CIRCULAR CHAOS GAME REPRESENTATION OF 1-D CHAOS AND ITS RELATION TO THE COMPLEX WEIERSTRASS FUNCTION

1999 ◽  
Vol 09 (10) ◽  
pp. 2069-2080 ◽  
Author(s):  
TAKASHI TSUCHIYA
Keyword(s):  
Weierstrass Function ◽  
Chaos Game Representation ◽  
One Dimensional ◽  
Circular Field ◽  
Shift Map ◽  
Fully Developed Chaos ◽  
Chaos Game ◽  
Triangular Field ◽  
Game Representation

Barnsley's chaos game which is originally played on a triangular field is generalized to a circular field and is used to visualize one-dimensional (1-D) fully developed chaos. It is shown that when the 1-D map used is the shift map or its extension (the r-adic map) the game point is exactly represented by the complex Weierstrass function.

Test on the Structure of Biological Sequences via Chaos Game Representation

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Peggy Cénac
Keyword(s):  
Markov Chain ◽  
Statistical Tests ◽  
Biological Sequences ◽  
Chaos Game Representation ◽  
New Family ◽  
Chaos Game ◽  
Tests For Independence ◽  
Game Representation

In this paper biological sequences are modelled by stationary ergodic sequences. A new family of statistical tests to characterize the randomness of the inputs is proposed and analyzed. Tests for independence and for the determination of the appropriate order of a Markov chain are constructed with the Chaos Game Representation (CGR), and applied to several genomes.

scholarly journals APPLICATION OF CHAOS GAME REPRESENTATION TO NONLINEAR TIME SERIES ANALYSIS

Fractals ◽  
2006 ◽  
Vol 14 (01) ◽  
pp. 27-35 ◽  
Author(s):  
TOMOYA SUZUKI ◽  
TOHRU IKEGUCHI ◽  
MASUO SUZUKI
Keyword(s):  
Time Series ◽  
Real Time ◽  
Dna Sequences ◽  
Surrogate Data ◽  
Nonlinear Time Series Analysis ◽  
Conditional Probabilities ◽  
Fractal Structures ◽  
Chaos Game Representation ◽  
Chaos Game ◽  
Game Representation

Iterative function systems are often used for investigating fractal structures. The method is also referred as Chaos Game Representation (CGR), and is applied for representing characteristic structures of DNA sequences visually. In this paper, we proposed an original way of plotting CGR to easily confirm the property of the temporal evaluation of a time series. We also showed existence of spurious characteristic structures of time series, if we carelessly applied the CGR to real time series. We revealed that the source of spurious identification came from non-uniformity of the frequency histograms of the time series, which is often the case of analyzing real time series. We also showed how to avoid such spurious identification by applying the method of surrogate data and introducing conditional probabilities of the time series.

scholarly journals Deep learning on chaos game representation for proteins

2019 ◽  
Vol 36 (1) ◽  
pp. 272-279 ◽  
Author(s):  
Hannah F Löchel ◽  
Dominic Eger ◽  
Theodor Sperlea ◽  
Dominik Heider
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Chemical Properties ◽  
Protein Sequences ◽  
Machine Learning Techniques ◽  
Supplementary Information ◽  
Support Vector ◽  
Chaos Game Representation ◽  
Chaos Game ◽  
Game Representation

AbstractMotivationClassification of protein sequences is one big task in bioinformatics and has many applications. Different machine learning methods exist and are applied on these problems, such as support vector machines (SVM), random forests (RF) and neural networks (NN). All of these methods have in common that protein sequences have to be made machine-readable and comparable in the first step, for which different encodings exist. These encodings are typically based on physical or chemical properties of the sequence. However, due to the outstanding performance of deep neural networks (DNN) on image recognition, we used frequency matrix chaos game representation (FCGR) for encoding of protein sequences into images. In this study, we compare the performance of SVMs, RFs and DNNs, trained on FCGR encoded protein sequences. While the original chaos game representation (CGR) has been used mainly for genome sequence encoding and classification, we modified it to work also for protein sequences, resulting in n-flakes representation, an image with several icosagons.ResultsWe could show that all applied machine learning techniques (RF, SVM and DNN) show promising results compared to the state-of-the-art methods on our benchmark datasets, with DNNs outperforming the other methods and that FCGR is a promising new encoding method for protein sequences.Availability and implementationhttps://cran.r-project.org/.Supplementary informationSupplementary data are available at Bioinformatics online.

Identifying anticancer peptides by using a generalized chaos game representation

2018 ◽  
Vol 78 (1-2) ◽  
pp. 441-463 ◽  
Author(s):  
Li Ge ◽  
Jiaguo Liu ◽  
Yusen Zhang ◽  
Matthias Dehmer
Keyword(s):  
Chaos Game Representation ◽  
Anticancer Peptides ◽  
Chaos Game ◽  
Game Representation
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