Taking the long way around: Improving continuous-time random walk precision
Taking the long way around: Improving continuous-time random walk precision lead image
With broad-ranging uses across physics, chemistry, biology and even stock trading, continuous-time random walks have become a foundational idea in understanding the behavior of objects as they change states. In many applications, reaching a specific state triggers events like an explosion or the sale of stock. The event times fluctuate strongly, since they are the result of a random process. In Chaos, one pair of scientists has proposed a method for making such event timing more precise.
Researchers introduced a novel way of controlling first-passage time — the time to first reach a particular threshold — in continuous-time random walks by using an exponential transient that describes relaxation of environmental conditions. They found a relative fluctuation minimum of first-passage times of linear chains of states for a specific, resonant length of the chain. The resonant number of steps from the inhibited state to the excitation threshold, and slow recovery from negative feedback, provide optimal timing noise reduction and information transmission.
This simple and efficient noise control improved relative fluctuation precision by about an order of magnitude. Their results are closely related to the timing of repetitive excitations, coherence resonance and information transmission by noisy excitable systems, and they apply to both Markovian and non-Markovian systems.
The team also found that its results matched the behavior of cellular signaling by calcium ion concentration spike sequences. This system uses relaxational recovery from negative feedback to improve timing of individual spikes, and thus the information transmission rate. This mechanism relates the phenomenon of resonant lengths to coherence resonance in excitable systems.
Source: “The stretch to stray on time: Resonant length of random walks in a transient,” by Martin Falcke and Victor Nicolai Friedhoff, Chaos (2018). The article can be accessed at https://doi.org/10.1063/1.5023164 .
