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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

3D localization of electrophysiology catheters from a single x-ray cone-beam projection

Purpose: X-ray images allow the visualization of percutaneous devices such as catheters in real time but inherently lack depth information. The provision of 3D localization of these devices from cone beam x-ray projections would be advantageous for interventions such as electrophysiology (EP), whereby the operator needs to return a device to the same anatomical locations during the procedure. A method to achieve real-time 3D single view localization (SVL) of an object of known geometry from a single x-ray image is presented. SVL exploits the change in the magnification of an object as its distance from the x-ray source is varied. The x-ray projection of an object of interest is compared to a synthetic x-ray projection of a model of said object as its pose is varied. Methods: SVL was tested with a 3 mm spherical marker and an electrophysiology catheter. The effect of x-ray acquisition parameters on SVL was investigated. An independent reference localization method was developed to compare results when imaging a catheter translated via a computer controlled three-axes stage. SVL was also performed on clinical fluoroscopy image sequences. A commercial navigation system was used in some clinical image sequences for comparison. Results: SVL estimates exhibited little change as x-ray acquisition parameters were varied. The reproducibility of catheter position estimates in phantoms denoted by the standard deviations, (σ{sub x}, σ{sub y}, σ{sub z}) = (0.099 mm, 0.093 mm, 2.2 mm), where x and y are parallel to the detector plane and z is the distance from the x-ray source. Position estimates (x, y, z) exhibited a 4% systematic error (underestimation) when compared to the reference method. The authors demonstrated that EP catheters can be tracked in clinical fluoroscopic images. Conclusions: It has been shown that EP catheters can be localized in real time in phantoms and clinical images at fluoroscopic exposure rates. Further work is required to characterize performance in clinical images as well as the sensitivity to clinical image quality.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Dosimetric evaluation of three adaptive strategies for prostate cancer treatment including pelvic lymph nodes irradiation

Purpose: The movements of the prostate relative to the pelvic lymph nodes during intensity-modulated radiation therapy treatment can limit margin reduction and affect the protection of the organs at risk (OAR). In this study, the authors performed an analysis of three adaptive treatment strategies that combine information from both bony and gold marker registrations. The robustness of those treatments against the interfraction prostate movements was evaluated. Methods: A retrospective study was conducted on five prostate cancer patients with 7–13 daily cone-beam CTs (CBCTs). The clinical target volumes (CTVs) consisting of pelvic lymph nodes, prostate, and seminal vesicles as well as the OARs were delineated on each CBCT and the initial CT. Three adaptive strategies were analyzed. Two of these methods relied on a two-step patient positioning at each fraction. First step: a bony registration was used to deliver the nodal CTV prescription. Second step: a gold marker registration was then used either to (1) complete the dose delivered to the prostate (complement); (2) or give almost the entire prescription to the prostate with a weak dose gradient between the targets to compensate for possible motions (gradient). The third method (COR) used a pool of precalculated plans based on images acquired at previous treatment fractions. At each new fraction, a plan is selected from that pool based on the daily position of prostate center-of-mass. The dosimetric comparison was conducted and results are presented with and without the systematic shift in the prostate position on the CT planning. The adaptive strategies were compared to the current clinical standard where all fractions are treated with the initial nonadaptive plan. Results: The minimum daily prostate D{sub 95%} is improved by 2%, 9%, and 6% for the complement, the gradient, and the COR approaches, respectively, compared to the nonadaptive method. The average nodal CTV D{sub 95%} remains constant across the strategies, except for the gradient approach where a reduction of 7% is observed. However, a correction of the systematic shift reduced the problem, and the adaptive strategies remain robust against the prostate movement across the fraction. The bladder V{sub 55Gy} is reduced by 35% on average for the adaptive strategies. Conclusions: Because they offer increased CTV coverage and OAR sparing, adaptive methods may be suitable candidates for simple and efficient adaptive treatment strategies for prostate cancer. Margin reduction and systematic error correction in the prostate position improve the protection of the OAR and the dose coverage. A cumulative dose to simulate a complete treatment would show real effects and allow a better comparison between each method.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Enhancing atlas based segmentation with multiclass linear classifiers

