Efficient and Stable Voxel-Based Algorithm for Computing 3D Zernike Moments and Shape Reconstruction

3D Zernike moments based on 3D Zernike polynomials have been successfully applied to the field of voxelized 3D shape retrieval and have attracted more attention in biomedical image processing. As the order of 3D Zernike moments increases, both computational efficiency and numerical accuracy decrease. Due to this phenomenon, a more efficient and stable method for computing high-order 3D Zernike moments was proposed in this study. The proposed recursive formula for computing 3D Zernike radial polynomials combines the recursive calculation of spherical harmonics to develop a voxel-based algorithm for the calculation of 3D Zernike moments. The algorithm was applied to the 3D shape Michelangelo's David with a size of 150×150×150 voxels. As compared to the method without additional acceleration, the proposed method uses a group action of order sixteen orthogonal group and saving unnecessary iterations, the factor of speed-up is 56.783±3.999 when the order of Zernike moments is between 10 and 450. The proposed method also obtained an accurate reconstructed shape with the error rate (normalized mean square error) of 0.00 (4.17×10^-3) when the reconstruction was computed for all moments up to order 450.

On recursive expressions for statistics of decimated sequences

In what follows we introduce the recursive approach for calculating statistical moments of decimated realizations. We prove the corollaries referring to recursive calculation and present an example for any realization of 17 sample.

Impact of big data congestion in IT: an adaptive knowledge-based bayesian network

Recent progress on real-time systems are growing high in information technology which is showing importance in every single innovative field. Different applications in IT simultaneously produce the enormous measure of information that should be taken care of. In this paper, a novel algorithm of adaptive knowledge-based Bayesian network is proposed to deal with the impact of big data congestion in decision processing. A Bayesian system show is utilized to oversee learning arrangement toward all path for the basic leadership process. Information of Bayesian systems is routinely discharged as an ideal arrangement, where the examination work is to find a development that misuses a measurably inspired score. By and large, available information apparatuses manage this ideal arrangement by methods for normal hunt strategies. As it required enormous measure of information space, along these lines it is a tedious method that ought to be stayed away from. The circumstance ends up unequivocal once huge information include in hunting down ideal arrangement. A calculation is acquainted with achieve quicker preparing of ideal arrangement by constraining the pursuit information space. The proposed algorithm consists of recursive calculation intthe inquiry space. The outcome demonstrates that the ideal component of the proposed algorithm can deal with enormous information by processing time, and a higher level of expectation rates.

Strapdown Attitude Computation: Functional Iterative Integration versus Taylor Series Expansion

There are two basic approaches to strapdown attitude computation, namely, the traditional Taylor series expansion approach and the Picard iterative method. The latter was recently implemented in a recursive form basing on the Chebyshev polynomial approximation and resulted in the so-called functional iterative integration approach. Up to now a detailed comparison of these two approaches with arbitrary number of gyroscope samples has been lacking for the reason that the first one is based on the simplified rotation vector equation while the second one uses the exact form. In this paper, the mainstream algorithms are considerably extended by the Taylor series expansion approach using the exact differential equation and recursive calculation of high-order derivatives, and the functional iterative integration approach is re-implemented on the normal polynomial. This paper applies the two approaches to solve the strapdown attitude problem, using the attitude parameter of quaternion as a demonstration. Numerical results under the classical coning motion are reported to assess all derived attitude algorithms. It is revealed that in the low and middle relative conic frequency range all algorithms have the same order of accuracy, but in the range of high relative frequency the algorithm by the functional iterative integration approach performs the best in both accuracy and robustness if the Chebyshev polynomials and a larger number of gyroscope samples are to be used. The main conclusion applies to other attitude parameters as well.

A Generalized Language Model in Tensor Space

In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling language. Developing a higher-order tensor representation is challenging, in terms of deriving an effective solution and showing its generality. In this paper, we propose a language model named Tensor Space Language Model (TSLM), by utilizing tensor networks and tensor decomposition. In TSLM, we build a high-dimensional semantic space constructed by the tensor product of word vectors. Theoretically, we prove that such tensor representation is a generalization of the n-gram language model. We further show that this high-order tensor representation can be decomposed to a recursive calculation of conditional probability for language modeling. The experimental results on Penn Tree Bank (PTB) dataset and WikiText benchmark demonstrate the effectiveness of TSLM.

Relationships between step and cumulative PMI and E-factors: implications on estimating material efficiency with respect to charting synthesis optimization strategies

This report describes mathematical relationships between step and cumulative process mass intensities (PMIs) for synthesis plans, and analogous parameters applied to E-factors. It is shown that both step E-factors and step PMIs are not additive for synthesis plans. It is also shown that a recursive calculation of cumulative PMIs from step PMIs is a rapid method of determining overall PMIs for synthesis plans, though cumulative PMIs are not sufficiently informative as step PMIs or step E-factors to identify bottlenecks in synthesis plans. Illustrations on the use of these metrics to track the material efficiency of published synthesis plans for the pharmaceutical, apixaban, are given as a template example. Advantages and disadvantages of each metric are discussed. A general algorithm to select the most promising candidate synthesis plans considered at the design stage for a given molecular target that most likely satisfy “green” material efficiency criteria is also presented.