On generalized Kneser hypergraph colorings

In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs \KG{r}{\pmb s}{\calS}, "generalized $r$-uniform Kneser hypergraphs with intersection multiplicities $\pmb s$." It generalized previous lower bounds by Kriz (1992/2000) for the case ${\pmb s}=(1,...,1)$ without intersection multiplicities, and by Sarkaria (1990) for \calS=\tbinom{[n]}k. Here we discuss subtleties and difficulties that arise for intersection multiplicities $s_i>1$: 1. In the presence of intersection multiplicities, there are two different versions of a "Kneser hypergraph," depending on whether one admits hypergraph edges that are multisets rather than sets. We show that the chromatic numbers are substantially different for the two concepts of hypergraphs. The lower bounds of Sarkaria (1990) and Ziegler (2002) apply only to the multiset version. 2. The reductions to the case of prime $r$ in the proofs Sarkaria and by Ziegler work only if the intersection multiplicities are strictly smaller than the largest prime factor of $r$. Currently we have no valid proof for the lower bound result in the other cases. We also show that all uniform hypergraphs without multiset edges can be represented as generalized Kneser hypergraphs.Comment: 9 pages; added examples in Section 2; added reference ([11]), corrected minor typos; to appear in J. Combinatorial Theory, Series

The Role of Family-Based Designs in Genome-Wide Association Studies

Genome-Wide Association Studies (GWAS) offer an exciting and promising new research avenue for finding genes for complex diseases. Traditional case-control and cohort studies offer many advantages for such designs. Family-based association designs have long been attractive for their robustness properties, but robustness can mean a loss of power. In this paper we discuss some of the special features of family designs and their relevance in the era of GWAS.Comment: Published in at http://dx.doi.org/10.1214/08-STS280 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

First-principles calculations of the vibrational properties of bulk CdSe and CdSe nanowires

We present first-principles calculations on bulk CdSe and CdSe nanowires with diameters of up to 22 \AA. Density functional linear combination of atomic orbitals and plane wave calculations of the electronic and structural properties are presented and discussed. We use an iterative, symmetry-based method to relax the structures into the ground state. We find that the band gap depends on surface termination. Vibrational properties in the whole Brillouin zone of bulk CdSe and the zone-center vibrations of nanowires are calculated and analyzed. We find strongly size-dependent and nearly constant modes, depending on the displacement directions. A comparison with available experimental Raman data is be given

Metallurgy In Costa-Rica

Anthropolog

Charmed Hadrons from Fragmentation and B Decays

The fragmentation functions of $D^0$, $D^{\pm}$, $D_s^{\pm}$, $D^{*o}$, $D^{*\pm}$ and $\Lambda_c^{\pm}$ at $\sqrt{s}$$\simeq$10.6 GeV are measured with a data set of 102.7 fb$^{-1}$. Fragmentation model parametrizations (Peterson, Kartvelishvili, Collins-Spiller, Lund, and Bowler models) are compared to the data. The data at high $x$$\simeq$1 indicate a contribution of non-perturbative QCD processes.Comment: presented at CHARM2006, International Workshop on Tau-Charm Physics, Beijing, June 5-7, 200

Explicit correlation and intermolecular interactions: Investigating carbon dioxide complexes with the CCSD(T)-F12 method

We have optimized the lowest energy structures and calculated interaction energies for the CO₂–Ar, CO₂–N₂, CO₂–CO, CO₂–H₂O, and CO₂–NH₃ dimers with the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)]-F12 methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. The relatively modest increase in the computational cost between explicit and conventional CCSD(T) is more than compensated for by the impressive accuracy of the CCSD(T)-F12 method. We recommend use of the CCSD(T)-F12 methods in combination with the VXZ-F12 basis sets for the accurate determination of equilibrium geometries and interaction energies of weakly bound electron donor acceptor complexes

The development of a treadle pump: Lessons from the South African experience

Manual pumps / Design / South Africa

Time domain simulations of dynamic river networks

The problem of simulating a river network is considered. A river network is considered to comprise of rivers, dams/lakes as well as weirs. We suggest a numerical approach with specific features that enable the correct representation of these assets. For each river the flow of water is described by the shallow water equations which is a system of hyperbolic partial differential equations and at the junctions of the rivers, suitable coupling conditions, viewed as interior boundary conditions are used to couple the dynamics. A different model for the dams is also presented. Numerical test cases are presented which show that the model is able to reproduce the expected dynamics of the system. Other aspects of the modelling such as rainfall, run-off, overflow/flooding, evaporation, absorption/seepage, bed-slopes, bed friction have not been incorporated in the model due to their specific nature

Quantifying cooperative intermolecular interactions for improved carbon dioxide capture materials

We have optimized the geometry and calculated interaction energies for over 100 different complexes of CO₂ with various combinations of electron accepting (Lewis acid) and electron donating (Lewis base) molecules. We have used the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)-F12] methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. We observe only modest changes in the geometric parameters of CO₂ upon complexation, which suggests that the geometry of CO₂ adsorbed in a nanoporous material should be similar to that of CO₂ in gas phase. When CO₂ forms a complex with two Lewis acids via the two electron rich terminal oxygen atoms, the interaction energy is less than twice what would be expected for the same complex involving a single Lewis acid. We consider a series of complexes that exhibit simultaneous CO₂-Lewis acid and CO₂-Lewis base intermolecular interactions, with total interaction energies spanning 14.1–105.9 kJ mol⁻¹. For these cooperative complexes, we find that the total interaction energy is greater than the sum of the interaction energies of the constituent complexes. Furthermore, the intermolecular distances of the cooperative complexes are contracted as compared to the constituent complexes. We suggest that metal-organic-framework or similar nanoporous materials could be designed with adsorption sites specifically tailored for CO₂ to allow cooperative intermolecular interactions, facilitating enhanced CO₂ adsorption

A family of Prym-Tyurin varieties of exponent 3

We investigate a family of correspondences associated to \'etale coverings of degree 3 of hyperelliptic curves. They lead to Prym-Tyurin varieties of exponent 3. We identify these varieties and derive some consequences.Comment: names of authors correcte