## 24, the Monster, and quantum gravity

Originally shared by Richard Green

24, the Monster, and quantum gravity

Think of a prime number other than 2 or 3. Multiply the number by itself and then subtract 1. The result is a multiple of 24. This observation might appear to be a curiosity, but it turns out to be the tip of an iceberg, with far-reaching connections to other areas of mathematics and physics.

This result works for more than just prime numbers. It works for any number that is relatively prime to 24. For example, 25 is relatively prime to 24, because the only positive number that is a factor of both of them is 1. (An easy way to check this is to notice that 25 is not a multiple of 2, or 3, or both.) Squaring 25 gives 625, and 624=(24×26)+1.

A mathematician might state this property of the number 24 as follows:

If m is relatively prime to 24, then m^2 is congruent to 1 modulo 24.

One might ask if any numbers other than 24 have this property. The answer is “yes”, but the only other numbers that exhibit this property are 12, 8, 6, 4, 3, 2 and 1; in other words, the factors of 24.

The mathematicians John H. Conway and Simon P. Norton used this property of 24 in their seminal 1979 paper entitled Monstrous Moonshine. In the paper, they refer to this property as “the defining property of 24”. The word “monstrous” in the title is a reference to the Monster group, which can be thought of as a collection of more than 8×10^53 symmetries; that is, 8 followed by 53 other digits. The word “moonshine” refers to the perceived craziness of the intricate relationship between the Monster group and the theory of modular functions.

The existence of the Monster group, M, was not proved until shortly after Conway and Norton wrote their paper. It turns out that the easiest way to think of M in terms of symmetries of a vector space over the complex numbers is to use a vector space of dimension 196883. This number is close to another number that is related to the Leech lattice. The Leech lattice can be thought of as a stunningly efficient way to pack unit spheres together in 24 dimensional space. In this arrangement, each sphere will touch 196560 others. The closeness of the numbers 196560 and 196883 is not a coincidence and can be explained using the theory of monstrous moonshine.

It is now known that lying behind monstrous moonshine is a certain conformal field theory having the Monster group as symmetries. In 2007, the physicist Edward Witten proposed a connection between monstrous moonshine and quantum gravity. Witten concluded that pure gravity with maximally negative cosmological constant is dual to the Monster conformal field theory. This theory predicts a value for the semiclassical entropy estimate for a given black hole mass, in the large mass limit. Witten’s theory estimates the value of this quantity as the natural logarithm of 196883, which works out at about 12.19. As a comparison, the work of Jacob Bekenstein and Stephen Hawking gives an estimate of 4π, which is about 12.57.

Wikipedia on the Monster group: http://en.wikipedia.org/wiki/Monster_group

Wikipedia on the Leech lattice: http://en.wikipedia.org/wiki/Leech_lattice

Wikipedia on Monstrous Moonshine: http://en.wikipedia.org/wiki/Monstrous_moonshine

A 2004 survey paper about Monstrous Moonshine by Terry Gannon: http://arxiv.org/abs/math/0402345

#mathematics

## SciTech #ScienceSunday Digest, 15/14.

SciTech  ScienceSunday Digest, 15/14.

Programmable microfluidics, Nanobot computers, stem cell mastery, organ rejuvenation, reinforced graphene, self-assembled films, software radio, atom-photon coupling.

1. Punch-Card Programmable Microfluidics.

A programmable microfluidic system based on the principles of a type of music box that operates with a pattern of holes punched in a paper tape that causes an array of cogs to strike different metal “notes” is deceptively simple yet carries transformative potential http://phys.org/news/2014-04-music-stanford-bioengineer-chemistry-video.html & see Stanford bioengineer creates \$5 chemistry set. In the device a pattern of holes causes cogs to strike valves in a microfluidic chip interfaced to the device in order to produce a droplet of [1 or 15 different] chemicals that flow along a chip; a suitable pattern of holes can thus produce a desired chain of microfluidic chemical reactions. Applications include synthesising new chemicals from feedstocks, running diagnostic assays, and testing samples. The device can be 3D printed for \$5, and the simplicity of the crank and punch card tape could be replaced with an Arduino microcontroller and electric motors for added control and a “limitless” tape length. Combine this with the simple microfluidics from last week and click-linked DNA and future versions might produce any desired DNA sequence in your home for example.

2. DNA Origami Produced Nanorobots Function as Computer Inside Animals.

That is a headline from the future if ever there was one. Researchers have produced a variety of DNA Origami sequences that self-assemble into different nanorobots capable of interacting with biological substrates, and each other, while inside a living animal and, further, such interactions generate logical outputs capable of switching molecular payloads on or off that were used to build AND, OR, XOR, NAND, NOT, CNOT, half-adder logic gates as part of a functional computational system http://www.newscientist.com/article/dn25376-dna-nanobots-deliver-drugs-in-living-cockroaches.html#.U0QqJKL3t94. The system successfully carried out a simple program inside a cockroach and interacted with the insect’s cells. The group believe that they can scale the computational power for such a system inside an animal up to the equivalent of an 8-bit computer like the Commodore 64 and further enhance stability for use in mammals. Future systems will deliver drugs to you in future, based on sensed inputs (your genotype) and releasing the correct output (drug for your genotype and not another). The above microfluidic systems will also produce these DNA origami systems cheaply and in your home should you wish.

3. Just Two Signals Turn Stem Cells into Embryos.

In a significant advance it has been discovered that just two molecular signals are required to trigger a stem cell to develop into a complete functional embryo are now able to direct embryonic development and formation of tissues and organs by controlling signal locations and concentrations http://news.virginia.edu/content/uva-smashes-barrier-growing-organs-stem-cells. The group plans to replicate the findings in mice before attempting humans and if the mechanisms prove similar then in future we can expect to be able to turn any of our stem cells into any organ that we might need.

4. Graphene Reinforced with Carbon Nanotubes.

A new processing technique allows carbon nanotubes to be added to sheets of graphene, functioning as reinforcing bars and improving the stability and strength of the overall structure http://news.rice.edu/2014/04/07/rebar-technique-strengthens-case-for-graphene/. The tubes become covalently bound in many places and were even observed to get thinner when the material was stretched and placed under tension. Many fabrication processes produce imperfect graphene sheets comprised of large domains connected at different angles and the tubes help bridge these interfaces and improve overall conductivity and electrical performance. The group hopes to develop multi-layered versions of “rebar” graphene capable of displacing indium-tin-oxide in many electronic display applications.

5. Spray-Painting Self-Assembling Nanoparticle Films.

A solvent solution comprising flat nanoparticles – or nanoplatelets – with specific functional groups of either side can be applied to a surface via a conventional off-the-shelf spray can http://phys.org/news/2014-04-common-gun-self-assembling-nanoparticle.html. As the solvent evaporates the nanoplatelets connect and self-assemble into a structured film or coating with interesting properties. The proof-of-concept was simply a barrier to oxygen molecules, suitable in gas separation applications. But with different nanoplatelets engineered as photovoltaics, thermoelectrics, LEDs this could possibly lead in future to the ability to spray-paint your roof into one continuous solar panel or your inner walls as huge lighting and digital displays for example.

6. One Signal to Regenerate & Rejuvenate a Living Organ for the First Time.

The thymus, an organ critical for the development and function of the immune system but whose function rapidly declines with age, has been regenerated and rejuvenated in aged mice for the first time http://www.mrc.ac.uk/Newspublications/News/MRC009803. The thymus in the aged mice took on the structure, histology, and gene expression profile of a young and healthy thymus, which began making more T-Cells. Furthermore, this incredible feat was achieved by up-regulating the activity of just a single transcription factor, FOXN1, which instructed stem cell-like cells to rebuild the organ. Further work will test this further before moving to humans and hopefully restoring youthful immune function in compromised patients and elderly people; similar interventions may allow a range of other organs to be restored to youthful function in this way too.

7. Fruitful Battles Between Software-Defined Radio Algorithms.

A diverse range of software-defined radio algorithms battled it out as part of DARPA’s Spectrum Challenge, aiming to see which algorithm was better able to use a given communication channel in the presence of other users and interfering signals http://spectrum.ieee.org/telecom/wireless/radio-wrestlers-fight-it-out-at-the-darpa-spectrum-challenge. Two different divisions separately tested (i) the ability to send a batch of pre-defined packets on a slice of spectrum on which others are trying to do the same and to simultaneously interfere with and prevent others from doing so; such adaptive radio was obvious military applications, (ii) the ability to optimise data-throughput on spectrum shared with other users, with obvious commercial and consumer applications and benefits. The competition format encouraged rapid innovation; six months ago algorithms typically lacked feedback, spectrum sensing, or adaptation, but they now all exploit these tools.

