Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Can one see the fundamental frequency of a drum?

We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open subset G of R^n with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of G which is defined as the maximal possible radius of a ball B which has a negligible intersection with the complement of G. Here negligibility of a subset F in B means that the Wiener capacity of F does not exceed gamma times the capacity of B, where gamma is an arbitrarily fixed constant between 0 and 1. We provide explicit values of constants in the two-sided estimates.Comment: 18 pages, some misprints correcte

Uniform algebras and approximation on manifolds

Let $\Omega \subset \mathbb{C}^n$ be a bounded domain and let $\mathcal{A} \subset \mathcal{C}(\bar{\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\Omega$ and $F$ we show that the only obstruction to $\mathcal{A} = \mathcal{C}(\bar{\Omega})$ is that there is a holomorphic disk $D \subset \bar{\Omega}$ such that all functions in $F$ are holomorphic on $D$, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguished boundary of the) bidisk

Long-term MRA follow-up after coiling of intracranial aneurysms: impact on mood and anxiety

Magnetic resonance angiography (MRA) screening for recurrence of a coiled intracranial aneurysm and formation of new aneurysms long-term after coiling may induce anxiety and depression. In coiled patients, we evaluated effects on mood and level of anxiety from long-term follow-up MRA in comparison to general population norms. Of 162 patients participating in a long-term (> 4.5 years) MRA follow-up after coiling, 120 completed the EQ-5D questionnaire, a visual analog health scale and a self-developed screening related questionnaire at the time of MRA. Three months later, the same questionnaires were completed by 100 of these 120 patients. Results were compared to general population norms adjusted for gender and age. Any problem with anxiety or depression was reported in 56 of 120 patients (47%; 95%CI38a dagger"56%) at baseline and 42 of 100 patients (42%; 95%CI32a dagger"52%) at 3 months, equally for screen-positives and -negatives. Compared to the reference population, participants scored 38% (95%CI9a dagger"67%) and 27% (95%CI4a dagger"50%) more often any problem with anxiety or depression. Three months after screening, 21% (20 of 92) of screen-negatives and 13% (one of eight) of screen-positives reported to be less afraid of subarachnoid hemorrhage (SAH) compared to before screening. One of eight screen-positives reported increased fear of SAH. Patients with coiled intracranial aneurysms participating in long-term MRA screening reported significantly more often to be anxious or depressed than a reference group. Screening did not significantly increase anxiety or depression temporarily. However, subjectively, patients did report an increase in anxiety caused by screening, which decreased after 3 months

Women, lipids, and atherosclerotic cardiovascular disease:a call to action from the European Atherosclerosis Society

Cardiovascular disease is the leading cause of death in women and men globally, with most due to atherosclerotic cardiovascular disease (ASCVD). Despite progress during the last 30 years, ASCVD mortality is now increasing, with the fastest relative increase in middle-aged women. Missed or delayed diagnosis and undertreatment do not fully explain this burden of disease. Sex-specific factors, such as hypertensive disorders of pregnancy, premature menopause (especially primary ovarian insufficiency), and polycystic ovary syndrome are also relevant, with good evidence that these are associated with greater cardiovascular risk. This position statement from the European Atherosclerosis Society focuses on these factors, as well as sex-specific effects on lipids, including lipoprotein(a), over the life course in women which impact ASCVD risk. Women are also disproportionately impacted (in relative terms) by diabetes, chronic kidney disease, and auto-immune inflammatory disease. All these effects are compounded by sociocultural components related to gender. This panel stresses the need to identify and treat modifiable cardiovascular risk factors earlier in women, especially for those at risk due to sex-specific conditions, to reduce the unacceptably high burden of ASCVD in women

Non-coding RNAs versus protein biomarkers to diagnose and differentiate acute stroke:Systematic review and meta-analysis

