The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model

This paper develops a two gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by $\sigma_{via}$, yields a viable organism with first order growth rate constant $k > 1$ if it is equal to some target ``master'' sequence $\sigma_{via, 0}$. The second gene, denoted by $\sigma_{rep}$, yields an organism capable of genetic repair if it is equal to some target ``master'' sequence $\sigma_{rep, 0}$. This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on \mu \equiv L\eps , the product of sequence length and per base pair replication error probability, and \eps_r , the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of three possible ``phases.'' In the first phase, the population is localized about the viability and repairing master sequences. As \eps_r exceeds the fraction of deleterious mutations, the population undergoes a ``repair'' catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds \ln k/\eps_r , while above the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds $\ln k/f_{del}$, where $f_{del}$ denotes the fraction of deleterious mutations.Comment: 14 pages, 3 figures. Submitted to Physical Review

Formation & evolution of the Galactic bulge: constraints from stellar abundances

We compute the chemical evolution of the Galactic bulge in the context of an inside-out model for the formation of the Milky Way. The model contains updated stellar yields from massive stars. The main purpose of the paper is to compare the predictions of this model with new observations of chemical abundance ratios and metallicity distributions in order to put constraints on the formation and evolution of the bulge. We computed the evolution of several alpha-elements and Fe and performed several tests by varying different parameters such as star formation efficiency, slope of the initial mass function and infall timescale. We also tested the effect of adopting a primary nitrogen contribution from massive stars. The [alpha/Fe] abundance ratios in the Bulge are predicted to be supersolar for a very large range in [Fe/H], each element having a different slope. These predictions are in very good agreement with most recent accurate abundance determinations. We also find a good fit of the most recent Bulge stellar metallicity distributions. We conclude that the Bulge formed on a very short timescale (even though timescales much shorter than about 0.1 Gyr are excluded) with a quite high star formation efficiency of about 20 Gyr$^{-1}$ and with an initial mass function more skewed toward high masses (i.e. x <= 0.95) than the solar neighbourhood and rest of the disk. The results obtained here are more robust than previous ones since they are based on very accurate abundance measurements.Comment: 26 pages, 9 figures, accepted for publication in A&

Quantum tomographic cryptography with Bell diagonal states: non-equivalence of classical and quantum distillation protocols

We present a generalized tomographic quantum key distribution protocol in which the two parties share a Bell diagonal mixed state of two qubits. We show that if an eavesdropper performs a coherent measurement on many quantum ancilla states simultaneously, classical methods of secure key distillation are less effective than quantum entanglement distillation protocols. We also show that certain Bell diagonal states are resistant to any attempt of incoherent eavesdropping.Comment: 9 pages. 2 figures There was an error in the formula 4 (transformation of Bell states). This error does not change the main result of the paper, namely, that quantum distillation is more powerful than classical advantage distillatio

Collective excitations of a periodic Bose condensate in the Wannier representation

We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a renormalization of the s-wave scattering length and the solution of the Bogolubov - de Gennes equations is formulated in terms of the appropriate Wannier functions. Some exact properties of a periodic one-dimensional condensate are easily demonstrated: (i) the lowest band at positive energy refers to phase modulations of the condensate and has a linear dispersion relation near the Brillouin zone centre; (ii) the higher bands arise from the superposition of localized excitations with definite phase relationships; and (iii) the wavenumber-dependent current under a constant force in the semiclassical transport regime vanishes at the zone boundaries. Early results by J. C. Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron energy bands are used to specify the conditions under which the Wannier functions may be approximated by on-site tight-binding orbitals of harmonic- oscillator form. In this approximation the connections between the low-lying excitations in a lattice and those in a harmonic well are easily visualized. Analytic results are obtained in the tight-binding scheme and are illustrated with simple numerical calculations for the dispersion relation and semiclassical transport in the lowest energy band, at values of the system parameters which are relevant to experiment.Comment: 20 pages, 2 figures, 22 reference

Duality and semi-group property for backward parabolic Ito equations

We study existence, uniqueness, semi-group property, and a priori estimates for solutions for backward parabolic Ito equations in domains with boundary. We study also duality between forward and backward equations. The semi-group for backward equations is established in the form of some anti-causality. The novelty is that the semi-group property involves the diffusion term that is a part of the solution

Localized anomalies in orbifold gauge theories

We apply the path-integral formalism to compute the anomalies in general orbifold gauge theories (including possible non-trivial Scherk-Schwarz boundary conditions) where a gauge group G is broken down to subgroups H_f at the fixed points y=y_f. Bulk and localized anomalies, proportional to \delta(y-y_f), do generically appear from matter propagating in the bulk. The anomaly zero-mode that survives in the four-dimensional effective theory should be canceled by localized fermions (except possibly for mixed U(1) anomalies). We examine in detail the possibility of canceling localized anomalies by the Green-Schwarz mechanism involving two- and four-forms in the bulk. The four-form can only cancel anomalies which do not survive in the 4D effective theory: they are called globally vanishing anomalies. The two-form may cancel a specific class of mixed U(1) anomalies. Only if these anomalies are present in the 4D theory this mechanism spontaneously breaks the U(1) symmetry. The examples of five and six-dimensional Z_N orbifolds are considered in great detail. In five dimensions the Green-Schwarz four-form has no physical degrees of freedom and is equivalent to canceling anomalies by a Chern-Simons term. In all other cases, the Green-Schwarz forms have some physical degrees of freedom and leave some non-renormalizable interactions in the low energy effective theory. In general, localized anomaly cancellation imposes strong constraints on model building.Comment: 30 pages, 4 figures. v2: reference adde