Universal performance bounds of restart

As has long been known to computer scientists, the performance of probabilistic algorithms characterized by relatively large runtime fluctuations can be improved by applying a restart, i.e., episodic interruption of a randomized computational procedure followed by initialization of its new statistically independent realization. A similar effect of restart-induced process acceleration could potentially be possible in the context of enzymatic reactions, where dissociation of the enzyme-substrate intermediate corresponds to restarting the catalytic step of the reaction. To date, a significant number of analytical results have been obtained in physics and computer science regarding the effect of restart on the completion time statistics in various model problems, however, the fundamental limits of restart efficiency remain unknown. Here we derive a range of universal statistical inequalities that offer constraints on the effect that restart could impose on the completion time of a generic stochastic process. The corresponding bounds are expressed via simple statistical metrics of the original process such as harmonic mean h, median value m, and mode M, and, thus, are remarkably practical. We test our analytical predictions with multiple numerical examples, discuss implications arising from them and important avenues of future work.

Conformational statistics of non-equilibrium polymer loops in Rouse model with active loop extrusion

Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper, we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in the statistics of the extruded loop, regardless of the specific time dependence of the extrusion velocity. In addition, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits.

Bilateral vestibulopathy and age: experimental considerations for testing dynamic visual acuity on a treadmill

INTRODUCTION

Bilateral vestibulopathy (BVP) can affect visual acuity in dynamic conditions, like walking. This can be assessed by testing Dynamic Visual Acuity (DVA) on a treadmill at different walking speeds. Apart from BVP, age itself might influence DVA and the ability to complete the test. The objective of this study was to investigate whether DVA tested while walking, and the drop-out rate (the inability to complete all walking speeds of the test) are significantly influenced by age in BVP-patients and healthy subjects.

METHODS

Forty-four BVP-patients (20 male, mean age 59 years) and 63 healthy subjects (27 male, mean age 46 years) performed the DVA test on a treadmill at 0 (static condition), 2, 4 and 6 km/h (dynamic conditions). The dynamic visual acuity loss was calculated as the difference between visual acuity in the static condition and visual acuity in each walking condition. The dependency of the drop-out rate and dynamic visual acuity loss on BVP and age was investigated at all walking speeds, as well as the dependency of dynamic visual acuity loss on speed.

RESULTS

Age and BVP significantly increased the drop-out rate (p ≤ 0.038). A significantly higher dynamic visual acuity loss was found at all speeds in BVP-patients compared to healthy subjects (p < 0.001). Age showed no effect on dynamic visual acuity loss in both groups. In BVP-patients, increasing walking speeds resulted in higher dynamic visual acuity loss (p ≤ 0.036).

CONCLUSION

DVA tested while walking on a treadmill, is one of the few "close to reality" functional outcome measures of vestibular function in the vertical plane. It is able to demonstrate significant loss of DVA in bilateral vestibulopathy patients. However, since bilateral vestibulopathy and age significantly increase the drop-out rate at faster walking speeds, it is recommended to use age-matched controls. Furthermore, it could be considered to use an individual "preferred" walking speed and to limit maximum walking speed in older subjects when testing DVA on a treadmill.