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Ryo Muramatsu

Publications and source records attributed to Ryo Muramatsu.

5 recordsLinked to original sources

Wave front set of solutions to the fractional Schrödinger equation

In this paper, we characterize the wave front sets of solutions to fractional Schrödinger equations \(i\partial_{t}u =(-Δ)^{θ/2}u + V(x)u\) with $0<θ<2$ via the wave packet transform (short-time Fourier transform). We clarify the relationship between the order \(θ\) of the fractional Laplacian and the growth rate of the potential in the problem of propagation of singularities. In particular, we present a theorem that bridges the propagation mechanisms of singularities for the Schrödinger and wave equations.

math.AP

Wave front set of solutions to Schrödinger equations with time-dependent magnetic fields

In this paper, we determine the wave front set of solutions to the Schrödinger equation with time-dependent magnetic fields. We considered time-dependent and `not so small' magnetic fields through the method using the wave packet transform established by K. Kato, M. Kobayashi and S. Ito. Furthermore, we checked that the fundamental solution of the Schrödinger equation in a spatially decaying magnetic field has no singularities as a consequence of our result.

math.AP

Evaluation Framework for Performance Limitation of Autonomous Systems under Sensor Attack

Autonomous systems such as self-driving cars rely on sensors to perceive the surrounding world. Measures must be taken against attacks on sensors, which have been a hot topic in the last few years. For that goal one must first evaluate how sensor attacks affect the system, i.e. which part or whole of the system will fail if some of the built-in sensors are compromised, or will keep safe, etc. Among the relevant safety standards, ISO/PAS 21448 addresses the safety of road vehicles taking into account the performance limitations of sensors, but leaves security aspects out of scope. On the other hand, ISO/SAE 21434 addresses the security perspective during the development process of vehicular systems, but not specific threats such as sensor attacks. As a result the safety of autonomous systems under sensor attack is yet to be addressed. In this paper we propose a framework that combines safety analysis for scenario identification, and scenario-based simulation with sensor attack models embedded. Given an autonomous system model, we identify hazard scenarios caused by sensor attacks, and evaluate the performance limitations in the scenarios. We report on a prototype simulator for autonomous vehicles with radar, cameras and LiDAR along with attack models against the sensors. Our experiments show that our framework can evaluate how the system safety changes as parameters of the attacks and the sensors vary.

cs.CR