"If you push the system too hard, you have to take the car back to the shop." (Photo: Pxfuel)

A new paper by Professor Sid Redner and his collaborators Julien Randon-Furling and Benjamin De Bruyne has been chosen as an Editor’s Suggestion at the high-profile physics journal, Physical Review Letters

The paper, "Optimization in First-Passage Resetting,” was selected for being "particularly important, interesting, and well written,” according to an email from the PRL editors, who bestow the distinction on approximately one in six accepted manuscripts.

Though Redner demurs that the paper is “geeky,” and “kind of technical,” he has a relatable analogy for describing the research to non-physicists: Suppose you're driving a car you want to know how often you should you change your oil. If you're driving like the proverbial little old lady on her way to church on Sunday, you can go a year or more between oil changes. But if you're a New York City Uber driver speeding between traffic stops to meet your quota, you'd better change the oil more often. “Optimization in First-Passage Resetting” mathematically describes a random process where the rate at which a mechanical system breaks down depends on how hard it is pushed. If you push the system too hard, you have to re-start the process, or "take the car back to the shop.” By optimizing the ratio between the reward in pushing the system near its limit and the costliness of resetting, the paper can tell you whether, in Redner’s words, "you should drive the car into the ground, or if you should be more careful.”

“We were delighted to find that this nice problem had a unique solution where the system’s performance is high and the number of breakdowns is low,” says the paper’s first author Benjamin De Bruyne, a graduate student in physics at Paris-Saclay University. 

The notion of a random process being reset when it reaches a breakdown threshold is an example of a first-passage process. Other classic examples are the firing of a neuron when a fluctuating electrical signal first reaches a certain threshold or the triggering of a buy or sell order of a stock when it first hits a certain price.  (More examples can be found in Redner’s classic textbook, A Guide to First-Passage Processes.)

"The paper shows how some rather technical mathematical objects — random processes with endogenous resetting times — are applicable to a wide variety of optimization problems," explains co-author Julien Randon-Furling, a theoretical physicist at Université Paris Panthéon Sorbonne. "Some of these problems even pop up in everyday life, as the oil change analogy shows."

The work originated from a long-distance conversation between the three authors. During his international scholarship at the Perimeter Institute in Ontario, De Bruyne reached out to Redner “out of the blue,” Redner says, when Redner was based in Santa Fe and Randon-Furling was working at Columbia University as a mathematics professor with the Alliance program. At the time, Redner and Randon-Furling had been honing a suite of technical tools, but didn’t yet have a suitable problem to apply them to. With De Bruyne, they hit on the question of a random mover with a systematic component that wears down over time and must be reset.

The model could be extended to describe more complex mechanical systems, such as power grids, where operators might seek to optimize the frequency and cost of repairs. The authors note that the general class of first-passage resetting problems could also reveal intriguing problems in management science, for modeling random fluctuations in cash flows, and in biology, modeling the frequency of genetic variants in a population.

Read the paper, "Optimization in First-Passage Resetting,” in Physical Review Letters (July 28, 2020, paywall)

Read the synopsis, "A Statistical Model for Optimizing Output," on the APS Physics website (July 28, 2020)