Host-Parasite Co-evolution and Optimal Mutation Rates for Semi-conservative Quasispecies

In this paper, we extend a model of host-parasite co-evolution to incorporate the semi-conservative nature of DNA replication for both the host and the parasite. We find that the optimal mutation rate for the semi-conservative and conservative hosts converge for realistic genome lengths, thus maintaining the admirable agreement between theory and experiment found previously for the conservative model and justifying the conservative approximation in some cases. We demonstrate that, while the optimal mutation rate for a conservative and semi-conservative parasite interacting with a given immune system is similar to that of a conservative parasite, the properties away from this optimum differ significantly. We suspect that this difference, coupled with the requirement that a parasite optimize survival in a range of viable hosts, may help explain why semi-conservative viruses are known to have significantly lower mutation rates than their conservative counterparts

Comments on a new mathematical technique in the theory of complex spectra

A large body of work on the algebraic properties of the Gelfand labelling scheme for atoms with several electrons has recently been synthesized by Harter (see abstr. A31652 of 1974) into a compact procedure for the construction of total angular momentum eigenfunctions and the evaluation of angular coefficients. Certain ambiguities in the procedure are removed. Also, an improved method for the diagonalization of the angular momentum matrix in the Galfand basis set is presented. As an example, the doublet states of the f 3 configuration are discussed

Spin-orbit parameters by the Gelfand-Harter method-a test calculation

The spin-orbit parameters for the sextet states of the f5 configuration are computed using the Young-tableau techniques developed by Harter. The conceptual and computational advantages over traditional methods are discussed. © 1977 The American Physical Society

An Algorithm for constructing Hjelmslev planes

Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations of projective planes and affine planes. We present an algorithm for constructing a projective Hjelmslev planes and affine Hjelsmelv planes using projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv planes can be constructed in this way. As a corollary it is shown that all 2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014, Springer Proceedings in Mathematics & Statistics 13

QED calculation of the n=1 and n=2 energy levels in He-like ions

We perform ab initio QED calculations of energy levels for the $n=1$ and $n=2$ states of He-like ions with the nuclear charge in the range $Z = 12$-100. The complete set of two-electron QED corrections is evaluated to all orders in the parameter \aZ. Uncalculated contributions to energy levels come through orders \alpha^3 (\aZ)^2, \alpha^2 (\aZ)^7, and higher. The calculation presented is the first treatment for excited states of He-like ions complete through order \alpha^2 (\aZ)^4. A significant improvement in accuracy of theoretical predictions is achieved, especially in the high-$Z$ region.Comment: 23 pages, 5 figure

High precision variational calculations for H2 +

A double basis set in Hylleraas coordinates is used to obtain improved variational upper bounds for the nonrelativistic energy of the 1 1S (v = 0, R = 0), 2 1S (v = 1, R = 0) and 2 3P (v = 0, R = 1) states of H2 +. This method shows a remarkable convergence rate for relatively compact basis set expansions. A comparison with the most recent work is made. The accuracy of the wavefunctions is tested using the electron-proton Kato cusp condition

Long-range interactions of metastable helium atoms

Polarizabilities, dispersion coefficients, and long-range atom-surface interaction potentials are calculated for the n=2 triplet and singlet states of helium using highly accurate, variationally determined, wave functions.Comment: RevTeX, epsf, 4 fig

Vector-coupling approach to orbital and spin-dependent tableau matrix elements in the theory of complex spectra

The power of the Young tableau scheme for labeling a complete spin-adapted basis set in the theory of complex spectra lies in one\u27s ability to evaluate matrix elements of irreducible tensor operators directly in terms of the tableau labels and shapes. We show that the matrix-element rules stated by Harter for one-body operators can be easily derived from simple vector-coupling considerations. The graphical method of angular momentum analysis is used to derive closed-form expressions for the matrix elements of two-body operators. This study yields several interesting new relationships between spin-dependent operators and purely orbital operators. © 1977 The American Physical Society

Binding energy of the positronium negative ion: Relativistic and QED energy shifts

The leading relativistic and QED corrections to the ground-state energy of the three-body system e-e+e- are calculated numerically using a Hylleraas correlated basis set. The accuracy of the nonrelativistic variational ground state is discussed with respect to the convergence of the energy with increasing size of the basis set, and also with respect to the variance of the Hamiltonian. The corrections to this energy include the lowest order Breit interaction, the vacuum polarization potential, one and two photon exchange contributions, the annihilation interaction and spin-spin contact terms. The relativistic effects and the residual interactions considered here decrease the one-electron binding energy from the nonrelativistic value of 0.012 005 070 232 980 107 69(28) au to 0.011 981 051 246(2) au (78 831 530 ± 5 MHz). © 2005 IOP Publishing Ltd