From first principles by Ciro Santilli 35 Updated +Created
Quake (video game) by Ciro Santilli 35 Updated +Created
Krusader by Ciro Santilli 35 Updated +Created
The most powerful GUI file manager ever?? Infinite configurability??
Ciro Santilli wasted some time on it before he gave up on file managers altogether and started using only the CLI with a few aliases.
Exponential map (Lie theory) by Ciro Santilli 35 Updated +Created
Like everything else in Lie group theory, you should first look at the matrix version of this operation: the matrix exponential.
The exponential map links small transformations around the origin (infinitely small) back to larger finite transformations, and small transformations around the origin are something we can deal with a Lie algebra, so this map links the two worlds.
The idea is that we can decompose a finite transformation into infinitely arbitrarily small around the origin, and proceed just like the product definition of the exponential function.
The definition of the exponential map is simply the same as that of the regular exponential function as given at Taylor expansion definition of the exponential function, except that the argument can now be an operator instead of just a number.
Logarithm by Ciro Santilli 35 Updated +Created
Existence by Ciro Santilli 35 Updated +Created
Parallel postulate by Ciro Santilli 35 Updated +Created
Clausius entropy by Ciro Santilli 35 Updated +Created
If it ain't broke, don't fix it by Ciro Santilli 35 Updated +Created
Ohm by Ciro Santilli 35 Updated +Created
Sylvester's law of inertia by Ciro Santilli 35 Updated +Created
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:
A = Matrix([[2, sqrt(2)], [sqrt(2), 3]])
A.eigenvects()
and from the eigendecomposition of a real symmetric matrix we know that:
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.
Also, because is a diagonal matrix, and thus symmetric, it must be that:
What this does represent, is a general change of basis that maintains the matrix a symmetric matrix.
PDF by Ciro Santilli 35 Updated +Created
How to Fix a Drug Scandal (2020) by Ciro Santilli 35 Updated +Created
DNA profiling by Ciro Santilli 35 Updated +Created
De novo DNA synthesis by Ciro Santilli 35 Updated +Created
As of 2018, Ciro Santilli believes that this could be the next big thing in biology technology.
"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.
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
News coverage:
Video 1.
Nuclera eDNA enzymatic de novo DNA synthesis explanatory animation (2021)
Source. The video shows nicely how Nuclera's enzymatic DNA synthesis works:
DNA paternity testing by Ciro Santilli 35 Updated +Created
Eating by Ciro Santilli 35 Updated +Created
Database management system by Ciro Santilli 35 Updated +Created
A software that implements some database system, e.g. PostgreSQL or MySQL are two (widely extended) SQL implementations.
Relational database by Ciro Santilli 35 Updated +Created

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