dmm

dmm, 4 months ago to science

This paper describes the predatory bacterium Vampirococcus lugosii, which preys on members of the bacterial species of the genus Halochromatium [1].

This thing is incredible. For example: Vampirococcus lugosii has a severely reduced genome, something like 1.3 Mbp, and lacks the genes which code for many of the standard biosynthetic metabolic pathways (e.g. phospholipid synthesis, amino acid synthesis, and nucleotide synthesis). Yet it is somehow still alive.

How does this work?

One mechanism that Vampirococcus uses is to get these raw materials from its prey. An example of this are the nucleotides that Vampirococcus lugosii gets by chopping up the DNA that it sucks out of its prey. And amazingly, Vampirococcus lugosii uses a CRISPR-Cas system and various restriction enzymes to accomplish this. See the image for a cartoon of this system.

Predatory microbes.

Crazy.

---

Description of “Candidatus Vampirococcus lugosii”]

Lugosii after Bela Lugosi (1882–1956), who played the role of the vampire in the iconic 1931’s film “Dracula”. Epibiotic bacterium that preys on anoxygenic photosynthetic gammaproteobacterial species of the genus Halochromatium. Non-flagellated, small flat rounded cells (500–600 nm diameter and 200–250 nm height) that form piles of up to 10 cells attached to the surface of the host. Gram-positive cell wall structure. Complete genome sequence, GenBank/EMBL/DDBJ accession number PRJNA678638.

#biology #vampirococcuslugosii

References

[1] "Reductive evolution and unique infection and feeding mode in the CPR predatory bacterium Vampirococcus lugosii", https://www.nature.com/articles/s41467-021-22762-4

dmm, 2 months ago to nature

Weighing between 0.05 and 0.07 ounces with a head-to-body length of 1.14 to 1.29 inches and a wingspan of 5.1 to 5.7 inches, the bumblebee bat (aka Kitti’s hog-nosed bat) is the world's smallest mammal.

https://en.wikipedia.org/wiki/Kitti's_hog-nosed_bat

#nature #bats #bumblebeebat #biology

The bumblebee bat (aka Kitti’s hog-nosed bat)

dmm, 10 months ago to math

This is kind of cool: the Cistercian numerals are a forgotten number system developed by the Cistercian monastic order in the early thirteenth century [1,2].

Interestingly, Cistercian numerals are much more compact than Arabic or Roman numerals; with a single character you could write any integer from 1 to 9999.

#math #numbersystems

References

[1] "Cistercian numerals", https://en.wikipedia.org/wiki/Cistercian_numerals

[2] "The Forgotten Number System", https://www.youtube.com/watch?v=9p55Qgt7Ciw

dmm, 7 months ago to math

This is pretty amazing:

In 1801 the great German mathematician Carl Friedrich Gauss made the following conjecture [2,3]:

The ring of integers for a quadratic imaginary field
K = Q(√-d) is principal only for a finite number of d,
where d ∈ {1, 2, 3, 7, 11, 19, 43, 67, 163} .

Said another way, Gauss conjectured that the nine numbers in the sequence {1, 2, 3, 7, 11, 19, 43, 67, 163} are the only numbers who's negative square root can be adjoined to the integers to produce a ring with unique factorization [4].

So how did exactly did Gauss come up with the amazing conjecture that there were nine numbers (and just these nine numbers) that could be adjoined to ℤ to produce a unique factorization ring? The answer involves Gauss' work on the determinants of binary quadratic forms. There is quite a bit of commentary on this around the net; see [5] for example.

Gauss was unable to prove this conjecture; that would have to wait until 1952 when amateur mathematician Kurt Heegner proved the conjecture (up to a few minor flaws) [6]. Today these numbers are known as Heegner numbers [7].

A few of my notes here: https://davidmeyer.github.io/qc/galois_theory.pdf.
As always, questions/comments/corrections/* greatly appreciated.

