Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Intercomparison of C-14 Analysis of Carbonaceous Aerosols: Exercise 2009

Radiocarbon analysis of the carbonaceous aerosol allows an apportionment of fossil and non-fossil sources of airborne particulate matter (PM). A chemical separation of total carbon (TC) into its subfractions organic carbon (OC) and elemental carbon (EC) refines this powerful technique, as OC and EC originate from different sources and undergo different processes in the atmosphere. Although C-14 analysis of TC, EC, and OC has recently gained increasing attention, interlaboratory quality assurance measures have largely been missing, especially for the isolation of EC and OC. In this work, we present results from an intercomparison of 9 laboratories for C-14 analysis of carbonaceous aerosol samples on quartz fiber filters. Two ambient PM samples and 1 reference material (RM 8785) were provided with representative filter blanks. All laboratories performed C-14 determinations of TC and a subset of isolated EC and OC for isotopic measurement. In general, C-14 measurements of TC and OC agreed acceptably well between the laboratories, i.e. for TC within 0.015-0.025 (FC)-C-14 for the ambient filters and within 0.041 (FC)-C-14 for RM 8785. Due to inhomogeneous filter loading, RM 8785 demonstrated only limited applicability as a reference material for C-14 analysis of carbonaceous aerosols. C-14 analysis of EC revealed a large deviation between the laboratories of 28-79 as a consequence of different separation techniques. This result indicates a need for further discussion on optimal methods of EC isolation for C-14 analysis and a second stage of this intercomparison.

Association of a large lateral extension of the acromion with rotator cuff tears

BACKGROUND: Factors predisposing to tearing of the rotator cuff are poorly understood. We have observed that the acromion of patients with a rotator cuff tear very often appears large on anteroposterior radiographs or during surgery. The purpose of this study was to quantify the lateral extension of the acromion in patients with a full-thickness rotator cuff tear and in patients with an intact rotator cuff. METHODS: The lateral extension of the acromion was assessed on true anteroposterior radiographs made with the arm in neutral rotation. The distance from the glenoid plane to the lateral border of the acromion was divided by the distance from the glenoid plane to the lateral aspect of the humeral head to calculate the acromion index. This index was determined in a group of 102 patients (average age, 65.0 years) with a proven full-thickness rotator cuff tear, in an age and gender-matched group of forty-seven patients (average age, 63.7 years) with osteoarthritis of the shoulder and an intact rotator cuff, and in an age and gender-matched control group of seventy volunteers (average age, 64.4 years) with an intact rotator cuff as demonstrated by ultrasonography. RESULTS: The average acromion index (and standard deviation) was 0.73 +/- 0.06 in the shoulders with a full-thickness tear, 0.60 +/- 0.08 in those with osteoarthritis and an intact rotator cuff, and 0.64 +/- 0.06 in the asymptomatic, normal shoulders with an intact rotator cuff. The difference between the index in the shoulders with a full-thickness supraspinatus tear and the index in those with an intact rotator cuff was highly significant (p < 0.0001). CONCLUSIONS: A large lateral extension of the acromion appears to be associated with full-thickness tearing of the rotator cuff.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Electroweak Sudakov effects in W, Z and γ production at large transverse momentum

We study electroweak Sudakov effects in single W, Z and γ production at large transverse momentum using soft collinear effective theory. We present a factorized form of the cross section near the partonic threshold with both QCD and electroweak effects included and compute the electroweak corrections arising at different scales. We analyze their size relative to the QCD corrections as well as the impact of strong-electroweak mixing terms. Numerical results for the vector-boson cross sections at the Large Hadron Collider are presented.

Massive Boson Production at Small qT in Soft-Collinear Effective Theory

We study the differential cross sections for electroweak gauge-boson and Higgs production at small and very small transverse-momentum qT. Large logarithms are resummed using soft-collinear effective theory. The collinear anomaly generates a non-perturbative scale q⁎, which protects the processes from receiving large long-distance hadronic contributions. A numerical comparison of our predictions with data on the transverse-momentum distribution in Z-boson production at the Tevatron and LHC is given.

Educational Expansion and Persistent Inequalities of Education: Utilizing the Subjective Expected Utility Theory to Explain the Increasing Participation Rates in Upper Secondary School in the Federal Republic Of Germany

This investigation attempts to answer the question why more and more parents have chosen the Gymnasium for their children's secondary school education in post‐war West Germany. Based on the theory of subjective expected utility, the crucial mechanisms of parental educational decisions have been emphasized. From this perspective it is assumed that increasing educational motivation coupled with changes in the subjective evaluation of the cost–benefit of education were important conditions for an increasing participation in upper secondary schools. These were, however, in turn, the result of educational expansion. The empirical analyses for three time‐periods in the 1960s, 1970s, and 1980s confirm these assumptions to a large degree. Additionally, empirical evidence was found to suggest that in addition to the intentions of parents and the educational career of their children, structural moments of educational expansion and their own inertia played an important role in the pupils' transition from one educational level to the next. Finally, evidence was found that persistent class‐specific educational inequality stems from a constant balance in the relative cost–benefit advantages between social classes as well as from an increasing difference of primary origin effect between social classes in the realization of their educational choice.

