For Fractional quantum Hall effect for $\nu =1/m$.

This was so hot (no pun intended) and reproducible that the prize was awarded one year after discovery. Quite rare in those days already.

E.g. in humans the adenine nucleotide translocator is present in chromosome 4, not in mtDNA.

These have almost certainly been transferred to nuclear DNA in the course of evolution.

This isn't completely surprising, since when mitochondria die, their DNA is kind of left in the cell, so it is not hard to imagine how genes end up getting uptaken by the nucleus. This is suggested at Power, Sex, Suicide by Nick Lane (2006) page 196.

A limiting factor appears to be that you can't just past those genes in the nucleus, further mutations are necessary for mitochondrial protein import to work, apparenty some kind of tagging with extra amino acids.

However, you likely don't want to remove all genes from the mitochondria because mitochondria have DNA because they need to be controlled individually.

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.

To Brian Josephson for the prediction of the Josephson effect.

The key initial quantum electrodynamics experiments:

Nuclear magnetic resonance work:

Early electron diffraction experiment from 1927 that drastically confirmed the matter wave hypothesis.

Discovery of:

To Ernest Lawrence for the cyclotron.