Optimal 5-step nilpotent quadratic algebras

By the Golod–Shafarevich theorem, an associative algebra $R$ given by $n$ generators and $<n^2/3$ homogeneous quadratic relations is not 5-step nilpotent. We prove that this estimate is optimal. Namely, we show that for every positive integer $n$, there is an algebra $R$ given by $n$ generators and $\lceil n^2/3\rceil$ homogeneous quadratic relations such that $R$ is 5-step nilpotent.

Two problems from the Polishchuk and Positselski book on Quadratic algebras

In the book ’Quadratic algebras’ by Polishchuk and Positselski [23] algebras with a small number of generators (n = 2, 3) are considered. For some number r of relations possible Hilbert series are listed, and those appearing as series of Koszul algebras are specified. The first case, where it was not possible to do, namely the case of three generators n = 3 and six relations r = 6 is formulated as an open problem. We give here a complete answer to this question, namely for quadratic algebras with dimA_1 = dimA_2 = 3, we list all possible Hilbert series, and find out which of them can come from Koszul algebras, and which can not. As a consequence of this classification, we found an algebra, which serves as a counterexample to another problem from the same book [23] (Chapter 7, Sec. 1, Conjecture 2), saying that Koszul algebra of finite global homological dimension d has dimA_1 > d. Namely, the 3-generated algebra A given by relations xx + yx = xz = zy = 0 is Koszul and its Koszul dual algebra A^! has Hilbert series of degree 4: HA! (t) = 1 + 3t + 3t^2 + 2t^3 + t^4, hence A has global homological dimension 4.

Smoking during pregnancy by duration of residence among immigrants in Sweden 1991-2012 : A study on health inequalities

This study revisits the effect of duration by residence in relation to smoking during pregnancy. It contributes to the literature by incorporating a health inequity perspective, and discusses whether immigrants tend to converge with Swedish women’s smoking. The study is based on Swedish Medical Birth Register and includes 1 1864 52 pregnancies between 1991 and 2012. Logistic regression was performed to attain crude and adjusted Odds Ratios and 95 % confidence intervals. Immigrants’ are divided by categorizing countries of origin depending on levels of Human Development (IHDI). Overall immigrant women show low levels of smoking during pregnancy when they arrive to Sweden, by duration of residence levels of smoking increase and converge with smoking patterns of Swedish women. I found that there are differences in smoking patterns depending on IHDI of the country. Immigrant women of higher categories of IHDI show higher levels of smoking although the increase of smoking is higher among immigrant women from categories of lower IHDI. However, immigrant women’s smoking during pregnancy is affected by duration of residence, and the increased smoking is associated with health inequalities related to their country of origins IHDI, and by socioeconomic inequalities in Sweden. 

The Reversal of Gender Inequalities in Enrollment in Higher Education in Cape Verde

Higher education is nowadays the main driver of development of knowledge, science and hence, the wellbeing of various people in different countries. On the other hand, gender inequalities represent a delay toward this status. Gender inequalities have been proven to be a great barrier to the development of the full human being’s potential and if it manifests in education, their effect will be worse. This research paper seeks to determine what drives the reversal of gender inequalities in enrollment in higher education in Cape Verde. The paper outlines the struggles for a more equal society and look for different reasons behind this phenomenon. This study has brought out some barriers that interfere with an equal enrollment in that level of Education. The objective of this study is to raise awareness about the need to change the positive measures related to girls, and use some of them to encourage boys in the education field because they are lagging behind in all levels of education.

Local action on health inequalities: practice resources

These documents explain factors contributing to inequality in public health and set out methods for local bodies to reduce them. Documents The Marmot Review (2010) made a range of recommendations to reduce health inequalities in England. Building on the Review, the UCL Institute of Health Equity has produced 4 papers which include evidence, and examples of practical action that can be taken at a local level to reduce health inequalities. They are designed for people working in local services, particularly: directors of public health and public health teams people working in local authorities services that may influence health and wellbeing, such as planning health and wellbeing boards These practice resources build on a series of papers published in 2014 to support local action on health inequalities.