BACKGROUND: Stroke diagnosis is dependent on lengthy clinical and neuroimaging assessments, while rapid treatment initiation improves clinical outcome. Currently, more sensitive biomarker assays of both non-coding RNA- and protein biomarkers have improved their detectability, which could accelerate stroke diagnosis. This systematic review and meta-analysis compares non-coding RNA- with protein biomarkers for their potential to diagnose and differentiate acute stroke (subtypes) in (pre-)hospital settings.METHODS: We performed a systematic review and meta-analysis of studies evaluating diagnostic performance of non-coding RNA- and protein biomarkers to differentiate acute ischemic and hemorrhagic stroke, stroke mimics, and (healthy) controls. Quality appraisal of individual studies was assessed using the QUADAS-2 tool while the meta-analysis was performed with the sROC approach and by assessing pooled sensitivity and specificity, diagnostic odds ratios, positive- and negative likelihood ratios, and the Youden Index.SUMMARY OF REVIEW: 112 studies were included in the systematic review and 42 studies in the meta-analysis containing 11627 patients with ischemic strokes, 2110 patients with hemorrhagic strokes, 1393 patients with a stroke mimic, and 5548 healthy controls. Proteins (IL-6 and S100 calcium-binding protein B (S100B)) and microRNAs (miR-30a) have similar performance in ischemic stroke diagnosis. To differentiate between ischemic- or hemorrhagic strokes, glial fibrillary acidic protein (GFAP) levels and autoantibodies to the NR2 peptide (NR2aAb, a cleavage product of NMDA neuroreceptors) were best performing whereas no investigated protein or non-coding RNA biomarkers differentiated stroke from stroke mimics with high diagnostic potential.CONCLUSIONS: Despite sampling time differences, circulating microRNAs (&lt; 24 h) and proteins (&lt; 4,5 h) perform equally well in ischemic stroke diagnosis. GFAP differentiates stroke subtypes, while a biomarker panel of GFAP and UCH-L1 improved the sensitivity and specificity of UCH-L1 alone to differentiate stroke.</p

Cold extremities in migraine: a marker for vascular dysfunction in women

Background and purpose: Migraine is recognized as a vascular risk factor, especially in women. Presumably, migraine, stroke and cardiovascular events share pathophysiological mechanisms. Self-reported cold extremities were investigated as a marker for vascular dysfunction in migraine. Secondly, it was hypothesized that suffering from cold extremities affects sleep quality, possibly exacerbating migraine attack frequency. Methods: In this case–control study, a random sample of 1084 migraine patients and 348 controls (aged 22–65 years) from the LUMINA migraine cohort were asked to complete questionnaires concerning cold extremities, sleep quality and migraine. Results: A total of 594 migraine patients and 199 controls completed the questionnaires. In women, thermal discomfort and cold extremities (TDCE) were more often reported by migraineurs versus controls (odds ratio 2.3, 95% confidence interval 1.4–3.7; P < 0.001), but not significantly so in men (odds ratio 2.5, 95% confidence interval 0.9–6.9; P = 0.09). There was no difference in TDCE comparing migraine with or without aura. Female migraineurs who reported TDCE had higher attack frequencies compared to female migraineurs without TDCE (4 vs. 3 attacks per month; P = 0.003). The association between TDCE and attack frequency was mediated by the presence of difficulty initiating sleep (P = 0.02). Conclusion: Women with migraine more often reported cold extremities compared with controls, possibly indicating a sex-specific vascular vulnerability. Female migraineurs with cold extremities had higher attack frequencies, partly resulting from sleep disturbances. Future studies need to demonstrate whether cold extremities in female migraineurs are a predictor for cardiovascular and cerebrovascular events

Comparison between EQ-5D-5L and PROMIS-10 to evaluate health-related quality of life 3 months after stroke:a cross-sectional multicenter study

BACKGROUND: Although the use of patient-reported outcome measures to assess Health-Related Quality of Life (HRQoL) has been advocated, it is still open to debate which patient-reported outcome measure should be preferred to evaluate HRQoL after stroke.AIM: To compare the measurement properties (including concurrent validity and discriminant ability) between the 5-dimensional 5-level Euro-Qol (EQ-5D-5L) and the Patient-Reported Outcomes Measurement Information System 10-Question Global Health Short Form (PROMIS-10) to evaluate HRQoL 3 months after stroke.DESIGN: Cross-sectional study.SETTING: Neurology outpatient clinics in 6 Dutch hospitals.POPULATION: The participants 360 consecutive individuals with stroke. Their median age was 71 years, 143 (39.7%) were female and 335 (93.0%) had suffered an ischemic stroke.METHODS: The EQ-5D-5L, PROMIS-10, modified Rankin Scale and two items on experienced decrease in health and activities post-stroke were administered by a stroke nurse or nurse practitioner through a telephone interview 3 months after stroke. The internal consistency, distribution, floor/ceiling effects, inter-correlations and discriminant ability (using the modified Rankin Scale and experienced decrease in health and in activities post-stroke as external anchors) were calculated for both the EQ-5D-5L and PROMIS-10.RESULTS: Ninety-six percent of the participants were living at home and 50.9% experienced minimal or no disabilities (modified Rankin Scale 0-1) 3 months after stroke. A ceiling effect and a non-normal left skewed distribution were observed in the EQ-5D-5L. The PROMIS-10 showed higher internal consistency (alpha=0.90) compared to the EQ-5D-5L (alpha=0.75). Both the EQ-5D-5L and the PROMIS-10 were strongly correlated with the modified Rankin Scale (r=0.62 and 0.60 respectively). The PROMIS-10 showed better discriminant ability in less affected individuals with stroke, whereas the EQ-5D-5L showed slightly better discriminant ability in more affected individuals with stroke.CONCLUSIONS: Both EQ-5D-5L and PROMIS-10 prove to be useful instruments to evaluate HRQoL in patients who are living at home 3 months after stroke.CLINICAL REHABILITATION IMPACT: The clinical rehabilitation impact depended on the setting and underlying goal which patient-reported outcome measure is preferred to evaluate HRQoL 3 months after stroke. The PROMIS-10 should be preferred to detect differences in less affected stroke patients, whereas the EQ-5D-5L provides slightly more information in more affected stroke patients.Paroxysmal Cerebral Disorder

