Comparison of a General and Conditional Measure of E-Cigarette Harm Perceptions

Measures of tobacco product harm perceptions are important in research, given their association with tobacco use. Despite recommendations to use more specific harm and risk perception measures, limited research exists comparing different wordings. We present exploratory survey data comparing young adults’ (ages 18–29) responses to a general e-cigarette harm perception measure (“How harmful, if at all, do you think vaping/using an e-cigarette is to a user’s health?”) with a more specific conditional measure, which personalized the behavior/harm (“imagine you vaped,” “your health”) and presented a specific use condition (exclusive daily vaping) and timeframe (10 years). Data were collected in January 2019 (n = 1006). Measures were highly correlated (r = 0.76, Cronbach’s α = 0.86), and most (65%) provided consistent responses, although more participants rated e-cigarettes as very or extremely harmful using the conditional (51.6%) versus the general (43.9%) harm measure. However, significant differences in harm ratings were not observed among young adults who currently vaped. Correlations between each harm perception measure and measures of e-cigarette use intentions were similar. More specifically worded harm perception measures may result in somewhat higher e-cigarette harm ratings than general measures for some young adults. Additional research on best practices for measuring e-cigarette and other tobacco harm perceptions is warranted.

Ergodic SDEs on submanifolds and related numerical sampling schemes

In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure μ on the level set of a smooth function ξ : ℝd → ℝk, 1 ≤ k < d. A specially interesting case is the so-called conditional probability measure, which is useful in the study of free energy calculation and model reduction of diffusion processes. By Birkhoff’s ergodic theorem, one approach to estimate the mean value is to compute the time average along an infinitely long trajectory of an ergodic diffusion process on the level set whose invariant measure is μ. Motivated by the previous work of Ciccotti et al. (Commun. Pur. Appl. Math. 61 (2008) 371–408), as well as the work of Leliévre et al. (Math. Comput. 81 (2012) 2071–2125), in this paper we construct a family of ergodic diffusion processes on the level set of ξ whose invariant measures coincide with the given one. For the conditional measure, we propose a consistent numerical scheme which samples the conditional measure asymptotically. The numerical scheme doesn’t require computing the second derivatives of ξ and the error estimates of its long time sampling efficiency are obtained.

Universality for conditional measures of the Bessel point process

The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval [Formula: see text] is almost surely an orthogonal polynomial ensemble. In this paper, we show that if [Formula: see text] tends to infinity, one almost surely recovers the Bessel point process. In fact, we show this convergence for a deterministic class of probability measures, to which the conditional measure of the Bessel point process almost surely belongs.

Conditional measure and flip invariance of Bowen-Margulis and harmonic measures on manifolds of negative curvature

Kifer and Ledrappier have asked whether the harmonic measures {νx} on manifolds of negative curvature are equivalent to the conditional measures of the harmonic measure v of the geodesic flow associated with the fibration {SxM}x∈M. We settle this question with a rigidity result. We also clear up the same problem concerning the Patterson-Sullivan measure and the Bowen–Margulis measure.