Inequivalent Quantizations of the N = 3 Calogero model with Scale and Mirror-S_3 Symmetry

We study the inequivalent quantizations of the N = 3 Calogero model by separation of variables, in which the model decomposes into the angular and the radial parts. Our inequivalent quantizations respect the ` mirror-S_3\rq\ invariance (which realizes the symmetry under the cyclic permutations of the particles) and the scale invariance in the limit of vanishing harmonic potential. We find a two-parameter family of novel quantizations in the angular part and classify the eigenstates in terms of the irreducible representations of the S_3 group. The scale invariance restricts the quantization in the radial part uniquely, except for the eigenstates coupled to the lowest two angular levels for which two types of boundary conditions are allowed independently from all upper levels. It is also found that the eigenvalues corresponding to the singlet representations of the S_3 are universal (parameter-independent) in the family, whereas those corresponding to the doublets of the S_3 are dependent on one of the parameters. These properties are shown to be a consequence of the spectral preserving SU(2) (or its subrgoup U(1)) transformations allowed in the family of inequivalent quantizations.Comment: 24 pages, LaTe

The Complex Demographic History and Evolutionary Origin of the Western Honey Bee, Apis Mellifera.

The western honey bee, Apis mellifera, provides critical pollination services to agricultural crops worldwide. However, despite substantial interest and prior investigation, the early evolution and subsequent diversification of this important pollinator remain uncertain. The primary hypotheses place the origin of A. mellifera in either Asia or Africa, with subsequent radiations proceeding from one of these regions. Here, we use two publicly available whole-genome data sets plus newly sequenced genomes and apply multiple population genetic analysis methods to investigate the patterns of ancestry and admixture in native honey bee populations from Europe, Africa, and the Middle East. The combination of these data sets is critical to the analyses, as each contributes samples from geographic locations lacking in the other, thereby producing the most complete set of honey bee populations available to date. We find evidence supporting an origin of A. mellifera in the Middle East or North Eastern Africa, with the A and Y lineages representing the earliest branching lineages. This finding has similarities with multiple contradictory hypotheses and represents a disentangling of genetic relationships, geographic proximity, and secondary contact to produce a more accurate picture of the origins of A. mellifera. We also investigate how previous studies came to their various conclusions based on incomplete sampling of populations, and illustrate the importance of complete sampling in understanding evolutionary processes. These results provide fundamental knowledge about genetic diversity within Old World honey bee populations and offer insight into the complex history of an important pollinator

Nestmate recognition in social insects: overcoming physiological constraints with collective decision making.

Social insects rank among the most abundant and influential terrestrial organisms. The key to their success is their ability to form tightly knit social groups that perform work cooperatively, and effectively exclude non-members from the colony. An extensive body of research, both empirical and theoretical, has explored how optimal acceptance thresholds could evolve in individuals, driven by the twin costs of inappropriately rejecting true nestmates and erroneously accepting individuals from foreign colonies. Here, in contrast, we use agent-based modeling to show that strong nestmate recognition by individuals is often unnecessary. Instead, highly effective nestmate recognition can arise as a colony-level property from a collective of individually poor recognizers. Essentially, although an intruder can get by one defender when their odor cues are similar, it is nearly impossible to get past many defenders if there is the slightest difference in cues. The results of our models match observed rejection rates in studies of ants, wasps, and bees. We also show that previous research in support of the optimal threshold theory approach to the problem of nestmate recognition can be alternatively viewed as evidence in favor of the collective formation of a selectively permeable barrier that allows in nestmates (at a significant cost) while rejecting non-nestmates. Finally, this work shows that nestmate recognition has a stronger task allocation component than previously thought, as colonies can nearly always achieve perfect nestmate recognition if it is cost effective for them to do so at the colony level. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00265-010-1094-x) contains supplementary material, which is available to authorized users

Lattice study of semileptonic form factors with twisted boundary conditions

We apply twisted boundary conditions to lattice QCD simulations of three-point correlation functions in order to access spatial components of hadronic momenta different from the integer multiples of 2 pi / L. We calculate the vector and scalar form factors relevant to the K -> pi semileptonic decay and consider all the possible ways of twisting one of the quark lines in the three-point functions. We show that the momentum shift produced by the twisted boundary conditions does not introduce any additional noise and easily allows to determine within a few percent statistical accuracy the form factors at quite small values of the four-momentum transfer, which are not accessible when periodic boundary conditions are considered. The use of twisted boundary conditions turns out to be crucial for a precise determination of the form factor at zero-momentum transfer, when a precise lattice point sufficiently close to zero-momentum transfer is not accessible with periodic boundary conditions.Comment: latex 15 pages, 4 figures and 3 tables; modified intro and discussions of the results; version to appear in PR

Improved estimates of rare K decay matrix-elements from Kl3 decays

The estimation of rare K decay matrix-elements from Kl3 experimental data is extended beyond LO in Chiral Perturbation Theory. Isospin-breaking effects at NLO (and partially NNLO) in the ChPT expansion, as well as QED radiative corrections are now accounted for. The analysis relies mainly on the cleanness of two specific ratios of form-factors, for which the theoretical control is excellent. As a result, the uncertainties on the K+ --> pi+ nu nubar and KL --> pi0 nu nubar matrix-elements are reduced by a factor of about 7 and 4, respectively, and similarly for the direct CP-violating contribution to KL --> pi0 l+ l-. They could be reduced even further with better experimental data for the Kl3 slopes and the K+l3 branching ratios. As a result, the non-parametric errors for B(K --> pi nu nubar) and for the direct CP-violating contributions to B(KL --> pi0 l+ l-) are now completely dominated by those on the short-distance physics.Comment: 16 pages, 1 figure. Numerical analysis updated to include the recent Kl3 data. To appear in Phys. Rev.

