# brain: apropos of mandering minds, the 'default mode' network.

<< When your mind is wandering, your brain’s “default mode” network is active. Its discovery 20 years ago inspired a raft of research into networks of brain regions and how they interact with each other. >>

<< The default mode was one of the first brain networks characterized by science. It consists of a handful of brain regions, including a few at the front of the brain, like the dorsal and ventral medial prefrontal cortices, and others scattered throughout the organ, like the posterior cingulate cortex, the precuneus and the angular gyrus. These regions are associated with memory, experience replay, prediction, action consideration, reward/ punishment and information integration. >> ️

<< The default mode is clearly up to something complicated; it’s involved in many different processes that can’t be neatly described. >>

<< “It’s kind of silly to think that we’re ever going to be like, ‘This one brain region or one brain network does one thing,’” (..). “I don’t think that’s how it works.” (..) “Network interactions are more elucidating to study in some ways than just a network in isolation because they do work together and then come apart and then change what they’re doing over time”. >> Lucina Uddin.️

Lucina Uddin << is particularly interested in how the default mode network interacts with the ️salience network, which seems to help us identify the most relevant piece of information at any given time. Her work suggests that the salience network detects when something is important to pay attention to and then acts as an off switch for the default mode network. >>

Vinod Menon << has developed what he calls️ ️the triple network theory. It posits that abnormal interactions between the default mode network, the salience network and a third one called the frontoparietal network could contribute to mental health disorders. >>️

Nora Bradford. What Your Brain Is Doing When You’re Not Doing Anything.  quantamagazine.org. Feb 5, 2024. 

https://www.quantamagazine.org/what-your-brain-is-doing-when-youre-not-doing-anything-20240205/

FonT: the cat when it is in a contemplative state ... Who knows in what forms and with what results an artificial intelligence (AI) will be able to structure itself in networks of this type.

Also: brain, brain default mode network, in  https://pubmed.ncbi.nlm.nih.gov/?term=brain+default+mode+network

Also: brain, salience network, in https://pubmed.ncbi.nlm.nih.gov/?term=brain+salience+network

Also: brain, triple network theory, in https://pubmed.ncbi.nlm.nih.gov/?term=brain+triple+network+theory

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

Keywords: brain, mind, default mode network, salience network, triple network theory, AI

# gst: neural networks know their knots.

<< The use of neural networks in physics is booming. Recently, the tool has helped researchers uncover everything from new magnetic materials (..) to ways to reduce noise in electron beams produced at synchrotrons (..) Seeking their own neural network success, (AA) wondered if the tool could classify knots, a computationally challenging problem. >>

They << applied two different neural networks to the problem—a recurrent neural network (RNN) and a feed-forward neural network (FFNN). >>

<< The RNN achieved 99% accuracy >>

 

Katherine Wright. Neural Networks Know Their Knots. Physics 13, s19. Feb 11, 2020.

https://physics.aps.org/articles/v13/s19.

img  https://physics.aps.org/assets/b3a39285-5bde-4137-8a54-5f9d9b9e2738/es19_1.png

Olafs Vandans, Kaiyuan Yang, et al. Identifying knot types of polymer conformations by machine learning. Phys. Rev. E 101, 022502. Feb 11, 2020.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.022502

Also: network, neuro, in: https://www.inkgmr.net/kwrds.html

Keywords: gst, network, neural network, knots

# gst: apropos of 'transitions', slow dynamics of complex connected networks can control the rate of demixing

<< A space- spanning network structure is a basic morphology in phase separation of soft and biomatter, alongside a droplet one. Despite its fundamental and industrial importance, the physical principle underlying such network- forming phase separation remains elusive. >>

AA << find that phase- separation dynamics is controlled by mechanical relaxation of the network- forming dense phase, whose limiting process is permeation flow of the solvent for colloidal suspensions and heat transport for pure fluids. This universal coarsening law would contribute to the fundamental physical understanding of network-forming phase separation. >>

Michio Tateno, Hajime Tanaka. Power-law coarsening in network-forming phase separation governed by mechanical relaxation. Nat Commun 12, 912. doi: 10.1038/  s41467-020-20734-8. Feb 10,  2021.

https://www.nature.com/articles/s41467-020-20734-8

️

Discovery of a new law of phase separation. University of Tokyo. Feb 10, 2021. 

