Invariant tensors and Casimir operators for simple compact Lie groups

The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive Casimirs equal to the rank of the underlying group. A systematic derivation is presented of a complete set of identities expressing non-primitive symmetric tensors in terms of primitive tensors. Several examples are given including an application to an exceptional Lie algebra.Comment: 11 pages, LaTeX, minor changes, version in J. Math. Phy

Meta-analysis of genome-wide association studies identifies novel loci that influence cupping and the glaucomatous process

Glaucoma is characterized by irreversible optic nerve degeneration and is the most frequent cause of irreversible blindness worldwide. Here, the International Glaucoma Genetics Consortium conducts a meta-analysis of genome-wide association studies of vertical cup-disc ratio (VCDR), an important disease-related optic nerve parameter. In 21,094 individuals of European ancestry and 6,784 individuals of Asian ancestry, we identify 10 new loci associated with variation in VCDR. In a separate risk-score analysis of five case-control studies, Caucasians in the highest quintile have a 2.5-fold increased risk of primary open-angle glaucoma as compared with those in the lowest quintile. This study has more than doubled the known loci associated with optic disc cupping and will allow greater understanding of mechanisms involved in this common blinding condition

Targeting DNA Damage Response and Replication Stress in Pancreatic Cancer

Background and aims: Continuing recalcitrance to therapy cements pancreatic cancer (PC) as the most lethal malignancy, which is set to become the second leading cause of cancer death in our society. The study aim was to investigate the association between DNA damage response (DDR), replication stress and novel therapeutic response in PC to develop a biomarker driven therapeutic strategy targeting DDR and replication stress in PC. Methods: We interrogated the transcriptome, genome, proteome and functional characteristics of 61 novel PC patient-derived cell lines to define novel therapeutic strategies targeting DDR and replication stress. Validation was done in patient derived xenografts and human PC organoids. Results: Patient-derived cell lines faithfully recapitulate the epithelial component of pancreatic tumors including previously described molecular subtypes. Biomarkers of DDR deficiency, including a novel signature of homologous recombination deficiency, co-segregates with response to platinum (P < 0.001) and PARP inhibitor therapy (P < 0.001) in vitro and in vivo. We generated a novel signature of replication stress with which predicts response to ATR (P < 0.018) and WEE1 inhibitor (P < 0.029) treatment in both cell lines and human PC organoids. Replication stress was enriched in the squamous subtype of PC (P < 0.001) but not associated with DDR deficiency. Conclusions: Replication stress and DDR deficiency are independent of each other, creating opportunities for therapy in DDR proficient PC, and post-platinum therapy

Polymer grouts for plugging lost circulation in geothermal wells.

We have concluded a laboratory study to evaluate the survival potential of polymeric materials used for lost circulation plugs in geothermal wells. We learned early in the study that these materials were susceptible to hydrolysis. Through a systematic program in which many potential chemical combinations were evaluated, polymers were developed which tolerated hydrolysis for eight weeks at 500 F. The polymers also met material, handling, cost, and emplacement criteria. This screening process identified the most promising materials. A benefit of this work is that the components of the polymers developed can be mixed at the surface and pumped downhole through a single hose. Further strength testing is required to determine precisely the maximum temperature at which extrusion through fractures or voids causes failure of the lost circulation plug

Diet and the evolution of human amylase gene copy number variation.

Abstract Starch consumption is a prominent characteristic of agricultural societies and hunter-gatherers in arid environments. In contrast, rainforest and circum-arctic hunter-gatherers and some pastoralists consume much less starch 1-3 . This behavioral variation raises the possibility that different selective pressures have acted on amylase, the enzyme responsible for starch hydrolysis 4 . We found that salivary amylase gene (AMY1) copy number is correlated positively with salivary amylase protein levels, and that individuals from populations with high-starch diets have on average more AMY1 copies than those with traditionally low-starch diets. Comparisons with other loci in a subset of these populations suggest that the level of AMY1 copy number differentiation is unusual. This example of positive selection on a copy number variable gene is one of the first in the human genome. Higher AMY1 copy numbers and protein levels likely improve the digestion of starchy foods, and may buffer against the fitness-reducing effects of intestinal disease. Hominin evolution is characterized by significant dietary shifts, facilitated in part by the development of stone tool technology, the control of fire, and most recently the domestication of plants and animals 5-7 . Starch, for instance, has become an increasingly prominent component of the human diet, particularly among agricultural societies 8 . It stands to reason, therefore, that studies of the evolution of amylase in humans and our close primate relatives may provide insight into our ecological history. Because the human salivary amylase gene (AMY1) shows extensive variation in copy number 9,10 , we first assess whether a functional relationship exists between AMY1 copy number and the level of amylase protein expression i