Verhulst model with Levy white noise excitation

The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Levy process we study the nonlinear relaxation of the population density for three cases of white non-Gaussian noise: (i) shot noise, (ii) noise with a probability density of increments expressed in terms of Gamma function, and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover starting from an initial delta function distribution, we find a transition induced by the multiplicative Levy noise, from a trimodal probability distribution to a bimodal probability distribution in asymptotics. Finally we find a nonmonotonic behavior of the nonlinear relaxation time as a function of the Cauchy stable noise intensity.Comment: 9 pages, 12 figures, to appear in EPJ B (2008

The role of the pod in seed development: strategies for manipulating yield

Pods play a key role in encapsulating the developing seeds and protecting them from pests and pathogens. In addition to this protective function, it has been shown that the photosynthetically active pod wall contributes assimilates and nutrients to fuel seed growth. Recent work has revealed that signals originating from the pod may also act to coordinate grain filling and regulate the reallocation of reserves from damaged seeds to those that have retained viability. In this review we consider the evidence that pods can regulate seed growth and maturation, particularly in members of the Brassicaceae family, and explore how the timing and duration of pod development might be manipulated to enhance either the quantity of crop yield or its nutritional properties

The development of a HAMstring InjuRy (HAMIR) index to mitigate injury risk through innovative imaging, biomechanics, and data analytics : Protocol for an observational cohort study

Background The etiology of hamstring strain injury (HSI) in American football is multi-factorial and understanding these risk factors is paramount to developing predictive models and guiding prevention and rehabilitation strategies. Many player-games are lost due to the lack of a clear understanding of risk factors and the absence of effective methods to minimize re-injury. This paper describes the protocol that will be followed to develop the HAMstring InjuRy (HAMIR) index risk prediction models for HSI and re-injury based on morphological, architectural, biomechanical and clinical factors in National Collegiate Athletic Association Division I collegiate football players. Methods A 3-year, prospective study will be conducted involving collegiate football student-athletes at four institutions. Enrolled participants will complete preseason assessments of eccentric hamstring strength, on-field sprinting biomechanics and muscle–tendon volumes using magnetic-resonance imaging (MRI). Athletic trainers will monitor injuries and exposure for the duration of the study. Participants who sustain an HSI will undergo a clinical assessment at the time of injury along with MRI examinations. Following completion of structured rehabilitation and return to unrestricted sport participation, clinical assessments, MRI examinations and sprinting biomechanics will be repeated. Injury recurrence will be monitored through a 6-month follow-up period. HAMIR index prediction models for index HSI injury and re-injury will be constructed. Discussion The most appropriate strategies for reducing risk of HSI are likely multi-factorial and depend on risk factors unique to each athlete. This study will be the largest-of-its-kind (1200 player-years) to gather detailed information on index and recurrent HSI, and will be the first study to simultaneously investigate the effect of morphological, biomechanical and clinical variables on risk of HSI in collegiate football athletes. The quantitative HAMIR index will be formulated to identify an athlete’s propensity for HSI, and more importantly, identify targets for injury mitigation, thereby reducing the global burden of HSI in high-level American football players. Trial Registration The trial is prospectively registered on ClinicalTrials.gov (NCT05343052; April 22, 2022)