# gst: more on the three-body problem (695 families of collisionless orbits)

<< The famous three-body problem can be traced back to Isaac Newton in the 1680s >>

In a recent paper AA << numerically obtain 695 families of Newtonian periodic planar collisionless orbits of three-body system >>

Li, X. & Liao, S. More than six hundred new families of Newtonian periodic planar collisionless three-body orbits. Sci. China Phys. Mech. Astron. (2017) 60: 129511. doi: 10.1007/s11433-017-9078-5

https://link.springer.com/article/10.1007%2Fs11433-017-9078-5

the movies:

http://numericaltank.sjtu.edu.cn/three-body/three-body-unequal-mass-movies.htm

http://numericaltank.sjtu.edu.cn/three-body/three-body-unequal-mass.htm

http://numericaltank.sjtu.edu.cn/three-body/three-body.htm

Scientists discover more than 600 new periodic orbits of the famous three-body problem. Oct 12, 2017

https://m.phys.org/news/2017-10-scientists-periodic-orbits-famous-three-body.html

# gst: isles of regularity (depending on the initial setup) in a sea of chaos amid the gravitational three-body problem.

AA << study probes the presence of regular (i.e. non-chaotic) trajectories within the 3BP (three-body problem) and assesses their impact on statistical escape theories. >>

AA << analysis reveals that regular trajectories occupy a significant fraction of the phase space, ranging from 28% to 84% depending on the initial setup, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. >>

Alessandro Alberto Trani, Nathan W.C. Leigh, et al. Isles of regularity in a sea of chaos amid the gravitational three-body problem. A&A, 689, A24, Jun 25, 2024.

https://www.aanda.org/articles/aa/full_html/2024/09/aa49862-24/aa49862-24.html

"Islands" of Regularity Discovered in the Famously Chaotic Three-Body Problem. University of Copenhagen. Oct 11, 2024.

https://science.ku.dk/english/press/news/2024/islands-of-regularity-discovered-in-the-famously-chaotic-three-body-problem/

Also: three balls, escape, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, three balls, escape, chaos, transition 

# gene: 99 loci to drive general cognitive function

AA << combined cognitive and genetic data from the CHARGE and COGENT consortia, and UK Biobank (total N=280,360; age range = 16 to 102) >>

AA << found 9,714 genome-wide significant SNPs  [Single Nucleotide Polymorphism] (P<5 x 10-8) in 99 independent loci >>

<< Among many novel genes associated with general cognitive function were SGCZ, ATXN1, MAPT, AUTS2, and P2RY6 >>

Gail Davies, Max Lam, et al. Ninety-nine independent genetic loci influencing general cognitive function include genes associated with brain health and structure (N = 280,360). biorxiv. doi: 10.1101/176511 Aug18, 2017.

http://www.biorxiv.org/content/early/2017/08/18/176511

FonT

il sistema a 3 palle in fisica (three-body problem) qui genericamente estensibile a 99 ...

three-body problem:

Jon Cartwright. Physicists  Discover a Whopping 13 New  Solutions to Three-Body  Problem. Mar. 8, 2013

http://www.sciencemag.org/news/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem

Institute  of  Physics  Belgrade. Three-body gallery

http://suki.ipb.ac.rs/3body/

# gst: apropos of a immaginary transition (with a tipping point), which simulates the chaotic interactions of three black holes.

<< The interactions between three bodies such as stars or planets or black holes cannot be predicted with an elegant formula. Moerman (Arend Moerman) therefore used a computer that calculates what happens for a short period of time and then uses the result for the next period of time. >>

AA << varied the masses of the three interacting black holes. They started with one solar mass and went up to a billion times the mass of the sun. >>

<< Around ten million solar masses, there appeared to be a tipping point. In the simulations, black holes that are lighter than about ten million solar masses mostly eject each other through a gravitational slingshot. Black holes heavier than about ten million solar masses start to merge. First, two black holes merge. The third black hole will follow later. The black holes merge because they lose kinetic energy and that is because they emit gravitational waves. >>

<< Arend's work (..) has led to a new understanding of how black holes become supermassive. In the simulations, we see that heavy black holes no longer endlessly move around each other, but that, if they are heavy enough, they collide pretty much instantly. >> Simon Portegies Zwart. 

