Photo-induced degradation of PFASs: Excited-state mechanisms from real-time time-dependent density functional theory

Yamijala, Sharma S.R.K.C.; Shinde, Ravindra; Hanasaki, Kota; Ali, Zulfikhar A.; Wong, Bryan M.

doi:10.1016/j.jhazmat.2021.127026

DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are linear in the number of time-series, they are generally quadratic in time-series length. The exception is generalized time warping (GTW), which has linear computational cost. Yet, it can only identify simple time warping functions. There is a need for a new fast, high-quality multisequence alignment algorithm. We introduce trainable time warping (TTW), whose complexity is linear in both the number and the length of time-series. TTW performs alignment in the continuoustime domain using a sinc convolutional kernel and a gradient-based optimization technique. We compare TTW and GTW on S5 UCR datasets in time-series averaging and classification. TTW outperforms GTW on 67.1% of the datasets for the averaging tasks, and 61.2% of the datasets for the classification tasks.

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