Ciro Santilli @cirosantilli 40

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.

proteins also have a half-life, much like RNA. But it tends to be longer.

This is one of the first examples in most quantum field theory.

It usually does not involve any forces, just the interpretation of what the quantum field is.

www.youtube.com/watch?v=zv94slY6WqY&list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou&index=2 Quantization Of A Free Real Scalar Field by Dietterich Labs (2019)

There is no fundamental difference between them, a quantum algorithm is a quantum circuit, which can be seen as a super complicated quantum gate.

Perhaps the greats practical difference is that algorithms tend to be defined for an arbitrary number of N qubits, i.e. as a function for that each N produces a specific quantum circuit with N qubits solving the problem. Most named gates on the other hand have fixed small sizes.

TODO experimental discovery.

One major difference between the elliptic curve over a finite field or the elliptic curve over the rational numbers the elliptic curve over the real numbers is that not every possible $x$ generates a member of the curve.

This is because on the Equation "Definition of the elliptic curves" we see that given an $x$, we calculate $x^3+ax+b$, which always produces an element $y^2$.

But then we are not necessarily able to find an $y$ for the $y^2$, because not all fields are not quadratically closed fields.

For example: with $a=1$ and $b=1$, taking $x=1$ gives:and therefore there is no $y\in \mathbb{Q}$ that satisfies the equation. So $x=1$ is not on the curve if we consider this elliptic curve over the rational numbers.

That $x$ would also not belong to Elliptic curve over the finite field ${\mathbb{F}}_4$, because doing everything $\mathrm{mod}4$ we have:Therefore, there is no element $y\in {\mathbb{F}}_4$ such that $y\times y=2$ or $y\times y=3$, i.e. $2$ and $3$ don't have a multiplicative inverse.

For the real numbers, it would work however, because the real numbers are a quadratically closed field, and $\sqrt{3}\in \mathbb{R}$.

For this reason, it is not necessarily trivial to determine the number of elements of an elliptic curve.

Mentioned at: Video "Quantum Computing with Light by Quantum Light University of Sheffield (2015)" youtu.be/nyK-vhoOBpE?t=185.

Other examples include:

That example calculates and displays the final widths via JavaScript, making it easier to understand the calculations being done.

Answers: stackoverflow.com/questions/28473807/how-does-flex-grow0-get-interpreted/69995712#69995712

Bibliography:

This was the God OG physics journal of the early 20th century, before the Nazis fucked German science back to the Middle Ages!

Notable papers: