The main interest of this theorem is in classifying the indefinite orthogonal groups, which in turn is fundamental because the Lorentz group is an indefinite orthogonal groups, see: all indefinite orthogonal groups of matrices of equal metric signature are isomorphic.
It also tells us that a change of basis does not the alter the metric signature of a bilinear form, see matrix congruence can be seen as the change of basis of a bilinear form.
The theorem states that the number of 0, 1 and -1 in the metric signature is the same for two symmetric matrices that are congruent matrices.
For example, consider:
The eigenvalues of are and , and the associated eigenvectors are:symPy code:and from the eigendecomposition of a real symmetric matrix we know that:
A = Matrix([[2, sqrt(2)], [sqrt(2), 3]])
A.eigenvects()Now, instead of , we could use , where is an arbitrary diagonal matrix of type:With this, would reach a new matrix :Therefore, with this congruence, we are able to multiply the eigenvalues of by any positive number and . Since we are multiplying by two arbitrary positive numbers, we cannot change the signs of the original eigenvalues, and so the metric signature is maintained, but respecting that any value can be reached.
Note that the matrix congruence relation looks a bit like the eigendecomposition of a matrix:but note that does not have to contain eigenvalues, unlike the eigendecomposition of a matrix. This is because here is not fixed to having eigenvectors in its columns.
But because the matrix is symmetric however, we could always choose to actually diagonalize as mentioned at eigendecomposition of a real symmetric matrix. Therefore, the metric signature can be seen directly from eigenvalues.
What this does represent, is a general change of basis that maintains the matrix a symmetric matrix.
"De novo" means "starting from scratch", that is: you type the desired sequence into a computer, and the synthesize it.
The "de novo" part is important, because it distinguishes this from the already well solved problem of duplicating DNA from an existing DNA template, which is what all our cells do daily, and which can already be done very efficiently in vitro with polymerase chain reaction.
Many startup companies are attempting to create more efficient de novo synthesis methods:
Notably, the dream of most of those companies is to have a machine that sits on a lab bench, which synthesises whatever you want.
TODO current de novo synthesis costs/time to delivery after ordering a custom sequence.
The initial main applications are likely going to be:but the real pipe dream is building and bootstraping entire artificial chromosomes
- polymerase chain reaction primers (determine which region will be amplified
- creating a custom sequence to be inserted in a plasmid, i.e. artificial gene synthesis
News coverage:
- 2023-03 twitter.com/sethbannon/status/1633848116154880001
AnsaBio created the world's longest DNA oligo produced using de novo synthesis! 1,005 bases! 99.9% stepwise yield
- 2020-10-05 www.nature.com/articles/s41587-020-0695-9 "Enzymatic DNA synthesis enters new phase"
Nuclera eDNA enzymatic de novo DNA synthesis explanatory animation (2021)
Source. The video shows nicely how Nuclera's enzymatic DNA synthesis works:- they provide blocked nucleotides of a single type
- add them with the enzyme. They use a werid DNA polymerase called terminal deoxynucleotidyl transferase that adds a base at a time to a single stranded DNA strand rather than copying from a template
- wash everything
- do deblocking reaction
- and then repeat until done
A software that implements some database system, e.g. PostgreSQL or MySQL are two (widely extended) SQL implementations.
Marc Verdiell is a French electrical engineer born in 1963 or 1964[ref] and best known for being the creator and host of the CuriousMarc YouTube channel where he does mind blowing repairs and reverse engineering of vintage computers and other electronic equipment.
Marc made $58.4m from the sale of LightLogic, an optoelectronics company he founded, to Intel in April 2001. This was just after the dot-com crash, but Intel apparently still correctly believed that the networking and the Internet would continue to grow and was investing in the area. His associate Frank Shum sued claiming he should be credited for some of the inventions sold but lost and Marc got it all.[ref][ref][ref]. Marc was then almost immediately appointed an Intel fellow at the extremelly early age of 37, and then stayed for a few years at Intel until 2006 according to his LinkedIn.[ref][ref]
Marc's LinkedIn profile: www.linkedin.com/in/marc-verdiell-9742795/
Marc's full name is actualy Jean-Marc Verdiell, but Ciro Santilli remembers there was one YouTube video where he mentions he gave up on "Jean" partly because anglophones would murder its pronounciation all the time.
ppubs.uspto.gov/dirsearch-public/print/downloadPdf/20160274316 also suggests he may have a seldom used middle name "André", though that would be unusual in French custom
Marc's PhD thesis is listed at: theses.fr/1990PA112048 and it is entitled:which is translated into English as:but the full text is not available online.
