Sphere Configurations Research Articles

Position dependence of recovery coefficients in 177Lu-SPECT/CT reconstructions – phantom simulations and measurements

BackgroundAlthough the importance of quantitative SPECT has increased tremendously due to newly developed therapeutic radiopharmaceuticals, there are still no accreditation programs to harmonize SPECT imaging. Work is currently underway to develop an accreditation for quantitative 177Lu SPECT/CT. The aim of this study is to verify whether the positioning of the spheres within the phantom has an influence on the recovery and thus needs to be considered in SPECT harmonization. In addition, the effects of these recovery coefficients on a potential partial volume correction as well as absorbed-dose estimates are investigated.MethodsUsing a low-dose CT of a SPECT/CT acquisition, a computerized version of the NEMA body phantom was created using a semi-automatic threshold-based method. Based on the mass-density map, the detector orbit, and the sphere centers, realistic SPECT acquisitions of all possible 720 sphere configurations of both the PET and the SPECT versions of the NEMA Body Phantom were generated using Monte Carlo simulations. SPECT reconstructions with different numbers of updates were performed without (CASToR) and with resolution modeling (STIR). Recovery coefficients were calculated for all permutations, reconstruction methods, and phantoms, and their dependence on the sphere positioning was investigated. Finally, the simulation-based findings were validated using SPECT/CT acquisitions of six different sphere configurations.ResultsOur analysis shows that sphere positioning has a significant impact on the recovery for both of the reconstruction methods and the phantom type. Although resolution modeling resulted in significantly higher recovery, the relative variation in recovery within the 720 permutations was even larger. When examining the extreme values of the recovery, reconstructions without resolution modeling were influenced primarily by the sphere position, while with resolution modeling the volume of the two adjacent spheres had a larger influence. The SPECT measurements confirmed these observations, and the recovery curves showed good overall agreement with the simulated data.ConclusionOur study shows that sphere positioning has a significant impact on the recovery obtained in NEMA sphere phantom measurements and should therefore be considered in a future SPECT accreditation. Furthermore, the single-measurement method normally performed for PVC should be reconsidered to account for the position dependency.

Detailed analysis of the relativistic configuration of Bardeen anisotropic spheres in modified f(G) gravity

The aim of this work is to investigate anisotropic compact objects within the framework of f(G) modified theory of gravity. For our present work, we utilize Krori–Barua metrics, i.e., λ(r) = Xr 2 + Y and β(r) = Zr 2. We use some matching conditions of spherically symmetric spacetime with Bardeen’s model as an exterior geometry. Further, we establish some expressions of energy density and pressure components to analyze the stellar configuration of Bardeen compact stars by assuming viable f(G) models. We examine the energy conditions for different stellar structures to verify the viability of our considered models. Moreover, we also investigate some other physical features, such as equilibrium condition, equation of state parameters, adiabatic index, stability analysis, mass function, surface redshift, and compactness factor, respectively. It is worthwhile to mention here for the current study that our stellar structure in the background of Bardeen's model is more viable and stable.

Generalized geometric pore size distribution code GPSD-3D for periodic systems composed of monodisperse spheres

The generalized geometric pore size distribution P(r;rp|rc) as function of pore radius r, probe sphere radius rp, and coating thickness rc for a periodic two-dimensional system composed of circles (GPSD-2D) had been defined recently. For rp=rc=0 it reduces to the widely accepted pore radius distribution P(r) introduced by Gelb and Gubbins. The three-dimensional counterpart GPSD-3D for periodic systems composed of spheres is implemented here using an efficient Voronoi-based semi-analytic strategy that offers significant advantages compared with both a grid-based implementation and constrained nonlinear optimization with respect to speed, precision and memory requirements. Moreover, GPSD-3D is fully parallelized using OpenMP. Program summaryProgram title:GPSD-3DCPC library link to program files:https://doi.org/10.17632/ntcr87fgr5.1Developers repository link:https://github.com/mkmat/CODE-GPSD-3DLicensing provisions: MITProgramming languages:fortran, c++, perlNature of problem: Calculation of a set of pore radii for a user-provided configuration of (material) spheres contained in a periodic three-dimensional, rectangular box. This set depends on the user-specified radius rp of a probe sphere, and a user-specified hypothetical coating thickness rc of the material spheres. The variable size of the set, and thus the resolution of the resulting generalized geometric pore size distribution increases linearly with computing time.Solution method: Analytic calculation of pore radii from the Voronoi faces for the case of monodisperse systems, constrained nonlinear optimization or grid-based approach for polydisperse systems.Additional comments: This code requires a c++ compiler such as g++, a OpenMP-supporting fortran compiler such as gfortran, perl, and the voro++ library. Download links will be automatically provided during installation of GPSD-3D.