Chiral Corrections to the Hyperon Vector Form Factors

We present the complete calculation of the SU(3)-breaking corrections to the hyperon vector form factors up to O(p^4) in the Heavy Baryon Chiral Perturbation Theory. Because of the Ademollo-Gatto theorem, at this order the results do not depend on unknown low energy constants and allow to test the convergence of the chiral expansion. We complete and correct previous calculations and find that O(p^3) and O(1/M_0) corrections are important. We also study the inclusion of the decuplet degrees of freedom, showing that in this case the perturbative expansion is jeopardized. These results raise doubts on the reliability of the chiral expansion for hyperons.Comment: 20 pages, 4 figures, v2: published versio

Classical Aspects of Quantum Walls in One Dimension

We investigate the system of a particle moving on a half line x >= 0 under the general walls at x = 0 that are permitted quantum mechanically. These quantum walls, characterized by a parameter L, are shown to be realized as a limit of regularized potentials. We then study the classical aspects of the quantum walls, by seeking a classical counterpart which admits the same time delay in scattering with the quantum wall, and also by examining the WKB-exactness of the transition kernel based on the regularized potentials. It is shown that no classical counterpart exists for walls with L < 0, and that the WKB-exactness can hold only for L = 0 and L = infinity.Comment: TeX, 21 pages, 4 figures. v2: some parts of the text improved, new and improved figure

Taxonomically restricted genes are associated with the evolution of sociality in the honey bee

<p>Abstract</p> <p>Background</p> <p>Studies have shown that taxonomically restricted genes are significant in number and important for the evolution of lineage specific traits. Social insects have gained many novel morphological and behavioral traits relative to their solitary ancestors. The task repertoire of an advanced social insect, for example, can be 40-50 tasks, about twice that of a solitary wasp or bee. The genetic basis of this expansion in behavioral repertoire is still poorly understood, and a role for taxonomically restricted genes has not been explored at the whole genome level.</p> <p>Results</p> <p>Here we present comparative genomics results suggesting that taxonomically restricted genes may have played an important role in generating the expansion of behavioral repertoire associated with the evolution of eusociality. First, we show that the current honey bee official gene set contains about 700 taxonomically restricted genes. These are split between orphans, genes found only in the Hymenoptera, and genes found only in insects. Few of the orphans or genes restricted to the Hymenoptera have been the focus of experimental work, but several of those that have are associated with novel eusocial traits or traits thought to have changed radically as a consequence of eusociality. Second, we predicted that if taxonomically restricted genes are important for generating novel eusocial traits, then they should be expressed with greater frequency in workers relative to the queen, as the workers exhibit most of the novel behavior of the honey bee relative to their solitary ancestors. We found support for this prediction. Twice as many taxonomically restricted genes were found amongst the genes with higher expression in workers compared to those with higher expression in queens. Finally, we compiled an extensive list of candidate taxonomically restricted genes involved in eusocial evolution by analyzing several caste specific gene expression data sets.</p> <p>Conclusions</p> <p>This work identifies a large number of candidate taxonomically restricted genes that may have played a role in eusocial evolution. This work thus lays the foundation for future functional genomics work on the evolution of novelty in the context of social behavior. We also present preliminary evidence, based on biased patterns of gene expression, that taxonomically restricted genes may have played a role in the evolution of caste systems, a characteristic lineage specific social trait.</p

Kaon semileptonic decay (K_{l3}) form factors from the instanton vacuum

We investigate the kaon semileptonic decay (K_{l3}) form factors within the framework of the nonlocal chiral quark model from the instanton vacuum, taking into account the effects of flavor SU(3) symmetry breaking. We also consider the problem of gauge invariance arising from the momentum-dependent quark mass in the present work. All theoretical calculations are carried out without any adjustable parameter, the average instanton size (rho ~ 1/3 fm) and the inter-instanton distance (R ~ 1 fm) having been fixed. We also show that the present results satisfy the Callan-Treiman low-energy theorem as well as the Ademollo-Gatto theorem. Using the K_{l3} form factors, we evaluate relevant physical quantities. It turns out that the effects of flavor SU(3) symmetry breaking are essential in reproducing the kaon semileptonic form factors. The present results are in a good agreement with experiments, and are compatible with other model calculations.Comment: 12 pages, 3 figures, submitted to PR