scholarly journals A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves

2010 ◽  
Vol E93-D (7) ◽  
pp. 1807-1815
Author(s):  
Chih-Sheng CHEN ◽  
Shen-Yi LIN ◽  
Min-Hsuan FAN ◽  
Chua-Huang HUANG
Keyword(s):  
Hilbert Space ◽  
Construction Method ◽  
Space Filling ◽  
Space Filling Curves ◽  
Dimensional Hilbert Space

scholarly journals Using Peano–Hilbert space filling curves for fast bidimensional ensemble EMD realization

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Paulo Costa ◽  
João Barroso ◽  
Hugo Fernandes ◽  
Leontios J Hadjileontiadis
Keyword(s):  
Hilbert Space ◽  
Space Filling ◽  
Space Filling Curves

scholarly journals Neural Network Analysis of Electroencephalograms Graphical Representation

2020 ◽  
pp. short52-1-short52-9
Author(s):  
Aleksandr Bragin ◽  
Vladimir Spitsyn
Keyword(s):  
Hilbert Space ◽  
Measurement Accuracy ◽  
Graphical Representation ◽  
Space Filling ◽  
Good Tool ◽  
Motor Patterns ◽  
Space Filling Curves ◽  
Markov Transition ◽  
Time Signals ◽  
Electroencephalogram Eeg

The article is devoted to the problem of recognition of motor imagery based on electroencephalogram (EEG) signals, which is associated with many difficulties, such as the physical and mental state of a person, measurement accuracy, etc. Artificial neural networks are a good tool in solving this class of problems. Electroencephalograms are time signals, Gramian Angular Fields (GAF), Markov Transition Field (MTF) and Hilbert space-filling curves transformations are used to represent time series as images. The paper shows the possibility of using GAF, MTF and Hilbert space-filling curves EEG signal transforms for recognizing motor patterns, which is further applicable, for example, in building a brain-computer interface.

Lossless compression of medical images using Hilbert space-filling curves

2008 ◽  
Vol 32 (3) ◽  
pp. 174-182 ◽  
Author(s):  
Jan-Yie Liang ◽  
Chih-Sheng Chen ◽  
Chua-Huang Huang ◽  
Li Liu
Keyword(s):  
Hilbert Space ◽  
Medical Images ◽  
Lossless Compression ◽  
Space Filling ◽  
Space Filling Curves

Data-partitioning using the Hilbert space filling curves: Effect on the speed of convergence of Fuzzy ARTMAP for large database problems

2005 ◽  
Vol 18 (7) ◽  
pp. 967-984 ◽  
Author(s):  
José Castro ◽  
Michael Georgiopoulos ◽  
Ronald Demara ◽  
Avelino Gonzalez
Keyword(s):  
Hilbert Space ◽  
Data Partitioning ◽  
Fuzzy Artmap ◽  
Speed Of Convergence ◽  
Large Database ◽  
Space Filling ◽  
Space Filling Curves

scholarly journals Load balancing using Hilbert space-filling curves for parallel shallow water simulations

2019 ◽  
pp. 75-87
Author(s):  
А.В. Чаплыгин ◽  
Н.А. Дианский ◽  
А.В. Гусев
Keyword(s):  
Hilbert Space ◽  
Load Balancing ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
General Circulation ◽  
Sigma Model ◽  
Ocean Model ◽  
Computational Domain ◽  
Space Filling ◽  
Space Filling Curves

Представлен метод балансировки нагрузки вычислений с использованием кривых Гильберта применительно к параллельному алгоритму решения уравнений мелкой воды. Рассматриваемая система уравнений мелкой воды возникает в сигма-модели общей циркуляции океана INMOM (Institute of Numerical Mathematics Ocean Model) при разрешении гравитационных волн и является одним из основных блоков модели. Из-за наличия в океанах островов и берегов балансировка нагрузки вычислений на процессоры является особенно актуальной задачей. В качестве одного из таких методов был выбран метод балансировки нагрузки вычислений с использованием кривых Гильберта. Продемонстрирована большая эффективность этого метода по сравнению с равномерным разбиением без балансировки нагрузки и показано, что этот метод служит хорошей альтернативой библиотеке разбиений METIS. Оптимальность реализованного разбиения для мелкой воды точно соответствует оптимальности и для трехмерной сигма-модели INMOM в силу одинакового количества вертикальных уровней во всей расчетной области. This paper presents a method of load balancing using Hilbert space-filling curves applied to a parallel algorithm for solving shallow water equations. We consider the system of shallow water equations in the form presented in the ocean general circulation sigma-model INMOM (Institute of Numerical Mathematics Ocean Model). This system of equations is one of the basic blocks of the model. Due to land points in the computational grid, the load balancing is an especially urgent task. The method of load balancing using Hilbert space-filling curves is chosen as one of such methods. The paper demonstrates the greater efficiency of this method in comparison with the uniform partitioning without load balancing. It is shown that this method is a good alternative to the METIS standard library. Moreover, the optimality of the implemented partition for the shallow water equations exactly corresponds to the optimality for the INMOM three-dimensional sigma-model due to the same number of vertical levels in the entire computational domain.

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