scholarly journals SELF-SIMILARITY LIMITS OF GENOMIC SIGNATURES

Fractals ◽  
2003 ◽  
Vol 11 (01) ◽  
pp. 19-25 ◽  
Author(s):  
ZUO-BING WU
Keyword(s):  
Dna Sequence ◽  
Dna Sequences ◽  
Finite Sequence ◽  
Self Similarity ◽  
String Length ◽  
Chaos Game Representation ◽  
Genomic Signatures ◽  
Chaos Game ◽  
Representation Method ◽  
Complete Genomic

It is shown that metric representation of DNA sequences is one-to-one. By using the metric representation method, suppression of nucleotide strings in the DNA sequences is determined. For a DNA sequence, an optimal string length to display genomic signature in chaos game representation is obtained by eliminating effects of the finite sequence. The optimal string length is further shown as a self-similarity limit in computing information dimension. By using the method, self-similarity limits of bacteria complete genomic signatures are further determined.

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.

4D Graphical representation research of DNA sequences

2015 ◽  
Vol 08 (01) ◽  
pp. 1550004 ◽  
Author(s):  
Chengjie Tan ◽  
Shanshan Li ◽  
Ping Zhu
Keyword(s):  
Dna Sequence ◽  
Dna Sequences ◽  
Graphical Representation ◽  
Hierarchical Cluster ◽  
Positive Outcome ◽  
Biological Information ◽  
Terminal Point ◽  
Base Pairs ◽  
Representation Method ◽  
The Times

Graphical representation of DNA sequences is a key component in studying biological problems. In order to gain new insights in DNA sequences, this paper combined the digitized methods of single-base, base pairs and coding in triplet bases with the times of base appearing, and then a novel 4D graphical representation method of DNA sequences was put forward. It was a one-to-one correspondence of the arbitrary DNA sequence and 4D graphical representation, that avoided causing non-unique 4D graphical representation and overlapping lines. The method could reflect the biological information features of DNA sequence more comprehensively and effectively without any losses. Based on the 4D graphical representation, we used the geometric center of 4D graphical representation as eigenvalue of DNA sequences analyses, which kept the original features of the data, and then established the Euclidean distances and included angles between vectors' terminal point for similarity analyses of the first extron of the beta-globulin gene among 11 species. Finally, we established the graph of systematic hierarchical cluster analysis of 11 species to observe more easily the relationship between species. A positive outcome was reached, and the results were in accord with biological taxonomy, which also supported the rationality and effectiveness of the novel 4D graphical representation.

The spectrum of genomic signatures: from dinucleotides to chaos game representation

Gene ◽  
2005 ◽  
Vol 346 ◽  
pp. 173-185 ◽  
Author(s):  
Yingwei Wang ◽  
Kathleen Hill ◽  
Shiva Singh ◽  
Lila Kari
Keyword(s):  
Chaos Game Representation ◽  
Genomic Signatures ◽  
Chaos Game ◽  
Game Representation

CHAOS GAME CHARACTERIZATION OF TEMPORAL PRECIPITATION VARIABILITY: APPLICATION TO REGIONALIZATION

Fractals ◽  
2006 ◽  
Vol 14 (02) ◽  
pp. 87-99 ◽  
Author(s):  
J. M. GUTIÉRREZ ◽  
A. GALVÁN ◽  
A. S. COFIÑO ◽  
C. PRIMO
Keyword(s):  
Graphical Representation ◽  
Chaos Game Representation ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Aggregation Scheme ◽  
Chaos Game ◽  
Representation Method ◽  
Illustrative Application ◽  
Game Representation

We present an application of the fractal "chaos game representation" method in climatology for characterizing temporal precipitation aggregation patterns. To this aim, we establish an analogy with linguistic analysis considering precipitation as a discrete variable (e.g. rain, no rain). Each weekly, or monthly, symbolic sequence of observed precipitation is then considered a "word" and the climatological time series observed at a particular gauge defines a "language." The distribution of different words within the language characterizes the particular precipitation aggregation scheme. In this paper we show that the chaos game representation method provides a graphical representation (a fractal pattern, or fingerprint) of the distribution of words and also gives a quantitative characterization in terms of parameters such as the box-counting dimension and the entropy. We show that different climates exhibit characteristic patterns with different fractal exponents and entropies. As an illustrative application, the method is used for automatic regionalization of a set of gauges in the Iberian peninsula, showing that these new indices outperform standard averaged statistics (monthly means, etc.).

Application of chaos game representation method to visualize genome structure

1999 ◽  
Author(s):  
Alain Giron ◽  
Bernard Fertil ◽  
Djamel Brahmi ◽  
Joseph Vilain ◽  
Patrick Deschavanne
Keyword(s):  
Genome Structure ◽  
Chaos Game Representation ◽  
Chaos Game ◽  
Representation Method ◽  
Game Representation
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