We present inequalities related to generalized matrix function for positive semidefinite block matrices. introduce partial functions corresponding traces, and then provide a unified extension of the recent due Lin [Electron. J. Linear Algebra 27 (2014) 821-826], Zhang et al. [Linear Appl. 498 (2016) 99-105] 332-341] result Choi 532 (2017) 1-7]. Moreover, we demonstrate application $3\times 3$ m...

Generalized secret sharing is a method of constructing secret sharing from the perspective of access structure. In this paper, we propose a novel solution for achieving generalized secret sharing with linear hierarchical secrets. We use a matrix to model the relationship related to the access structure and transfer the matrix to modular arithmetic, which is calculated by Chinese Remainder Theor...

Cam contour fitting is greatly affected by data segmentation errors. Yet traditional methods are susceptible to noise and not able cope with of multiple curve type. Therefore, a new method proposed based on Generalized Cross Product (GCP), the arc cam taken as examples. Regarding series fragments, circular features each fragment transformed GCP norm vector mapping. Based robustness GCP, disturb...

In linear models with hierarchical interaction structures product type designs are shown to be D{optimal simultaneously for the whole parameter vector and for testing against any hierarchical submodel. Moreover, product type designs are also q {optimal for the highest order interactions.

Hierarchical learning algorithms have enjoyed tremendous growth in recent years, with many new algorithms being proposed and applied to a wide range of applications. However, despite the apparent success of hierarchical algorithms in practice, the theory of hierarchical architectures remains at an early stage. In this paper we study the theoretical properties of hierarchical algorithms from a m...