Relations Between the Soviet Union and the Vatican, According to Soviet Documents

If Stalin’s religious policy underwent radical changes after 1943, when the Moscow Patriarchate was re-established, in the context of post- war international relations and the configuration of spheres of influence, Nikita Khrushchev returns to the attitude of persecuting the Orthodox Church in the Soviet Union since year 1958, the reasons being completely different from those of Stalin. But, towards the middle of the 1960s, a change in the anti-religious attitude took shape in Khrushchevs case as well. An example in this sense are two documents from the Soviet archives, which show Khrushchevs position towards the establishment of relations between the Vatican and the Soviet Union, reflected in the instructions sent by the Soviet leader to the USSR ambassador in Cuba and the meeting with the American journalist Norman Cousins, on which occasion he the issue of the release of the Greek-Catholic archbishop Slipyi was addressed in particular.

Exotic self-assembly of hard spheres in a morphometric solvent

The self-assembly of spheres into geometric structures, under various theoretical conditions, offers valuable insights into complex self-assembly processes in soft systems. Previous studies have utilized pair potentials between spheres to assemble maximum contact clusters in simulations and experiments. The morphometric approach to solvation free energy that we utilize here goes beyond pair potentials; it is a geometry-based theory that incorporates a weighted combination of geometric measures over the solvent accessible surface for solute configurations in a solvent. In this paper, we demonstrate that employing the morphometric model of solvation free energy in simulating the self-assembly of sphere clusters results, under most conditions, in the previously observed maximum contact clusters. Under other conditions, it unveils an assortment of extraordinary sphere configurations, such as double helices and rhombohedra. These exotic structures arise specifically under conditions where the interactions take multibody potentials into account. This investigation establishes a foundation for comprehending the diverse range of geometric forms in self-assembled structures, emphasizing the significance of the morphometric approach in this context.

Isolated hypersurface singularities, spectral invariants, and quantum cohomology

Abstract We study the relation between isolated hypersurface singularities (e.g., ADE) and the quantum cohomology ring by using spectral invariants, which are symplectic measurements coming from Floer theory. We prove, under the assumption that the quantum cohomology ring is semi-simple, that (1) if the smooth Fano variety degenerates to a Fano variety with an isolated hypersurface singularity, then the singularity has to be an A m {A_{m}} -singularity, (2) if the symplectic manifold contains an A m {A_{m}} -configuration of Lagrangian spheres, then there are consequences for the Hofer geometry, and that (3) the Dehn twist reduces spectral invariants.

Relativistic configurations of Tolman stellar spheres in f(𝒢,𝒯 ) gravity

This study is devoted to investigate the formation of compact stars using Tolman–Kuchowicz space-time in [Formula: see text] gravity. By taking into account the physically reliable formulations of metric potentials, [Formula: see text] = [Formula: see text] and [Formula: see text] = [Formula: see text], we investigate the equation of motion for spherically symmetric space-time in the presence of an anisotropic matter distribution. Furthermore, matching conditions are employed to compute the unknown constants. By making use of dynamical equations, the pivotal relevant aspects, including energy density, radial and tangential pressures, dynamical equilibrium, anisotropy effect, energy conditions and stability, are physically tested in order to determine the physical acceptability of yielding celestial model, which are thoroughly compared with experimental facts and figures of ten different compact stars. Finally, we observe that obtained anisotropic outcomes are physically viable, free from geometrical and physical singularities. Moreover, these outcomes also provide circumstantial evidence for the existence of super-massive compact stars.

