Ciro Santilli @cirosantilli 37

This model can work well when there is a set of commonly used libraries that some developers often use together, but such that there isn't enough maintenance work for each one individually.

So what people do is to create a group that maintains all those projects, to try and get enough money to survive from the contributions done primarily for each one individually.

Examples:

The most important ones are:

Because a Git commit can have more than 1 parent due to merge commits when you do:

It can even have more than 2, there's no limit. Although that is not so common (with good reason, 2 is already one too many): softwareengineering.stackexchange.com/questions/314215/can-a-git-commit-have-more-than-2-parents/377903#377903

As mentioned by Craig Venter in 100 Greatest Discoveries by the Discovery Channel (2004-2005), the main outcomes of the project were:

Important predecessors:

For super-resolution microscopy.

This could have been a Nobel Prize in Physics as well!

TODO how to calculate

Since DNA is the centerpiece of life, Ciro Santilli is extremely excited about DNA-related technologies, see also: molecular biology technologies.

Since a matrix $M$ can be seen as a linear map $f_M(\vec{x})$, the product of two matrices $MN$ can be seen as the composition of two linear maps:One cool thing about linear functions is that we can easily pre-calculate this product only once to obtain a new matrix, and so we don't have to do both multiplications separately each time.

2022 page: www.cs.ox.ac.uk/teaching/courses/qsoft/ Half of the problems are Jupyter Notebooks, not bad.

Like Quantum Processes and Computation course of the University of Oxford, also ZX-calculus-heavy.

Kind of extends the complex numbers.

Some facts that make them stand out:

Solution $Z$ for given $X$ and $Y$ of:where $e$ is the exponential map.

If we consider just real number, $Z=X+Y$, but when X and Y are non-commutative, things are not so simple.

Furthermore, TODO confirm it is possible that a solution does not exist at all if $X$ and $Y$ aren't sufficiently small.

This formula is likely the basis for the Lie group-Lie algebra correspondence. With it, we express the actual group operation in terms of the Lie algebra operations.

Notably, remember that a algebra over a field is just a vector space with one extra product operation defined.

Vector spaces are simple because all vector spaces of the same dimension on a given field are isomorphic, so besides the dimension, once we define a Lie bracket, we also define the corresponding Lie group.

Since a group is basically defined by what the group operation does to two arbitrary elements, once we have that defined via the Baker-Campbell-Hausdorff formula, we are basically done defining the group in terms of the algebra.