Optimization and matrix constructions for classification of data

Max-plus algebras and more general semirings have many useful applications and have been actively investigated. On the other hand, structural matrix rings are also well known and have been considered by many authors. The main theorem of this article completely describes all optimal ideals in the more general structural matrix semirings. Originally, our investigation of these ideals was motivated by applications in data mining for the design of centroid-based classification systems, as well as for the design of multiple classification systems combining several individual classifiers

Playing with the Rules: Influences on the Development of Regulation in Sport

Sport today is a rule-governed practice: constitutive rules, both prescriptive and proscriptive, define required equipment and facilities as well as setting the formal rules of play; auxiliary rules specify and control eligibility: and regulatory rules place restraints on behaviour independent of the sport itself. This article offers a broad sweep examination of the historical process of rule development in sport including an assessment of the influence over time of gambling, fair play ideology, economic pressures, technological developments and legal intervention. En route a seven-stage scheme of constitutive rule development is postulated which it is hoped will set a research agenda for sports historians to test with case studies of particular sports

The Politics of Commerce : The Congress of Chambers of Commerce of the Empire, 1886-1914

Peer reviewedPublisher PD

Cumulative Prognostic Score Predicting Mortality in Patients Older Than 80 Years Admitted to the ICU.

OBJECTIVES: To develop a scoring system model that predicts mortality within 30 days of admission of patients older than 80 years admitted to intensive care units (ICUs). DESIGN: Prospective cohort study. SETTING: A total of 306 ICUs from 24 European countries. PARTICIPANTS: Older adults admitted to European ICUs (N = 3730; median age = 84 years [interquartile range = 81-87 y]; 51.8% male). MEASUREMENTS: Overall, 24 variables available during ICU admission were included as potential predictive variables. Multivariable logistic regression was used to identify independent predictors of 30-day mortality. Model sensitivity, specificity, and accuracy were evaluated with receiver operating characteristic curves. RESULTS: The 30-day-mortality was 1562 (41.9%). In multivariable analysis, these variables were selected as independent predictors of mortality: age, sex, ICU admission diagnosis, Clinical Frailty Scale, Sequential Organ Failure Score, invasive mechanical ventilation, and renal replacement therapy. The discrimination, accuracy, and calibration of the model were good: the area under the curve for a score of 10 or higher was .80, and the Brier score was .18. At a cut point of 10 or higher (75% of all patients), the model predicts 30-day mortality in 91.1% of all patients who die. CONCLUSION: A predictive model of cumulative events predicts 30-day mortality in patients older than 80 years admitted to ICUs. Future studies should include other potential predictor variables including functional status, presence of advance care plans, and assessment of each patient's decision-making capacity

Sepsis at ICU admission does not decrease 30-day survival in very old patients: a post-hoc analysis of the VIP1 multinational cohort study.

BACKGROUND: The number of intensive care patients aged ≥ 80 years (Very old Intensive Care Patients; VIPs) is growing. VIPs have high mortality and morbidity and the benefits of ICU admission are frequently questioned. Sepsis incidence has risen in recent years and identification of outcomes is of considerable public importance. We aimed to determine whether VIPs admitted for sepsis had different outcomes than those admitted for other acute reasons and identify potential prognostic factors for 30-day survival. RESULTS: This prospective study included VIPs with Sequential Organ Failure Assessment (SOFA) scores ≥ 2 acutely admitted to 307 ICUs in 21 European countries. Of 3869 acutely admitted VIPs, 493 (12.7%) [53.8% male, median age 83 (81-86) years] were admitted for sepsis. Sepsis was defined according to clinical criteria; suspected or demonstrated focus of infection and SOFA score ≥ 2 points. Compared to VIPs admitted for other acute reasons, VIPs admitted for sepsis were younger, had a higher SOFA score (9 vs. 7, p < 0.0001), required more vasoactive drugs [82.2% vs. 55.1%, p < 0.0001] and renal replacement therapies [17.4% vs. 9.9%; p < 0.0001], and had more life-sustaining treatment limitations [37.3% vs. 32.1%; p = 0.02]. Frailty was similar in both groups. Unadjusted 30-day survival was not significantly different between the two groups. After adjustment for age, gender, frailty, and SOFA score, sepsis had no impact on 30-day survival [HR 0.99 (95% CI 0.86-1.15), p = 0.917]. Inverse-probability weight (IPW)-adjusted survival curves for the first 30 days after ICU admission were similar for acute septic and non-septic patients [HR: 1.00 (95% CI 0.87-1.17), p = 0.95]. A matched-pair analysis in which patients with sepsis were matched with two control patients of the same gender with the same age, SOFA score, and level of frailty was also performed. A Cox proportional hazard regression model stratified on the matched pairs showed that 30-day survival was similar in both groups [57.2% (95% CI 52.7-60.7) vs. 57.1% (95% CI 53.7-60.1), p = 0.85]. CONCLUSIONS: After adjusting for organ dysfunction, sepsis at admission was not independently associated with decreased 30-day survival in this multinational study of 3869 VIPs. Age, frailty, and SOFA score were independently associated with survival

Relationship between the Clinical Frailty Scale and short-term mortality in patients ≥ 80 years old acutely admitted to the ICU: a prospective cohort study.

BACKGROUND: The Clinical Frailty Scale (CFS) is frequently used to measure frailty in critically ill adults. There is wide variation in the approach to analysing the relationship between the CFS score and mortality after admission to the ICU. This study aimed to evaluate the influence of modelling approach on the association between the CFS score and short-term mortality and quantify the prognostic value of frailty in this context. METHODS: We analysed data from two multicentre prospective cohort studies which enrolled intensive care unit patients ≥ 80 years old in 26 countries. The primary outcome was mortality within 30-days from admission to the ICU. Logistic regression models for both ICU and 30-day mortality included the CFS score as either a categorical, continuous or dichotomous variable and were adjusted for patient's age, sex, reason for admission to the ICU, and admission Sequential Organ Failure Assessment score. RESULTS: The median age in the sample of 7487 consecutive patients was 84 years (IQR 81-87). The highest fraction of new prognostic information from frailty in the context of 30-day mortality was observed when the CFS score was treated as either a categorical variable using all original levels of frailty or a nonlinear continuous variable and was equal to 9% using these modelling approaches (p < 0.001). The relationship between the CFS score and mortality was nonlinear (p < 0.01). CONCLUSION: Knowledge about a patient's frailty status adds a substantial amount of new prognostic information at the moment of admission to the ICU. Arbitrary simplification of the CFS score into fewer groups than originally intended leads to a loss of information and should be avoided. Trial registration NCT03134807 (VIP1), NCT03370692 (VIP2)

Safety, immunogenicity, and reactogenicity of BNT162b2 and mRNA-1273 COVID-19 vaccines given as fourth-dose boosters following two doses of ChAdOx1 nCoV-19 or BNT162b2 and a third dose of BNT162b2 (COV-BOOST): a multicentre, blinded, phase 2, randomised trial

Background Some high-income countries have deployed fourth doses of COVID-19 vaccines, but the clinical need, effectiveness, timing, and dose of a fourth dose remain uncertain. We aimed to investigate the safety, reactogenicity, and immunogenicity of fourth-dose boosters against COVID-19.Methods The COV-BOOST trial is a multicentre, blinded, phase 2, randomised controlled trial of seven COVID-19 vaccines given as third-dose boosters at 18 sites in the UK. This sub-study enrolled participants who had received BNT162b2 (Pfizer-BioNTech) as their third dose in COV-BOOST and randomly assigned them (1:1) to receive a fourth dose of either BNT162b2 (30 µg in 0·30 mL; full dose) or mRNA-1273 (Moderna; 50 µg in 0·25 mL; half dose) via intramuscular injection into the upper arm. The computer-generated randomisation list was created by the study statisticians with random block sizes of two or four. Participants and all study staff not delivering the vaccines were masked to treatment allocation. The coprimary outcomes were safety and reactogenicity, and immunogenicity (antispike protein IgG titres by ELISA and cellular immune response by ELISpot). We compared immunogenicity at 28 days after the third dose versus 14 days after the fourth dose and at day 0 versus day 14 relative to the fourth dose. Safety and reactogenicity were assessed in the per-protocol population, which comprised all participants who received a fourth-dose booster regardless of their SARS-CoV-2 serostatus. Immunogenicity was primarily analysed in a modified intention-to-treat population comprising seronegative participants who had received a fourth-dose booster and had available endpoint data. This trial is registered with ISRCTN, 73765130, and is ongoing.Findings Between Jan 11 and Jan 25, 2022, 166 participants were screened, randomly assigned, and received either full-dose BNT162b2 (n=83) or half-dose mRNA-1273 (n=83) as a fourth dose. The median age of these participants was 70·1 years (IQR 51·6–77·5) and 86 (52%) of 166 participants were female and 80 (48%) were male. The median interval between the third and fourth doses was 208·5 days (IQR 203·3–214·8). Pain was the most common local solicited adverse event and fatigue was the most common systemic solicited adverse event after BNT162b2 or mRNA-1273 booster doses. None of three serious adverse events reported after a fourth dose with BNT162b2 were related to the study vaccine. In the BNT162b2 group, geometric mean anti-spike protein IgG concentration at day 28 after the third dose was 23 325 ELISA laboratory units (ELU)/mL (95% CI 20 030–27 162), which increased to 37 460 ELU/mL (31 996–43 857) at day 14 after the fourth dose, representing a significant fold change (geometric mean 1·59, 95% CI 1·41–1·78). There was a significant increase in geometric mean anti-spike protein IgG concentration from 28 days after the third dose (25 317 ELU/mL, 95% CI 20 996–30 528) to 14 days after a fourth dose of mRNA-1273 (54 936 ELU/mL, 46 826–64 452), with a geometric mean fold change of 2·19 (1·90–2·52). The fold changes in anti-spike protein IgG titres from before (day 0) to after (day 14) the fourth dose were 12·19 (95% CI 10·37–14·32) and 15·90 (12·92–19·58) in the BNT162b2 and mRNA-1273 groups, respectively. T-cell responses were also boosted after the fourth dose (eg, the fold changes for the wild-type variant from before to after the fourth dose were 7·32 [95% CI 3·24–16·54] in the BNT162b2 group and 6·22 [3·90–9·92] in the mRNA-1273 group).Interpretation Fourth-dose COVID-19 mRNA booster vaccines are well tolerated and boost cellular and humoral immunity. Peak responses after the fourth dose were similar to, and possibly better than, peak responses after the third dose