Purpose: To present a method to enrich atlases for atlas based segmentation. Such enriched atlases can then be used as a single atlas or within a multiatlas framework. Methods: In this paper, machine learning techniques have been used to enhance the atlas based segmentation approach. The enhanced atlas defined in this work is a pair composed of a gray level image alongside an image of multiclass classifiers with one classifier per voxel. Each classifier embeds local information from the whole training dataset that allows for the correction of some systematic errors in the segmentation and accounts for the possible local registration errors. The authors also propose to use these images of classifiers within a multiatlas framework: results produced by a set of such local classifier atlases can be combined using a label fusion method. Results: Experiments have been made on the in vivo images of the IBSR dataset and a comparison has been made with several state-of-the-art methods such as FreeSurfer and the multiatlas nonlocal patch based method of Coupé or Rousseau. These experiments show that their method is competitive with state-of-the-art methods while having a low computational cost. Further enhancement has also been obtained with a multiatlas version of their method. It is also shown that, in this case, nonlocal fusion is unnecessary. The multiatlas fusion can therefore be done efficiently. Conclusions: The single atlas version has similar quality as state-of-the-arts multiatlas methods but with the computational cost of a naive single atlas segmentation. The multiatlas version offers a improvement in quality and can be done efficiently without a nonlocal strategy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-C-BRB-05: Determining the Adequacy of Auto-Contouring Via Probabilistic Assessment of Ensuing Treatment Plan Metrics in Comparison with Manual Contours

Purpose: To determine if auto-contour and manual-contour—based plans differ when evaluated with respect to probabilistic coverage metrics and biological model endpoints for prostate IMRT. Methods: Manual and auto-contours were created for 149 CT image sets acquired from 16 unique prostate patients. A single physician manually contoured all images. Auto-contouring was completed utilizing Pinnacle’s Smart Probabilistic Image Contouring Engine (SPICE). For each CT, three different 78 Gy/39 fraction 7-beam IMRT plans are created; PD with drawn ROIs, PAS with auto-contoured ROIs, and PM with auto-contoured OARs with the manually drawn target. For each plan, 1000 virtual treatment simulations with different sampled systematic errors for each simulation and a different sampled random error for each fraction were performed using our in-house GPU-accelerated robustness analyzer tool which reports the statistical probability of achieving dose-volume metrics, NTCP, TCP, and the probability of achieving the optimization criteria for both auto-contoured (AS) and manually drawn (D) ROIs. Metrics are reported for all possible cross-evaluation pairs of ROI types (AS,D) and planning scenarios (PD,PAS,PM). Bhattacharyya coefficient (BC) is calculated to measure the PDF similarities for the dose-volume metric, NTCP, TCP, and objectives with respect to the manually drawn contour evaluated on base plan (D-PD). Results: We observe high BC values (BC≥0.94) for all OAR objectives. BC values of max dose objective on CTV also signify high resemblance (BC≥0.93) between the distributions. On the other hand, BC values for CTV’s D95 and Dmin objectives are small for AS-PM, AS-PD. NTCP distributions are similar across all evaluation pairs, while TCP distributions of AS-PM, AS-PD sustain variations up to %6 compared to other evaluated pairs. Conclusion: No significant probabilistic differences are observed in the metrics when auto-contoured OARs are used. The prostate auto-contour needs improvement to achieve clinically equivalent plans.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-J-195: On the Performance of Four Dual Energy CT Formalisms for Extracting Proton Stopping Powers