https://phys.org/news/2021-02-discovery-law-phase.html

Also

keyword 'transition' in FonT

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

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

# gst: emergence of the traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera in a two-dimensional network

<< Neuronal synchronization being a phenomenon linked to several brain pathologies such as epilepsy, Parkinson diseases, Alzheimer, autism and schizophrenia, does not always appear in a singular way in neuronal networks. Its presence (state of coherence) accompanied simultaneously by an asynchronous state (state of incoherence) has been demonstrated (..) in the networks of identical oscillators not locally coupled. This phenomenon was later termed the chimera state. (..) Chimera states are analogously to the cerebral behaviors of certain aquatic mammals and migratory birds, which during their movements half part of their brains asleep while the rest are awake.  >>️

AA << study the emergence of the traveling chimera state in a two-dimensional network of (..) burst neurons with the mutual presence of local and non-local couplings. (AA) show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, ie the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of instantaneous local order parameter in two dimensions. >>️

Gael R. Simo, Patrick Louodop, et al. Traveling chimera patterns in two-dimensional neuronal network. arXiv:2106.08400v1. Jun 9, 2021.

https://arxiv.org/abs/2106.08400

# 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: self-repelling species could self-organize.

<< Catalytically active particles form clusters when they respond not only to their own chemical targets but to those of other catalysts, too. >>️

AA  << show that the phenomenon of self-organization depends strongly on the network topology. >>️

They << modeled a three-species system (..) systems where each species responds chemotactically only to its own substrate cannot self-organize unless one species is self-attracting. >>️

<< Next, they developed a model that allowed species to respond to both their substrates and their products. Pair interactions between different species in this more complex model drove an instability that spread throughout the three-species system, causing the catalysts to clump together. Surprisingly, this self-organization process occurred even among particles that were individually self-repelling. >>️

Rachel Berkowitz. Self-Repelling Species Still Self-Organize. Physics 16, s128. Sept 19, 2023. 

https://physics.aps.org/articles/v16/s128

Vincent Ouazan-Reboul, Ramin Golestanian, Jaime Agudo-Canalejo. Network effects lead to self-organization in metabolic cycles of self-repelling catalysts. Phys. Rev. Lett. 131, 128301. Sep 19, 2023. 

http://dx.doi.org/10.1103/PhysRevLett.131.128301

Also: self-assembly, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, self-assembly, network,  topology.

# behav: a viral marketing generated by low levels of advertising

<< What they discovered refutes Gladwell's (Malcolm Gladwell) concept that network position is always paramount. They found that in instances where there is even a small amount of advertising—even when it is just a quarter of a percent as strong as word-of-mouth—there's virtually no difference between the influence of the person at the center of a network and those further out on the string. >> 

 << It's not that word-of-mouth doesn't matter—it's that nobody is particularly important for the word-of-mouth process, (..) What we saw is that when advertising doesn't exist, when advertising is exactly zero, it looks like whoever is Mr. Popular, whoever has the most central connections, really matters. And in that scenario, if you start with that person at the center of the network, like the leader of an organization or company, rather than the intern, then whatever you're selling gets an uptick. >> Gabriel Rossman. 

Jessica Wolf. Forget what you think you know about viral marketing, study suggests. University of California, Los Angeles. Feb 25, 2021.

https://phys.org/news/2021-02-viral.html  

Gabriel Rossman,  Jacob C. Fisher. Network hubs cease to be influential in the presence of low levels of advertising. PNAS. 118 (7) e2013391118. doi: 10.1073/ pnas.2013391118. Feb 16, 2021. 

https://www.pnas.org/content/118/7/e2013391118

FonT

this could also occur in the generation of fake news ...

keyword "fake" in FonT

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

# brain: to trace transitions from consciousness to unconscious subliminal perception

AA << study the transition in the functional networks that characterize the human brains’ conscious-state to an unconscious subliminal state of perception >>

<< the most inner core (i.e., the most connected kernel) of the conscious-state functional network corresponds to areas which remain functionally active when the brain transitions from the conscious-state to the subliminal-state. That is, the inner core of the conscious network coincides with the subliminal-state. >>

<< This finding imposes constraints to theoretical models of consciousness, in that the location of the core of the functional brain network is in the unconscious part of the brain rather than in the conscious state as previously thought. >>