The level of digitalization of Russian enterprises in the investment and construction sector

Introduction. The modern vector of development of the Russian Federation is associated with the transition to a digital model in a variety of aspects: — from the penetration of information technologies into the social sphere and private life of people to their impact on the pace of development of industries and national economies, the effectiveness of public administration, the development of international cooperation. The configuration of global spheres of human activity is undergoing significant changes under the influence of digitalization and radically new emerging human needs and the enterprise management process. Various studies and analytical reviews are of key importance in determining the level of digitalization of the regions of the Russian Federation, allowing to assess the dynamics of the incremental level of digitalization in the business process of enterprises. The results of a study devoted to the analysis of the level of digitalization of Russian enterprises and organizations in the investment and construction sector are presented (ICS). Construction is one of the key sectors of the economy. Thus, its share in the gross domestic product (GDP) is estimated at 5–6 % (according to Rosstat, 5.6 % in 2019), and the share of employed in it is about 9 %. The scale and importance of the construction sector suggest that improving the efficiency of enterprises, including through the introduction of digital technologies as the main modern driver of productivity and efficiency processes, can have an impact on the development of the domestic economy as a whole.
 
 Materials and methods. The basis of the study is a selective correspondence direct survey in the format of an online questionnaire. The following methods were used: the system approach, general theoretical methods of cognition (analysis, synthesis, analogy, generalization, comparison, comparison and others), graphical modelling.
 
 Results. The results of respondents’ assessment of the level of digitalization of Russian enterprises in the investment and construction sector are presented, confirming the activation of the industry in the digital environment. The success factors of these processes are identified, which include: the availability of digital infrastructure and qualified personnel, which in turn is determined by the financial capabilities of enterprises, the presence of digital culture, as well as the ability to develop and retain personnel.
 
 Conclusions. The analysis proves that there are all prerequisites for the effective development of digital relations within enterprises and the industry as a whole. The transition to “digital” will ultimately increase the economic efficiency and manageability of all internal and external organizational and production processes of enterprises and increase the share of the industry’s GDP.

Evaluation of the applicability of the lattice radiotherapy technique at the National Cancer Institute - INCA.

Lattice is a 3-dimensional spatially fractionated radiotherapy that uses a distribution of high-doses, similar to spheres at vertices of a 3D network or matrix. These vertices that receive the high-dose are called peaks, while the rest of the target volume that receives a lower dose, is called the valley. This study aims to verify the technical feasibility for Spatially Fractionated Radiation Therapy treatment using the Lattice technique performed with VMAT at the National Cancer Institute José Alencar Gomes da Silva - INCA, Unit I. Ten patient cases were selected, with gross tumor volumes ranging from 90 to 1734 cc. A literature review was carried out to determine the geometry, the distribution of peaks and the peak to valley dose ratio that will be used in the Lattice technique plans. The dose distributions in the targets and organs at risk of the Lattice plans were clinically compared with the plans without the peaks. A configuration of spheres with diameter of 1.2 cm, separated center-to-center by 3 cm and with a prescription of 14 Gy in a single dose at these peaks was estabilished, while the valley had a prescription of 25 Gy in 5 fractions. Despite the increase in the prescribed equivalent dose in 2 Gy fractions from 40 Gy to 79.3 Gy, the median increase in doses to the OARs was 2.7%, with a maximum increase of 14.7%. The quality control of the plans was approved through the gamma analysis of the measurements performed with the Varian EPID. These findings demonstrate the technical feasibility of SFRT using the lattice technique with VMAT, and suggest that it may provide an effective delivery of high radiation therapy doses to tumors while minimizing the damage to surrounding healthy tissues.