NI health and social care inequalities monitoring system (HSCIMS) - health inequalities in Northern Ireland: key facts 2015

This key facts publication provides an interim update to the NI health & social care inequalities monitoring system (HSCIMS) regional reports which are published every other year. It presents a summary of the latest position and inequality gaps between the most deprived areas and both the least deprived areas and the NI average in addition to a regional comparison with rural areas for a range of health outcomes included within the HSCIMS series, in addition to the health survey Northern Ireland (HSNI).

Central banking and inequalities: taking off the blinders

What is the relation between monetary policy and inequalities in income and wealth? This question has received insufficient attention, especially in light of the unconventional policies introduced since the 2008 financial crisis. The article analyzes three ways in which the concern central banks show for inequalities in their official statements remains incomplete and underdeveloped. First, central banks tend to care about inequality for instrumental reasons only. When they do assign intrinsic value to containing inequalities, they shy away from trade-offs with the standard objectives of monetary policy that such a position entails. Second, central banks play down the causal impact monetary policy has on inequalities. When they do acknowledge it, they defend their actions by claiming that it is an unintended side effect, that it is temporary, and/or that any alternative policy would fare even worse. The article appeals to the doctrine of double effect to criticize these arguments. Third, even if one accepts that inequalities should be contained and that today’s monetary policies exacerbate them, is it both desirable and feasible to make containing inequalities part of the mandate of central banks? The article analyzes and rejects three attempts on the part of central banks to answer this question negatively.

The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields

Hexagonal Resonant Triad patterns are shown to exist as stable solutions of a particular type of nonlinear field where no cubic field nonlinearity is present. The zero ‘dc’ Fourier mode is shown to stabilize these patterns produced by a pure quadratic field nonlinearity. Closed form solutions and stability results are obtained near the critical point, complimented by numerical studies far from the critical point. These results are obtained using a neural field based on the Helmholtzian operator. Constraints on structure and parameters for a general pure quadratic neural field which supports hexagonal patterns are obtained.

Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.

Identifying health inequalities in individuals with major mental illness (MMI) using routine data

