Localization algebras and deformations of Koszul algebras

We show that the center of a flat graded deformation of a standard Koszul algebra behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed-point set. In particular, the center acts by characters on the deformed standard modules, providing a "localization map." We construct a universal graded deformation, and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming the Koszul dual algebra. This is an algebraic version of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers; we recover and generalize their result by showing that the center of the universal deformation for the ring governing a block of parabolic category $\mathcal{O}$ for $\mathfrak{gl}_n$ is isomorphic to the equivariant cohomology of a Spaltenstein variety. We also identify the center of the deformed version of the "category $\mathcal{O}$" of a hyperplane arrangement (defined by the authors in a previous paper) with the equivariant cohomology of a hypertoric variety.Comment: 39 pages; v3: final versio

Inclusive and flexible curriculum design framework in work-based learning: providing high-impact transnational education opportunities in Sub-Saharan Africa

Impactful pedagogies in Higher Education are required to meet the challenges of the 21st Century. This chapter outlines an inclusive, flexible and work-based learning curriculum design framework to respond to these needs. Two cases from Glasgow Caledonian University are used to illustrate this framework in a transnational educational context in Sub-Saharan Africa. Case one explores the impact of a Railway Operations Management programme in South Africa, where the views of two cohorts of 137 recent graduates were gathered through an online questionnaire. Case two examines the views of Optometry/Orthoptics students who undertook an intensive two-week clinical work experience on the train-based clinic (Phelophepa train) in South Africa; data was gathered through an online questionnaire from 58 participating students since 2014. Both examples highlight transformative personal experiences and impacts of their education beyond just their studies – to a clearer sense of personal and professional pride, to becoming role models for their families and to developing meta-cognitive skills to support lifelong learning. In the Railway Operations Management example, additional benefits were seen to their organisation – through improved interpersonal skills, decision making and problem solving and creating knowledge-sharing – whereas in the Optometry/Orthoptics case life-changing impacts to patients were delivered through this work experience

Performance of Deep Learning Architectures and Transfer Learning for Detecting Glaucomatous Optic Neuropathy in Fundus Photographs

The ability of deep learning architectures to identify glaucomatous optic neuropathy (GON) in fundus photographs was evaluated. A large database of fundus photographs (n = 14,822) from a racially and ethnically diverse group of individuals (over 33% of African descent) was evaluated by expert reviewers and classified as GON or healthy. Several deep learning architectures and the impact of transfer learning were evaluated. The best performing model achieved an overall area under receiver operating characteristic (AUC) of 0.91 in distinguishing GON eyes from healthy eyes. It also achieved an AUC of 0.97 for identifying GON eyes with moderate-to-severe functional loss and 0.89 for GON eyes with mild functional loss. A sensitivity of 88% at a set 95% specificity was achieved in detecting moderate-to-severe GON. In all cases, transfer improved performance and reduced training time. Model visualizations indicate that these deep learning models relied on, in part, anatomical features in the inferior and superior regions of the optic disc, areas commonly used by clinicians to diagnose GON. The results suggest that deep learning-based assessment of fundus images could be useful in clinical decision support systems and in the automation of large-scale glaucoma detection and screening programs

CRISPR/Cas9 mediated generation of an ovine model for infantile neuronal ceroid lipofuscinosis (CLN1 disease)

The neuronal ceroid lipofuscinoses (NCLs) are a group of devastating monogenetic lysosomal disorders that affect children and young adults with no cure or effective treatment currently available. One of the more severe infantile forms of the disease (INCL or CLN1 disease) is due to mutations in the palmitoyl-protein thioesterase 1 (PPT1) gene and severely reduces the child’s lifespan to approximately 9 years of age. In order to better translate the human condition than is possible in mice, we sought to produce a large animal model employing CRISPR/Cas9 gene editing technology. Three PPT1 homozygote sheep were generated by insertion of a disease-causing PPT1 (R151X) human mutation into the orthologous sheep locus. This resulted in a morphological, anatomical and biochemical disease phenotype that closely resembles the human condition. The homozygous sheep were found to have significantly reduced PPT1 enzyme activity and accumulate autofluorescent storage material, as is observed in CLN1 patients. Clinical signs included pronounced behavioral deficits as well as motor deficits and complete loss of vision, with a reduced lifespan of 17 ± 1 months at a humanely defined terminal endpoint. Magnetic resonance imaging (MRI) confirmed a significant decrease in motor cortical volume as well as increased ventricular volume corresponding with observed brain atrophy and a profound reduction in brain mass of 30% at necropsy, similar to alterations observed in human patients. In summary, we have generated the first CRISPR/Cas9 gene edited NCL model. This novel sheep model of CLN1 disease develops biochemical, gross morphological and in vivo brain alterations confirming the efficacy of the targeted modification and potential relevance to the human condition