A New Approach To Estimate The Collision Probability For Automotive Applications

We revisit the computation of probability of collision in the context of automotive collision avoidance (the estimation of a potential collision is also referred to as conflict detection in other contexts). After reviewing existing approaches to the definition and computation of a collision probability we argue that the question "What is the probability of collision within the next three seconds?" can be answered on the basis of a collision probability rate. Using results on level crossings for vector stochastic processes we derive a general expression for the upper bound of the distribution of the collision probability rate. This expression is valid for arbitrary prediction models including process noise. We demonstrate in several examples that distributions obtained by large-scale Monte-Carlo simulations obey this bound and in many cases approximately saturate the bound. We derive an approximation for the distribution of the collision probability rate that can be computed on an embedded platform. In order to efficiently sample this probability rate distribution for determination of its characteristic shape an adaptive method to obtain the sampling points is proposed. An upper bound of the probability of collision is then obtained by one-dimensional numerical integration over the time period of interest. A straightforward application of this method applies to the collision of an extended object with a second point-like object. Using an abstraction of the second object by salient points of its boundary we propose an application of this method to two extended objects with arbitrary orientation. Finally, the distribution of the collision probability rate is identified as the distribution of the time-to-collision.Comment: Revised and restructured version, discussion of extended vehicles expanded, section on TTC expanded, references added, other minor changes, 17 pages, 18 figure

Partial Supersymmetry Breaking from Five Dimensions

Theories of partial supersymmetry breaking N=2 -> N=1 in four dimensions are derived by coupling the N=2 massless gravitino multiplet to N=2 supergravity in five dimensions and performing a generalized dimensional reduction on S^1/Z_2 with the Scherk-Schwarz mechanism. These theories agree with results that were previously derived from four dimensions.Comment: 15 pages, Latex; introduction slightly changed, one reference adde

Effect of Positive Role Model on Young Girls

Richard RosenkranzThis project focuses on the effect that an older role model or mentor can have on a younger girl regarding her attitude toward health and self-image. It looks at attitudes toward exercise, eating habits, self-esteem, and various other health topics. The data was collected through Wildcat Wellness Coaching, and the subjects were young females generally between the ages of 8 and 12. Some of the girls were exposed to Wildcat Wellness Coaching that taught them how to prepare healthy snacks and make exercising more fun. The other girls were exposed to Wildcat Wellness Coaching that taught them about important health topics that may affect them in the future. This program allowed them to meet with a coach weekly for about an hour. Each semester the participants were different and their progress was monitored from start to finish. Results showed a change in attitude of the girls who participated in one of the interventions, but not in the other

Implications of Non-universal Soft Masses on Gauge Coupling Unification

We study the gauge coupling unification of the minimal supersymmetric standard model with non-universal soft scalar and gaugino masses. The unification scale of the gauge couplings is estimated for non-universal cases. It is sensitive to the non-universality. It turns out that these cases can be combined with the assumption of string unification, which leads to a prediction of $\sin^2 \theta_W(M_Z)$ and $k_1$, the normalisation of the $U(1)_Y$ generator. String unification predicts $k_1=1.3 - 1.4$. These values have non-trivial implications on string model building. Two-loop corrections are also calculated. Some of these cases exhibit a large discrepancy between experiment and string unification. We calculate string threshold corrections to explain the discrepancy.Comment: 25 pages, Latex, 4 figures (not included

N=6 gauged supergravities from generalized dimensional reduction

We construct new N=6 gauged supergravities in four and five dimensions using generalized dimensional reduction. Supersymmetry is spontaneously broken to N=4,2,0 with vanishing cosmological constant. We discuss the gaugings of the broken phases, the scalar geometries and the spectrum. Generalized orbifold reduction is also considered and an N=3 no-scale model is obtained with three independent mass parameters.Comment: 1+9 pages, accepted for publication in Physics Letters