# behav: unfrequent events under radical uncertainty; rats tend to avoid black swan situations.

AA << present a novel experimental design that aims at measuring the extent to which animal subjects are sensitive to rare and extreme events and, in addition, how rats respond to those very unfrequent events under radical uncertainty. (..) the novelty of (AA) design is that it provides two direct measures that help interpreting (..) behavioral data: Total Sensitivity to Rare and Extreme Events, and One-sided Sensitivity to Rare and Extreme Events with Black-Swan Avoidance/Jackpot-Seeking behaviors as limiting cases. >>️

<< First, most rats (..) can be grouped into a moderate to high Total Sensitivity group. This means that most rats diversify their choices across options in such a way that they more often rely on convex ones than on concave ones overall. Therefore, they tend to seek extreme gains/Jackpots and to avoid extreme losses/ Black Swans. In addition, most rats (..) tend to exhibit Black Swan Avoidance, which indicates that, given Total Sensitivity, they tend to try more often to avoid Black Swans than to seek Jackpots. (AA) interpret such a behavior as significant aversion towards uncertainty about rare and extreme losses.  >>️

<< all rats diversify their choices across a set of options, which is reminiscent of observed behaviors such as, for example, bet-hedging in animals and financial portfolio strategies used by humans >>

️

<< results from similar experiments among different species might be of interest for the analysis of neurobiological substrates involved in decision-making and its evolutionary traits in the context of rare and extreme events. >>️

Mickael Degoulet, Louis-Matis Willem, et al. Decision-Making in Rats is Sensitive to Rare and Extreme Events: the Black Swan Avoidance. bioRxiv 10.1101/2021.11.01.466806v1. Nov 04, 2021. 

https://www.biorxiv.org/content/10.1101/2021.11.01.466806v1

 Keywords: behav, game, decision-making, bet-hedging, trading, uncertainty, gain, loss, black swan 

# game: in a iterated prisoner's dilemma scenario forgiveness turns out to be an adaptation

<< Prisoner’s dilemma is used to represent a range of real life phenomena such as economics, commerce, nature and wildlife. >>

<< Researchers working on iterated prisoner's dilemma (IPD) with limited memory inspected the outcome of different forgetting strategies in homogeneous environment, within which all agents adopt the same forgetting strategy at a time. In this work, with the intention to represent real life more realistically, (AA) improve existing forgetting strategies, offer new ones, and conduct experiments in heterogeneous environment that contains mixed agents and compare the results with previous research as well as homogeneous environment >>

<< in a more realistic environment consisting of all types of agents, in terms of both cooperation probabilities and forgetting strategies, agents who forget defectors consistently outperform other forgetting strategies for all memory ratio values. Moreover, the best performing defectors are also the ones that forget other defectors. In other words, agents who “forgive” defectors are the best performers. Hence, forgiveness is an adaptation. >>

FMC : Forget most cooperator first 

FMP : Forget most played first 

FMU : Forget most unpredictable first 

FR :  Forget randomly 

FLP : Forget least played first 

FMD : Forget most defector first 

Meliksah Turker, Haluk O. Bingol. Forgiveness is an Adaptation in Iterated Prisoner's Dilemma with Memory. arXiv:2112.07894v1 [cs.GT]. Dec 15, 2021

https://arxiv.org/abs/2112.07894

Also

keyword 'game' | 'tit-for-tat' in FonT

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

https://flashontrack.blogspot.com/search?q=tit-for-tat

keyword 'game' | 'tit-for-tat' in Notes

(quasi-stochastic poetry)

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

https://inkpi.blogspot.com/search?q=tit-for-tat

Keywords: game, iterated prisoner's dilemma, forgiveness, adaptation

# 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.

# life; apropos of #1or2achoos from Wuhan ...

Messrs. A, B, C & D state - between the lines, undertrack, at least a year late -

Commissione DuPre (Dubbio e Precauzione ) live streaming 8/12/2021 

https://youtu.be/_ZLFlY7y_2w

that the official anti covid19 apparatus it appears to be a big, very big mess (i.e. 'un grande pastrokkio') ...

probably Messrs. A, B, C & D could be accused of being thieves, sexual maniacs, they could block their career and make their spouses do twenty years of precariousness ...

their future pensioners' allowance could be taken away or reduced ... 

as well as more ... 

I suppose & anzicheforse ...

luckily for everyone, the 'bushman  variant' of sarscov-2 (Covid-19 B.1.1.529 Omicron) 

Republic of Botswana - new covid 19 variant detected in Botswana -  Presidential covid-19 task force.

https://pbs.twimg.com/media/FFC53NUXIAEqae5?format=jpg&name=large 

could save in short-term, perhaps, the world from this big trouble (i.e.  'grande impiccio').

Here there are three simple questions: 

(a) Why in anticipation of the 'great tea trolley disaster' (after SARS appearance in Nov 2002, Guangdong, China; after MERS in Nov 2012, Gedda, Saudi Arabia) spray forms of antiviral drugs (e.g. remdesivir,  remdesivir like) have not been prepared?

e.g.  https://pubmed.ncbi.nlm.nih.gov/?term=antiviral+drugs+sars-cov-2

(b) Why in the meantime, hitech reusable anti-viral anti-bacterial fabrics not been studied and tested?

(c) Does it seem serious to propose a vaccine - to treat every six/eight months eight billion people inside a window of 15/30 days - to confine (sic) a mutant virus (one mutation every week) that is transmitted by air? 

