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

Effects of Neutron Irradiation on Carbon Doped MgB2 Wire Segments

We have studied the evolution of superconducting and normal state properties of neutron irradiated Mg(B$_{.962}$C$_{.038}$)$_2$ wire segments as a function of post exposure annealing time and temperature. The initial fluence fully suppressed superconductivity and resulted in an anisotropic expansion of the unit cell. Superconductivity was restored by post-exposure annealing. The upper critical field, H$_{c2}$(T=0), approximately scales with T$_c$ starting with an undamaged T$_c$ near 37 K and H$_{c2}$(T=0) near 32 T. Up to an annealing temperature of 400 $^ o$C the recovery of T$_c$ tends to coincide with a decrease in the normal state resistivity and a systematic recovery of the lattice parameters. Above 400 $^ o$C a decrease in order along the c- direction coincides with an increase in resistivity, but no apparent change in the evolution of T$_c$ and H$_{c2}$. To first order, it appears that carbon doping and neutron damaging effect the superconducting properties of MgB$_2$ independently

Model counting for CNF formuals of bounded module treewidth

The modular treewidth of a graph is its treewidth after the contraction of modules. Modular treewidth properly generalizes treewidth and is itself properly generalized by clique-width. We show that the number of satisfying assignments of a CNF formula whose incidence graph has bounded modular treewidth can be computed in polynomial time. This provides new tractable classes of formulas for which #SAT is polynomial. In particular, our result generalizes known results for the treewidth of incidence graphs and is incomparable with known results for clique-width (or rank-width) of signed incidence graphs. The contraction of modules is an effective data reduction procedure. Our algorithm is the first one to harness this technique for #SAT. The order of the polynomial time bound of our algorithm depends on the modular treewidth. We show that this dependency cannot be avoided subject to an assumption from Parameterized Complexity

Adaptive Dispersion Compensation for Remote Fiber Delivery of NIR Femtosecond Pulses

We report on remote delivery of 25 pJ broadband near-infrared femtosecond light pulses from a Ti:sapphire laser through 150 meters of single-mode optical fiber. Pulse distortion due to dispersion is overcome with pre-compensation using adaptive pulse shaping techniques, while nonlinearities are mitigated using an SF10 rod for the final stage of pulse compression. Near transform limited pulse duration of 130 fs is measured after the final compression.Comment: 3 pages, 4 figure

Crossover to Non-universal Microscopic Spectral Fluctuations in Lattice Gauge Theory

The spectrum of the Dirac operator near zero virtuality obtained in lattice gauge simulations is known to be universally described by chiral random matrix theory. We address the question of the maximum energy for which this universality persists. For this purpose, we analyze large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions. We calculate the disconnected scalar susceptibility and the microscopic number variance for the chiral symplectic ensemble of random matrices and compare the results with lattice Dirac spectra for quenched SU(2). The crossover to a non-universal regime is clearly identified and found to scale with the square of the linear lattice size and with $f_{\pi}^2$, in agreement with theoretical expectations.Comment: 11 pages, 7 figures, misprint in Eq. (13) corrected, minor modifications, to appear in Phys. Lett.

Nanoscale grains, high irreversibility field, and large critical current density as a function of high energy ball milling time in C-doped magnesium diboride

Magnesium diboride (MgB2) powder was mechanically alloyed by high energy ball milling with C to a composition of Mg(B0.95C0.05)2 and then sintered at 1000 C in a hot isostatic press. Milling times varied from 1 minute to 3000 minutes. Full C incorporation required only 30-60 min of milling. Grain size of sintered samples decreased with increased milling time to less than 30 nm for 20-50 hrs of milling. Milling had a weak detrimental effect on connectivity. Strong irreversibility field (H*) increase (from 13.3 T to 17.2 T at 4.2 K) due to increased milling time was observed and correlated linearly with inverse grain size (1/d). As a result, high field Jc benefited greatly from lengthy powder milling. Jc(8 T, 4.2 K) peaked at > 80,000 A/cm2 with 1200 min of milling compared with only ~ 26,000 A/cm2 for 60 min of milling. This non-compositional performance increase is attributed to grain refinement of the unsintered powder by milling, and to the probable suppression of grain growth by milling-induced MgO nano-dispersions.Comment: 12 pages, 11 figure

Co-Evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes

Co-evolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this co-adaptive model, besides the classical error catastrophe for high virus mutation rates, a second ``adaptation-'' catastrophe occurs, when virus mutation rates are too small to escape immune attack. Maximizing both regimes of viral error catastrophes is a possible strategy for an optimal immune response, reducing the range of allowed viral mutation rates to a minimum. From this requirement one obtains constraints on B-cell mutation rates and receptor lengths, yielding an estimate of somatic hypermutation rates in the germinal center in accordance with observation.Comment: 4 pages RevTeX including 2 figure

A transmission x ray microscopy and NEXAFS approach for studying corroded silicate glasses at the nanometre scale

In this study transmission X ray microscopy TXM was tested as a method to investigate the chemistry and structure of corroded silicate glasses at the nanometer scale. Three different silicate glasses were altered in static corrosion experiments for 1 336 hours at temperatures between 60 C and 85 C using a 25 HCl solution. Thin lamellas were cut perpendicular to the surface of corroded glass monoliths and were analysed with conventional TEM as well as with TXM. By recording optical density profiles at photon energies around the Na and O K edges, the shape of the corrosion rim pristine glass interfaces and the thickness of the corrosion rims has been determined. Na and O near edge X ray absorption fine structure spectra NEXAFS were obtained without inducing irradiation damage and have been used to detect chemical changes in the corrosion rims. Spatially resolved NEXAFS spectra at the O K edge provided insight to structural changes in the corrosion layer on the atomic scale. By comparison to O K edge spectra of silicate minerals and hydrous albite glass as well as to O K edge NEXAFS of model structures simulated with ab initio calculations, evidence is provided that changes of the fine structure at the O K edge are assigned to the formation of siloxane groups in the corrosion ri

Potential, core-level and d band shifts at transition metal surfaces

We have extended the validity of the correlation between the surface 3d-core-level shift (SCLS) and the surface d band shift (SDBS) to the entire 4d transition metal series and to the neighboring elements Sr and Ag via accurate first-principles calculations. We find that the correlation is quasilinear and robust with respect to the differencies both between initial and final-state calculations of the SCLS's and two distinct measures of the SDBS's. We show that despite the complex spatial dependence of the surface potential shift (SPS) and the location of the 3d and 4d orbitals in different regions of space, the correlation exists because the sampling of the SPS by the 3d and 4d orbitals remains similar. We show further that the sign change of the SCLS's across the transition series does indeed arise from the d band-narrowing mechanism previously proposed. However, while in the heavier transition metals the predicted increase of d electrons in the surface layer relative to the bulk arises primarily from transfers from s and p states to d states within the surface layer, in the lighter transition metals the predicted decrease of surface d electrons arises primarily from flow out into the vacuum.Comment: RevTex, 22 pages, 5 figures in uufiles form, to appear in Phys.Rev.