Simulating chaotic interactions of three black holes. Netherlands Research School for Astronomy. Oct 20, 2021. 

https://phys.org/news/2021-10-simulating-chaotic-interactions-black-holes.html

Tjarda C. N. Boekholt, Arend Moerman, Simon F. Portegies Zwart. Relativistic Pythagorean three-body problem. Phys. Rev. D 104, 083020. 14 Oct 14,  2021. 

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.083020

Also

more on the three-body problem (695 families of collisionless orbits). FonT. Oct 16, 2017. 

https://flashontrack.blogspot.com/2017/10/gst-more-on-three-body-problem-695.html

keyword 'black hole' | 'astro' in FonT

https://flashontrack.blogspot.com/search?q=black+hole

https://flashontrack.blogspot.com/search?q=astro

keyword 'transition' | 'transitional' in FonT

https://flashontrack.blogspot.com/search?q=transition

https://flashontrack.blogspot.com/search?q=transitional

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=transition

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transizioni

keywords: gst, black hole, three-body problem, transition, chaos, chaotic interaction, tipping point.

# gst: the three-body problem approach using deep neural networks

AA << show that an ensemble of solutions obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (..) that, over a bounded time interval, provides accurate solutions at fixed computational cost and up to 100 million times faster than a state-of-the-art solver. >>

Philip G. Breen, Christopher N. Foley,  et al. Newton vs the machine: solving the chaotic three-body problem using deep neural networks. arXiv: 1910.07291v1 [astro-ph.GA] Oct 16, 2019

https://arxiv.org/abs/1910.07291

A neural net solves the three-body problem 100 million times faster. By Emerging Technology from the arXiv. 

Oct 26, 2019. 

https://www.technologyreview.com/s/614597/a-neural-net-solves-the-three-body-problem-100-million-times-faster/

Also

keyword "three" in FonT    

https://flashontrack.blogspot.com/search?q=three

keyword "three" in Notes      

https://inkpi.blogspot.com/search?q=three

# gst: reshaping Kuramoto model, when a collective dynamics becomes chaotic, with a surprisingly weak coupling.

<< The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model (..) Collective synchronization is a phenomenon in which an ensemble of heterogeneous, self-sustained oscillatory units (commonly known as oscillators) spontaneously entrain their rhythms. This is a pervasive phenomenon observed in natural systems and man-made devices, covering a wide range of spatio-temporal scales, from cell aggregates to swarms of fireflies >>

<< However, this is only partly true, (..) Kuramoto’s perturbative phase-reduction approach is valid for weak coupling. Specifically, oscillator heterogeneity and interactions appear at zeroth and linear orders in the coupling constant, respectively. >> 

AA << have introduced the ‘enlarged Kuramoto model’; a population of phase oscillators in which three-body interactions enter in a perturbative way. Remarkably, this makes a world of difference, drastically reshaping the traditional Kuramoto scenario. The ‘enlarged Kuramoto model’ exhibits a variety of unsteady states, including collective chaos and hyperchaos. >>

Ivan Leon, Diego Pazo. Enlarged Kuramoto Model: Secondary Instability and Transition to Collective Chaos. arXiv: 2112.00176v1 [nlin.AO]. Nov 30, 2021.

https://arxiv.org/abs/2112.00176

Also

More on the three-body problem (695 families of collisionless orbits). FonT. Oct 16, 2017. 

https://flashontrack.blogspot.com/2017/10/gst-more-on-three-body-problem-695.html

Keywords: gst, behav, instability, Kuramoto model, three-body interactions, chaos, collective chaos, hyperchaos.

