Geometrical Setup Research Articles

Normal coordinates based on curved tangent space

Riemann normal coordinates (RNC) at a regular event $p_0$ of a spacetime manifold $\mathcal{M}$ are constructed by imposing: (i) $g_{\textsf{ab}}|_{p_0}=\eta_{ab}$, and (ii) $\Gamma^\textsf{a}_{\phantom{\textsf a}\textsf{bc}}|_{p_0}=0$. There is, however, a third, $independent$, assumption in the definition of RNC which essentially fixes the $density$ $of$ $geodesics$ emanating from $p_0$ to its value in flat spacetime, viz.: (iii) the tangent space $\mathcal{T}_{p_0}(\mathcal{M})$ is $flat$. We relax (iii) and obtain the normal coordinates, along with the metric $g_{\textsf{ab}}$, when $\mathcal{T}_{p_0}(\mathcal{M})$ is a maximally symmetric manifold $\widetilde{\mathcal M}_{\Lambda}$ with curvature length $|\Lambda|^{-1/2}$. In general, the "rest" frame defined by these coordinates is non-inertial with an additional acceleration $\boldsymbol a = - ({\Lambda}/3) \, \boldsymbol x$ depending on the curvature of tangent space. Our geometric set-up provides a convenient probe of local physics in a universe with a cosmological constant $\Lambda$, now embedded into the local structure of spacetime as a fundamental constant associated with a curved tangent space. We discuss classical and quantum implications of the same.

Automated Detection of Interesting Properties in Regular Polygons

We demonstrate a systematic, automated way of discovery of a large number of new geometry theorems on regular polygons. The applied theory includes a formula by Watkins and Zeitlin on minimal polynomials of cos frac{2pi }{n}, and a method by Recio and Vélez to discover a property in a plane geometry construction. This method exploits Wu’s idea on algebraizing the geometric setup and utilizes the theory of Gröbner bases. Also a bijective function is given that maps the investigated cases to the first natural numbers. Finally, several examples are shown that are all previously unknown results in planar Euclidean geometry.

Covariant mass and geometrical setup in Euclidean gauge theories

A nonlocal mass operator can be consistently set in local form through the introduction of a set of additional fields with geometrical appropriated properties. A local and polynomial gauge invariant action is thus identified. Equations compatible with the study of renormalization, from the algebraic point of view, are presented in the Landau Gauge.

Physical Features and Deep Learning-based Appearance Features for Vehicle Classification from Rear View Videos

Currently, there are many approaches for vehicle classification, but there is no specific study on automated, rear view, and video-based robust vehicle classification. The rear view is important for intelligent transportation systems since not all states in the United States require a frontal license plate on a vehicle. The classification of vehicles, from their rear views, is challenging since vehicles have only subtle appearance differences and there are changing illumination conditions and the presence of moving shadows. In this paper, we present a novel multi-class vehicle classification system that classifies a vehicle into one of four possible classes (sedan, minivan, SUV, and a pickup truck) from its rear view video, using physical and visual features. For a given geometric setup of the camera on highways, we make physical measurements on a vehicle. These measurements include visual rear ground clearance, the height of the vehicle, and the distance between the license plate and the rear bumper. We call these distances as the physical features. The visual features, also called appearance-based features, are extracted using convolutional neural networks from the input images. We achieve a classification accuracy of 93.22% and 91.52% using physical and visual features, respectively. Furthermore, we achieve a higher classification accuracy of 94.81% by fusing both the features together. The results are shown on a dataset consisting of 1831 rear view videos of vehicles and they are compared with various approaches, including deep learning techniques.