Abstract and Summary of Thesis: Background: Individuals with Major Mental Illness (such as schizophrenia and bipolar disorder) experience increased rates of physical health comorbidity compared to the general population. They also experience inequalities in access to certain aspects of healthcare. This ultimately leads to premature mortality. Studies detailing patterns of physical health comorbidity are limited by their definitions of comorbidity, single disease approach to comorbidity and by the study of heterogeneous groups. To date the investigation of possible sources of healthcare inequalities experienced by individuals with Major Mental Illness (MMI) is relatively limited. Moreover studies detailing the extent of premature mortality experienced by individuals with MMI vary both in terms of the measure of premature mortality reported and age of the cohort investigated, limiting their generalisability to the wider population. Therefore local and national data can be used to describe patterns of physical health comorbidity, investigate possible reasons for health inequalities and describe mortality rates. These findings will extend existing work in this area. Aims and Objectives: To review the relevant literature regarding: patterns of physical health comorbidity, evidence for inequalities in physical healthcare and evidence for premature mortality for individuals with MMI. To examine the rates of physical health comorbidity in a large primary care database and to assess for evidence for inequalities in access to healthcare using both routine primary care prescribing data and incentivised national Quality and Outcome Framework (QOF) data. Finally to examine the rates of premature mortality in a local context with a particular focus on cause of death across the lifespan and effect of International Classification of Disease Version 10 (ICD 10) diagnosis and socioeconomic status on rates and cause of death. Methods: A narrative review of the literature surrounding patterns of physical health comorbidity, the evidence for inequalities in physical healthcare and premature mortality in MMI was undertaken. Rates of physical health comorbidity and multimorbidity in schizophrenia and bipolar disorder were examined using a large primary care dataset (Scottish Programme for Improving Clinical Effectiveness in Primary Care (SPICE)). Possible inequalities in access to healthcare were investigated by comparing patterns of prescribing in individuals with MMI and comorbid physical health conditions with prescribing rates in individuals with physical health conditions without MMI using SPICE data. Potential inequalities in access to health promotion advice (in the form of smoking cessation) and prescribing of Nicotine Replacement Therapy (NRT) were also investigated using SPICE data. Possible inequalities in access to incentivised primary healthcare were investigated using National Quality and Outcome Framework (QOF) data. Finally a pre-existing case register (Glasgow Psychosis Clinical Information System (PsyCIS)) was linked to Scottish Mortality data (available from the Scottish Government Website) to investigate rates and primary cause of death in individuals with MMI. Rate and primary cause of death were compared to the local population and impact of age, socioeconomic status and ICD 10 diagnosis (schizophrenia vs. bipolar disorder) were investigated. Results: Analysis of the SPICE data found that sixteen out of the thirty two common physical comorbidities assessed, occurred significantly more frequently in individuals with schizophrenia. In individuals with bipolar disorder fourteen occurred more frequently. The most prevalent chronic physical health conditions in individuals with schizophrenia and bipolar disorder were: viral hepatitis (Odds Ratios (OR) 3.99 95% Confidence Interval (CI) 2.82-5.64 and OR 5.90 95% CI 3.16-11.03 respectively), constipation (OR 3.24 95% CI 3.01-3.49 and OR 2.84 95% CI 2.47-3.26 respectively) and Parkinson’s disease (OR 3.07 95% CI 2.43-3.89 and OR 2.52 95% CI 1.60-3.97 respectively). Both groups had significantly increased rates of multimorbidity compared to controls: in the schizophrenia group OR for two comorbidities was 1.37 95% CI 1.29-1.45 and in the bipolar disorder group OR was 1.34 95% CI 1.20-1.49. In the studies investigating inequalities in access to healthcare there was evidence of: under-recording of cardiovascular-related conditions for example in individuals with schizophrenia: OR for Atrial Fibrillation (AF) was 0.62 95% CI 0.52 - 0.73, for hypertension 0.71 95% CI 0.67 - 0.76, for Coronary Heart Disease (CHD) 0.76 95% CI 0.69 - 0.83 and for peripheral vascular disease (PVD) 0.83 95% CI 0.72 - 0.97. Similarly in individuals with bipolar disorder OR for AF was 0.56 95% CI 0.41-0.78, for hypertension 0.69 95% CI 0.62 - 0.77 and for CHD 0.77 95% CI 0.66 - 0.91. There was also evidence of less intensive prescribing for individuals with schizophrenia and bipolar disorder who had comorbid hypertension and CHD compared to individuals with hypertension and CHD who did not have schizophrenia or bipolar disorder. Rate of prescribing of statins for individuals with schizophrenia and CHD occurred significantly less frequently than in individuals with CHD without MMI (OR 0.67 95% CI 0.56-0.80). Rates of prescribing of 2 or more anti-hypertensives were lower in individuals with CHD and schizophrenia and CHD and bipolar disorder compared to individuals with CHD without MMI (OR 0.66 95% CI 0.56-0.78 and OR 0.55 95% CI 0.46-0.67, respectively). Smoking was more common in individuals with MMI compared to individuals without MMI (OR 2.53 95% CI 2.44-2.63) and was particularly increased in men (OR 2.83 95% CI 2.68-2.98). Rates of ex-smoking and non-smoking were lower in individuals with MMI (OR 0.79 95% CI 0.75-0.83 and OR 0.50 95% CI 0.48-0.52 respectively). However recorded rates of smoking cessation advice in smokers with MMI were significantly