# gst: networks of pendula with diffusive interactions, chaotic regime seems to emerge at low energies.

AA << study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian; as such, the energy is conserved. >>️

<< The behaviour observed showcases a mechanism for the appearance of chaotic oscillations in conservative systems. For Hamiltonians with two degrees of freedom, it has been shown how chaos can emerge near a saddle-centre equilibrium possessing a homoclinic orbit. (AA) have seen that higher-dimensional systems having mixed equilibria, i.e., generalisations of a saddle-center where the eigenvalues are only imaginary and reals, also show chaotic behaviour close to those points.  >>️

AA << complement the analysis with some numerical simulations showing the interplay between bifurcations of the origin and transitions to chaos of nearby orbits. A key feature is that the observed chaotic regime emerges at low energies. >>

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Riccardo Bonetto, Hildeberto Jardón-Kojakhmetov, Christian Kuehn. Networks of Pendula with Diffusive Interactions. arXiv: 2408.02352v1 [math.DS]. Aug 5, 2024.

https://arxiv.org/abs/2408.02352

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

Keywords: gst, pendulum, network, transition, chaos, bifurcation

# gst: emergent chirality in active rotation even with spontaneous chiral symmetry breaking.

<< Collective cell dynamics play a crucial role in many developmental and physiological contexts. While two-dimensional (2D) cell migration has been widely studied, how three-dimensional (3D) geometry and topology interplay with collective cell behavior to determine dynamics and functions remains an open question. >>️

<< Using murine pancreas-derived organoids as a model system, (AA) find that epithelial spheres exhibit persistent rotation, rotational axis drift, and rotation arrest. Using a 3D vertex model, (they) demonstrate how the combined action of traction force and polarity alignment can account for these distinct rotational dynamics near a solid to flow transition. Furthermore, (their) analysis shows that the spherical tissue rotates as an active solid occasionally switching to a flowing state and exhibits spontaneous chiral symmetry breaking. >>️

Tzer Han Tan, Aboutaleb Amiri, et al. Emergent chirality in active solid rotation of pancreas spheres. PRX Life 2, 033006. Aug 8, 2024.

https://journals.aps.org/prxlife/abstract/10.1103/PRXLife.2.033006

AA << say their work shows how symmetry-breaking processes in living active matter can be induced by the interplay of geometry, topology, and collective dynamics. >>️

Charles Day. Emergent Chirality in Active Rotation. Physics 17, s102. Aug 8, 2024. 

https://physics.aps.org/synopsis-for/10.1103/PRXLife.2.033006 

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

Keywords: gst, transition, chiral, chiral symmetry breaking 

# gst: tracking criticality in unknown noise

<< Many real-world systems undergo abrupt changes in dynamics as they move across critical points, often with dramatic and irreversible consequences. >>️

AA << aim to develop noise-robust indicators of the distance to criticality (DTC) for systems affected by dynamical noise in two cases: when the noise amplitude is either fixed or is unknown and variable across recordings. (They) present a highly comparative approach to this problem that compares the ability of over 7000 candidate time-series features to track the DTC in the vicinity of a supercritical Hopf bifurcation. >>️

<< in the variable-noise setting, where these conventional indicators perform poorly, (AA) highlight new types of high-performing time-series features and show that their success is accomplished by capturing the shape of the invariant density (which depends on both the DTC and the noise amplitude) relative to the spread of fast fluctuations (which depends on the noise amplitude). >>

AA << introduce a new high-performing time-series statistic, the rescaled autodensity (RAD), that combines these two algorithmic components. >>️

️

Brendan Harris, Leonardo L. Gollo, Ben D. Fulcher. Tracking the Distance to Criticality in Systems with Unknown Noise. Phys. Rev. X 14, 031021. Aug 8, 2024.

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.031021

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

Keywords: gst, noise, brain, mouse visual cortex

# ai-bot: Cybloids − Creation and Control of Cybernetic Colloids.

FIG. 11. Particle clusters formed for different parameters of the feedback potential.

AA << present an idea to create particles with freely selectable properties. The properties might depend, for example, on the presence of other particles (hence mimicking specific pair or many-body interactions), previous configurations (hence introducing some memory or feedback), or a directional bias (hence changing the dynamics). Without directly interfering with the sample, each particle is fully controlled and can receive external commands through a predefined algorithm that can take into account any input parameters. This is realized with computer-controlled colloids, which (AA) term cybloids - short for cybernetic colloids. >>

<< For a single particle, this programming can cause subdiffusive behavior or lend activity. For many colloids, the programmed interaction potential allows to select a crystal structure at wish. Beyond these examples, (AA) discuss further opportunities which cybloids offer. >>️

Debasish Saha, Sonja Tarama, et al. Cybloids − Creation and Control of Cybernetic Colloids. arXiv: 2408.00336v1 [cond-mat.soft]. 

https://arxiv.org/abs/2408.00336

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

Keywords: AI, Artificial Intell, BOT, AI-BOT, colloids, cybernetic colloids, cybloids

# gst: when a continuous attractor could survive seemingly destructive bifurcations

<< Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general--they are destroyed by most infinitesimal changes of the dynamical law that defines them. >>️

AA << build on the persistent manifold theory to explain the commonalities between bifurcations from and approximations of continuous attractors. Fast-slow decomposition analysis uncovers the persistent manifold that survives the seemingly destructive bifurcation. Moreover, recurrent neural networks trained on analog memory tasks display approximate continuous attractors with predicted slow manifold structures. >>️

<< continuous attractors are functionally robust and remain useful as a universal analogy for understanding analog memory. >>

Ábel Ságodi, Guillermo Martín-Sánchez, Piotr Sokół, Il Memming Park. Back to the Continuous Attractor. arXiv: 2408.00109v1 [q-bio.NC]. Jul 31, 2024. 

https://arxiv.org/abs/2408.00109

Also: attractor, analogy, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, attractor, continuous attractor, analogy, brain

# gst: evolution of turbulence using a random jet array

AA << perform a series of laboratory experiments in which (They) alter the parameters of the randomized algorithm, along with the jet spacing and outlet velocity of the jets. (They) first determine the location where turbulence transitions to a fully developed state and show that it is a function of jet penetration length, ℒ𝒥, and effective jet spacing, 𝑆𝑒. (AA)  identify three distinct regions for the spatial decay of turbulence in RJA (Random Jet Array) facilities and notably, (They) find different decay rates, unlike previous studies that report only one spatial decay rate using similar facilities. These regions are shown to depend on the variations of input parameters yet independent of the strength of the mean flow. (AA) also find the strength of the mean flow does not affect the homogeneity, nor the production, transport, or advection terms of the turbulent kinetic energy budget equation. >>

Finally, AA << address a longstanding question toward estimating turbulence metrics with an RJA based on the input parameters. >>

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Arefe Ghazi Nezami, Blair Anne Johnson. Evolution of turbulence using a random jet array. Phys. Rev. Fluids 9, 074610. Jul 26, 2024.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.074610

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

Keywords: gst, turbulence

# behav: swarms and hybrids, an approach to create and control collective motions (on demand)

AA << demonstrate that it is possible to generate coordinated structures in collective behavior at desired moments with intended global patterns by fine-tuning an inter-agent interaction rule. (Their) strategy employs deep neural networks, obeying the laws of dynamics, to find interaction rules that command desired collective structures. The decomposition of interaction rules into distancing and aligning forces, expressed by polynomial series, facilitates the training of neural networks to propose desired interaction models. Presented examples include altering the mean radius and size of clusters in vortical swarms, timing of transitions from random to ordered states, and continuously shifting between typical modes of collective motions. This strategy can even be leveraged to superimpose collective modes, resulting in hitherto unexplored but highly practical hybrid collective patterns, such as protective security formations. >>

Dongjo Kim, Jeongsu Lee, Ho-Young Kim. Navigating the swarm: Deep neural networks command emergent behaviours. arXiv: 2407.11330v1 [cs.NE]. Jul 16, 2024.️

https://arxiv.org/abs/2407.11330

Also: swarm, flock, behav, AI (artificial intell), in https://www.inkgmr.net/kwrds.html 

Keywords: behav, swarm, flock, AI, artificial intelligence