Trouble understanding what a natural transformation is
What intuitive notion is formalized by "natural transformation" in category theory?
How can I run an external program from C and parse its output? I've got a utility that outputs a list of files required by a game.  How can I run that utility within a C program and grab its output so I can act on it within the same program? UPDATE: Good call on the lack of information.  The utility spits out a series of strings, and this is supposed to be portable across Mac/Windows/Linux.  Please note, I'm looking for a programmatic way to execute the utility and retain its output (which goes to stdout). How to get straight quotation marks? How do I get straight quotation marks, i.e., " and ' in TeX?  (No, \verb changes the font and this is unacceptable.)  [Edit]  I forgot to mention that I’m using XeLaTeX, and fontspec is a necessity.  The first two proposed answers did work, without fontspec. I was loading an image resource with the following code and it works fine from my dev environment (netbeans) but threw an exception as soon as it ran from the desktop.  new ImageIcon(Images.class.getResource("images/highlighter24.gif"));   I traced it down to my file having different case than in the code.  Fine, my bad, but why the inconsistent behavior?  Gremlins?  Note: I'm running on windows before you ask. So far, I didn't have the chance to use either of these services. Before starting, I would like to hear your opinions. What are the advantages and disadvantages? Why should I choose one over the other? I am mainly interested in the technical side, but I would also love to hear comments also regarding the plans and prices. I've discovered a rather weird behaviour of PdfLaTeX. In this example  \documentclass{article} \usepackage[breaklinks]{hyperref} \begin{document} \url{http://www.emarketer.com/blog/index.php/quick-stat-smartphone-users-account-38-mobile-phone-users/} \end{document}   PdfLaTeX won't break the URL and create a too long line. However, if I replace \url with \href like this:  \documentclass{article} \usepackage{hyperref} \begin{document} \href{http://www.emarketer.com/blog/index.php/quick-stat-smartphone-users-account-38-mobile-phone-users/}{http://www.emarketer.com/blog/index.php/quick-stat-smartphone-users-account-38-mobile-phone-users/} \end{document}   I get the line broken, but the font of the link is not right any more of course (normal instead of texttt). Why doesn't URL break the line at dashes and what could I do to get a nicely typeset line-broken link? What can I do to increase passive HF RFID read range? I am working on a prototype, one function of which is to detect whether an object is "in range" by a few cm. Right now I'm just using an Arduino and a cheap  that operates at 13.56 MHz:    I've successfully gotten it to detect the tag, but only at a distance of about 3-4 cm when the tag is oriented parallel to the antenna.  According to my  , the HF band allows read ranges of between 10 cm and 1 m for passive tags, depending on factors like antenna size, tag size and orientation, and transceiver power.  I realize this inexpensive reader is not up to task as-is, but I'm interested in building something that achieves read ranges of 15-20 cm.  Some criteria:   No need to read multiple tags; only whether one tag is in range or not. No need to write to the tag. Cannot use an active tag.   I'm not experienced with RFID reader construction (yet) but am interested in knowing what I should pursue.  Here are some things I've considered:   Ditch the embedded antenna on the cheap RFID reader and construct my own, larger antenna. I'd need to see if the onboard  is up to the task of providing additional power. Look for a different IC around which to build a reader from scratch. Find a ready-made solution instead of trying to build one (more cost-effective?). Use something other than RFID for simple proximity detection.   I am experienced with microcontrollers and basic electronics, and have made audio and lighting projects, but this is a first with RFID. Since I don't need to read multiple tags, which RFID is suitable for, I've considered maybe some sort of magnet and hall-effect sensor, but the range does not seem adequate. I considered using an ultrasonic proximity detector, but the application calls for detecting the tagged object while ignoring untagged ones (ultrasonic would produce false positives on untagged objects). I've considered some sort of reflective surface placed on the object, and detecting reflected light, but the object orientation is not reliable enough to maintain alignment.  So, in a nutshell, What modifications can I make to my existing reader, or what alternate technology should I pursue to achieve 15-20 cm detection of a passively tagged object?  I plan on connecting whatever proximity detector is used to a microcontroller using SPI. How to extract and install .deb without the command dpkg? I am running Debian jessie stable in order to understand how the .deb package interacts with the system. What is the correct way to extract and install a packge_name.deb without the command dpkg? is there a way to find suitable ratio for matches to controls (using "ratio" in Matchit package in R or other programs) I am using matchit package in R to find a control set for my treated units and I am testing the model with different ratio to get suitable control set. Is there a way to find suitable ratio and I will use that to find my control set. What are the subcategories of ordered sets / groups? Books on Number Theory for Layman I have a very large dataset and about 5% random values are missing. These variables are correlated with each other. The following example R dataset is just a toy example with dummy correlated data.  set.seed(123)  # matrix of X variable  xmat &lt;- matrix(sample(-1:1, 2000000, replace = TRUE), ncol = 10000) colnames(xmat) &lt;- paste ("M", 1:10000, sep ="") rownames(xmat) &lt;- paste("sample", 1:200, sep = "") #M variables are correlated   N &lt;- 2000000*0.05 # 5% random missing values  inds &lt;- round ( runif(N, 1, length(xmat)) ) xmat[inds] &lt;- NA  &gt; xmat[1:10,1:10]          M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 sample1  -1 -1  1 NA  0 -1  1 -1  0  -1 sample2   1  1 -1  1  0  0  1 -1 -1   1 sample3   0  0  1 -1 -1 -1  0 -1 -1  -1 sample4   1  0  0 -1 -1  1  1  0  1   1 sample5  NA  0  0 -1 -1  1  0 NA  1  NA sample6  -1  1  0  1  1  0  1  1 -1  -1 sample7  NA  0  1 -1  0  1 -1  0  1  NA sample8   1 -1 -1  1  0 -1 -1  1 -1   0 sample9   0 -1  0 -1  1 -1  1 NA  0   1 sample10  0 -1  1  0  1  0  0  1 NA   0   Is there a (best) way to impute missing values in this situation? Is the Random Forest algorithm helpful? Any working solution in R would be much appreciated.  