Phenomenology of 10^32 Dark Sectors

We postulate an exact permutation symmetry acting on 10^32 Standard Model copies as the largest possible symmetry extension of the Standard Model. This setup automatically lowers the fundamental gravity cutoff down to TeV, and thus, accounts for the quantum stability of the weak scale. We study the phenomenology of this framework and show that below TeV energies the copies are well hidden, obeying all the existing observational bounds. Nevertheless, we identify a potential low energy window into the hidden world, the oscillation of the neutron into its dark copies. At the same time, proton decay can be suppressed by gauging the diagonal baryon number of the different copies. This framework offers an alternative approach to several particle physics questions. For example, we suggest a novel mechanism for generating naturally small neutrino masses that are suppressed by the number of neutrino species. The mirror copies of the Standard Model naturally house dark matter candidates. The general experimentally observable prediction of this scenario is an emergence of strong gravitational effects at the LHC. The low energy permutation symmetry powerfully constrains the form of this new gravitational physics and allows to make observational predictions, such as, production of micro black-holes with very peculiar properties.Comment: 36 pages. v2, note added on oscillation of neutral state, Refs. adde

Evolution of sexual dimorphism of wing shape in the Drosophila melanogaster subgroup

Background: Sexual dimorphism of body size has been the subject of numerous studies, but few have examined sexual shape dimorphism (SShD) and its evolution. Allometry, the shape change associated with size variation, has been suggested to be a main component of SShD. Yet little is known about the relative importance of the allometric and non-allometric components for the evolution of SShD. Results: We investigated sexual dimorphism in wing shape in the nine species of the Drosophila melanogaster subgroup. We used geometric morphometrics to characterise wing shape and found significant SShD in all nine species. The amount of shape difference and the diversity of the shape changes evolved across the group. However, mapping the divergence of SShD onto the phylogeny of the Drosophila melanogaster subgroup indicated that there is little phylogenetic signal. Finally, allometry accounted for a substantial part of SShD, but did not explain the bulk of evolutionary divergence in SShD because allometry itself was found to be evolutionarily plastic. Conclusion: SShD in the Drosophila wing can evolve rapidly and therefore shows only weak phylogenetic structure. The variable contribution of allometric and non-allometric components to the evolutionary divergence of SShD and the evolutionary plasticity of allometry suggest that SShD and allometry are influenced by a complex interaction of processes

Global existence for a class of reaction-diffusion systems with mass action kinetics and concentration-dependent diffusivities

In this work we study the existence of classical solutions for a class of reaction-diffusion systems with quadratic growth naturally arising in mass action chemistry when studying networks of reactions of the type $A_i+A_j \rightleftharpoons A_k$ with Fickian diffusion, where the diffusion coefficients might depend on time, space and on all the concentrations $c_i$ of the chemical species. In the case of one single reaction, we prove global existence for space dimensions $N\leq 5$. In the more restrictive case of diffusion coefficients of the type $d_i(c_i)$, we use an $L^2$-approach to prove global existence for $N\leq 9$. In the general case of networks of such reactions we extend the previous method to get global solutions for general diffusivities if $N\leq 3$ and for diffusion of type $d_i(c_i)$ if $N\leq 5$. In the latter quasi-linear case of $d_i(c_i)$ and for space dimensions $N=2$ and $N=3$, global existence holds for more than quadratic reactions. We can actually allow for more general rate functions including fractional power terms, important in applications. We obtain global existence under appropriate growth restrictions with an explicit dependence on the space dimension $N$

Do Community-Level Models Account for the Effects of Biotic Interactions? A Comparison of Community-Level and Species Distribution Modeling of Rocky Mountain Conifers

Community-level models (CLMs) aim to improve species distribution modeling (SDM) methods by attempting to explicitly incorporate the influences of interacting species. However, the ability of CLMs to appropriately account for biotic interactions is unclear. We applied CLM and SDM methods to predict the distributions of three dominant conifer tree species in the U.S. Rocky Mountains and compared CLM and SDM predictive accuracy as well as the ability of each approach to accurately reproduce species co-occurrence patterns. We specifically evaluated the performance of two statistical algorithms, MARS and CForest, within both CLM and SDM frameworks. Across all species, differences in SDM and CLM predictive accuracy were slight and can be attributed to differences in model structure rather than accounting for the effects of biotic interactions. In addition, CLMs generally over-predicted species cooccurrence, while SDMs under-predicted cooccurrence. Our results demonstrate no real improvement in the ability of CLMs to account for biotic interactions relative to SDMs. We conclude that alternative modeling approaches are needed in order to accurately account for the effects of biotic interactions on species distributions