Random variables with completely independent subcollections

AbstractWe investigate the algebra and geometry of the independence conditions on discrete random variables in which we consider a collection of random variables and study the condition of independence of some subcollections. We interpret independence conditions as an ideal of algebraic relations. After a change of variables, this ideal is generated by generalized 2×2 minors of multi-way tables and linear forms. In particular, let Δ be a simplicial complex on some random variables and A be the table corresponding to the product of those random variables. If A is Δ-independent table then A can be written as the entrywise sum AI+A0 where AI is a completely independent table and A0 is identically 0 in its Δ-margins.We compute the isolated components of the original ideal, showing that there is only one component that could correspond to probability distributions, and relate the algebra and geometry of the main component to that of the Segre embedding. If Δ has fewer than three facets, we are able to compute generators for the main component, show that it is Cohen–Macaulay, and give a full primary decomposition of the original ideal

Exact ground states for a class of one-dimensional frustrated quantum spin models

We have found the exact ground state for two frustrated quantum spin-1/2 models on a linear chain. The first model describes ferromagnet- antiferromagnet transition point. The singlet state at this point has double-spiral ordering. The second model is equivalent to special case of the spin-1/2 ladder. It has non-degenerate singlet ground state with exponentially decaying spin correlations and there is an energy gap. The exact ground state wave function of these models is presented in a special recurrent form and recurrence technics of expectation value calculations is developed.Comment: 16 pages, 3 figures, RevTe

Generalized Toda Theory from Six Dimensions and the Conifold

Recently, a physical derivation of the Alday-Gaiotto-Tachikawa correspondence has been put forward. A crucial role is played by the complex Chern-Simons theory arising in the 3d-3d correspondence, whose boundary modes lead to Toda theory on a Riemann surface. We explore several features of this derivation and subsequently argue that it can be extended to a generalization of the AGT correspondence. The latter involves codimension two defects in six dimensions that wrap the Riemann surface. We use a purely geometrical description of these defects and find that the generalized AGT setup can be modeled in a pole region using generalized conifolds. Furthermore, we argue that the ordinary conifold clarifies several features of the derivation of the original AGT correspondence.Comment: 27+2 pages, 3 figure

Lessons learned from rapid environmental risk assessments for prioritization of alien species using expert panels

Limiting the spread and impacts of invasive alien species (IAS) on biodiversity and ecosystems has become a goal of global, regional and national biodiversity policies. Evidence based management of IAS requires support by risk assessments, which are often based on expert judgment. We developed a tool to prioritize potentially new IAS based on their ecological risks, socio-economic impact and feasibility of management using multidisciplinary expert panels. Nine expert panels reviewed scientific studies, grey literature and expert knowledge for 152 species. The quality assessment of available knowledge revealed a lack of peer-reviewed data and high dependency on best professional judgments, especially for impacts on ecosystem services and feasibility of management. Expert consultation is crucial for conducting and validating rapid assessments of alien species. There is still a lack of attention for systematic and methodologically sound assessment of impacts on ecosystem services and weighting negative and positive effects of alien species.Peer reviewe

DarkSUSY: Computing Supersymmetric Dark Matter Properties Numerically

The question of the nature of the dark matter in the Universe remains one of the most outstanding unsolved problems in basic science. One of the best motivated particle physics candidates is the lightest supersymmetric particle, assumed to be the lightest neutralino - a linear combination of the supersymmetric partners of the photon, the Z boson and neutral scalar Higgs particles. Here we describe DarkSUSY, a publicly-available advanced numerical package for neutralino dark matter calculations. In DarkSUSY one can compute the neutralino density in the Universe today using precision methods which include resonances, pair production thresholds and coannihilations. Masses and mixings of supersymmetric particles can be computed within DarkSUSY or with the help of external programs such as FeynHiggs, ISASUGRA and SUSPECT. Accelerator bounds can be checked to identify viable dark matter candidates. DarkSUSY also computes a large variety of astrophysical signals from neutralino dark matter, such as direct detection in low-background counting experiments and indirect detection through antiprotons, antideuterons, gamma-rays and positrons from the Galactic halo or high-energy neutrinos from the center of the Earth or of the Sun. Here we describe the physics behind the package. A detailed manual will be provided with the computer package.Comment: 35 pages, no figure