Dr. Akhilesh Nandan from MPINB explaines: “Changing the framework that the dynamics is governed by stable states, or attractors, to a framework where the dynamics is dictated by formally unstable structures such as ghost-based scaffolds, enabled us to obtain a potential description for what has been experimentally observed across broad range of systems. Crucial for defining this framework was the mathematical characterization of these abstract ghost objects.”
Understanding Degrading Ecosystems or Climate Change
In their publication, the scientists demonstrate that ghost-based scaffolds better capture the properties of long transients in noisy systems compared to traditional models. Instead of relying on precise knowledge or existence of (un)stable fixed points, this novel framework centers on slow directed flows organized by ghost sets in ghost channels and ghost cycles.
An exciting implication from this study is that ghost structures seem to underline many different processes across biological and natural systems once you know what to look for. “We have identified ghost channels in models relevant for cell fate decisions during development, but also models of tipping cascades in climate systems that are used to explore how tipping e.g. of the Atlantic Meridional Overturning Circulation (AMOC) could affect the dynamics of other climate sub-systems”, says Dr. Daniel Koch. Therefore, these new findings open many doors for future research, from theoretical understanding how neuronal networks encode smell or taste, to potentially better prediction of shifts in ecosystems or the climate. “What we are most excited about, however, is the potential this powerful theoretical framework can bring for biological and artificial intelligence research”, says Dr. Aneta Koseska who leads the group of Cellular computations and learning at the MPINB in Bonn. “We already started investigating how ghost scaffolds can aid learning of natural and artificial neuronal networks, and use them to overcome the current obstacles of catastrophic forgetting.”
This framework therefore could possibly provide potential umbrella to study long transients, but also to identify the limits of the current mathematical frameworks and where further expansions are necessary to tackle long-standing open questions of quasi-stable transient dynamics across living, natural and man-made systems.
D. Koch, A. Nandan, G. Ramesan, I. Tyukin, A. Gorban, and A. Koseska. Ghost Channels and Ghost Cycles Guiding Long Transients in Dynamical Systems.
Phys. Rev. Lett. 133, 047202 – Published 25 July 2024 Link.
Max Planck Institute for Neurobiology of Behavior – caesar
