Reduction of a metapopulation genetic model to an effective one island model

We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than by artificially imposing a fixed population size. The increased complexity of the model is managed by employing techniques often used in the physical sciences, namely exploiting time-scale separation to eliminate fast variables and then constructing an effective model from the slow modes. Remarkably, an initial model with 2$\mathcal{D}$ variables, where $\mathcal{D}$ is the number of islands in the metapopulation, can be reduced to a model with a single variable. We analyze this effective model and show that the predictions for the probability of fixation of the alleles and the mean time to fixation agree well with those found from numerical simulations of the original model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure

Pressure-Tuned Collapse of the Mott-Like State in Ca_{n+1}Ru_nO_{3n+1} (n=1,2): Raman Spectroscopic Studies

We report a Raman scattering study of the pressure-induced collapse of the Mott-like phases of Ca_3Ru_2O_7 (T_N=56 K) and Ca_2RuO_4 (T_N=110 K). The pressure-dependence of the phonon and two-magnon excitations in these materials indicate: (i) a pressure-induced collapse of the antiferromagnetic (AF) insulating phase above P* ~ 55 kbar in Ca_3Ru_2O_7 and P* ~ 5-10 kbar in Ca_2RuO_4, reflecting the importance of Ru-O octahedral distortions in stabilizing the AF insulating phase; and (ii) evidence for persistent AF correlations above the critical pressure of Ca_2RuO_4, suggestive of phase separation involving AF insulator and ferromagnetic metal phases.Comment: 3 figure

Bound-state beta-decay of a neutron in a strong magnetic field

The beta-decay of a neutron into a bound $(pe^-)$ state and an antineutrino in the presence of a strong uniform magnetic field ($B \gtrsim 10^{13}$ G) is considered. The beta-decay process is treated within the framework of the standard model of weak interactions. A Bethe-Salpeter formalism is employed for description of the bound $(pe^-)$ system in a strong magnetic field. For the field strengths $10^{13}$ G$\lesssim B \lesssim10^{18}$ G the estimate for the ratio of the bound-state decay rate $w_b$ and the usual (continuum-state) decay rate $w_c$ is derived. It is found that in such strong magnetic fields $w_b/w_c \sim 0.1-0.4$. This is in contrast to the field-free case, where $w_b/w_c \simeq 4.2 \times 10^{-6}$ [J. N. Bahcall, Phys. Rev. {\bf 124}, 495 (1961); L. L. Nemenov, Sov. J. Nucl. Phys. {\bf 15}, 582 (1972); X. Song, J. Phys. G: Nucl. Phys. {\bf 13}, 1023 (1987)]. The dependence of the ratio $w_b/w_c$ on the magnetic field strength $B$ exhibits a logarithmic-like behavior. The obtained results can be important for applications in astrophysics and cosmology.Comment: 22 pages (revtex4), 1 figure; v2: more detailed discussion on astrophysical applications in conclusion section, accepted for publication in Phys. Rev.

Tradeoff between short-term and long-term adaptation in a changing environment

We investigate the competition dynamics of two microbial or viral strains that live in an environment that switches periodically between two states. One of the strains is adapted to the long-term environment, but pays a short-term cost, while the other is adapted to the short-term environment and pays a cost in the long term. We explore the tradeoff between these alternative strategies in extensive numerical simulations, and present a simple analytic model that can predict the outcome of these competitions as a function of the mutation rate and the time scale of the environmental changes. Our model is relevant for arboviruses, which alternate between different host species on a regular basis.Comment: 9 pages, 3 figures, PRE in pres

Schwinger Boson Formulation and Solution of the Crow-Kimura and Eigen Models of Quasispecies Theory

We express the Crow-Kimura and Eigen models of quasispecies theory in a functional integral representation. We formulate the spin coherent state functional integrals using the Schwinger Boson method. In this formulation, we are able to deduce the long-time behavior of these models for arbitrary replication and degradation functions. We discuss the phase transitions that occur in these models as a function of mutation rate. We derive for these models the leading order corrections to the infinite genome length limit.Comment: 37 pages; 4 figures; to appear in J. Stat. Phy

On the muon neutrino mass

During the runs of the PS 179 experiment at LEAR of CERN, we photographed an event of antiproton-Ne absorption, with a complete pi+ -> mu+ ->e+ chain. From the vertex of the reaction a very slow energy pi+ was emitted. The pi+ decays into a mu+ and subsequently the mu+ decays into a positron. At the first decay vertex a muon neutrino was emitted and at the second decay vertex an electron neutrino and a muon antineutrino. Measuring the pion and muon tracks and applying the momentum and energy conservation and using a classical statistical interval estimator, we obtained an experimental upper limit for the muon neutrino mass: m_nu < 2.2 MeV at a 90% confidence level. A statistical analysis has been performed of the factors contributing to the square value of the neutrino mass limit.Comment: 18 pages, 5 eps figure

Optimal discrete stopping times for reliability growth tests

Often, the duration of a reliability growth development test is specified in advance and the decision to terminate or continue testing is conducted at discrete time intervals. These features are normally not captured by reliability growth models. This paper adapts a standard reliability growth model to determine the optimal time for which to plan to terminate testing. The underlying stochastic process is developed from an Order Statistic argument with Bayesian inference used to estimate the number of faults within the design and classical inference procedures used to assess the rate of fault detection. Inference procedures within this framework are explored where it is shown the Maximum Likelihood Estimators possess a small bias and converges to the Minimum Variance Unbiased Estimator after few tests for designs with moderate number of faults. It is shown that the Likelihood function can be bimodal when there is conflict between the observed rate of fault detection and the prior distribution describing the number of faults in the design. An illustrative example is provided

Dobinski-type relations and the Log-normal distribution

We consider sequences of generalized Bell numbers B(n), n=0,1,... for which there exist Dobinski-type summation formulas; that is, where B(n) is represented as an infinite sum over k of terms P(k)^n/D(k). These include the standard Bell numbers and their generalizations appearing in the normal ordering of powers of boson monomials, as well as variants of the "ordered" Bell numbers. For any such B we demonstrate that every positive integral power of B(m(n)), where m(n) is a quadratic function of n with positive integral coefficients, is the n-th moment of a positive function on the positive real axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure

Developing patient-friendly genetic and genomic test reports: formats to promote patient engagement and understanding

10.1186/s13073-014-0058-6Genome Medicine675