Langevin dynamics with a tilted periodic potential

We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $\gamma$ and subject to a further external field $\alpha$. For a suitable choice of the parameters $\alpha$ and $\gamma$ the related deterministic dynamics yields heteroclinic orbits. In such a regime, in absence of stochastic noise both confined and unbounded orbits coexist. We prove that, with the inclusion of an arbitrarly small noise only the confined orbits survive in a sub-exponential time scale.Comment: 38 pages, 6 figure

Test-Retest Reliability of a Semi-Structured Interview to Aid in Pediatric Traumatic Brain Injury Diagnosis

Objective: Retrospective self-report is typically used for diagnosing previous pediatric traumatic brain injury (TBI). A new semi-structured interview instrument (New Mexico Assessment of Pediatric TBI; NewMAP TBI) investigated test-retest reliability for TBI characteristics in both the TBI that qualified for study inclusion and for lifetime history of TBI. Method: One-hundred and eight-four mTBI (aged 8-18), 156 matched healthy controls (HC), and their parents completed the NewMAP TBI within 11 days (subacute; SA) and 4 months (early chronic; EC) of injury, with a subset returning at 1 year (late chronic; LC). Results: The test-retest reliability of common TBI characteristics [loss of consciousness (LOC), post-traumatic amnesia (PTA), retrograde amnesia, confusion/disorientation] and post-concussion symptoms (PCS) were examined across study visits. Aside from PTA, binary reporting (present/absent) for all TBI characteristics exhibited acceptable (≥0.60) test-retest reliability for both Qualifying and Remote TBIs across all three visits. In contrast, reliability for continuous data (exact duration) was generally unacceptable, with LOC and PCS meeting acceptable criteria at only half of the assessments. Transforming continuous self-report ratings into discrete categories based on injury severity resulted in acceptable reliability. Reliability was not strongly affected by the parent completing the NewMAP TBI. Conclusions: Categorical reporting of TBI characteristics in children and adolescents can aid clinicians in retrospectively obtaining reliable estimates of TBI severity up to a year post-injury. However, test-retest reliability is strongly impacted by the initial data distribution, selected statistical methods, and potentially by patient difficulty in distinguishing among conceptually similar medical concepts (i.e., PTA vs. confusion). Copyright © INS. Published by Cambridge University Press, 2021.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]