Cellular dosimetry of [177Lu]Lu-DOTA-[Tyr3]octreotate radionuclide therapy: the impact of modeling assumptions on the correlation with in vitro cytotoxicity

BackgroundSurvival and linear-quadratic model fitting parameters implemented in treatment planning for targeted radionuclide therapy depend on accurate cellular dosimetry. Therefore, we have built a refined cellular dosimetry model for [177Lu]Lu-DOTA-[Tyr3]octreotate (177Lu-DOTATATE) in vitro experiments, accounting for specific cell morphologies and sub-cellular radioactivity distributions.MethodsTime activity curves were measured and modeled for medium, membrane-bound, and internalized activity fractions over 6 days. Clonogenic survival assays were performed at various added activities (0.1–2.5 MBq/ml). 3D microscopy images (stained for cytoplasm, nucleus, and Golgi) were used as reference for developing polygonal meshes (PM) in 3DsMax to accurately render the cellular and organelle geometry. Absorbed doses to the nucleus per decay (S values) were calculated for 3 cellular morphologies: spheres (MIRDcell), truncated cone-shaped constructive solid geometry (CSG within MCNP6.1), and realistic PM models, using Geant4-10.03. The geometrical set-up of the clonogenic survival assays was modeled, including dynamic changes in proliferation, proximity variations, and cell death. The absorbed dose to the nucleus by the radioactive source cell (self-dose) and surrounding source cells (cross-dose) was calculated applying the MIRD formalism. Finally, the correlation between absorbed dose and survival fraction was fitted using a linear dose-response curve (high α/β or fast sub-lethal damage repair half-life) for different assumptions, related to cellular shape and localization of the internalized fraction of activity.ResultsThe cross-dose, depending on cell proximity and colony formation, is a minor (15%) contributor to the total absorbed dose. Cellular volume (inverse exponential trend), shape modeling (up to 65%), and internalized source localization (up to + 149% comparing cytoplasm to Golgi) significantly influence the self-dose to nucleus. The absorbed dose delivered to the nucleus during a clonogenic survival assay is 3-fold higher with MIRDcell compared to the polygonal mesh structures. Our cellular dosimetry model indicates that 177Lu-DOTATATE treatment might be more effective than suggested by average spherical cell dosimetry, predicting a lower absorbed dose for the same cellular survival. Dose-rate effects and heterogeneous dose delivery might account for differences in dose-response compared to x-ray irradiation.ConclusionOur results demonstrate that modeling of cellular and organelle geometry is crucial to perform accurate in vitro dosimetry.

Heavily Doped Semiconductor Metamaterials for Mid‐Infrared Multispectral Perfect Absorption and Thermal Emission

AbstractA metamaterial perfect absorber based on layered, doped and undoped semiconductors is experimentally and theoretically investigated. Design rules are given to control the multispectral, narrow, strong absorption features (>98% absorption) in the mid‐IR spectrum. The proposed sub‐wavelength grating structures support localized surface plasmons and photonic resonances associated to the quarter wavelength optical thickness of the undoped spacer layer. The resonances hybridize depending on the geometric setup of the metamaterial and the material properties of the heavily doped semiconductor. The angular response of the resonances is studied to determine the acceptance angle. While the absorption is best at near‐normal incidence, the spectral position of the absorption bands is weakly dependent on the angular incidence up to angles of 45°. Complementary to the polarization‐dependent grating design of the metamaterial, an alternative based on a crossed grating nanopattern is also investigated for polarization insensitivity. Furthermore, it is demonstrated that the metamaterial perfect absorber provides a tailored thermal emission spectrum. Based on the heavily doped InAsSb/GaSb metamaterial platform, integrable and miniaturized perfect absorbers and thermal sources can be built.

Low-dimensional moderators at ESS and compact neutron sources

Low-dimensional moderators were designed for the European Spallation Source (ESS), and the same concepts can be applied to compact sources. At ESS, quasi two-dimensional (2D) high-brightness moderators will serve all the instruments of the initial suite. The design of the moderators is influenced by several factors, such as the layout of the facility, the requirements for beam extraction, and the number of instruments; these constraints led to the choice of the 2D “butterfly” moderator for ESS. In an accelerator-based compact source, such moderators can be designed in an even more efficient way than for high-power sources, taking advantage of the lower heat loads and of the more compact arrangement of the target-moderator system, which gives more freedom in the optimization of the geometrical setup. Some promising design options have been explored.

