H∞ filtering for two-dimensional continuous-time Markovian jump systems with deficient transition descriptions

Markovian language model of the DNA and its information content

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.