An algebraic formulation of nonassociative quantum mechanics

We develop a suitably general version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is based on the universal enveloping algebra of a general nonassociative algebra. We formulate properties of states together with notions of trace, and use them to develop GNS constructions. We describe Heisenberg and Schrodinger pictures of completely positive dynamics, and we illustrate our formalism on the explicit examples of finite-dimensional matrix Jordan algebras as well as the octonion algebra.Comment: 34 pages; v2: minor correction

Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics

We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.Comment: 38 pages; v2: typos corrected, reference added; v3: typos corrected, comments about cyclicity added in section 4.2, references updated; Final version to be published in Journal of Mathematical Physic

Characterization of an Insoluble and Soluble Form of Melanin Produced by Streptomyces cavourensis SV 21, a Sea Cucumber Associated Bacterium

Melanin is a widely distributed and striking dark-colored pigment produced by countless living organisms. Although a wide range of bioactivities have been recognized, there are still major constraints in using melanin for biotechnological applications such as its fragmentary known chemical structure and its insolubility in inorganic and organic solvents. In this study, a bacterial culture of Streptomyces cavourensis SV 21 produced two distinct forms of melanin: (1) a particulate, insoluble form as well as (2) a rarely observed water-soluble form. The here presented novel, acid-free purification protocol of purified particulate melanin (PPM) and purified dissolved melanin (PDM) represents the basis for an in-depth comparison of their physicochemical and biological properties, which were compared to the traditional acid-based precipitation of melanin (AM) and to a synthetic melanin standard (SM). Our data show that the differences in solubility between PDM and PPM in aqueous solutions may be a result of different adjoining cation species, since the soluble PDM polymer is largely composed of Mg2+ ions and the insoluble PPM is dominated by Ca2+ ions. Furthermore, AM shared most properties with SM, which is likely attributed to a similar, acid-based production protocol. The here presented gentler approach of purifying melanin facilitates a new perspective of an intact form of soluble and insoluble melanin that is less chemical altered and thus closer to its original biological form

Anti-Fouling Effects of Saponin-Containing Crude Extracts from Tropical Indo-Pacific Sea Cucumbers

Sea cucumbers are bottom dwelling invertebrates, which are mostly found on subtropical and tropical sea grass beds, sandy reef flats, or reef slopes. Although constantly exposed to fouling communities in these habitats, many species are surprisingly free of invertebrate epibionts and microfouling algae such as diatoms. In our study, we investigated the anti-fouling (AF) activities of different crude extracts of tropical Indo-Pacific sea cucumber species against the fouling diatom Cylindrotheca closterium. Nine sea cucumber species from three genera (i.e., Holothuria, Bohadschia, Actinopyga) were selected and extracted to assess their AF activities. To verify whether the sea cucumber characteristic triterpene glycosides were responsible for the observed potent AF activities, we tested purified fractions enriched in saponins isolated from Bohadschia argus, representing one of the most active anti-fouling extracts. Saponins were quantified by vanillin-sulfuric acid colorimetric assays and identified by LC-MS and LC-MS/MS analyses. We were able to demonstrate that AF activities in sea cucumber extracts were species-specific, and growth inhibition as well as attachment of the diatom to surfaces is dependent on the saponin concentration (i.e., Actinopyga contained the highest quantities), as well as on the molecular composition and structure of the present saponins (i.e., Bivittoside D derivative was the most bioactive compound). In conclusion, the here performed AF assay represents a promising and fast method for selecting the most promising bioactive organism as well as for identifying novel compounds with potent AF activities for the discovery of potentially novel pharmacologically active natural products

Coral Larvae Every Day: Leptastrea purpurea, a Brooding Species That Could Accelerate Coral Research

Sexually produced larvae are used in various fields of coral research. Because the vast majority of scleractinians reproduces only on one or few occasions per year through simultaneous release of gametes, and because an ex situ spawning induction is still very hard to achieve, great efforts are required to obtain planula larvae. Brooding corals have been used to harvest planulae although their larvae often differ in various traits from most spawning corals, e.g., in settlement behavior. Other cnidarians, such as Aiptasia spp., have been substituting for scleractinians in many aspects of coral research. However, organisms such as Aiptasia differ strongly from scleractinians, thus limiting the transferability of obtained results. This study examines the potential of Leptastrea purpurea as a reliable source of larvae for coral research. Larval output as well as settlement behavior of planulae was investigated. Our results show that colonies of L. purpurea released a daily average of 3.7 (±0.2) larvae during a period of 65 days, thus allowing continual access to planula larvae. We collected a total of 58127 larvae from our broodstock of 243 colonies. Larval settlement is induced by the same and/or similar cues as in many spawning species which increases the transferability of conclusions. We discuss the utility of L. purpurea for research on scleractinian physiology, ecology and larval settlement and conclude that L. purpurea is a well-suited organism to accelerate progress in many fields of coral research