# gst: apropos of transitions, a perpetual dance between states of meta-stability and chaos (in brain).

img: https://wp.technologyreview.com/wp-content/uploads/2023/02/Radio_image_15.jpeg?fit=2160,1214

<< Hello! Today: new research is shining a light on how our brains flit between states of stability and chaos, depending on what we’re doing. >>

<< Our brains exist in a state somewhere between stability and chaos as they help us make sense of the world, according to recordings of brain activity taken from volunteers over the course of a week. >>

<< As we go from reading a book to chatting with a friend, for example, our brains shift from one semi-stable state to another—but only after chaotically zipping through multiple other states in a pattern that looks completely random. >>

<< Understanding how our brains restore some degree of stability after chaos could help us work out how to treat disorders at either end of this spectrum. Too much chaos is probably what happens when a person has a seizure, whereas too much stability might leave a person comatose. >>

Jessica Hamzelou. Neuroscientists listened in on people’s brains for a week. They found order and chaos. Rhiannon Williams. MIT Download. Feb 8, 2023.

https://mailchi.mp/technologyreview.com/mass-market-military-drones-have-changed-the-way-wars-are-fought-839014

<< The team (Avniel Ghuman, Maxwell Wang, et al.) found some surprising patterns in brain activity over the course of the week. Specific brain networks seemed to communicate with each other in what looked like a “dance,” with one region appearing to “listen” while the other “spoke,” say the researchers, who presented their findings at the Society for Neuroscience annual meeting in San Diego last year. >>

Jessica Hamzelou. MIT Tech Rev. Feb 7, 2023. 

https://www.technologyreview.com/2023/02/07/1067951/brains-week-order-chaos

Also 

keyword 'danza' in Notes

(quasi-stochastic poetry)

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

keyword 'dance' in FonT

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

keyword 'cervello' | 'brain' in Notes

(quasi-stochastic poetry)

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keyword 'brain' in FonT

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keyword 'chaos' | 'chaotic' in Font

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keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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<< Amico, qualunque  cosa suonerai . . . >>  Jelly Roll Morton. cit.: 2113 - soniche a ramulo. Jan 28, 2007

http://inkpi.blogspot.it/2007/01/2113-soniche-ramulo.html

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

Keywords: gst, brain, transition, chaos, dance

# gst: a scenario in which System Theory meets Poetry, bird's-eye vistas into a primitive chaos

<< The notion of primitive chaos was proposed [J. Phys. Soc. Jpn. 79, 15002 (2010)] as a notion closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility. In this letter, (AA) introduce the notion of bird's-eye view into the primitive chaos, and (they) find a new hierarchic structure of the primitive chaos. This means that if we find a chaos in a real phenomenon or a computer simulation, behind it, we can clearly realize the possibility of tremendous varieties of chaos in the hierarchic structure unless we can see them visually. >>

<< This fact provides a totally new method of viewing our world. >>️️

Yoshihito Ogasawara. Bird's-Eye View of Primitive Chaos. arXiv:2105.04796v2 [nlin.CD]. May 17, 2021. 

https://arxiv.org/abs/2105.04796

Also

Ludwig von Bertalanffy  (gst)  

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

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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

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# gst: labyrinth chaos: revisiting the elegant, chaotic and hyperchaotic walks

<< Labyrinth chaos was discovered by Otto Rossler and Rene' Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, (AA) celebrate their discovery by considering a single labyrinth walks system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behaviour, reminiscent of chimera-like states, a peculiar synchronisation phenomenon. >>

 << As all Rossler’s pioneering contributions, labyrinth chaos still holds promise for very interesting further developments. Its simplicity and elegance, both in terms of symmetries, topology and feedback-circuit structure, makes it a good candidate to compare it with other nonlinear, cyclically coupled systems, such as the Arabesques, the Lotka-Voltera system and its variants, and the Arnold-Beltrami-Childress  model. >> 

Vasileios Basios, Chris G. Antonopoulos, Anouchah Latifi. Labyrinth chaos: Revisiting the elegant, chaotic and hyperchaotic walks. arXiv: 2011.11009v1. Nov 22, 2020.

https://arxiv.org/abs/2011.11009

# gst: quantum chaos to approach the evolution of a dynamic system

<< A study on the evolution of dynamic systems [..] has unexpectedly led to a better understanding of the chaos in the quantum world >>

<< The tools needed to explore the rigidity of dynamic systems [..] far exceeded those currently available, forcing the team to learn from neighboring disciplines >>

