This was THE craze thing in Brazil before Pokemon, it was shown from 1994 to 1997. In particular the collectible action figures! It was possibly more popular in Brazil than e.g. in the US: www.quora.com/Why-was-Saint-Seiya-so-popular-in-Brazil

The thing as quite violent, rated for 14-year olds, but no one gave a fuck, 7 yo Ciro was happily watching it. We protect children too much.

That series also had quite a religious feel to it (as obviously suggested by the series English name itself). It must also have been a great motivator to getting young kids into astronomy!

Ciro's favorite character was definitely Andromeda Shun. He was smart and thoughtful, and had the coolest most complex weapon: his chain whips. He's also a bit effeminate, with his pink clothing and a gentle way. Perhaps that is the reason for adult Ciro's mild fascination with the Andromeda Galaxy.

The English name is horrendous... the Portuguese/French name is so much better: Knights of the Zodiac! Saying this in English just reminded Ciro Santilli of the Zodiac Killer. But nevermind.

RSA vs Diffie-Hellman key exchange are the dominant public-key cryptography systems as of 2020, so it is natural to ask how they compare:

As its name indicates, Diffie-Hellman key exchange is a key exchange algorithm. TODO verify: this means that in order to transmit a message, both parties must first send data to one another to reach a shared secret key. For RSA on the other hand, you can just take the public key of the other party and send encrypted data to them, the receiver does not need to send you any data at any point.

Basically the same as classical limit, but more for quantum mechanics.

There's a tiny little crosshair that you can drag around to set the center of rotation.

And there's a button to make that crosshair snap: inkscape.org/forums/questions/can-a-pivotingtransfrom-crosshair-be-moved-and-made-to-snap-to-a-node-or-a-grid-point/#c14432

Quantum superposition is really weird because it is fundamentally different than "either definite state but I don't know which", because the superposition state leads to different measurements than the non-superposition state.

Examples:

Sequencing the DNA tells us what the organism can do. Sequencing the RNA tells us what the organism is actually doing at a given point in time. The problem is not killing the cell while doing that. Is it possible to just take a chunk of the cell to sequence without killing it maybe?

A Baidu Baike page: baike.baidu.hk/item/層層水瀾/12386243 mentions that the score was published in 1970 by Tao Yimo (陶一陌) in a eponymous score book.

Boooooring.

The $U(1)$ unitary group is one very over-generalized way of looking at it :-)

These are also required for test tube replication.

They seem to be doing hardware acceleration for post-quantum cryptography algorithm.

One has to feel bad for them as they likely threw out entire chip designs over NIST Post-Quantum Cryptography Standardization algorithm breakeges.

This is the order in which you would want to transverse to read the chapters of a book.

Like breadth-first search, this also has the property of visiting parents before any children.

There are infinitely many prime k-tuples for every admissible tuple.

Generalization of the Twin prime conjecture.

As of 2023, there was no specific admissible tuple for which it had been proven that there infinite of, only bounds of type:But these do not specify which specific tuple, e.g. Yitang Zhang's theorem.

Given a bunch of points in $n$ dimensions, PCA maps those points to a new $p$ dimensional space with $p\le n$.

$p$ is a hyperparameter, $p=1$ and $p=2$ are common choices when doing dataset exploration, as they can be easily visualized on a planar plot.

The mapping is done by projecting all points to a $p$ dimensional hyperplane. PCA is an algorithm for choosing this hyperplane and the coordinate system within this hyperplane.

The hyperplane choice is done as follows:

www.sartorius.com/en/knowledge/science-snippets/what-is-principal-component-analysis-pca-and-how-it-is-used-507186 provides an OK-ish example with a concrete context. In there, each point is a country, and the input data is the consumption of different kinds of foods per year, e.g.:so in this example, we would have input points in 4D.

The question is then: we want to be able to identify the country by what they eat.

Suppose that every country consumes the same amount of flour every year. Then, that number doesn't tell us much about which country each point represents (has the least variance), and the first PCA axes would basically never point anywhere near that direction.

Another cool thing is that PCA seems to automatically account for linear dependencies in the data, so it skips selecting highly correlated axes multiple times. For example, suppose that dry codfish and olive oil consumption are very high in Portugal and Spain, but very low in Germany and Poland. Therefore, the variation is very high in those two parameters, and contains a lot of information.

However, suppose that dry codfish consumption is also directly proportional to olive oil consumption. Because of this, it would be kind of wasteful if we selected:since the information about codfish already tells us the olive oil. PCA apparently recognizes this, and instead picks the first axis at a 45 degree angle to both dry codfish and olive oil, and then moves on to something else for the second axis.

We can see that much like the rest of machine learning, PCA can be seen as a form of compression.