I'm thinking of purchasing a photo on iStock to make a poster size print. I'm pretty familiar with resolution and how it works, but before forking out the money and ending up with a print that might not be how I want, I just want to see how much I can scale the image, which is now 5474 x 3649 px (18.25 x 12.16 in.) @ 300 dpi, before the quality shifts. I'd like to keep it as sharp as possible, but I did want to have either the height or width at least 30in. If I try to do that with this particular image will it noticeably ruin/distort the quality?
(This question is meant to be a resource to direct others to given that this is a common question.)  Given the task of creating an image that will be printed at a certain size, what pixel dimensions and resolution should I be setting my file at?
The glorified global variable - becomes a gloried global class. Some say breaking object-oriented design.  Give me scenarios, other than the good old logger where it makes sense to use the singleton. How to send an SMS in iOS 10 I have a file, which was encrypted with AES-128 in ECB mode. I know the format of the original file and know that all files in this format have the same headers. So, I have an encrypted block and the original block.  Can I get the encryption key, using this information? I am in 1.13 Pre-Release 7 trying to make a one command creation and I need an item with a specific name. The command I use is /give @p diamond_sword{display:{Name:"Sword of Power"}} and it gives my a diamond sword, but it doesn't have the name.   This is me running the command.   This is the command not working. Prove that every prime larger than $3$ gives a remainder of $1$ or $5$ if divided by $6$ Can we prove that every prime larger than $3$ gives a remainder of $1$ or $5$ if divided by $6$ and if so, which formulas can be used while proving? Removing columns in a SpatialPolygonsDataFrame in R? My spatial polygon data frame (SPDF) contains too many columns (variables) and I want to remove most of the columns entirely.   I know how to do this with a regular data frame in R, but I am unsure how to do this when dealing with object of class SpatialPolygonsDataFrame? Badge Notification Repeats For linear regression, we can check the diagnostic plots (residuals plots, Normal QQ plots, etc) to check if the assumptions of linear regression are violated.  For logistic regression, I am having trouble finding resources that explain how to diagnose the logistic regression model fit. Digging up some course notes for GLM, it simply states that checking the residuals is not helpful for performing diagnosis for a logistic regression fit.  Looking around the internet, there also seems to be various "diagnosis" procedures, such as checking the model deviance and performing chi-squared tests, but other sources state that this is inappropriate, and that you should perform a Hosmer-Lemeshow goodness of fit test. Then I find other sources that state that this test may be highly dependent on the actual groupings and cut-off values (may not be reliable).  So how should one diagnose the logistic regression fit? ] inside an optional argument I accidentally discovered () that a closing square bracket within an optional argument delimited by [ ] can cause problems.  Here is example code illustrating the issue:  \documentclass{article}   \begin{document}  \tableofcontents  \section[Square brackets ([ and ])]{Square brackets: [ and ]} % bad: the TOC now has "Square brackets ([ and", and the actual title is a mere ")".  Some text.  \section[{Square brackets ([ and ])}]{Square brackets: [ and ]} % good (works as originally intended)  Some text.  \end{document}   The text to be used as the optional (as well as the non-optional) argument contains a ], and this character is not supposed to function as the optional argument terminator but as a matching square bracket/parenthesis. Perhaps this is as it should be, but the question is how to best circumvent any potential problems. Enclosing this in a group works, but I don't know whether doing this has other side effects (perhaps not here in the case of \section but hopefully someone else has a better example of where grouping could lead to a problem). There is no (obvious) way other than writing [{ }] because [ and ] are not normally escaped. That [ and ] are normal characters and bear syntactic function (as optional argument delimiters) creates this potentially problematic situation.  Is simply enclosing the entire optional argument in a group ({ }) a good solution? Are there other/better ways? How to understand degrees of freedom? What's the best way to deal with hot/stuck pixels in long exposure night photographs? I discovered red/blue/white pixels on my night photographs tonight. Trying to confirm this, I took a black image with the lens on and indeed I saw a whole lot of them (I didn't count them but at least a good fifty on the whole picture).   I'm not exactly sure if they are hot pixels, stuck pixels or anything else.  I quickly gave a check to my last exported JPEG files (I get RAW out of the camera) and couldn't find anything. After a quick search, I've seen that Lightroom is caring about those pixels after RAW conversion.  I've read that, with Canon DSLRs, there is a software process that could take care of that directly on my camera. I don't know if I can use it without getting things even more messy.   