Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

Public health insurance and entry into self-employment

We estimate the impact of a differential treatment of paid employees versus self-employed workers in a public health insurance system on the entry rate into entrepreneurship. In Germany, the public health insurance system is mandatory for most paid employees, but not for the selfemployed, who usually buy private health insurance. Private health insurance contributions are relatively low for the young and healthy, and until 2013 also for males, but less attractive at the other ends of these dimensions and if membership in the public health insurance allows other family members to be covered by contribution-free family insurance. Therefore, the health insurance system can create incentives or disincentives to starting up a business depending on the family’s situation and health. We estimate a discrete time hazard rate model of entrepreneurial entry based on representative household panel data for Germany, which include personal health information, and we account for non- random sample selection. We estimate that an increase in the health insurance cost differential between self-employed workers and paid employees by 100 euro per month decreases the annual probability of entry into selfemployment by 0.38 percentage points, i.e. about a third of the average annual entry rate. The results show that the phenomenon of entrepreneurship lock, which an emerging literature describes for the system of employer provided health insurance in the USA, can also occur in a public health insurance system. Therefore, entrepreneurial activity should be taken into account when discussing potential health care reforms, not only in the USA and in Germany

Long term costs and effects of reducing the number of twin pregnancies in IVF by single embryo transfer: the TwinSing study

Contains fulltext : 87274.pdf (publisher's version ) (Open Access)BACKGROUND: Pregnancies induced by in vitro fertilisation (IVF) often result in twin gestations, which are associated with both maternal and perinatal complications. An effective way to reduce the number of IVF twin pregnancies is to decrease the number of embryos transferred from two to one. The interpretation of current studies is limited because they used live birth as outcome measure and because they applied limited time horizons. So far, research on long-term outcomes of IVF twins and singletons is scarce and inconclusive. The objective of this study is to investigate the short (1-year) and long-term (5 and 18-year) costs and health outcomes of IVF singleton and twin children and to consider these in estimating the cost-effectiveness of single embryo transfer compared with double embryo transfer, from a societal and a healthcare perspective. METHODS/DESIGN: A multi-centre cohort study will be performed, in which IVF singletons and IVF twin children born between 2003 and 2005 of whom parents received IVF treatment in one of the five participating Dutch IVF centres, will be compared. Data collection will focus on children at risk of health problems and children in whom health problems actually occurred. First year of life data will be collected in approximately 1,278 children (619 singletons and 659 twin children). Data up to the fifth year of life will be collected in approximately 488 children (200 singletons and 288 twin children). Outcome measures are health status, health-related quality of life and costs. Data will be obtained from hospital information systems, a parent questionnaire and existing registries. Furthermore, a prognostic model will be developed that reflects the short and long-term costs and health outcomes of IVF singleton and twin children. This model will be linked to a Markov model of the short-term cost-effectiveness of single embryo transfer strategies versus double embryo transfer strategies to enable the calculation of the long-term cost-effectiveness. DISCUSSION: This is, to our knowledge, the first study that investigates the long-term costs and health outcomes of IVF singleton and twin children and the long-term cost-effectiveness of single embryo transfer strategies versus double embryo transfer strategies

Evaluation of the effect of sodium–glucose co‐transporter 2 inhibition with empagliflozin on morbidity and mortality of patients with chronic heart failure and a reduced ejection fraction: rationale for and design of the EMPEROR‐Reduced trial