Edits:  (1) Missing values are randomly distributed among the variables and samples.As number of variables is very large (here in the example - 10000), while the number of samples is small here in the above dummy example it is about 200. So when we look at any sample over all the variables (10000), there is high chances that there will be missing value at some variable - due to large number of variables. So just deleting the sample is not option.   (2) The variable can be treated both as quantitative or qualitative (binary) in the process of imputing. The only judgement is how well we can predict it (accuracy). So predictions like 0.98 instead of 1 might be acceptable rather 0 vs 1 or -1 vs 1. I might need to tradeoff between computing time and accuracy.   (3)  The issue I have thinking how overfitting can affect the results as the number of variables are large compared to number of samples.   (4) As the total quantity of missing values is about 5% and is random (not concentrated in any variables or samples as precaution was taken to remove the variables or samples that have very high missing values)   (5) Making data complete for analysis is first objective and accuracy is secondary. So not too sensitive to accuracy. Presheaf which is not a sheaf -- holomorphic functions which admit a holomorphic square root I'm thinking about a problem in Ravi Vakil's algebraic geometry notes  (Exercise 3.2B) and I'm having trouble with the second part of the exercise as my understanding of complex analysis is quite rudimentary.   If to every open set $U\subset \mathbb{C}$ we associate the ring of holomorphic functions which admit a holomorphic square root, this defines a presheaf on $\mathbb{C}$ (I can see this).   Apparently however this is not a sheaf -- supposedly it fails to satisfy the gluing property.   To prove this, we need to take an open cover $\{U_i\}$ of some open $U\subseteq \mathbb{C}$, a holomorphic function $f_i:U_i\to \mathbb{C}$ for each $i$ which has a holomorphic square root (i.e. there exists a holomorphic function $g_i$ for each $i$ such that $f_i(z)=g_i(z)^2$ for all $z\in U_i$), which all agree nicely on the intersections of the various open sets, but such that it is impossible to find a holomorphic function $f:U\to \mathbb{C}$ with a holomorphic function which restricts to $f_i$ on each $U_i$.   Any help would be great -- my problem is in showing that such a function cannot exist. How align 2 adjacent divs horizontally WITHOUT float? C++11: defining function on std::array I want LaTeX not to give warnings for overfull hboxes up to some maximum of say 2 pts. How to achieve this? How to split strings into text and number? How to show that $f$ is differentiable at $x=0.$ Im trying to have the bibliography defined for my document using BibTeX and the natbib citation management package. Styles such as unsrtnat give me the references in order of appearance in text. However, I have a problem that I cannot get around. Basically if a reference is supposed to look like:     Tyson J.P. Dikstra M. Holmes F.M.R. Theoretical Analysis on Effect of   Anomalous Low Friction. International journal of Placticity,   34(3-4):413, 1997.   after typesetting it appears as :     Dikstra M. Holmes F.M.R. Tyson J.P. Theoretical Analysis on Effect of   Anomalous Low Friction. International journal of Placticity,   34(3-4):413, 1997.   In other words, it puts the first author in the last place. Is there any method of getting around this?  The entry as it appears in the .bib file (refs.bib) is:  @ARTICLE{Tyson1997, author={Tyson, J.P., Dikstra, M., Holmes, F.M.R.}, title={Theoretical Analysis on Effect of Anomalous Low Friction.}, journal={International journal of Plasticity}, year={1997}, volume={34}, number={3-4}, pages={413}, document_type={Article} }   An excerpt from the tex file:  \usepackage[round,comma]{natbib} \begin{document}  As an alternative method of analysis, \citet{Tyson1997} ...  \bibliographystyle{unsrtnat}  \bibliography{refs}  \end{document} It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our sampling and CI-computation procedures  many times, 95% of thusly computed CIs would contain the population mean. It also seems to be the consensus that this definition does not permit one to conclude from a single 95%CI that there is a 95% chance that the mean falls somewhere within the CI. However, I don't understand how the former doesn't imply the latter insofar as, having imagined many CIs 95% of which contain the population mean, shouldn't our uncertainty (with regards to whether our actually-computed CI contains the population mean or not) force us to use the base-rate of the imagined cases (95%) as our estimate of the probability that our actual case contains the CI?   I've seen posts argue along the lines of "the actually-computed CI either contains the population mean or it doesn't, so its probability is either 1 or 0", but this seems to imply a strange definition of probability that is dependent on unknown states (i.e. a friend flips fair coin, hides the result, and I am disallowed from saying there is a 50% chance that it's heads).  Surely I'm wrong, but I don't see where my logic has gone awry... Can the definite article be omitted when referring to a person qualified by a noun?