<< As a by-product of this process, researchers have identified the applicability of this project to quantum mechanics, which has led them to formulate a new theorem of thermodynamic quantum chaos combining ideas from large networks. Large networks — such as Big Data, social networks, convolutional neural networks of Artificial Intelligence models — which, although commonly used today, do not yet have adequate theories to explain their operation >>

Shakes Gilles. Study of dynamical systems leads to better understanding of quantum chaos. March 27, 2018.

https://www.thetalkingdemocrat.com/2018/03/study-of-dynamical-systems-leads-to-better-understanding-of-quantum-chaos/

# gst: weird Nature; randomly arranged nanowire networks seem to behave, at the edge of chaos, like cortical neuronal cultures

<< an artificial network of nanowires can be tuned to respond in a brain-like way when electrically stimulated. >>️

<< If the signal stimulating the network was too low, then the pathways were too predictable and orderly and did not produce complex enough outputs to be useful. If the electrical signal overwhelmed the network, the output was completely chaotic and useless for problem solving. The optimal signal for producing a useful output was at the edge of this chaotic state. >>️

<< Some theories in neuroscience suggest the human mind could operate at this edge of chaos, or what is called the critical state, (..) Some neuroscientists think it is in this state where we achieve maximal brain performance. (..) What's so exciting about this result is that it suggests that these types of nanowire networks can be tuned into regimes with diverse, brain-like collective dynamics, which can be leveraged to optimize information processing. >> Zdenka Kuncic.️

<< In the nanowire network the junctions between the wires allow the system to incorporate memory and operations into a single system. This is unlike standard computers, which separate memory (RAM) and operations (CPUs). >>

<< These junctions act like computer transistors but with the additional property of remembering that signals have traveled that pathway before. As such, they are called 'memristors', >> Joel Hochstetter.

️

'Edge of chaos' opens pathway to artificial intelligence discoveries. University of Sydney. Jun 29, 2021.

https://phys.org/news/2021-06-edge-chaos-pathway-artificial-intelligence.html

Joel Hochstetter, Ruomin Zhu, et al. Avalanches and edge-of-chaos learning in neuromorphic nanowire networks. Nat Commun 12, 4008. doi: 10.1038/ s41467-021-24260-z. Jun 29, 2021.

https://www.nature.com/articles/s41467-021-24260-z

# gst: the solitary route to chimera states.

AA << show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit (they) demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. (AA) demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators. >>

<<  While it is well known that self-organized wave patterns typically coexist within an interval of possible different wave numbers (..)(AA) show here the coexistence of coherence-incoherence patterns with different numbers of incoherent oscillators, which are in fact coexisting chaotic attractors with different Lyapunov dimensions. The incoherent oscillators in these coexisting attractors show extensive chaos of different dimensions. The total share of incoherent oscillators in a chimera state is a macroscopic quantity. Hence, within the range of such shares, where stable chimera states exist, (AA) find, for large systems, an increasing number of coexisting attractors with their numbers of incoherent oscillators increasing as well. (They) showed that, varying the coupling parameter, this extensive scenario is linked to the thermodynamic limit of the solitary regime, where the range of admissible numbers of incoherent oscillators shrinks down to one single oscillator in an infinitely large system. For this case, the emergence of the chaotic motion of the single incoherent oscillator could be shown in a period doubling cascade. >>

Leonhard Schulen, Alexander Gerdes, et al. The solitary route to chimera states. arXiv:2204.00385v1 [nlin.CD]. Apr 1, 2022.

https://arxiv.org/abs/2204.00385

Also

keyword 'FitzHugh-Nagumo oscillators' in APS | PubMed

https://journals.aps.org/search/

https://pubmed.ncbi.nlm.nih.gov/?term=FitzHugh-Nagumo+oscillators

keyword 'chaos' | 'chaotic' in Font

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keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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keywords: gst, solitons, solitary states, period-doubling cascade, chaos, Lyapunov dimension, FitzHugh-Nagumo oscillator, chimera state, dynamical systems.

# gst: it would use chaos to compute efficiently

<< When you’re really harried, you probably feel like your head is brimful of chaos. You’re pretty close. Neuroscientists say your brain operates in a regime termed the “edge of chaos,” and it’s actually a good thing. It’s a state that allows for fast, efficient analog computation of the kind that can solve problems that grow vastly more difficult as they become bigger in size >>

<< A micrograph shows the construction of a Mott memristor composed of an 8-nanometer-thick layer of niobium dioxide between two layers of titanium nitride >>

Samuel K. Moore. Memristor-Driven Analog Compute Engine Would Use Chaos to Compute Efficiently. Oct  9, 2017

https://spectrum.ieee.org/nanoclast/semiconductors/devices/memristordriven-analog-compute-engine-would-use-chaos-to-compute-efficiently

FonT

"When you’re really harried" ... only?

