The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...

One of the most crucial factors involved in the optimum design and cost estimation of rock sawing process is the rock abrasivity that could result in a significant cost increase. Various methods including direct and indirect tests have been introduced in order to measure rock abrasivity. The Schimazek’s F-abrasiveness factor ( ) is one of the most common indices to assess rock abrasivity.  is t...

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

BACKGROUND The purpose of this study was to test the hypothesis that direct vertebral derotation by pedicle screws (PS) causes hypokyphosis of the thoracic spine in adolescent idiopathic scoliosis (AIS) patients, using computer simulation. METHODS Twenty AIS patients with Lenke type 1 or 2 who underwent posterior correction surgeries using PS were included in this study. Simulated corrections...

This paper presents a novel technique to correct for bias in a classical estimator using a learning approach. We apply a learned bias correction to a lidar-only motion estimation pipeline. Our technique trains a Gaussian process (GP) regression model using data with ground truth. The inputs to the model are high-level features derived from the geometry of the point-clouds, and the outputs are t...