Composition of the Ant Fauna (Hymenoptera: Formicidae) in Public Squares in Southern Brazil

The composition of the ant fauna was examined in public squares of three municipalities that compose the hydrographic basin of the Upper Tiete River: Biritiba Mirim, Salesopolis, and Mogi das Cruzes. Richness, frequency of occurrence, similarity, and influence of seasons on the species composition were examined. The method was standardized as sampling units consisted of a set of three baits arranged in a triangle with vertices two meters apart. Sardines in oil were used as attractant. A total of 86 species was collected. Myrmicinae and Pheidole were the richest subfamily and genus, respectively. Eighty species were collected in Mogi das Cruzes, 49 in Salesopolis, and 45 in Biritiba Mirim, with 34 species common to the three areas. The ordination analysis (NMDS) revealed the presence of two distinct communities: one in Mogi das Cruzes and another in Biritiba Mirim-Salesopolis. These data were supported by the dendogram based on the Bray-Curtis dissimilarity index. This result might be associated with the distinct geographic and demographic characteristics of the areas. Regarding seasonality, the composition of the fauna of Mogi das Cruzes is independent of the season of the year, unlike the observed in Biritiba Mirim and Salesopolis.

Predicting epidemic outbreak from individual features of the spreaders

Knowing which individuals can be more efficient in spreading a pathogen throughout a determinate environment is a fundamental question in disease control. Indeed, over recent years the spread of epidemic diseases and its relationship with the topology of the involved system have been a recurrent topic in complex network theory, taking into account both network models and real-world data. In this paper we explore possible correlations between the heterogeneous spread of an epidemic disease governed by the susceptible-infected-recovered (SIR) model, and several attributes of the originating vertices, considering Erdos-Renyi (ER), Barabasi-Albert (BA) and random geometric graphs (RGG), as well as a real case study, the US air transportation network, which comprises the 500 busiest airports in the US along with inter-connections. Initially, the heterogeneity of the spreading is achieved by considering the RGG networks, in which we analytically derive an expression for the distribution of the spreading rates among the established contacts, by assuming that such rates decay exponentially with the distance that separates the individuals. Such a distribution is also considered for the ER and BA models, where we observe topological effects on the correlations. In the case of the airport network, the spreading rates are empirically defined, assumed to be directly proportional to the seat availability. Among both the theoretical and real networks considered, we observe a high correlation between the total epidemic prevalence and the degree, as well as the strength and the accessibility of the epidemic sources. For attributes such as the betweenness centrality and the k-shell index, however, the correlation depends on the topology considered.

Mejillonesite, a new acid sodium, magnesium phosphate mineral, from Mejillones, Antofagasta, Chile

Mejillonesite, ideally NaMg(2)(PO(3)OH)(PO(4))(OH)center dot H(5)O(2), is a new mineral approved by the CNMNC (IMA 2010-068). It occurs as isolated crystal aggregates in thin zones in fine-grained opal-zeolite aggregate on the north slope of Cerro Mejillones, Antofagasta, Chile. Closely associated minerals are bobierrite, opal, clinoptilolite-Na, clinoptilolite-K, and gypsum. Mejillonesite forms orthorhombic, prismatic, and elongated thick tabular crystals up to 6 mm long, usually intergrown in radiating aggregates. The dominant form is pinacoid {100}. Prisms {hk0}, {h0l}, and {0kl} are also observed. The crystals are colorless, their streak is white, and the luster is vitreous. The mineral is transparent. It is non-fluorescent under ultraviolet light. Mohs' hardness is 4, tenacity is brittle. Cleavage is perfect on {100}, good on {010} and {001}, and fracture is stepped. The measured density is 2.36(1) g/cm(3); the calculated density is 2.367 g/cm(3). Mejillonesite is biaxial (-), alpha= 1.507(2), beta= 1.531(2), gamma= 1.531(2), 2V(meas) = 15(10)degrees, 2V(calc) = 0 degrees (589 nm). Orientation is X= a, Z= elongation direction. The mineral is non-pleochroic. Dispersion is r> v, medium. The IR spectrum contains characteristic bands of the Zundel cation (H(5)O(2)(+), or H(+)center dot 2H(2)O) and the groups P-OH and OH(-). The chemical composition is (by EDS, H(2)O by the Alimarin method, wt%): Na(2)O 9.19, MgO 26.82, P(2)O(5) 46.87, H(2)O 19, total 101.88. The empirical formula, based on 11 oxygen atoms, is Na(0.93)Mg(2.08)(PO(3)OH)(1.00) (PO(4)) (OH)(0.86) .0.95H(5)O(2) The strongest eight X-ray powder-diffraction lines [d in angstrom(I)(hkl)] are: 8.095(100)(200), 6.846(9) (210), 6.470(8)(111), 3.317(5)(302), 2.959(5)(132), 2.706(12)(113), 2.157(19)(333), and 2.153(9) (622). The crystal structure was solved on a single crystal (R = 0.055) and gave the following data: orthorhombic, Pbca, a = 16.295(1), b = 13.009(2), c = 8.434(1) angstrom, V= 1787.9(4) angstrom(3), Z = 8. The crystal structure of mejillonesite is based on a sheet (parallel to the b-c plane) formed by two types of MgO(6) octahedra, isolated tetrahedra PO(4) and PO(3)OH whose apical vertices have different orientation with respect to the sheet. The sheets are connected by interlayer, 5-coordinated sodium ions, proton hydration complexes, and hydroxyl groups. The structure of mejillonesite is related to that of angarfite, NaFe(5)(3+)(PO(4))(4)(OH)(4).4H(2)O and bakhchisaraitsevite, Na(2)Mg(5)(PO(4))(4)center dot 7H(2)O.

Properly coloured copies and rainbow copies of large graphs with small maximum degree

Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? assigns each colour to at most (n - 2)/(22.4?2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by ?. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409433, 2003]. On the other hand, if ? assigns each colour to at most n/(51?2) edges of Kn, then there is a copy of G in Kn such that each edge of G receives a different colour from ?. This proves a conjecture of Frieze and Krivelevich [Electron. J. Comb. 15(1), R59, 2008]. Our proofs rely on a framework developed by Lu and Szekely [Electron. J. Comb. 14(1), R63, 2007] for applying the local lemma to random injections. In order to improve the constants in our results we use a version of the local lemma due to Bissacot, Fernandez, Procacci, and Scoppola [preprint, arXiv:0910.1824]. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 425436, 2012

Interactive quadrangulation with reeb atlases and connectivity textures

Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the user's own subjective requirements.

Maximum Series-Parallel Subgraph

Consider the NP-hard problem of, given a simple graph G, to find a series-parallel subgraph of G with the maximum number of edges. The algorithm that, given a connected graph G, outputs a spanning tree of G, is a 1/2-approximation. Indeed, if n is the number of vertices in G, any spanning tree in G has n-1 edges and any series-parallel graph on n vertices has at most 2n-3 edges. We present a 7/12 -approximation for this problem and results showing the limits of our approach.

Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size

Let k and l be positive integers. With a graph G, we associate the quantity c(k,l)(G), the number of k-colourings of the edge set of G with no monochromatic matching of size l. Consider the function c(k,l) : N --> N given by c(k,l)(n) = max {c(k,l)(G): vertical bar V(G)vertical bar = n}, the maximum of c(k,l)(G) over all graphs G on n vertices. In this paper, we determine c(k,l)(n) and the corresponding extremal graphs for all large n and all fixed values of k and l.

High temperature limit in static backgrounds

We prove that the hard thermal loop contribution to static thermal amplitudes can be obtained by setting all the external four-momenta to zero before performing the Matsubara sums and loop integrals. At the one-loop order we do an iterative procedure for all the one-particle irreducible one-loop diagrams, and at the two-loop order we consider the self-energy. Our approach is sufficiently general to the extent that it includes theories with any kind of interaction vertices, such as gravity in the weak field approximation, for d space-time dimensions. This result is valid whenever the external fields are all bosonic.

Hypergraphs with many Kneser colorings

For fixed positive integers r, k and E with 1 <= l < r and an r-uniform hypergraph H, let kappa(H, k, l) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least l elements. Consider the function KC(n, r, k, l) = max(H epsilon Hn) kappa(H, k, l), where the maximum runs over the family H-n of all r-uniform hypergraphs on n vertices. In this paper, we determine the asymptotic behavior of the function KC(n, r, k, l) for every fixed r, k and l and describe the extremal hypergraphs. This variant of a problem of Erdos and Rothschild, who considered edge colorings of graphs without a monochromatic triangle, is related to the Erdos-Ko-Rado Theorem (Erdos et al., 1961 [8]) on intersecting systems of sets. (C) 2011 Elsevier Ltd. All rights reserved.

UNIVERSALITY OF RANDOM GRAPHS

We prove that asymptotically (as n -> infinity) almost all graphs with n vertices and C(d)n(2-1/2d) log(1/d) n edges are universal with respect to the family of all graphs with maximum degree bounded by d. Moreover, we provide an efficient deterministic embedding algorithm for finding copies of bounded degree graphs in graphs satisfying certain pseudorandom properties. We also prove a counterpart result for random bipartite graphs, where the threshold number of edges is even smaller but the embedding is randomized.

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

Weak quasi-randomness for uniform hypergraphs

We study quasi-random properties of k-uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung-Graham-Wilson theorem for quasi-random graphs. Moreover, let K(k) be the complete graph on k vertices and M(k) the line graph of the graph of the k-dimensional hypercube. We will show that the pair of graphs (K(k),M(k)) has the property that if the number of copies of both K(k) and M(k) in another graph G are as expected in the random graph of density d, then G is quasi-random (in the sense of the Chung-Graham-Wilson theorem) with density close to d. (C) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 1-38, 2012

QCD sum rules for the 'Z POT + IND C' (3900) state.

We use the QCD sum rules to study the recently observed charmonium-like structure Z+ c (3900) as a tetraquark state. We evaluate the three-point function and extract the coupling constants of the Z+ c J/ψ π+, Z+ c ηc ρ+ and Z+ c D+ ¯D∗0 vertices and the corresponding decay widths in these channels. The results obtained are in good agreement with the experimental data and supports to the tetraquark picture of this state.