Sphere Partition Function of Calabi-Yau GLSMs.

The sphere partition function of Calabi-Yau gauged linear sigma models (GLSMs) has been shown to compute the exact Kähler potential of the Kähler moduli space of a Calabi-Yau. We propose a universal expression for the sphere partition function evaluated in hybrid phases of Calabi-Yau GLSMs that are fibrations of Landau-Ginzburg orbifolds over some base manifold. Special cases include Calabi-Yau complete intersections in toric ambient spaces and Landau-Ginzburg orbifolds. The key ingredients that enter the expression are Givental's I/J-functions, the Gamma class and further data associated to the hybrid model. We test the proposal for one- and two-parameter abelian GLSMs, making connections, where possible, to known results from mirror symmetry and FJRW theory.

Map and model-moving from observation to prediction in toxicogenomics.

BACKGROUND: Chemicals induce compound-specific changes in the transcriptome of an organism (toxicogenomic fingerprints). This provides potential insights about the cellular or physiological responses to chemical exposure and adverse effects, which is needed in assessment of chemical-related hazards or environmental health. In this regard, comparison or connection of different experiments becomes important when interpreting toxicogenomic experiments. Owing to lack of capturing response dynamics, comparability is often limited. In this study, we aim to overcome these constraints. RESULTS: We developed an experimental design and bioinformatic analysis strategy to infer time- and concentration-resolved toxicogenomic fingerprints. We projected the fingerprints to a universal coordinate system (toxicogenomic universe) based on a self-organizing map of toxicogenomic data retrieved from public databases. Genes clustering together in regions of the map indicate functional relation due to co-expression under chemical exposure. To allow for quantitative description and extrapolation of the gene expression responses we developed a time- and concentration-dependent regression model. We applied the analysis strategy in a microarray case study exposing zebrafish embryos to 3 selected model compounds including 2 cyclooxygenase inhibitors. After identification of key responses in the transcriptome we could compare and characterize their association to developmental, toxicokinetic, and toxicodynamic processes using the parameter estimates for affected gene clusters. Furthermore, we discuss an association of toxicogenomic effects with measured internal concentrations. CONCLUSIONS: The design and analysis pipeline described here could serve as a blueprint for creating comparable toxicogenomic fingerprints of chemicals. It integrates, aggregates, and models time- and concentration-resolved toxicogenomic data.