#math #maths #gauss #heegnernumber #uniquefactorizationring

References

[1] "Carl Friedrich Gauss", https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

[2] "Disquisitiones Arithmeticae", https://en.wikipedia.org/wiki/Disquisitiones_Arithmeticae

[3] "A conjecture which implies the theorem of Gauss-Heegner-Stark-Baker", https://www.jstor.org/stable/43678652

[4] "Unique Factorization", https://mathworld.wolfram.com/UniqueFactorization.html

[5] "How did Gauss conjecture there were nine Heegner numbers?", https://math.stackexchange.com/questions/3138747/how-did-gauss-conjecture-there-were-nine-heegner-numbers

(1/2)

dmm, 5 months ago to physics

#onthisday in 1915: Albert Einstein submitted a paper to the journal "Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin" that would fundamentally alter our understanding of the universe [1]. The four page paper contained what became known as the Einstein field equations, which relate the geometry of spacetime to the distribution of matter within it [2].

Einstein's field equations were presented in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor) [3].

#einstein #generalrelativity #einsteinfieldequations #physics #maths #maths

[Image credit: https://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/echo/einstein/sitzungsberichte/6E3MAXK4/index.meta]

References

[1] "Die Feldgleichungen der Gravitation", https://einsteinpapers.press.princeton.edu/vol6-doc/273

[2] "Einstein field equations", https://en.wikipedia.org/wiki/Einstein_field_equations

3] "Einstein tensor", https://en.wikipedia.org/wiki/Einstein_tensor

dmm, 5 months ago to math

Did you know that the roots of a cubic polynomial can be visualized using an equilateral triangle?

In this incredibly cool animation from Freya Holmér (@acegikmo):

🔵 the vertices of the triangle map to the roots
🔴 the incenter is the inflection point
🟢 the incircle boundaries are the local minima/maxima

#math #maths #mathematics #cuberooots #cubicpolynomial

video/mp4

dmm, 5 months ago to random

Born #onthisday 208 years ago, Ada Lovelace wrote the world’s first computer program (which calculated Bernoulli numbers) and worked with Charles Babbage on the Analytical engine [1,2,3].

She was also the only legitimate child of poet Lord Byron and Lady Byron [4].

#adalovelace #analyticalengine

References

[1] "Ada Lovelace’s skills with language, music and needlepoint contributed to her pioneering work in computing", https://theconversation.com/ada-lovelaces-skills-with...

[2] "Charles Babbage", https://en.wikipedia.org/wiki/Charles_Babbage

[3] "ADA BYRON, COUNTESS OF LOVELACE", https://www.sdsc.edu/ScienceWomen/lovelace.html

[4] "Ada Lovelace", https://www.biography.com/scholar/ada-lovelace

dmm, 11 months ago to science

Évariste Galois was a French mathematical prodigy, political activist, and all-around trouble maker who, as a teenager, solved a 350-year-old problem regarding the condition necessary for a polynomial to be solvable by radicals. His work laid a foundation for a major branch of abstract algebra which today we call Galois theory.

#onthisday in 1832 Galois wrote to a friend accurately predicting that he would die in a duel taking place the next morning (legend has it that the duel was over a woman). In his final letter, Galois describes his work in mathematics and closed with, "Eventually there will be, I hope, some people who will find it profitable to decipher this mess."

Galois was only 20 years old at the time of his death.

#math #galois #galoistheory #abstractalgebra

References

[1] "Évariste Galois", https://mathshistory.st-andrews.ac.uk/Biographies/Galois

dmm, 15 days ago to random

Epic #onthisday in blues/music history:

Robert Johnson was born on this day in 1911 in Hazlehurst, Mississippi. His landmark recordings in 1936 and 1937 display a combination of singing, guitar skills, and songwriting talent that has influenced later generations of musicians. Although his recording career spanned only seven months, he is recognized as a master of the blues, particularly the Delta blues style, and as one of the most influential musicians of the 20th century.

