A Multiresolution Graphical Representation for Similarity Relationship and Multiresolution Clustering for Biological Sequences

2017 ◽  
Vol 24 (4) ◽  
pp. 299-310 ◽  
Author(s):  
Lianping Yang ◽  
Weilin Zhang
Keyword(s):  
Graphical Representation ◽  
Biological Sequences ◽  
Similarity Relationship

Mapping Biomolecular Sequences: Graphical Representations - their Origins, Applications and Future Prospects

2021 ◽  
Vol 24 ◽  
Author(s):  
Ashesh Nandy
Keyword(s):  
Dna Sequences ◽  
Graphical Representation ◽  
Sequence Data ◽  
Basic Unit ◽  
Graphical Representations ◽  
Biological Sequences ◽  
Biological Sequence ◽  
New Approach ◽  
3D Space ◽  
2D And 3D

The exponential growth in the depositories of biological sequence data have generated an urgent need to store, retrieve and analyse the data efficiently and effectively for which the standard practice of using alignment procedures are not adequate due to high demand on computing resources and time. Graphical representation of sequences has become one of the most popular alignment-free strategies to analyse the biological sequences where each basic unit of the sequences – the bases adenine, cytosine, guanine and thymine for DNA/RNA, and the 20 amino acids for proteins – are plotted on a multi-dimensional grid. The resulting curve in 2D and 3D space and the implied graph in higher dimensions provide a perception of the underlying information of the sequences through visual inspection; numerical analyses, in geometrical or matrix terms, of the plots provide a measure of comparison between sequences and thus enable study of sequence hierarchies. The new approach has also enabled studies of comparisons of DNA sequences over many thousands of bases and provided new insights into the structure of the base compositions of DNA sequences In this article we review in brief the origins and applications of graphical representations and highlight the future perspectives in this field.

ON THE VISUALIZATION OF STRINGS AND FRACTALS OF SOME FORBIDDEN WORDS

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 1-14 ◽  
Author(s):  
CHENGXING HUANG ◽  
JIANPING LI ◽  
SHOULI PENG
Keyword(s):  
Graphical Representation ◽  
Biological Sequences ◽  
Index Set ◽  
Unit Square ◽  
Circular Codes ◽  
Representation Method

By using the frame representation method proposed by B. L. Hao et al. in 20001,2 and a method provided by P. Tino,3,4 we will devise the generalized graphical representation for the strings defined on an alphabet Σ = {0, 1, …, n - 1} with cardinal n but all these graphs are still shown in a unit square, and generate its corresponding struture tables automatically. In particular, the words defined on Σ are mapped into n-adic numbers so that the index set Ind(B) can be computed. Thus, the fractals of the forbidden words can be naturally constructed. It has already been known that for biological sequences, the circular codes can be applied to some special bacteria and their forbidden words are the 5-necklaces. In this paper, we notice that the fractals of the forbidden words are particularly useful to represent the circular codes for some biological sequences.

A Generalized Iterative Map for Analysis of Protein Sequences

2020 ◽  
Vol 23 ◽  
Author(s):  
Jiahe Huang ◽  
Qi Dai ◽  
Yuhua Yao ◽  
Ping-An He
Keyword(s):  
Amino Acids ◽  
Amino Acid ◽  
Correlation Analysis ◽  
Physicochemical Properties ◽  
Graphical Representation ◽  
Protein Sequences ◽  
Biological Sequences ◽  
Alignment Method ◽  
Alignment Free ◽  
Comparison Results

Aim and Objective: The similarities comparison of biological sequences is the important task in bioinformatics. The methods of the similarities comparison for biological sequences are divided into two classes: sequence alignment method and alignment-free method. The graphical representation of biological sequences is a kind of alignment-free methods, which constitutes a tool for analyzing and visualizing the biological sequences. In this article, a generalized iterative map of protein sequences was suggested to analyze the similarities of biological sequences. Materials and Methods: Based on the normalized physicochemical indexes of 20 amino acids, each amino acid can be mapped into a point in 5D space. A generalized iterative function system was introduced to outline a generalized iterative map of protein sequences, which can not only reflect various physicochemical properties of amino acids but also incorporate with different compression ratios of component of generalized iterative map. Several properties were proved to illustrate the advantage of generalized iterative map. The mathematical description of generalized iterative map was suggested to compare the similarities and dissimilarities of protein sequences. Based on this method, similarities/dissimilarities were compared among ND5 proteins sequences, as well as ND6 protein sequences of ten different species. Results: By correlation analysis, the ClustalW results were compared with our similarity/dissimilarity results and other graphical representation results to show the utility of our approach. The comparison results show that our approach has better correlations with ClustalW for all species than other approaches and illustrate the effectiveness of our approach. Conclusion: Two examples show that our method not only has good performances and effects in the similarity/dissimilarity analysis of protein sequences but also does not require complex computation.

Missing Data - Better "Not to Have Them", but What If You Do? (Part 1)

Marketing ZFP ◽  
2019 ◽  
Vol 41 (4) ◽  
pp. 21-32
Author(s):  
Dirk Temme ◽  
Sarah Jensen
Keyword(s):  
Missing Data ◽  
Statistical Power ◽  
Missing Values ◽  
Graphical Representation ◽  
Marketing Research ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Full Information Maximum Likelihood ◽  
Definition Of ◽  
Traditional Approaches

Missing values are ubiquitous in empirical marketing research. If missing data are not dealt with properly, this can lead to a loss of statistical power and distorted parameter estimates. While traditional approaches for handling missing data (e.g., listwise deletion) are still widely used, researchers can nowadays choose among various advanced techniques such as multiple imputation analysis or full-information maximum likelihood estimation. Due to the available software, using these modern missing data methods does not pose a major obstacle. Still, their application requires a sound understanding of the prerequisites and limitations of these methods as well as a deeper understanding of the processes that have led to missing values in an empirical study. This article is Part 1 and first introduces Rubin’s classical definition of missing data mechanisms and an alternative, variable-based taxonomy, which provides a graphical representation. Secondly, a selection of visualization tools available in different R packages for the description and exploration of missing data structures is presented.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

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