On the Geometry of Bayesian Inference

We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the observation that the marginal likelihood can be regarded as an inner product between the prior and the likelihood. A key concept in our geometry is that of compatibility, a measure which is based on the same construction principles as Pearson correlation, but which can be used to assess how much the prior agrees with the likelihood, to gauge the sensitivity of the posterior to the prior, and to quantify the coherency of the opinions of two experts. Estimators for all the quantities involved in our geometric setup are discussed, which can be directly computed from the posterior simulation output. Some examples are used to illustrate our methods, including data related to on-the-job drug usage, midge wing length, and prostate cancer.

Decoupling network for Tx/Rx body coil for 7T MRI

The parallel imaging technique is widely used in 7T MRI scanners. It employs multichannel RF coil arrays to apply a concurrent excitation and acquisition method. Concurrent excitation faces significant challenges in terms of electromagnetic coupling between the RF coil elements. In order to prevent interference between the RF coil elements' exciters, several decoupling methods have been developed to compensate for coupling and to permit independent work for the exciters. This paper studies the coupling between meander coils arranged in two different geometrical setups and investigates the isolation performance between the coils by applying two different decoupling networks depending on the geometrical setup of the coils. These two decoupling networks in addition to a T-shaped decoupling network have been integrated into a Tx/Rx body coil for 7 T to compensate for mutual coupling between array coil elements. The results have been obtained by using CST Microwave Studio (CST AG, Darmstadt, Germany)

Single- and double-helix vortex breakdown as two dominant global modes in turbulent swirling jet flow

In this paper, we study the shape and dynamics of helical coherent structures found in the flow field of an annular swirling jet undergoing vortex breakdown. The flow field is studied by means of time-resolved tomographic particle image velocimetry measurements. The obtained flow fields are analysed using both classic and spectral proper orthogonal decomposition. Despite the simple geometrical set-up of the annular jet, the flow field is very complex. Two distinct large-scale helical flow structures are identified: a single and a double helix, both co-rotating with the swirl direction, and it is revealed that these structures are not higher harmonics of each other. The structures have a relatively low energy content which makes it hard to separate them from other dynamics of the flow field, notably turbulent motions. Because of this, classic proper orthogonal decomposition fails to identify both structures properly. Spectral proper orthogonal decomposition, on the other hand, allows them to be identified accurately when the filter size is set at around eight times the precession period. The precession frequencies of the single and double helices correspond to Strouhal numbers of 0.273 and , respectively. A global stability analysis of the mean flow field shows that these structures correspond to two separate global modes. The precessing frequencies obtained by the stability analysis and the related spatial structures match very well with the experimental observations. The current work extends our knowledge on turbulent vortex breakdown and on mean field global stability theory in general. It leads to the following conclusions. Firstly, single- and double-helix vortex breakdown are both manifestations of global modes. Previous studies have shown that both and modes can coexist in swirling jets. However, the mode has been identified as a second harmonic of the first mode, while this study identifies both as two independent global modes. Secondly, this work shows that the simultaneous occurrence of multiple helical global modes is possible within a turbulent flow and their shapes and frequencies are very well predicted by mean field stability analysis. The latter finding is of general interest as it applies to a wide class of fluid problems dominated by multiple oscillatory structures.

Relaxation of Residual Stresses in Bearing Rings Based on the Optimal Geometric Setup of Equipment for Centerless Running

This paper discusses the technological method of residual stress relaxation of bearing rings by centerless running with cylindrical rolls. Described a new approach to relieve residual stresses by centerless running of elastically-deforming rolls on the basis of the geometrical setup of the equipment. It was found that geometrical setup of the equipment influences an elastic strain of parts and the degree of residual stress relaxation. We obtained a mathematical model for calculation of setup parameters to ensure the required variation value of elastic strain of the part. The results of experiments confirm the influence of the geometric setup on the magnitude of residual stress relaxation.

