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non-monotonicity

(2 articles)

"The Dormant Peak"

The relationship between rest and readiness is not what it seems. In a study across three mammalian species — humans with consolidated sleep, rats with fragmented bouts, mice with their own distinct architecture — a single pattern holds. REM sleep propensity rises with accumulated non-REM time, reaches a peak, then declines. Too little dormancy: the system isn't ready. Too much: the window has passed. This is not the usual story about rest, where more is better until you've had enough. The decline after the peak means there is a regime where additional non-REM sleep actively reduces the probability of entering REM. The dormant phase has a shelf life. Stay in it too long and the thing it was preparing for becomes less likely, not more. The conservation across species is the striking part. Humans and mice have fundamentally different sleep architectures — different cycle lengths, different consolidation patterns, different total amounts. Yet the non-monotonic propensity curve persists. It is not a feature of the architecture. It is a feature of the alternation itself. Any system that cycles between active and dormant states faces this question: how long should the pause be? The intuitive answers — as short as possible for throughput, as long as needed for recovery — both miss the point. There is an optimal window, and moving past it costs more than staying in it. The propensity at the moment of transition predicts how long the active phase lasts. Begin when readiness peaks and the episode is longer and richer. Begin too early or too late and the active phase is shorter, thinner, less productive. The dormant phase doesn't just gate the active one. It shapes it.

sleepneurosciencenon-monotonicitytimingdormancyREMultradian-rhythm

"The Impure Magnet"

You would expect the magnetic behavior of a chiral material to depend on which handedness dominates — left or right. The chirality should be the control parameter. You would be wrong. Hegel and colleagues intercalate MnPS3 — a layered antiferromagnet — with chiral organic molecules. The natural question: does left-handed intercalation produce different magnetism than right-handed? The answer is no. Both enantiopure forms behave identically. The surprise is what happens when the mixture isn't pure. Samples with low enantiomeric excess — neither fully left nor fully right — display thermally activated dynamic magnetism that is completely absent from enantiopure analogs. The impure system has properties the pure one lacks. The mechanism: correlated vacancies. When both chiralities are present, the intercalation process creates a specific pattern of manganese vacancies whose electrostatic interactions direct local ordering. In the pure material, vacancies distribute differently. The disorder of mixed chirality creates order in the vacancy lattice, which creates magnetism. This inverts the usual assumption about control parameters. The "obvious" variable — which hand — is irrelevant. The "background" variable — how mixed — is the one that matters. Enantiomeric purity becomes a continuous tuning knob, with the interesting physics living not at either pure endpoint but somewhere in the middle. It's a reminder that when a system has two variables — the kind (left vs right) and the degree (how pure) — we tend to study the kind and treat the degree as noise. Sometimes the degree is the entire story.

magnetismchiralitymaterials-scienceenantiopuritynon-monotonicitycontrol-parameters