On the sigma-model of deformed special geometry

We discuss the deformed sigma-model that arises when considering four-dimensional N=2$N=2$ abelian vector multiplets in the presence of an arbitrary chiral background field. In addition, we allow for a class of deformations of special geometry by non-holomorphic terms. We analyze the geometry of the sigma-model in terms of intrinsic torsion classes. We show that, generically, the deformed geometry is non-Kähler. We illustrate our findings with an example. We also express the deformed sigma-model in terms of the Hesse potential that underlies the real formulation of special geometry.     

Relations between (κ, τ)-regular sets and star complements

Let G be a finite graph with an eigenvalue µ of multiplicity m. A set X of m vertices in G is called a star set for µ in G if µ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (κ, τ)-regular if it induces a κ-regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a (κ, τ)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.     

Computing the noncentral gamma distribution, its inverse and the noncentrality parameter

The noncentral gamma distribution can be viewed as a generalization of the noncentral chi-squared distribution and it can be expressed as a mixture of a Poisson density function with a incomplete gamma function. The noncentral gamma distribution is not available in free conventional statistical programs. This paper aimed to propose an algorithm for the noncentral gamma by combining the method originally proposed by Benton and Krishnamoorthy (Comput Stat Data Anal 43(2):249–267, 2003) for the noncentral distributions with the method of inversion of the distribution function with respect to the noncentrality parameter using Newton–Raphson. The algorithms are available in pseudocode and implemented as R functions. To evaluate the accuracy and speed of computation of the algorithms implemented in R, results of the distribution function, density function, quantiles and noncentrality parameter of the noncentral incomplete gamma and its particular case, the noncentral chi-squared, were obtained for the arguments settings used by Benton and Krishnamoorthy (Comput Stat Data Anal 43(2):249–267, 2003) and Chen (J Stat Comput Simul 75(10):813–829, 2005). The implemented routines performed well and, in general, were as accurate than other approximations. The R package denoted ncg is available to download on the CRAN-R package repository http://cran.r-project.org/.     

Anti-Leishmania and cytotoxic activities of perillaldehyde epoxide synthetic positional isomers

Leishmaniasis belongs to a complex of zoonotic disease caused by protozoa of the genus Leishmania and is considered a major public health problem. Several essential oil chemical components have inhibitory effect against protozoa, including Leishmania donovani. Thus, the aim of this study was to evaluate for the first time the anti-Leishmania activity of two p-menthane monoterpene isomers (EPER-1: perillaldehyde 1,2-epoxide and EPER-2: perillaldehyde 8,9-epoxide) against L. donovani promastigotes as well as evaluating cytotoxic effect on mononuclear peripheral blood cells. Results of anti-Leishmania assay revealed that EPER-2 (IC₅₀ = 3.8 μg.mL^?1) was 16-fold more potent than its isomer EPER-1 (IC₅₀ = 64.6 μg.mL^?1). In contrast to PBMC cells, EPER-2 was not cytotoxic (IC₅₀ > 400 μg.mL^?1) when compared to positive control. These data suggest that the disposition of epoxide group into the p-menthane skeleton affects the anti-Leishmania activity, being that the presence of the exocyclic epoxide group considerably increased potency. Thus, it was possible to observe that the location of the epoxide group into the p-menthane skeleton resulted in different potencies.     

GC×GC/qMS analyses of Campomanesia guazumifolia (Cambess.) O. Berg essential oils and their antioxidant and antimicrobial activity

The present study investigated the essential oil obtained from Campomanesia guazumifolia (Cambess.) O. Berg, an aromatic plant used in Brazilian folk medicine. The chemical composition was performed by GC×GC/qMS. The antioxidant and antimicrobial activities were evaluated by DPPH and BCB and, MIC assays, respectively. Sixty-eight compounds were identified in the oil, where the major compounds were bicyclogermacrene (15%), globulol (5%) and spathulenol (5%). Sesquiterpene hydrocarbons (29 compounds) and oxygenated sesquiterpenes (20 compounds) were the most representative classes of terpenes. DPPH (IC₅₀ value 26.1 ± 0.5 μg/mL) and BCB (68.3 ± 1.5%) values indicated a significant antioxidant activity. The essential oil strongly inhibited Staphylococcus aureus (MIC 15 ± 0.1 μg/mL), Escherichia coli (MIC 25 ± 0.2 μg/mL) and Candida albicans (MIC 5 ± 0.1 μg/mL). The results give a deeper understanding of the chemical composition and report for the first time the antioxidant and antimicrobial potential of the C. guazumifolia essential oil.     

Confinement of monopole field lines in a superconductor at T ≠ 0

We apply the Bogoliubov-de Gennes equations to the confinement of a monopole-antimonopole pair in a superconductor. This is related to the problem of a quark-antiquark pair bound by a confining string, consisting of a colour-electric flux tube, dual to the magnetic vortex of type-II superconductors. We study the confinement of the field lines due to the superconducting state and calculate the effective potential between the two monopoles. The monopoles can be simulated in a real experiment inserting two long and thin magnetic rods. At short distances the potential is Coulombic and at large distances the potential is linear, as previously determined solving the Ginzburg-Landau equations. The magnetic field lines and the string tension are also studied as a function of the temperature T. Because we take into account the explicit fermionic degrees of freedom, this work may open new perspectives to the breaking of chiral symmetry or to colour superconductivity.     

Truncated States Obtained by Iteration

We introduce the concept of truncated states obtained via iterative processes （TSI） and study its statistical features, making an analogy with dynamical systems theory （DST）. As a specific example, we have studied TSI for the doubling and the logistic functions, which are standard functions in studying chaos. TSI for both the doubling and logistic functions exhibit certain similar patterns when their statistical features are compared from the point of view of DST.     

In Vitro Calli Production Resulted in Different Profiles of Plant-Derived Medicinal Compounds in Phyllanthus amarus

The efficient production of plant-derived medicinal compounds (PDMCs) from in vitro plants requires improvements in knowledge about control of plant or organ development and factors affecting the biosynthesis pathway of specific PDMCs under in vitro conditions, leading to a realistic large-scale tool for in vitro secondary metabolite production. Thus, this study aimed to develop an in vitro technique, through the induction and proliferation of calli, for production of plant fresh weight, and to compare the PDMC profile obtained from the plants versus in vitro calli of Phyllanthus amarus. It was successfully possible to obtain and proliferate two types of calli, one with a beige color and a friable appearance, obtained in the dark using Murashige and Skoog (MS) medium plus 2,4-dichlorophenoxyacetic acid (2,4-D), and a second type with a green color, rigid consistency, and nonfriable appearance obtained under light conditions and MS medium plus 6-benzyladenine (6-BA). In vitro micropropagated plants that gave rise to calli were also acclimatized in a greenhouse and cultivated until obtaining the mass for PDMC analysis and used as a control. While the micropropagated-derived plants concentrated the lignans niranthin, nirtetralin, and phyllanthin, the Phyllanthus amarus calli proliferated in vitro concentrated a completely different biochemical profile and synthesis of compounds, such as betulone, squalene, stigmasterol, and β-sitosterol, in addition to others not identified by GC-MS database. These results demonstrate the possibility of applying the calli in vitro from Phyllanthus amarus for production of important PDMCs unlike those obtained in cultures of differentiated tissues from field plants.