Ciro Santilli @cirosantilli 35

A multilinear form with a domain that looks like:where $V\ast$ is the dual space.

Because a tensor is a multilinear form, it can be fully specified by how it act on all combinations of basis sets, which can be done in terms of components. We refer to each component as:where we remember that the raised indices refer dual vector.

Some examples:

Explain it properly bibliography:

Conveyor belt 2D top down mining like Factorio, but with more emphasis on tower defense/real-time strategy, PvP looks a lot like StarCraft or Age of Empires.

As of pre alpha 135, the most annoying thing is that you can't easily start a campaign scenario from fresh, if you lose you have to start from wave 1 but with everything already half built as you left it. This gives you a huge advantage...

It is also annoying that you have to manually rebuild everything that was destroyed afer each attack, unless you have some unit that you can only unlock later on...

mindustry-unofficial.fandom.com/wiki/Future_Content#New_Google_Play_Listing suggests freemium features being considered, but they are mostly minor or plaform specific. There seems to be no server list by default however, making the Steam multiplayer freemium valuable.

www.youtube.com/watch?v=o5ThSECaAwA suggests code drop is used.

It is a bit annoying that you have to unlock the tech tree little by little in campaign, but it does serve as a reasonable introduction to the general order of development. Games with progression state are boring, except when there is permadeath. But custom play scenarios have everything unlocked immediately, much better.

It is very cool that you can copy chunks of buildings as macros, and save them for later.

The game runs very well it feels like.

The logic blocks are particularly interesting, and allow you to program a block yourself.

Great overview of the earlier history of unit standardization.

Gives particular emphasis to the invention of gauge blocks.

Poet warriors monkeys? Or Code peasants (码农) according to the Chinese.

Ciro Santilli claims to be one of them.

Much like a pianist plays his piano, a software engineer plays his computer.

This section groups conjectures that are famous, solved or unsolved.

They are usually conjectures that have a strong intuitive reasoning, but took a very long time to prove, despite great efforts.

The list: en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics

This technique has managed to determine protein 3D structures for proteins that people were not able to crystallize for X-ray crystallography.

It is said however that cryoEM is even fiddlier than X-ray crystallography, so it is mostly attempted if crystallization attempts fail.

By looking at Figure 1. "A cryoEM image", you can easily understand the basics of cryoEM.

We just put a gazillion copies of our molecule of interest in a solution, and then image all of them in the frozen water.

Each one of them appears in the image in a random rotated view, so given enough of those point of view images, we can deduce the entire 3D structure of the molecule.

Ciro Santilli once watched a talk by Richard Henderson about cryoEM circa 2020, where he mentioned that he witnessed some students in the 1980's going to Germany, and coming into contact with early cryoEM. And when they came back, they just told their principal investigator: "I'm going to drop my PhD theme and focus exclusively on cryoEM". That's how hot the cryo thing was! So cool.

Elliptic curve point addition is the group operation of an elliptic curve group, i.e. it is a function that takes two points of an elliptic curve as input, and returns a third point of the elliptic curve as its output, while obeying the group axioms.

The operation is defined e.g. at en.wikipedia.org/w/index.php?title=Elliptic_curve_point_multiplication&oldid=1168754060#Point_operations. For example, consider the most common case for two different points different. If the two points are given in coordinates:then the addition is defined in the general case as:with some slightly different definitions for point doubling $P+P$ and the identity point.

This definition relies only on operations that we know how to do on arbitrary fields:and it therefore works for elliptic curves defined over any field.

Just remember that:means:and that $y^{-1}$ always exists because it is the inverse element, which is guaranteed to exist for multiplication due to the group axioms it obeys.

The group function is usually called elliptic curve point addition, and repeated addition as done for DHKE is called elliptic curve point multiplication.

The BBC 1979-1982 adaptations of John Le Carré's novels are the best miniseries ever made:They are the most realistic depiction of spycraft ever made.

Some honorable mentions:

Bibliography:

Too many fun skit videos for Ciro Santilli's taste, but does have some serious derivations in quantum electrodynamics.