Also 

the unmentionable GTTD - Great Tea Trolley Disaster, by Bristow

https://flashontrack.blogspot.com/search?q=Great+Tea+Trolley+Disaster

keyword 'virus' | 'sars-cov-2' | 'sars' in FonT: 

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

https://flashontrack.blogspot.com/search?q=sars-cov-2

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

keyword 'virus' in Notes 

(quasi-stochastic poetry):

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

keyword 'bosciman*' | 'nomad*' in Notes

(quasi-stochastic poetry)

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

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

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

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

keyword 'bushmen' | 'nomads' in FonT 

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

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

keywords: virus, coronavirus, sars, mers, sars-cov-2, covid-19, 2019ncov, bushman  variant, B.1.1.529, Omicron, 1or2achoos, mask

# life: apropos of 'dancing at a fixed point'

the last interview to Dr Albert Bourla (Pfizer) about the annual (or maybe semi-annual (?)) shot reiteration of the vaccine against #sars-cov-2   remember to me the 'homoclinic dynamics' that I cited at the 13th Meeting of the Internat Epidemiol Associat - IEA (Sydney, 1993) ... after a large trajectories started at zero point (i.e.  the fixed point), the final point of the dynamic returns at the same zero point ...

<< People will be likely to need to have annual Covid vaccinations for many years to come, the head of Pfizer [Dr Albert Bourla ] has told the BBC >>️

Fergus Walsh. Pfizer boss: Annual Covid jabs for years to come. Dec 2, 2021. 

https://www.bbc.com/news/health-59488848

Who knows if there is a convincing reason that explains why to treat a virus with a high frequency of mutations one should prefer a vaccine approach instead of an antiviral drug ...

to find: 'antiviral drugs covid-19'  

https://pubmed.ncbi.nlm.nih.gov/?term=antiviral+drugs+covid-19&filter=datesearch.y_1

Apropos of 'homoclinic orbits' ...

<< the reinjection of the departing trajectories in the vicinity of an unstable fixed point of the saddle-focus type [..] is frequently associated with the emergence of orbits of a rather exceptional type known as 'homoclinic orbits'. These are trajectories that leave the fixed point but come back to it; in other words, they tend to the same limit when time t goes to +∞ as well as to -∞ . [..]. Homoclinic orbits are very sensitive to variation of parameter [parms] values and are generally destroyed if the [parms] do not satisfy a strict equality (in the terminology of [..] they are structurally unstable). However, for nearby values of the [parms] their disappearance leaves a very rich structure of orbit in phase space, some of which behave chaotically. >>️

Nicolis G., Prigogine I. Exploring complexity. Freeman, NY (1989): 130-131.

https://www.amazon.com/Exploring-Complexity-Introduction-Gregoire-Nicolis/dp/0716718596

Apropos of: [+∞ , -∞] plus infinity, minus infinity; 

<< In modern mysticism, the infinity symbol has become identified with a variation of the ouroboros, an ancient image of a snake eating its own tail that has also come to symbolize the infinite, [..] >> 

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

Also 

Onda omoclina. Notes. Tuesday, Jan  11, 2005 (quasi-stochastic poetry)

<< ed assistere al mutar dell' onda omoclina / (..) >>

️

https://inkpi.blogspot.com/2005/01/1639b-onda-omoclina.html

Also

Inchingolo GM.  Cultural transitions and epidemiology.  Proceedings of the 13th Scientific Meeting of the International Epidemiological Association - IEA, Sydney, Australia, Sept 26-29, 1993: 129.   Med Hypotheses 1994; 43(4): 201-206.

https://pubmed.ncbi.nlm.nih.gov/7838001/

Also

Onda di carambola. Notes. Nov  29, 2004. (quasi-stochastic poetry)

https://inkpi.blogspot.com/2004/11/1619-onda-di-carambola.html

keywords: life, dance, fixed point, homoclinic orbits, instability, chaos,  virus, coronavirus, sars-cov-2,  covid19, 2019ncov, drugs, antiviral drug, vaccine, jabs, Covid jabs.

# gst: small-scale random perturbations, Arnold's cat spontaneously stochastic

<< Multi-scale systems (..) may possess a fascinating property of spontaneous stochasticity: a small-scale initial uncertainty develops into a randomly chosen largescale state in a finite time, and this behavior is not sensitive to the nature and magnitude of uncertainty (..). >>

A << intriguing form is the Eulerian spontaneous stochasticity (ESS) of the velocity field itself: an infinitesimal small-scale noise triggers stochastic evolution of velocity field at finite scales and times. >>

AA << prove that a formally deterministic system with scaling symmetry yields a stochastic process with Markovian properties if it is regularized with a vanishing small-scale random perturbation. Besides its significance for understanding turbulence, (their) model extends the phenomenon of ESS beyond the scope of fluid dynamics: (AA) discuss a prototype of a feasible experiment for observing ESS in optics or electronics, as well as potential applications in other physical systems.>>

Alexei A. Mailybaev, Artem Raibekas. Spontaneously stochastic Arnold's cat. arXiv:2111.03666v1 [nlin.CD]. Nov 5,  2021.

https://arxiv.org/abs/2111.03666

keywords: gst, Arnold's cat, randomness, stochasticity, spontaneous stochasticity, small-scale random perturbations, noise, turbulence, chaos