Purpose: Dual energy CT can predict stopping power ratios (SPR) for ion therapy treatment planning. Several approaches have been proposed recently, however accuracy and practicability in a clinical workflow are unaddressed. The aim of this work is to provide a fair comparison of available approaches in a human-like phantom to find the optimal method for tissue characterization in a clinical situation. Methods: The SPR determination accuracy is investigated using simulated DECT images. A virtual human-like phantom is created containing 14 different standard human tissues. SECT (120 kV) and DECT images (100 kV and 140 kV Sn) are simulated using the software ImaSim. The single energy CT (SECT) stoichiometric calibration method and four recently published calibration-based DECT methods are implemented and used to predict the SPRs from simulated images. The difference between SPR predictions and theoretical SPR are compared pixelwize. Mean, standard deviation and skewness of the SPR difference distributions are used as measures for bias, dispersion and symmetry. Results: The average SPR differences and standard deviations are (0.22 ± 1.27)% for SECT, and A) (−0.26 ± 1.30)%, B) (0.08 ± 1.12)%, C) (0.06 ± 1.15)% and D) (−0.05 ± 1.05)% for the four DECT methods. While SPR prediction using SECT is showing a systematic error on SPR, the DECT methods B, C and D are unbiased. The skewness of the SECT distribution is 0.57%, and A) −0.19%, B) −0.56%, C) −0.29% and D) −0.07% for DECT methods respectively. Conclusion: The here presented DECT methods B, C and D outperform the commonly used SECT stoichiometric calibration. These methods predict SPR accurately without a bias and within ± 1.2% (68th percentile). This indicates that DECT potentially improves accuracy of range predictions in proton therapy. A validation of these findings using clinical CT images of real tissues is necessary.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-300: Impact of Electron Density Modeling of ArcCHECK Cylindricaldiode Array On 3DVH Patient Specific QA Software Tool Analysis

Purpose: 3DVH software is a patient specific quality assurance tool which estimates the 3D dose to the patient specific geometry with the help of Planned Dose Perturbation algorithm. The purpose of this study is to evaluate the impact of HU value of ArcCHECK phantom entered in Eclipse TPS on 3D dose & DVH QA analysis. Methods: Manufacturer of ArcCHECK phantom provides CT data set of phantom & recommends considering it as a homogeneous phantom with electron density (1.19 gm/cc or 282 HU) close to PMMA. We performed this study on Eclipse TPS (V13, VMS) & trueBEAM STx VMS Linac & ArcCHECK phantom (SNC). Plans were generated for 6MV photon beam, 20cm×20cm field size at isocentre & SPD (Source to phantom distance) of 86.7 cm to deliver 100cGy at isocentre. 3DVH software requires patients DICOM data generated by TPS & plan delivered on ArcCHECK phantom. Plans were generated in TPS by assigning different HU values to phantom. We analyzed gamma index & the dose profile for all plans along vertical down direction of beam’s central axis for Entry, Exit & Isocentre dose. Results: The global gamma passing rate (2% & 2mm) for manufacturer recommended HU value 282 was 96.3%. Detector entry, Isocentre & detector exit Doses were 1.9048 (1.9270), 1.00(1.0199) & 0.5078(0.527) Gy for TPS (Measured) respectively.The global gamma passing rate for electron density 1.1302 gm/cc was 98.6%. Detector entry, Isocentre & detector exit Doses were 1.8714 (1.8873), 1.00(0.9988) & 0.5211(0.516) Gy for TPS (Measured) respectively. Conclusion: Electron density value assigned by manufacturer does not hold true for every user. Proper modeling of electron density of ArcCHECK in TPS is essential to avoid systematic error in dose calculation of patient specific QA.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-394: Impact of PTV Margins With Taking Into Account Shape Variation On IMRT Plans For Prostate Cancer