# s-acad: imparare bene due accordi ...

<< impara bene due accordi; prima di imparare il terzo procurati un buon avvocato >>

Anonymous. Virgin Radio, http://www.virginradio.it. 2016.06.06 16:27

more (three body problem):

Jon Cartwright. Physicists  Discover  a  Whopping  13  New  Solutions  to  Three-Body  Problem. Mar. 8, 2013 , 4:30  PM

http://www.sciencemag.org/news/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem

Institute  of  Physics  Belgrade. Three-body gallery

http://suki.ipb.ac.rs/3body/

# gst: switch to three players within the Parrondo game

<< Parrondo's paradox indicates a paradoxical situation in which a winning expectation may occur in sequences of losing games. There are many versions of the original Parrondo's games in the literature, but the games are played by two players in all of them. (AA) introduce a new extended version of games played by three players and a three-sided biased dice instead of two players and a biased coin in this work.  >>️

<< Figure 11 shows the result of combination switches A and B for the fair probabilities in set S_5. The simulation results are performed so on until 100 steps were done, and each step is averaged over 10000 repeats. This strategy, different from the others and even the original Parrondo's paradox, produces a fair expectation from two noisy switches in which the combination of two fair switches is fair. >>

️

Atiyeh Fotoohinasab. A new generalization of Parrondo's games to three players and its application in genetic switches.  arXiv: 2101.11401v2 [q-bio.PE]. Feb 2, 2021. 

https://arxiv.org/abs/2101.11401 

Also

keyword 'parrondo' in FonT

https://flashontrack.blogspot.com/search?q=parrondo

keyword 'parrondo' in Notes  (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=parrondo

keyword 'three-body' in FonT

https://flashontrack.blogspot.com/search?q=three-body

Keywords: gst, games, parrondo, three-body

# life: a proposito di bizzarri scenari, qui un ipotetico scenario22 dipinto dal reale ...

img: Congo Square, New Orleans, Louisiana (wikipedia.org)

In definitiva qui si configurerebbe un - intrigante assai - scenario che, grosso modo, si potrebbe sinteticamente 'dipingere' in questi termini: 

(i) entità tre palle destrogire, animate aciclicamente da interazioni attrattive- repulsive a causa di già a suo tempo disvelate pulsioni neuro cognitive arcaiche, riconducibili a visioni neuro predatorie CTZ estreme, perciò ipoteticamente (si fa per dire) a-priori ad esiti immediati e in prospettiva drammaticamente lesivi- autolesivi; 

(ii) entità tre palle levogire, animate da analoghe pulsività, purtuttavia in.forme  tenui, in modalità sottotraccia, frenate da feed-back a modalità allosterica, ombreggiate, stemperate, diluite, discrete, timidamente celate, talvolta fantasmatiche perfino, quasi ma non del tutto mai silenti, perciò anch'esse a tutti gli effetti operative, sebbene a dinamiche più fluide, lente, meno dirompenti rispetto alle destrogire; 

(iii) entrambe l'Entità destrogire e levogire animat(t)rici,  generat(t)rici di dinamiche bi-multi-forcate, transeunti, con picchi di improvvisi aciclici burst ad effetti RAG-time diretti e inversi;

(iv) lo scenario al contorno e forse anche all'interno, nei vari specifici contesti, riconducibile grosso modo alla formazione aciclica di ipotetici buchi neri non inerti, caratterizzati da aciclicità in compressione e dilatazione - come fossero fisarmoniche - animati (in perpetuo?) da multi vortici in ingresso e in uscita;

Non so se basti compulsare un manuale delle funzioni speciali per formalizzare in qualche adatto topo-modo questo pulsatile multi scenario, purtuttavia assolutamente intrigante ... 

