A model is presented for the structure and evolution of the eukaryotic and vertebrate mitochondrial genetic codes, based on the representation theory of the Lie superalgebra A(5,0) approximately sl(6/1). A key role is played by pyrimidine and purine exchange symmetries in codon quartets.
The supersymmetric model of 1] for the evolution of the genetic code is elaborated. Energy considerations in nucleic acid strand modelling, using sl(2) polarity spin and sl(2=1) family box quartet symmetry, lead for the case of codons and anticodons to assignments of codons to 64-dimensional sl(6=1) ' A(5; 0) multiplets. In a previous paper 1] we… (More)
Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding R-matrices. It is also shown that a class of generalized Heisenberg algebras including those underlying physical models such as that of Calogero-Sutherland, is… (More)
The combinatorics of the BPHZ subtraction scheme for a class of ladder graphs for the three point vertex in φ 3 theory is transcribed into certain connectivity relations for marked chord diagrams (knots with transversal intersections). The resolution of the singular crossings using the equivalence relations in these examples provides confirmation of a… (More)
Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems, forming a quantum statistical model of a particle (walker) immersed in a bath of other particles (coins). Quantum walks following the so called U-and ε-quantization rules are presented. The former rule involves unitary… (More)
Brownian motion on a smash line algebra (a smash or braided version of the algebra resulting by tensoring the real line and the generalized paragrassmann line algebras), is constructed by means of its Hopf algebraic structure. Further, statistical moments, non stationary generalizations and its diffusion limit are also studied. The ensuing diffusion… (More)