Lyapunov exponents for temporal networks

Annalisa Caligiuri, Victor M. Eguíluz, Leonardo Di Gaetano, Tobias Galla, and Lucas Lacasa

Phys. Rev. E 107, 044305

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network and construct a measure to estimate the network maximum Lyapunov exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low- and high-dimensional chaos and finally discuss potential applications.

Read the full article at: link.aps.org

End Times by Peter Turchin

From the pioneering co-founder of cliodynamics, the groundbreaking new interdisciplinary science of history, a big-picture explanation for America’s civil strife and its possible endgames

Peter Turchin, one of the most interesting social scientists of our age, has infused the study of history with approaches and insights from other fields for more than a quarter century. End Times is the culmination of his work to understand what causes political communities to cohere and what causes them to fall apart, as applied to the current turmoil within the United States. 

Back in 2010, when Nature magazine asked leading scientists to provide a ten-year forecast, Turchin used his models to predict that America was in a spiral of social disintegration that would lead to a breakdown in the political order circa 2020. The years since have proved his prediction more and more accurate, and End Times reveals why.

The lessons of world history are clear, Turchin argues: When the equilibrium between ruling elites and the majority tips too far in favor of elites, political instability is all but inevitable. As income inequality surges and prosperity flows disproportionately into the hands of the elites, the common people suffer, and society-wide efforts to become an elite grow ever more frenzied. He calls this process the wealth pump; it’s a world of the damned and the saved. And since the number of such positions remains relatively fixed, the overproduction of elites inevitably leads to frustrated elite aspirants, who harness popular resentment to turn against the established order. Turchin’s models show that when this state has been reached, societies become locked in a death spiral it’s very hard to exit.

In America, the wealth pump has been operating full blast for two generations. As cliodynamics shows us, our current cycle of elite overproduction and popular immiseration is far along the path to violent political rupture.  That is only one possible end time, and the choice is up to us, but the hour grows late.

More at: www.penguinrandomhouse.com

Neuromorphic learning, working memory, and metaplasticity in nanowire networks

Alon Loeffler,  Adrian Diaz-Alvarez,  Ruomin Zhu,  Natesh Ganesh, James M. Shine, Tomonobu Nakayama, Zdenka Kuncic

SCIENCE ADVANCES 21 Apr 2023 Vol 9, Issue 1

Nanowire networks (NWNs) mimic the brain’s neurosynaptic connectivity and emergent dynamics. Consequently, NWNs may also emulate the synaptic processes that enable higher-order cognitive functions such as learning and memory. A quintessential cognitive task used to measure human working memory is the n-back task. In this study, task variations inspired by the n-back task are implemented in a NWN device, and external feedback is applied to emulate brain-like supervised and reinforcement learning. NWNs are found to retain information in working memory to at least n = 7 steps back, remarkably similar to the originally proposed “seven plus or minus two” rule for human subjects. Simulations elucidate how synapse-like NWN junction plasticity depends on previous synaptic modifications, analogous to “synaptic metaplasticity” in the brain, and how memory is consolidated via strengthening and pruning of synaptic conductance pathways.

Read the full article at: www.science.org