Parallel Distributed Detection of an Invariant Feature Associated with Self-Similar Patterns

1997 ◽  
Vol 11 (07) ◽  
pp. 1051-1064 ◽  
Author(s):  
Kohji Kamejima
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Projection Algorithm ◽  
Parallel Projection ◽  
Contraction Mappings ◽  
Computable Set ◽  
Invariant Feature ◽  
Fractal Patterns ◽  
Self Similar ◽  
Distributed Scheme

A parallel distributed scheme is presented for extracting a computable feature associated with self similar patterns. Observed patterns are assumed to be specified in terms of a set of contraction mappings that evokes an "avalanche of exploration" in image field. This intrinsically non-deterministic imaging process yields a conditional probability that is represented on a diffusion system. For identifying mapping set, a parallel projection algorithm is designed on a computable set of local minimums of the conditional distribution. The scheme is applied to dynamic detection of fractal patterns.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

scholarly journals Symmetries and Metamorphoses

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 907
Author(s):  
Giuseppe Vitiello
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Arrow Of Time ◽  
Quantum Field ◽  
Continuous Symmetry ◽  
Spontaneous Breakdown ◽  
Symmetry Properties ◽  
Fractal Patterns ◽  
Symmetry Transformations ◽  
Self Similar

In quantum field theory with spontaneous breakdown of symmetry, the invariance of the dynamics under continuous symmetry transformations manifests itself in observable ordered patterns with different symmetry properties. Such a dynamical rearrangement of symmetry describes, in well definite formal terms, metamorphosis processes. The coherence of the correlations generating order and self-similar fractal patterns plays a crucial role. The metamorphosis phenomenon is generated by the loss of infrared contributions in physical states and observables due to their localized nature. The dissipative dynamics and evolution, the arising of the arrow of time and entanglement are also discussed. The conclusions may be extended to biology and neuroscience and to some aspects of linguistics in the transition from syntax to semantics (generation of meanings).

scholarly journals Fractal-based techniques for physiological time series: An updated approach

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 741-750 ◽  
Author(s):  
José Luis Roca ◽  
German Rodríguez-Bermúdez ◽  
Manuel Fernández-Martínez
Keyword(s):  
Time Series ◽  
State Of The Art ◽  
Self Similarity ◽  
High Quality ◽  
Detailed Review ◽  
Physiological Time ◽  
Wide Range ◽  
Fractal Patterns ◽  
Self Similar ◽  
And Performance

AbstractAlong this paper, we shall update the state-of-the-art concerning the application of fractal-based techniques to test for fractal patterns in physiological time series. As such, the first half of the present work deals with some selected approaches to deal with the calculation of the self-similarity exponent of time series. They include broadly-used procedures as well as recent advances improving their accuracy and performance for a wide range of self-similar processes. The second part of this paper consists of a detailed review of high-quality studies carried out in the context of electroencephalogram signals. Both medical and non-medical applications have been deeply reviewed. This work is especially recommended to all those researchers especially interested in fractal pattern recognition for physiological time series.

CODING AND DISTANCE CALCULATING OF SEPARATELY RANDOM FRACTALS AND APPLICATION TO GENERATING RIVER NETWORKS

Fractals ◽  
2005 ◽  
Vol 13 (01) ◽  
pp. 57-71 ◽  
Author(s):  
CHUN-PO HUNG ◽  
RU-YIH WANG
Keyword(s):  
Topological Distance ◽  
Starting Point ◽  
Coding Method ◽  
Wide Range ◽  
Width Function ◽  
Instantaneous Unit Hydrograph ◽  
Fractal Patterns ◽  
Self Similar ◽  
Hydrologic Responses ◽  
Northern Taiwan

This work develops a preliminary method for coding random self-similar patterns as a series of numbers and investigates the corresponding algorithm to calculate the topological distance between starting point and the link in the generated fractal pattern from the code series. With reference to the wide range of stochastic property in natural patterns, a process for generating fractal patterns with various generating probabilities of the pattern links denoted as separately random self-similar generation or separately random fractal is proposed. To assess the adaptability of the process, the coding method is applied to the generation of a random self-similar river network and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. The width function-based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results show that the separately random self-similar generating algorithm can be implemented successfully to calculate hydrologic responses.

scholarly journals Entropy Spectrum of Self-Similar Fractal Patterns

1995 ◽  
Vol 94 (5) ◽  
pp. 737-744 ◽  
Author(s):  
H. Honjo ◽  
M. Sano
Keyword(s):  
Entropy Spectrum ◽  
Fractal Patterns ◽  
Self Similar

scholarly journals Fractal graphic as digital objectless art

2014 ◽  
Vol 6 (1) ◽  
pp. 68-76
Author(s):  
Dmitry Yurievich Nekrasov
Keyword(s):  
Sea Urchins ◽  
Computer Software ◽  
Visual Language ◽  
Mathematical Skills ◽  
Painting Technique ◽  
Modern Computer ◽  
Digital Painting ◽  
Fractal Patterns ◽  
Fractal Images ◽  
Self Similar

This article analyses the phenomenon of digital computer graphics, based on mathematical calculations, and possibilities of using it in different modern art techniques. Digital fractal patterns are irregular, self-similar structures, which are based on natural objects' group of similar characteristics, such as: corals, starfishes, sea urchins, snowflakes, crowns of the trees. The principle of such image shaping is natural, so its worthwhile to trace down it's digital mathematic simulation. Contrary to digital graphic and painting, fractal graphic does not base on classic art traditions. The closest to the fractal graphics are objectless ornamental traditions, inheriting principles of infinite spatial creation of similar groups. The article includes the comparison of general ornamental rules and features of fractal images. Due to the fact that modern computer software allows to create the digital fractal graphics without special mathematical skills, an artist can combine traditional and digital painting and abstract fractal graphic to reach that level of balance and fortuity of an image, that abstract artist has tried to get, using traditional techniques. The fractal graphic is examined as a digital counterpart of traditional painting technique of monotyping in complex art work. Author underlines the likeness of many digital and material ways of creating images. Finally, the visual language of a piece of art still remains more important, than technological details of its production.

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