Avoiding or limiting regularities in words

International audienceIt is commonly admitted that the origin of combinatorics on words goes back to the work of Axel Thue in the beginning of the twentieth century, with his results on repetition-free words. Thue showed that one can avoid cubes on infinite binary words and squares on ternary words. Up to now, a large part of the work on the theoretic part of combinatorics on words can be viewed as extensions or variations of Thue’s work, that is, showing the existence (or nonexistence) of infinite words avoiding, or limiting, a repetition-like pattern. The goal of this chapter is to present the state of the art in the domain and also to present general techniques used to prove a positive or a negative result. Given a repetition pattern P and an alphabet, we want to know if an infinite word without P exists. If it exists, we are also interested in the size of the language of words avoiding P, that is, the growth rate of the language. Otherwise, we are interested in the minimum number of factors P that a word must contain. We talk about limitation of usual, fractional, abelian, and k-abelian repetitions and other generalizations such as patterns and formulas. The last sections are dedicated to the presentation of general techniques to prove the existence or the nonexistence of an infinite word with a given property

The systems biology graphical notation

Circuit diagrams and Unified Modeling Language diagrams are just two examples of standard visual languages that help accelerate work by promoting regularity, removing ambiguity and enabling software tool support for communication of complex information. Ironically, despite having one of the highest ratios of graphical to textual information, biology still lacks standard graphical notations. The recent deluge of biological knowledge makes addressing this deficit a pressing concern. Toward this goal, we present the Systems Biology Graphical Notation (SBGN), a visual language developed by a community of biochemists, modelers and computer scientists. SBGN consists of three complementary languages: process diagram, entity relationship diagram and activity flow diagram. Together they enable scientists to represent networks of biochemical interactions in a standard, unambiguous way. We believe that SBGN will foster efficient and accurate representation, visualization, storage, exchange and reuse of information on all kinds of biological knowledge, from gene regulation, to metabolism, to cellular signaling