Qui una AI operativa nella formalizzazione di analogie potrebbe modellizzare, forse ... (e.g. https://flashontrack.blogspot.com/2021/08/aibot-mechanism-of-analogy-could-be.html )

Quello che appare evidente è la complessità d'insieme, un bizzarro dipinto, uno scenario dinamico che, al confronto, le storiche danze in Congo Square potrebbero sembrare semplici, ordinate coreografie ... queste, rispetto a quelle, delle topo-forme  'primitive', per dire ed anzicheforse.

In sintesi, i riferimenti (ovviamente generici) del bizzarro scenario: 

(:) buco nero con vortici 

https://flashontrack.blogspot.com/2022/09/astro-black-holes-as-q-ball-type.html

(:) scenari generati da 3 palle 

(a)

https://flashontrack.blogspot.com/2017/10/gst-more-on-three-body-problem-695.html  

(b)

https://flashontrack.blogspot.com/search?q=three-body

(:) effetti RAG-time (RAG: Ralph, Al, George) 

(a) (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=rag   

(b)

https://flashontrack.blogspot.com/search?q=rag

(:) pulsioni predatorie supportate / giustificate da visioni neuro- post- CTZ nelle modalità arcaiche oppure friendly 

https://flashontrack.blogspot.com/2019/06/brain-immagini-ctz-cicliche.html

(:) Congo Square, jazz 

(a)

https://en.m.wikipedia.org/wiki/Congo_Square   

(b)

https://flashontrack.blogspot.com/search?q=jazz   

(c) (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=jazz

(:) approccio Bertalanffy 

( https://it.m.wikipedia.org/wiki/Ludwig_von_Bertalanffy ) al reale 

https://flashontrack.blogspot.com/search?q=gst

(:) un bizzarro tracciatore 

https://flashontrack.blogspot.com/2022/10/life-proposito-di-transizioni-un.html

Anche

"Amico, qualunque cosa suonerai ... "

(a) (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=jelly+roll  

(b)

https://flashontrack.blogspot.com/search?q=jelly+roll

Keywords: life, gst, Congo Square, jazz, Jelly Roll, transition, three-body, RAG, CTZ, black hole, bizarre tracker

# phys: trace the birth and evolution of a quasiparticle entity

<< The idea of quasiparticles was first introduced in the 1930s by physicist Lev Landau, who was trying to gain a better understanding of complex quantum systems. >>

<< Over the past decades, physicists worldwide have been trying to gain a better understanding of non-equilibrium dynamics in quantum many-body systems. Some studies investigated what are known as quasiparticles, disturbances or entities in physical systems that exhibit behavior similar to that of particles. >>

In this study AA << observed three distinct regimes of impurity evolution marked by dynamic transitions. These regimes then link initial few-body and later many-body physical dynamics. >>

Ingrid Fadelli. Observing the birth of a quasiparticle. Mar 11, 2021.

https://phys.org/news/2021-03-birth-quasiparticle.html

<<  These results offer a systematic picture of polaron formation from weak to strong impurity interactions. They reveal three distinct regimes of evolution with dynamical transitions that provide a link between few-body processes and many-body dynamics. Our measurements reveal universal dynamical behaviour in interacting many-body systems and demonstrate new pathways to study non-equilibrium quantum phenomena. >>

Magnus G. Skou, Thomas G. Skov, et al. Non-equilibrium quantum dynamics and formation of the Bose polaron. 

Nat. Phys. (2021). doi: 10.1038/ s41567-021-01184-5. Feb 25, 2021.

https://www.nature.com/articles/s41567-021-01184-5

"three distinct regimes"  

https://www.nature.com/articles/s41567-021-01184-5.epdf?no_publisher_access=1&r3_referer=nature

# life: a proposito di bizzarri scenari, qui una transizione 'a gradino' di ipotetico scenario22

Congo Square, New Orleans (img from web).  https://en.m.wikipedia.org/wiki/Congo_Square

Una senz'altro immaginifica transizione di un sistema anch'esso senz'altro immaginifico "3vs3 palle" 

https://flashontrack.blogspot.com/2022/10/life-proposito-di-bizzarri-scenari-qui.html

qui potrebbe verificarsi una improvvisa mutazione "3vs3" verso un sistema auto- riconfigurato in "4vs2" palle.