Correlated magnetic noise from anisotropic lightning sources and the detection of stochastic gravitational waves

Direct detection of gravitational waves (GWs) from compact binary systems suggests that the merger rate of such events is large, and the sum of their GWs can be viewed as stochastic signals. Because of its random nature, cross-correlating the signals from multiple detectors is essential to disentangle the GWs from instrumental noise. However, the global magnetic fields in the Earth-ionosphere cavity produce the environmental disturbances at low-frequency bands, known as Schumann resonances, and coupled with GW detectors, they potentially contaminate the stochastic GW signal as a correlated noise. Previously, we have presented a simple analytical model to estimate its impact on the detection of stochastic GWs. Here, extending the analysis to further take account of the effects of anisotropic lightning source distributions, we present a comprehensive study of the impact of correlated magnetic noise at low-frequency bands, including non-tensor-type GWs, as well as circularly polarized tensor-type GWs. We find that as opposed to a naive expectation, the impact of correlated magnetic noise does not always increase with anisotropies in the lighting source distribution. Even in the presence of large anisotropies, there is a robust detector pair for which the amplitude of correlated magnetic noise becomes comparable to or well below detectable amplitude of stochastic GWs. The results indicate that the properties of the correlated magnetic noise depend crucially on both the geometrical and geographical setup of the detector's pair, and Virgo and KAGRA would be potentially the most insensitive detector pair against the correlated magnetic for both tensor- and non-tensor-type stochastic GWs.

AN INTEGRATED SYSTEM FOR PROCESS-FIXTURE LAYOUT DESIGN OPTIMISATION FOR CUBICAL PARTS

In this article, an integrated computer-assisted process-planning and computer-assisted fixture layout planning system is presented for the automatic generation of process and fixture maps. The part feature model is created using various algorithms and the geometric reasoning approach. The feature-based methodology based on the machining database is then applied for the generation of process maps. The setup scheme algorithm allocates each feature to a definite setup based on its location. The part geometric database and setup plan aids the fixture layout planning process. During fixture layout planning, the standard fixture rules are applied to determine the locating arrangement and feasible datum along with the suitable positions using a fixture database for initial fixture layout planning data. Visual C++ is used to implement the proposed methodology because it interacts with current computer-aided design software. Then a case study is presented to develop an initial fixture layout. Afterwards, the ANSYS parametric design language optimisation tool is applied to automatically optimise locator and clamp positions that yield minimum workpiece deformation. At the end, finite element analysis results depicting deformation magnitudes are presented.

Characterization of the effects of detector angular misalignments and accuracy enhancement of X-ray CT dimensional measurements

Characterization of the effects of detector angular misalignments and accuracy enhancement of X-ray CT dimensional measurements

Exposure-time Correction for the ZTF Camera

A correction factor is derived to account for nonuniformities in the exposure time as seen by different positions on the focal plane of the ZTF camera. These nonuniformities arise from a combination of the shutter opening and closing motion; the geometrical setup of the telescope; and the presence of obstructions in the beam beyond the pupil plane. The correction to the exposure time is measured by comparing a set of dome-flat images taken with multiple shutter opening/closing motions to those obtained with a normal exposure of the same total duration. The correction to the exposure time is small, of the order of 30 ms averaged over the entire field of view with peaks of ∼60 ms at the east and west edges of the camera. The effect is thus of the order of 0.1% on average for the nominal ZTF survey exposures of 30 s. Comparing the results obtained from three sets of dedicated observations acquired in 2017 December, we assess the stability of the correction factor to be better than 7% both in time and with respect to variations of the experimental conditions.