Purpose: The purpose of this study was to investigate the impact of planning target volume (PTV) margins with taking into consideration clinical target volume (CTV) shape variations on treatment plans of intensity modulated radiation therapy (IMRT) for prostate cancer. Methods: The systematic errors and the random errors for patient setup errors in right-left (RL), anterior-posterior (AP), and superior-inferior (SI) directions were obtained from data of 20 patients, and those for CTV shape variations were calculated from 10 patients, who were weekly scanned using cone beam computed tomography (CBCT). The setup error was defined as the difference in prostate centers between planning CT and CBCT images after bone-based registrations. CTV shape variations of high, intermediate and low risk CTVs were calculated for each patient from variances of interfractional shape variations on each vertex of three-dimensional CTV point distributions, which were manually obtained from CTV contours on the CBCT images. PTV margins were calculated using the setup errors with and without CTV shape variations for each risk CTV. Six treatment plans were retrospectively made by using the PTV margins with and without CTV shape variations for the three risk CTVs of 5 test patients. Furthermore, the treatment plans were applied to CBCT images for investigating the impact of shape variations on PTV margins. Results: The percentages of population to cover with the PTV, which satisfies the CTV D98 of 95%, with and without the shape variations were 89.7% and 74.4% for high risk, 89.7% and 76.9% for intermediate risk, 84.6% and 76.9% for low risk, respectively. Conclusion: PTV margins taking into account CTV shape variation provide significant improvement of applicable percentage of population (P < 0.05). This study suggested that CTV shape variation should be taken consideration into determination of the PTV margins.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Sensitive detection of structural dynamics using a statistical framework for comparative crystallography

Chemical and conformational changes are crucial to protein function and its pharmacological control. X-ray crystallography can reveal these changes in atomic detail, but standard analysis methods, which refine separate datasets, often overlook differences that are subtle or arise in only a subset of molecules. Direct comparison of crystallographic datasets is, in principle, more powerful, but systematic errors (“scales”) often mask changes in the crystallographic observables (“structure factors”). Machine learning algorithms that jointly estimate scales and structure factors can address this limitation. Here, we augment this approach with multivariate, structured priors derived from crystallographic theory, implemented in the variational deep learning framework Careless. Doing so strongly improves the detection of protein dynamics, element-specific anomalous signals, and the binding of drug candidates, offering a robust approach to comparative crystallography and, potentially, to detection of protein dynamics by other structure determination methods.

Hekstra, Doeke R. [Harvard Univ., Cambridge, MA (U↗
DOE OSTI2025

Global models predict clouds at the wrong time of day: Does it matter for radiation and climate?

Accurate prediction of future climate change hinges upon the ability of Earth system models (ESMs) to simulate clouds and their radiative effects. Even if an ESM can simulate the correct clouds, a systematic error in the amount of sunlight reflected by clouds (and, thus, cloud radiative effect) can exist if the clouds are simulated at the incorrect time of day. In this work, we develop an analytical model connecting diurnal cloud biases to emergent mean state radiative biases. With the use of satellite observations, we demonstrate that there are errors in the time of day that clouds are occurring in ESMs that would cause bias in shortwave cloud radiative effect (SWCRE) that is greater than 45% of the total SWCRE bias, but such errors in the cloud diurnal cycle are masked by other compensating errors, indicating that these ESMs are getting the right answer for the wrong reasons.

Geosciences↗
DOE OSTI2016

Neutron electric dipole moment and possibilities of increasing accuracy of experiments

The paper reports the results of an experiment on searching for the neutron electric dipole moment (EDM), performed on the ILL reactor (Grenoble, France). The double-chamber magnetic resonance spectrometer (Petersburg Nuclear Physics Institute (PNPI)) with prolonged holding of ultra cold neutrons has been used. Sources of possible systematic errors are analyzed, and their influence on the measurement results is estimated. The ways and prospects of increasing accuracy of the experiment are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Structural Analysis of Sr{sub 3}NbFe{sub 3}Si{sub 2}O{sub 14} Single Crystal from the Langasite Family and Finding of Negative Thermal Expansion in the Range of 83–110 K

Iron-containing Sr{sub 3}NbFe{sub 3}Si{sub 2}O{sub 14} single crystals from the langasite family, which are interesting for researchers due to their magnetic ordering at T{sub N} = 26 K, have been grown by the floating zone melting method. Accurate X-ray diffraction analysis is performed at 293 and 90.5 K using the data collected on a CCD diffractometer. To compensate for systematic errors, two data sets are collected at each temperature. The structure is refined based on averaged data set: sp. gr. P321, Z = 1, sin θ/λ ≤ 1.35 Å{sup –1}; a = 8.2609(4) Å, c = 5.1313(3) Å at 293 K and a = 8.2344(6) Å, c = 5.1243(6) Å at 90.5 K; the agreement factors are R/wR = 1.18/1.03% and Δρ{sub min}/Δρ{sub max} =–0.57/0.25 e/Å3 for 3583 independent reflections at 293 K and R/wR = 1.18/1.13% and Δρ{sub min}/Δρ{sub max} =–0.54/0.23 e/Å3 for 3638 reflections at 90.5 K. Negative thermal expansion in the direction of the cell c axis is revealed in the range of 83–110 K.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Data on photoneutron reactions from various experiments for {sup 133}Cs, {sup 138}Ba and {sup 209}Bi nuclei

