Mathematics Is Physics

In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within ..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics. This version of the essay contains an addendum responding to Slyvia Wenmackers' essay and comments that were made on the FQXi website.Comment: 15 pages, LaTeX. Second prize winner in 2015 FQXi Essay Contest (see http://fqxi.org/community/forum/topic/2364

Association of statin use and clinical outcomes in heart failure patients: A systematic review and meta-analysis

Background The role of statins in patients with heart failure (HF) of different levels of left ventricular ejection fraction (LVEF) remains unclear especially in the light of the absence of prospective data from randomized controlled trials (RCTs) in non-ischemic HF, and taking into account potential statins’ prosarcopenic effects. We assessed the association of statin use with clinical outcomes in patients with HF. Methods We searched PubMed, EMBASE, Scopus, Google Scholar and Cochrane Central until August 2018 for RCTs and prospective cohorts comparing clinical outcomes with statin vs non-statin use in patients with HF at different LVEF levels. We followed the guidelines of the 2009 PRISMA statement for reporting and applied independent extraction by multiple observers. Meta-analyses of hazard ratios (HRs) of effects of statins on clinical outcomes used generic inverse variance method and random model effects. Clinical outcomes were all-cause mortality, cardiovascular (CV) mortality and CV hospitalization. Results Finally we included 17 studies (n = 88,100; 2 RCTs and 15 cohorts) comparing statin vs non-statin users (mean follow-up 36 months). Compared with non-statin use, statin use was associated with lower risk of all-cause mortality (HR 0.77, 95% confidence interval [CI], 0.72–0.83, P < 0.0001, I2 = 63%), CV mortality (HR 0.82, 95% CI: 0.76–0.88, P < 0.0001, I2 = 63%), and CV hospitalization (HR 0.78, 95% CI: 0.69–0.89, P = 0.0003, I2 = 36%). All-cause mortality was reduced on statin therapy in HF with both EF < 40% and ≥ 40% (HR: 0.77, 95% Cl: 0.68–0.86, P < 0.00001, and HR 0.75, 95% CI: 0.69–0.82, P < 0.00001, respectively). Similarly, CV mortality (HR 0.86, 95% CI: 0.79–0.93, P = 0.0003, and HR 0.83, 95% CI: 0.77–0.90, P < 0.00001, respectively), and CV hospitalizations (HR 0.80 95% CI: 0.64–0.99, P = 0.04 and HR 0.76 95% CI: 0.61–0.93, P = 0.009, respectively) were reduced in these EF subgroups. Significant effects on all clinical outcomes were also found in cohort studies’ analyses; the effect was also larger and significant for lipophilic than hydrophilic statins. Conclusions In conclusion, statins may have a beneficial effect on CV outcomes irrespective of HF etiology and LVEF level. Lipophilic statins seem to be much more favorable for patients with heart failure.Revisión por pare

Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Peer support for discharge from inpatient mental health care versus care as usual in England (ENRICH): a parallel, two-group, individually randomised controlled trial.