Identification of integrated geometric errors of rotary axis and setup position errors for 5-axis machine tools based on machining test

As a fundamental error source, geometric errors of 5-axis machine tools have a negative influence on a machine tool’s motion accuracy. Large numbers of efficient and robust geometric error measurement and compensation methods have been developed by existing researches to improve the performance of the machine tools during the automatic machining of the workpiece. However, influence of the geometric errors on workpiece clamping is hard to measure and evaluate in most of the clamping processes since manual operations are involved. It is important to identify both geometric errors and setup position errors to control the entire machining process, standing from the perspective of a manufacturer. In this study, a position-dependent geometric error and setup position error identification method is investigated based on machining test. A kinematic model for a 5-axis machine tool with tilting rotary table is constructed while considering both geometric errors of the two rotary axes and setup position errors. Machining patterns and calculation algorithm are designed to analytically calibrate these errors. Experimental demonstration is conducted to validate the feasibility of the proposed measurement method.

Potential benefit of MRI-guided IMRT for flank irradiation in pediatric patients with Wilms’ tumor

Purpose/Objective: Flank irradiation for Wilms' tumor (WT) is currently performed at our institute using a cone-beam computed tomography-guided volumetric modulated arc (VMATCBCT) workflow. By adding real-time magnetic resonance imaging (MRI) guidance to the treatment, safety margins could be reduced. The study purpose was to quantify the potential reduction of the planning target volume (PTV) margin and its dosimetric impact when using an MRI-guided intensity modulated radiation therapy (IMRTMRI) workflow compared to the VMATCBCT workflow.Material/Methods: 4D-CT, MRI and CBCT scans acquired during preparation and treatment of 15 patients, were used to estimate both geometric, motion and patient set-up systematic (∑) and random (σ) errors for VMATCBCT and IMRTMRI workflows. The mean PTV (PTVmean) expansion was calculated using the van Herk formula. Treatment plans were generated using five margin scenarios (PTVmean ± 0, 1 and 2 mm). Furthermore, the IMRTMRI plans were optimized with a 1.5T transverse magnetic field turned-on to realistically model an MRI-guided treatment. Plans were evaluated using dose-volume statistics (p<.01, Wilcoxon).Results: Analysis of ∑ and σ errors resulted in a PTVmean of 5 mm for the VMATCBCT and 3 mm for the IMRTMRI workflows in each orthogonal direction. Target coverage was unaffected by the margin decrease with a mean V95%=100% for all margin scenarios. For the PTVmean, an average reduction of the mean dose to the organs at risk (OARs) was achieved with IMRTMRI compared to VMATCBCT: 3.4 ± 2.4% (p<.01) for the kidney, 3.4 ± 2.1% (p<.01) for the liver, 2.8 ± 3.0% (p<.01) for the spleen and 4.9 ± 3.8% (p<.01) for the pancreas, respectively.Conclusions: Imaging data in children with WT demonstrated that the PTV margin could be reduced isotropically down to 2 mm when using the IMRTMRI compared to the VMATCBCT workflow. The former results in a dose reduction to the OARs while maintaining target coverage.

7. Dosimetric effects of setup error, range and dose calculation uncertainties: comparison between Pencil Beam and Monte Carlo algorithm

