Existence theorem and global asymptotical stability for low-dimensional dynamical models of plasma turbulence

2020 ◽  
Vol 61 (4) ◽  
pp. 042702
Author(s):  
Shintaro Kondo ◽  
Ryusuke Numata
Keyword(s):  
Existence Theorem ◽  
Plasma Turbulence ◽  
Asymptotical Stability ◽  
Global Asymptotical Stability ◽  
Dynamical Models ◽  
Low Dimensional

scholarly journals Projection Analysis Optimization for Human Transition Motion Estimation

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Wanyi Li ◽  
Feifei Zhang ◽  
Qiang Chen ◽  
Qian Zhang
Keyword(s):  
Video Game ◽  
Human Motion ◽  
High Dimensional ◽  
Dynamical Models ◽  
Excellent Performance ◽  
3 Dimensional ◽  
Latent Space ◽  
Projection Analysis ◽  
Low Dimensional ◽  
Working Efficiency

It is a difficult task to estimate the human transition motion without the specialized software. The 3-dimensional (3D) human motion animation is widely used in video game, movie, and so on. When making the animation, human transition motion is necessary. If there is a method that can generate the transition motion, the making time will cost less and the working efficiency will be improved. Thus a new method called latent space optimization based on projection analysis (LSOPA) is proposed to estimate the human transition motion. LSOPA is carried out under the assistance of Gaussian process dynamical models (GPDM); it builds the object function to optimize the data in the low dimensional (LD) space, and the optimized data in LD space will be obtained to generate the human transition motion. The LSOPA can make the GPDM learn the high dimensional (HD) data to estimate the needed transition motion. The excellent performance of LSOPA will be tested by the experiments.

GALTON'S QUINCUNX: RANDOM WALK OR CHAOS?

2007 ◽  
Vol 17 (12) ◽  
pp. 4463-4469 ◽  
Author(s):  
KEVIN JUDD
Keyword(s):  
Dynamical System ◽  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Mechanical Device ◽  
Dynamical Models ◽  
The Central Limit Theorem ◽  
Random Events ◽  
Low Dimensional ◽  
Deterministic Dynamical System

In 1873 Francis Galton had constructed a simple mechanical device where a ball is dropped vertically through a harrow of pins that deflect the ball sideways as it falls. Galton called the device a quincunx, although today it is usually referred to as a Galton board. Statisticians often employ (conceptually, if not physically) the quincunx to illustrate random walks and the central limit theorem. In particular, how a Binomial or Gaussian distribution results from the accumulation of independent random events, that is, the collisions in the case of the quincunx. But how valid is the assumption of "independent random events" made by Galton and countless subsequent statisticians? This paper presents evidence that this assumption is almost certainly not valid and that the quincunx has the richer, more predictable qualities of a low-dimensional deterministic dynamical system. To put this observation into a wider context, the result illustrates that statistical modeling assumptions can obscure more informative dynamics. When such dynamical models are employed they will yield better predictions and forecasts.

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