(-) In prima approx il sistema destrogiro "4palle", sebbene caotico,  quasisticastico, potrebbe dimostrare chance di creativa stabilizzazione, anche a medio-lungo termine, anche grazie a non del tutto improbabili episodi di drammatiche funzionali fagocitosi (e.g. nelle forme predatorie del cannibalismo/ auto- cannibalismo, anche orgiastico estremo) al proprio interno.

(-) Il sistema levogiro "2palle" potrebbe invece lui medesimo risultare vincente sull'altro destrogiro nel caso riuscisse nell'im.probabile stabilizzazione,  ristrutturazione funzionale - dimostrando pubblicamente non banali capacità di risoluzione/ reimpostazione di problemi - perciò animandosi in modalità attrattive, coagulative su una parte significativa del 50% di quelle moltitudini verosimilmente costituite da entità fluttuanti nella solitaria condizione di pulviscoli erratici in emarginata sublimazione.

L'immagini, senz'altro campate in aria purtuttavia intriganti:  'episodi di drammatiche funzionali fagocitosi', 'cannibalismo, auto-cannibalismo anche orgiastico estremo' e 'solitaria condizione di pulviscoli erratici in emarginata sublimazione' meriterebbero una serie di poetiche, quasistocastiche perfino

https://inkpi.blogspot.com

ma mi astengo.

# life: a proposito di bizzarri scenari, qui un ipotetico scenario22 dipinto dal reale ... FonT.  Oct 17,  2022.

https://flashontrack.blogspot.com/2022/10/life-proposito-di-bizzarri-scenari-qui.html

Also

<< Tornando all'analogia con la fisica, il potere, come l'energia, muta continuamente di forma >>. In: Onda anti rumore. Notes (quasi-stochastic poetry). April 21, 2005.

https://inkpi.blogspot.com/2005/04/1644b-onda-anti-rumore.html

keyword 'dance' | 'dancing' in FonT

https://flashontrack.blogspot.com/search?q=dance

https://flashontrack.blogspot.com/search?q=dancing

keyword 'danza' | 'danzant*' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=danza

https://inkpi.blogspot.com/search?q=danzante

https://inkpi.blogspot.com/search?q=danzanti

Keywords: life, gst, Congo Square, danza, dance, jazz, Jelly Roll, transition, three-body

# s-esobio: self-assembled azotosomes by convective activity, a kind of proto-life on Titan.

<< vinyl cyanide (C2H3CN; also known as acrylonitrile or propenenitrile) would be the best candidate species for the formation of (..) cell-like membranes, known as “azotosomes” >>

AA << report the first spectroscopic detection of vinyl cyanide in Titan’s atmosphere, obtained using archival data from the Atacama Large Millimeter/submillimeter Array (ALMA), collected from February to May 2014 >>

AA << detect the three strongest rotational lines of C2H3CN in the frequency range of 230 to 232 GHz, each with >4σ confidence >>

the << production rate of vinyl cyanide and its saturation mole fraction imply the availability of sufficient dissolved material to form ~107 cell membranes/cm3 in Titan’s sea Ligeia Mare (Titan's second largest liquid body) >>

<< Reactions of hydrocarbons with hydrogen, both readily available on Titan, release energy, which could provide support for methanogenic life. The sedimentation time of atmospheric organics depends on the particle size and convective activity in the troposphere. This coupling of Titan’s atmosphere and surface completes the picture regarding the astrobiological importance of (..) detection of vinyl cyanide in Titan’s middle/upper atmosphere >>