Purpose (1) To compare the dosimetric effect of setup error and range uncertainties with the effect of using two dose calculation algorithms (Pencil Beam (PB) vs. Monte Carlo (MC)) on protontherapy treatment plans, and (2) To assess which uncertainties affect the most the difference between the nominal and actual dose distribution. Methods 12 treatment plans designed for clinical treatment at the Proton Therapy Centre in Trento were selected, covering four anatomical sites: brain, head and neck, chordoma of the spine, and craniospinal axis. The plans, which were initially optimized with the PB algorithm, were recalculated with MC with a statistical uncertainty of 1%. Then, we evaluated the effect of geometrical (setup) and range uncertainties on the planned dose distribution with an in–house software. This software simulates 8 setup errors and 2 range errors (16 calculations per plan in total), in order to estimate near worst-case scenarios for target volume and organs at risks (OAR). We evaluated the differences between MC vs. PB distribution and the robustness of PBS plans using the same dosimetric indices used to optimize the plan (e.g. D1 and D99 for the target volume D1 for serially responding complications, etc.). Results In Table 1 , we show CTV and OAR dosimetric indices for the plans optimized with PB, then recalculated with MC, and also the worst-case scenario after robustness analysis. CTV D99 in MC plans are smaller than in PBS plans. Furthermore, except for plans of intracranial treatments, MC dose distributions are in general worse than the worst-case scenario (Fig. 1). Consequently, sparing of OARs with MC is obtained. For instance, the lacrimal gland mean dose is lower by 9% and 50% in MC vs PB for the static case and the worst case scenario, respectively. Conclusions In 2 out of the 4 disease sites we studied, the effect of using two dose calculation algorithms is greater than the effect of setup error and range uncertainties especially in CTV coverage. Considering MC as a gold standard, the minimum dose to the CTV isn’t guaranteed when plans are designed with PB.

155. Evaluation and comparison of geometrical set-up uncertainties in hypofractionated prostate cancer radiotherapy using two different immobilization systems

Purpose In 2015 a robotic table with six degrees of freedom (Hexapod, Elekta) was installed at our institution and has been introduced in our clinical practice. The aim of this work is to determine and compare the patient inter-fraction set-up error in prostate cancer radiotherapy using two different immobilization systems: ConFeet which is not compatible with Hexapod and Combifix, which instead, using only the cushions without the baseplate, is compatible with Hexapod. Methods Twenty-six prostate cancer patients have been treated at our institution between July and November 2017 either with IMRT or VMAT. The patients were divided into two groups based on the type of immobilization used for their treatment. Thirteen patients were immobilized with ConFeet and thirteen with Combifix. The prostate position was assessed before each fraction, through grey scale matching between the reference CT and the online acquired CBCT image. A total of 675 CBCT has been used for this analysis. The corrections were registered for the three principal axes, left-right(X), supero-inferior(Y), antero-posterior(Z), and for the three rotational angles pitch, roll and yaw. Results The values obtained for the two groups are shown in the Table and Figure. The prostate translation in the vertical axis(z) and the pitch have a greater systematic and random error, for both groups. Statistically significant difference between the two immobilization systems is observed for the roll, the yaw and the translations in the y and z axis. Differences were verified using t-test and Mann–Whitney’s test and considered significant if the p-value was under 0.05. Conclusions ConFeet appears to be more precise, but the combination Combifix with Hexapod still remains the favorited immobilization method, since it allows submillimetre and rotation correction. A study evaluating the set-up residual error and the impact of the translation and rotation errors on the dosimetric distribution is ongoing.

Evaluation of radioprotection properties of some selected ceramic samples

Abstract In this study, the gamma radiation attenuation features of barium zirconat, barium titanate (IV), magnesium nitride, barium pyrophosphate and silicon carbide were studied using the narrow beam geometrical setup in the energy range of 81 keV–1333 keV. The mass attenuation coefficients have been measured and then used to obtain half value layers, mean free paths and effective atomic numbers of the present materials. It is found that the change in the mass attenuation coefficient is considerable for low photon energies (between 81 and 276 keV), whereas the change in this parameter is comparatively small between 303 and 835 keV photon energies. At high energies (1173, 1275 and 1333 keV), the results showed that the mass attenuation coefficient values for all samples are almost the same which revealed that the present ceramics does not have a significant effect on the amount of attenuation of photon at higher energies. The radiation protection efficiency results revealed that BaZrO3 has the maximum capability in attenuation of gamma photons followed by BaTiO3 and Ba2P2O7, especially at low energies.