BACKGROUND: High numbers of patients discharged from psychiatric hospital care are readmitted within a year. Peer support for discharge has been suggested as an approach to reducing readmission post-discharge. Implementation has been called for in policy, however, evidence of effectiveness from large rigorous trials is missing. We aimed to establish whether peer support for discharge reduces readmissions in the year post-discharge. METHODS: We report a parallel, two-group, individually randomised, controlled superiority trial, with trial personnel masked to allocation. Patients were adult psychiatric inpatients (age ≥18 years) with at least one previous admission in the preceding 2 years, excluding those who had a diagnosis of any organic mental disorder, or a primary diagnosis of learning disability, an eating disorder, or drug or alcohol dependency, recruited from seven state-funded mental health services in England. Patients were randomly assigned (1:1) to the intervention (peer support plus care as usual) or control (care as usual) groups by an in-house, online randomisation service, stratified by site and diagnostic group (psychotic disorders, personality disorders, and other eligible non-psychotic disorders) with randomly permuted blocks of randomly varying length to conceal the allocation sequence and achieve the allocation ratio. The peer support group received manual-based, one-to-one peer support, focused on building individual strengths and engaging with activities in the community, beginning during the index admission and continuing for 4 months after discharge, plus care as usual. Care as usual consisted of follow-up by community mental health services within 7 days of discharge. The primary outcome was psychiatric readmission 12 months after discharge (number of patients readmitted at least once), analysed on an intention-to-treat basis. All patients were included in a safety analysis, excluding those who withdrew consent for use of their data. The trial is registered with the ISRCTN registry, ISRCTN10043328. The trial was complete at the time of reporting. FINDINGS: Between Dec 1, 2016, and Feb 8, 2019, 590 patients were recruited and randomly assigned, with 294 allocated to peer support (287 included in the analysis after withdrawals and loss to follow-up), and 296 to care as usual (291 in the analysis). Mean age was 39·7 years (SD 13·7; range 18-75). 306 patients were women, 267 were men, three were transgender, and two preferred not to say. 353 patients were White, 94 were Black, African, Caribbean, or Black British, 68 were Asian or Asian British, 48 were of mixed or multiple ethnic groups, and 13 were of other ethnic groups. In the peer support group, 136 (47%) of 287 patients were readmitted at least once within 12 months of discharge. 146 (50%) of 291 were readmitted in the care as usual group. The adjusted risk ratio of readmission was 0·97 (95% CI 0·82-1·14; p=0·68), and the adjusted odds ratio for readmission was 0·93 (95% CI 0·66-1·30; p=0·68). The unadjusted risk difference was 0·03 (95% CI -0·11 to 0·05; p=0·51) in favour of the peer support group. Serious adverse events were infrequent (67 events) and similar between groups (34 in the peer support group, 33 in the care as usual group). Threat to life (self-harm) was the most common serious adverse event (35 [52%] of 67 serious adverse events). 391 other adverse events were reported, with self-harm (not life threatening) the most common (189 [48%] of 391). INTERPRETATION: One-to-one peer support for discharge from inpatient psychiatric care, plus care as usual, was not superior to care as usual alone in the 12 months after discharge. This definitive, high-quality trial addresses uncertainty in the evidence base and suggests that peer support should not be implemented to reduce readmission post-discharge for patients at risk of readmission. Further research needs to be done to improve engagement with peer support in high-need groups, and to explore differential effects of peer support for people from different ethnic communities. FUNDING: UK National Institute for Health Research

Trends in future health financing and coverage: future health spending and universal health coverage in 188 countries, 2016–40

Background: Achieving universal health coverage (UHC) requires health financing systems that provide prepaid pooled resources for key health services without placing undue financial stress on households. Understanding current and future trajectories of health financing is vital for progress towards UHC. We used historical health financing data for 188 countries from 1995 to 2015 to estimate future scenarios of health spending and pooled health spending through to 2040. Methods: We extracted historical data on gross domestic product (GDP) and health spending for 188 countries from 1995 to 2015, and projected annual GDP, development assistance for health, and government, out-of-pocket, and prepaid private health spending from 2015 through to 2040 as a reference scenario. These estimates were generated using an ensemble of models that varied key demographic and socioeconomic determinants. We generated better and worse alternative future scenarios based on the global distribution of historic health spending growth rates. Last, we used stochastic frontier analysis to investigate the association between pooled health resources and UHC index, a measure of a country's UHC service coverage. Finally, we estimated future UHC performance and the number of people covered under the three future scenarios. Findings: In the reference scenario, global health spending was projected to increase from US$10 trillion (95$20 trillion (18 trillion to 22 trillion) in 2040. Per capita health spending was projected to increase fastest in upper-middle-income countries, at 4·2% (3·4–5·1) per year, followed by lower-middle-income countries (4·0%, 3·6–4·5) and low-income countries (2·2%, 1·7–2·8). Despite global growth, per capita health spending was projected to range from only $40 (24–65) to$413 (263–668) in 2040 in low-income countries, and from $140 (90–200) to$1699 (711–3423) in lower-middle-income countries. Globally, the share of health spending covered by pooled resources would range widely, from 19·8% (10·3–38·6) in Nigeria to 97·9% (96·4–98·5) in Seychelles. Historical performance on the UHC index was significantly associated with pooled resources per capita. Across the alternative scenarios, we estimate UHC reaching between 5·1 billion (4·9 billion to 5·3 billion) and 5·6 billion (5·3 billion to 5·8 billion) lives in 2030. Interpretation: We chart future scenarios for health spending and its relationship with UHC. Ensuring that all countries have sustainable pooled health resources is crucial to the achievement of UHC. Funding: The Bill & Melinda Gates Foundation

National trends in total cholesterol obscure heterogeneous changes in HDL and non-HDL cholesterol and total-to-HDL cholesterol ratio : a pooled analysis of 458 population-based studies in Asian and Western countries

Background: Although high-density lipoprotein (HDL) and non-HDL cholesterol have opposite associations with coronary heart disease, multi-country reports of lipid trends only use total cholesterol (TC). Our aim was to compare trends in total, HDL and nonHDL cholesterol and the total-to-HDL cholesterol ratio in Asian and Western countries. Methods: We pooled 458 population-based studies with 82.1 million participants in 23 Asian and Western countries. We estimated changes in mean total, HDL and non-HDL cholesterol and mean total-to-HDL cholesterol ratio by country, sex and age group. Results: Since similar to 1980, mean TC increased in Asian countries. In Japan and South Korea, the TC rise was due to rising HDL cholesterol, which increased by up to 0.17 mmol/L per decade in Japanese women; in China, it was due to rising non-HDL cholesterol. TC declined in Western countries, except in Polish men. The decline was largest in Finland and Norway, at similar to 0.4 mmol/L per decade. The decline in TC in most Western countries was the net effect of an increase in HDL cholesterol and a decline in non-HDL cholesterol, with the HDL cholesterol increase largest in New Zealand and Switzerland. Mean total-to-HDL cholesterol ratio declined in Japan, South Korea and most Western countries, by as much as similar to 0.7 per decade in Swiss men (equivalent to similar to 26% decline in coronary heart disease risk per decade). The ratio increased in China. Conclusions: HDL cholesterol has risen and the total-to-HDL cholesterol ratio has declined in many Western countries, Japan and South Korea, with only a weak correlation with changes in TC or non-HDL cholesterol.Peer reviewe

The global, regional, and national burden of cirrhosis by cause in 195 countries and territories, 1990-2017 : a systematic analysis for the Global Burden of Disease Study 2017

Background Cirrhosis and other chronic liver diseases (collectively referred to as cirrhosis in this paper) are a major cause of morbidity and mortality globally, although the burden and underlying causes differ across locations and demographic groups. We report on results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 on the burden of cirrhosis and its trends since 1990, by cause, sex, and age, for 195 countries and territories. Methods We used data from vital registrations, vital registration samples, and verbal autopsies to estimate mortality. We modelled prevalence of total, compensated, and decompensated cirrhosis on the basis of hospital and claims data. Disability-adjusted life-years (DALYs) were calculated as the sum of years of life lost due to premature death and years lived with disability. Estimates are presented as numbers and age-standardised or age-specific rates per 100 000 population, with 95% uncertainty intervals (UIs). All estimates are presented for five causes of cirrhosis: hepatitis B, hepatitis C, alcohol-related liver disease, non-alcoholic steatohepatitis (NASH), and other causes. We compared mortality, prevalence, and DALY estimates with those expected according to the Socio-demographic Index (SDI) as a proxy for the development status of regions and countries. Findings In 2017, cirrhosis caused more than 1.32 million (95% UI 1.27-1.45) deaths (440000 [416 000-518 000; 33.3%] in females and 883 000 [838 000-967 000; 66.7%] in males) globally, compared with less than 899 000 (829 000-948 000) deaths in 1990. Deaths due to cirrhosis constituted 2.4% (2.3-2.6) of total deaths globally in 2017 compared with 1.9% (1.8-2.0) in 1990. Despite an increase in the number of deaths, the age-standardised death rate decreased from 21.0 (19.2-22.3) per 100 000 population in 1990 to 16.5 (15.8-18-1) per 100 000 population in 2017. Sub-Saharan Africa had the highest age-standardised death rate among GBD super-regions for all years of the study period (32.2 [25.8-38.6] deaths per 100 000 population in 2017), and the high-income super-region had the lowest (10.1 [9.8-10-5] deaths per 100 000 population in 2017). The age-standardised death rate decreased or remained constant from 1990 to 2017 in all GBD regions except eastern Europe and central Asia, where the age-standardised death rate increased, primarily due to increases in alcohol-related liver disease prevalence. At the national level, the age-standardised death rate of cirrhosis was lowest in Singapore in 2017 (3.7 [3.3-4.0] per 100 000 in 2017) and highest in Egypt in all years since 1990 (103.3 [64.4-133.4] per 100 000 in 2017). There were 10.6 million (10.3-10.9) prevalent cases of decompensated cirrhosis and 112 million (107-119) prevalent cases of compensated cirrhosis globally in 2017. There was a significant increase in age-standardised prevalence rate of decompensated cirrhosis between 1990 and 2017. Cirrhosis caused by NASH had a steady age-standardised death rate throughout the study period, whereas the other four causes showed declines in age-standardised death rate. The age-standardised prevalence of compensated and decompensated cirrhosis due to NASH increased more than for any other cause of cirrhosis (by 33.2% for compensated cirrhosis and 54.8% for decompensated cirrhosis) over the study period. From 1990 to 2017, the number of prevalent cases snore than doubled for compensated cirrhosis due to NASH and more than tripled for decompensated cirrhosis due to NASH. In 2017, age-standardised death and DALY rates were lower among countries and territories with higher SDI. Interpretation Cirrhosis imposes a substantial health burden on many countries and this burden has increased at the global level since 1990, partly due to population growth and ageing. Although the age-standardised death and DALY rates of cirrhosis decreased from 1990 to 2017, numbers of deaths and DALYs and the proportion of all global deaths due to cirrhosis increased. Despite the availability of effective interventions for the prevention and treatment of hepatitis B and C, they were still the main causes of cirrhosis burden worldwide, particularly in low-income countries. The impact of hepatitis B and C is expected to be attenuated and overtaken by that of NASH in the near future. Cost-effective interventions are required to continue the prevention and treatment of viral hepatitis, and to achieve early diagnosis and prevention of cirrhosis due to alcohol-related liver disease and NASH. Copyright (C) 2020 The Author(s). Published by Elsevier Ltd.Peer reviewe

Estimates, trends, and drivers of the global burden of type 2 diabetes attributable to PM2.5 air pollution, 1990-2019 : an analysis of data from the Global Burden of Disease Study 2019

