Realizability toposes and ordered PCA's

Partial combinatory algebras (pca's, for short), are well-known to form the basic ingredient for the construction of various realizability toposes, of which the Eective Topos is undoubtedly the most famous. There is more than one way to present the realizability topos associated to a pca; one may take the exact completion of the category of partitioned assemblies (see [7]), or one can use tripos theory. Triposes built from pca's are, together with those from locales, the most important and most extensively studied instances of triposes, but from a structural point of view, there are important dierences between the two; whereas locales are organized in a well-behaved category, which is a re ective subcategory of the category of toposes, it is not immediately clear what an appropriate category for pca's may look like. Moreover, there are various nice properties in the localic case, such as the fact that there is a one-to-one correspondence between maps of locales and geometric morphisms between the corresponding sheaf toposes, and also the fact that this correspondence preserves epi-mono factorizations; such anintimate connection is absent for pca's

Aggregation of ecological indicators for mapping aquatic nature quality : overview of existing methods and case studies

Indicators for aquatic nature quality are calculated using ecological monitoring data from individual sampling stations. For reporting purposes, these results need to be aggregated and scaled up to higher levels (catchment area, country). This report provides an overview of different existing spatial aggregation methods for this purpose, including an evaluation of their suitability for aquatic ecological indicators. So-called „model-based„ methods, consisting of some sort of „kriging¿ step followed by calculation of the arithmetic mean, appeared to be the most appropriate. Application of these methods to multimetric indicators of aquatic macroinvertebrates in two Dutch subcatchment areas confirmed their suitability. However, the methods that were used were based on aggregation (using kriging) over Euclidian (straight), distances. It is recommended to conduct further research on the suitability of interpolation through stream networks, i.e., through the waterways themselves

Ultracold atoms in optical lattices

Bosonic atoms trapped in an optical lattice at very low temperatures, can be modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson approach for dealing with the Bose-Hubbard model, which enables us to analytically describe the physics of this model at nonzero temperatures. With our approach the phase diagram for this model at nonzero temperatures can be quantified.Comment: 29 pages, 10 figure

Quantum phases in a resonantly-interacting Bose-Fermi mixture

We consider a resonantly-interacting Bose-Fermi mixture of $^{40}$K and $^{87}$Rb atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for $^{40}$K and $^{87}$Rb atoms, and $^{40}$K-$^{87}$Rb molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.Comment: 4 pages, 3 figure