8,988 research outputs found

### Quantum Field Theory and Phylogenetic Branching

A calculational framework is proposed for phylogenetics, using nonlocal
quantum field theories in hypercubic geometry. Quadratic terms in the
Hamiltonian give the underlying Markov dynamics, while higher degree terms
represent branching events. The spatial dimension L is the number of leaves of
the evolutionary tree under consideration. Momentum conservation modulo
${\mathbb Z}_{2}^{times L}$ in $L \leftarrow 1$ scattering corresponds to tree
edge labelling using binary L-vectors. The bilocal quadratic term allows for
momentum-dependent rate constants - only the tree(s) compatible with selected
nonzero edge rates contribute to the branching probability distribution.
Applications to models of evolutionary branching processes are discussed.Comment: LaTex file, 6 pages, 1 postscript figure. Typographical errors
corrected, minor changes added. Submitted to J.Phys.Lett.

### A base pairing model of duplex formation I: Watson-Crick pairing geometries

We present a base-pairing model of oligonuleotide duplex formation and show
in detail its equivalence to the Nearest-Neighbour dimer methods from fits to
free energy of duplex formation data for short DNA-DNA and DNA-RNA hybrids
containing only Watson Crick pairs. In this approach the connection between
rank-deficient polymer and rank-determinant oligonucleotide parameter, sets for
DNA duplexes is transparent. The method is generalised to include RNA/DNA
hybrids where the rank-deficient model with 11 dimer parameters in fact
provides marginally improved predictions relative to the standard method with
16 independent dimer parameters ($\Delta G$ mean errors of 4.5 and 5.4 %
respectively).Comment: Latex file, 13 pages, no figures. Refereed draft of manuscript
submitted to Biopolymer

### Modified Relativity from the kappa-deformed Poincare Algebra

The theory of the $\kappa$-deformed Poincare algebra is applied to the
analysis of various phenomena in special relativity, quantum mechanics and
field theory. The method relies on the development of series expansions in
$\kappa^{-1}$ of the generalised Lorentz transformations, about the
special-relativistic limit. Emphasis is placed on the underlying assumptions
needed in each part of the discussion, and on in principle limits for the
deformation parameter, rather than on rigorous numerical bounds. In the case of
the relativistic Doppler effect, and the Michelson-Morley experiment,
comparisons with recent experiemntal tests yield the relatively weak lower
bounds on $\kappa c$ of 90eV and 250 keV, respectively. Corrections to the
Casimir effect and the Thomas precession are also discussed.Comment: 11 pages long, to appear in 'Class Q Grav

### Systematics of the Genetic Code and Anticode: History, Supersymmetry, Degeneracy and Periodicity

Important aspects of the process of information storage and retrieval in DNA
and RNA, and its evolution, are the role of the anticodons and associated
$t$RNA's, and correlations between anticodons and amino acids; the degeneracy
of the genetic code, and the periodicity of many amino acid physico-chemical
properties. Such factors are analysed in the context of a $sl(6/1)$
supersymmetric model of the genetic code.Comment: 4 pages LaTex, uses icmp.sty, 2 figures, Contribution to proceedings
of oXXII International Colloquium on Group Theoretical Methods in Physics
(Group22) Hobart, 13-17 July 1998, to be published by International Pres

### Using the tangle: a consistent construction of phylogenetic distance matrices for quartets

Distance based algorithms are a common technique in the construction of
phylogenetic trees from taxonomic sequence data. The first step in the
implementation of these algorithms is the calculation of a pairwise distance
matrix to give a measure of the evolutionary change between any pair of the
extant taxa. A standard technique is to use the log det formula to construct
pairwise distances from aligned sequence data. We review a distance measure
valid for the most general models, and show how the log det formula can be used
as an estimator thereof. We then show that the foundation upon which the log
det formula is constructed can be generalized to produce a previously unknown
estimator which improves the consistency of the distance matrices constructed
from the log det formula. This distance estimator provides a consistent
technique for constructing quartets from phylogenetic sequence data under the
assumption of the most general Markov model of sequence evolution.Comment: 18 Pges. Submitted to Mathematical Bioscience

