Fuzzy Nambu-Goldstone Physics

In spacetime dimensions larger than 2, whenever a global symmetry G is spontaneously broken to a subgroup H, and G and H are Lie groups, there are Nambu-Goldstone modes described by fields with values in G/H. In two-dimensional spacetimes as well, models where fields take values in G/H are of considerable interest even though in that case there is no spontaneous breaking of continuous symmetries. We consider such models when the world sheet is a two-sphere and describe their fuzzy analogues for G=SU(N+1), H=S(U(N-1)xU(1)) ~ U(N) and G/H=CP^N. More generally our methods give fuzzy versions of continuum models on S^2 when the target spaces are Grassmannians and flag manifolds described by (N+1)x(N+1) projectors of rank =< (N+1)/2. These fuzzy models are finite-dimensional matrix models which nevertheless retain all the essential continuum topological features like solitonic sectors. They seem well-suited for numerical work.Comment: Latex, 18 pages; references added, typos correcte

Unlocking the performance potential of functionally diverse teams: The paradoxical role of leader mood

In a multisource, lagged design field study of 66 consulting teams, we investigated the role of leader mood in unlocking the performance potential of functionally diverse teams. In line with our hypotheses, we found that, given high levels of leader positive mood, functional diversity was positively related to collective team identification. In contrast, given high levels of l

A separability criterion for density operators

We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.Comment: REVTeX, 5 page

Local Index Formula on the Equatorial Podles Sphere

We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one. After the identification of the smooth pre-$C^*$-algebra we compute the dimension spectrum and residues. We check the nontriviality of the (noncommutative) Chern character of the associated Fredholm modules by computing the pairing with the fundamental projector of the $C^*$-algebra (the nontrivial generator of the $K_0$-group) as well as the pairing with the $q$-analogue of the Bott projector. Finally, we show that the local index formula is trivially satisfied.Comment: 18 pages, no figures; minor correction

Dry season diets of sympatric ungulates in lowland Nepal: competition and facilitation in alluvial tall grasslands

Based on microhistological analyses of faecal material, we compared the early dry season diets of greater one-horned rhinoceros Rhinoceros unicornis, swamp deer Cervus duvauceli and hog deer Axis porcinus, which inhabit the same alluvial grassland habitat complex in lowland Nepal. Their diets were quite similar, both at the forage category level and within subcategories of graminoids and woody plants. Early successional tall grasses, especially Saccharum spontaneum, were the dominant food of all three species, underlining the key role of the threatened alluvial floodplains in large mammal conservation in South Asia. The two deer species ate significantly more graminoids (>66.5%) than did rhino (45.5%), and although they did not differ in proportions of graminoids, swamp deer ate significantly more late successional tall grasses (Narenga porphyrocoma and Themeda spp.) and short grasses (mainly Imperata cylindrica) than hog deer. The two deer consumed almost equal proportions of woody browse (ca. 10%), significantly less than that of rhino (33.0%). The prediction of the Jarman¿Bell hypothesis, that large-bodied herbivores are less selective and subsist on lower quality graminoids than smaller ruminants, was not supported by the data. Based on this and previous studies in the same area we propose a conceptual model where the larger megaherbivores (rhino and elephant Elephas maximus) facilitate the smaller swamp deer and hog deer during the monsoonal growing season, while the smaller and more selective deer species outcompete the larger during the dry season when food is more limited. Owing to the all-year sprouting ability of S. spontaneum, facilitation may occur also in the dry season with low numbers of megaherbivores, thus accentuating competitive exclusion at higher deer densities

Full regularity for a C*-algebra of the Canonical Commutation Relations. (Erratum added)

The Weyl algebra,- the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect in that it has a large number of representations which are not regular and these cannot model physical fields. Here, we construct explicitly a C*-algebra which can reproduce the CCRs of a countably dimensional symplectic space (S,B) and such that its representation set is exactly the full set of regular representations of the CCRs. This construction uses Blackadar's version of infinite tensor products of nonunital C*-algebras, and it produces a "host algebra" (i.e. a generalised group algebra, explained below) for the \sigma-representation theory of the abelian group S where \sigma(.,.):=e^{iB(.,.)/2}. As an easy application, it then follows that for every regular representation of the Weyl algebra of (S,B) on a separable Hilbert space, there is a direct integral decomposition of it into irreducible regular representations (a known result). An Erratum for this paper is added at the end.Comment: An erratum was added to the original pape

Quantum line bundles on noncommutative sphere

Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call them quantum line bundles) and define a multiplicative structure in their family. Also, we compute a pairing between certain quantum line bundles and finite dimensional representations of the NC sphere in the spirit of the NC index theorem. A new approach to constructing the differential calculus on a NC sphere is suggested. The approach makes use of the projective modules in question and gives rise to a NC de Rham complex being a deformation of the classical one.Comment: LaTeX file, 15 pp, no figures. Some clarifying remarks are added at the beginning of section 2 and into section

Further results on the cross norm criterion for separability

In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that the greatest cross norm criterion induces a novel computable separability criterion for bipartite systems. This new criterion is a necessary but in general not a sufficient criterion for separability. It is shown, however, that for all pure states, for Bell diagonal states, for Werner states in dimension d=2 and for isotropic states in arbitrary dimensions the new criterion is necessary and sufficient. Moreover, it is shown that for Werner states in higher dimensions (d greater than 2), the new criterion is only necessary.Comment: REVTeX, 19 page

Metagenomics: A viable tool for reconstructing herbivore diet

Metagenomics can generate data on the diet of herbivores, without the need for primer selection and PCR enrichment steps as is necessary in metabarcoding. Metagenomic approaches to diet analysis have remained relatively unexplored, requiring validation of bioinformatic steps. Currently, no metagenomic herbivore diet studies have utilized both chloroplast and nuclear markers as reference sequences for plant identification, which would increase the number of reads that could be taxonomically informative. Here, we explore how in silico simulation of metagenomic data sets resembling sequences obtained from faecal samples can be used to validate taxonomic assignment. Using a known list of sequences to create simulated data sets, we derived reliable identification parameters for taxonomic assignments of sequences. We applied these parameters to characterize the diet of western capercaillies (Tetrao urogallus) located in Norway, and compared the results with metabarcoding trnL P6 loop data generated from the same samples. Both methods performed similarly in the number of plant taxa identified (metagenomics 42 taxa, metabarcoding 43 taxa), with no significant difference in species resolution (metagenomics 24%, metabarcoding 23%). We further observed that while metagenomics was strongly affected by the age of faecal samples, with fresh samples outperforming old samples, metabarcoding was not affected by sample age. On the other hand, metagenomics allowed us to simultaneously obtain the mitochondrial genome of the western capercaillies, thereby providing additional ecological information. Our study demonstrates the potential of utilizing metagenomics for diet reconstruction but also highlights key considerations as compared to metabarcoding for future utilization of this technique

Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification of three-geometries) and derive the K-amenability of Lie groups associated with locally symmetric spaces listed in this case. More complicated examples of T-duality and topology change from fluxes are also considered. We analyse D-branes and fluxes in type II string theory on ${\mathbb C}P^3\times \Sigma_g \times {\mathbb T}^2$ with torsion $H-$flux and demonstrate in details the conjectured T-duality to ${\mathbb R}P^7\times X^3$ with no flux. In the simple case of $X^3 = {\mathbb T}^3$, T-dualizing the circles reduces to duality between ${\mathbb C}P^3\times {\mathbb T}^2 \times {\mathbb T}^2$ with $H-$flux and ${\mathbb R}P^7\times {\mathbb T}^3$ with no flux.Comment: 27 pages, tex file, no figure