Do higher-order interactions promote synchronization?
Apr 2023, phys.org
Researchers use networks to model the dynamics of coupled systems ranging from food webs to neurological processes. Those models originally focused on pairwise interactions, or behaviors that emerge from interactions between two entities. But in the last few years, network theorists have been asking, what about phenomena that involve three or more?
AKA the Three Body Problem
Network theorists call these phenomena "higher-order interactions." Now scientists show how the choice of network representation can influence the observed effects, focusing on the phenomenon of synchronization, which emerges in systems from circadian clocks to vascular networks.They compared hypergraphs of "hyperedges" to connect three or more nodes, and simplicial complexes, more structured and using triangles to represent connections.In the paper, Zhang and his colleagues reported that networks modeled with hypergraphs easily give rise to synchronization, while simplicial complexes tend to complicate the process due to their highly heterogeneous structure. That suggests choices in higher-order representations can influence the outcome, and Zhang suspects the results can be extended to other dynamical processes such as diffusion or contagion."Structural heterogeneity is important not just in synchronization, but is fundamental to most dynamic processes," he says. "Whether we model the system as a hypergraph or simplicial complex can drastically affect our conclusions."
via Santa Fe Institute: Yuanzhao Zhang et al, Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes, Nature Communications (2023). DOI: 10.1038/s41467-023-37190-9
Mostly unrelated image credit: Lab Based Ambient Pressure X-ray Photoelectron Spectroscopy at CFN Brookhaven National Laboratory
Researchers investigate the veracity of 'six degrees of separation'
Jun 2023, phys.org
I don't think I understand why 6 and not another number; but it appears that the big deal here is that the mechanism behind 'why 6' is based on a cost-benefit algorithm.
The intriguing phenomenon, they show, is linked to another social experience we all know too well -- the struggle of cost vs. benefit in establishing new social ties.
"6 Degrees" is from Stanley Milgram at Harvard in 1967 who used the United States Postal System to perform experiments on and model our social network.
(This point in itself is interesting to consider, in light of having the access to the electronic communications network that is the internet, and which later proved these experiments on the scale of millions not hundreds, that we did have already such a pervasive, well-functioning network at hand, in the form of the United States Postal Service.)
Milgram sent letters to random people, with instructions to try and make it back to one of his professor-friends somewhere else across the country. The experiment found that it only takes about six handshakes to bridge between two random people.
So what is the common denominator?
The objective of using a social network for the individual, is not simply to pursue a large number of connections, but to obtain the right connections, for example, seeking a junction that bridges between many pathways, and hence funnels much of the flow of information in the network.But social capital does not come for free. It requires constant maintenance. A constant buzz driven by the ambition for social centrality."We discovered an amazing result: this process always ends with social paths centered around the number six. This is quite surprising." (Dark side reminder: "Indeed, within six infection cycles, a virus can cross the globe.")
via Bar-Ilan University as well as collaborators from Israel, Spain, Italy, Russia, Slovenia and Chile: I. Samoylenko et al, Why Are There Six Degrees of Separation in a Social Network?, Physical Review X (2023). DOI: 10.1103/PhysRevX.13.021032
Post Script: The book Bursts by Albert-László Barabási does a great job of looking at these kinds of social network effects, following the travels of the Where's George campaign of dollar bills through the US for example. He took the incipient revelations of network science (the 6 degrees rule) and gave it a temporal dimension -- he showed how our activities can be measured in short bursts followed by not much activity at all. It's not just the '2-dimensional' shape of the network, but the extra time dimension that defines the salient behavior of the social network.
Bursts: The Hidden Pattern Behind Everything We Do
Albert-László Barabási, 2010
Researchers identify mathematical rule behind the distribution of neurons in our brains
Aug 2023, phys.org
I don't see the word network science in here but it is --
Researchers have uncovered the ubiquitous lognormal distribution of neuron densities across and within cortical areas in the mammalian brain, suggesting a fundamental organizational principle.
via Human Brain Project, Forschungszentrum Jülich and the University of Cologne: Aitor Morales-Gregorio et al, Ubiquitous lognormal distribution of neuron densities in mammalian cerebral cortex, Cerebral Cortex (2023). DOI: 10.1093/cercor/bhad160