My question is: Considering my crazy pixels are not visible on my pictures, should I get too emotional about them? My camera is under warranty but is it really worth it to return it to Canon? If it's only to receive it back 1 month later after Canon just used the very same menu to map out the pixels, it's a bit ridiculous. Could this be a sign that my camera has a bigger problem?  It seems related to shutter speed. When shooting a black image at 1/250s I get nothing. When shooting the same setup but 1s, I get a few of them. The more I increase the shutter speed, the more crazy pixels I get. Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$ I'm self studying from Category Theory in Context by Emily Riehl and have encountered the following question regarding slice categories:     Let $\text{C}$ be a category and $c$ be an object in $\text{C}$. Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$    The exercise appears in an chapter that introduces the notion of opposite categories and duality proofs.     My intuition of why the statement is true comes from the following observation:  Let $x,y$ be objects in $\mathbf{C}$ (or equivalently $\mathbf{C}^{\text{op}}$). Let $g^{\text{op}} : c \to y$ and $f^{\text{op}} : c \to x$ be objects in $c/(\mathbf{C}^{\text{op}})$. By the definition of slice category, there exists a morphism $h^{\text{op}} : y \to x$ in $\mathbf{C}^{\text{op}}$ such that the diagram below commutes:  $\hskip2in$   Now the 'corresponding diagram' in the opposite category $(c/(\mathbf{C}^{\text{op}}))^{\text{op}}$ would be:  $\hskip2in$    which, as I understand it, would also be commutative. Now, to me, this indicates:   that the objects in $(c/(\mathbf{C}^{\text{op}}))^{\text{op}}$ are the same as the objects in $\mathbf{C}/c$, namely, a morphism in $\mathbf{C}$ from an object $z \in \mathbf{C}$ to $c$. the commutativity of the seconds diagram describes morphisms $h$ in both $\mathbf{C}/c$ and $(c/(\mathbf{C}^{\text{op}}))^{\text{op}}$ if you reverse the arrows again you return to the same diagram. This makes me think you could construct a map between morphisms by first making a map from $ \mathbf{C}/c \to (\mathbf{C}/c)^{\text{op}} ( \cong c/(\mathbf{C}^{\text{op}}) )$ by $h \mapsto h^{op}$     Now, what I am really looking for is a way to structure a proof. I feel like I have some intuition but am very unsure of how to write it down in a concise way. I am new to category theory so I'm still very much learning how to construct these types of proofs using duality; I feel like what I have written is maybe overkill but I'm trying to be as explicit as possible to make sure I understand everything.  In particular, I don't know how I would get a concrete correspondence between morphisms in the two categories that respects associativity of composition etc.  Any help or pointers would be appreciated! Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$ Find the following limit: $$\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$$   Well I tried to do the $\exp\left(\frac{ \ln\frac{\sin x}{x}}{x^2}\right)$ then apply LHR but I seem to get to endless dervivations...   There's got to be a more simple approach. How to show that the commutator subgroup is a normal subgroup It is suggested as an exercise in Serge Lang's book "Algebra" to show that the commutator subgroup $G^c$ of a group $G$ is a normal subgroup.   I'd like to do that but I am afraid I need help,   I think the first thing I need to figure out is how a general element in the commutator subgroup looks like, so that I can check that the defining condition for normality is satisfied.  That is, supposing for a moment that a general element in $G^c$ is denoted by $g$, I need to show that $aga^{-1} \in G^c,$ for all $a \in G$.  But here I get stuck, first because I am unsure how to write a general element in $G^c$ - a simple product in $G^c$ is of the form $xyx^{-1}y^{-1}aba^{-1}b^{-1}$ where $a,b \in G$. I cannot see a way to simplify this - I am sure there is one, but somehow I am blind today.  The second thing then is, even if one tries out the conjugation of a simple element like $xyx^{-1}y^{-1}$ in $G^c$, again not simplification offers itself easily I think .. what am I missing ?  An alternative would be to find a homomorphism of $G$ whose kernel is precisely $G^c$ - here I tried to think of this as a map $G \times G \to G$ but whatever I cook up is not a homomorphism.  Thanks for your hints !! Story about building up speed leading to increased quality of life How would one go about proving that the rationals are not the countable intersection of open sets? I'm trying to connect 32 I²C "root of trust"  devices.    I'm thinking about a good way that does that, I mean what kind of communication should I use? A digital multiplexer that selects a device? but based on what? switching on the VDD source? but that needs reinitialization of the device and that takes time. Show sub reasons in close review queue Currently close vote review queue shows the top level close reason in the header, but some close reasons, for instance, off topic have very different sub reasons. For instance, "demonstrate minimal understanding" is different from "This question belongs on a different site in the stack exchange network".  It would be nice if sub close reasons were also shown. Calculating a spherical polygon centroid UITableViewCell content overlaps delete button when in editing mode in iOS7