11 documents found, page 1 of 2
Can power laws help us understand gene and proteome information?
Costa, António Cardoso; Machado, J.A.Tenreiro; Quelhas, DulceProteins are biochemical entities consisting of one or more blocks typically folded in a 3D pattern. Each block (a polypeptide) is a single linear sequence of amino acids that are biochemically bonded together. The amino acid sequence in a protein is defined by the sequence of a gene or several genes encoded in the DNA-based genetic code. This genetic code typically uses twenty amino acids, but in certain organ...
A multidimensional scaling analysis of musical sounds based on pseudo phase plane
Lima, Miguel; Costa, António Cardoso; Machado, J. A. TenreiroThis paper studies musical opus from the point of view of three mathematical tools: entropy, pseudo phase plane (PPP), and multidimensional scaling (MDS). The experiments analyze ten sets of different musical styles. First, for each musical composition, the PPP is produced using the time series lags captured by the average mutual information. Second, to unravel hidden relationships between the musical styles th...
Analysis and visualization of chromosome information
Costa, António Cardoso; Machado, J. A. Tenreiro; Quelhas, DulceThis paper analyzes the DNA code of several species in the perspective of information content. For that purpose several concepts and mathematical tools are selected towards establishing a quantitative method without a priori distorting the alphabet represented by the sequence of DNA bases. The synergies of associating Gray code, histogram characterization and multidimensional scaling visualization lead to a col...
On the DNA of eleven mammals
Costa, António Cardoso; Machado, J. A. Tenreiro; Quelhas, DulceThis paper studies the DNA code of eleven mammals from the perspective of fractional dynamics. The application of Fourier transform and power law trendlines leads to a categorical representation of species and chromosomes. The DNA information reveals long range memory characteristics.
Multi-dimensional scaling applied to histogram-based DNA analysis
Costa, António Cardoso; Machado, J. A. Tenreiro; Quelhas, DulceThis paper aims to study the relationships between chromosomal DNA sequences of twenty species. We propose a methodology combining DNA-based word frequency histograms, correlation methods, and an MDS technique to visualize structural information underlying chromosomes (CRs) and species. Four statistical measures are tested (Minkowski, Cosine, Pearson product-moment, and Kendall τ rank correlations) to analyze t...
Shannon, rényie and tsallis entropy analysis of DNA using phase plane
Costa, António Cardoso; Machado, J. A. Tenreiro; Quelhas, DulceThis paper analyzes DNA information using entropy and phase plane concepts. First, the DNA code is converted into a numerical format by means of histograms that capture DNA sequence length ranging from one up to ten bases. This strategy measures dynamical evolutions from 4 up to 410 signal states. The resulting histograms are analyzed using three distinct entropy formulations namely the Shannon, Rényie and Tsal...
Histogram-based DNA analysis for the visualization of chromosome, genome and sp...
Costa, António Cardoso; Machado, J. A. Tenreiro; Quelhas, DulceWe describe a novel approach to explore DNA nucleotide sequence data, aiming to produce high-level categorical and structural information about the underlying chromosomes, genomes and species. The article starts by analyzing chromosomal data through histograms using fixed length DNA sequences. After creating the DNA-related histograms, a correlation between pairs of histograms is computed, producing a global co...
Entropy analysis of DNA code dynamics in human chromosomes
Costa, António Cardoso; Machado, J. A. Tenreiro; Quelhas, DulceDeoxyribonucleic acid, or DNA, is the most fundamental aspect of life but present day scientific knowledge has merely scratched the surface of the problem posed by its decoding. While experimental methods provide insightful clues, the adoption of analysis tools supported by the formalism of mathematics will lead to a systematic and solid build-up of knowledge. This paper studies human DNA from the perspective o...
Dynamical analysis of compositions
Costa, António Cardoso; Machado, J. A. Tenreiro; Lima, MiguelThis paper analyzes musical opus from the point of view of two mathematical tools, namely the entropy and the multidimensional scaling (MDS). The Fourier analysis reveals a fractional dynamics, but the time rhythm variations are diluted along the spectrum. The combination of time-window entropy and MDS copes with the time characteristics and is well suited to treat a large volume of data. The experiments focus ...
Fractional dynamics in DNA
Costa, António Cardoso; Machado, J. A. Tenreiro; Quelhas, DulceThis paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.