lower than the recorded rates of smoking cessation advice in smokers with diabetes (88.7% vs. 98.0%, p<0.001), smokers with CHD (88.9% vs. 98.7%, p<0.001) and smokers with hypertension (88.3% vs. 98.5%, p<0.001) without MMI. The odds ratio of NRT prescription was also significantly lower in smokers with MMI without diabetes compared to smokers with diabetes without MMI (OR 0.75 95% CI 0.69-0.81). Similar findings were found for smokers with MMI without CHD compared to smokers with CHD without MMI (OR 0.34 95% CI 0.31-0.38) and smokers with MMI without hypertension compared to smokers with hypertension without MMI (OR 0.71 95% CI 0.66-0.76). At a national level, payment and population achievement rates for the recording of body mass index (BMI) in MMI was significantly lower than the payment and population achievement rates for BMI recording in diabetes throughout the whole of the UK combined: payment rate 92.7% (Inter Quartile Range (IQR) 89.3-95.8 vs. 95.5% IQR 93.3-97.2, p<0.001 and population achievement rate 84.0% IQR 76.3-90.0 vs. 92.5% IQR 89.7-94.9, p<0.001 and for each country individually: for example in Scotland payment rate was 94.0% IQR 91.4-97.2 vs. 96.3% IQR 94.3-97.8, p<0.001. Exception rate was significantly higher for the recording of BMI in MMI than the exception rate for BMI recording in diabetes for the UK combined: 7.4% IQR 3.3-15.9 vs. 2.3% IQR 0.9-4.7, p<0.001 and for each country individually. For example in Scotland exception rate in MMI was 11.8% IQR 5.4-19.3 compared to 3.5% IQR 1.9-6.1 in diabetes. Similar findings were found for Blood Pressure (BP) recording: across the whole of the UK payment and population achievement rates for BP recording in MMI were also significantly reduced compared to payment and population achievement rates for the recording of BP in chronic kidney disease (CKD): payment rate: 94.1% IQR 90.9-97.1 vs.97.8% IQR 96.3-98.9 and p<0.001 and population achievement rate 87.0% IQR 81.3-91.7 vs. 97.1% IQR 95.5-98.4, p<0.001. Exception rates again were significantly higher for the recording of BP in MMI compared to CKD (6.4% IQR 3.0-13.1 vs. 0.3% IQR 0.0-1.0, p<0.001). There was also evidence of differences in rates of recording of BMI and BP in MMI across the UK. BMI and BP recording in MMI were significantly lower in Scotland compared to England (BMI:-1.5% 99% CI -2.7 to -0.3%, p<0.001 and BP: -1.8% 99% CI -2.7 to -0.9%, p<0.001). While rates of BMI and BP recording in diabetes and CKD were similar in Scotland compared to England (BMI: -0.5 99% CI -1.0 to 0.05, p=0.004 and BP: 0.02 99% CI -0.2 to 0.3, p=0.797). Data from the PsyCIS cohort showed an increase in Standardised Mortality Ratios (SMR) across the lifespan for individuals with MMI compared to the local Glasgow and wider Scottish populations (Glasgow SMR 1.8 95% CI 1.6-2.0 and Scotland SMR 2.7 95% CI 2.4-3.1). Increasing socioeconomic deprivation was associated with an increased overall rate of death in MMI (350.3 deaths/10,000 population/5 years in the least deprived quintile compared to 794.6 deaths/10,000 population/5 years in the most deprived quintile). No significant difference in rate of death for individuals with schizophrenia compared with bipolar disorder was reported (6.3% vs. 4.9%, p=0.086), but primary cause of death varied: with higher rates of suicide in individuals with bipolar disorder (22.4% vs. 11.7%, p=0.04). Discussion: Local and national datasets can be used for epidemiological study to inform local practice and complement existing national and international studies. While the strengths of this thesis include the large data sets used and therefore their likely representativeness to the wider population, some limitations largely associated with using secondary data sources are acknowledged. While this thesis has confirmed evidence of increased physical health comorbidity and multimorbidity in individuals with MMI, it is likely that these findings represent a significant under reporting and likely under recognition of physical health comorbidity in this population. This is likely due to a combination of patient, health professional and healthcare system factors and requires further investigation. Moreover, evidence of inequality in access to healthcare in terms of: physical health promotion (namely smoking cessation advice), recording of physical health indices (BMI and BP), prescribing of medications for the treatment of physical illness and prescribing of NRT has been found at a national level. While significant premature mortality in individuals with MMI within a Scottish setting has been confirmed, more work is required to further detail and investigate the impact of socioeconomic deprivation on cause and rate of death in this population. It is clear that further education and training is required for all healthcare staff to improve the recognition, diagnosis and treatment of physical health problems in this population with the aim of addressing the significant premature mortality that is seen. Conclusions: Future work lies in the challenge of designing strategies to reduce health inequalities and narrow the gap in premature mortality reported in individuals with MMI. Models of care that allow a much more integrated approach to diagnosing, monitoring and treating both the physical and mental health of individuals with MMI, particularly in areas of social and economic deprivation may be helpful. Strategies to engage this “hard to reach” population also need to be developed. While greater integration of psychiatric services with primary care and with specialist medical services is clearly vital the evidence on how best to achieve this is limited. While the National Health Service (NHS) is currently undergoing major reform, attention needs to be paid to designing better ways to improve the current disconnect between primary and secondary care. This should then help to improve physical, psychological and social outcomes for individuals with MMI.

