What kind of hot pink eggs are these?
What is this agglomeration of pink cells I found attached to a stone?
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. Ramsey Number Inequality: $R(\underbrace{3,3,...,3,3}_{k+1}) \le (k+1)(R(\underbrace{3,3,...3}_k)-1)+2$ I want to prove that:  $$R(\underbrace{3,3,...,3,3}_{k+1}) \le (k+1)(R(\underbrace{3,3,...3}_k)-1)+2$$  where R is a Ramsey number. In the LHS, there are $k+1$ $3$'s, and in the RHS, there are $k$ $3's$. I really have no clue how to start this proof. Any help is appreciated! How do I use itertools.groupby()? I haven't been able to find an understandable explanation of how to actually use Python's itertools.groupby() function.  What I'm trying to do is this:  Take a list - in this case, the children of an objectified lxml element Divide it into groups based on some criteria Then later iterate over each of these groups separately.  I've reviewed , but I've had trouble trying to apply them beyond a simple list of numbers. So, how do I use of itertools.groupby()?  Is there another technique I should be using?  Pointers to good &quot;prerequisite&quot; reading would also be appreciated. Find a plane that passes through a point and is perpendicular to 2 planes Find an equation of a plane that passes through $p(1,5,1)$ and is perpendicular to planes $2x+y-2z = 2$ and $x+3z=4$.  I basically need the 2 other points to make the vector and perform the cross product.  Since $ax+by+cz+d=0$ is the form of a plane. Can I obtain the points as $(a,b,c)$ of the 2 planes given? Also, how can I set them up to obtain the points? Including Interaction Terms in Random Forest Suppose we have a response Y and predictors X1,....,Xn. If we were to try to fit Y via a linear model of X1,....,Xn, and it just so happened that the true relationship between Y and X1,...,Xn wasn't linear, we might be able to fix the model by transforming the X's somehow and then fitting the model. Moreover, if it just so happened that the X1,...,XN didn't affect y independent of the other features, we also might be able to improve the model by including interaction terms, x1*x3 or x1*x4*x7 or something of the like. So in the linear case, interaction terms might bring value by fixing non-linearity or independence violations between the response and the features.  However, Random Forests don't really make these assumptions. Is including interaction terms important when fitting a Random Forest? Or will just including the individual terms and choosing appropriate parameters allow Random Forests to capture these relationships? $\nabla U=0 \implies U=\mathrm{constant}$ only if $U$ is defined on a connected set? Monitor cell value and copy it to another cell How to emulate titletoc with tocloft I was using titletoc until I realized that it has some incompatibilities with hyperref. The thing is, that titletoc can do the same thing in a easier way, less one.  \titlecontents*{subsection}[5.4em] {\small} {\thecontentslabel~ } {} {} [.~\textbullet\ ] [.]   this part does the subsection as a paragraph (with section number and without page number). I have realized that the problem is the pseudo-code used by tocloft for the entries in the TOC  {\cftXfont {\cftXpresnum SNUM\cftXaftersnum\hfil} \cftXaftersnumb TITLE}% {\cftXleader}{\cftXpagefont PAGE}\cftXafterpnum\par   I mean, the last command \par make impossible to leave two subsection entries in the same textline. Any idea? Another interesting solution is with etoolbox, some examples with that package are awesome, but it's not on my hands.  This is a MWE:  \documentclass{book}  \usepackage{titletoc} \titlecontents*{subsection}[5.4em]{\small} {\thecontentslabel~ }{}{}[.~\textbullet\ ][.]  \begin{document}  \tableofcontents  \chapter{Test Chapter 1} \section{Test Section 1.1} \subsection{First Test Subsection} \subsection{Second Test Subsection} \subsection{Third Test Subsection} \subsection{Fourth Test Subsection} \section{Test Section 1.2} \subsection{First Test Subsection} \subsection{Second Test Subsection}  \chapter{Test Chapter 2} \section{Test Section 2.1} \subsection{First Test Subsection} \subsection{Second Test Subsection} \subsection{Third Test Subsection} \subsection{Fourth Test Subsection} \section{Test Section 2.2} \subsection{First Test Subsection} \subsection{Second Test Subsection}  \end{document} The limit of a sum $\sum_{k=1}^n \frac{n}{n^2+k^2}$ as $n\rightarrow\infty$ How to compute this limit:  $$\lim_{n\to\infty}\left(\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\cdots+\frac{n}{n^2+n^2}\right)$$  Please give me some hint. I have this:  If String.IsNullOrEmpty(editTransactionRow.pay_id.ToString()) = False Then     stTransactionPaymentID = editTransactionRow.pay_id 'Check for null value End If   Now, when editTransactionRow.pay_id is Null Visual Basic throws an exception. Is there something wrong with this code? How can a complete web page be saved and viewed on an Android device? There are situations I require to save a "complete" web page for offline reading. I can easily do that on Windows by saving the web page, but not on Android.  I am using Chrome on Android and I don't see a "save" option. Instead, I see "Save link" which, I believe, saves "only" the "pure HTML" version of a site of which the link leads to.  I have tried this but, when I view it in the HTML Viewer a lot of necessary CSS formatting and all the images were lost, which made the information misleading and incomplete respectively. (PS I thought I downloaded the complete page and the fault was that of the HTML Viewer for not rendering every thing, but I was wrong, as the desktop Chrome also displayed the "only HTML" version when I transferred those pages to my laptop through Bluetooth).  So, my question is: How can I download "a complete" web page on my Android smart-phone. It's OK if I can't view it on my smart-phone, but every thing should be in place when I view it on my laptop after transferring it. It is also OK if it is saved as a PDF file.  (PS I'm asking this as I use internet very often in my smartphone because my laptop is not connected to the internet. Also I want to transfer it to my laptop because I don't want to view those "important" pages on a small screen, it's inconvenient). What are homologous chromosomes? Where are some good places to find royalty free stock images? I'm always on the hunt for free stock images to use while I design, what are some good resources for images that are under a a royalty free or creative commons licence? Use induction to prove the following: $1! + 2! + .... + n! \le (n + 1)!$ I can always find that in some articles the production of higgs decay written as &quot;$\rm H\to {ZZ}^*\to 4l$&quot;, &quot;$\rm H\to ZZ\to 4l$&quot;, &quot;$\rm H\to Z\gamma^*\to\ldots$” What dose it mean when some particles with a superscript *? Such as “$\rm Z^*, W^*, \gamma^*, \ldots$&quot;. What’s the difference between them and &quot;$\rm Z, W, \gamma$&quot;? I have a Windows XP box (NTFS filesystem) on which I found a file named NUL. I have not been able to remove this file in any usual way. The file appears to be owned by Administrator in the SYSTEM group, unlike any other file in the same directory (the other files are owned by my user id).  How do I get rid of this file? Where did it come from? I want to merge two shape files in which one is of point geometry type and other is polygon type in order to get a single layer containing both points and polygon in a single map. I can't understand where the final keyword is really handy when it is used on method parameters.    If we exclude the usage of anonymous classes, readability and intent declaration then it seems almost worthless to me.   Enforcing that some data remains constant is not as strong as it seems.    If the parameter is a primitive then it will have no effect since the parameter is passed to the method as a value and changing it will have no effect outside the scope.  If we are passing a parameter by reference, then the reference itself is a local variable and if the reference is changed from within the method, that would not have any effect from outside of the method scope.    Consider the simple test example below. This test passes although the method changed the value of the reference given to it, it has no effect.  public void testNullify() {     Collection&lt;Integer&gt; c  = new ArrayList&lt;Integer&gt;();           nullify(c);     assertNotNull(c);            final Collection&lt;Integer&gt; c1 = c;     assertTrue(c1.equals(c));     change(c);     assertTrue(c1.equals(c)); }  private void change(Collection&lt;Integer&gt; c) {     c = new ArrayList&lt;Integer&gt;(); }  public void nullify(Collection&lt;?&gt; t) {     t = null; } How to calculate last four digits of $2^{2017}$? can u suggest me any short trick of solving these kind of problems. How to find last four digits of any number raised to some power ? A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.