Basic methods for determining cross sections for photoneutron partial reactions are examined. They are obtained directly in experiments with quasimonoeneregetic annihilation photons or from the cross section for the (γ, xn) = (γ, 1n) + 2(γ, 2n) + 3(γ, 3n) +... neutron-yield reaction in experiments with bremsstrahlung photons by introducing corrections based on statistical nuclear-reaction theory. The difference in the conditions of these experiments, which leads to discrepancies between their results because of sizable systematic errors, is analyzed. Physical criteria are used to study the reliability of data on the photodisintegration of {sup 133}Cs, {sup 138}Ba, and {sup 209}Bi nuclei. The cross sections for partial and total reactions satisfying the reliability criteria are evaluated within the experimental–theoretical method (σ{sup eval}(γ, in) = F{sub i}{sup theor} × σ{sup expt}(γ, xn)) on the basis of the experimental cross sections σ{sup expt}(γ, xn) and the results of the calculations within the combined model of photonuclear reactions.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Two examples of in-flight spin flippers

In precise experiments with polarized beam it’s very often appear a necessity to change beam polarization on opposite. If such operation does not change other beam parameters, it helps to avoid or minimize some systematic errors. It is especially important in experiments, where spin dependent effect is small enough. This paper describes two set of equipments, that make spin flip for extracted beams. In both cases, these devices are absolutely distinct, because they are appropriate for different particles and at different energy range. The first of them is intended for future muon (g-2) experiment, which is under preparation now at JPARC. Here, the muon spin flip will be done by chain of electrostatic and magnetic bends at the kinetic energy 340 keV. A beam matching is provided by a number of short solenoids. The other flipper (or Siberian snake) will rotate spin of protons or antiprotons, which come from Λ-meson decay with the energy up to 40 GeV. This experiment (no. 24) is planed at IHEP, Protvino. In this case, two superconducting helical magnets with opposite helicities and magnetic field 4.5 T will be used. To correct beam trajectory, additional dipole correctors are required.

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

Detection of reflected Cherenkov light from extensive air showers in the SPHERE experiment as a method of studying superhigh energy cosmic rays

Although a large number of experiments were carried out during the last few decades, the uncertainty in the spectrum of all nuclei of primary cosmic rays (PCRs) with superhigh energies is still high, and the results of many experiments on nuclear composition of PCRs are contradictory. An overview of the SPHERE experiment on detecting Vavilov-Cherenkov radiation from extensive air shower (EAS) reflected from a ground snow surface is given. A number of experimental studies implementing this method are presented and their results are analyzed. Some other popular methods of studying PCRs with superhigh energies (E{sub 0} > 10{sup 15} eV) and their main advantages and drawbacks are briefly considered. The detecting equipment of the SPHERE-2 experiment and the technique of its calibration are considered. The optical properties of snow, which are important for experiments on reflected Cherenkov light (CL) from EAS, are discussed and the history of observing reflected EAS CL is described. The algorithm of simulating the detector response and calculating the fiducial acceptance of shower detection is described. The procedure of processing the experimental data with a subsequent reconstruction of the spectrum of all PCR nuclei and analysis of the mass composition is shown. The first results of reconstructing the spectrum and separating groups of cosmic-ray nuclei with high energies in the SPHERE-2 experiment are presented. Main sources of systematic errors are considered. The prospects of developing the technique of observation of reflected EAS CL in future experiments are discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Current status of new SAGE project with 51 Cr neutrino source

A very short-baseline neutrino oscillation experiment with an intense 51 Cr neutrino source is currently under construction at the Baksan Neutrino Observatory of the Institute for Nuclear Research RAS (BNO). The experiment, which is based on the existing SAGE experiment, will use an upgraded Gallium-Germanium Neutrino Telescope (GGNT) and an artificial 51 Cr neutrino source with activity ~3 MCi to search for transitions of active neutrinos to sterile states with Δm 2 ~1 eV 2 . The neutrino source will be placed in the center of a liquid Ga metal target that is divided into two concentric zones, internal and external. The average path length of neutrinos in each zone will be the same and the neutrino capture rate will be measured separately in each zone. The oscillation signature, which comes from the ratio of events in the near and far gallium volumes, will be largely free of systematic errors, such as may occur from cross section and source strength uncertainties, and will provide a clean signal of electron neutrino disappearance into a sterile state at baselines of about 0.6 and 2.0 m. The sensitivity to the disappearance of electron neutrinos is expected to be a few percent. Construction of this set of new facilities, including a two-zone tank for irradiation of 50 tons of Ga metal with the intense 51 Cr source, as well as additional modules of the GGNT counting and extraction systems, is close to completion. In order to check the new facilities they will first be used for SAGE solar neutrino measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Limits of Majorana neutrino mass from combined analysis of data from {sup 76}Ge and {sup 136}Xe neutrinoless double beta decay experiments

We present effective Majorana neutrino mass limits obtained from the joint analysis of the recently published results of {sup 76}Ge and {sup 136}Xe neutrinoless double beta decay (0νββ) experiments, which was carried out by using the Bayesian calculations. Nuclear matrix elements (NMEs) used for the analysis are taken from the works, in which NMEs of {sup 76}Ge and {sup 136}Xe were simultaneously calculated. This reduced systematic errors connected with NME calculation techniques. The new effective Majorana neutrino mass limits less than [85.4–197.0] meV are much closer to the inverse neutrino mass hierarchy region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Latest results from Double Chooz

Double Chooz is a short-baseline neutrino disappearance experiment. It detects ν̄{sub e }produced in the power plant of Chooz, France, where is located. The main goal of the experiment is the measurement of θ{sub 13} mixing angle and in 2011 for the first time the experiment observed an indication for a non zero value of such an oscillation parameter. The mixing angle was successively measured using only the far detector finding the best fit value of sin{sup 2}(2θ{sub 13}) = 0.090{sup +0.032}{sub −0.029} . The near detector is under construction and will start data taking by the middle of 2014 allowing the reduction of the systematic errors. In this paper I make a review of the Double Chooz experiment, focusing in particular on the latest results of the measurement of the mixing angle θ{sub 13} relying on the neutron absorption on Gadolinium. I also present results proving the capability of Double Chooz to identify the ortho-positronium. This has been done in an event-by-event basis for the first time in a large liquid scintillator experiments, and can be an additional handle for the electron/positron discrimination in future detectors based on such technology.

42 ENGINEERING↗
DOE OSTI2018

Sterile Neutrino Search in the Neutrino-4 Experiment at the SM-3 Reactor

First results on the energy spectrum and flux of reactor antineutrinos as a function of the distance L from the reactor core, measured in the Neutrino-4 experiment for 6 < L < 12 m, are presented. The flux L ‑dependence fits to the 1/ L {sup 2} form with a statistical significance of ~10% corresponding to 1.64σ, so that the measured spectrum deviates from the 1/ L {sup 2} law at a confidence level ~90%. The measured energy spectrum deviates from the predicted one at a similar confidence level ~90%. That both deviations are best described with oscillation parameters in the same regions of Δm{sub 14}{sup 2}≈0.7-0.8 eV{sup 2}and sin{sup 2}2Θ{sub 14}≈0.10-0.15 boosts the overall confidence level to ~95% (2σ). These results suggest that antineutrinos oscillate to a sterile state, but still fall short of reliably establishing the oscillation phenomenon. At present, the possibility of mimicking the oscillation effect by systematic errors cannot be completely excluded.

79 ASTRONOMY AND ASTROPHYSICS↗