A simple approach to quasicrystal structure and phason defect formulation

1990 ◽  
Vol 46 (2) ◽  
pp. 142-149 ◽  
Author(s):  
F. H. Li ◽  
Y. F. Cheng
Keyword(s):  
Crystal Structure ◽  
Dimensional Space ◽  
Physical Space ◽  
Simple Approach ◽  
High Dimensional ◽  
Periodic Lattice ◽  
Structure Model ◽  
Continuous Rotation ◽  
Geometrical Relationship ◽  
Quasicrystal Structure

The advantages of the cut or section method in describing quasicrystal structures and phason defects are given. The real and reciprocal quasilattice formulation is derived straightforwardly. It is shown that the linear phason strain which leads to the quasilattice distortion is equivalent to a rotation of physical space relative to the high-dimensional space. A continuous rotation of the physical space will make the quasilattice deviate from its idealized form and turn gradually into a periodic lattice. The derivation of a geometrical relationship between the icosahedral quasilattice and the corresponding b.c.c. lattice becomes simple and clear. This will be beneficial to the construction of a quasicrystal structure model by reference to the corresponding b.c.c. crystal structure.

Neural networks trained with high-dimensional functions approximation data in high-dimensional space

2021 ◽  
pp. 1-12
Author(s):  
Jian Zheng ◽  
Jianfeng Wang ◽  
Yanping Chen ◽  
Shuping Chen ◽  
Jingjin Chen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Data Distribution ◽  
High Dimensional ◽  
Sufficient Information ◽  
Sufficient Data ◽  
High Dimensional Space ◽  
Positive Effects ◽  
The Neural Networks ◽  
Using Data

Neural networks can approximate data because of owning many compact non-linear layers. In high-dimensional space, due to the curse of dimensionality, data distribution becomes sparse, causing that it is difficulty to provide sufficient information. Hence, the task becomes even harder if neural networks approximate data in high-dimensional space. To address this issue, according to the Lipschitz condition, the two deviations, i.e., the deviation of the neural networks trained using high-dimensional functions, and the deviation of high-dimensional functions approximation data, are derived. This purpose of doing this is to improve the ability of approximation high-dimensional space using neural networks. Experimental results show that the neural networks trained using high-dimensional functions outperforms that of using data in the capability of approximation data in high-dimensional space. We find that the neural networks trained using high-dimensional functions more suitable for high-dimensional space than that of using data, so that there is no need to retain sufficient data for neural networks training. Our findings suggests that in high-dimensional space, by tuning hidden layers of neural networks, this is hard to have substantial positive effects on improving precision of approximation data.

scholarly journals Analysis of the Morpho-Geometrical Changes of the Root Canal System Produced by TF Adaptive vs. BioRace: A Micro-Computed Tomography Study

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 531
Author(s):  
Loai Alsofi ◽  
Muhannad Al Harbi ◽  
Martin Stauber ◽  
Khaled Balto
Keyword(s):  
Surface Area ◽  
Root Canal ◽  
Type I ◽  
Structure Model ◽  
Canal Surface ◽  
Canal System ◽  
Structure Model Index ◽  
Continuous Rotation ◽  
Before And After ◽  
Root Canal System

We aimed to analyze the morpho-geometric changes of the root canal system created by two rotary systems (TF Adaptive and BioRace) using micro-CT technology. Two concepts of rotary file system kinematics, continuous rotation and adaptive kinematics, were used in root canal preparation. Twenty mandibular molars (n = 20) were selected with the following criteria: the teeth have mesial roots with a single and continuous isthmus connecting the mesiobuccal and mesiolingual canals (Vertucci’s Type I configuration) and distal roots with independent canals. Teeth were scanned at a resolution of 14 μm. Canals were divided equally into two groups and then enlarged sequentially using the BioRace system and TF Adaptive system according to manufacturer protocol. Co-registered images, before and after preparation, were evaluated for morphometric measurements of canal surface area, volume, structure model index, thickness, straightening, and un-instrumented surface area. Before and after preparation, data were statistically analyzed using a paired sample t-test. After preparation, data were analyzed using an unpaired sample test. The preparation by both systems significantly changed canal surface area, volume, structure model index, and thickness in both systems. There were no significant differences between instrument types with respect to these parameters (p > 0.05). TF Adaptive was associated with less straightening (8% compared with 17% for BioRace in the mesial canal, p > 0.05). Both instrumentation systems produced canal preparations with adequate geometrical changes. BioRace straightened the mesial canals more than TF Adaptive.

scholarly journals A System to Assess the Semantic Content of Student Essays

2001 ◽  
Vol 24 (3) ◽  
pp. 305-320 ◽  
Author(s):  
Benoit Lemaire ◽  
Philippe Dessus
Keyword(s):  
Latent Semantic Analysis ◽  
Semantic Analysis ◽  
Dimensional Space ◽  
Semantic Content ◽  
High Dimensional ◽  
High Dimensional Space

This paper presents Apex, a system that can automatically assess a student essay based on its content. It relies on Latent Semantic Analysis, a tool which is used to represent the meaning of words as vectors in a high-dimensional space. By comparing an essay and the text of a given course on a semantic basis, our system can measure how well the essay matches the text. Various assessments are presented to the student regarding the topic, the outline and the coherence of the essay. Our experiments yield promising results.

Effective approximation of high-dimensional space using neural networks

2021 ◽  
Author(s):  
Jian Zheng ◽  
Jianfeng Wang ◽  
Yanping Chen ◽  
Shuping Chen ◽  
Jingjin Chen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
High Dimensional ◽  
High Dimensional Space ◽  
Effective Approximation

scholarly journals A Novel Bat Algorithm Based on Differential Operator and Lévy Flights Trajectory

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Jian Xie ◽  
Yongquan Zhou ◽  
Huan Chen
Keyword(s):  
Differential Operator ◽  
Dimensional Space ◽  
Bat Algorithm ◽  
High Dimensional ◽  
Local Minima ◽  
Lévy Flights ◽  
Levy Flights ◽  
Mutation Strategy ◽  
Differential Algorithm ◽  
Simulation Results

Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy flights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy “DE/best/2” in differential algorithm. Lévy flights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are tested; the simulation results not only show that the proposed algorithm is feasible and effective, but also demonstrate that this proposed algorithm has superior approximation capabilities in high-dimensional space.

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