How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co

Assessment of left ventricular ejection fraction in patients eligible for ICD therapy: Discrepancy between cardiac magnetic resonance imaging and 2D echocardiography

OBJECTIVE: Implantable cardioverter defibrillators (ICD) and cardiac resynchronisation therapy (CRT) have substantially improved the survival of patients with cardiomyopathy. Eligibility for this therapy requires a left ventricular ejection fraction (LVEF) <35 %. This is largely based on studies using echocardiography. Cardiac magnetic resonance imaging (CMR) is increasingly utilised for LVEF assessment, but several studies have shown differences between LVEF assessed by CMR and echocardiography. The present study compared LVEF assessment by CMR and echocardiography in a heart failure population and evaluated effects on eligibility for device therapy. METHODS: 152 patients (106 male, mean age 65.5 ± 9.9 years) referred for device therapy were included. During evaluation of eligibility they underwent both CMR and echocardiographic LVEF assessment. CMR volumes were computed from a stack of short-axis images. Echocardiographic volumes were computed using Simpson’s biplane method. RESULTS: The study population demonstrated an underestimation of end-diastolic volume (EDV) and end-systolic volume (ESV) by echocardiography of 71 ± 53 ml (mean ± SD) and 70 ± 49 ml, respectively. This resulted in an overestimation of LVEF of 6.6 ± 8.3 % by echocardiography compared with CMR (echocardiographic LVEF 31.5 ± 8.7 % and CMR LVEF 24.9 ± 9.6 %). 28 % of patients had opposing outcomes of eligibility for cardiac device therapy depending on the imaging modality used. CONCLUSION: We found EDV and ESV to be underestimated by echocardiography, and LVEF assessed by CMR to be significantly smaller than by echocardiography. Applying an LVEF cut-off value of 35 %, CMR would significantly increase the number of patients eligible for device implantation. Therefore, LVEF cut-off values might need reassessment when using CMR

Entangled Photons from Small Quantum Dots

We discuss level schemes of small quantum-dot turnstiles and their applicability in the production of entanglement in two-photon emission. Due to the large energy splitting of the single-electron levels, only one single electron level and one single hole level can be made resonant with the levels in the conduction band and valence band. This results in a model with nine distinct levels, which are split by the Coulomb interactions. We show that the optical selection rules are different for flat and tall cylindrically symmetric dots, and how this affects the quality of the entanglement generated in the decay of the biexciton state. The effect of charge carrier tunneling and of a resonant cavity is included in the model.Comment: 10 pages, 8 figure

Survey on solar X-ray flares and associated coherent radio emissions

The radio emission during 201 X-ray selected solar flares was surveyed from 100 MHz to 4 GHz with the Phoenix-2 spectrometer of ETH Zurich. The selection includes all RHESSI flares larger than C5.0 jointly observed from launch until June 30, 2003. Detailed association rates of radio emission during X-ray flares are reported. In the decimeter wavelength range, type III bursts and the genuinely decimetric emissions (pulsations, continua, and narrowband spikes) were found equally frequently. Both occur predominantly in the peak phase of hard X-ray (HXR) emission, but are less in tune with HXRs than the high-frequency continuum exceeding 4 GHz, attributed to gyrosynchrotron radiation. In 10% of the HXR flares, an intense radiation of the above genuine decimetric types followed in the decay phase or later. Classic meter-wave type III bursts are associated in 33% of all HXR flares, but only in 4% they are the exclusive radio emission. Noise storms were the only radio emission in 5% of the HXR flares, some of them with extended duration. Despite the spatial association (same active region), the noise storm variations are found to be only loosely correlated in time with the X-ray flux. In a surprising 17% of the HXR flares, no coherent radio emission was found in the extremely broad band surveyed. The association but loose correlation between HXR and coherent radio emission is interpreted by multiple reconnection sites connected by common field lines.Comment: Solar Physics, in pres

Reduction of blood culture contamination rate by an educational intervention

Background: Although mechanical dyssynchrony parameters derived by speckle tracking echocardiography (STE) may predict response to cardiac resynchronization therapy (CRT), comparability of parameters derived with different STE vendors is unknown. Methods: In the MARC study, echocardiographic images of heart failure patients obtained before CRT implantation were prospectively analysed with vendor specific STE software (GE EchoPac and Philips QLAB) and vendor-independent software (TomTec 2DCPA). Response was defined as change in left ventricular (LV) end-systolic volume between examination before and six-months after CRT implantation. Basic longitudinal strain and mechanical dyssynchrony parameters (septal to lateral wall delay (SL-delay), septal systolic rebound stretch (SRSsept), and systolic stretch index (SSI)) were obtained from either separate septal and lateral walls, or total LV apical four chamber. Septal strain patterns were categorized in three types. The coefficient of variation and intra-class correlation coefficient (ICC) were analysed. Dyssynchrony parameters were associated with CRT response using univariate regression analysis and C-statistics. Results: Two-hundred eleven patients were analysed. GE-cohort (n = 123): age 68 years (interquartile range (IQR): 61-73), 67% male, QRS-duration 177ms (IQR: 160-192), LV ejection fraction: 26 +/- 7%. Philips-cohort (n = 88): age 67 years (IQR: 59-74), 60% male, QRS-duration: 179 ms (IQR: 166-193), LV ejection fraction: 27 +/- 8. LV derived peak strain was comparable in the GE-(GE: -7.3 +/- 3.1%, TomTec: -6.4 +/- 2.8%, ICC: 0.723) and Philips-cohort (Philips: -7.7 +/- 2.7%, TomTec: -7.7 +/- 3.3%, ICC: 0.749). SL-delay showed low ICC values (GE vs. TomTec: 0.078 and Philips vs. TomTec: 0.025). ICC's of SRSsept and SSI were higher but only weak (GE vs. TomTec: SRSsept: 0.470, SSI: 0.467) (Philips vs. QLAB: SRSsept: 0.419, SSI: 0.421). Comparability of septal strain patterns was low (Cohen's kappa, GE vs. TomTec: 0.221 and Philips vs. TomTec: 0.279). Septal strain patterns, SRSsept and SSI were associated with changes in LV end-systolic volume for all vendors. SRSsept and SSI had relative varying C-statistic values (range: 0.530-0.705) and different cut-off values between vendors. Conclusions: Although global longitudinal strain analysis showed fair comparability, assessment of dyssynchrony parameters was vendor specific and not applicable outside the context of the implemented platform. While the standardization taskforce took an important step for global peak strain, further standardization of STE is still warranted

