Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late

Homologous recombination DNA repair defects in PALB2-associated breast cancers

© 2019, The Author(s). Mono-allelic germline pathogenic variants in the Partner And Localizer of BRCA2 (PALB2) gene predispose to a high-risk of breast cancer development, consistent with the role of PALB2 in homologous recombination (HR) DNA repair. Here, we sought to define the repertoire of somatic genetic alterations in PALB2-associated breast cancers (BCs), and whether PALB2-associated BCs display bi-allelic inactivation of PALB2 and/or genomic features of HR-deficiency (HRD). Twenty-four breast cancer patients with pathogenic PALB2 germline mutations were analyzed by whole-exome sequencing (WES, n = 16) or targeted capture massively parallel sequencing (410 cancer genes, n = 8). Somatic genetic alterations, loss of heterozygosity (LOH) of the PALB2 wild-type allele, large-scale state transitions (LSTs) and mutational signatures were defined. PALB2-associated BCs were found to be heterogeneous at the genetic level, with PIK3CA (29%), PALB2 (21%), TP53 (21%), and NOTCH3 (17%) being the genes most frequently affected by somatic mutations. Bi-allelic PALB2 inactivation was found in 16 of the 24 cases (67%), either through LOH (n = 11) or second somatic mutations (n = 5) of the wild-type allele. High LST scores were found in all 12 PALB2-associated BCs with bi-allelic PALB2 inactivation sequenced by WES, of which eight displayed the HRD-related mutational signature 3. In addition, bi-allelic inactivation of PALB2 was significantly associated with high LST scores. Our findings suggest that the identification of bi-allelic PALB2 inactivation in PALB2-associated BCs is required for the personalization of HR-directed therapies, such as platinum salts and/or PARP inhibitors, as the vast majority of PALB2-associated BCs without PALB2 bi-allelic inactivation lack genomic features of HRD

Polygenic Risk Scores for Prediction of Breast Cancer and Breast Cancer Subtypes.

Stratification of women according to their risk of breast cancer based on polygenic risk scores (PRSs) could improve screening and prevention strategies. Our aim was to develop PRSs, optimized for prediction of estrogen receptor (ER)-specific disease, from the largest available genome-wide association dataset and to empirically validate the PRSs in prospective studies. The development dataset comprised 94,075 case subjects and 75,017 control subjects of European ancestry from 69 studies, divided into training and validation sets. Samples were genotyped using genome-wide arrays, and single-nucleotide polymorphisms (SNPs) were selected by stepwise regression or lasso penalized regression. The best performing PRSs were validated in an independent test set comprising 11,428 case subjects and 18,323 control subjects from 10 prospective studies and 190,040 women from UK Biobank (3,215 incident breast cancers). For the best PRSs (313 SNPs), the odds ratio for overall disease per 1 standard deviation in ten prospective studies was 1.61 (95%CI: 1.57-1.65) with area under receiver-operator curve (AUC) = 0.630 (95%CI: 0.628-0.651). The lifetime risk of overall breast cancer in the top centile of the PRSs was 32.6%. Compared with women in the middle quintile, those in the highest 1% of risk had 4.37- and 2.78-fold risks, and those in the lowest 1% of risk had 0.16- and 0.27-fold risks, of developing ER-positive and ER-negative disease, respectively. Goodness-of-fit tests indicated that this PRS was well calibrated and predicts disease risk accurately in the tails of the distribution. This PRS is a powerful and reliable predictor of breast cancer risk that may improve breast cancer prevention programs

The effect of isolated nocturnal oxygen desaturations on serum hs‐CRP and IL‐6 in patients with chronic obstructive pulmonary disease

IntroductionA majority of patients with chronic obstructive pulmonary disease (COPD) die of cardiovascular disease (CVD), yet the mechanisms responsible for this association are not fully understood. It remains unknown if isolated nocturnal oxygen desaturation (iNOD) could be one of the potential pathways by which the 'inflammatory COPD' phenotype leads to CVD.ObjectivesWe aimed to evaluate if COPD patients who meet the Medicare guidelines for nocturnal oxygen therapy (iNOT+) had higher serum hs-CRP and IL-6 than those who did not meet the guidelines for iNOT (iNOT-).MethodsPatients with moderate to severe COPD (ie FEV1 < 80% and FEV1/FVC < 70), who were not on oxygen, underwent nocturnal oximetry on room air. Serum IL-6 and hs-CRP were collected the morning after the nocturnal oximetry testing.ResultsA total of 28 patients were included in the study, 8 of whom had more than 5 minutes and 5% of their sleep time spent at oxygen saturation less than 88% and constituted the iNOT+ group. Only serum hs-CRP was significantly higher in iNOT+ than iNOT- (P = 0.050). There was no difference in the rate of COPD exacerbations at one and three months, or five-year survival between the groups (P > 0.3).ConclusionCOPD patients who have more than 5 minutes and 5% of their sleep time spent at oxygen saturation less than 88% have increased hs-CRP, which is associated with increased risk of future CVD

Antacid Medication and Antireflux Surgery in Patients with Idiopathic Pulmonary Fibrosis A Systematic Review and Meta-Analysis

Rationale: Idiopathic pulmonary fibrosis (IPF) is a fibrosing interstitial pneumoniawith impaired survival. Previous guidelines recommend antacidmedication to improve respiratory outcomes in patientswith IPF. Objectives: This systematic review was undertaken during the development of an American Thoracic Society, European Respiratory Society, Japanese Respiratory Society, and Asociacion Latinoamericana del Torax guideline. The clinical question was, "Should patients with IPF who have documented abnormal gastroesophageal reflux (GER) with or without symptoms of GER disease 1) be treated with antacidmedication or 2) undergo antireflux surgery to improve respiratory outcomes?"Methods: Medline, Embase, the Cochrane Central Register of Controlled Trials, and the gray literature were searched through June 30, 2020. Studies that enrolled patients with IPF and 1) compared antacid medication to placebo or no medication or 2) compared antireflux surgery to no surgery were selected. Metaanalyses were performed when possible. Outcomes included disease progression, mortality, exacerbations, hospitalizations, lung function, respiratory symptoms, GER severity, and adverse effects/complications. Results: For antacidmedication,when two studieswere aggregated, therewas no statistically significant effect on disease progression, defined as a 10% ormore decline in FVC,more than 50-mdecline in 6-minute walking distance, or death (risk ratio [RR], 0.88; 95% confidence interval [CI], 0.76-1.03).Aseparate study that could not be included in themetaanalysis found no statistically significant effect on disease progression when defined as a 5% ormore decline in FVC or death (RR, 1.10; 95% CI, 1.00-1.21) and an increase in disease progressionwhen defined as a 10% ormore decline in FVC or death (RR, 1.28; 95% CI, 1.08-1.51). For antireflux surgery, therewas also no statistically significant effect on disease progression (RR, 0.29; 95% CI, 0.06-1.26).Neither antacid medications nor antireflux surgerywas associated with improvements in the other outcomes. Conclusions: There is insufficient evidence to conclude that antacid medication or antireflux surgery improves respiratory outcomes in patientswith IPF,most ofwhomhad not had abnormalGER confirmed. Well-designed and adequately powered prospective studieswith objective evaluation forGER are critical to elucidate the role of antacidmedication and antireflux surgery for respiratory outcomes in patientswith IPF