Vehicular Fog Computing Enabled Real-time Collision Warning via Trajectory Calibration

Vehicular fog computing (VFC) has been envisioned as a promising paradigm for enabling a variety of emerging intelligent transportation systems (ITS). However, due to inevitable as well as non-negligible issues in wireless communication, including transmission latency and packet loss, it is still challenging in implementing safety-critical applications, such as real-time collision warning in vehicular networks. In this paper, we present a vehicular fog computing architecture, aiming at supporting effective and real-time collision warning by offloading computation and communication overheads to distributed fog nodes. With the system architecture, we further propose a trajectory calibration based collision warning (TCCW) algorithm along with tailored communication protocols. Specifically, an application-layer vehicular-to-infrastructure (V2I) communication delay is fitted by the Stable distribution with real-world field testing data. Then, a packet loss detection mechanism is designed. Finally, TCCW calibrates real-time vehicle trajectories based on received vehicle status including GPS coordinates, velocity, acceleration, heading direction, as well as the estimation of communication delay and the detection of packet loss. For performance evaluation, we build the simulation model and implement conventional solutions including cloud-based warning and fog-based warning without calibration for comparison. Real-vehicle trajectories are extracted as the input, and the simulation results demonstrate that the effectiveness of TCCW in terms of the highest precision and recall in a wide range of scenarios

Stability manifolds of Kuznetsov components of prime Fano threefolds

Let $X$ be a cubic threefold, quartic double solid or Gushel--Mukai threefold, and $\mathcal{K}u(X)\subset \mathrm{D}^b(X)$ be its Kuznetsov component. We show that a stability condition $\sigma$ on $\mathcal{K}u(X)$ is Serre-invariant if and only if its homological dimension is at most $2$. As a corollary, we prove that all Serre-invariant stability conditions on $\mathcal{K}u(X)$ form a contractible connected component of the stability manifold.Comment: 19 pages, comments are very welcome