Ciro Santilli @cirosantilli 37

Super-resolution means resolution beyond the diffraction limit.

First you shine a lot of light which saturates most fluorophores, leaving very few active.

They you can observe fluorophores firing one by one. Their exact position is a bit stochastic and beyond the diffraction limit, but so long as there aren't to many in close proximity, you can wait for it to fire a bunch of times, and the center of the Gaussian is the actual location.

From this we see that super-resolution microscopy is basically a space-time tradeoff: the more time we wait, the better spacial resolution we get. But we can't do it if things are moving too fast in the sample.

Tradeoff with cryoEM: you get to see things moving in live cell. Electron microscopy fully kills cells, so you have no chance of seeing anything that moves ever.

Caveats:

The set of all algebraic numbers forms a field.

This field contains all of the rational numbers, but it is a quadratically closed field.

Like the rationals, this field also has the same cardinality as the natural numbers, because we can specify and enumerate each of its members by a fixed number of integers from the polynomial equation that defines them. So it is a bit like the rationals, but we use potentially arbitrary numbers of integers to specify each number (polynomial coefficients + index of which root we are talking about) instead of just always two as for the rationals.

Each algebraic number also has a degree associated to it, i.e. the degree of the polynomial used to define it.

Materials paywalled: www.cs.ox.ac.uk/teaching/courses/2022-2023/algorithms/

One major advantage: eukaryotes can do phagocytosis due to their cytoskeleton.

Wikipedia mentions that it is completely analogous to Planck's law.

The school that believes only in the Pali Canon, i.e. the best school.

Subcase of symmetric multilinear map:

Requires the two inputs $x$ and $y$ to be in the same vector space of course.

The most important example is the dot product, which is also a positive definite symmetric bilinear form.

Funding rounds:

About their qubit: