flatter | Deep object graph to a plain flat properties

So, this is something I think I'm complicating far too much but it also has some of my other colleagues stumped as well.

I've got a set of areas represented by polygons and I've got a column in the dataframe holding their areas. The distribution of areas is heavily right skewed. Essentially I want to randomly sample them based upon a distribution of sampling probabilities that is inversely proportional to their area. Rescaling the values to between zero and one (using the {​​​​​​​​x-min(x)}​​​​​​​​/{​​​​​​​​max(x)-min(x)}​​​​​​​​ method) and subtracting them from 1 would seem to be the intuitive approach, but this would simply mean that the smallest are almost always the one sampled.

I'd like a flatter (but not uniform!) right-skewed distribution of sampling probabilities across the values, but I am unsure on how to do this while taking the area values into account. I don't think stratifying them is what I am looking for either as that would introduce arbitrary bounds on the probability allocations.

Reproducible code below with the item of interest (the vector of probabilities) given by prob_vector. That is, how to generate prob_vector given the above scenario and desired outcomes?

I have two lists foo and bar, where length(foo) > length(bar). I want to apply a function length(bar) times to each element of bar and store the output of each application in is own list and store all of the applications of the function to each element of bar in their own lists. This nested list output structure is important as I am passing it to functions that require nested lists. Examples of what I have and desired are in the minimal example.

While this works nicely with nested for-loops, I've been trying to accomplish this with purrr's map functions. I've managed to do this by creating (a) a list of length(bar) where each element is foo, (b) passing this new list and bar to an anonymous function in purrr::pmap(), and then (c) passing this to an anonymous function in purrr:map().

While this works, it seems very antithetical to the purpose of purrr:

• Instead of .x, .y, and ~ syntax, I'm defining anonymous functions.
• Instead of passing my raw lists (which vary in length), I'm converting one to a nested list to match the other's length. This can be memory-intensive, slow, etc.
• I'm working with nested lists rather than flatter lists/dataframes I then partition into my desired data structure.

Is there an alternative way of working with different-length lists in purrr than my aproach? How might I modify my code (minimal example below) to better-exploit the syntax of purrr? One idea (Handling vectors of different lengths in purrr) is to use cross() or some equivalent to generate a single object for passing to pmap(), but I'm not how how to then generate the nested list structure.

I'm trying to flatter an array of objects that can each contain children like the with typescript:

I was playing around with the seaborn library for data visualization and trying to display a standard normal distribution. The basics in this case look something like:

How to compare the slope of multiple regressions?

As you can see the slope is not comparable. The slope in graphic 3 is clearly flatter than graphic 1 but the slope value is much higher.

Or is there a better measure for the steepness of the line?

I have two meshes (call them A and B) which I am interacting within python using the open3d library (happy to use import trimesh or something else if it works better). Mesh A is a curved structure and mesh B approximates to a flatter surface.

I need to rotate the meshes so that the surface I am interested in is facing the camera. To identify the surfaces that I need I have written functions to turn the meshes into point clouds and create the best fit sphere for mesh A and a best-fit plane for mesh B. These work really well and match the objects nicely.

I need to rotate the meshes and have gotten stuck with how to perform the rotation.

The input data that I have:

for mesh A: centroid of mesh A coords and coords of its best fit sphere (+ its radius) - I want to rotate the mesh so that is perpendicular to the vector described by the above data?

for mesh B: centroid of mesh B coords and vector of the normal of the best fit plane - I want to rotate the mesh so that is perpendicular to the vector described by the above data

I have a numpy.ndarray data that looks like below and I want to flatten it out so that i can manipulate it. Please find my sample data below:

To make the header sticky when this responsive HTML5 template is resized to mobile phone dimensions.

I cannot seem to find the correct element to add the CSS position property to. No matter what DIV I add the 'sticky' class to, it just won't stay fixed to the top of the screen.

Desktop Mode Works Fine

Mobile Size Fails

I have tried to attach a class, like this...

I'm working on a Reagent App to manage seasons for a hotel-booking-site. The data is shown in a tabular view and is currently stored in an atom holding a nested map with season-ids as keys, like so: