# gst: apropos of viscoelastic flow instabilities, uncertainty in elastic turbulence.

<< Elastic turbulence can lead to increased flow resistance, mixing and heat transfer. Its control - either suppression or promotion - has significant potential, and there is a concerted ongoing effort by the community to improve our understanding. >>

AA << identify four regimes of uncertainty evolution, characterised by I) rapid transfer to large scales, with large scale growth rates of τ6 (where τ represents time), II) a dissipative reduction of uncertainty, III) exponential growth at all scales, and IV) saturation. These regimes are governed by the interplay between advective and polymeric contributions (which tend to amplify uncertainty), viscous, relaxation and dissipation effects (which reduce uncertainty), and inertial contributions. >>

<< In elastic turbulence, reducing Reynolds number increases uncertainty at short times, but does not significantly influence the growth of uncertainty at later times. At late times, the growth of uncertainty increases with Weissenberg number, with decreasing polymeric diffusivity, and with the logarithm of the maximum length scale, as large flow features adjust the balance of advective and relaxation effects. >>

Jack R. C. King, Robert J. Poole, et al. Uncertainty in Elastic Turbulence. arXiv: 2501.09421v1 [physics.flu-dyn]. Jan 16, 2025. 

https://arxiv.org/abs/2501.09421

Also: uncertainty, elastic, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, uncertainty, elastic, elasticity, turbulence 

# gst: uncertainty growth in stably stratified turbulence.

<< ️(AA) investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, (They) quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. >>

<< ️At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. (AA) systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. >>

<< (They) find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. >>

<< ️An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. (AA) results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows. >>

Mrinal Jyoti Powdel, Samriddhi Sankar Ray. Uncertainty growth in stably stratified turbulence. Phys. Rev. Fluids 11, 064615. Jun 23, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/xblr-vpl3

arXiv: 2512.05656v1 [physics.flu-dyn].

https://arxiv.org/abs/2512.05656

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

Keywords: gst, chaos, turbulence, transitions, uncertainty growth, three-dimensional turbulence, stratified turbulence, infinitesimal perturbations, stratification strength, anisotropy. 

# brain: ubiquity of uncertainty in neuron systems.

AA << demonstrate that final-state uncertainty is ubiquitous in multistable systems of coupled neuronal maps, meaning that predicting whether one such system will eventually be chaotic or nonchaotic is often nearly impossible. (They) propose a "chance synchronization" mechanism that governs the emergence of unpredictability in neuron systems and support it by using basin classification, uncertainty exponent, and basin entropy techniques to analyze five simple discrete-time systems, each consisting of a different neuron model. >>

Their << ️results illustrate that uncertainty in neuron systems is not just a product of noise or high-dimensional complexity; it is also a fundamental property of low-dimensional, deterministic models, which has profound implications for understanding brain function, modeling cognition, and interpreting unpredictability in general multistable systems. >>

Brandon B. Le, Bennett Lamb, et al. Ubiquity of Uncertainty in Neuron Systems. arXiv: 2507.15702v1 [q-bio.NC]. Jul 21, 2025.

https://arxiv.org/abs/2507.15702

Also: brain, uncertainty, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: brain, uncertainty, noise, coupled neuronal maps, chance synchronization.

# brain: network representations reveal structured uncertainty in music.

<< ️Music, as a structured yet perceptually rich experience, can be modeled as a network to uncover how humans encode and process auditory information. While network-based representations of music are increasingly common, the impact of feature selection on structural properties and cognitive alignment remains underexplored. >>

<< ️In this study, (AA) evaluated eight network models, each constructed from symbolic representations of piano compositions using distinct combinations of pitch, octave, duration, and interval, designed to be representative of existing approaches in the literature. By comparing these models through topological metrics, entropy analysis, and divergence with respect to inferred cognitive representations, (They) assessed both their structural and perceptual efficiency.  >>

<< ️(AA) findings reveal that simpler, feature-specific models better match human perception, whereas complex, multidimensional representations introduce cognitive inefficiencies. These results support the view that humans rely on modular, parallel cognitive networks--an architecture consistent with theories of predictive processing and free energy minimization. >>

<< ️Moreover, (AA) find that musical networks are structurally organized to guide attention toward transitions that are both uncertain and inferable. The resulting structure concentrates uncertainty in a few frequently visited nodes, creating local entropy gradients that alternate between stable and unpredictable regions, thereby enabling the expressive dynamics of tension and release that define the musical experience. >> 

<< ️These findings show that network structures make the organization of uncertainty in music observable, offering new insight into how patterned flows of expectation shape perception, and open new directions for studying how musical structures evolve across genres, cultures, and historical periods through the lens of network science. >>

Lluc Bono Rosselló, Robert Jankowski, et al. Network representations reveal structured uncertainty in music. arXiv: 2509.14053v1 [physics.soc-ph]. 17 Sep 17,  2025.

https://arxiv.org/abs/2509.14053

Also: brain, music, jazz, perception, uncertainty, network, in https://www.inkgmr.net/kwrds.html 

Keywords: brain, music, jazz, perception, auditory information, networks, structural properties, cognitive alignment, uncertainty, uncertain-- inferable transitions.

# gst: apropos of uncertainty, notes on uncertainty, information, and classical dynamics.

<< Survival in this world is an adventure because we are so ignorant and everything around us seems so uncertain. In fact, it is hard to think of any realistic phenomenon that is completely free from one of the three kinds of uncertainty—deterministic (chaotic), stochastic, and quantum; more often than not, all of the three are present in various degrees. Thus, in order to gain any knowledge about any realistic system, one must understand how to characterize, quantify, and interpret these uncertainties. >>️

Sagar Chakraborty. Eclectic Notes on Uncertainty, Information, and Classical Dynamics. arXiv: 2404.13511v1 [physics.class-ph]. Apr 21, 2024.

https://arxiv.org/abs/2404.13511

Also: uncertainty, noise, error, in  https://www.inkgmr.net/kwrds.html 

Keywords: gst, information, uncertainty, ambiguity, noise, error 

# gst: taming uncertainty, a tutorial by NaN et Al.

<< All models are wrong, but some are useful. >>. George Box. ️

Nan Chen, Stephen Wiggins, Marios Andreou. Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification - A Tutorial for Beginners. arXiv: 2408.01823v1 [math.DS]. Aug 3, 2024. 

https://arxiv.org/abs/2408.01823

Also: NaN 'Not a Number'. In: Onda pneica. Apr 10, 2005 (quasi-stochastic poetry) https://inkpi.blogspot.com/2005/04/1694b-onda-pneica.html ;  nan(). In: Linux manual. https://www.man7.org/linux/man-pages/man3/nanf.3.html

Also: << Amico, qualunque  cosa suonerai . . . >>. Jelly Roll Morton. In: Soniche a ramulo. Jan 28, 2007 (quasi-stochastic poetry). https://inkpi.blogspot.com/2007/01/2113-soniche-ramulo.html  

Also: uncertainty, Mr. Jelly Roll Morton, jazz, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, uncertainty, Jelly Roll, jazz

# gst: approaching uncertainty among many-body real-time dynamics

<< Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. >>️

AA << examines the interplay of errors arising from simulation of approximate time evolution with those due to practical, real-world device constraints. >>️

Nikita A. Zemlevskiy, Henry F. Froland, Stephan Caspar. Optimization of algorithmic errors in analog quantum simulations. Phys. Rev. A 109, 052425. May 15, 2024. 

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.052425

<< The new technique focuses on two sources of error that arise from the approximations used to map the quantum system of interest to the analog quantum simulator. In a real-world simulator, these error sources are linked in a complex way, and individually minimizing each error can increase the overall uncertainty of a simulation. (AA) tackled this problem by first isolating the two error sources and then carefully studying their interplay. This analysis enabled the researchers to finely tune a simulation’s parameters to minimize its overall uncertainty and to maximize its precision. >>️

Ryan Wilkinson. Quantifying Uncertainties in Quantum Simulations. 

Physics 17, s51. May 15, 2024. 

https://physics.aps.org/articles/v17/s51

Also: uncertainty, error, noise in https://www.inkgmr.net/kwrds.html 

Keywords: gst, uncertainty, error, noise

# gst: the physics of squeezing; how to squeeze out (quantum) noise

<< 'Squeezing' is used in physics, among other things, to improve the resolution of measuring instruments. It allows disturbing noise to be suppressed in a way that smaller signals can be detected more sensitively. (..) (AA) has now been able to show how such a squeezed state can be measured in a much simpler way than with the existing methods. Moreover, the new method allows examining squeezed states in systems where such measurements were not possible before. >> [1]

<< In the experiment (..) the thermal fluctuations of a vibrating nanomechanical string resonator are squeezed. The nanostring can be thought of as a tiny guitar string, a thousand times thinner and shorter than a human hair. (..)  If the string is deflected far enough, it ceases to behave linearly. This means that the force that deflects the string is no longer proportional to the force that pulls it back to its original position. The strong drive alters the thermal fluctuations as a result of a violation of the time reversal symmetry. In phase space, they no longer look like a circle but like an ellipse: At least in one direction, its diameter, i.e. the noise, becomes significantly smaller—it is squeezed. >> [1]

<< Quantum squeezing was a theory that was first proposed in the 1980s, the general idea being that quantum vacuum noise can be represented as a sphere of uncertainty along two main axes: phase and amplitude. If this sphere were squeezed, like a stress ball, in a way that constricted the sphere along the amplitude axis, this would in effect shrink the uncertainty in the amplitude state of a vacuum (the squeezed part of the stress ball), while increasing the uncertainty in the phase state (stress ball's displaced, distended portion). Since it is predominantly the phase uncertainty that contributes noise to LIGO, shrinking it could make the detector more sensitive to astrophysical signals. (..) The heart of the squeezer is an optical parametric oscillator, or OPO — a bowtie-shaped device that holds a small crystal within a configuration of mirrors. When the researchers direct a laser beam to the crystal, the crystal's atoms facilitate interactions between the laser and the quantum vacuum in a way that rearranges their properties of phase versus amplitude, creating a new, "squeezed" vacuum that then continues down each of the detector's arm as it normally would. This squeezed vacuum has smaller phase fluctuations than an ordinary vacuum, allowing scientists to better detect gravitational waves. >> [2]

[1] - Measure squeezing in a novel way. University of Konstanz. Jun 25, 2020.   https://phys.org/news/2020-06-measure-squeezing-in-a-novel.html ; 

J. S. Huber, G. Rastelli, et al. Spectral Evidence of Squeezing of a Weakly Damped Driven Nanomechanical Mode.  Phys. Rev. X 10, 021066 – Jun 23,  2020.   https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.021066 

[2] - Jennifer Chu. New instrument extends LIGO’s reach. Technology "squeezes" out quantum noise so more gravitational wave signals can be detected. MIT. Dec 5, 2019.   https://news.mit.edu/2019/ligo-reach-quantum-noise-wave-1205

# 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 

# brain: spontaneous emergence of metacognition in neuronal computation.

<< ️Metacognition, a hallmark of human intelligence, enables individuals to assess prediction uncertainty, providing an advantage over artificial intelligence in anticipating risks and performing tasks that demand trustworthiness and reliability. >>

<< ️Here, (AA) demonstrate that metacognition can naturally emerge in recurrent neural networks trained on cognitive tasks without guidance from any probabilistic inference rules or additional network architectures. Through naturally embedded nonlinear coupling with the mean of the network output, the covariance of the network output engages in metacognition by assessing the uncertainty associated with the mean, which represents the task responses. >>

<< ️(AA) further propose testable predictions about how key features of neuronal computation in the brain—noise, neuronal correlations, and heterogeneity—contribute to metacognition. >>

Hengyuan Ma, Wenlian Lu, Jianfeng Feng. Spontaneous emergence of metacognition in neuronal computation. Phys. Rev. Research 7, 033188. Aug 22, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/f1hv-bf1f

Also: brain, network, uncertainty, noise, chaos, in  https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, cognition, metacognition, learning, memory, networks, biological neural networks, biological information processing, decision making, uncertainty, stochasticity, noise, chaos.

# behav: the benefit of ignorance for traffic through a random congestible network.

<< When traffic is routed through a network that is susceptible to congestion, the self-interested decisions made by individual users do not, in general, produce the optimal flow. This discrepancy is quantified by the so-called "price of anarchy." >>

AA << consider whether the traffic produced by self-interested users is made better or worse when users have uncertain knowledge about the cost functions of the links in the network, and define a parallel concept that (They) call the "price of ignorance."  >>

AA << introduce a simple model in which fast, congestible links and slow, incongestible links are mixed randomly in a large network and users plan their routes with finite uncertainty about which of the two cost functions describes each link. >>

<< One of (Their) key findings is that a small level of user ignorance universally improves traffic, regardless of the network composition. Further, there is an optimal level of ignorance which, in (the) model, causes the self-interested user behavior to coincide with the optimum. Many features of (AA) model can be understood analytically, including the optimal level of user ignorance and the existence of critical scaling near the percolation threshold for fast links, where the potential benefit of user ignorance is greatest. >>️

Alican Saray, Calvin Pozderac, et al. The benefit of ignorance for traffic through a random congestible network. arXiv: 2503.09684v1 [cond-mat.dis-nn]. Mar 12, 2025.

https://arxiv.org/abs/2503.09684

Also:  network, behav, random, uncertainty, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, behavior,  randomness, uncertainty, price of anarchy, price of ignorance

# life: detecting hallucinations (in large language models) using semantic entropy.

<< Large language model (LLM) systems, such as ChatGPT or Gemini, can show impressive reasoning and question-answering capabilities but often ‘hallucinate’ false outputs and unsubstantiated answers. >>

<< Here (AA) develop new methods grounded in statistics, proposing entropy-based uncertainty estimators for LLMs to detect a subset of hallucinations— confabulations— which are arbitrary and incorrect generations. (Their) method addresses the fact that one idea can be expressed in many ways by computing uncertainty at the level of meaning rather than specific sequences of words. >>

Their method << works across datasets and tasks without a priori knowledge of the task, requires no task-specific data and robustly generalizes to new tasks not seen before. By detecting when a prompt is likely to produce a confabulation, helps users understand when they must take extra care with LLMs and opens up new possibilities for using LLMs that are otherwise prevented by their unreliability. >>️️

Sebastian Farquhar, Jannik Kossen, et al. Detecting hallucinations in large language models using semantic entropy. Nature 630, 625–630. Jun 19, 2024.

https://www.nature.com/articles/s41586-024-07421-0

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

Keywords: life, artificial intelligence,  LLMs, confabulations, uncertainty, hallucinations, entropy, semantic entropy

# life: apropos of birth-and-death processes, framework for fluctuating times and counting observables in stochastic excursions.

<< ️Many natural systems exhibit dynamics characterized by alternating phases or recurring sets of states. Describing the fluctuations of such systems over stochastic trajectories is necessary across diverse fields, from biological motors to quantum thermal machines. >>

<< ️In an accompanying Letter, (AA) introduced the notion of stochastic excursions−a framework to analyze out of equilibrium processes via sub-trajectories. Through counting observables, this framework captures finite-time fluctuations and trajectory-level behavior, which provides insights into thermodynamical trade-offs between thermodynamic quantities of interest, such as entropy production and dynamical activity. >>

<< ️In this work, (AA) enhance this formalism by providing a suite of technical results on how to efficiently compute excursion-related quantities. (Their) analytical results provide explicit formulas for general moments of counting variables and excursion duration, as well as their covariance and conditional moments. (They) show that excursion statistics recover full counting statistics results, and uncover a relation between fluctuations of counting observables at single-excursion level and the steady state diffusion coefficient (noise). >> 

<< ️(AA) also discuss a fluctuation theorem for individual excursions and show that it implies a modified thermodynamic uncertainty relation at the excursion level. In addition, (They) explore how analyzing excursions and using the results developed here can yield insights into three problems of interest: the three-qubit absorption refrigerator, cellular sensing, and birth-and-death processes. >>

Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Framework for fluctuating times and counting observables in stochastic excursions.

Phys. Rev. E 114, 024129. Aug 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/jydr-1853

arXiv: 2506.05160v3 [cond-mat.stat-mech]. Aug 19, 2026.

https://arxiv.org/abs/2506.05160

Also: Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Counting observables in stochastic excursions. Phys. Rev. E 114, L022102 (2026). 

https://journals.aps.org/pre/abstract/10.1103/1blp-2b27

Also: walk, walking, uncertainty, fluctuations, random, noise, behav, Nomads, in https://www.inkgmr.net/kwrds.html 

Keywords: walk, walking, noise, uncertainty, behavior, fluctuations, randomness, stochasticity, stochastic excursions, Nomads. 

# gst: effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop.

<< ️The introduction of stochastic forcing to dynamical systems has been shown to induce qualitatively different behaviors, such as attractor hopping, to otherwise stable systems as they approach bifurcation. In this (AA) study, the effect of stochastic forcing on systems that have already undergone bifurcation and evolve on a chaotic attractor is explored. Markov and state-independent models of turbulence-induced stochasticity are developed, and their effects on a natural circulation loop operating in the chaotic regime are compared. >>

<< ️Stochasticity introduces considerable uncertainty into the duration of the initial chaotic transient but tends to accelerate it on average. An Ornstein-Uhlenbeck model of turbulent fluctuations is shown to produce results equivalent to a bootstrapped raw direct numerical simulation signal. >>

<< Similar, though less pronounced, effects are found for systems operating in the chaotic itinerant regime. The Markov model of chaotic itinerancy which is typically applied to this class of problems is shown to be invalid for this system and the Lorenz system, to which it has been applied in the past. >>

<< ️Off-discrete transitions and an upper limit on the time between flow reversals are explained by near misses of the attractor ruins caused by lingering excitation of high-order modes during chaotic itinerancy. >>

John Matulis, Hitesh Bindra. Effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop. Phys. Rev. E 112, 044223. Oct 23, 2025

https://journals.aps.org/pre/abstract/10.1103/42pn-wttx

Also: disorder & fluctuations, turbulence, attractor, chaos, transition, uncertainty, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, fluctuations, turbulence, attractor, chaos, transition, uncertainty, stochasticity, flow instability, chaotic itinerancy, noise-induced transitions.

# gst: trade-off between coherence and dissipation for excitable phase oscillators.

<< Thermodynamic uncertainty relation (TUR) bounds coherence in stochastic oscillatory systems. In this paper, (AA) show that both dynamical and thermodynamic bounds play important roles for the excitable oscillators, e.g. neurons. >>

<< Excitable systems such as neurons have distinctive coherence features compared with other oscillators having no excitability. >>️

AA << combined the well-established results, i.e. the fluctuation of the ISI (inter-spike-interval) limited by 1/3 and the coherence resonance phenomenon, together with the TUR developed in recent years to investigate the coherence in the excitable phase oscillators. (AA) find quite different trade-off relation in the subthreshold (excitable) region and superthreshold (oscillatory) region, separated by the SNIC (saddle-node on an invariant circle) bound but meanwhile lower bounded by the TUR. Furthermore, (They) found that there is an optimal entropy production corresponding to the maximum coherence, which could serve as an alternative interpretation of the coherence resonance. It implies that more entropy production does not necessarily result in higher accuracy of currents. >>️

Chunming Zheng. Trade-off between coherence and dissipation for excitable phase oscillators. arXiv: 2412.16603v1 [cond-mat.stat-mech]. Dec 21, 2024.

https://arxiv.org/abs/2412.16603

Also: brain, entropy, dissipation, uncertainty, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, neurons, entropy, oscillators, excitable phase oscillators, coherence, dissipation, uncertainty

# gst: noisy active matter

<< ️Noise threads every scale of the natural world. Once dismissed as mere background hiss, it is now recognized as both a currency of information and a source of order in systems driven far from equilibrium. >>

<< ️From nanometer-scale motor proteins to meter-scale bird flocks, active collectives harness noise to break symmetry, explore decision landscapes, and poise themselves at the cusp where sensitivity and robustness coexist. >>

<< ️(AA) review the physics that underpins this paradox: how energy-consuming feedback rectifies stochastic fluctuations, how multiplicative noise seeds patterns and state transitions, and how living ensembles average the residual errors. Bridging single-molecule calorimetry, critical flocking, and robophysical swarms, (They) propose a unified view in which noise is not background blur but a tunable resource for adaptation and emergent order in biology and engineered active matter. >>

Atanu Chatterjee, Tuhin Chakrabortty, Saad Bhamla. Noisy active matter. arXiv:2508.16031v1 [cond-mat.soft]. Aug 22, 2025.

https://arxiv.org/abs/2508.16031

Also: transition, noise, track changes in noise, erratic, random, error, mistake, uncertainty, disorder & fluctuations, walk, walking, dance, jazz, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, noise, track changes in noise, erratic, random, error, mistake, uncertainty, disorder & fluctuations, deposition (analogy, abstraction), walk, walking, life, dance, jazz. 

# gst: apropos of (unexpected?) transitions; the bizarre role of noise as operational control

<< ️Stochastic systems have a control-theoretic interpretation in which noise plays the role of control. In the weak-noise limit, relevant at low temperatures or in large populations, this leads to a precise mathematical mapping: The most probable trajectory between two states minimizes an action functional and corresponds to an optimal control strategy.  >>

<< ️In Langevin dynamics, the noise term itself serves as the control. For general Markov jump processes, such as chemical reaction networks or electronic circuits, (AA) use the Doi-Peliti formalism to identify the “response” (or “momentum”) field 𝜋 as the control variable. This resolves a long-standing interpretational problem in the field-theoretic description of stochastic systems: Although 𝜋 evolves backward in time, it has a clear physical role as the control that steers the system along rare trajectories. >>

<< ️This implies that nature is constantly sampling control strategies.  >>

<< ️(AA) illustrate the mapping on multistable chemical reaction networks, systems with unstable fixed points, and specifically on stochastic resonance and Brownian ratchets. >>

<< ️ The noise-control mapping justifies agential descriptions of these phenomena and builds intuition for otherwise puzzling phenomena of stochastic systems: why probabilities are generically nonsmooth functions of state out of thermal equilibrium; why biological mechanisms can work better in the presence of noise; and how agential behavior emerges naturally without recourse to mysticism. >>

Eric De Giuli. Noise equals control. Phys. Rev. E 112, 024142. Aug 29, 2025.

https://journals.aps.org/pre/abstract/10.1103/vlx8-spc6

arXiv:2503.15670v3 [q-bio.MN]. 

https://arxiv.org/abs/2503.15670

Also: transition, noise, track changes in noise, erratic, random, error, mistake, uncertainty, disorder & fluctuations, walk, walking, dance, jazz, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, noise, track changes in noise, erratic, random, error, mistake, uncertainty, disorder & fluctuations, deposition (analogy, abstraction), walk, walking, life, dance, jazz. 

# gst: ambiguous signals and efficient codes.

<< In many biological networks the responses of individual elements are ambiguous. (AA) consider a scenario in which many sensors respond to a shared signal, each with limited information capacity, and ask that the outputs together convey as much information as possible about an underlying relevant variable. In a low noise limit where can make analytic progress, (They) show that individually ambiguous responses optimize overall information transmission. >>

Marianne Bauer, William Bialek. Ambiguous signals and efficient codes. arXiv: 2512.23531v1 [physics.bio-ph]. Dec 29, 2025. 

https://arxiv.org/abs/2512.23531

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

Keywords: gst, networks, uncertainty, noise, ambiguity, ambiguous encodings, mixed selectivity, optimization, signal-to-noise ratio. 

# 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 

# acad: oops! the scientific world is abuzz ... scientists first and foremost should "embrace uncertainty" and "be thoughtful, open and modest." ...

<< The scientific world is abuzz following recommendations by two of the most prestigious scholarly journals – The American Statistician and Nature – that the term "statistical significance" be retired. In their introduction to the special issue of The American Statistician on the topic, the journal’s editors urge "moving to a world beyond 'p<0.05,'" the famous 5 percent threshold for determining whether a study’s result is statistically significant.  (..) scientists first and foremost should "embrace uncertainty" and "be thoughtful, open and modest." >>

Valen E. Johnson.  Is it the end of 'statistical significance'? The battle to make science more uncertain. Texas A&M University. April 1, 2019.
 
http://theconversation.com/is-it-the-end-of-statistical-significance-the-battle-to-make-science-more-uncertain-114161  

Ronald L. Wasserstein, Allen L. Schirm,   Nicole A. Lazar. Moving to a World Beyond "p < 0.05". Am Statistician. Pages 1-19  Mar 20,  2019. doi: 10.1080/ 00031305.2019.1583913

https://www.tandfonline.com/doi/full/10.1080/00031305.2019.1583913

Scientists rise up against statistical significance. Valentin Amrhein, Sander Greenland, Blake McShane and more than 800 signatories call for an end to hyped claims and the dismissal of possibly crucial effects. Nature. COMMENT. Mar 20, 2019.

https://www.nature.com/articles/d41586-019-00857-9