Analysis of Evacuation Trajectory Data Using Tensor Decomposition

Owing to the advances in information technology and heightened awareness regarding disaster response, many evacuation simulations have been performed by researchers in recent years. It is necessary to develop suitable disaster prevention plans or evacuation plans using data generated by such simulations. However, it is difficult to understand the simulation results in their original form because of the detailed and voluminous data generated. In this study, we focus on tensor decomposition, which is employed for analyzing multi-dimensional data, in order to analyze the evacuation simulation data, which often consists of multiple dimensions such as time and space. Tensor decomposition is applied to the movement trajectory data generated in the evacuation simulation with the objective of acquiring important disaster or evacuation patterns.

Application of the Feynman-tree theorem together with BCFW recursion relations

Recently, it has been shown that on-shell scattering amplitudes can be constructed by the Feynman-tree theorem combined with the BCFW recursion relations. Since the BCFW relations are restricted to tree diagrams, the preceding application of the Feynman-tree theorem is essential. In this way, amplitudes can be constructed by on-shell and gauge-invariant tree amplitudes. Here, we want to apply this method to the electron–photon vertex correction. We present all the single, double, and triple phase-space tensor integrals explicitly and show that the sum of amplitudes coincides with the result of the conventional calculation of a virtual loop correction.