# gst: chaotic dynamics modulate complex systems, even in the presence of extrinsic and intrinsic noise

AA << find that chaotic dynamics modulates gene expression and up-regulates certain families of low-affinity genes, even in the presence of extrinsic and intrinsic noise. Furthermore, this leads to an increase in the production of protein complexes and the efficiency of their assembly. Finally, (AA) show how chaotic dynamics creates a heterogeneous population of cell states, and describe how this can be beneficial in multi-toxic environments. >>

Mathias L. Heltberg, Sandeep Krishna, Mogens H. Jensen. On chaotic dynamics in transcription factors and the associated effects in differential gene regulation.  Nature Comm. volume 10, Article number: 71 Jan 8, 2019.   https://www.nature.com/articles/s41467-018-07932-1  

<< Chaos in bodily regulation can optimize our immune system according to a recent discovery made by researchers at the University of Copenhagen's Niels Bohr Institute. The discovery may prove to be of great significance for avoiding serious diseases such as cancer and diabetes.  >>

Chaos in the body tunes up your immune system. Niels Bohr Institute.
Jan 16, 2019.   https://m.medicalxpress.com/news/2019-01-chaos-body-tunes-immune.html

Also

'l'immaginifico "tracciante ... che svagola nella macina ...'    in:  2149 - onda di predazione (to knock seals off the ice). Notes. Dec 17, 2007.    https://inkpi.blogspot.com/2007/12/2149-onda-di-predazione-to-knock-seals.html

Also

never boring with chaos and tit-for-tat theories. F.on.T. Jun 12, 2016.  https://flashontrack.blogspot.com/2016/06/s-gst-never-boring-with-chaos-and-tit.html

# gst: a chaos-inducing approach against superbugs evolution

<< The CHAOS [Controlled Hindrance of Adaptation of OrganismS] method takes advantage of this effect, pulling multiple genetic levers in order to build up stress on the bacterial cell and eventually trigger a cascading failure, leaving the bug more vulnerable to current treatments. The technique does not alter the bug's DNA itself, only the expression of individual genes, similar to the way a coded message is rendered useless without the proper decryption. >>

<< We now have a way to cut off the evolutionary pathways of some of the nastiest bugs and potentially prevent future bugs from emerging at all, >> Peter Otoupal

Chaos-inducing genetic approach stymies antibiotic-resistant superbugs. University of Colorado at Boulder. Sept 3, 2018.

https://m.phys.org/news/2018-09-chaos-inducing-genetic-approach-stymies-antibiotic-resistant.html 

<< While individual perturbations improved fitness during antibiotic exposure, multiplexed perturbations caused large fitness loss in a significant epistatic fashion. >>

Peter B. Otoupal, William T. Cordell, et al. Multiplexed deactivated CRISPR-Cas9 gene expression perturbations deter bacterial adaptation by inducing negative epistasis. Comm  Biol 1 (129) Sept 3, 2018

https://www.nature.com/articles/s42003-018-0135-2

# gst: even tight-binding billiards could exhibit chaotic behaviors

<< Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common property of all quantum-chaotic quadratic Hamiltonians studied in this context so far is the presence of random terms that act as a source of disorder. >>

AA << introduce tight-binding billiards in two dimensions, which are described by non-interacting spinless fermions on a disorder-free square lattice subject to curved open boundaries. >>

They <<  show that many properties of tight-binding billiards match those of quantum-chaotic quadratic Hamiltonians (..) these properties indeed appear to be consistent with the emergence of quantum chaos in tight-binding billiards. This statement nevertheless needs to be taken with some care since there exist a sub-extensive (in lattice volume) set of single-particle eigenstates that are degenerate in the middle of the spectrum at zero energy (i.e., zero modes), for which the agreement with RMT (random matrix theory) predictions may not be established. >>

Iris Ulcakar, Lev Vidmar. Tight-binding billiards. arXiv:2206.07078v1 [cond-mat.stat-mech]. Jun 14, 2022. 

https://arxiv.org/abs/2206.07078

Also

keyword 'billiard' in FonT

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

keyword 'chaos' | 'chaotic' in Font

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keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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

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

keywords: gst, billiard, chaos, chaotic behavior

# 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.

# gst: evolving disorder and chaos induces acceleration of elastic waves.

<< Static or frozen disorder, characterised by spatial heterogeneities, influences diverse complex systems, encompassing many-body systems, equilibrium and nonequilibrium states of matter, intricate network topologies, biological systems, and wave-matter interactions. >>

