Ciro Santilli @cirosantilli 35

Under: graphviz.

Confusingly, in LaTeX:

Analogous to what the Euler-Lagrange equation is to Lagrangian mechanics, Hamilton's equations give the equations of motion from a given input Hamiltonian:So once you have the Hamiltonian, you can write down this system of partial differential equations which can then be numerically solved.

A series of systems usually derived from the International System of Units that are more convenient for certain applications.

Ciro Santilli appreciates this concept of "remembering the suffering of others" a lot due to Ciro Santilli's self perceived compassionate personality and Ciro Santilli's cheapness.

Basically: why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics?s.

This ISA basically completely dominated the smartphone market of the 2010s and beyond, but it started appearing in other areas as the end of Moore's law made it more economical logical for large companies to start developing their own semiconductor, e.g. Google custom silicon, Amazon custom silicon.

It is exciting to see ARM entering the server, desktop and supercomputer market circa 2020, beyond its dominant mobile position and roots.

Ciro Santilli likes to see the underdogs rise, and bite off dominant ones.

The excitement also applies to RISC-V possibly over ARM mobile market one day conversely however.

Basically, as long as were a huge company seeking to develop a CPU and able to control your own ecosystem independently of Windows' desktop domination (held by the need for backward compatibility with a billion end user programs), ARM would be a possibility on your mind.

As mentioned at Section "Plancherel theorem", some people call this part of Plancherel theorem, while others say it is just a corollary.

This is an important fact in quantum mechanics, since it is because of this that it makes sense to talk about position and momentum space as two dual representations of the wave function that contain the exact same amount of information.

The easy and less generic integral. The harder one is the Lebesgue integral.

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: