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

Milk progesterone as a tool to improve fertility in dairy cows

Milk progesterone offers an opportunity to objectively study fertility in dairy cows, in contrast to traditional measures of dairy cow fertility, which in general are highly influenced by on-farm management decisions. The aim of this thesis was to study how milk progesterone could be used as a genetic and management tool to improve fertility in dairy cows. Progesterone-based measures were influenced by different systematic factors, e.g. breed, parity, season, housing and lameness, studied in a dataset from a Swedish experimental herd. The repeatabilities were higher for progesterone-based measures compared with traditional measures of fertility based on insemination data. If a cow had an atypical progesterone profile in one lactation, the risk of an atypical profile in the next lactation was increased. Genetic parameters for progesterone measures based on different milk sampling intervals were estimated in a British dataset. Heritability estimates were moderate, but decreased with increased sampling intervals. It was shown that progesterone analysis of monthly milk samples, resembling milk sampling as in the current Swedish milk recording system, could be used to increase the accuracy of genetic evaluation for an earlier start of cyclical ovarian activity after calving. Inclusion of monthly milk sampling for progesterone analysis in predictive models could also be used to identify cows with delayed ovarian cyclicity with a high accuracy already two months after calving. This enables an earlier treatment of ovarian dysfunction and therefore, probably, a shorter calving interval. In conclusion, this thesis shows that milk progesterone may be used for improved management and genetic evaluation of dairy cow fertility

Cyclicity for categorified quantum groups

We equip the categorified quantum group attached to a KLR algebra and an arbitrary choice of scalars with duality functor which is cyclic, that is, such that f=f^** for all 2-morphisms f. This is accomplished via a modified diagrammatic formalism.Comment: 12 pages, xy-pic diagram