Tackling health inequalities in primary care: an exploration of GPs’ experience at the frontline

In Scotland, life expectancy and health outcomes are strongly tied to socioeconomic status. Specifically, socioeconomically deprived areas suffer disproportionately from high levels of premature multimorbidity and mortality. To tackle these inequalities in health, challenges in the most deprived areas must be addressed. One avenue that merits attention is the potential role of general medical practitioners (GPs) in helping to address health inequalities, particularly due to their long-term presence in deprived communities, their role in improving patient and population health, and their potential advocacy role on behalf of their patients. GPs can be seen as what Lipsky calls ‘street-level bureaucrats’ due to their considerable autonomy in the decisions they make surrounding individual patient needs, yet practising under the bureaucratic structure of the NHS. While previous research has examined the applicability of Lipsky’s framework to the role of GPs, there has been very little research exploring how GPs negotiate between the multiple identities in their work, how GPs ‘socially construct’ their patients, how GPs view their potential role as ‘advocate’, and what this means in terms of the contribution of GPs to addressing existing inequalities in health. Using semi-structured interviews, this study explored the experience and views of 24 GPs working in some of Scotland’s most deprived practices to understand how they might combat this growing health divide via the mitigation (and potential prevention) of existing health inequalities. Participants were selected based on several criteria including practice deprivation level and their individual involvement in the Deep End project, which is an informal network comprising the 100 most deprived general practices in Scotland. The research focused on understanding GPs’ perceptions of their work including its broader implications, within their practice, the communities within which they practise, and the health system as a whole. The concept of street-level bureaucracy proved to be useful in understanding GPs’ frontline work and how they negotiate dilemmas. However, this research demonstrated the need to look beyond Lipsky’s framework in order to understand how GPs reconcile their multiple identities, including advocate and manager. As a result, the term ‘street-level professional’ is offered to capture more fully the multiple identities which GPs inhabit and to explain how GPs’ elite status positions them to engage in political and policy advocacy. This study also provides evidence that GPs’ social constructions of patients are linked not only to how GPs conceptualise the causes of health inequalities, but also to how they view their role in tackling them. In line with this, the interviews established that many GPs felt they could make a difference through advocacy efforts at individual, community and policy/political levels. Furthermore, the study draws attention to the importance of practitioner-led groups—such as the Deep End project—in supporting GPs’ efforts and providing a platform for their advocacy. Within this study, a range of GPs’ views have been explored based on the sample. While it is unclear how common these views are amongst GPs in general, the study revealed that there is considerable scope for ‘political GPs’ who choose to exercise discretion in their communities and beyond. Consequently, GPs working in deprived areas should be encouraged to use their professional status and political clout not only to strengthen local communities, but also to advocate for policy change that might potentially affect the degree of disadvantage of their patients, and levels of social and health inequalities more generally.

Holography, probe branes and isoperimetric inequalities

In many instances of holographic correspondences between a d-dimensional boundary theory and a (. d+. 1)-dimensional bulk, a direct argument in the boundary theory implies that there must exist a simple and precise relation between the Euclidean on-shell action of a (. d-. 1)-brane probing the bulk geometry and the Euclidean gravitational bulk action. This relation is crucial for the consistency of holography, yet it is non-trivial from the bulk perspective. In particular, we show that it relies on a nice isoperimetric inequality that must be satisfied in a large class of Poincaré-Einstein spaces. Remarkably, this inequality follows from theorems by Lee and Wang.

Iterated responsive threshold search for the quadratic multiple knapsack problem

International audience

The Impact of Education and Socioeconomic and Occupational Conditions on Self-Perceived and Mental Health Inequalities Among Immigrants and Native Workers in Spain

There is limited evidence on the influence of social determinants on the self-perceived and mental health of immigrants settled at least 8 years in Spain. The aim of this study was to examine differences between workers related to migrant-status, self-perceived and mental health, and to assess their relationship to occupational conditions, educational level and occupational social class, stratified by sex. Using data from the Spanish National Health Survey of 2011/12, we computed prevalence, odds ratios and explicative fractions. Mental (OR 2.02; CI 1.39–2.93) and self-perceived health (OR 2.64; CI 1.77–3.93) were poorer for immigrant women compared to natives. Occupational social class variable contributes 25 % to self-perceived health OR in immigrant women. Settled immigrant women workers are a vulnerable group in Spain.