Stimulated Raman Adiabatic Passage (STIRAP) Among Degenerate-Level Manifolds

We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (g, e and f) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction (g - e) and to the Stokes-pulse interaction (e-f). We show that in general a sufficient condition for complete population removal from the g set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence g, e and f. We show that when this condition holds it is possible to achieve the degenerate counterpart of conventional STIRAP, whereby adiabatic passage produces complete population transfer. Indeed, the system is equivalent to a set of independent three-state systems, in each of which a STIRAP procedure can be implemented. We describe a scheme of unitary transformations that produces this result. We also examine the cases when this degeneracy constraint does not hold, and show what can be accomplished in those cases. For example, for angular momentum states when the degeneracy of the g and f levels is less than that of the e level we show how a special choice for the pulse polarizations and phases can produce complete removal of population from the g set. Our scheme can be a powerful tool for coherent control in degenerate systems, because of its robustness when selective addressing of the states is not required or impossible. We illustrate the analysis with several analytically solvable examples, in which the degeneracies originate from angular momentum orientation, as expressed by magnetic sublevels.Comment: 21 pages, 17 figure

Indirect Genetic Effects and the Spread of Infectious Disease: Are We Capturing the Full Heritable Variation Underlying Disease Prevalence?

Reducing disease prevalence through selection for host resistance offers a desirable alternative to chemical treatment. Selection for host resistance has proven difficult, however, due to low heritability estimates. These low estimates may be caused by a failure to capture all the relevant genetic variance in disease resistance, as genetic analysis currently is not taylored to estimate genetic variation in infectivity. Host infectivity is the propensity of transmitting infection upon contact with a susceptible individual, and can be regarded as an indirect effect to disease status. It may be caused by a combination of physiological and behavioural traits. Though genetic variation in infectivity is difficult to measure directly, Indirect Genetic Effect (IGE) models, also referred to as associative effects or social interaction models, allow the estimation of this variance from more readily available binary disease data (infected/non-infected). We therefore generated binary disease data from simulated populations with known amounts of variation in susceptibility and infectivity to test the adequacy of traditional and IGE models. Our results show that a conventional model fails to capture the genetic variation in infectivity inherent in populations with simulated infectivity. An IGE model, on the other hand, does capture some of the variation in infectivity. Comparison with expected genetic variance suggests that there is scope for further methodological improvement, and that potential responses to selection may be greater than values presented here. Nonetheless, selection using an index of estimated direct and indirect breeding values was shown to have a greater genetic selection differential and reduced future disease risk than traditional selection for resistance only. These findings suggest that if genetic variation in infectivity substantially contributes to disease transmission, then breeding designs which explicitly incorporate IGEs might help reduce disease prevalence

Finite-Dimensional Bicomplex Hilbert Spaces

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including the spectral decomposition theorem. Applications to concepts relevant to quantum mechanics, like the evolution operator, are pointed out.Comment: 21 page

Quasi-local energy-momentum and two-surface characterization of the pp-wave spacetimes

In the present paper the determination of the {\it pp}-wave metric form the geometry of certain spacelike two-surfaces is considered. It has been shown that the vanishing of the Dougan--Mason quasi-local mass $m_{\$}$, associated with the smooth boundary $\$:=\partial\Sigma\approx S^2$ of a spacelike hypersurface $\Sigma$, is equivalent to the statement that the Cauchy development $D(\Sigma)$ is of a {\it pp}-wave type geometry with pure radiation, provided the ingoing null normals are not diverging on $\$$ and the dominant energy condition holds on $D(\Sigma)$. The metric on $D(\Sigma)$ itself, however, has not been determined. Here, assuming that the matter is a zero-rest-mass-field, it is shown that both the matter field and the {\it pp}-wave metric of $D(\Sigma)$ are completely determined by the value of the zero-rest-mass-field on $\$$ and the two dimensional Sen--geometry of $\$$ provided a convexity condition, slightly stronger than above, holds. Thus the {\it pp}-waves can be characterized not only by the usual Cauchy data on a {\it three} dimensional $\Sigma$ but by data on its {\it two} dimensional boundary $\$$ too. In addition, it is shown that the Ludvigsen--Vickers quasi-local angular momentum of axially symmetric {\it pp}-wave geometries has the familiar properties known for pure (matter) radiation.Comment: 15 pages, Plain Tex, no figure

