Nature
This is a review.
Neural networks
Boltzmann brain paradox
We would like to argue that this is not the case. Suppose we do not look at the whole box at once, but only at a piece of the box. Then, at a certain moment, suppose we discover a certain amount of order. In this little piece, white and black are separate. What should we deduce about the condition in places where we have not yet looked? If we really believe that the order arose from complete disorder by a fluctuation, we must surely take the most likely fluctuation which could produce it, and the most likely condition is not that the rest of it has also become disentangled! Therefore, from the hypothesis that the world is a fluctuation, all of the predictions are that if we look at a part of the world we have never seen before, we will find it mixed up, and not like the piece we just looked at. If our order were due to a fluctuation, we would not expect order anywhere but where we have just noticed it.
-- Richard Philips Feynman, quoted by Sean Carroll, Discover Magazine, Richard Feynman on Boltzmann Brains
What about biological neurons and y = σ(W * x + b)y=σ(W∗x+b)? There’s nothing particularly special about this formula; it’s just a simple and flexible example of a highly-parameterised non-linear function. In fact, it’s probably the worst such function in most cases. A single neural net layer can, in principle, classify cat pictures, but only by the relatively uninteresting trick of acting as a lookup table. It’s guaranteed to work! – but the small print warns that you may need more parameters than there are atoms in the universe. To actually make it work you need to encode problem structure in the model – which is where it starts to look a lot more like traditional programming.
-- On Differentiable Programming
A Beginner's Guide to Attention Mechanisms and Memory Networks
Can Neural Networks dream? Compare
Calculus for the Practical Man - see Feynman's notebook of calculus.
Neural nets and the Game of Life
You have a grid of cells, black cells are considered dead, white cells are considered alive, and there are a few rules for updating the grid which are inspired by biological processes. For instance, if a dead cell has exactly three live cells in its 3×3 neighbourhood then it's born.
-- https://danielrapp.github.io/cnn-gol/
A CNN can be trained to learn rules of games, like the Conway's Game of Life.
The first thing to do is define a function that takes a game board as input and returns the next state. Luckily there are plenty of implementations available online
-- https://kylewbanks.com/blog/conways-game-of-life-convolutional-neural-network-keras
Physics
What is a functional?
Newton's studies of nature
Newton felt that just as the writings of ancient philosophers, scholars, and Biblical figures contained within them unknown sacred wisdom, the same was true of their architecture. He believed that these men had hidden their knowledge in a complex code of symbolic and mathematical language that, when deciphered, would reveal an unknown knowledge of how nature works.
-- Wikipedia, https://en.wikipedia.org/wiki/Isaac_Newton's_occult_studies#"The_Key"_aka_Newton's_Clavis
Mathematics
Group theory is the study of symmetry. Objects in nature (math, physics, chemistry, etc.) have beautiful symmetries and group theory is the algebraic language we use to unlock that beauty.
-- The Art of Problem Solving, AoPS Online
Mathematical conundrums
What is the title of this book?
Master thesis
System Architecture
Examples:
Information science
"There are two hard things in computer science: cache invalidation, naming things, and off-by-one errors."
Algorytm Dekkera – pierwszy algorytm poprawnie rozwiązujący problem wzajemnego wykluczania się równolegle działających procesów. Tylko jeden z nich może w danej chwili wykonywać ich wspólną sekcję krytyczną.
Modeling and validation of concurrent systems
Coloured Petri Nets: Modelling and Validation of Concurrent Systems (2009)
An exercise example about Petri nets and server load is shown in the image below.