Background Experimental and epidemiological studies indicate an association between exposure to particulate matter (PM) air pollution and increased risk of type 2 diabetes. In view of the high and increasing prevalence of diabetes, we aimed to quantify the burden of type 2 diabetes attributable to PM2.5 originating from ambient and household air pollution.Methods We systematically compiled all relevant cohort and case-control studies assessing the effect of exposure to household and ambient fine particulate matter (PM2.5) air pollution on type 2 diabetes incidence and mortality. We derived an exposure-response curve from the extracted relative risk estimates using the MR-BRT (meta-regression-Bayesian, regularised, trimmed) tool. The estimated curve was linked to ambient and household PM2.5 exposures from the Global Burden of Diseases, Injuries, and Risk Factors Study 2019, and estimates of the attributable burden (population attributable fractions and rates per 100 000 population of deaths and disability-adjusted life-years) for 204 countries from 1990 to 2019 were calculated. We also assessed the role of changes in exposure, population size, age, and type 2 diabetes incidence in the observed trend in PM2.5-attributable type 2 diabetes burden. All estimates are presented with 95% uncertainty intervals.Findings In 2019, approximately a fifth of the global burden of type 2 diabetes was attributable to PM2.5 exposure, with an estimated 3.78 (95% uncertainty interval 2.68-4.83) deaths per 100 000 population and 167 (117-223) disability-adjusted life-years (DALYs) per 100 000 population. Approximately 13.4% (9.49-17.5) of deaths and 13.6% (9.73-17.9) of DALYs due to type 2 diabetes were contributed by ambient PM2.5, and 6.50% (4.22-9.53) of deaths and 5.92% (3.81-8.64) of DALYs by household air pollution. High burdens, in terms of numbers as well as rates, were estimated in Asia, sub-Saharan Africa, and South America. Since 1990, the attributable burden has increased by 50%, driven largely by population growth and ageing. Globally, the impact of reductions in household air pollution was largely offset by increased ambient PM2.5.Interpretation Air pollution is a major risk factor for diabetes. We estimated that about a fifth of the global burden of type 2 diabetes is attributable PM2.5 pollution. Air pollution mitigation therefore might have an essential role in reducing the global disease burden resulting from type 2 diabetes. Copyright (C) 2022 The Author(s). Published by Elsevier Ltd.Peer reviewe

Estimates, trends, and drivers of the global burden of type 2 diabetes attributable to PM2.5 air pollution, 1990-2019 : An analysis of data from the Global Burden of Disease Study 2019

Background Experimental and epidemiological studies indicate an association between exposure to particulate matter (PM) air pollution and increased risk of type 2 diabetes. In view of the high and increasing prevalence of diabetes, we aimed to quantify the burden of type 2 diabetes attributable to PM2·5 originating from ambient and household air pollution. Methods We systematically compiled all relevant cohort and case-control studies assessing the effect of exposure to household and ambient fine particulate matter (PM2·5) air pollution on type 2 diabetes incidence and mortality. We derived an exposure–response curve from the extracted relative risk estimates using the MR-BRT (meta-regression—Bayesian, regularised, trimmed) tool. The estimated curve was linked to ambient and household PM2·5 exposures from the Global Burden of Diseases, Injuries, and Risk Factors Study 2019, and estimates of the attributable burden (population attributable fractions and rates per 100 000 population of deaths and disability-adjusted life-years) for 204 countries from 1990 to 2019 were calculated. We also assessed the role of changes in exposure, population size, age, and type 2 diabetes incidence in the observed trend in PM2·5-attributable type 2 diabetes burden. All estimates are presented with 95% uncertainty intervals. Findings In 2019, approximately a fifth of the global burden of type 2 diabetes was attributable to PM2·5 exposure, with an estimated 3·78 (95% uncertainty interval 2·68–4·83) deaths per 100 000 population and 167 (117–223) disability-adjusted life-years (DALYs) per 100 000 population. Approximately 13·4% (9·49–17·5) of deaths and 13·6% (9·73–17·9) of DALYs due to type 2 diabetes were contributed by ambient PM2·5, and 6·50% (4·22–9·53) of deaths and 5·92% (3·81–8·64) of DALYs by household air pollution. High burdens, in terms of numbers as well as rates, were estimated in Asia, sub-Saharan Africa, and South America. Since 1990, the attributable burden has increased by 50%, driven largely by population growth and ageing. Globally, the impact of reductions in household air pollution was largely offset by increased ambient PM2·5. Interpretation Air pollution is a major risk factor for diabetes. We estimated that about a fifth of the global burden of type 2 diabetes is attributable PM2·5 pollution. Air pollution mitigation therefore might have an essential role in reducing the global disease burden resulting from type 2 diabetes