Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Cesarean section and rate of subsequent stillbirth, miscarriage and ectopic pregnancy: a Danish register-based cohort study

Background: With cesarean section rates increasing worldwide, clarity regarding negative effects is essential. This study aimed to investigate the rate of subsequent stillbirth, miscarriage, and ectopic pregnancy following primary cesarean section, controlling for confounding by indication. Methods and Findings: We performed a population-based cohort study using Danish national registry data linking various registers. The cohort included primiparous women with a live birth between January 1, 1982, and December 31, 2010 (n = 832,996), with follow-up until the next event (stillbirth, miscarriage, or ectopic pregnancy) or censoring by live birth, death, emigration, or study end. Cox regression models for all types of cesarean sections, sub-group analyses by type of cesarean, and competing risks analyses for the causes of stillbirth were performed. An increased rate of stillbirth (hazard ratio [HR] 1.14, 95% CI 1.01, 1.28) was found in women with primary cesarean section compared to spontaneous vaginal delivery, giving a theoretical absolute risk increase (ARI) of 0.03% for stillbirth, and a number needed to harm (NNH) of 3,333 women. Analyses by type of cesarean section showed similarly increased rates for emergency (HR 1.15, 95% CI 1.01, 1.31) and elective cesarean (HR 1.11, 95% CI 0.91, 1.35), although not statistically significant in the latter case. An increased rate of ectopic pregnancy was found among women with primary cesarean overall (HR 1.09, 95% CI 1.04, 1.15) and by type (emergency cesarean, HR 1.09, 95% CI 1.03, 1.15, and elective cesarean, HR 1.12, 95% CI 1.03, 1.21), yielding an ARI of 0.1% and a NNH of 1,000 women for ectopic pregnancy. No increased rate of miscarriage was found among women with primary cesarean, with maternally requested cesarean section associated with a decreased rate of miscarriage (HR 0.72, 95% CI 0.60, 0.85). Limitations include incomplete data on maternal body mass index, maternal smoking, fertility treatment, causes of stillbirth, and maternally requested cesarean section, as well as lack of data on antepartum/intrapartum stillbirth and gestational age for stillbirth and miscarriage. Conclusions: This study found that cesarean section is associated with a small increased rate of subsequent stillbirth and ectopic pregnancy. Underlying medical conditions, however, and confounding by indication for the primary cesarean delivery account for at least part of this increased rate. These findings will assist women and health-care providers to reach more informed decisions regarding mode of delivery.