Prime number races

Sous l’hypothèse de Riemann généralisée et l’hypothèse d’indépendance linéaire, Rubinstein et Sarnak ont prouvé que les valeurs de x > 1 pour lesquelles nous avons plus de nombres premiers de la forme 4n + 3 que de nombres premiers de la forme 4n + 1 en dessous de x ont une densité logarithmique d’environ 99,59%. En général, l’étude de la différence #{p < x : p dans A} − #{p < x : p dans B} pour deux sous-ensembles de nombres premiers A et B s’appelle la course entre les nombres premiers de A et de B. Dans ce mémoire, nous cherchons ultimement à analyser d’un point de vue numérique et statistique la course entre les nombres premiers p tels que 2p + 1 est aussi premier (aussi appelés nombres premiers de Sophie Germain) et les nombres premiers p tels que 2p − 1 est aussi premier. Pour ce faire, nous présentons au préalable l’analyse de Rubinstein et Sarnak pour pouvoir repérer d’où vient le biais dans la course entre les nombres premiers 1 (mod 4) et les nombres premiers 3 (mod 4) et émettons une conjecture sur la distribution des nombres premiers de Sophie Germain.Under the Generalized Riemann Hypothesis and the Linear Independence Hypothesis, Rubinstein and Sarnak proved that the values of x which have more prime numbers less than or equal to x of the form 4n + 3 than primes of the form 4n + 1 have a logarithmic density of approximately 99.59%. In general, the study of the difference #{p < x : p in A} − #{p < x : p in B} for two subsets of the primes A and B is called the prime number race between A and B. In this thesis, we will analyze the prime number race between the primes p such that 2p + 1 is also prime (these primes are called the Sophie Germain primes) and the primes p such that 2p − 1 is also prime. To understand this, we first present Rubinstein and Sarnak’s analysis to understand where the bias between primes that are 1 (mod 4) and the ones that are 3 (mod 4) comes from and give a conjecture on the distribution of Sophie Germain primes

Time Availability and Relative Resources as Determinants of the Sexual Division of Domestic Work

Based on data from the 1992 Canadian General Social Survey on time-use, the time spent in housework and in child care are analyzed for women and men who are working full-time in dual-earner families. It is found that living with children under 19 years of age increases the average time spent in housework and child care and reduces that in paid work for both men and women. Time availability considerations, associated with the time demands of the family and the capacity to respond given the time in paid work, are found to be important determinants, especially for time spent in child care. However, there were also important elements of gender asymmetry in the results, pointing to the importance of relative resources and gender itself as relevant considerations. In particular, women\u27s time in housework is increased when their husbands spend more time in paid work, but men are not affected by the employment time of their wives. In addition, women do less housework when they earn more than half of family income

A randomized phase 2 study of paclitaxel and carboplatin with or without conatumumab for first-line treatment of advanced non-small-cell lung cancer

Introduction: This study evaluated the efficacy, safety, and pharmacokinetics of conatumumab combined with paclitaxel-carboplatin (PC) as first-line treatment for advanced non-small-cell lung cancer (NSCLC). Methods: Patients (aged >18 years) with previously untreated advanced or recurrent NSCLC were randomized 1: 1: 1 (stratified by Eastern Cooperative Oncology Group performance status and disease stage) to receive up to six 3-week cycles of PC combined with conatumumab (arm 1, 3 mg/kg; arm 2, 15 mg/kg) or placebo (arm 3) every 3 weeks. The primary endpoint was progression-free survival (PFS). This study is registered with ClinicalTrials.gov (NCT00534027). Results: Between August 8, 2007 and April 9, 2009, 172 patients were randomized (arm 1, n = 57; arm 2, n = 56; arm 3, n = 59). Median PFS was 5.4 months (95% confidence interval [CI] 4.1-6.3) in arm 1 (hazard ratio [HR] 0.84 [95% CI 0.57-1.24]; p = 0.41), 4.8 months (95% CI 3.2-6.5) in arm 2 (HR 0.93 [0.64-1.35]; p = 0.57), and 5.5 months (95% CI 4.3-5.7) in arm 3. There was an interaction between tumor histology and the effect of conatumumab on PFS (squamous HR 0.47 [0.23-0.94]; nonsquamous HR 1.08 [0.74-1.57]; interaction p = 0.039). The most common grade of three or more adverse events were neutropenia, anemia, and thrombocytopenia. There was no evidence of pharmacokinetic interactions between conatumumab and PC. Of 158 patients assessable for FCGR3A polymorphisms, conatumumab treatment was associated with a trend toward longer overall survival (HR 0.72 [0.43-1.23]) among V-allele carriers (V/V or F/V; n = 54) but not among F-allele homozygotes (n = 34; HR 1.37 [0.66-2.86]). Conclusion: Although well tolerated, the addition of conatumumab to PC did not improve outcomes in unselected patients with previously untreated advanced NSCLC

Study protocol for a randomised controlled trial of haloperidol plus promethazine plus chlorpromazine versus haloperidol plus promethazine for rapid tranquilisation for agitated psychiatric patients in the emergency setting (TREC-Lebanon)

Background: Agitated and aggressive behaviours are common in the psychiatric setting and rapid tranquilisation is sometimes unavoidable. A survey of Lebanese practice has shown that an intramuscular haloperidol, promethazine and chlorpromazine combination is a preferred form of treatment but there are no randomised trials of this triple therapy.Methods: This is a pragmatic randomised trial. Setting - the psychiatric wards of the Psychiatric Hospital of the Cross, Jal Eddib, Lebanon. Participants - any adult patient in the hospital who displays an aggressive episode for whom rapid tranquilisation is unavoidable, who has not been randomised before, for whom there are no known contraindications. Randomisation – stratified (by ward) randomisation and concealed in closed opaque envelope by independent parties. Procedure – if the clinical situation arises requiring rapid tranquilisation, medical residents overseeing the patient will open a TREC-Lebanon envelope in which will be notification of which group of treatments should be preferred [Haloperidol + Promethazine + Chlorpromazine (HPC) or Haloperidol + Promethazine (HP)], along with forms for primary, secondary and serious adverse effects. Treatment is not given blindly. Outcome - primary outcome is calm or tranquil at 20 minutes post intervention. Secondary outcomes are calm/tranquil at 40, 60 and 120 minutes post intervention, asleep, adverse effects, use of straitjacket and leaving the ward. Follow-up will be up to two weeks post randomisation.Discussion: Findings from this study will compare the HPC versus HP combination used in Lebanon’s psychiatry emergency routine practice.Trial registration: ClinicalTrials.gov NCT03639558. Registration date, August 21, 2018

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment