiger}         \end{subfigure}         ~ %add desired spacing between images, e. g. ~, \quad, \qquad etc.           %(or a blank line to force the subfigure onto a new line)         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{mouse}                 \caption{A mouse}                 \label{fig:mouse}         \end{subfigure}         \caption{Pictures of animals}\label{fig:animals} \end{figure} \end{document}   As I have mentioned above, it works for three figures.  But I can not use it for four figures. What should I change?   What does  width=\textwidth mean?   I changed    \begin{subfigure}[b]{0.3\textwidth}   to  \begin{subfigure}[b]{0.2\textwidth}   but it didn't help.  Then, I changed     \includegraphics[width=\textwidth]{mouse}   to  \includegraphics[width=0.5\textwidth]{mouse}   Still no solution. Does the sum of reciprocals of primes converge? Is this series known to converge, and if so, what does it converge to (if known)?  Where $p_n$ is prime number $n$, and $p_1 = 2$,  $$\sum\limits_{n=1}^\infty \frac{1}{p_n}$$