The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates xn. However, the path integral expression cannot be connected to the dynamics of classical mechanics, even though, superficially, there is some similarity between them. Further, the f...

Consider the square [0, n] with points from a Poisson point process of intensity 1 distributed within it. In [4] it was shown that the length Ln of a maximal increasing path (an increasing path that contains the most number of points) when properly centered and scaled converges to the Tracy-Widom distribution. Later [16] showed that all maximal paths have a displacement of n 2 3 +o(1) from the ...

This paper presents a cooperative path planning approach for teams of vehicles operating under timing constraints. A cooperative control approach based on coordination variables and coordination functions is introduced and applied to cooperative timing problems. Three types of timing constraints are considered: simultaneous arrival, tight sequencing, and loose sequencing. Simulation results dem...

We propose using the Global Dynamic Critical Path to diagnose system-wide bottlenecks using representative benchmarks to direct embedded SoC optimizations. We provide real-world experience of implementing the global critical path (GCP) analysis framework on a GloballyAsynchronous Locally-Synchronous (GALS) SoC built around the LEON3 CPU. We perform our analysis at the RTL level and extend our e...

Data security, energy consumption, and computation speed have all become crucial criteria in the new era of computing and communication technology. Cryptography plays an important role for data security and integrity and is widely adopted. On one hand, we want to reduce the computation overhead of cryptography algorithms; on the other hand, we also want to reduce the energy consumption associat...