Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger complexity classes. We study the power of nonuniform reductions for NP-completeness, obtaining both separations and upper bounds for nonuniform completeness vs un...

We examine the question of reconstruction of signals from periodic nonuniform samples. This involves discarding samples from a uniformly sampled signal in some periodic fashion. We give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform sampling pattern has been fixed. We give an implicit characterization of the reconstruction system, and a...

Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize ultimately reach a uniform state. However, this scenario only holds when velocity field is nondivergent has no normal component boundary. If either condition unmet, such as for active particles in bounded region, floating particles, or filter...

Dynamic time warping (DTW) is a fundamental technique in time series analysis for comparing one curve to another using a flexible time-warping function. However, it was designed to compare a single pair of curves. In many applications, such as in metabolomics and image series analysis, alignment is simultaneously needed for multiple pairs. Because the underlying warping functions are often rela...

Given two time series, possibly of different lengths, time warping is a method to construct an optimal alignment obtained by stretching or contracting time intervals. Unlike pairwise alignment of amino acid sequences, classical time warping, originally introduced for speech recognition, is not symmetric in the sense that the time warping distance between two time series is not necessarily equal...

Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is 3 times as large as that without trigonal warping and 6 times larger than that in single layer graphene. Although the trigonal warping of t...

We previously introduced three different fiducial marker-based correction methods (2D projection shifting, 2D projection warping, and 3D image warping) for patients’ involuntary motion in the lower body during weight-bearing Carm CT scanning. The 3D warping method performed better than 2D methods since it could more accurately take into account the lower body motion in 3D. However, as the 3D wa...