Francesca Arese Lucini, Gino Del Ferraro, et al. How the Brain Transitions from Conscious to Subliminal Perception. Neuroscience. Volume 411, Jul 15, 2019, Pages 280-290.

https://www.sciencedirect.com/science/article/abs/pii/S0306452219302052

<< The k-core of the conscious state is reduced to three active regions of the brain, the fusiform gyrus (left and right) and the precentral gyrus. These regions are the only active in the subliminal state. >>

Physicists use mathematics to trace neuro transitions. City College of New York. Jul 18, 2019.

https://m.medicalxpress.com/news/2019-07-physicists-mathematics-neuro-transitions.html  

# gst: soft and stiff modes in colloidal particle networks

<< Floppy microscale spring networks are widely studied in theory and simulations, but no well-controlled experimental system currently exists. >> 

AA << show that square lattices consisting of colloid-supported lipid bilayers functionalized with DNA linkers act as microscale floppy spring networks. (AA) extract their normal modes by inverting the particle displacement correlation matrix, showing the emergence of a spectrum of soft modes with low effective stiffness in addition to stiff modes that derive from linker interactions. >>

<< Evaluation of the softest mode, a uniform shear mode, reveals that shear stiffness decreases with lattice size. >>

 AA << results reveal the importance of entropic steric effects. >>

️

Julio Melio, Silke E. Henkes, Daniela J. Kraft. Soft and Stiff Normal Modes in Floppy Colloidal Square Lattices. Phys. Rev. Lett. 132, 078202. Feb 14, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.078202

Also: particle, nano, colloids, network, in https://www.inkgmr.net/kwrds.html

Keywords: gst, particle, nano, colloids, network, colloidal network

# life: even a slime mold takes smart decisions about the future (Physarum polycephalum)

<< The slime mold Physarum polycephalum has been puzzling researchers for many decades. Existing at the crossroads between the kingdoms of animals, plants and fungi, this unique organism provides insight into the early evolutionary history of eukaryotes. Its body is a giant single cell made up of interconnected tubes that form intricate networks. This single amoeba-like cell may stretch several centimeters or even meters, featuring as the largest cell on earth in the Guinness Book of World Records. >>

<< The striking abilities of the slime mold to solve complex problems such as finding the shortest path through a maze earned it the attribute "intelligent," intrigued the research community and kindled questions about decision making on the most basic levels of life. >> 

<<  The decision-making ability of Physarum is especially fascinating given that its tubular network constantly undergoes fast reorganization—growing and disintegrating its tubes—while completely lacking an organizing center. The researchers discovered that the organism weaves memories of food encounters directly into the architecture of the network-like body and uses the stored information when making future decisions. >>

Researchers find a single-celled slime mold with no nervous system that remembers food locations. Max Planck Society. Feb 23, 2021.  

https://phys.org/news/2021-02-single-celled-slime-mold-nervous-food.html

Mirna Kramar, Karen Alim. Encoding memory in tube diameter hierarchy of living flow network. PNAS. 118 (10).  e2007815118. doi: 10.1073/ pnas.2007815118

https://www.pnas.org/content/118/10/e2007815118 

# brain: networks that may underlie our perception of free will

<< Our perception of free will is composed of a desire to act (volition) and a sense of responsibility for our actions (agency). >>

AA << study focal brain lesions that disrupt volition, causing akinetic mutism (..), or disrupt agency, causing alien limb syndrome (..), to better localize these processes in the human brain. >>

<< Lesion locations causing akinetic mutism all fell within one network, defined by connectivity to the anterior cingulate cortex. Lesion locations causing alien limb fell within a separate network, defined by connectivity to the precuneus. >>

AA << results demonstrate that lesions in different locations causing disordered volition and agency localize to unique brain networks, lending insight into the neuroanatomical substrate of free will perception. >>

R. Ryan Darby, Juho Joutsa, et al. Lesion network localization of free will. PNAS Oct 1, 2018.  doi: 10.1073/pnas.1814117115  

http://www.pnas.org/content/early/2018/09/25/1814117115 

Study looks at brain networks involved with free will. Vanderbilt University Medical Center. Oct 1, 2018

https://m.medicalxpress.com/news/2018-10-brain-networks-involved-free.html  

# s-brain: imprinting and recalling inside a single network of brain cells with thin beam of light (as if switching on a TV ) ...

<< a set of neurons trained to fire in unison could be reactivated as much as a day later if just one neuron in the network was stimulated. >>

AA <<  injected the mouse with a virus containing light-sensitive proteins engineered to reach specific brain cells. Once inside a cell, the proteins allowed researchers to remotely activate the neuron with light, as if switching on a TV >>

<< But then I saw the results and said "Holy moly, this whole thing is plastic". We're dealing with a plastic computer that's constantly learning and changing >>  Rafael Yuste.

Researchers Reprogram Network of Brain Cells in Mice With Thin Beam of Light. Neuroscience News. August 11, 2016

http://neurosciencenews.com/optogenetics-brain-plasticity-4832/

Luis Carrillo-Reid, Weijian Yang, et al. Imprinting and recalling cortical ensembles. Science.12 Aug 2016: Vol. 353,  Issue  6300,  pp.  691-694 DOI:  10.1126/science.aaf7560.

http://science.sciencemag.org/content/353/6300/691

# gst: an approach to delay solitary states within complex networks

AA << present a technique to engineer solitary states by means of delayed links in a network of neural oscillators and in coupled chaotic maps. Solitary states are intriguing partial synchronization patterns, where a synchronized cluster coexists with solitary nodes displaced from this cluster and distributed randomly over the network. >>

<< It is shown that the extent of displacement and the position of solitary elements can be completely controlled by the choice (values) and positions (locations) of the incorporated delays, reshaping the delay engineered solitary states in the network. >>

Leonhard Schulen, Saptarshi Ghosh, et al. Delay engineered solitary states in complex networks. arXiv:1908.01295v1 [nlin.AO] Aug 4, 2019.

https://arxiv.org/abs/1908.01295

# gst: an approach to information content in the music of J. S. Bach

<< Music has a complex structure that expresses emotion and conveys information. Humans process that information through imperfect cognitive instruments that produce a gestalt, smeared version of reality. What is the information that humans see? And how does their perception relate to (and differ from) reality? To address these questions quantitatively, (AA) analyze J. S. Bach's music through the lens of network science and information theory. >>

They << find that Bach's music is structured for efficient communication; that is, it communicates large amounts of information while maintaining small deviations of the inferred network from reality. >>

They << probe the network structures that enable this rapid and efficient communication of information -- namely, high heterogeneity and strong clustering. (..) More generally, (they) gain insight into features that make networks of information effective for communication. >>

Suman Kulkarni, Sophia U. David, et al. Information content of note transitions in the music of J. S. Bach. arXiv: 2301.00783v1 [physics.soc-ph]. Jan 2, 2023. 

https://arxiv.org/abs/2301.00783

Also

keyword 'music' in FonT

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

keyword 'jazz' in FonT

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

keyword 'jazz' in Notes 

(quasi-stochastic poetry)

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

Keywords: gst, music, jazz, information theory, note transitions, Bach

# gst: near the Hopf boundary, Intermittency and chimera states.

AA << study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. >>️

<< For analysis, (AA) first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. >>

<< Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks. >>️

Anjuman Ara Khatun, Yusra Ahmed Muthanna, et al. Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states. Phys. Rev. E 109, 034208. March 15, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.034208

Also: transition, intermittency, chaos, chimera, network, in https://www.inkgmr.net/kwrds.html

Keywords: gst, transition, intermittency, chaos, chimera, network

# gst: apropos of coexistence of coherent and incoherent oscillators, chaotic chimera attractors in a triangular network.

<< A prominent type of collective dynamics in networks of coupled oscillators is the coexistence of coherently and incoherently oscillating domains known as chimera states. >>️

<< In a three-population network of identical Kuramoto-Sakaguchi phase oscillators, stationary and periodic symmetric chimeras were previously studied on a reduced manifold in which two populations behaved identically. >>

<< In this paper, (AA) study the full phase space dynamics of such three-population networks. (They) demonstrate the existence of macroscopic chaotic chimera attractors that exhibit aperiodic antiphase dynamics of the order parameters. >>

<< The chaotic chimera states coexist with a stable chimera solution on the Ott-Antonsen manifold that displays periodic antiphase oscillation of the two incoherent populations and with a symmetric stationary chimera solution, resulting in tristability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold. >>️

Seungjae Lee, Katharina Krischer. Chaotic chimera attractors in a triangular network of identical oscillators. Phys. Rev. E 107, 054205. May 8, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.054205

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

Keywwords: gst, chimera, bifurcations, chaos, synchronization

# gst: sudden phase transitions among nonconservative system with nonreciprocal interactions

<< A nonconservative system with nonreciprocal interaction has been found to reveal exotic features where sudden phase transitions can occur. >>️

Here AA reported << the emanation of a chimera in a network of Stuart-Landau oscillators. >>

<< The findings could have pragmatic implications in the areas of active matter, networks, and photonics. >>

️

M. Paul Asir. Emergence of chimeras: An impetus by exceptional points. Phys. Rev. E 108, 024220. Aug 22, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.024220

Also: Stuart–Landau equation. 

https://en.m.wikipedia.org/wiki/Stuart%E2%80%93Landau_equation

Also: network, transition, chimera, chaos, in: https://www.inkgmr.net/kwrds.html

Keywords: network, transition, chimera, chaos, pattern formation

# life: transitions in the edges; to stimulate a shift in thinking, target small groups of people in the "outer edge" or fringe of a network.

<< social influencers are unlikely to change a person's behavior by example. To stimulate a shift in people's thinking, target small groups of people in the outer edge or fringe of a network. (..) as prominent and revered as social influencers seem to be, in fact, they are unlikely to change a person's behavior by example -- and might actually be detrimental to the cause. >>

<< When social influencers present ideas that are dissonant with their followers' worldviews (..) they can unintentionally antagonize the people they are seeking to persuade because people typically only follow influencers whose ideas confirm their beliefs about the world,"  >> Damon Centola. ️

<< To stimulate a shift in thinking, target small groups of people in the "outer edge" or fringe of a network. >>

️

Study finds surprising source of social influence. University of Pennsylvania.  Jul 20, 2021. 

https://www.sciencedaily.com/releases/2021/07/210720114345.htm

Douglas Guilbeault, Damon Centola.  Topological measures for identifying and predicting the spread of complex contagions. Nat Commun 12, 4430. doi: 10.1038/ s41467-021-24704-6. Jul 20  2021.

https://www.nature.com/articles/s41467-021-24704-6

Also

1829 - catalisi d' interferenza periferica (c.i.p.)  Notes. Nov 24, 2004. (quasi-stochastic poetry).

https://inkpi.blogspot.com/2004/11/1829-catalisi-d-interferenza.html

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

# s-brain: all rely on one central function: emulation

<< Our brain's fronto-parietal network is responsible for a range of highly diverse functions, from planning and executing movements to mental rotation, and from spatial attention to working memory. But how can a single network participate in such a wide variety of functions? >>

[AA]  << have recently put forward an original hypothesis — all these cognitive functions rely on one central function: emulation. This function creates an abstract dynamic 'image' of movements, thereby enabling the brain to strengthen its motor skills and construct a precise and lasting representation of them. >>

Acting and thinking — are they the same for our brain?

http://www.unige.ch/communication/communiques/en/2017/cdp120617/

Radek Ptak, Armin Schnider, Julia Fellrath. The Dorsal Frontoparietal Network: A Core System for Emulated Action. Trends in Cognitive Sciences. Publ. June 01, 2017. doi: 10.1016/j.tics.2017.05.002

http://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(17)30100-6

# gst: rare transitions in noisy net scenarios

AA << study small white noise perturbations of planar dynamical systems with heteroclinic networks in the limit of vanishing noise. (They)  show that the probabilities of transitions between various cells that the network tessellates the plane into decay as powers of the noise magnitude. (They) show that the most likely scenario for the realization of these rare transition events involves spending atypically long times in the neighborhoods of certain saddle points of the network. >>️

Yuri Bakhtin, Hong-Bin Chen, Zsolt Pajor-Gyulai. Rare transitions in noisy heteroclinic networks. arXiv: 2205.00326v1 [math.PR]. Apr 30, 2022.    https://arxiv.org/abs/2205.00326

Also

keyword 'noise'  in FonT 

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

keyword 'rumore'  in Notes

(quasi-stochastic poetry)

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

Keywords: gst, transitions, networks, heteroclinic networks, noise