Probabilistic computations of virial coefficients of polymeric structures described by rigid configurations of spherical particles: A fundamental extension of the ZENO program.

We describe an extension of the ZENO program for polymer and nanoparticle characterization that allows for precise calculation of the virial coefficients, with uncertainty estimates, of polymeric structures described by arbitrary rigid configurations of hard spheres. The probabilistic method of virial computation used for this extension employs a previously developed Mayer-sampling Monte Carlo method with overlap sampling that allows for a reduction of bias in the Monte Carlo averaging. This capability is an extension of ZENO in the sense that the existing program is also based on probabilistic sampling methods and involves the same input file formats describing polymer and nanoparticle structures. We illustrate the extension's capabilities, demonstrate its accuracy, and quantify the efficiency of this extension of ZENO by computing the second, third, and fourth virial coefficients and metrics quantifying the difficulty of their calculation, for model polymeric structures having several different shapes. We obtain good agreement with literature estimates available for some of the model structures considered.

Critical pore radius and transport properties of disordered hard- and overlapping-sphere models

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δ_{c}. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δ_{c} is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)10.1016/j.advwatres.2020.103565] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ^{2}〉, which is easier to determine than δ_{c}. Here, we compare δ_{c} to the second moment of the pore size 〈δ^{2}〉, and indeed confirm that, for all porosities and all models considered, δ_{c}^{2} is to a good approximation proportional to 〈δ^{2}〉. However, unlike 〈δ^{2}〉, the permeability estimate based on δ_{c}^{2} does not predict the correct ranking of k for our models. Thus, we confirm 〈δ^{2}〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.

A Fully Compressible Nonhydrostatic Deep-Atmosphere Equations Solver for MPAS

AbstractA solver for the nonhydrostatic deep-atmosphere equations of motion is described that extends the capabilities of the Model for Prediction Across Scales-Atmosphere (MPAS-A) beyond the existing shallow-atmosphere equations solver. The discretization and additional terms within this extension maintain the C-grid staggering, hybrid height vertical coordinate, and spherical centroidal Voronoi mesh used by MPAS, and also preserve the solver’s conservation properties. Idealized baroclinic wave test results, using Earth-radius and reduced-radius sphere configurations, verify the correctness of the solver and compare well with published results from other models. For these test cases, the time evolution of the maximum horizontal wind speed, and the total energy and its components, are presented as additional solution metrics that may allow for further discrimination in model comparisons. The test case solutions are found to be sensitive to the configuration of dissipation mechanisms in MPAS-A, and many of the differences among models in previously published test case solutions appear to arise because of their differing dissipation configurations. For the deep-atmosphere reduced-radius sphere test case, small-scale noise in the numerical solution was found to arise from the analytic initialization that contains unstable lapse rates in the tropical lower troposphere. By adjusting a parameter in this initialization, the instability is removed and the unphysical large-scale overturning no longer occurs. Inclusion of the deep-atmosphere capability in the MPAS-A solver increases the dry dynamics cost by less than 5% on CPU-based architectures, and configuration of either the shallow- or deep-atmosphere equations is controlled by a simple switch.

Radioactive 3D printing for the production of molecular imaging phantoms

Quality control tests of molecular imaging systems are hampered by the complexity of phantom preparation. It is proposed that radioisotopes can be directly incorporated into photo-polymer resins. Use of the radio-polymer in a 3D printer allows phantoms with more complex and reliable activity distributions to be produced whilst simplifying source preparation.Initial tests have been performed to determine the practicality of integrating Tc-99m into a photo-polymer and example phantoms produced to test suitability for quality control. Samples of build and support resins were extracted from the print cartridges of an Objet30Pro Polyjet 3D printer. The response of the resin to external factors including ionising radiation, light and dilution with Tc-99m pertechnetate were explored. After success of the initial tests the radio-polymer was used in the production of different phantoms. Radionuclide dose calibrator and gamma camera acquisitions of the phantoms were used to test accuracy of activity concentration, print consistency, uniformity and heterogeneous reproducibility. Tomographic phantoms were also produced including a uniform hot sphere, a complex configuration of spheres and interlacing torus’s and a hot rod phantom.The coefficient of variation between repeat prints of a 12 g disk phantom was 0.08%. Measured activity within the disks agreed to within 98 ± 2% of the expected activity based on initial resin concentration. Gamma camera integral uniformity measured across a 3D printed flood field phantom was 5.2% compared to 6.0% measured with a commercial Co-57 flood source. Heterogeneous distributions of activity were successfully reproduced for both 2D and 3D imaging phantoms. Count concentration across regions of heterogeneity agreed with the planned activity assigned to those regions on the phantom design.3D printing of radioactive phantoms has been successfully demonstrated and is a promising application for quality control of Positron Emission Tomography and Single Photon Emission Computed Tomography systems.

Vibrational Properties of Hard and Soft Spheres Are Unified at Jamming.

The unconventional thermal properties of jammed amorphous solids are directly related to their density of vibrational states. While the vibrational spectrum of jammed soft sphere solids has been fully described, the vibrational spectrum of hard spheres, a model glass former often related to physical colloidal glasses, is still unknown due to the difficulty of treating the nonanalytic interaction potential. We bypass this difficulty using the recently described effective interaction potential for the free energy of thermal hard spheres. By minimizing this effective free energy, we mimic the rapid compression of hard spheres and produce typical configurations of the thermal system. We measure the resulting vibrational spectrum and characterize its evolution toward the jamming point where configurations of hard and soft spheres are trivially unified. For densities approaching jamming from below, we observe low-frequency modes which agree with those found in numerical simulations of jammed soft spheres. Our measurements of the vibrational structure demonstrate that the jamming universality extends away from jamming: hard sphere thermal systems below jamming exhibit the same vibrational spectra as thermal and athermal soft sphere systems above the transition.

Lagrangian cobordisms, Lefschetz Fibrations and Quantum Invariants

We study Lagrangian cobordisms with the tools provided by Lagrangian quantum homology. In particular, we develop the theory for the setting of Lagrangian cobordisms or Lagrangians with cylindrical ends in a Lefschetz fibration, and put the different versions of the quantum homology groups into relation by a long exact sequence. We prove various practical relations of maps in this long exact sequence and we extract invariants that generalize the notion of discriminants to Lagrangian cobordisms in Lefschetz fibrations. We prove results on the relation of the discriminants of the ends of a cobordism and the cobordism itself. We also give examples arising from Lagrangian spheres and relate the discriminant to open Gromov Witten invariants. We show that for some configurations of Lagrangian spheres the discriminant always vanishes. We study a set of examples that arise from Lefschetz pencils of complex quadric hypersurfaces of the complex projective space. These quadrics are symplectic manifolds endowed with real structures and their real part are the Lagrangians of interest. Using the results established in this thesis, we compute the discriminants of all these Lagrangians by reducing the calculation to the previously established case of a real Lagrangian sphere in the quadric.

Relativistic charged spheres: compact stars, compactness and stable configurations

This paper aims to explore a class of static stellar equilibrium configuration of relativistic charged spheres made of a charged perfect fluid. For solving the Einstein-Maxwell field equations, we consider a particularized metric potential, Buchdahl ansatz [1] and then by using a simple transformation. The study is developed by matching the interior region with Riessner-Nordström metric as an exterior solution. The matter content the charged sphere satisfies all the energy conditions and hydrostatic equilibrium equation, i.e. the modified Tolman-Oppenheimer-Volkoff (TOV) equation for the charged case is maintained. In addition to this, we also discuss some important properties of the charged sphere such as total electric charge, mass-radius relation, surface redshift, and the speed of sound. Obtained solutions are presented by the graphical representation that provides strong evidence for a more realistic and viable stellar structure. Obtained results are compared with analogue objects with similar mass and radii, such as SAX J1808.4-3658, 4U 1538-52, PSR J1903+327, Vela X-1, and 4U1608-52. It is also noted that the Buchdahl ansatz for a given transformation provides a physically viable solution only for the charged case when 0 < K < 1, where density and pressure are maximum at the center and monotonically decreasing towards the boundary. Obtained results are also quite important both from theoretical and astrophysical scale to analyze other compact objects such as white dwarfs, neutron stars, boson stars, and quark stars.

Equilibrium configurations of hard spheres in a cylindrical harmonic potential

A line of hard spheres confined by a transverse harmonic potential, with hard walls at its ends, exhibits a variety of buckled structures as it is compressed longitudinally. Here we show that these may be conveniently observed in a rotating liquid-filled tube (originally introduced by Lee et al. (Adv. Mater., 29 (2017) 1704274) to assemble ordered three-dimensional structures at higher compressions). The corresponding theoretical model is transparent and easily investigated numerically, as well as by analytic approximations. Hence we explore a wide range of predicted structures occurring via bifurcation, of which the stable ones are also observed in our experiments. Qualitatively similar structures have previously been found in trapped ion systems.

Engineering morphology configurations of hierarchical flower-like MoSe2 spheres enable excellent low-frequency and selective microwave response properties

MoSe2 is a compelling narrow-band-gap semiconductor with particular lamellar crystal structure, but which is rarely used as microwave absorber filler. Owing to the analogue molecular structure with MoS2, it may be a potential dielectric dissipation candidate. The hierarchical flower-like structure has been wide accepted as attractive morphology due to its possible strong multiple scattering and reflecting abilities for microwave, thus, in this study, we employed a facile solvothermal process to fabricate the unique flower-like MoSe2 spheres for eliminating microwave interference issue. Further through the precise tuning of morphology configurations of flower-like MoSe2, the effective absorption to specific microwave frequency band can be well optimized, even including low-frequency band. The microwave absorption (MA) performance results show that the dense-flower samples could achieve full absorption in Ku-band and blooming-flower samples cover the entire X-band. The hollow-flower sample is good at absorption in low frequency of C-band and X-band. Our work not only develops outstanding microwave absorber candidates through delicate nanostructure design, but also paves a new way for tuning effective frequency band via tailoring morphology configurations.

Minimal Surface Convex Hulls of Spheres

We present and solve a new computational geometry optimization problem. Spheres with given radii should be arranged such that (a) they do not overlap and (b) the surface area of the boundary of the convex hull enclosing the spheres is minimized. An additional constraint could be to fit the spheres into a specified geometry, e.g., a rectangular solid. To tackle the problem, we derive closed non-convex NLP models for this sphere arrangement or sphere packing problem. For two spheres, we prove that the minimal area of the boundary of the convex hull is identical to the sum of the surface areas of the two spheres. For special configurations of spheres we provide theoretical insights and we compute analytically minimal-area configurations. Numerically, we have solved problems containing up to 200 spheres.

High-Pressure Methane Adsorption in Porous Lennard-Jones Crystals.

Decades of research have yet to yield porous adsorbents that meet the U.S. Department of Energy's methane storage targets. To better understand why, we calculated high-pressure methane adsorption in 600 000 randomly generated porous crystals, or "pseudomaterials," using atomistic grand canonical Monte Carlo (GCMC) simulations. These pseudomaterials were periodic configurations of Lennard-Jones spheres whose coordinates in space, along with corresponding well depths and radii, were all chosen at random. GCMC simulations were performed for pressures of 35 and 65 bar at a temperature of 298 K. Methane adsorption was compared for all materials against a range of other properties: average well depths and radii, number density, helium void fraction, and volumetric surface area. The results reveal structure-property relationships that resemble those previously observed for metal-organic frameworks and other porous materials. We contend that our computational methodology can be useful for discovering useful structure-property relationships related to gas adsorption without requiring experimentally accessible structural data.