Synchrony between things, especially organisms

Entrainment, synchronisation, dancing together

November 3, 2014 — April 23, 2022

dynamical systems
making things
music
signal processing
sync
Figure 1

When complicated things sync to each other. For application to music, see rhythm.

1 Mathematical basis of synchronisation

🚧TODO🚧 clarify

2 Neurological basis of synchronisation

Excited to read the new one by Jonathan Cannon A Bayesian perspective on entrainment with behavioral support.

Doelling:

“We’ve isolated the rhythms in the brain that match rhythms in music,” explains Keith Doelling, an NYU Ph.D. student and the study’s lead author. “Specifically, our findings show that the presence of these rhythms enhances our perception of music and of pitch changes.” […] Brain rhythms, they add, therefore appear to play a role in parsing and grouping sound streams into ‘chunks’ that are then analyzed as speech or music.

Or how about a dynamical systems approach? Famously, (Haken, Kelso, and Bunz 1985) does this: I found this paper fascinating, although the fact they spun several books out of it afterwards seemed to me to be gilding the lily.

3 Interpersonal synchronisation

Much to wonder about. For now, see the review in Basso, Satyal, and Rugh (2021) of stuff like (Basso, Satyal, and Rugh 2021; Kinreich et al. 2017; Toppi et al. 2016; Valencia and Froese 2020).

we synthesize findings from anthropology, sociology, psychology, dance pedagogy, and neuroscience to propose The Synchronicity Hypothesis of Dance, which states that humans dance to enhance both intra- and inter-brain synchrony

Brains Might Sync As People Interact — and That Could Upend Consciousness Research

People synchronize in various ways when we interact with one another. We subconsciously match our footsteps when we walk. During conversations, we mirror each other’s postures and gestures.

To that end, studies have shown that people synchronize heart rates and breathing when watching emotional films together. The same happens when romantic partners share a bed. Some scientists think we do this to build trust and perceive people as similar to ourselves, which encourages us to behave compassionately.

Surprisingly, people synchronize their neural rhythms, too. Researchers like Tom Froese, a cognitive scientist from the Okinawa Institute of Science and Technology in Japan, think that these findings could upend our current models of consciousness.

Pretty much everything up-ends our current models of consciousness though, apparently, so…

Figure 2

4 Incoming

  • correlograms
  • “vector strength” and event-based doohickeys versus continuous-signal systems
  • Kuramoto oscillators
  • Circle map
  • phase locked loops
  • “Entrainment” (Is that phase locking from the analysis rather than design perspective?)
  • The attraction of Pythagorean rhythms
  • machine listening for it
  • Lucky People Center International
  • Autocorrelation structures and simulating point processes from them

