Ciro Santilli @cirosantilli  40

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.

The leading no-royalties options as of 2020.

China has been a major RISC-V potential user in the late 2010s, since the country is trying to increase its semiconductor industry independence, especially given economic sanctions imposed by the USA.

E.g. a result of this, the RISC-V Foundation moved its legal headquarters to Switzerland in 2019 to try and overcome some of the sanctions.

Owned/developed by Google as of 2020.

Early on jumpstarted from several acquisitions, notably Keyhole Inc. and Where 2 Technologies.

It is rare to find a project with such a ridiculously high importance over funding ratio.

E.g., as of 2020, their help login help.openstreetmap.org/ shows MyOpenID as an option, which was discontinued in 2014, and not Google OAuth.

They do still seem to have a bit more activity than gis.stackexchange.com/questions/tagged/openstreetmap on Stack Exchange.

Complaints:

All of this is a shame, because they do have some incredible data that you cannot find easily on other maps because people just edited it up.

Has some of the best map data available for the United Kingdom, but their data appears to be proprietary?

The first Bitcoin exchange. Coded as a hack, and they didn't manage to fix the hacks as the site evolved in a major way, which led to massive hacks.

Their creation is clearly visible on the archive history of bitcoin.org: web.archive.org/web/20100701000000*/bitcoin.org which started having massively more archives since Mt. Gox opened.

Size: 1-2 micrometers long and about 0.25 micrometer in diameter, so: 2 * 0.5 * 0.5 * 10e-18 and thus 0.5 micrometer square.

Reference strain: E. Coli K-12 MG1655.

Genome:

Synthesis project: www.sciencemag.org/news/2016/08/biologists-are-close-reinventing-genetic-code-life

Omics modeling: www.ncbi.nlm.nih.gov/pmc/articles/PMC5611438/ Tools for Genomic and Transcriptomic Analysis of Microbes at Single-Cell Level Zixi Chen, Lei Chen, Weiwen Zhang.

Bibliography:

Maybe the most famous one is Mycoplasma genitalium byt there are others, and notably with lower biosafety levels:

This is a good first concrete example of a Lie algebra. Shown at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" has an example.

We can use use the following parametrization of the special linear group on variables $x$, $y$ and $z$:

Every element with this parametrization has determinant 1:Furthermore, any element can be reached, because by independently settting $x$, $y$ and $z$, $M_{00}$, $M_{01}$ and $M_{10}$ can have any value, and once those three are set, $M_{11}$ is fixed by the determinant.

To find the elements of the Lie algebra, we evaluate the derivative on each parameter at 0:

Remembering that the Lie bracket of a matrix Lie group is really simple, we can then observe the following Lie bracket relations between them:

One key thing to note is that the specific matrices $M_x$, $M_y$ and $M_z$ are not really fundamental: we could easily have had different matrices if we had chosen any other parametrization of the group.

TODO confirm: however, no matter which parametrization we choose, the Lie bracket relations between the three elements would always be the same, since it is the number of elements, and the definition of the Lie bracket, that is truly fundamental.

Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" then calculates the exponential map of the vector $x{M}_x+y{M}_y+z{M}_z$ as:with:

TODO now the natural question is: can we cover the entire Lie group with this exponential? Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation" explains why not.

This makes it clear how the Lie bracket can be seen as a "measure of non-commutativity"

Because the Lie bracket has to be a bilinear map, all we need to do to specify it uniquely is to specify how it acts on every pair of some basis of the Lie algebra.

Then, together with the Baker-Campbell-Hausdorff formula and the Lie group-Lie algebra correspondence, this forms an exceptionally compact description of a Lie group.

The one parameter subgroup of a Lie group for a given element $M$ of its Lie algebra is a subgroup of $G$ given by:

Intuitively, $M$ is a direction, and $t$ is how far we move along a given direction. This intuition is especially vivid in for example in the case of the Lie algebra of $SO(3)$, the rotation group.

One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.

Example at: Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation".