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A dynamic L-cube polynomial is proposed to analyze dynamic three-dimensional pulse images (d3DPIs), as an extension of the previous static L-cube polynomial. In this paper, a weighted least squares (WLS) method is proposed to fit the amplitude C(t) of d3DPI at four physiological key points in addition to the best fit of L-cube polynomials to the measured normal and cold-pressor-test (CPT)-induced taut 3DPIs. Compared with other two fitting functions, C(t) of a dynamic L-cube polynomial can be well matched by the proposed WLS method with the least relative error at four physiological key points in one beat with statistical significance, in addition to the best fit of the measured 3DPIs. Therefore, a dynamic L-cube polynomial can reflect dynamic time characteristics of normal and CPT-induced hypertensive taut 3DPIs, which can be used as an evidence of hypertension diagnosis. [ABSTRACT FROM AUTHOR]

This article presents recent efforts in improving the efficiency and scalability of the mixed cell computation step in the context of the Polyhedral Homotopy method. Solving systems of polynomial equations is an important problem in applied mathematics. The Polyhedral Homotopy method is an important numerical method for this task. In this method, a necessary preprocessing step, known as the “mixed cell computation” problem has been the main bottleneck in the parallel efficiency and scalability. This article presents recent remarkable improvements in the parallel scalability of the algorithm that are applicable to a wide range of hardware architectures including multi-core systems, NUMA systems, computer clusters, and GPUs devices. [ABSTRACT FROM AUTHOR]