Bias, accuracy, and impact of indirect genetic effects in infectious diseases

Selection for improved host response to infectious disease offers a desirable alternative to chemical treatment but has proven difficult in practice, due to low heritability estimates of disease traits. Disease data from field studies is often binary, indicating whether an individual has become infected or not following exposure to an infectious disease. Numerous studies have shown that from this data one can infer genetic variation in individuals’ underlying susceptibility. In a previous study, we showed that with an indirect genetic effect (IGE) model it is possible to capture some genetic variation in infectivity, if present, as well as in susceptibility. Infectivity is the propensity of transmitting infection upon contact with a susceptible individual. It is an important factor determining the severity of an epidemic. However, there are severe shortcomings with the Standard IGE models as they do not accommodate the dynamic nature of disease data. Here we adjust the Standard IGE model to (1) make expression of infectivity dependent on the individuals’ disease status (Case Model) and (2) to include timing of infection (Case-ordered Model). The models are evaluated by comparing impact of selection, bias, and accuracy of each model using simulated binary disease data. These were generated for populations with known variation in susceptibility and infectivity thus allowing comparisons between estimated and true breeding values. Overall the Case Model provided better estimates for host genetic susceptibility and infectivity compared to the Standard Model in terms of bias, impact, and accuracy. Furthermore, these estimates were strongly influenced by epidemiological characteristics. However, surprisingly, the Case-Ordered model performed considerably worse than the Standard and the Case Models, pointing toward limitations in incorporating disease dynamics into conventional variance component estimation methodology and software used in animal breeding

A unifying theory for genetic epidemiological analysis of binary disease data

BACKGROUND: Genetic selection for host resistance offers a desirable complement to chemical treatment to control infectious disease in livestock. Quantitative genetics disease data frequently originate from field studies and are often binary. However, current methods to analyse binary disease data fail to take infection dynamics into account. Moreover, genetic analyses tend to focus on host susceptibility, ignoring potential variation in infectiousness, i.e. the ability of a host to transmit the infection. This stands in contrast to epidemiological studies, which reveal that variation in infectiousness plays an important role in the progression and severity of epidemics. In this study, we aim at filling this gap by deriving an expression for the probability of becoming infected that incorporates infection dynamics and is an explicit function of both host susceptibility and infectiousness. We then validate this expression according to epidemiological theory and by simulating epidemiological scenarios, and explore implications of integrating this expression into genetic analyses. RESULTS: Our simulations show that the derived expression is valid for a range of stochastic genetic-epidemiological scenarios. In the particular case of variation in susceptibility only, the expression can be incorporated into conventional quantitative genetic analyses using a complementary log-log link function (rather than probit or logit). Similarly, if there is moderate variation in both susceptibility and infectiousness, it is possible to use a logarithmic link function, combined with an indirect genetic effects model. However, in the presence of highly infectious individuals, i.e. super-spreaders, the use of any model that is linear in susceptibility and infectiousness causes biased estimates. Thus, in order to identify super-spreaders, novel analytical methods using our derived expression are required. CONCLUSIONS: We have derived a genetic-epidemiological function for quantitative genetic analyses of binary infectious disease data, which, unlike current approaches, takes infection dynamics into account and allows for variation in host susceptibility and infectiousness

The origin of aubrites: Evidence from lithophile trace element abundances and oxygen isotope compositions

We report the abundances of a selected set of “lithophile” trace elements (including lanthanides, actinides and high field strength elements) and high-precision oxygen isotope analyses of a comprehensive suite of aubrites. Two distinct groups of aubrites can be distinguished: (a) the main-group aubrites display flat or light-REE depleted REE patterns with variable Eu and Y anomalies; their pyroxenes are light-REE depleted and show marked negative Eu anomalies; (b) the Mount Egerton enstatites and the silicate fraction from Larned display distinctive light-REE enrichments, and high Th/Sm ratios; Mount Egerton pyroxenes have much less pronounced negative Eu anomalies than pyroxenes from the main-group aubrites. Leaching experiments were undertaken to investigate the contribution of sulfides to the whole rock budget of the main-group aubrites. Sulfides contain in most cases at least 50% of the REEs and of the actinides. Among the elements we have analyzed, those displaying the strongest lithophile behaviors are Rb, Ba, Sr and Sc. The homogeneity of the Δ17O values obtained for main-group aubrite falls [Δ17O = +0.009 ± 0.010‰ (2σ)] suggests that they originated from a single parent body whose differentiation involved an early phase of large-scale melting that may have led to the development of a magma ocean. This interpretation is at first glance in agreement with the limited variability of the shapes of the REE patterns of these aubrites. However, the trace element concentrations of their phases cannot be used to discuss this hypothesis, because their igneous trace-element signatures have been modified by subsolidus exchange. Finally, despite similar O isotopic compositions, the marked light-REE enrichments displayed by Mount Egerton and Larned suggest that they are unrelated to the main-group aubrites and probably originated from a distinct parent body