Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.Comment: 42 page

Optimizing the linearity in high-speed photodiodes

Analog photonic links require high-fidelity, high-speed optical-to-electrical conversion for applications such as radio-over-fiber, synchronization at kilometer-scale facilities, and low-noise electronic signal generation. Photodetector nonlinearity is a particularly vexing problem, causing signal distortion and excess noise, especially in systems utilizing ultrashort optical pulses. Here we show that photodetectors designed for high power handling and high linearity can perform optical-to-electrical conversion of ultrashort optical pulses with unprecedented linearity over a large photocurrent range. We also show that the broadband, complex impedance of the circuit following the photodiode modifies the linearity significantly. By externally manipulating the circuit impedance, we extend the detector's linear range to higher photocurrents, with over 50 dB rejection of amplitude-to-phase conversion for photocurrents up to 40 mA. This represents a 1000-fold improvement over state-of-the-art photodiodes and significantly extends the attainable microwave power by a factor of four. As such, we eliminate the long-standing requirement in ultrashort pulse detection of precise tuning of the photodiode's operating parameters (average photocurrent, bias voltage or temperature) to coincide with a nonlinearity minimum. These results should also apply more generally to reduce nonlinear distortion in a range of other microwave photonics applications

The HERA-B Ring Imaging Cherenkov Counter

The HERA-B RICH uses a radiation path length of 2.8 m in C_4F_10 gas and a large 24 square meters spherical mirror for imaging Cherenkov rings. The photon detector consists of 2240 Hamamatsu multi-anode photomultipliers with about 27000 channels. A 2:1 reducing two-lens telescope in front of each PMT increases the sensitive area at the expense of increased pixel size, resulting in a contribution to the resolution which roughly matches that of dispersion. The counter was completed in January of 1999, and its performance has been steady and reliable over the years it has been in operation. The design performance of the RICH was fully reached: the average number of detected photons in the RICH for a beta=1 particle was found to be 33 with a single hit resolution of 0.7 mrad and 1 mrad in the fine and coarse granularity regions, respectively.Comment: 29 pages, 23 figure

Swiftly Computing Center Strings

Hufsky F, Kuchenbecker L, Jahn K, Stoye J, Böcker S. Swiftly Computing Center Strings. BMC Bioinformatics. 2011;12(1): 106

Outcome of Stage IV Completely Necrotic Wilms Tumour and Local Stage III Treated According to the SIOP 2001 Protocol

Objective: Wilms tumour (WT) patients with a localised completely necrotic nephroblastoma after preoperative chemotherapy are a favourable outcome group. Since the introduction of the SIOP 2001 protocol, the SIOP– Renal Tumour Study Group (SIOP–RTSG) has omitted radiotherapy for such patients with low-risk, local stage III in an attempt to reduce treatment burden. However, for metastatic patients with local stage III, completely necrotic WT, the recommendations led to ambiguous use. The purpose of this descriptive study is to demonstrate the outcomes of patients with metastatic, completely necrotic and local stage III WT in relation to the application of radiotherapy or not. Methods and materials: all metastatic patients with local stage III, completely necrotic WT after 6 weeks of preoperative chemotherapy who were registered in the SIOP 2001 study were included in this analysis. The pattern of recurrence according to the usage of radiation treatment and 5 year event-free survival (EFS) and overall survival (OS) was analysed. Results: seven hundred and three metastatic WT patients were registered in the SIOP 2001 database. Of them, 47 patients had a completely necrotic, local stage III WT: 45 lung metastases (11 combined localisations), 1 liver/peritoneal, and 1 tumour thrombus in the renal vein and the inferior vena cava with bilateral pulmonary arterial embolism. Abdominal radiotherapy was administered in 29 patients (62%; 29 flank/abdominal irradiation and 9 combined with lung irradiation). Eighteen patients did not receive radiotherapy. Median follow-up was 6.6 years (range 1–151 months). Two of the 47 patients (4%) developed disease recurrence in the lung (one combined with abdominal relapse) and eventually died of the disease. Both patients had received abdominal radiotherapy, one of them combined with lung irradiation. Five-year EFS and OS were 95% and 95%, respectively. Conclusions: the outcome of patients with stage IV, local stage III, completely necrotic Wilms tumours is excellent. Our results suggest that abdominal irradiation in this patient category may not be of added value in first-line treatment, consistent with the current recommendation in the SIOP–RTSG 2016 UMBRELLA protocol

