We consider the diffusion dx(r)=b(x(t))dt + J~a ( x ( t ) ) d w in a domain D which contains a unique asymptotically stable critical point of the ODE dx((r))= h(x(t))dt. Using probabilistic estimates we prove the following:I) The principal eigenfunction of the differential generator for lhe process s(t) converges to a constant as 6-0, boundedly in D and uniformly on compacts.2) If T, is the exit time of x(r) from D, then AtD converges in distribution to an enyurtall;a: ~*ii&iii ariabic wi:h ncm I. (,I ir: rhr ~r i r~i p a l dgevvrl~ir ) Both of these rcsults were known previously in the special case of a gradient flow: h = 1/2aV$, where u = a a T . Our arguments apply in the general non-gradient case.
People's social and political opinions are grounded in their moral concerns about right and wrong. We examine whether five moral foundations-harm, fairness, ingroup, authority, and purity-can influence political attitudes of liberals and conservatives across a variety of issues. Framing issues using moral foundations may change political attitudes in at least two possible ways: 1. Entrenching: relevant moral foundations will strengthen existing political attitudes when framing pro-attitudinal issues (e.g., conservatives exposed to a free-market economic stance). 2. Persuasion: mere presence of relevant moral foundations may also alter political attitudes in counter-attitudinal directions (e.g., conservatives exposed to an economic regulation stance). Studies 1 and 2 support the entrenching hypothesis. Relevant moral foundation-based frames bolstered political attitudes for conservatives (Study 1) and liberals (Study 2). Only Study 2 partially supports the persuasion hypothesis. Conservative-relevant moral frames of liberal issues increased conservatives' liberal attitudes.
We consider regularity properties of the quasipotential function V defined by A. D. Ventcel and M. I. Freidlin in their work on asymptotically small random perturbations of stable dynamical systems. The regularity properties of V are important for the success of various asymptotic calculations carried out in the literature. Employing classical techniques from the calculus of variations and differential equations, we prove various results about the smoothness of V and its level sets. Among other things, there exists a dense connected open set, containing the stable point for the underlying dynamical system, in which V is continuously differentiable to the same degree as the Lagrangian involved in the defining variational problem.
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