Butterfly diagram from cooley-tukey algorithm

I am trying to understand the logic of this algorithm so i can implement my own but i am not understanding this diagram i see appearing many times in a fair few articles on the topic, i am teaching myself so i don’t have a computer science degree to help. But i understand the general idea behind the algorithm.

But this butterfly diagram is confusing me.

enter image description here

How do you interpret this diagram from left to right mathematically speaking? It’s so confusing.. what are the arrows telling me to do in terms of math operations on the functions?

Need help designing ER Diagram

I am not a database engineer, I am just getting started with designing data models.

A User registers to my application. My application has Funds that are predefined with an InvestmentStrategy. A user deposits cash into their account Bankroll. A user invests from their Bankroll into a Fund or multiple. A fund buys into Investments. A User selects Picks to guide the InvestmentStrategy. The InvestmentStrategy uses historical Pick evidence by User to determine which Investments to make. Investments have Results, which pay Users based on performance. A User can leave a Fund. A User can withdraw from their Bankroll. A InvestmentStrategy can also pay percentage of profit to User.

This leads to a wide array of circular relationships. I am having a hard time drawing an ER diagram describing the entities and relationships above. Does anyone have examples or suggestions for how to create their model? Thanks!

Why does this finite state machine state transition diagram solution has more states than my solution?

I can’t figure out what is wrong with my solution and why does it differ from book’s solution. I think the only thing that matters is the previous state of A so that there should be two states, one for previous A=0 and one for previous A=1. Where am I mistaken? I would really appreciate any explanation.

this is the question

this is book's solution here

this is my solution

Is my use case UML diagram too complicated?

The user of my app has access to two tools within my app. Each tool is comprised of multiple tables that the user has to fill with information.
The app is more complex but that’s roughly what’s it’s about.
This is the UML Diagram that I have designed based on the app:
enter image description here I am wondering whether the use case diagram should be designed otherwise. Maybe, I should design the use case diagram for each tool independently. That way, it will be less cumbersome.
But, this will mean that each tool represents its own system. And I don’t know if from a UML viewpoint, that is the right thing to do.