Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems

We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a certain kind of generalized inverses of differential operators. We answer the question when the product of two generalized Green's operators is again a generalized Green's operator for the product of the corresponding differential operators and which boundary problem it solves. Moreover, we show that---provided a factorization of the underlying differential operator---a generalized boundary problem can be factored into lower order problems corresponding to a factorization of the respective Green's operators. We illustrate our results by examples using the Maple package IntDiffOp, where the presented algorithms are implemented.Comment: 19 page

A Comprehensive Pan-Cancer Molecular Study of Gynecologic and Breast Cancers

We analyzed molecular data on 2,579 tumors from The Cancer Genome Atlas (TCGA) of four gynecological types plus breast. Our aims were to identify shared and unique molecular features, clinically significant subtypes, and potential therapeutic targets. We found 61 somatic copy-number alterations (SCNAs) and 46 significantly mutated genes (SMGs). Eleven SCNAs and 11 SMGs had not been identified in previous TCGA studies of the individual tumor types. We found functionally significant estrogen receptor-regulated long non-coding RNAs (lncRNAs) and gene/lncRNA interaction networks. Pathway analysis identified subtypes with high leukocyte infiltration, raising potential implications for immunotherapy. Using 16 key molecular features, we identified five prognostic subtypes and developed a decision tree that classified patients into the subtypes based on just six features that are assessable in clinical laboratories. By performing molecular analyses of 2,579 TCGA gynecological (OV, UCEC, CESC, and UCS) and breast tumors, Berger et al. identify five prognostic subtypes using 16 key molecular features and propose a decision tree based on six clinically assessable features that classifies patients into the subtypes

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Variation in the interaction between familial and reproductive factors on the risk of breast cancer according to age, menopausal status, and degree of familiality

International Journal of Epidemiology292214-223IJEP

The effects of interaction between familial and reproductive factors on breast cancer risk: A combined analysis of seven case-control studies

British Journal of Cancer7791525-1536BJCA

Mammographic surveillance in women aged 35–39 at enhanced familial risk of breast cancer (FH02)

Although there have been encouraging recent studies showing a potential benefit from annual mammography in women aged 40-49 years of age with an elevated breast cancer risk due to family history there is little evidence of efficacy in women aged <40 years of age. A prospective study (FH02) has been developed to assess the efficacy of mammography screening in women aged 35-39 years of age with a lifetime breast cancer risk of ? 17 % who are not receiving MRI screening. Retrospective analyses from five centres with robust recall systems identified 47 breast cancers (n = 12 in situ) with an interval cancer rate of 15/47 (32%). Invasive tumour size, lymph node status and current vital status were all significantly better than in two control groups of unscreened women (including those with a family history) recruited to the POSH study. Further evaluation of the prospective arm of FH02 is required to assess the potential added value of digital mammography and the cancer incidence rates in moderate and high risk women in order to inform cost effectiveness analyse