Formal proofs for broadcast algorithms

Standard distributed algorithmic solutions to recurring distributed problems are commonly specified and described informally. A proper understanding of these distributed algorithms that clarifies ambiguities requires formal descriptions. However, formalisation tends to yield complex descriptions. We formally study two broadcast algorithms and present an encoding framework using a process descriptive language and formalise these algorithms and their specifications using this framework. Following these new formal encodings we discuss correctness proofs for the same algorithms.peer-reviewe

Formal fault-tolerance proofs for distributed algorithms

Distributed Algorithms express problems as concurrent failing processes which co- operate and interact towards a common goal. Such algorithms arise in a wide range of applications, including distributed information processing, banking systems and airline reservation systems amongst others. It is desirable that distributed algorithms are well be- haved both in a failure free environment and even in the presence of failure (i.e. fault tolerant). To ensure well behavedness for all executions of distributed algorithms formal correctness proofs are needed. This is due to the concurrent nature of such algorithms, where executions of the algorithms result in different interleavings amongst parallel pro- cesses (i.e. there is a large number of possible execution paths).peer-reviewe

Effect of Hydrocortisone on Mortality and Organ Support in Patients With Severe COVID-19: The REMAP-CAP COVID-19 Corticosteroid Domain Randomized Clinical Trial.

Importance: Evidence regarding corticosteroid use for severe coronavirus disease 2019 (COVID-19) is limited. Objective: To determine whether hydrocortisone improves outcome for patients with severe COVID-19. Design, Setting, and Participants: An ongoing adaptive platform trial testing multiple interventions within multiple therapeutic domains, for example, antiviral agents, corticosteroids, or immunoglobulin. Between March 9 and June 17, 2020, 614 adult patients with suspected or confirmed COVID-19 were enrolled and randomized within at least 1 domain following admission to an intensive care unit (ICU) for respiratory or cardiovascular organ support at 121 sites in 8 countries. Of these, 403 were randomized to open-label interventions within the corticosteroid domain. The domain was halted after results from another trial were released. Follow-up ended August 12, 2020. Interventions: The corticosteroid domain randomized participants to a fixed 7-day course of intravenous hydrocortisone (50 mg or 100 mg every 6 hours) (n = 143), a shock-dependent course (50 mg every 6 hours when shock was clinically evident) (n = 152), or no hydrocortisone (n = 108). Main Outcomes and Measures: The primary end point was organ support-free days (days alive and free of ICU-based respiratory or cardiovascular support) within 21 days, where patients who died were assigned -1 day. The primary analysis was a bayesian cumulative logistic model that included all patients enrolled with severe COVID-19, adjusting for age, sex, site, region, time, assignment to interventions within other domains, and domain and intervention eligibility. Superiority was defined as the posterior probability of an odds ratio greater than 1 (threshold for trial conclusion of superiority >99%). Results: After excluding 19 participants who withdrew consent, there were 384 patients (mean age, 60 years; 29% female) randomized to the fixed-dose (n = 137), shock-dependent (n = 146), and no (n = 101) hydrocortisone groups; 379 (99%) completed the study and were included in the analysis. The mean age for the 3 groups ranged between 59.5 and 60.4 years; most patients were male (range, 70.6%-71.5%); mean body mass index ranged between 29.7 and 30.9; and patients receiving mechanical ventilation ranged between 50.0% and 63.5%. For the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively, the median organ support-free days were 0 (IQR, -1 to 15), 0 (IQR, -1 to 13), and 0 (-1 to 11) days (composed of 30%, 26%, and 33% mortality rates and 11.5, 9.5, and 6 median organ support-free days among survivors). The median adjusted odds ratio and bayesian probability of superiority were 1.43 (95% credible interval, 0.91-2.27) and 93% for fixed-dose hydrocortisone, respectively, and were 1.22 (95% credible interval, 0.76-1.94) and 80% for shock-dependent hydrocortisone compared with no hydrocortisone. Serious adverse events were reported in 4 (3%), 5 (3%), and 1 (1%) patients in the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively. Conclusions and Relevance: Among patients with severe COVID-19, treatment with a 7-day fixed-dose course of hydrocortisone or shock-dependent dosing of hydrocortisone, compared with no hydrocortisone, resulted in 93% and 80% probabilities of superiority with regard to the odds of improvement in organ support-free days within 21 days. However, the trial was stopped early and no treatment strategy met prespecified criteria for statistical superiority, precluding definitive conclusions. Trial Registration: ClinicalTrials.gov Identifier: NCT02735707

Mammographic surveillance in women younger than 50 years who have a family history of breast cancer: tumour characteristics and projected effect on mortality in the prospective, single-arm, FH01 study.

BACKGROUND: Evidence supports a reduction in mortality from breast cancer with mammographic screening in the general population of women aged 40-49 years, but the effect of family history is not clear. We aimed to establish whether screening affects the disease stage and projected mortality of women younger than 50 years who have a clinically significant family history of breast cancer. METHODS: In the single-arm FH01 study, women at intermediate familial risk who were younger than 50 years were enrolled from 76 centres in the UK, and received yearly mammography. Women with BRCA mutations were not explicitly excluded, but would be rare in this group. To compare the FH01 cohort with women not receiving screening, two external comparison groups were used: the control group of the UK Age Trial (106,971 women aged 40-42 years at recruitment, from the general population [ie, average risk], followed up for 10 years), and a Dutch study of women with a family history of breast cancer (cancer cases aged 25-77 years, diagnosed 1980-2004). Study endpoints were size, node status, and histological grade of invasive tumours, and estimated mortality calculated from the Nottingham prognostic index (NPI) score, and adjusted for differences in underlying risk between the FH01 cohort and the control group of the UK Age Trial. This study is registered with the National Research Register, number N0484114809. FINDINGS: 6710 women were enrolled between Jan 16, 2003, and Feb 28, 2007, and received yearly mammography for a mean of 4 years (SD 2) up until Nov 30, 2009; surveillance and reporting of cancers is still underway. 136 women were diagnosed with breast cancer: 105 (77%) at screening, 28 (21%) symptomatically in the interval between screening events, and three (2%) symptomatically after failing to attend their latest mammogram. Invasive tumours in the FH01 study were significantly smaller (p=0·0094), less likely to be node positive (p=0·0083), and of more favourable grade (p=0·0072) than were those in the control group of the UK Age Trial, and were significantly less likely to be node positive than were tumours in the Dutch study (p=0·012). Mean NPI score was significantly lower in the FH01 cohort than in the control group of the UK Age Trial (p=0·00079) or the Dutch study (p<0·0001). After adjustment for underlying risk, predicted 10-year mortality was significantly lower in the FH01 cohort (1·10%) than in the control group of the UK Age Trial (1·38%), with relative risk of 0·80 (95% CI 0·66-0·96; p=0·022). INTERPRETATION: Yearly mammography in women with a medium familial risk of breast cancer is likely to be effective in prevention of deaths from breast cancer

Effect of Antiplatelet Therapy on Survival and Organ Support–Free Days in Critically Ill Patients With COVID-19

International audienc