If you are not familiar with Johnson's music, there is a nice playlist here: https://www.youtube.com/playlist?list=PLYPx-lRv1uyB8Rrw1GNrluTznSqO5-FBN

The Wikipedia also has a nice piece on Johnson: https://en.wikipedia.org/wiki/Robert_Johnson.

And of course, there's this: https://www.youtube.com/watch?v=ycNtYoxNuW8.

[Image credit: https://en.wikipedia.org/wiki/Robert_Johnson#/media/File:Robert_Johnson.png]

#robertjohnson #blues #deltablues

dmm, 1 year ago to science

Born #onthisday 117 years ago, Kurt Gödel was an Austrian mathematician and philosopher. Gödel discovered the “Incompleteness Theorem”, which essentially states that there will always be theorems in mathematics that are impossible to prove. Gödel''s discovery of the Incompleteness Theorems effectively drove a stake though the heart of Hilbert's Program [1] (or at least badly damaged it; see Hilbert's Second Problem [2]).

In 1949 Gödel demonstrated the existence of solutions to Einstein's field equations in General Relativity which involve "rotating universes" and featured closed timeline curves which allow for time travel to the past. Gödel's solutions are known as the Gödel metric and are an exact solution of the Einstein field equations [3].

Along with Aristotle, Alfred Tarski and Gottlob Frege, Gödel is considered to be one of the most significant logicians in history and had an immense effect upon scientific and philosophical thinking in the 20th century (and beyond).

Read more about Gödel's life and times here: https://mathshistory.st-andrews.ac.uk/Biographies/Godel/

#math #incompletenesstheorem

References

[1] "Hilbert’s Program", https://plato.stanford.edu/entries/hilbert-program/

[2] "Hilbert's second problem", https://en.wikipedia.org/wiki/Hilbert%27s_second_problem

[3] "THE GODEL SOLUTION TO THE EINSTEIN FIELD EQUATIONS", http://www.math.toronto.edu/~colliand/426/Papers/A_Monin.pdf

Incompleteness Theorem

dmm, 8 months ago to random

If you've never looked into the Antikythera Mechanism [1] (or even if you have) there is a nice overview article that contains quite a bit of interesting background information on the Mechanism here: https://greekreporter.com/2023/08/26/ancient-greece-antikythera-mechanism.

How the ancient Greeks conceived of, designed and built the Mechanism is really mind boggling and worth a look.

A few of my notes on how the Mechanism works (and in particular, how Derek J. de Solla Price’s [2] proposed Metonic cycle gear train works, as well as Michael Wright’s [3] scheme for turning the Mechanism's Metonic pointer, which appears to be the generally accepted architecture) are here: https://davidmeyer.github.io/astronomy/prices_metonic_gear_train.pdf. The LaTeX source is here: https://www.overleaf.com/read/ndpvkytkhmbv.

As is so frequently the case (or so it seems), these notes were a work in progress that has never quite been finished...In any event, questions/comments/corrections/* are greatly appreciated (as always).

References

[1] "An Ancient Greek Astronomical Calculation Machine Reveals New Secrets", https://www.scientificamerican.com/article/an-ancient-greek-astronomical-calculation-machine-reveals-new-secrets

[2] "Derek J. de Solla Price", https://en.wikipedia.org/wiki/Derek_J._de_Solla_Price

[3] "Michael T. Wright", https://en.wikipedia.org/wiki/Michael_T._Wright

How the ancient Greeks conceived of, designed and built the Mechanism is really mind boggling and worth a look.
How the ancient Greeks conceived of, designed and built the Mechanism is really mind boggling and worth a look.

dmm, 9 months ago to science

I love this picture (from [1]). It shows just how much of a latecomer adaptive immunity really is. Adaptive immunity is only a couple of hundred million years old; plants, invertebrates and fungi (and really most other organisms) survive just fine without adaptive immune systems.

The use of combinatorial diversity to make all kinds of randomly generated antigen receptors from our couple of hundred antibody genes is really spectacular.

BTW, these Mayo Clinic videos are really informative.

#biology #immunesystem #adaptiveImmunity

References

[1] "2015 B Cell Biology and T Follicular Helper Cells – The Fundamentals", https://www.youtube.com/watch?v=tuITLpoWdXU

dmm, 5 months ago to machinelearning

This is a nice tutorial if you are interested in how and why overfitting (etc) happens, how/why regularization helps to alleviate overfitting, ...

"The Theory Behind Overfitting, Cross Validation, Regularization, Bagging, and Boosting: Tutorial", Benyamin Ghojogh, Mark Crowley

#machinelearning #overfitting

https://arxiv.org/abs/1905.12787

dmm, 29 days ago to space

M104 (aka Messier 104, NGC 4594, and the Sombrero Galaxy) is a fantastic spiral galaxy which is famous for its nearly edge-on profile featuring a broad ring of obscuring dust lanes. Seen here in silhouette against an extensive central bulge of stars, the swath of cosmic dust lends a broad brimmed hat-like appearance to the galaxy suggesting its more popular moniker, the Sombrero Galaxy.

This sharp view of the well-known galaxy was made from over 10 hours of Hubble Space Telescope image data, processed to bring out faint details often lost in the overwhelming glare of M104's bright central bulge. The Sombrero galaxy can be seen across the spectrum, and is host to a central supermassive black hole. About 50,000 light-years across and 28 million light-years away, M104 is one of the largest galaxies at the southern edge of the Virgo Galaxy Cluster. Still, the spiky foreground stars in this field of view lie well within our own Milky Way.

APOD: Messier 104 (2022 Apr 23)
Image Credit: NASA, ESA, Hubble Legacy Archive;
Processing & Copyright: Ignacio Diaz Bobillo
https://apod.nasa.gov/apod/ap220423.html

#m104 #sombrerogalaxy. #nasa #astronomy

dmm, 4 months ago to quantumcomputing

Interesting commentary if you happen to be interested in these topics...

https://spectrum.ieee.org/quantum-computing-skeptics

#quantumcomputing

dmm, 4 months ago to math

Here's a curious and beautiful integral:

#math #maths #integralcalculus

dmm, 3 months ago to random

14 years after Alan Turing's death, an unpublished manuscript emerged where he suggested the idea of a "disordered" computer that anticipated the rise of connectionism.

https://www.cs.virginia.edu/~robins/Alan_Turing%27s_Forgotten_Ideas.pdf

#alanturing #connectionism #neuralnetworks

dmm, 5 months ago to math

One of my favorite mathematicians, Srinivasa Ramanujan, was born #onthisday in 1887 [1]. Ramanujan had many important and fascinating results in number theory including his famous formula for π shown below. There is also the Hardy–Ramanujan number, 1729, and the wonderful story that goes along with it [2].

Ramanujan has so many important results that would be hard to list even a small fraction of them here. That said, one of my favorite Ramanujan results concerns what are called "continued fractions" and is known as the Rogers–Ramanujan continued fraction [3]. A few of my notes on Ramanujan and nested radicals are here: https://davidmeyer.github.io/qc/nested_radicals.pdf. The LaTeX source is here: https://www.overleaf.com/read/qwhvvhrzrgct. As always, questions/comments/corrections/* greatly appreciated.

There is also a nice movie about Ramanujan's life called "The Man Who Knew Infinity" [4]. Burkard Polster (aka Mathologer) has many interesting videos about Ramanujan and his results, e.g. [5].

Sadly Ramanujan died of tuberculosis in 1920 at the young age of 32.

Read more about Ramanujan's life and times here: https://royalsociety.org/blog/2018/10/revisiting-ramanujan.