Mise en phase de reseaux de lasers a semi-conducteur
Phase locking of semiconductor laser arrays
Profile of Marc Verdiell by Gizmodo (2018)
Source. youtu.be/tJ2-kkhghD4?t=74 gives his house's location Atherton, California, part of Silicon Valley. youtu.be/tJ2-kkhghD4?t=279 shows his amazing garden a bit more.
youtu.be/ZgAreiFXhJk?t=253 lists some famous people who live there. It's like a micro heaven.
And a person who makes open educational content like Marc, truly deserves it.
radaris.com/p/Jean-Marc/Verdiell/ and many other sources list the exact address as:On Google Maps: maps.app.goo.gl/LM2iN9fz6YBteggp8
48 Linden Ave, Atherton, CA 94027
www.realtyhop.com/property-records/search/hoang-oanh-verdiell mentions that the property was bought on 2013-11-07 for $8,650,000 and lists other properties they've bought and sold and possibly inhabited:
- 2002-03-21: sold 4159 El Camino Way, Palo Alto, CA Unit B
- 2001-06-18: bought 763 Florales Dr, Palo Alto, CA
www.youtube.com/watch?v=gEcnjh0lSsY give a tour of the house given by the real state agent Ken DeLeon. The dude has a very suspicious Wikipedia page: en.wikipedia.org/wiki/Ken_DeLeon He is mentioend e.g. at www.forbes.com/sites/erincarlyle/2013/12/20/ken-deleon-top-silicon-valley-sales-agent-why-chinese-buyers-love-palo-alto/ as selling a lot to the Chinese.
A quick look on Google Maps show that that area is full of some incredible mansions. They managed to keep the entire place green and every house has a pool. Wikipedia comments web.archive.org/web/20220906010554/https://www.forbes.com/home-improvement/features/most-expensive-zip-codes-us/:and Forbes confirms it for 2022: web.archive.org/web/20220906010554/https://www.forbes.com/home-improvement/features/most-expensive-zip-codes-us/, by far on top.
Atherton is known for its wealth; in 1990 and 2019, Atherton was ranked as having the highest per capita income among U.S. towns with a population between 2,500 and 9,999, and it is regularly ranked as the most expensive ZIP Code in the United States [(94027)]. The town has very restricting zoning, only permitting one single-family home per acre and no sidewalks. The inhabitants have strongly opposed proposals to permit more housing construction
Starting in 2016, Marc appears to be have had a small court battle with some building contractors led by the Yip family, Cynthia Yip and Wai Yip, as Javelin Construction Inc. for selling them "a brand-new but defective home for $9m. The Verdiells then spent $5.3m further renewing it."[ref]. After endless back-and-forth, the Verdiell's won $1.2m in 2024.[ref]
Soyuz Clock Part 4: How accurate is it? by CuriousMarc (2020)
Source. The timestamp youtu.be/HKsjwT53yXw?t=580 mentions that his wife is called "Lori", and that she escaped the Soviet Union, and two of her brothers went to jail in the escape process.
The name is kind of hard to hear, but Google resolves it for us e.g. she and Marc were donnors to the Computer History Museum d1yx3ys82bpsa0.cloudfront.net/core/core-2019.pdf
2.5.0 manual prebuilt download install on Ubuntu 20.04 just worked. Launch directly from unzip without install. Play with examples under
install/ExamplesTheir docs are a reasonable way to learn Csound: cabbageaudio.com/docs/introduction/
Generate public private key, test encrypt and test decrypt:
# Create your pubkey.
gpg --gen-key
gpg --armor --output pubkey.gpg --export <myemail>
# Encrypt using someone's pubkey.
gpg --import pubkey2.gpg
echo 'hello world' > hello.txt
gpg --output hello.txt.gpg --encrypt --recipient <other-email> hello.txt
# Double check it is not plaintext in the encrypted message.
grep hello hello.txt.gpg
# Decrypt.
gpg --output hello.decrypt.txt --decrypt --recipient <myemail> hello.txt.gpg
diff -u hello.decrypt.txt hello.txt There are unlisted articles, also show them or only show them.