AA << investigate elastic wave propagation in a one-dimensional heterogeneous medium with diagonal disorder. (They) examine two types of complex elastic materials: one with static disorder, where mass density randomly varies in space, and the other with evolving disorder, featuring random variations in both space and time. (AA) results indicate that evolving disorder enhances the propagation speed of Gaussian pulses compared to static disorder. Additionally, (They) demonstrate that the acceleration effect also occurs when the medium evolves chaotically rather than randomly over time. The latter establishes that evolving randomness is not a unique prerequisite for observing wavefront acceleration, introducing the concept of chaotic acceleration in complex media. >>️

M. Ahumada, L. Trujillo, J. F. Marín. Evolving disorder and chaos induces acceleration of elastic waves. arXiv: 2403.02113v1 [cond-mat.dis-nn]. Mar 4, 2024. 

https://arxiv.org/abs/2403.02113

Also: waves, elastic, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, elastic, chaos, transition

# brain: actually there is chaos in the brain

<< Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes >>

Schiepek GK, Viol K, et al. Psychotherapy Is Chaotic - (Not Only) in a Computational World. Front Psychol. 2017 Apr 24;8:379. doi: 10.3389/fpsyg.2017.00379. eCollection 2017.

https://www.ncbi.nlm.nih.gov/m/pubmed/28484401/

<< Cambridge-based researchers provide new evidence that the human brain lives "on the edge of chaos", at a critical transition point between randomness and order. The study provides experimental data on an idea previously fraught with theoretical speculation >>

Public Library of Science. The Human Brain Is On The Edge Of Chaos. Mar 23, 2009.

https://www.sciencedaily.com/releases/2009/03/090319224532.htm  

Manfred G. Kitzbichler, Marie L. Smith, et al. Broadband Criticality of Human Brain Network Synchronization. PLoS Comput Biol 2009; 5 (3): e1000314. doi: 10.1371/journal.pcbi.1000314. Mar 20, 2009.

http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1000314

# gst: approaching chaotic dynamics to trace the complexity of rough nanostructured surfaces

AA << use the basic ingredients of chaotic dynamics (stretching and folding of phase space points) for the characterization of the complexity of microscopy images of rough surfaces. The key idea is to use an image as the initial condition of a chaotic discrete dynamical system, such as the Arnold cat map, and track its transformations during the first iterations of the map. Since the basic effects of the Arnold map are the stretching and folding of image texture, the application of the map leads to an enhancement of the high frequency content of images along with an increase of discontinuities in pixel intensities. (AA) exploit these effects to quantify the complexity of S type (lying between homogeneity and randomness) of the image texture since the first (enhancement of high frequencies) can be used to quantify the distance of texture from randomness and noise and the second (the proliferation of discontinuities) the distance from order and homogeneity. The method is validated in synthetic images which are generated from computer generated surfaces with controlled correlation length and fractal dimension and it is applied in real images of nanostructured surfaces obtained from a scanning electron microscope with very interesting results. >>️

A. Kondi, V. Constantoudis, P. Sarkiris, K. Ellinas, and E. Gogolides. Using chaotic dynamics to characterize the complexity of rough surfaces. Phys. Rev. E 107, 014206. Jan 11, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.014206

https://twitter.com/PhysRevE/status/1613569770338533376

Also

Able to track changes in noise. 

(quasi-stochastic poetry) 

Notes. Sep 13, 2007. 

https://inkpi.blogspot.com/2007/09/2147-able-to-track-changes-in-noise.html

Also

keyword 'chaos' | 'chaotic' in Font

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

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

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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

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

Keywords: gst, chaos, chaotic, nano, roughness, wetting, surfaces, etching scanning 

# gst: chaos from a double pendulum

<< Three double pendulums, all starting with near identical initial conditions, all rapidly diverging. >>

Ari Rubinsztejn. Chaos and the Double Pendulum. Nov 19, 2018.

https://gereshes.com/2018/11/19/chaos-and-the-double-pendulum

# gst: scrambling does not necessitate chaos.

<< Focusing on semiclassical systems, (AA) show that the parametrically long exponential growth of out-of-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in an integrable model. >>

Tianrui Xu, Thomas Scaffidi, Xiangyu Cao. Does scrambling equal chaos? arXiv:1912.11063v1 [cond-mat.stat-mech] Dec 23, 2019.

https://arxiv.org/abs/1912.11063

# gst: transitions, how two saddles can increase the transient times.

FIG. 8. Attractor and chaotic saddles (..) amplified around three bands of the chaotic attractor.  The global chaotic saddle is colored blue, and the local chaotic saddle is colored red. The attractors are colored black. 

