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Objective:To discuss the potential for adverse consequences that could arise from the quest to prolong the functional life span of the human ovary. Methods:A series of arguments are presented that: (a) question the dogma that monthly ovulatory menstrual cycles are critical for women’s health; (b) review adverse consequences of decades of menstrual cyclicity; (c) review the evidence for a longevity benefit of ovarian steroid hormone treatment after the age at natural menopause has been achieved; and (d) utilize a mathematical model of ovarian follicle loss over time to raise the possibility that current strategies directed at delaying menopause might well backfire and in fact cause a woman to have a prolonged menopause transition. Results:Regular, monthly menstrual cycles have not been the reality for women for most of history. Rather, when not pregnant, lactational amenorrhea and nutritionally based hypothalamic amenorrhea were the norm for reproductive-aged women. Moreover, monthly menstrual cycles cause substantial morbidity for women during their reproductive years. Providing steroid hormones after menopause has failed to demonstrate an increase in the female life span. Restoring ovarian follicles either surgically or medically has a high probability of causing women to spend more years of life in the menopause transition. Conclusions:Strategies to prevent or delay menopause would benefit from careful consideration of unintended consequences as they are implemented. Directing treatment trials to those with the greatest chance for benefit should be undertaken before adopting this type of treatment for a broader population. 

Cover times quantify the speed of exhaustive search. In this work, we approximate the moments of cover times of a wide range of stochastic search processes in d-dimensional continuous space and on an arbitrary discrete network under frequent stochastic resetting. These approximations apply to a large class of resetting time distributions and search processes including diffusion, run-and-tumble particles, and Markov jump processes. We illustrate these results in several examples; in the case of diffusive search, we show that the errors of our approximations vanish exponentially fast. Finally, we derive a criterion for when endowing a discrete state search process with minimal stochastic resetting reduces the mean cover time. 

Proteins can form droplets via liquid–liquid phase separation (LLPS) in cells. Recent experiments demonstrate that LLPS is qualitatively different on two-dimensional (2D) surfaces compared to three-dimensional (3D) solutions. In this paper, we use mathematical modeling to investigate the causes of the discrepancies between LLPS in 2D and 3D. We model the number of proteins and droplets inducing LLPS by continuous-time Markov chains and use chemical reaction network theory to analyze the model. To reflect the influence of space dimension, droplet formation and dissociation rates are determined using the first hitting times of diffusing proteins. We first show that our stochastic model reproduces the appropriate phase diagram and is consistent with the relevant thermodynamic constraints. After further analyzing the model, we find that it predicts that the space dimension induces qualitatively different features of LLPS, which are consistent with recent experiments. While it has been claimed that the differences between 2D and 3D LLPS stem mainly from different diffusion coefficients, our analysis is independent of the diffusion coefficients of the proteins since we use the stationary model behavior. Our results thus give new hypotheses about how space dimension affects LLPS. 

Abstract Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work we determine hitting probabilities for stochastic search processes conditioned on being faster than a random short time. Such times have been used to model stochastic resetting or stochastic inactivation. These results apply to any search process, diffusive or otherwise, whose unconditional short-time behavior can be adequately approximated, which we characterize for broad classes of stochastic search. We illustrate these results in several examples and show that the conditional hitting probabilities depend predominantly on the relative geodesic lengths between the initial position of the searcher and the targets. Finally, we apply these results to a canonical evidence accumulation model for decision making.