Ciro Santilli @cirosantilli 37

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Muhammad Iqbal Updated 2025-07-16

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Numerical method to solve a partial differential equation Updated 2025-07-16

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The finite element method is one of the most common ways to solve PDEs in practice.

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Pipa Updated 2025-07-16

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Unicellular organism Updated 2025-07-16

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Semidirect product Updated 2025-07-16

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As per en.wikipedia.org/w/index.php?title=Semidirect_product&oldid=1040813965#Properties, unlike the Direct product, the semidirect product of two goups is neither unique, nor does it always exist, and there is no known algorithmic way way to tell if one exists or not.

This is because reaching the "output" of the semidirect produt of two groups requires extra non-obvious information that might not exist. This is because the semi-direct product is based on the product of group subsets. So you start with two small and completely independent groups, and it is not obvious how to join them up, i.e. how to define the group operation of the product group that is compatible with that of the two smaller input groups. Contrast this with the Direct product, where the composition is simple: just use the group operation of each group on either side.

Product of group subsets

So in other words, it is not a function like the Direct product. The semidiret product is therefore more like a property of three groups.

The semidirect product is more general than the direct product of groups when thinking about the group extension problem, because with the direct product of groups, both subgroups of the larger group are necessarily also normal (trivial projection group homomorphism on either side), while for the semidirect product, only one of them does.

Conversely, en.wikipedia.org/w/index.php?title=Semidirect_product&oldid=1040813965 explains that if

G = N ⋊ H

, and besides the implied requirement that N is normal, H is also normal, then

G = N \times H

Smallest example:

D_{6} = C_{3} ⋊ C_{2}

where

D

is a dihedral group and

C

are cyclic groups.

C_{3}

(the rotation) is a normal subgroup of

D_{6}

, but

C_{2}

(the flip) is not.

Note that with the Direct product instead we get

C_{6}

and not

D_{6}

, i.e.

C_{3} \times C_{2} = C_{6}

as per the direct product of two cyclic groups of coprime order is another cyclic group.

TODO:

why does one of the groups have to be normal in the definition?
what is the smallest example of a non-simple group that is neither a direct nor a semi-direct product of any two other groups?

Bibliography: math.stackexchange.com/questions/1726939/is-this-intuition-for-the-semidirect-product-of-groups-correct

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Perfect information Updated 2025-07-16

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SHA-2 Updated 2025-07-16

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Virus classification Updated 2025-07-16

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Group isomorphism Updated 2025-07-16

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French university Updated 2025-07-16

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GNU make Updated 2025-07-16

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Indian politician Updated 2025-07-16

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Uranium-238 Updated 2025-07-16

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John Rowell Updated 2025-07-16

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Linear algebra Updated 2025-07-16

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Polyhedron Updated 2025-07-16

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Ernest Hemingway Updated 2025-07-16

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List of compilers Updated 2025-07-16

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How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it / Overview of the experiment Updated 2025-07-16

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For those that know biology and just want to do the thing, see: Section "Protocols used".

The PuntSeq team uses an Oxford Nanopore MinION DNA sequencer made by Oxford Nanopore Technologies to sequence the 16S region of bacterial DNA, which is about 1500 nucleotides long.

This kind of "decode everything from the sample to see what species are present approach" is called "metagenomics".

This is how the MinION looks like: Figure 1. "Oxford Nanopore MinION top".

The 16S region codes for one of the RNA pieces that makes the bacterial ribosome.

Before sequencing the DNA, we will do a PCR with primers that fit just before and just after the 16S DNA, in well conserved regions expected to be present in all bacteria.

The PCR replicates only the DNA region between our two selected primers a gazillion times so that only those regions will actually get picked up by the sequencing step in practice.

Eukaryotes also have an analogous ribosome part, the 18S region, but the PCR primers are selected for targets around the 16S region which are only present in prokaryotes.

This way, we amplify only the 16S region of bacteria, excluding other parts of bacterial genome, and excluding eukaryotes entirely.

Despite coding such a fundamental piece of RNA, there is still surprisingly variability in the 16S region across different bacteria, and it is those differences will allow us to identify which bacteria are present in the river.

The variability exists because certain base pairs are not fundamental for the function of the 16S region. This variability happens mostly on RNA loops as opposed to stems, i.e. parts of the RNA that don't base pair with other RNA in the RNA secondary structure as shown at: Code 1. "RNA stem-loop structure".

                A-U
               /   \
A-U-C-G-A-U-C-G     C
| | | | | | | |     |
U-A-G-C-U-A-G-C     G
               \   /
                U-A
|             ||    |
+-------------++----+
    stem        loop

Code 1.

RNA stem-loop structure

This is how the 16S RNA secondary structure looks like in its full glory: Figure 5. "16S RNA secondary structure".

height=800 — Figure 5.
16S RNA secondary structure
. Source.

Since loops don't base pair, they are less crucial in the determination of the secondary structure of the RNA.

The variability is such that it is possible to identify individual species apart if full sequences are known with certainty.

With the experimental limitations of experiment however, we would only be able to obtain family or genus level breakdowns.

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Sandy Maguire Updated 2025-07-16

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Lots of similar ideologies to Ciro Santilli, love it:

sandymaguire.me/about/:
- he's an idealist
I might best be described somewhere between independent researcher and voluntarily-unemployed bum. At the ripe old age of 27 I decided to quit my highly-lucrative engineering job and decide to focus more on living than on grinding for the man. It's what you might call a work in progress.
sandymaguire.me/blog/reaching-climbing/: don't be a pussy
Last Friday was my final day at work. According to my facebook profile, I am now "happily retired." As of today, I don't plan to do another day of "traditional work" in my life. That's not to say that I'll be sitting idle playing tiddly winks. I want to build things, to dedicate my life to independent study, and to get really, really good with building communities. I don't have time for any of this "work" stuff that somehow pervades our entire culture, choking our inspiration and sapping our energy away from the things we'd rather be doing.
One is also reminded of Gwern Branwen. Sandy is also into self-improvement stuff, so even more like Gwern. This is a point Ciro diverges on. Ciro works actively on self-worsening.
he thinks university is useless:
- sandymaguire.me/blog/where-uni-fails/ Where University Fails (2018), mostly talking about backward design
- sandymaguire.me/blog/gatekept/ rejected from Imperial College PhD program due to grade being slightly too low for their stupid requirements, even though he had a referral already, and an amazing CV
he likes jazz: sandymaguire.me/blog/too-smart/

Other interesting points:

sandymaguire.me/blog/sandy-runback/ he changed his own name to Sandy because he didn't like it, he was born Alexander
algebradriven.design/ closed source books though, ouch. At least they seem to have been made with leanpub though, could be worse.

He's a Haskell person.

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