Recognizing Members of the Tournament Equilibrium Set is NP-hard

A recurring theme in the mathematical social sciences is how to select the "most desirable" elements given a binary dominance relation on a set of alternatives. Schwartz's tournament equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions that have been proposed so far in this context. Due to its unwieldy recursive definition, little is known about TEQ. In particular, its monotonicity remains an open problem up to date. Yet, if TEQ were to satisfy monotonicity, it would be a very attractive tournament solution concept refining both the Banks set and Dutta's minimal covering set. We show that the problem of deciding whether a given alternative is contained in TEQ is NP-hard.Comment: 9 pages, 3 figure

1. Transport of Mass, Momentum and Energy in Planetary Magnetodisc Regions

The rapid rotation of the gas giant planets, Jupiter and Saturn, leads to the formation of magnetodisc regions in their magnetospheric environments. In these regions, relatively cold plasma is confined towards the equatorial regions, and the magnetic field generated by the azimuthal (ring) current adds to the planetary dipole, forming radially distended field lines near the equatorial plane. The ensuing force balance in the equatorial magnetodisc is strongly influenced by centrifugal stress and by the thermal pressure of hot ion populations, whose thermal energy is large compared to the magnitude of their centrifugal potential energy. The sources of plasma for the Jovian and Kronian magnetospheres are the respective satellites Io (a volcanic moon) and Enceladus (an icy moon). The plasma produced by these sources is globally transported outwards through the respective magnetosphere, and ultimately lost from the system. One of the most studied mechanisms for this transport is flux tube interchange, a plasma instability which displaces mass but does not displace magnetic flux—an important observational constraint for any transport process. Pressure anisotropy is likely to play a role in the loss of plasma from these magnetospheres. This is especially the case for the Jovian system, which can harbour strong parallel pressures at the equatorial segments of rotating, expanding flux tubes, leading to these regions becoming unstable, blowing open and releasing their plasma. Plasma mass loss is also associated with magnetic reconnection events in the magnetotail regions. In this overview, we summarise some important observational and theoretical concepts associated with the production and transport of plasma in giant planet magnetodiscs. We begin by considering aspects of force balance in these systems, and their coupling with the ionospheres of their parent planets. We then describe the role of the interaction between neutral and ionized species, and how it determines the rate at which plasma mass and momentum are added to the magnetodisc. Following this, we describe the observational properties of plasma injections, and the consequent implications for the nature of global plasma transport and magnetodisc stability. The theory of the flux tube interchange instability is reviewed, and the influences of gravity and magnetic curvature on the instability are described. The interaction between simulated interchange plasma structures and Saturn’s moon Titan is discussed, and its relationship to observed periodic phenomena at Saturn is described. Finally, the observation, generation and evolution of plasma waves associated with mass loading in the magnetodisc regions is reviewed

Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra

We study the basic features of BPS quiver mutations in 4D $\mathcal{N}=2$ supersymmetric quantum field theory with $G=ADE$ gauge symmetries.\ We show, for these gauge symmetries, that there is an isotropy group $\mathcal{G}_{Mut}^{G}$ associated to a set of quiver mutations capturing information about the BPS spectra. In the strong coupling limit, it is shown that BPS chambers correspond to finite and closed groupoid orbits with an isotropy symmetry group $\mathcal{G}_{strong}^{G}$ isomorphic to the discrete dihedral groups $Dih_{2h_{G}}$ contained in Coxeter$(G)$ with $$ the Coxeter number of G. These isotropy symmetries allow to determine the BPS spectrum of the strong coupling chamber; and give another way to count the total number of BPS and anti-BPS states of $\mathcal{N}=2$ gauge theories. We also build the matrix realization of these mutation groups $\mathcal{G}_{strong}^{G}$ from which we read directly the electric-magnetic charges of the BPS and anti-BPS states of $\mathcal{N}=2$ QFT$_{4}$ as well as their matrix intersections. We study as well the quiver mutation symmetries in the weak coupling limit and give their links with infinite Coxeter groups. We show amongst others that $\mathcal{G}_{weak}^{su_{2}}$ is contained in ${GL}({2,}\mathbb{Z})$; and isomorphic to the infinite Coxeter ${I_{2}^{\infty}}$. Other issues such as building $\mathcal{G}$ and $\mathcal{G}_{weak}^{su_{3}}$ are also studied.Comment: LaTeX, 98 pages, 18 figures, Appendix I on groupoids adde

Soft X‐ray and ENA Imaging of the Earth’s Dayside Magnetosphere

The LEXI and SMILE missions will provide soft X‐ray images of the Earth's magnetosheath and cusps after their anticipated launch in 2023 and 2024, respectively. The IBEX mission showed the potential of an Energetic Neutral Atom (ENA) instrument to image dayside magnetosheath and cusps, albeit over the long hours required to raster an image with a single pixel imager. Thus, it is timely to discuss the two imaging techniques and relevant science topics. We simulate soft X‐ray and low‐ENA images that might be observed by a virtual spacecraft during two interesting solar wind scenarios: a southward turning of the interplanetary magnetic field and a sudden enhancement of the solar wind dynamic pressure. We employ the OpenGGCM global magnetohydrodynamics model and a simple exospheric neutral density model for these calculations. Both the magnetosheath and the cusps generate strong soft X‐rays and ENA signals that can be used to extract the locations and motions of the bow shock and magnetopause. Magnetopause erosion corresponds closely to the enhancement of dayside reconnection rate obtained from the OpenGGCM model, indicating that images can be used to understand global‐scale magnetopause reconnection. When dayside imagers are installed with high‐ENA inner‐magnetosphere and FUV/UV aurora imagers, we can trace the solar wind energy flow from the bow shock to the magnetosphere and then to the ionosphere in a self‐standing manner without relying upon other observatories. Soft X‐ray and/or ENA imagers can also unveil the dayside exosphere density structure and its response to space weather

Safety and immunogenicity of the candidate tuberculosis vaccine MVA85A in West Africa.

