Recent progress on the notion of global hyperbolicity

Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked singularities, and the space of the causal curves connecting two events. The latter includes structural results on globally hyperbolic spacetimes, their embeddability in Lorentz-Minkowski, and the recently revised notions of both, causal and conformal boundaries. Moreover, two criteria for checking global hyperbolicity are reviewed. The first one applies to general splitting spacetimes. The second one characterizes accurately global hyperbolicity and spacelike Cauchy hypersurfaces for standard stationary spacetimes, in terms of a naturally associated Finsler metric.Comment: 18 pages, 1 figure. Extended and updated contribution to the meeting "New Developments in Lorentzian Geometry" Berlin, Nov. 200

Optimizing Engagement Simulations Through the Advanced Framework for Simulation, Integration, and Modeling (AFSIM) Software

The ability to effectively model and simulate military missions holds the potential to save lives, money, and resources for the United States. The Advanced Framework for Simulation, Integration, and Modeling (AFSIM) software is a tool used to rapidly simulate and model new technologies and mission level scenarios. In this thesis, our objective is to integrate a closed loop optimization routine with AFSIM to identify an effective objective function to assess optimal inputs for engagement scenarios. Given the many factors which impact a mission level engagement, we developed a tool which interfaces with AFSIM to observe the effects from multiple inputs in an engagement scenario. Our tool operates under the assumption that simulation results have met an acceptable convergence threshold. The objective function evaluates the effectiveness and associated cost with a scenario using a genetic algorithm and a particle swarm optimization algorithm. From this, a statistical analysis was performed to assess risk from the distribution of effectiveness and cost at each point. The method allows an optimal set of inputs to be selected for a desired result from the selected engagement scenario.No embargoAcademic Major: Mechanical Engineerin

Collaborative Consent: harnessing the strengths of the Internet for consent in the online environment

Consent in the online environment is a crucial issue at this stage of the development of the Internet, and at the same time, in practice it is generally dealt with only on a superficial level. However, while the Internet offers significant challenges in terms of consent, it also provides unparalleled opportunities, which, if grasped, could enable a new level of consent, particularly where consent is required for services such as behavioural advertising systems. Through an examination of the failure of Phorm, the paper introduces a new concept, 'collaborative consent', treating consent not as a discrete, one-off decision but as a collaborative and communicative process, an ongoing relationship between the individual and the enterprise. The Internet provides a medium for immediate and interactive communication that could allow information to be given and choices to be made in real time - a first step to real, informed consent in the online world

The fallout from the McAlpine saga threatens the role of Twitter in public life

The fallout from the McAlpine saga has led to increasing fears that legal action will have a ‘chilling effect’ on the microblogging platform. Paul Bernal argues that Twitter provides something quite special for the media and that it should be nurtured. It’s possible a defence may develop naturally from the legal processes McAlpine’s team bring about but, if not, we ought to work to develop it

Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes

The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth time function $\tau$ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting $M= \R \times {\cal S}$, $g= - \beta(\tau,x) d\tau^2 + \bar g_\tau$, (b) if a spacetime $M$ admits a (continuous) time function $t$ (i.e., it is stably causal) then it admits a smooth (time) function $\tau$ with timelike gradient $\nabla \tau$ on all $M$.Comment: 9 pages, Latex, to appear in Commun. Math. Phys. Some comments on time functions and stably causal spacetimes are incorporated, and referred to gr-qc/0411143 for further detail