### Entanglement Invariants and Phylogenetic Branching

It is possible to consider stochastic models of sequence evolution in
phylogenetics in the context of a dynamical tensor description inspired from
physics. Approaching the problem in this framework allows for the well
developed methods of mathematical physics to be exploited in the biological
arena. We present the tensor description of the homogeneous continuous time
Markov chain model of phylogenetics with branching events generated by
dynamical operations. Standard results from phylogenetics are shown to be
derivable from the tensor framework. We summarize a powerful approach to
entanglement measures in quantum physics and present its relevance to
phylogenetic analysis. Entanglement measures are found to give distance
measures that are equivalent to, and expand upon, those already known in
phylogenetics. In particular we make the connection between the group invariant
functions of phylogenetic data and phylogenetic distance functions. We
introduce a new distance measure valid for three taxa based on the group
invariant function known in physics as the "tangle". All work is presented for
the homogeneous continuous time Markov chain model with arbitrary rate
matrices.Comment: 21 pages, 3 Figures. Accepted for publication in Journal of
Mathematical Biolog

### Markov invariants for phylogenetic rate matrices derived from embedded submodels

We consider novel phylogenetic models with rate matrices that arise via the
embedding of a progenitor model on a small number of character states, into a
target model on a larger number of character states. Adapting
representation-theoretic results from recent investigations of Markov
invariants for the general rate matrix model, we give a prescription for
identifying and counting Markov invariants for such `symmetric embedded'
models, and we provide enumerations of these for low-dimensional cases. The
simplest example is a target model on 3 states, constructed from a general 2
state model; the `2->3' embedding. We show that for 2 taxa, there exist two
invariants of quadratic degree, that can be used to directly infer pairwise
distances from observed sequences under this model. A simple simulation study
verifies their theoretical expected values, and suggests that, given the
appropriateness of the model class, they have greater statistical power than
the standard (log) Det invariant (which is of cubic degree for this case).Comment: 16 pages, 1 figure, 1 appendi

### Resolution of the GL(3) - O(3) state labelling problem via O(3)-invariant Bethe subalgebra of the twisted Yangian

The labelling of states of irreducible representations of GL(3) in an O(3)
basis is well known to require the addition of a single O(3)-invariant
operator, to the standard diagonalisable set of Casimir operators in the
subgroup chain GL(3) - O(3) - O(2). Moreover, this `missing label' operator
must be a function of the two independent cubic and quartic invariants which
can be constructed in terms of the angular momentum vector and the quadrupole
tensor. It is pointed out that there is a unique (in a well-defined sense)
combination of these which belongs to the O(3) invariant Bethe subalgebra of
the twisted Yangian Y(GL(3);O(3)) in the enveloping algebra of GL(3).Comment: 7 pages, LaTe

### Exactly solvable three-level quantum dissipative systems via bosonisation of fermion gas-impurity models

We study the relationship between one-dimensional fermion gas-impurity models
and quantum dissipative systems, via the method of constructive bosonisation
and unitary transformation. Starting from an anisotropic Coqblin-Schrieffer
model, a new, exactly solvable, three-level quantum dissipative system is
derived as a generalisation of the standard spin-half spin-boson model. The new
system has two environmental oscillator baths with ohmic coupling, and admits
arbitrary detuning between the three levels. All tunnelling matrix elements are
equal, up to one complex phase which is itself a function of the longitudinal
and transverse couplings in the integrable limit. Our work underlines the
importance of re-examining the detailed structure of fermion-gas impurity
models and spin chains, in the light of connections to models for quantum
dissipative systems.Comment: 12 pages, accepted for publication in Journal of Physics A:
Mathematical and Theoretical. (Extended discussion section, some references
added and some typos corrected

### Polar decomposition of a Dirac spinor

Local decompositions of a Dirac spinor into `charged' and `real' pieces
psi(x) = M(x) chi(x) are considered. chi(x) is a Majorana spinor, and M(x) a
suitable Dirac-algebra valued field. Specific examples of the decomposition in
2+1 dimensions are developed, along with kinematical implications, and
constraints on the component fields within M(x) sufficient to encompass the
correct degree of freedom count. Overall local reparametrisation and
electromagnetic phase invariances are identified, and a dynamical framework of
nonabelian gauge theories of noncompact groups is proposed. Connections with
supersymmetric composite models are noted (including, for 2+1 dimensions,
infrared effective theories of spin-charge separation in models of high-Tc
superconductivity).Comment: 12 pages, LaTe

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