Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page

UGC 7388: a galaxy with two tidal loops

We present the results of spectroscopic and morphological studies of the galaxy UGC7388 with the 8.1-m Gemini North telescope. Judging by its observed characteristics, UGC7388 is a giant late-type spiral galaxy seen almost edge-on. The main body of the galaxy is surrounded by two faint (\mu(B) ~ 24 and \mu(B) ~ 25.5) extended (~20-30 kpc) loop-like structures. A large-scale rotation of the brighter loop about the main galaxy has been detected. We discuss the assumption that the tidal disruption of a relatively massive companion is observed in the case of UGC7388. A detailed study and modeling of the observed structure of this unique galaxy can give important information about the influence of the absorption of massive companions on the galactic disks and about the structure of the dark halo around UGC7388.Comment: 8 pages, 5 figure

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Dexamethasone impairs the expression of antimicrobial mediators in lipopolysaccharide-activated primary macrophages by inhibiting both expression and function of interferon β

Glucocorticoids potently inhibit expression of many inflammatory mediators, and have been widely used to treat both acute and chronic inflammatory diseases for more than seventy years. However, they can have several unwanted effects, amongst which immunosuppression is one of the most common. Here we used microarrays and proteomic approaches to characterise the effect of dexamethasone (a synthetic glucocorticoid) on the responses of primary mouse macrophages to a potent pro-inflammatory agonist, lipopolysaccharide (LPS). Gene ontology analysis revealed that dexamethasone strongly impaired the lipopolysaccharide-induced antimicrobial response, which is thought to be driven by an autocrine feedback loop involving the type I interferon IFNβ. Indeed, dexamethasone strongly and dose-dependently inhibited the expression of IFNβ by LPS-activated macrophages. Unbiased proteomic data also revealed an inhibitory effect of dexamethasone on the IFNβ-dependent program of gene expression, with strong down-regulation of several interferon-induced antimicrobial factors. Surprisingly, dexamethasone also inhibited the expression of several antimicrobial genes in response to direct stimulation of macrophages with IFNβ. We tested a number of hypotheses based on previous publications, but found that no single mechanism could account for more than a small fraction of the broad suppressive impact of dexamethasone on macrophage type I interferon signaling, underlining the complexity of this pathway. Preliminary experiments indicated that dexamethasone exerted similar inhibitory effects on primary human monocyte-derived or alveolar macrophages.</p

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

Aggregation Bias: A Proposal to Raise Awareness Regarding Inclusion in Visual Analytics

Data is a powerful tool to make informed decisions. They can be used to design products, to segment the market, and to design policies. However, trusting so much in data can have its drawbacks. Sometimes a set of indicators can conceal the reality behind them, leading to biased decisions that could be very harmful to underrepresented individuals, for example. It is challenging to ensure unbiased decision-making processes because people have their own beliefs and characteristics and be unaware of them. However, visual tools can assist decision-making processes and raise awareness regarding potential data issues. This work describes a proposal to fight biases related to aggregated data by detecting issues during visual analysis and highlighting them, trying to avoid drawing inaccurate conclusions

About females and males: continuity and discontinuity in flies

Through the decades of relentless and dedicated studies in Drosophila melanogaster, the pathway that governs sexual development has been elucidated in great detail and has become a paradigm in understanding fundamental cell-fate decisions. However, recent phylogenetic studies show that the molecular strategy used in Drosophila deviates in some important aspects from those found in other dipteran flies and suggest that the Drosophila pathway is likely to be a derivative of a simpler and more common principle. In this essay, I will discuss the evolutionary plasticity of the sex-determining pathway based on studies in the common housefly, Musca domestica. Diversification appears to primarily arise from subtle differences in the regulation of the key switch gene transformer at the top of the pathway. On the basis of these findings I propose a new idea on how the Drosophila pathway may have evolved from a more archetypal system such as in M. domestica. In essence, the arrival of an X counting mechanism mediated by Sex-lethal to compensate for X linked gene dose differences set the stage for an intimate coupling of the two pathways. Its precedent recruitment to the dosage compensation pathway allowed for an intervention in the regulation of transformer where it gradually and eventually' completely substituted for a need of transformer autoregulation