AA << consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems, they are responsible for chaotic transients, fractal basin boundaries, chaotic scattering and they mediate interior crises. >>

<< In this work (AA) discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. (They) show how the presence of two saddles increase the transient times and analyze the phenomenon of crisis induced intermittency. >>️

Rodrigo Simile Baroni, Ricardo Egydio de Carvalho, et al. Chaotic saddles and interior crises in a dissipative nontwist system. arXiv: 2211.06921v1 [nlin.CD]. Nov 13, 2022. 

https://arxiv.org/abs/2211.06921

Also

keyword 'intermittency' in FonT

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

keyword 'dissipation' in FonT

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

keyword 'saddle' in FonT

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keyword 'chaos' | 'chaotic' in Font

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keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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

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

Keywords: gst, transitions, dissipation, 

dissipative systems, chaos, saddle, chaotic saddle, crisis, interior crisis, intermittency

# gst: Parrondo paradox revisited, a chaotic switching approach

<< Parrondo's paradox is a phenomenon where the switching of two losing games results in a winning outcome. >>

<< Suppose I present to you the outcome of the quantum walker at the end of 100 coin tosses, knowing the initial position, can you tell me the sequence of tosses that lead to this final outcome?" (..) In the case of random switching, it is almost impossible to determine the sequence of tosses that lead to the end result. However, for periodic tossing, we could get the sequence of tosses rather easily, because a periodic sequence has structure and is deterministic. >> Joel Lai.

<< This led to the idea of incorporating chaotic sequences as a means to perform the switching. The authors discovered that using chaotic switching through a pre-generated chaotic sequence significantly enhances the work. For an observer who does not know parts of the information required to generate the chaotic sequence, deciphering the sequence of tosses is analogous to determining a random sequence. However, for an agent with information on how to generate the chaotic sequence, this is analogous to a periodic sequence. According to the authors, this information on generating the chaotic sequence is likened to the keys in encryption. >>

Using quantum Parrondo's random walks for encryption. Singapore University of Technology and Design. Oct15, 2021.

https://phys.org/news/2021-10-quantum-parrondo-random-encryption.html

Joel Weijia Lai, Kang Hao Cheong. Chaotic switching for quantum coin Parrondo's games with application to encryption. Phys. Rev. Research 3, L022019. June 2, 2021. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L022019

Also

<< usando l'output di una logistica (per certi valori dei parms) un ipotetico Donald potrebbe avere il vezzo di ottenere stessi risultati con serialita' numerica generata meccanicamente anziche' in modalita' casuale; >>️

#POTUS race: Donald, what he can do (with less than four lines ...). FonT. May 23, 2016. 

https://flashontrack.blogspot.com/2016/05/p-usa-potus-race-donald-what-he-can-do.html

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

Also

keyword 'chaos' | 'chaotic' in Font

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

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

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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

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

keywords: gst, games, life, chaos, Parrondo, Parrondo chaotic switching approach

# gst: solitary wave billiards

<<  In the present work (AA) introduce the concept of solitary wave billiards. I.e., instead of a point particle, (they) consider a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. >>

J. Cuevas-Maraver, P.G. Kevrekidis, H. Zhang. Solitary wave billiards. arXiv: 2203.09489v1 [nlin.PS]. Mar 17, 2022. 

https://arxiv.org/abs/2203.09489

Also 

keyword 'chaos' | 'chaotic' in Font

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

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

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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

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

keyword | 'soliton' in FonT

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

keywords: gst, waves, solitons, billiard, chaos 

# s-phys: "entanglement entropy of a qubit", the begin ...

<< All systems are fundamentally quantum systems (..) but the means of describing in a quantum sense the chaotic behavior of, say, air molecules in an evacuated room, remains limited >>

<< To investigate, [AA] devised an experiment using three quantum bits, the basic computational units of the quantum computer >>

<< By manipulating these qubits with electronic pulses, [AA] caused them to interact, rotate and evolve in the quantum analog of a highly sensitive classical [chaotic] system >>

<< The result is a map of entanglement entropy of a qubit that, over time, comes to strongly resemble that of classical dynamics — the regions of entanglement in the quantum map resemble the regions of chaos on the classical map >>

Sonia Fernandez. Researchers at UCSB blur the line between classical and quantum physics by connecting chaos and entanglement.  Monday, July 11, 2016

http://www.news.ucsb.edu/2016/017014/entanglement-chaos

C. Neill, P. Roushan, et al.  Ergodic dynamics and thermalization in an isolated quantum system. Nature Physics (2016) DOI: doi:10.1038/nphys3830. Published online 11 July 2016

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3830.html