Factorizable Language: From Dynamics to Biology

Hao, Bailin; Xie, Hao

doi:10.1002/9783527626359.ch5

Cited by 4 publications

(8 citation statements)

References 50 publications

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“…The uniqueness problem is more interesting and it has a natural relation to the number of Eulerian loops in a graph. It may also be set in the framework of so-called factorizable language, a kind of formal languages (Shi et al, 2007;Li and Xie, 2008;Hao and Xie, 2008). In fact, most of natural proteins do have a unique reconstruction at K = 5 or 6 (Xia and Zhou, 2007).…”

Section: The Protein Sequence Decomposition and Reconstruction Problemmentioning

confidence: 98%

Composition vector approach to whole-genome-based prokaryotic phylogeny: Success and foundations

Hao

2010

Journal of Biotechnology

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Section: The Protein Sequence Decomposition and Reconstruction Problemmentioning

confidence: 98%

Composition vector approach to whole-genome-based prokaryotic phylogeny: Success and foundations

Hao

2010

Journal of Biotechnology

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“…In the symbolic sequences of our DNA model there are forbidden words, words that were considered in [ 18 ] to characterize the DNA, but in our symbolic space there are no forbidden groups of words. Any two groups of words is separated by the same small number 2 L n of nucleotides.…”

Section: Determination Of the Approximate Markov Partition: Specificamentioning

confidence: 99%

“…These models of the DNA capture the recurrence property of codons (a word formed by three nucleotides) [ 17 ] by measuring the statistics of the symbolic distance separation between two codons. In the work of Hao & Xie [ 18 ], they have shown how to analyse the long DNA sequences by converting it to an image. The DNA was characterized by the fractal-like patterns appearing in this image as a result of the forbidden words.…”

Section: Introductionmentioning

confidence: 99%

“…Our model allows for an easy calculation of entropy rates from groups of words with short length, a quantity that is usually calculated over very long words demanding high computational costs. In our model of DNA, there are forbidden words as in [ 18 ] but no forbidden group of words, all words contain and are formed by the same small symbolic sequence length of

, and any two words separated by

nucleotides are roughly decorrelated. There are N 2 groups of words.…”

Section: Introductionmentioning

confidence: 99%

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Markovian language model of the DNA and its information content

Srivastava¹,

Baptista²

2016

R. Soc. open sci.

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This work proposes a Markovian memoryless model for the DNA that simplifies enormously the complexity of it. We encode nucleotide sequences into symbolic sequences, called words, from which we establish meaningful length of words and groups of words that share symbolic similarities. Interpreting a node to represent a group of similar words and edges to represent their functional connectivity allows us to construct a network of the grammatical rules governing the appearance of groups of words in the DNA. Our model allows us to predict the transition between groups of words in the DNA with unprecedented accuracy, and to easily calculate many informational quantities to better characterize the DNA. In addition, we reduce the DNA of known bacteria to a network of only tens of nodes, show how our model can be used to detect similar (or dissimilar) genes in different organisms, and which sequences of symbols are responsible for most of the information content of the DNA. Therefore, the DNA can indeed be treated as a language, a Markovian language, where a ‘word’ is an element of a group, and its grammar represents the rules behind the probability of transitions between any two groups.

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“…For a more detailed elaboration of factorizable languages and the uniqueness problem please consult our review papers. 27,28 Based on the mathematical knowledge outlined above one can write at least three computer programs. The first program implements brute-force reconstructions using K-tuples from a given collection.…”

Section: Decomposition and Reconstruction Of Symbolic Sequences: Probmentioning

confidence: 99%

CVTree: A WHOLE-GENOME-BASED AND ALIGNMENT-FREE APPROACH TO MICROBIAL PHYLOGENY

Hao

2012

Int. J. Mod. Phys. Conf. Ser.

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The number of sequenced genomes of Archaea, Bacteria, and Fungi accumulates rapidly. Several thousands genomes of these unicellular organisms will be available in a few years. Due to the extremely large difference in genome size and gene content it is difficult to use the traditional alignment-based method to infer phylogeny from the genomes. An alignment-free and whole-genome-based approach called CVTree has been developed and successfully applied to these organisms. As CVTree has been successfully applied to genomes of viruses, chloroplasts, Bacteria, Archaea and fungi, in this brief review we will mainly touch on some mathematical problems related to the foundation of the new approach, including a few yet unsolved problems, such as the violation of the triangular inequalities of the dissimilarity measure used in the CVTree method.

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Factorizable Language: From Dynamics to Biology

Cited by 4 publications

References 50 publications

Composition vector approach to whole-genome-based prokaryotic phylogeny: Success and foundations

Composition vector approach to whole-genome-based prokaryotic phylogeny: Success and foundations

Markovian language model of the DNA and its information content

CVTree: A WHOLE-GENOME-BASED AND ALIGNMENT-FREE APPROACH TO MICROBIAL PHYLOGENY

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