Added Predictive Value of Female-Specific Factors and Psychosocial Factors for the Risk of Stroke in Women Under 50

Background and Objectives: Female-specific factors and psychosocial factors may be important in the prediction of stroke but are not included in prediction models that are currently used. We investigated whether addition of these factors would improve the performance of prediction models for the risk of stroke in women younger than 50 years.Methods: We used data from the Stichting Informatievoorziening voor Zorg en Onderzoek, population-based, primary care database of women aged 20-49 years without a history of cardiovascular disease. Analyses were stratified by 10-year age intervals at cohort entry. Cox proportional hazards models to predict stroke risk were developed, including traditional cardiovascular factors, and compared with models that additionally included female-specific and psychosocial factors. We compared the risk models using the c-statistic and slope of the calibration curve at a follow-up of 10 years. We developed an age-specific stroke risk prediction tool that may help communicating the risk of stroke in clinical practice.Results: We included 409,026 women with a total of 3,990,185 person-years of follow-up. Stroke occurred in 2,751 women (incidence rate 6.9 [95% CI 6.6-7.2] per 10,000 person-years). Models with only traditional cardiovascular factors performed poorly to moderately in all age groups: 20-29 years: c-statistic: 0.617 (95% CI 0.592-0.639); 30-39 years: c-statistic: 0.615 (95% CI 0.596-0.634); and 40-49 years: c-statistic: 0.585 (95% CI 0.573-0.597). After adding the female-specific and psychosocial risk factors to the reference models, the model discrimination increased moderately, especially in the age groups 30-39 (Δc-statistic: 0.019) and 40-49 years (Δc-statistic: 0.029) compared with the reference models, respectively.Discussion: The addition of female-specific factors and psychosocial risk factors improves the discriminatory performance of prediction models for stroke in women younger than 50 years.</p

Added Predictive Value of Female-Specific Factors and Psychosocial Factors for the Risk of Stroke in Women Under 50

Background and Objectives: Female-specific factors and psychosocial factors may be important in the prediction of stroke but are not included in prediction models that are currently used. We investigated whether addition of these factors would improve the performance of prediction models for the risk of stroke in women younger than 50 years.Methods: We used data from the Stichting Informatievoorziening voor Zorg en Onderzoek, population-based, primary care database of women aged 20-49 years without a history of cardiovascular disease. Analyses were stratified by 10-year age intervals at cohort entry. Cox proportional hazards models to predict stroke risk were developed, including traditional cardiovascular factors, and compared with models that additionally included female-specific and psychosocial factors. We compared the risk models using the c-statistic and slope of the calibration curve at a follow-up of 10 years. We developed an age-specific stroke risk prediction tool that may help communicating the risk of stroke in clinical practice.Results: We included 409,026 women with a total of 3,990,185 person-years of follow-up. Stroke occurred in 2,751 women (incidence rate 6.9 [95% CI 6.6-7.2] per 10,000 person-years). Models with only traditional cardiovascular factors performed poorly to moderately in all age groups: 20-29 years: c-statistic: 0.617 (95% CI 0.592-0.639); 30-39 years: c-statistic: 0.615 (95% CI 0.596-0.634); and 40-49 years: c-statistic: 0.585 (95% CI 0.573-0.597). After adding the female-specific and psychosocial risk factors to the reference models, the model discrimination increased moderately, especially in the age groups 30-39 (Δc-statistic: 0.019) and 40-49 years (Δc-statistic: 0.029) compared with the reference models, respectively.Discussion: The addition of female-specific factors and psychosocial risk factors improves the discriminatory performance of prediction models for stroke in women younger than 50 years.</p