scholarly journals An Effective Algorithm for the Synthesis of Irreducible Polynomials over a Galois Fields of Arbitrary Characteristics

2021 ◽  
Vol 20 ◽  
pp. 508-519
Author(s):  
Anatoly Beletsky

The known algorithms for synthesizing irreducible polynomials have a significant drawback: their computational complexity, as a rule, exceeds the quadratic one. Moreover, consequently, as a consequence, the construction of large-degree polynomials can be implemented only on computing systems with very high performance. The proposed algorithm is base on the use of so-called fiducial grids (ladders). At each rung of the ladder, simple recurrent modular computations are performers. The purpose of the calculations is to test the irreducibility of polynomials over Galois fields of arbitrary characteristics. The number of testing steps coincides with the degree of the synthesized polynomials. Upon completion of testing, the polynomial is classifieds as either irreducible or composite. If the degree of the synthesized polynomials is small (no more than two dozen), the formation of a set of tested polynomials is carried out using the exhaustive search method. For large values of the degree, the test polynomials are generating by statistical modeling. The developed algorithm allows one to synthesize binary irreducible polynomials up to 2Kbit on personal computers of average performance


2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Faming Gong ◽  
Haihua Chen ◽  
Shibao Li ◽  
Jianhang Liu ◽  
Zhaozhi Gu ◽  
...  

We address the problem of DOA estimation in positioning of nodes in wireless sensor networks. The Stochastic Maximum Likelihood (SML) algorithm is adopted in this paper. The SML algorithm is well-known for its high resolution of DOA estimation. However, its computational complexity is very high because multidimensional nonlinear optimization problem is usually involved. To reduce the computational complexity of SML estimation, we do the following work. (1) We point out the problems of conventional SML criterion and explain why and how these problems happen. (2) A local AM search method is proposed which could be used to find the local solution near/around the initial value. (3) We propose an algorithm which uses the local AM search method together with the estimation of DML or MUSIC as initial value to find the solution of SML. Simulation results are shown to demonstrate the effectiveness and efficiency of the proposed algorithms. In particular, the algorithm which uses the local AM method and estimation of MUSIC as initial value has much higher resolution and comparable computational complexity to MUSIC.



Alloy Digest ◽  
2017 ◽  
Vol 66 (12) ◽  

Abstract Alloy C688 is a high-performance copper alloy with very high conductivity. This datasheet provides information on composition, physical properties, hardness, elasticity, tensile properties, and bend strength. It also includes information on corrosion resistance as well as forming and joining. Filing Code: Cu-867. Producer or source: Gebr. Kemper GmbH + Company KG Metallwerke.



Alloy Digest ◽  
2017 ◽  
Vol 66 (10) ◽  

Abstract Alloy KHP 7025 (UNS C70250) is a high-performance copper alloy with very high conductivity. Uses include connector springs, tabs, contact springs, switches, relays, and leadframes. This datasheet provides information on composition, physical properties, hardness, elasticity, tensile properties, and bend strength. It also includes information on corrosion resistance as well as forming, machining, and joining. Filing Code: Cu-865. Producer or source: Gebr. Kemper GmbH + Company KG Metallwerke.



2017 ◽  
pp. 96-103 ◽  
Author(s):  
Gillian Eggleston ◽  
Isabel Lima ◽  
Emmanuel Sarir ◽  
Jack Thompson ◽  
John Zatlokovicz ◽  
...  

In recent years, there has been increased world-wide concern over residual (carry-over) activity of mostly high temperature (HT) and very high temperature (VHT) stable amylases in white, refined sugars from refineries to various food and end-user industries. HT and VHT stable amylases were developed for much larger markets than the sugar industry with harsher processing conditions. There is an urgent need in the sugar industry to be able to remove or inactivate residual, active amylases either in factory or refinery streams or both. A survey of refineries that used amylase and had activated carbon systems for decolorizing, revealed they did not have any customer complaints for residual amylase. The use of high performance activated carbons to remove residual amylase activity was investigated using a Phadebas® method created for the sugar industry to measure residual amylase in syrups. Ability to remove residual amylase protein was dependent on the surface area of the powdered activated carbons as well as mixing (retention) time. The activated carbon also had the additional benefit of removing color and insoluble starch.



Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 223
Author(s):  
Yen-Ling Tai ◽  
Shin-Jhe Huang ◽  
Chien-Chang Chen ◽  
Henry Horng-Shing Lu

Nowadays, deep learning methods with high structural complexity and flexibility inevitably lean on the computational capability of the hardware. A platform with high-performance GPUs and large amounts of memory could support neural networks having large numbers of layers and kernels. However, naively pursuing high-cost hardware would probably drag the technical development of deep learning methods. In the article, we thus establish a new preprocessing method to reduce the computational complexity of the neural networks. Inspired by the band theory of solids in physics, we map the image space into a noninteraction physical system isomorphically and then treat image voxels as particle-like clusters. Then, we reconstruct the Fermi–Dirac distribution to be a correction function for the normalization of the voxel intensity and as a filter of insignificant cluster components. The filtered clusters at the circumstance can delineate the morphological heterogeneity of the image voxels. We used the BraTS 2019 datasets and the dimensional fusion U-net for the algorithmic validation, and the proposed Fermi–Dirac correction function exhibited comparable performance to other employed preprocessing methods. By comparing to the conventional z-score normalization function and the Gamma correction function, the proposed algorithm can save at least 38% of computational time cost under a low-cost hardware architecture. Even though the correction function of global histogram equalization has the lowest computational time among the employed correction functions, the proposed Fermi–Dirac correction function exhibits better capabilities of image augmentation and segmentation.





Author(s):  
Peter Frank Perroni ◽  
Myriam Regattieri Delgado ◽  
Daniel Weingaertner


Author(s):  
Nikolay Kondratyuk ◽  
Vsevolod Nikolskiy ◽  
Daniil Pavlov ◽  
Vladimir Stegailov

Classical molecular dynamics (MD) calculations represent a significant part of the utilization time of high-performance computing systems. As usual, the efficiency of such calculations is based on an interplay of software and hardware that are nowadays moving to hybrid GPU-based technologies. Several well-developed open-source MD codes focused on GPUs differ both in their data management capabilities and in performance. In this work, we analyze the performance of LAMMPS, GROMACS and OpenMM MD packages with different GPU backends on Nvidia Volta and AMD Vega20 GPUs. We consider the efficiency of solving two identical MD models (generic for material science and biomolecular studies) using different software and hardware combinations. We describe our experience in porting the CUDA backend of LAMMPS to ROCm HIP that shows considerable benefits for AMD GPUs comparatively to the OpenCL backend.



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