#ramanujan #nestedradicals #math #maths #mathematics

[Right image credit: https://in.pinterest.com/SHUBHAMRAJ54/srinivasa-ramanujan]

References

[1] "Srinivasa Ramanujan", https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

[2] "1729_(number)", https://en.wikipedia.org/wiki/1729_(number)

[3] "Rogers–Ramanujan continued fraction", https://en.wikipedia.org/wiki/Rogers%E2%80%93Ramanujan_continued_fraction

[4] "The Man Who Knew Infinity", https://en.wikipedia.org/wiki/The_Man_Who_Knew_Infinity

[5] "Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.", https://www.youtube.com/watch?v=jcKRGpMiVTw

Ramanujan

dmm, 1 month ago to physics

RIP Peter Higgs

https://www.bbc.com/news/science-environment-68774195?utm_source=press.coop

#peterhiggs #higgsboson #physics

dmm, 1 month ago to internet

Happy birthday RFC 1!

RFC 1 was published on #onthisday in 1969. Impressive work and insight by Steve and by the IETF community over the last 55 years/9K+ RFCs.

Well done!

#IETF #RFC #internet

dmm, 1 month ago to math

When I made the figure below I used LaTeX, powerpoint and then LaTeX again. Having learned some TikZ I now think I could draw it using TikZ, but apparently I'm too lazy...

A few of my notes on the subject of this figure (and other stuff) are here: https://davidmeyer.github.io/qc/dual_beam_experiment.pdf. As always, questions/comments/corrections/* greatly appreciated.

#math #maths #physics #quantumphysics #texlatex #tikz

dmm, 29 days ago to ChatGPT

"No, A → B is not equivalent to - B → - A in logic."

Except that the truth table that ChatGPT [1] generated says the opposite. Also, see the law of contraposition [2].

Claude [3] makes the same mistake.

I've had pretty good luck with the chatbots. This is the first thing that I have asked that all of them seem to get wrong.

Interesting.

References

[1] "ChatGPT", https://chat.openai.com

[2] "Contraposition", https://en.wikipedia.org/wiki/Contraposition

[3] "Claude", https://claude.ai

#chatgpt #claude3 #firstorderpredicatelogic #math #maths #logic

dmm, 2 months ago to physics

English polymath Isaac Newton, who was a mathematician, physicist, astronomer, alchemist, and theologian, died #onthisday in 1727.

His pioneering book Philosophiæ Naturalis Principia Mathematica (1687) consolidated many previous results and established classical mechanics [1]. He also made seminal contributions to optics (among many other things), and shares credit with Gottfried Wilhelm Leibniz for developing calculus.

Books by Newton at Project Gutenberg: https://www.gutenberg.org/ebooks/author/6288

[Image credits: https://en.wikipedia.org/wiki/Isaac_Newton and https://www.westminster-abbey.org/abbey-commemorations/commemorations/sir-isaac-newton]

References

[1] "Newton’s Philosophiae Naturalis Principia Mathematica", https://plato.stanford.edu/entries/newton-principia/

#newton #calculus #physics #optics #math #maths

dmm, 6 days ago to random

Later that very same morning...

#dow40K

dmm, 4 days ago to random

On May 17, 1902, Valerios Stais discovered the Antikythera Mechanism in a wooden box in the Antikythera shipwreck on the Greek island of Antikythera. The Mechanism is the oldest known mechanical computer and can accurately calculate various astronomical quantities.

As Tony Freeth says, "It is a work of stunning genius" [1].

A few of my notes on the Mechanism are here: https://davidmeyer.github.io/astronomy/prices_metonic_gear_train.pdf. The LaTeX source is here: https://www.overleaf.com/read/ndpvkytkhmbv.

As always, questions/comments/corrections/* greatly appreciated.

#antikytheramechanism

References

"The Antikythera Mechanism: A Shocking Discovery from Ancient Greece", https://www.youtube.com/watch?v=xWVA6TeUKYU