Maureen Y. Palmer, Martin A. Cordiner, et al. ALMA detection and astrobiological potential of vinyl cyanide on Titan. Science Advances  28 Jul 2017: Vol. 3, no. 7, e1700022
doi: 10.1126/sciadv.1700022

http://advances.sciencemag.org/content/3/7/e1700022.full

# ai: apropos of Black Box in Generative Artificial Intelligence, the scientific XAI.

<< The scientific method is the cornerstone of human progress across all branches of the natural and applied sciences, from understanding the human body to explaining how the universe works. The scientific method is based on identifying systematic rules or principles that describe the phenomenon of interest in a reproducible way that can be validated through experimental evidence. In the era of artificial intelligence (AI), there are discussions on how AI systems may discover new knowledge. >>

<< More specifically, knowing what data AI systems used to make decisions can be a point of contact with domain experts and scientists, that can lead to divergent or convergent views on a given scientific problem. Divergent views may spark further scientific investigations leading to new scientific knowledge. Convergent views may instead reassure that the AI system is operating within bounds deemed reasonable to humans. >>️

<< The perspective (AA) present here was inspired by several authors that published on the topic of AI for science in the past few years, but perhaps one contribution stands out: the inspiring New York Times editorial by Steven Strogatz (Strogatz, S. One giant step for a chess-playing machine. New York Times 26 (2018)) covering the winning of AlphaZero against Stockfish. In that piece, Strogatz states: “What is frustrating about machine learning, however, is that the algorithms can’t articulate what they’re thinking. We don’t know why they work, so we don’t know if they can be trusted. AlphaZero gives every appearance of having discovered some important principles about chess, but it can’t share that understanding with us.”. He additionally cites Garry Kasparov (the former world chess champion) that stated: “we would say that its [AlphaZero] style reflects the truth. This superior understanding allowed it to outclass the world’s top traditional program despite calculating far fewer positions per second.” >>️

AA highlights the importance of three aspects regarding scientific XAI (explainable Artificial Intelligence): accuracy, reproducibility, understandability, ️

Apropos of 'understandability', << The machine view should be understandable to scientists and domain experts. (..) If we want a scientist to make sense of the data used by a machine, this data should contain viable features that allow a scientist to tap into its existing corpus of knowledge. >>

<< XAI may also alleviate some of the risks that we may face when using AI for scientific discovery, that we share with Messeri and Crockett (‘adopting AI in scientific research can bind to our cognitive limitations and impede scientific understanding despite promising to improve it’). >>

️

Gianmarco Mengaldo. Explain the Black Box for the Sake of Science: Revisiting the Scientific Method in the Era of Generative Artificial Intelligence. arXiv: 2406.10557v1 [cs.AI]. Jun 15, 2024.

https://arxiv.org/abs/2406.10557

Also: ai (artificial intell), in https://www.inkgmr.net/kwrds.html 

Keywords: AI, XAI, Artificial Intelligence

# astro: differential rotation in Jupiter

<< Jupiter's atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second >>

<< The discovery by the Juno spacecraft that Jupiter's gravity field is north–south asymmetric [..] demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops >>

AA << find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere >>

AA << expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs >>

Guillot T, Miguel Y, et al. A suppression of differential rotation in Jupiter’s deep interior. Nature. 2018; 555; 227 - 30.  doi: 10.1038/nature25775. Mar 8, 2018.

https://www.nature.com/articles/nature25775

<< Scientists have long wondered what lies beneath Jupiter's surface. Now, using data from NASA's Juno mission, four research teams have published studies revealing incredible new information about the gas giant >>

Chelsea Gohd.  We Now Know What Lies Beneath Jupiter's Clouds. Mar 7, 2018.

https://futurism.com/beneath-jupiters-clouds/

NASA Juno Findings - Jupiter's Jet - Streams Are Unearthly.  March 7, 2018.

https://www.nasa.gov/feature/jpl/nasa-juno-findings-jupiter-s-jet-streams-are-unearthly