scholarly journals Space-filling curves of self-similar sets (II): edge-to-trail substitution rule

Nonlinearity ◽  
2019 ◽  
Vol 32 (5) ◽  
pp. 1772-1809 ◽  
Author(s):  
Xin-Rong Dai ◽  
Hui Rao ◽  
Shu-Qin Zhang
Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050028
Author(s):  
HUI RAO ◽  
SHU-QIN ZHANG

Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. In a previous paper by Dai and the authors [Space-filling curves of self-similar sets (II): Edge-to-trail substitution rule, Nonlinearity 32(5) (2019) 1772–1809] it was shown that for all the connected self-similar sets with a skeleton satisfying the open set condition, space-filling curves can be constructed. In this paper, we give a criterion of existence of skeletons by using the so-called neighbor graph of a self-similar set. In particular, we show that a connected self-similar set satisfying the finite-type condition always possesses skeletons: an algorithm is obtained here.


2020 ◽  
Vol 10 (1) ◽  
pp. 65-70
Author(s):  
Andrei Gorchakov ◽  
Vyacheslav Mozolenko

AbstractAny real continuous bounded function of many variables is representable as a superposition of functions of one variable and addition. Depending on the type of superposition, the requirements for the functions of one variable differ. The article investigated one of the options for the numerical implementation of such a superposition proposed by Sprecher. The superposition was presented as a three-layer Feedforward neural network, while the functions of the first’s layer were considered as a generator of space-filling curves (Peano curves). The resulting neural network was applied to the problems of direct kinematics of parallel manipulators.


2010 ◽  
Vol 50 (2) ◽  
pp. 370-386 ◽  
Author(s):  
P. J. Couch ◽  
B. D. Daniel ◽  
Timothy H. McNicholl

Author(s):  
Paulo Costa ◽  
João Barroso ◽  
Hugo Fernandes ◽  
Leontios J Hadjileontiadis

2009 ◽  
pp. 2674-2675
Author(s):  
Mohamed F. Mokbel ◽  
Walid G. Aref

Author(s):  
Panagiotis Tsinganos ◽  
Bruno Cornelis ◽  
Jan Cornelis ◽  
Bart Jansen ◽  
Athanassios Skodras

Over the past few years, Deep learning (DL) has revolutionized the field of data analysis. Not only are the algorithmic paradigms changed, but also the performance in various classification and prediction tasks has been significantly improved with respect to the state-of-the-art, especially in the area of computer vision. The progress made in computer vision has produced a spillover in many other domains, such as biomedical engineering. Some recent works are directed towards surface electromyography (sEMG) based hand gesture recognition, often addressed as an image classification problem and solved using tools such as Convolutional Neural Networks (CNN). This paper extends our previous work on the application of the Hilbert space-filling curve for the generation of image representations from multi-electrode sEMG signals, by investigating how the Hilbert curve compares to the Peano- and Z-order space-filling curves. The proposed space-filling mapping methods are evaluated on a variety of network architectures and in some cases yield a classification improvement of at least 3%, when used to structure the inputs before feeding them into the original network architectures.


Sign in / Sign up

Export Citation Format

Share Document