8. Massively Improved Communication Channels Between Genetic Circuit Elements.

A significant development in synthetic biology comprises the engineering of much more sensitive, robust, and rapid communication channels between various genetic circuit elements and processors http://phys.org/news/2014-04-bacterial-fm-radio.html. This new platform comprises a tool-set to enable rapid and tunable post-translational coupling of genetic circuits, solving the problem of noisy genetic circuits with limited communication channels and highly variable circuit performance limited by inefficiencies in reusing different parts of a program, and achieves order-of-magnitude improvements in response time. In related news synthetic gene circuits boost the activity of cellular degradation pathways to clear misfolded protein junk, offering a tantalising possibility to treat a range of diseases of the aged http://phys.org/news/2014-04-synthetic-gene-circuits-cell.html

9. The Promise of Enzyme-Powered Microfluidic Micropumps.

A self-powered enzyme micropump has been developed that is able to autonomously deliver small molecules and proteins in response to different stimuli http://phys.org/news/2014-04-mechanobiology-enzyme-micropump-autonomously-insulin.html. The device functions by anchoring desired enzymes to the surface of a fluidic chip, and the enzymes act as a pump when their substrates are present, setting up a directional flow of fluid through the chip. The proof-of-concept demonstration involved the release of insulin at a rate depending on and proportional to the concentration of glucose; pumping volume is dependent on stimulus concentration; basically an artificial pancreas. The group are expanding the work to incorporate multienzyme cascades and microfluidic logic gates. Future devices might be created with above, and implanted to controllably process any biological molecule as desired. Optimum chemical reaction conditions can now also be easily determined http://phys.org/news/2014-04-reactor-enables-optimum-conditions-chemical.html

10. Dual Development of Coupling Atoms and Photons for Quantum Logic.

A group from MIT & Harvard, and another from Max-Planck, have both independently developed the means to precisely couple individual atoms and photons in such a way that might allow the creation of quantum logic gates; http://newsoffice.mit.edu/2014/new-switch-could-power-quantum-computing-0409 and http://www.alphagalileo.org/ViewItem.aspx?ItemId=140833&CultureCode=en respectively. The former involved trapping a lone rubidium atom close to the surface of a photonic crystal, while the latter involved trapping lone atoms in mirrored cavities, and both enabled the atom to “quantumly” interact with individual photons. Future possible applications could include quantum communications or computation.

ScienceSunday, with your hosts Buddhini Samarasinghe, Rajini Rao, Chad Haney, Allison Sekuler, Robby Bowles, Carissa Braun, and Aubrey Francisco!

## Now Bat Influenza Viruses!

Originally shared by Deeksha Tare

Picture below: The flat-faced fruit bat Artibeus planirostris.

Bats to blame

Bats, already known culprits for viruses like Nipah, Hendra, and other coronaviruses, filoviruses, and lyssaviruses, have now been found to harbor Influenza viruses of a novel subtype. Scientists have found these Influenza viruses in Peruvian flat-faced fruit bats (Artibeus planirostris) and yellow-shouldered bats from Guatemala. Thus, there are yet another Mammalian hosts for this respiratory virus.

The two subtypes

The Influenza virus isolated from the Guatemala bats was classified in the subtype H17N10. Whereas the Peruvian viruses, being somewhat related, but vastly diverse from H17N10, have been classified as belonging to the H18N11 subtype. Its HA and NA genes being more genetically different (nucleotide sequence identity of 48.7–62.3%).

The surface proteins

♦ HA- The Hemagglutinin protein of the Peru virus bears only 49.1% similarity to the existing HA proteins of other subtypes. That is why it warrants a separate subtype of its own- H18.

The bat H18 HA does not recognize sialic acid receptors (which is the receptor in case of all Influenza viruses), and its receptor remains to be defined.

♦NA- The Neuraminidase protein too, bears only 29.6% identity with all the other NA subtypes. And hence it has been designated as N11. It is so different from the other NAs that the authors refer to it as the NA-like (NAL) protein.

In spite of the vast difference in sequence, structurally, the N11 is quite similar to common NAs.

Other findings

♦ A high frequency of antibodies is consistent with widespread circulation of these viruses in bat populations from the Americas.

♦  Bat influenza HA and/or NAL mediate host cell entry and release via different receptors compared to other influenza viruses..

♦ Attempts to propagate this virus in mammalian and avian cell cultures have been unsuccessful.

♦ These influenza viruses have evolved in bats for an extended period of time.

In conclusion

The present study is another reminder of the widely transient nature of Influenza viruses. Their discovery in different hosts and their constantly mutating nature may be indicative of the possibility of a species jump.

Whatever the scenario may be, this unpredictable virus is sure going to keep scientists on their toes!

#viromania

Yet another post for ScienceSunday . Tagging Rajini Rao Chad Haney Buddhini Samarasinghe Allison Sekuler and Robby Bowles .

(Via Kirk Douglas on

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