Geocenter coordinates estimated from GNSS data as viewed by perturbation theory

Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global’naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008–2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters. A fair agreement for GPS and GLONASS was found in the geocenter x- and y-coordinate series. Our tests, however, clearly reveal artifacts in the z-component determined with the GLONASS data. Large periodic excursions in the GLONASS geocenter z-coordinates of about 40 cm peak-to-peak are related to the maximum elevation angles of the Sun above/below the orbital planes of the satellite system and thus have a period of about 4 months (third of a year). A detailed analysis revealed that the artifacts are almost uniquely governed by the differences of the estimates of direct solar radiation pressure (SRP) in the two solution series (with and without geocenter estimation). A simple formula is derived, describing the relation between the geocenter z-coordinate and the corresponding parameter of the SRP. The effect can be explained by first-order perturbation theory of celestial mechanics. The theory also predicts a heavy impact on the GNSS-derived geocenter if once-per-revolution SRP parameters are estimated in the direction of the satellite’s solar panel axis. Specific experiments using GPS observations revealed that this is indeed the case. Although the main focus of this article is on GNSS, the theory developed is applicable to all satellite observing techniques. We applied the theory to satellite laser ranging (SLR) solutions using LAGEOS. It turns out that the correlation between geocenter and SRP parameters is not a critical issue for the SLR solutions. The reasons are threefold: The direct SRP is about a factor of 30–40 smaller for typical geodetic SLR satellites than for GNSS satellites, allowing it in most cases to not solve for SRP parameters (ruling out the correlation between these parameters and the geocenter coordinates); the orbital arc length of 7 days (which is typically used in SLR analysis) contains more than 50 revolutions of the LAGEOS satellites as compared to about two revolutions of GNSS satellites for the daily arcs used in GNSS analysis; the orbit geometry is not as critical for LAGEOS as for GNSS satellites, because the elevation angle of the Sun w.r.t. the orbital plane is usually significantly changing over 7 days.

Psychosocial aspects in cardiac rehabilitation: From theory to practice. A position paper from the Cardiac Rehabilitation Section of the European Association of Cardiovascular Prevention and Rehabilitation of the European Society of Cardiology

A large body of empirical research shows that psychosocial risk factors (PSRFs) such as low socio-economic status, social isolation, stress, type-D personality, depression and anxiety increase the risk of incident coronary heart disease (CHD) and also contribute to poorer health-related quality of life (HRQoL) and prognosis in patients with established CHD. PSRFs may also act as barriers to lifestyle changes and treatment adherence and may moderate the effects of cardiac rehabilitation (CR). Furthermore, there appears to be a bidirectional interaction between PSRFs and the cardiovascular system. Stress, anxiety and depression affect the cardiovascular system through immune, neuroendocrine and behavioural pathways. In turn, CHD and its associated treatments may lead to distress in patients, including anxiety and depression. In clinical practice, PSRFs can be assessed with single-item screening questions, standardised questionnaires, or structured clinical interviews. Psychotherapy and medication can be considered to alleviate any PSRF-related symptoms and to enhance HRQoL, but the evidence for a definite beneficial effect on cardiac endpoints is inconclusive. A multimodal behavioural intervention, integrating counselling for PSRFs and coping with illness should be included within comprehensive CR. Patients with clinically significant symptoms of distress should be referred for psychological counselling or psychologically focused interventions and/or psychopharmacological treatment. To conclude, the success of CR may critically depend on the interdependence of the body and mind and this interaction needs to be reflected through the assessment and management of PSRFs in line with robust scientific evidence, by trained staff, integrated within the core CR team.

Effect of large doses of parenteral vitamin D on glycaemic control and calcium/phosphate metabolism in patients with stable type 2 diabetes mellitus: a randomised, placebo-controlled, prospective pilot study.

OBJECTIVE Vitamin D (D₃) status is reported to correlate negatively with insulin production and insulin sensitivity in patients with type 2 diabetes mellitus (T2DM). However, few placebo-controlled intervention data are available. We aimed to assess the effect of large doses of parenteral D3 on glycosylated haemoglobin (HbA(₁c)) and estimates of insulin action (homeostasis model assessment insulin resistance: HOMA-IR) in patients with stable T2DM. MATERIALS AND METHODS We performed a prospective, randomised, double-blind, placebo-controlled pilot study at a single university care setting in Switzerland. Fifty-five patients of both genders with T2DM of more than 10 years were enrolled and randomised to either 300,000 IU D₃ or placebo, intramuscularly. The primary endpoint was the intergroup difference in HbA(₁c) levels. Secondary endpoints were: changes in insulin sensitivity, albuminuria, calcium/phosphate metabolism, activity of the renin-aldosterone axis and changes in 24-hour ambulatory blood pressure values. RESULTS After 6 months of D₃ supply, there was a significant intergroup difference in the change in HbA(₁c) levels (relative change [mean ± standard deviation] +2.9% ± 1.5% in the D₃ group vs +6.9% ± 2.1% the in placebo group, p = 0.041) as HOMA-IR decreased by 12.8% ± 5.6% in the D₃ group and increased by 10% ± 5.4% in the placebo group (intergroup difference, p = 0.032). Twenty-four-hour urinary albumin excretion decreased in the D₃ group from 200 ± 41 to 126 ± 39, p = 0.021). There was no significant intergroup difference for the other secondary endpoints. CONCLUSIONS D₃ improved insulin sensitivity (based on HOMA-IR) and affected the course of HbA(₁c) positively compared with placebo in patients with T2DM.