BACKGROUND: Vaccination with a recombinant modified vaccinia Ankara expressing antigen 85A from Mycobacterium tuberculosis, MVA85A, induces high levels of cellular immune responses in UK volunteers. We assessed the safety and immunogenicity of this new vaccine in West African volunteers. METHODS AND FINDINGS: We vaccinated 21 healthy adult male subjects (11 BCG scar negative and 10 BCG scar positive) with MVA85A after screening for evidence of prior exposure to mycobacteria. We monitored them over six months, observing for clinical, haematological and biochemical adverse events, together with assessment of the vaccine induced cellular immune response using ELISPOT and flow cytometry. MVA85A was well tolerated with no significant adverse events. Mild local and systemic adverse events were consistent with previous UK trials. Marked immunogenicity was found whether individuals had a previous BCG scar or not. There was not enhanced immunogenicity in those with a BCG scar, and induced T cell responses were better maintained in apparently BCG-naïve Gambians than previously studied BCG-naïve UK vaccinees. Although responses were predominantly attributable to CD4+ T cells, we also identified antigen specific CD8+ T cell responses, in subjects who were HLA B-35 and in whom enough blood was available for more detailed immunological analysis. CONCLUSIONS: These data on the safety and immunogenicity of MVA85A in West Africa support its accelerated development as a promising booster vaccine for tuberculosis. TRIAL REGISTRATION: ClinicalTrials.gov NCT00423839

Simulation of Intermetallic Solidification using Phase-Field Techniques

We present current ideas towards developing a phase-field model appropriate to the solidification of intermetallic phases. Such simulation presents two main challenges (i) dealing with faceted interfaces and (ii) the complex sub-lattice models used to describe the thermodynamics of such phases. Although models are already existent for the simulation of faceted crystals, some of these can be shown to produce highly unrealistic Wulff shapes. The model present here uses a parameterization of the Wulff shape as a direct input to the model, allowing the simulation of arbitrary crystal shapes. In addition, an anti-trapping current that can be used with arbitrary (including sub-lattice) thermodynamics is presented. Such antitrapping currents are vital in the simulation of intermetallic phases where the steep liquidus slope means small deviations in solute partitioning behaviour can translate to a significant change in tip undercooling

Study of Zγ events and limits on anomalous ZZγ and Zγγ couplings in pp̄ collisions at s=1.96TeV

We present a measurement of the Zγ production cross section and limits on anomalous ZZγ and Zγγ couplings for form-factor scales of Λ=750 and 1000 GeV. The measurement is based on 138 (152) candidates in the eeγ (μμγ) final state using 320(290)pb-1 of pp̄ collisions at s=1.96TeV. The 95% C.L. limits on real and imaginary parts of individual anomalous couplings are |h10,30Z|<0.23, |h20,40Z|<0.020, |h10,30γ|<0.23, and |h20,40γ|<0.019 for Λ=1000GeV. © 2005 The American Physical Society

Towards a science of climate and energy choices

The linked problems of energy sustainability and climate change are among the most complex and daunting facing humanity at the start of the twenty-first century. This joint Nature Energy and Nature Climate Change Collection illustrates how understanding and addressing these problems will require an integrated science of coupled human and natural systems; including technological systems, but also extending well beyond the domain of engineering or even economics. It demonstrates the value of replacing the stylized assumptions about human behaviour that are common in policy analysis, with ones based on data-driven science. We draw from and engage articles in the Collection to identify key contributions to understanding non-technological factors connecting economic activity and greenhouse gas emissions, describe a multi-dimensional space of human action on climate and energy issues, and illustrate key themes, dimensions and contributions towards fundamental understanding and informed decision making

Variants of the FADS1 FADS2 Gene Cluster, Blood Levels of Polyunsaturated Fatty Acids and Eczema in Children within the First 2 Years of Life

Association of genetic-variants in the FADS1-FADS2-gene-cluster with fatty-acid-composition in blood of adult-populations is well established. We analyze this genetic-association in two children-cohort-studies. In addition, the association between variants in the FADS-gene-cluster and blood-fatty-acid-composition with eczema was studied. Data of two population-based-birth-cohorts in The Netherlands and Germany (KOALA, LISA) were pooled (n = 879) and analyzed by (logistic) regression regarding the mutual influence of single-nucleotide-polymorphisms (SNPs) in the FADS-gene-cluster (rs174545, rs174546, rs174556, rs174561, rs3834458), on polyunsaturated fatty acids (PUFA) in blood and parent-reported eczema until the age of 2 years. All SNPs were highly significantly associated with all PUFAs except for alpha-linolenic-acid and eicosapentaenoic-acid, also after correction for multiple-testing. All tested SNPs showed associations with eczema in the LISA-study, but not in the KOALA-study. None of the PUFAs was significantly associated with eczema neither in the pooled nor in the analyses stratified by study-cohort. PUFA-composition in young children's blood is under strong control of the FADS-gene-cluster. Inconsistent results were found for a link between these genetic-variants with eczema. PUFA in blood was not associated with eczema. Thus the hypothesis of an inflammatory-link between PUFA and eczema by the metabolic-pathway of LC-PUFAs as precursors for inflammatory prostaglandins and leukotrienes could not be confirmed by these data

Isolated and dynamical horizons and their applications

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modeled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity; suggested a phenomenological model for hairy black holes; provided novel techniques to extract physics from numerical simulations; and led to new laws governing the dynamics of black holes in exact general relativity.Comment: 77 pages, 12 figures. Typos and references correcte