Economic evaluation of pharmacogenomic-guided antiplatelet treatment in Spanish patients suffering from acute coronary syndrome participating in the U-PGx PREPARE study

BackgroundCardiovascular diseases and especially Acute Coronary Syndrome (ACS) constitute a major health issue impacting millions of patients worldwide. Being a leading cause of death and hospital admissions in many European countries including Spain, it accounts for enormous amounts of healthcare expenditures for its management. Clopidogrel is one of the oldest antiplatelet medications used as standard of care in ACS.MethodsIn this study, we performed an economic evaluation study to estimate whether a genome-guided clopidogrel treatment is cost-effective compared to conventional one in a large cohort of 243 individuals of Spanish origin suffering from ACS and treated with clopidogrel. Data were derived from the U-PGx PREPARE clinical trial. Effectiveness was measured as survival of individuals while study data on safety and efficacy, as well as on resource utilization associated with each adverse drug reaction were used to measure costs to treat these adverse drug reactions. A generalized linear regression model was used to estimate cost differences for both study groups.ResultsBased on our findings, PGx-guided treatment group is cost-effective. PGx-guided treatment demonstrated to have 50% less hospital admissions, reduced emergency visits and almost 13% less ADRs compared to the non-PGx approach with mean QALY 1.07 (95% CI, 1.04-1.10) versus 1.06 (95% CI, 1.03-1.09) for the control group, while life years for both groups were 1.24 (95% CI, 1.20-1.26) and 1.23 (95% CI, 1.19-1.26), respectively. The mean total cost of PGx-guided treatment was 50% less expensive than conventional therapy with clopidogrel [euro883 (95% UI, euro316-euro1582), compared to euro1,755 (95% UI, euro765-euro2949)].ConclusionThese findings suggest that PGx-guided clopidogrel treatment represents a cost-effective option for patients suffering from ACS in the Spanish healthcare setting.Personalised Therapeutic

Isolation of Flow and Nonflow Correlations by Two- and Four-Particle Cumulant Measurements of Azimuthal Harmonics in sNN=\sqrt{s_{_{\rm NN}}} = 200 GeV Au+Au Collisions

A data-driven method was applied to measurements of Au+Au collisions at $\sqrt{s_{_{\rm NN}}} =$ 200 GeV made with the STAR detector at RHIC to isolate pseudorapidity distance $\Delta\eta$-dependent and $\Delta\eta$-independent correlations by using two- and four-particle azimuthal cumulant measurements. We identified a component of the correlation that is $\Delta\eta$-independent, which is likely dominated by anisotropic flow and flow fluctuations. It was also found to be independent of $\eta$ within the measured range of pseudorapidity $|\eta|<1$. The relative flow fluctuation was found to be $34\% \pm 2\% (stat.) \pm 3\% (sys.)$ for particles of transverse momentum $p_{T}$ less than $2$ GeV/$c$. The $\Delta\eta$-dependent part may be attributed to nonflow correlations, and is found to be $5\% \pm 2\% (sys.)$ relative to the flow of the measured second harmonic cumulant at $|\Delta\eta| > 0.7$

Charged-to-neutral correlation at forward rapidity in Au+Au collisions at sNN\sqrt{s_{NN}}=200 GeV

Event-by-event fluctuations of the ratio of inclusive charged to photon multiplicities at forward rapidity in Au+Au collision at $\sqrt{s_{NN}}$=200 GeV have been studied. Dominant contribution to such fluctuations is expected to come from correlated production of charged and neutral pions. We search for evidences of dynamical fluctuations of different physical origins. Observables constructed out of moments of multiplicities are used as measures of fluctuations. Mixed events and model calculations are used as baselines. Results are compared to the dynamical net-charge fluctuations measured in the same acceptance. A non-zero statistically significant signal of dynamical fluctuations is observed in excess to the model prediction when charged particles and photons are measured in the same acceptance. We find that, unlike dynamical net-charge fluctuation, charge-neutral fluctuation is not dominated by correlation due to particle decay. Results are compared to the expectations based on the generic production mechanism of pions due to isospin symmetry, for which no significant (<1%) deviation is observed.Comment: 14 pages, 6 figure