General practitioners’ perspectives on campaigns to promote rapid help-seeking behaviour at the onset of rheumatoid arthritis

Objective. To explore general practitioners’ (GPs’ ) perspectives on public health campaigns to encourage people with the early symptoms of rheumatoid arthritis (RA) to seek medical help rapidly. Design. Nineteen GPs participated in four semistructured focus groups. Focus groups were audio-recorded, transcribed verbatim, and analysed using thematic analysis. Results. GPs recognised the need for the early treatment of RA and identified that facilitating appropriate access to care was important. However, not all held the view that a delay in help seeking was a clinically significant issue. Furthermore, many were concerned that the early symptoms of RA were often non-specific, and that current knowledge about the nature of symptoms at disease onset was inadequate to inform the content of a help-seeking campaign. They argued that a campaign might not be able to specifically target those who need to present urgently. Poorly designed campaigns were suggested to have a negative impact on GPs’ workloads, and would “clog up” the referral pathway for genuine cases of RA. Conclusions. GPs were supportive of strategies to improve access to Rheumatological care and increase public awareness of RA symptoms. However, they have identified important issues that need to be considered in developing a public health campaign that forms part of an overall strategy to reduce time to treatment for patients with new onset RA. This study highlights the value of gaining GPs’ perspectives before launching health promotion campaigns

Tropical air-sea interaction in general circulation models

An intercomparison is undertaken of the tropical behavior of 17 coupled ocean-atmosphere models in which at least one component may be termed a general circulation model (GCM). The aim is to provide a taxonomy—a description and rough classification—of behavior across the ensemble of models, focusing on interannual variability. The temporal behavior of the sea surface temperature (SST) field along the equator is presented for each model, SST being chosen as the primary variable for intercomparison due to its crucial role in mediating the coupling and because it is a sensitive indicator of climate drift. A wide variety of possible types of behavior are noted among the models. Models with substantial interannual tropical variability may be roughly classified into cases with propagating SST anomalies and cases in which the SST anomalies develop in place. A number of the models also exhibit significant drift with respect to SST climatology. However, there is not a clear relationship between climate drift and the presence or absence of interannual oscillations. In several cases, the mode of climate drift within the tropical Pacific appears to involve coupled feedback mechanisms similar to those responsible for El Niño variability. Implications for coupled-model development and for climate prediction on seasonal to interannual time scales are discussed. Overall, the results indicate considerable sensitivity of the tropical coupled ocean-atmosphere system and suggest that the simulation of the warm-pool/cold-tongue configuration in the equatorial Pacific represents a challenging test for climate model parameterizations

Prevalence of vertebral fractures in a disease activity steered cohort of patients with early active rheumatoid arthritis

<p>Abstract</p> <p>Objective</p> <p>To determine the prevalence of vertebral fractures (VFs) after 5 years of disease activity score (DAS)-steered treatment in patients with early rheumatoid arthritis (RA) and to investigate the association of VFs with disease activity, functional ability and bone mineral density (BMD) over time.</p> <p>Methods</p> <p>Five-year radiographs of the spine of 275 patients in the BeSt study, a randomized trial comparing four treatment strategies, were used. Treatment was DAS-steered (DAS ≤ 2.4). A height reduction >20% in one vertebra was defined a vertebral fracture. With linear mixed models, DAS and Health Assessment Questionnaire (HAQ) scores over 5 years were compared for patients with and without VFs. With generalized estimating equations the association between BMD and VFs was determined.</p> <p>Results</p> <p>VFs were observed in 41/275 patients (15%). No difference in prevalence was found when stratified for gender, prednisone use and menopausal status. Disease activity over time was higher in patients with VFs, mean difference 0.20 (95% CI: 0.05-0.36), and also HAQ scores were higher, independent of disease activity, with a mean difference of 0.12 (95% CI: 0.02-0.2). Age was associated with VFs (OR 1.06, 95% CI: 1.02-1.09), mean BMD in spine and hip over time were not (OR 95% CI, 0.99: 0.78-1.25 and 0.94: 0.65-1.36, respectively).</p> <p>Conclusion</p> <p>After 5 years of DAS-steered treatment, 15% of these RA patients had VFs. Higher age was associated with the presence of VFs, mean BMD in hip and spine were not. Patients with VFs have greater functional disability over time and a higher disease activity, suggesting that VFs may be prevented by optimal disease activity suppression.</p

Two-nucleon spectral function of 16O at high momenta.

A procedure for the calculation of the two-body spectral function of a finite nucleus is presented. This spectral function is used to calculate the longitudinal part of th