Notation, quantitative limitations

The paper is organized as follows. Section 2 presents the state of the art and highlights the current limitations of existing approaches for sequences assessment. Section 3 introduces the theoretical framework of the probabilistic languages (Garg et al. 1999) and the used notations. In section 4 is introduced the case study which is used like a support for the rest of the paper. Section 5 develops a theoretical framework based on probabilistic languages for quantitative assessment of events sequences. This proposed approach is illustrated using the case study in the section 6. Finally, section 7 presents the conclusions of this work and identifies some future research directions. 

The standard tetrahedral radii obtained by Pauling and Huggins have sometimes been referred to as tetrahedral covalent radii, but we prefer the original notation since we wish to reserve the term covalent for bonds to which each atom provides one electron. We shall return to this point in Sect. 9. Since these radii can only be used to predict bond distances between atoms that are both tetrahedrally coordinated, they are of limited utility. They were nevertheless of great interest at the time since they were the first radii that provided a quantitative illustration of the decrease of atomic bonding radii across the short periods of the periodic table and their increase as a group is descended. 

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