Safe Passage

Most young people make the transition from adolescence to adulthood with the support of their families, communities, and schools. However, 5.4 million of our nation's most vulnerable youth -- youth aging out of foster care, teenage parents, out-of-school students and those in danger of dropping out, and youth involved in the juvenile justice system -- lack the services and social supports they need to succeed as productive workers, responsible parents, and engaged citizens. Fortunately, a host of social ills -- from violence and urban decay to persistent poverty and homelessness to lost wages and the high costs of incarceration -- can be prevented by investing in cost-effective community supports that help young people who are, or who are in danger of becoming, disconnected. The strategies outlined in the YTFG publication Safe Passage highlight some of the ways we can make more prudent and effective investments in our young people

Temporal Passage

This article explains that time flow is a subjective, mind-dependent phenomenon. The paper describes the nature of the subjective "present" of consciousness, and defines the mechanism that brings about this present's motion from past to future. The first section of the article demonstrates that existence is a dynamic process and shows that time arises from this process. The second section presents a geometric analysis of the present's motion. The third section contrasts space with time. In the last section, consciousness and time are discussed within the context of Einstein's theory of relativity

First-Passage Duality

We show that the distribution of times for a diffusing particle to first hit an absorber is \emph{independent} of the direction of an external flow field, when we condition on the event that the particle reaches the target for flow away from the target. Thus, in one dimension, the average time for a particle to travel to an absorber a distance $\ell$ away is $\ell/|v|$, independent of the sign of $v$. This duality extends to all moments of the hitting time. In two dimensions, the distribution of first-passage times to an absorbing circle in the radial velocity field $v(r)=Q/(2\pi r)$ again exhibits duality. Our approach also gives a new perspective on how varying the radial velocity is equivalent to changing the spatial dimension, as well as the transition between transience and strong transience in diffusion.Comment: 12 pages, 1 figure, IOP format. Updated version has minor changes in response to referees. Latest version: various minor typos fixed. For publication in JSTA

Inhomogeneous first-passage percolation

We study first-passage percolation where edges in the left and right half-planes are assigned values according to different distributions. We show that the asymptotic growth of the resulting inhomogeneous first-passage process obeys a shape theorem, and we express the limiting shape in terms of the limiting shapes for the homogeneous processes for the two weight distributions. We further show that there exist pairs of distributions for which the rate of growth in the vertical direction is strictly larger than the rate of growth of the homogeneous process with either of the two distributions, and that this corresponds to the creation of a defect along the vertical axis in the form of a `pyramid'.Comment: 25 pages, 1 figur

The inverse first-passage problem and optimal stopping

Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that the solution of the inverse first- passage problem coincides with the solution of a related optimal stopping problem. Consequently, methods from optimal stopping theory may be applied in the study of the inverse first-passage problem. We illustrate this with a study of the associated integral equation for the boundary