3 papers
math.CA2025
The Fourier Ratio and complexity of signals
K. Aldaleh, W. Burstein, G. Garza +12
We study the Fourier ratio of a signal , \[ \mathrm{FR}(f)\ :=\ \sqrt{N}\,\frac{\|\widehat f\|_{L^1(μ)}}{\|\widehat f\|_{L^2(μ)}} \ =\ \frac{\|\widehat…
cs.AI2025
Verification-Guided Falsification for Safe RL via Explainable Abstraction and Risk-Aware Exploration
Tuan Le, Risal Shefin, Debashis Gupta +2
Ensuring the safety of reinforcement learning (RL) policies in high-stakes environments requires not only formal verification but also interpretability and targeted falsification.…
math.CA2024
Buffon Needle Problem Over Convex Sets
M. Dannenberg, W. Hagerstrom, G. Hart +4
We solve a variant of the classical Buffon Needle problem. More specifically, we inspect the probability that a randomly oriented needle of length originating in a bounded conv…