Narayana Pandita, also known as Narayana Pandit or simply Narayana, was a notable Indian mathematician and scholar who lived during the 14th century. He is best known for his contributions to combinatorics and number theory. One of his most famous works is the "Ganita Kaumudi," which is a comprehensive treatise on arithmetic, geometry, and combinatorial mathematics.

Alternative to the Lorentz gauge, but less used in general as it is not as nice for relativity invariance.

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

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

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.

With all this ready, we opened the Nanopore flow cell, which is the 500 dollar consumable piece that goes in the sequencer.

We then had to pipette the final golden Eppendorf into the flow cell. My anxiety levels were going through the roof: Figure 4. "Oxford nanopore MinION flow cell pipette loading.".

At this point bio people start telling lab horror stories of expensive solutions being spilled and people having to recover them from fridge walls, or of how people threw away golden Eppendorfs and had to pick them out of trash bins with hundreds of others looking exactly the same etc. (but also how some discoveries were made like this). This reminded Ciro of: youtu.be/89UNPdNtOoE?t=919 Alfred Maddock's plutonium spill horror story.

Luckily this time, it worked out!

We then just had to connect the MinION to the computer, and wait for 2 days.

During this time, the DNA would be sucked through the pores.

As can be seen from Video 1. "Oxford Nanopore MinION software channels pannel on Mac." the software tells us which pores are still working.

Pores go bad sooner or later randomly, until there are none left, at which point we can stop the process and throw the flow cell away.

48 hours was expected to be a reasonable time until all pores went bad, and so we called it a day, and waited for an email from the PuntSeq team telling us how things went.

We reached a yield of 16 billion base pairs out of the 30Gbp nominal maximum, which the bio people said was not bad.

The Suruga Trough is a deep-sea trench located off the coast of Shizuoka Prefecture in Japan. It is part of the Nankai Trough system and runs parallel to the Izu Peninsula. The trench reaches depths of approximately 2,500 meters (about 8,200 feet) and is primarily significant for geological and geophysical studies.

"Radio 1's Live Lounge – Volume 2" is a compilation album released by BBC Radio 1, featuring various artists performing live covers and original songs. This series showcases popular musicians and bands as they put their unique spin on notable tracks, often blending genres and styles. The Live Lounge sessions are well-known for their intimate setting and the creative reinterpretations of songs.

Pincherle polynomials are a class of polynomials that arise in the context of functional analysis and operator theory, particularly in the study of linear differential and difference equations. Named after the Italian mathematician Antonio Pincherle, these polynomials can be defined through certain recurrence relations or orthogonality properties. In a more specific context, Pincherle polynomials can be used to express solutions to certain classes of problems involving linear transformations or series expansions.

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Walther von Dyck (1856–1934) was a notable German mathematician known for his contributions to various areas in mathematics, including algebra, geometry, and especially for his work in number theory and the theory of forms. He studied and worked on topics such as algebraic integers and their properties. Von Dyck is also known for his role in the development of modern algebra, and he made significant contributions to the understanding of group theory and its applications.

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Subprime lending refers to the practice of extending loans to individuals with poor credit histories or limited creditworthiness. These borrowers typically have credit scores below the thresholds considered "prime," which is generally around 620 and above. As a result of their higher perceived risk, subprime loans often come with higher interest rates and less favorable terms compared to prime loans. Subprime lending is most commonly associated with mortgages, auto loans, and personal loans.

The number 836 is an integer that follows 835 and precedes 837. It can be broken down in various ways, including: - **In terms of its digits**: It consists of three digits—8, 3, and 6. - **In mathematical terms**: It is an even number, as it ends in 6. It can also be factored into its prime components: \(836 = 2^2 \times 11 \times 19\).

Firefox for Android is a web browser developed by Mozilla specifically for Android devices. It is designed to provide a fast, secure, and customizable browsing experience on smartphones and tablets. Key features of Firefox for Android include: 1. **Privacy and Security**: Firefox includes features such as tracking protection and private browsing mode, which help users maintain their privacy while surfing the web. 2. **Speed**: The browser is optimized for performance, allowing for quick page loading and smooth navigation.

An optical mouse is a type of computer mouse that uses light to detect movement relative to a surface. Unlike traditional mice that use a mechanical ball to track movement, optical mice use an LED (light-emitting diode) or a laser to illuminate the surface beneath them and a sensor to detect the reflected light. This allows for more precise tracking and eliminates issues that can arise with dirt and debris that might affect the functioning of a mechanical mouse.