5 References

Absil, Mahony, and Sepulchre. 2008. Optimization algorithms on matrix manifolds.
Acebrón, Bonilla, Pérez Vicente, et al. 2005. The Kuramoto Model: A Simple Paradigm for Synchronization Phenomena.” Reviews of Modern Physics.
Basso, Satyal, and Rugh. 2021. Dance on the Brain: Enhancing Intra- and Inter-Brain Synchrony.” Frontiers in Human Neuroscience.
Boumal. 2013. On Intrinsic Cramér-Rao Bounds for Riemannian Submanifolds and Quotient Manifolds.” IEEE Transactions on Signal Processing.
Boumal, Singer, and Absil. 2013. Robust Estimation of Rotations from Relative Measurements by Maximum Likelihood.” In 52nd IEEE Conference on Decision and Control.
Boumal, Singer, Absil, et al. 2014. Cramér-Rao Bounds for Synchronization of Rotations.” Information and Inference.
Buhusi, and Meck. 2005. What Makes Us Tick? Functional and Neural Mechanisms of Interval Timing.” Nature Reviews Neuroscience.
Canavier, and Achuthan. 2007. Pulse Coupled Oscillators.” Scholarpedia.
Cannon. 2021. Expectancy-Based Rhythmic Entrainment as Continuous Bayesian Inference.” PLOS Computational Biology.
Carter. 1987. Coherence and Time Delay Estimation.” Proceedings of the IEEE.
Clayton. 1997. “Metre and Tal in North Indian Music.”
———. 2001. Time in Indian Music: Rhythm, Metre, and Form in North Indian Rag Performance. Oxford Monographs on Music.
Collins, and Stewart. 1992. Symmetry-Breaking Bifurcation: A Possible Mechanism for 2:1 Frequency-Locking in Animal Locomotion.” Journal of Mathematical Biology.
Demaine, Gomez-Martin, Meijer, et al. 2005. The Distance Geometry of Deep Rhythms and Scales. In CCCG.
———, et al. 2009. The Distance Geometry of Music.” In Computational Geometry.
Doelling, and Poeppel. 2015. Cortical Entrainment to Music and Its Modulation by Expertise.” Proceedings of the National Academy of Sciences.
Ellis, Cotton, and Mandel. 2008. Cross-Correlation of Beat-Synchronous Representations for Music Similarity.” In IEEE International Conference on Acoustics, Speech and Signal Processing, 2008. ICASSP 2008.
Elman. 1990. Finding Structure in Time.” Cognitive Science.
Feldman, and Crutchfield. 2004. Synchronizing to Periodicity: The Transient Information and Synchronization Time of Periodic Sequences.” Advances in Complex Systems.
Fischer, Vicente, Buldú, et al. 2006. “Zero-Lag Long-Range Synchronization via Dynamical Relaying.”
Fokker. 1968. Unison Vectors and Periodicity Blocks in the Three-Dimensional (3-5-7) Harmonic Lattice of Notes.
Freidlin, Mark, and Weber. 1998. Random Perturbations of Nonlinear Oscillators.” The Annals of Probability.
Freidlin, Mark I., and Wentzell. 1993. Diffusion Processes on Graphs and the Averaging Principle.” The Annals of Probability.
Fries. 2005. A Mechanism for Cognitive Dynamics: Neuronal Communication Through Neuronal Coherence.” Trends in Cognitive Sciences.
———. 2015. Rhythms for Cognition: Communication Through Coherence.” Neuron.
Glass. 1991. Cardiac Arrhythmias and Circle Maps−A Classical Problem.” Chaos: An Interdisciplinary Journal of Nonlinear Science.
———. 2001. Synchronization and Rhythmic Processes in Physiology.” Nature.
Gozli. 2023. Principles of Categorization: A Synthesis.” Seeds of Science.
Guevara, and Glass. 1982. Phase Locking, Period Doubling Bifurcations and Chaos in a Mathematical Model of a Periodically Driven Oscillator: A Theory for the Entrainment of Biological Oscillators and the Generation of Cardiac Dysrhythmias.” Journal of Mathematical Biology.
Haken, Kelso, and Bunz. 1985. A Theoretical Model of Phase Transitions in Human Hand Movements.” Biological Cybernetics.
Hennig, Fleischmann, Fredebohm, et al. 2011. The Nature and Perception of Fluctuations in Human Musical Rhythms.” PLoS ONE.
Hennig, Fleischmann, and Geisel. 2012. Musical Rhythms: The Science of Being Slightly Off.” Physics Today.
Hunt. n.d. The ‘Easy Part’ of the Hard Problem: A Resonance Theory of Consciousness.”
Ichinomiya. 2004. Frequency Synchronization in a Random Oscillator Network.” Physical Review E.
Keith, and Rand. 1984. 1∶1 and 2∶1 Phase Entrainment in a System of Two Coupled Limit Cycle Oscillators.” Journal of Mathematical Biology.
Kinreich, Djalovski, Kraus, et al. 2017. Brain-to-Brain Synchrony During Naturalistic Social Interactions.” Scientific Reports.
Mateo, Horsevad, Hassani, et al. 2019. Optimal Network Topology for Responsive Collective Behavior.” Science Advances.
McLennan-Smith. 2019. On the Simulation of Stochastic Processes and Noise Driven Synchronisation Models.”
Mirollo, and Strogatz. 1990. Synchronization of Pulse-Coupled Biological Oscillators.” SIAM Journal on Applied Mathematics.
Mirollo, and Strogatz. 2007. The Spectrum of the Partially Locked State for the Kuramoto Model.” Journal of Nonlinear Science.
Moreno, and Pacheco. 2004. Synchronization of Kuramoto Oscillators in Scale-Free Networks.” EPL (Europhysics Letters).
Parncutt. 1994. A Perceptual Model of Pulse Salience and Metrical Accent in Musical Rhythms.” Music Perception: An Interdisciplinary Journal.
Pikovsky, and Rosenblum. 2007. Synchronization.” Scholarpedia.
Pikovsky, Rosenblum, and Kurths. 2003. Synchronization: A Universal Concept in Nonlinear Sciences.
Roberts. 2008. A Linear Reformulation of the Kuramoto Model of Self-Synchronizing Oscillators.” Physical Review E.
Roberts, and Teodorescu. 2008. A Linear Path Toward Synchronization: Anomalous Scaling in a New Class of Exactly Solvable Kuramoto Models.” The European Physical Journal Special Topics.
Rodrigues, Peron, Ji, et al. 2016. The Kuramoto Model in Complex Networks.” Physics Reports, The Kuramoto model in complex networks,.
Schöner. 2002. Timing, Clocks, and Dynamical Systems.” Brain and Cognition.
Semjen, Vorberg, and Schulze. 1998. Getting Synchronized with the Metronome: Comparisons Between Phase and Period Correction.” Psychological Research.
Strogatz. 2000. From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators.” Physica D: Nonlinear Phenomena.
———. 2004. Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life.
Toppi, Borghini, Petti, et al. 2016. Investigating Cooperative Behavior in Ecological Settings: An EEG Hyperscanning Study.” PLOS ONE.
Toussaint. 2004. A Comparison of Rhythmic Similarity Measures. In ISMIR.
———. 2013. The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good?
Valencia, and Froese. 2020. What Binds Us? Inter-Brain Neural Synchronization and Its Implications for Theories of Human Consciousness.” Neuroscience of Consciousness.