Drugs that inhibit the sodium–glucose co‐transporter 2 (SGLT2) have been shown to reduce the risk of hospitalizations for heart failure in patients with type 2 diabetes. In populations that largely did not have heart failure at the time of enrolment, empagliflozin, canagliflozin and dapagliflozin decreased the risk of serious new‐onset heart failure events by ≈30%. In addition, in the EMPA‐REG OUTCOME trial, empagliflozin reduced the risk of both pump failure and sudden deaths, the two most common modes of death among patients with heart failure. In none of the three trials could the benefits of SGLT2 inhibitors on heart failure be explained by the actions of these drugs as diuretics or anti‐hyperglycaemic agents. These observations raise the possibility that SGLT2 inhibitors could reduce morbidity and mortality in patients with established heart failure, including those without diabetes. The EMPEROR‐Reduced trial is enrolling ≈3600 patients with heart failure and a reduced left ventricular ejection fraction (≤ 40%), half of whom are expected not to have diabetes. Patients are being randomized to placebo or empagliflozin 10 mg daily, which is added to all appropriate treatment with inhibitors of the renin–angiotensin system and neprilysin, beta‐blockers and mineralocorticoid receptor antagonists. The primary endpoint is the time‐to‐first event analysis of the combined risk of cardiovascular death and hospitalization for heart failure, but the trial will also evaluate the effects of empagliflozin on renal function, cardiovascular death, all‐cause mortality, and recurrent hospitalization events. By adjusting eligibility based on natriuretic peptide levels to the baseline ejection fraction, the trial will preferentially enrol high‐risk patients. A large proportion of the participants is expected to have an ejection fraction < 30%, and the estimated annual event rate is expected to be at least 15%. The EMPEROR‐Reduced trial is well‐positioned to determine if the addition of empagliflozin can add meaningfully to current approaches that have established benefits in the treatment of chronic heart failure with left ventricular systolic dysfunction

Evaluation of the effects of sodium–glucose co‐transporter 2 inhibition with empagliflozin on morbidity and mortality in patients with chronic heart failure and a preserved ejection fraction: rationale for and design of the EMPEROR‐Preserved Trial

Background: The principal biological processes that characterize heart failure with a preserved ejection fraction (HFpEF) are systemic inflammation, epicardial adipose tissue accumulation, coronary microcirculatory rarefaction, myocardial fibrosis and vascular stiffness; the resulting impairment of left ventricular and aortic distensibility (especially when accompanied by impaired glomerular function and sodium retention) causes increases in cardiac filling pressures and exertional dyspnoea despite the relative preservation of left ventricular ejection fraction. Independently of their actions on blood glucose, sodium–glucose co‐transporter 2 (SGLT2) inhibitors exert a broad range of biological effects (including actions to inhibit cardiac inflammation and fibrosis, antagonize sodium retention and improve glomerular function) that can ameliorate the pathophysiological derangements in HFpEF. Such SGLT2 inhibitors exert favourable effects in experimental models of HFpEF and have been found in large‐scale trials to reduce the risk for serious heart failure events in patients with type 2 diabetes, many of whom were retrospectively identified as having HFpEF. Study design: The EMPEROR‐Preserved Trial is enrolling ≈5750 patients with HFpEF (ejection fraction >40%), with and without type 2 diabetes, who are randomized to receive placebo or empagliflozin 10 mg/day, which is added to all appropriate treatments for HFpEF and co‐morbidities. Study aims: The primary endpoint is the time‐to‐first‐event analysis of the combined risk for cardiovascular death or hospitalization for heart failure. The trial will also evaluate the effects of empagliflozin on renal function, cardiovascular death, all‐cause mortality and recurrent hospitalization events, and will assess a wide range of biomarkers that reflect important pathophysiological mechanisms that may drive the evolution of HFpEF. The EMPEROR‐Preserved Trial is well positioned to determine if empagliflozin can have a meaningful impact on the course of HFpEF, a disorder for which there are currently few therapeutic options

Understanding, diagnosing, and treating Myalgic encephalomyelitis/chronic fatigue syndrome - State of the art: Report of the 2nd international meeting at the Charité fatigue center.

Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS) is a devastating disease affecting millions of people worldwide. Due to the 2019 pandemic of coronavirus disease (COVID-19), we are facing a significant increase of ME/CFS prevalence. On May 11th to 12th, 2023, the second international ME/CFS conference of the Charité Fatigue Center was held in Berlin, Germany, focusing on pathomechanisms, diagnosis, and treatment. During the two-day conference, more than 100 researchers from various research fields met on-site and over 700 attendees participated online to discuss the state of the art and novel findings in this field. Key topics from the conference included: the role of the immune system, dysfunction of endothelial and autonomic nervous system, and viral reactivation. Furthermore, there were presentations on innovative diagnostic measures and assessments for this complex disease, cutting-edge treatment approaches, and clinical studies. Despite the increased public attention due to the COVID-19 pandemic, the subsequent rise of Long COVID-19 cases, and the rise of funding opportunities to unravel the pathomechanisms underlying ME/CFS, this severe disease remains highly underresearched. Future adequately funded research efforts are needed to further explore the disease etiology and to identify diagnostic markers and targeted therapies