latex | Python wrappers for calling LaTeX/building LaTeX documents

I'm trying to annotate a few figures I created in python. So, I'm generating an image containing the specified text (using PIL ImageDraw) and concatenating it with the image. Now, I want to include a math notation into the text. Is there a way to write text in latex math when creating the image of text? This answer suggests a work-around by using unicode text, but I would prefer writing the text in latex directly.

MWE:

So I'm preparing for a technical interview, and one of my practice questions is the Kth smallest number. I know that I can do a sort for O(n * log(n)) time and use a heap for O(n * log(k)). However I also know I can partition it (similar to quicksort) for an average case of O(n).

The actual calculated average time complexity should be:

I've double checked this math using WolframAlpha, and it agrees.

So I've coded my solution, and then I calculated the actual average time complexity on random data sets. For small values of n, it's pretty close. For example n=5 might give me an actual of around 6.2 when I expect around 5.7. This slightly more error is consistent.

This only gets worse as I increase the value of n. For example, for n=5000, I get around 15,000 for my actual average time complexity, when it should be slightly less than 10,000.

So basically, my question is where are these extra iterations coming from? Is my code wrong, or is it my math? My code is below:

I am Arch GNU/Linux user who usually manages almost every package with pacman; I manage TeX and LaTeX-related things with tlmgr. I installed tlmgr from source.

I am writing paper. I would like to use bibliography.

When I tried latexmk -pdflua main.ltx:

I just learned how to insert (a limited number of) LaTeX expressions into my plot titles with expression(). How can I generate plots containing LaTeX in their titles using a loop? For example, say I have:

I ran into this error while trying to compile my overleaf latex;

"Server Error Sorry, something went wrong and your project could not be compiled. Please try again in a few moments".

Your response will be helpful. Thanks

Can LaTeX escapes for accents be used in Rd files? I tried the standard \'e and many variants (\'{e}, {\'e}, \\'e, \\'{e}, {\\'e}, etc.), but none is rendered as an accented character in the PDF or HTML output.

I want my References section (i.e. \references{}) to be rendered with accented characters, but I do not want to type non-ASCII characters in my Rd files. Is there good/recommended practice? Should I simply replace non-ASCII characters with their ASCII equivalents (é → e, ø → o)?

To be clear, I know it is possible to type accented characters (e.g., é) directly in UTF-8-encoded files, but I would prefer to keep ASCII-encoded files.

This question is not about

• how to type special/accented letters in LaTeX
• how to use UTF-8 in LaTeX
• accents/special characters in R Markdown

or variants.

Package structure

I am currently having issue with the implementation of the Metropolis-Hastings algorithm.

I am trying to use the algorithm to calculate integrals of the form

In using this algorithm, we can obtain a long chain of configurations ( in this case, each configuration is just a single numbers) such that in the tail-end of the chain the probability of having a particular configuration follows (or rather tends to) a gaussian distribution.

My code seems to be messing up with obtaining the said gaussian distributions. There is a strange dependence on the transition probablity (the probablity of picking a new candidate configuration depending on the previous configuration in the chain). However, if this transition probability is symmetric, there should be no dependence on this function at all (it only affects speed at which phase space [space of potential configurations] is explored and how quickly the chain converges to the desired distribution)!

In my case I am using a normal distribution transition function (which satisfies the need to be symmetric), with width d. For each d I use I do indeed get a gaussian distribution however the standard deviation, sigma, depends on my choice of d. The resulting gaussian should have a sigma of roughly 0.701 but I find that the value I actually get depends on the parameter d, when it shouldn't.

I am not sure where the error in this code is, any help would be greatly appreciated!

I'm working on some heavy algorithm, and now I'm trying to make it multithreaded. It has a loop with 2 nested loops:

Let's say I have the following rmd: