Full Summation Research Articles

Comparison of Quantitative X-ray Diffraction Mineral Analysis Methods

X-ray diffraction (XRD) analysis, as one of the most powerful methods, has been widely used to identify and quantify minerals in earth science. How to improve the precision of mineral quantitative analysis is still a hot topic. To date, several quantitative methods have been proposed for different purposes and accompanied by diverse software. In this study, three quantitative mineral analysis methods, including the reference intensity ratio (RIR), Rietveld, and full pattern summation (FPS) methods, are compared and evaluated to systematically investigate their accuracy and applicability. The results show that the analytical accuracy of these methods is basically consistent for mixtures free from clay minerals. However, there are significant differences in accuracy for clay-mineral-containing samples. In comparison, it seems that the FPS method has wide applicability, which is more appropriate for sediments. The Rietveld method has been shown to be capable of quantifying complicated non-clay samples with a high analytical accuracy; nevertheless, most conventional Rietveld software fails to accurately quantify phases with a disordered or unknown structure. The RIR method represents a handy approach but with lower analytical accuracy. Overall, the present results are expected to provide a potentially important reference for the quantitative analysis of minerals in sediments.

Analysis of Contribution of Full Summation Hydrodynamic Load to Dynamic Response of Floating Offshore Wind Turbine Structure Operating in Extreme Environments

Analysis of Contribution of Full Summation Hydrodynamic Load to Dynamic Response of Floating Offshore Wind Turbine Structure Operating in Extreme Environments

PowdR: An R package for quantitative mineralogy using full pattern summation of X-ray powder diffraction data

X-ray powder diffraction (XRPD) is consistently found to be the most accurate analytical technique for qualitative and quantitative mineralogy. For environmental samples such as rocks, sediments and soils that can contain a range of crystalline, disordered and amorphous components, quantitative XRPD methods implemented in Excel-based programmes such as FULLPAT and RockJock have proved particularly appropriate. Such programmes quantify phase concentrations in complex mixtures by treating the diffractogram of a given mixture as the sum of contributions from individual components. Thus, using this full pattern summation (FPS) approach, an observed diffractogram of a sample can be modelled by scaling the contributions of the diffractograms for all pure phases within it and then phase concentrations computed using reference intensity ratios.Here the principles implemented in FULLPAT, RockJock and an in-house application for FPS have together been used to create the powdR package for R. The powdR package advances on previous implementations of FPS in terms of functionality, speed (parallel computation) and adaptability (via use of bespoke R code), and includes a Shiny web application for user-friendly analysis. powdR can be used to quantify samples prepared either with or without an internal standard, and includes the public domain RockJock library of 169 pure diffractograms that cover a wide range of phases that may be encountered in soil and rock samples. Furthermore, powdR contains functionality for automated phase quantification, which can select appropriate phases from a comprehensive reference library (e.g., RockJock). Here the FPS functions implemented in powdR and their use are described in detail.

Resistance and ductility of FRP composite hybrid joints

An experimental investigation of the load-bearing behavior and ductility of FRP hybrid double-lap joints composed of both adhesively-bonded and bolted connection parts was conducted. Amongst other things, the effects of the adherends’ fiber architecture (uni- or multidirectional), adhesive type (stiff or flexible), and displacement rate were examined. The resistances of the hybrid joints with flexible adhesive corresponded to the full summation of the resistances of the bonded and bolted connection parts. The ultimate failure loads of these joints were furthermore significantly improved by increasing the displacement rate, while the deformation capacity did not decrease. The hybrid joints with multidirectional adherends and flexible adhesive exhibited high joint efficiencies and excellent ductility and thus may increase the overall safety of redundant engineering structures composed of brittle FRP members. These joints may also fulfill fail-safe conditions as required in European standards.

Linear Response Theory for Decomposition Energies of Stokes Shift in Proteins.

In aqueous solution, fluorescence Stokes shift experiments monitor the relaxation of the solute-solvent interactions upon photon excitation of the solute chromophore. Linear response (LR) theory expects the identical dynamics between the Stokes shift and the system's spontaneous fluctuations. Whether this identity guarantees similar dynamics between the nonequilibrated and equilibrium processes for the decomposition energy of the Stokes shift is the main focus of this study. In our previous work [Li, T. J. Chem. Theory Comput. 2017, 13, 1867-1873], Stokes shift is properly correlated with various order time-correlation functions. As a continuation, its decomposition energy from the subsystem is further represented as the full summation of all of the cross-time correlation functions between the decomposition energy and the total solute-solvent interactions. Gaussian statistics of the total solute-solvent interactions ensure the same decay rates among the odd orders not only for the time-correlation functions but also for the cross-time correlation functions, validating the LR of the Stokes shift and the decompositions, respectively. The above mechanism is verified by molecular dynamics simulations in the protein Staphylococcus nuclease and is robust even as the decomposed energy associated with an individual residue exhibits typical non-Gaussian properties. Further examinations reveal the consistent molecular motions for a specific residue over the nonequilibrium and equilibrium processes, which are responsible for the nonequilibrium dynamics of the associated decomposed energy. Our results show the appropriateness of LR on finer molecular scales.

The Subprimary Range of Firing Is Present in Both Cat and Mouse Spinal Motoneurons and Its Relationship to Force Development Is Similar for the Two Species.

In the motor system, force gradation is achieved by recruitment of motoneurons and rate modulation of their firing frequency. Classical experiments investigating the relationship between injected current to the soma during intracellular recording and the firing frequency (the I-f relation) in cat spinal motoneurons identified two clear ranges: a primary range and a secondary range. Recent work in mice, however, has identified an additional range proposed to be exclusive to rodents, the subprimary range (SPR), due to the presence of mixed mode oscillations of the membrane potential. Surprisingly, fully summated tetanic contractions occurred in mice during SPR frequencies. With the mouse now one of the most popular models to investigate motor control, it is crucial that such discrepancies between observations in mice and basic principles that have been widely accepted in larger animals are resolved. To do this, we have reinvestigated the I-f relation using ramp current injections in spinal motoneurons in both barbiturate-anesthetized and decerebrate (nonanesthetized) cats and mice. We demonstrate the presence of the SPR and mixed mode oscillations in both species and show that the SPR is enhanced by barbiturate anesthetics. Our measurements of the I-f relation in both cats and mice support the classical opinion that firing frequencies in the higher end of the primary range are necessary to obtain a full summation. By systematically varying the leg oil pool temperature (from 37°C to room temperature), we found that only at lower temperatures can maximal summation occur at SPR frequencies due to prolongation of individual muscle twitches.SIGNIFICANCE STATEMENT This work investigates recent revelations that mouse motoneurons behave in a fundamentally different way from motoneurons of larger animals with respect to the importance of rate modulation of motoneuron firing for force gradation. The current study systematically addresses the proposed discrepancies between mice and larger species (cats) and demonstrates that mouse motoneurons, in fact, use rate modulation as a mechanism of force modulation in a similar manner to the classical descriptions in larger animals.

Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling.

We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three-dimensional periodic systems in second-order Møller-Plesset perturbation theory (MP2). In particular we measure the scaling behavior of the sample variance and probe whether this stochastic approach is competitive if accuracies well below 1 meV per valence orbital are required, as it is necessary for calculations of adsorption, binding, or surface energies. The algorithm is based on the Laplace transformed MP2 (LTMP2) formulation in the plane wave basis. The time-dependent Hartree-Fock orbitals, appearing in the LTMP2 formulation, are stochastically rotated in the occupied and unoccupied Hilbert space. This avoids a full summation over all combinations of occupied and unoccupied orbitals, as inspired by the work of Neuhauser, Rabani, and Baer [J. Chem. Theory Comput. 9, 24 (2013)]. Additionally, correlated sampling is introduced, accelerating the statistical convergence significantly.

The Whole is Other Than the Sum: Perceived Contrast Summation Within Color and Luminance Plaids.

The apparent contrast of a plaid is a reflection of the neural relationship between the responses to its two orthogonal component gratings. To investigate the perceived contrast summation of the responses to component gratings in plaids, we compared the apparent contrasts of monocular plaids to a component grating presented alone across chromaticity and spatial frequency. Observers performed a contrast-matching task for red–green color and luminance stimuli at low- and medium-spatial frequencies. Using the measured points of subjective equality between plaids and gratings, we evaluate perceived contrast summation across conditions, which may vary between 1 (no summation) and 2 (full summation). We show that achromatic plaids have higher perceived contrast summation than chromatic plaids. The greatest difference occurs at the medium-spatial frequency, with summation highest for achromatic plaids (1.87) and lowest for chromatic plaids (1.49), while at low-spatial frequencies, there is a smaller summation difference between achromatic (1.72) and chromatic (1.65) plaids. These results are consistent with recent theories of distinct cross-orientation suppression and summation mechanisms in color and luminance vision. Two control experiments for binocular versus monocular viewing, and the overall size of the stimulus patches did not reveal any differences from our main results.

