Pointwise discontinuous functions

Approved and recommended for acceptance as fulfilling the requirements for a thesis toward the degree of Master of Arts May 15th 1912TypescriptM.A. University of Missouri 1912The concept of pointwise discontinuity is a fairly recent one in mathematics. Originally introduced as a convenient term in the study of integration, it has quite outgrown its former sphere of usefulness and has had an ever-widening field of application in modern analysis. The appearance in 1899 of the doctor's thesis of M. Baire, in which he investigated the properties of a function approached by continuous functions and found that the necessary and sufficient condition for such approach involves the idea of pointwise discontinuity, firmly grounded the conception in the fundamentals of mathematical theory. The considerations of the present paper involve a number of investigations into certain phases of the subject of pointwise discontinuity; such as, the construction and classification of pointwise discontinuous functions; their properties, singly and in combination, etc. We have just remarked that this subject is closely related to the question of approach of continuous functions, and this phase of the subject is treated in Chapter III. The final chapter is devoted to a short study of the oscillation function in the general case.Includes bibliographical reference

Edge- and Node-Disjoint Paths in P Systems

In this paper, we continue our development of algorithms used for topological network discovery. We present native P system versions of two fundamental problems in graph theory: finding the maximum number of edge- and node-disjoint paths between a source node and target node. We start from the standard depth-first-search maximum flow algorithms, but our approach is totally distributed, when initially no structural information is available and each P system cell has to even learn its immediate neighbors. For the node-disjoint version, our P system rules are designed to enforce node weight capacities (of one), in addition to edge capacities (of one), which are not readily available in the standard network flow algorithms.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Adding abiraterone or docetaxel to long-term hormone therapy for prostate cancer: directly randomised data from the STAMPEDE multi-arm, multi-stage platform protocol.

Adding abiraterone acetate with prednisolone (AAP) or docetaxel with prednisolone (DocP) to standard-of-care (SOC) each improved survival in STAMPEDE: a multi-arm multi-stage platform randomised controlled protocol recruiting patients with high-risk locally advanced or metastatic PCa starting long-term androgen deprivation therapy (ADT). The protocol provides the only direct, randomised comparative data of SOC+AAP vs SOC+DocP

Special cases : moons, rings, comets, trojans

Non-planetary bodies provide valuable insight into our current under- standing of planetary formation and evolution. Although these objects are challeng- ing to detect and characterize, the potential information to be drawn from them has motivated various searches through a number of techniques. Here, we briefly review the current status in the search of moons, rings, comets, and trojans in exoplanet systems and suggest what future discoveries may occur in the near future.Comment: Invited review (status August 2017

Phenome-wide association analysis of LDL-cholesterol lowering genetic variants in PCSK9

BACKGROUND: We characterised the phenotypic consequence of genetic variation at the PCSK9 locus and compared findings with recent trials of pharmacological inhibitors of PCSK9. METHODS: Published and individual participant level data (300,000+ participants) were combined to construct a weighted PCSK9 gene-centric score (GS). Seventeen randomized placebo controlled PCSK9 inhibitor trials were included, providing data on 79,578 participants. Results were scaled to a one mmol/L lower LDL-C concentration. RESULTS: The PCSK9 GS (comprising 4 SNPs) associations with plasma lipid and apolipoprotein levels were consistent in direction with treatment effects. The GS odds ratio (OR) for myocardial infarction (MI) was 0.53 (95% CI 0.42; 0.68), compared to a PCSK9 inhibitor effect of 0.90 (95% CI 0.86; 0.93). For ischemic stroke ORs were 0.84 (95% CI 0.57; 1.22) for the GS, compared to 0.85 (95% CI 0.78; 0.93) in the drug trials. ORs with type 2 diabetes mellitus (T2DM) were 1.29 (95% CI 1.11; 1.50) for the GS, as compared to 1.00 (95% CI 0.96; 1.04) for incident T2DM in PCSK9 inhibitor trials. No genetic associations were observed for cancer, heart failure, atrial fibrillation, chronic obstructive pulmonary disease, or Alzheimer's disease - outcomes for which large-scale trial data were unavailable. CONCLUSIONS: Genetic variation at the PCSK9 locus recapitulates the effects of therapeutic inhibition of PCSK9 on major blood lipid fractions and MI. While indicating an increased risk of T2DM, no other possible safety concerns were shown; although precision was moderate

Nivolumab versus placebo in patients with relapsed malignant mesothelioma (CONFIRM): a multicentre, double-blind, randomised, phase 3 trial

Background No phase 3 trial has yet shown improved survival for patients with pleural or peritoneal malignant mesothelioma who have progressed following platinum-based chemotherapy. The aim of this study was to assess the efficacy and safety of nivolumab, an anti-PD-1 antibody, in these patients. Methods This was a multicentre, placebo-controlled, double-blind, parallel group, randomised, phase 3 trial done in 24 hospitals in the UK. Adult patients (aged ≥18 years) with an Eastern Cooperative Oncology Group performance status of 0 or 1, with histologically confirmed pleural or peritoneal mesothelioma, who had received previous first-line platinum-based chemotherapy and had radiological evidence of disease progression, were randomly assigned (2:1) to receive nivolumab at a flat dose of 240 mg every 2 weeks over 30 min intravenously or placebo until disease progression or a maximum of 12 months. The randomisation sequence was generated within an interactive web response system (Alea); patients were stratified according to epithelioid versus non-epithelioid histology and were assigned in random block sizes of 3 and 6. Participants and treating clinicians were masked to group allocation. The co-primary endpoints were investigator-assessed progression-free survival and overall survival, analysed according to the treatment policy estimand (an equivalent of the intention-to-treat principle). All patients who were randomly assigned were included in the safety population, reported according to group allocation. This trial is registered with Clinicaltrials.gov, NCT03063450. Findings Between May 10, 2017, and March 30, 2020, 332 patients were recruited, of whom 221 (67%) were randomly assigned to the nivolumab group and 111 (33%) were assigned to the placebo group). Median follow-up was 11·6 months (IQR 7·2–16·8). Median progression-free survival was 3·0 months (95% CI 2·8–4·1) in the nivolumab group versus 1·8 months (1·4–2·6) in the placebo group (adjusted hazard ratio [HR] 0·67 [95% CI 0·53–0·85; p=0·0012). Median overall survival was 10·2 months (95% CI 8·5–12·1) in the nivolumab group versus 6·9 months (5·0–8·0) in the placebo group (adjusted HR 0·69 [95% CI 0·52–0·91]; p=0·0090). The most frequently reported grade 3 or worse treatment-related adverse events were diarrhoea (six [3%] of 221 in the nivolumab group vs two [2%] of 111 in the placebo group) and infusion-related reaction (six [3%] vs none). Serious adverse events occurred in 90 (41%) patients in the nivolumab group and 49 (44%) patients in the placebo group. There were no treatment-related deaths in either group. Interpretation Nivolumab represents a treatment that might be beneficial to patients with malignant mesothelioma who have progressed on first-line therapy. Funding Stand up to Cancer–Cancer Research UK and Bristol Myers Squibb

Mortality and pulmonary complications in patients undergoing surgery with perioperative sars-cov-2 infection: An international cohort study

Background The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (740%) had emergency surgery and 280 (248%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (261%) patients. 30-day mortality was 238% (268 of 1128). Pulmonary complications occurred in 577 (512%) of 1128 patients; 30-day mortality in these patients was 380% (219 of 577), accounting for 817% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 175 [95% CI 128-240], p<00001), age 70 years or older versus younger than 70 years (230 [165-322], p<00001), American Society of Anesthesiologists grades 3-5 versus grades 1-2 (235 [157-353], p<00001), malignant versus benign or obstetric diagnosis (155 [101-239], p=0046), emergency versus elective surgery (167 [106-263], p=0026), and major versus minor surgery (152 [101-231], p=0047). Interpretation Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio