237 research outputs found
Sum rules of codon usage probabilities
In the crystal basis model of the genetic code, it is deduced that the sum of
usage probabilities of the codons with C and A in the third position for the
quartets and/or sextets is independent of the biological species for
vertebrates. A comparison with experimental data shows that the prediction is
satisfied within about 5 %.Comment: 7 page
Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
We classify all Hamiltonians with rank 1 symmetry, acting on a periodic
three-state spin chain, and solvable through (generalisation of) the coordinate
Bethe ansatz (CBA). We obtain in this way four multi-parametric extensions of
the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev,
Izergin-Korepin, Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians,
there exists 17-vertex and 14-vertex Hamiltonians that cannot be viewed as
subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonian, we get a
generalization of the genus 5 special branch found by Martins, plus three new
ones. We get also two 14-vertex Hamiltonians.
We solve all these Hamiltonians using CBA, and provide their spectrum,
eigenfunctions and Bethe equations. A special attention is made to provide the
specifications of our multi-parametric Hamiltonians that give back known
Hamiltonians.Comment: 30 pages; web page: http://www.coulomb.univ-montp2.fr/3Ha
Crystalizing the genetic code
New developments are presented in the framework of the model introduced by
the authors in refs. [1,2] and in which nucleotides as well as codons are
classified in crystal bases of the quantum group U_q(sl(2)+sl(2)) in the limit
q -> 0. An operator which gives the correspondence between the amino-acids and
the codons is now obtained for any known genetic code. The free energy released
by base pairing of dinucleotides as well as the relative hydrophilicity and
hydrophobicity of the dinucleosides are also computed. For the vertebrate
series, a universal behaviour in the ratios of codon usage frequencies is put
in evidence and is shown to fit nicely in our model. Then a first attempt to
represent the mutations relative to the deletion of a pyrimidine by action of a
suitable crystal spinor operator is proposed. Finally recent theoretical
descriptions are reviewed and compared with our model
Many-body spin Berry phases emerging from the -flux state: antiferromagnetic/valence-bond-solid competition
We uncover new topology-related features of the -flux saddle-point
solution of the =2+1 Heisenberg antiferromagnet. We note that symmetries of
the spinons sustain a built-in competition between antiferromagnetic (AF) and
valence-bond-solid (VBS) orders, the two tendencies central to recent
developments on quantum criticality. An effective theory containing an analogue
of the Wess-Zumino-Witten term is derived, which generates quantum phases
related to AF monopoles with VBS cores, and reproduces Haldane's hedgehog Berry
phases. The theory readily generalizes to -flux states for all .Comment: 4 pages, revise
On Casimir's Ghost
We define on the universal enveloping superalgebra of osp(1|2n) a nonstandard
adjoint action, endowing it with a module structure. This allows, in
particular, to construct a bosonic operator which anticommutes with all the
fermionic generators and which appears to be the square root of a certain
Casimir operator.Comment: LaTeX2e, 13 pages,also available at
http://lapphp0.in2p3.fr/preplapp/psth/ENSLAPP587.ps.gz ; one sentence removed
and a note added. Not a major revisio
A minimum principle in mRNA editing ?
mRNA editing of sequences of many species is analyzed. The nature of the
inserted nucleotides and the position of the insertion sites, once fixed the
edited peptide chain, are explained by introducing a minimum principle in the
framework of the crystal basis model of the genetic code introduced by the
authors.Comment: revised extended version - includes analysis on more dat
Dictionary on Lie Superalgebras
The main definitions and properties of Lie superalgebras are proposed a la
facon de a short dictionary, the different items following the alphabetical
order. The main topics deal with the structure of simple Lie superalgebras and
their finite dimensional representations; rather naturally, a few pages are
devoted to supersymmetry. This modest booklet has two ambitious goals: to be
elementary and easy to use. The beginner is supposed to find out here the main
concepts on superalgebras, while a more experimented theorist should recognize
the necessary tools and informations for a specific use.Comment: 145p LaTeX Document, also available at
http://lapphp0.in2p3.fr/preplapp/psth/DICTIONARY_SUPER.ps.g
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