A NUMERICAL EVALUATION OF VACUUM POLARIZATION TENSOR IN CONSTANT EXTERNAL MAGNETIC FIELDS

Hattori–Itakura have recently derived the full Landau-level summation form for the photon vacuum polarization tensor in constant external magnetic fields at the one-loop level. The Landau-level summation form is essential when the photon momentum exceeds the threshold of the pair creation of charged particles in a magnetic field stronger than the squared mass of the charged particle. The tensor has three different form factors depending on the tensor direction with respect to the external magnetic field. The renormalization is nontrivial because these form factors are expressed in terms of double or triple summation forms. We give a numerical UV subtraction method which can be applied to numerically evaluate the form factors in constant external magnetic fields. We numerically investigate the photon vacuum polarization tensor in the form of the Landau-level summation and estimate the systematic errors coming from truncation of the Landau-level summation in a parameter region realized in heavy ion collision experiments. We find that the error is practically controllable at an O(10-2) level for electrons and muons in strong magnetic fields expected in heavy ion collisions in the experimentally feasible kinematic parameter regions.

Interaction of fluids with physically patterned solid surfaces

We derive coarse-grained potentials for the interaction of a fluid atom with a solid substrate patterned with cylindrical or rectangular pillars, as well as with rectangular grooves. These potentials rely on the assumption of pairwise Lennard-Jones (LJ) (12-6) interactions of a fluid atom with a surface that has a uniform density of solid atoms. In the limit of a flat, semi-infinite surface, this potential becomes the LJ 9-3 potential. Simplified forms of the potentials are presented that are valid for sufficiently large pillars or grooves. The potentials can be truncated for greater computational efficiency while retaining similar accuracy to the full form. Both the full and simplified potentials exhibit the same features as a full summation of LJ (12-6) interactions, and these may be used in simulation studies to resolve phenomena associated with the interaction of fluids with patterned surfaces.

Approximate Inference on Planar Graphs using Loop Calculus and Belief Propagation

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006a) allows to express the exact partition function of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze the performance of the algorithm for models with binary variables and pairwise interactions on grids and other planar graphs. We study in detail both the loop series and the equivalent Pfaffian series and show that the first term of the Pfaffian series for the general, intractable planar model, can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state of the art methods for approximate inference.

Magnetic and Transport Characterization of NbTi Strands as a Basis for the Design of Fusion Magnets

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We present the results of an extended measurement campaign carried out on available NbTi commercial strands to be used in the design of fusion reactor magnets, including candidate strands for the ITER high field Poloidal Coils, PF1/6, and for the Toroidal Field Coils of the JT-60SA Tokamak. Magnetic and transport measurements have been carried out at variable temperature and magnetic field. From magnetization cycles we were able to extract information about AC hysteretic losses, and to extend the current density determination to lower fields, thus enabling the optimization of numerical fits in a wider magnetic field range. It has been found that the normalized bulk pinning force of the material, though showing good temperature scaling throughout the explored range, cannot be described by a single function of the type <formula formulatype="inline"> <tex Notation="TeX">${\rm b}^{\alpha}(1-{\rm b})^{\beta}$</tex></formula>. On the contrary, the full summation of two contributions, each dominant in a different magnetic field range, returns a good fit of the data. Extending this 2-components description to an expression for the critical current density, a very good agreement with experimental measurements is obtained over the whole explored B, T range. Collecting a database of available strands performances, especially in the range of relatively high temperatures <formula formulatype="inline"> <tex Notation="TeX">$({\rm T}&gt;5.5\ {\rm K})$</tex></formula> and magnetic fields <formula formulatype="inline"><tex Notation="TeX">$({\rm B}\sim 6\ {\rm T})$</tex></formula>, typical of applications in large coils for fusion reactors, constitutes a sound basis for magnets design, which should be based on strand properties measured in the operation-relevant temperature and magnetic field range. </para>

Multilevel summation of electrostatic potentials using graphics processing units

Physical and engineering practicalities involved in microprocessor design have resulted in flat performance growth for traditional single-core microprocessors. The urgent need for continuing increases in the performance of scientific applications requires the use of many-core processors and accelerators such as graphics processing units (GPUs). This paper discusses GPU acceleration of the multilevel summation method for computing electrostatic potentials and forces for a system of charged atoms, which is a problem of paramount importance in biomolecular modeling applications. We present and test a new GPU algorithm for the long-range part of the potentials that computes a cutoff pair potential between lattice points, essentially convolving a fixed 3D lattice of “weights” over all sub-cubes of a much larger lattice. The implementation exploits the different memory subsystems provided on the GPU to stream optimally sized data sets through the multiprocessors. We demonstrate for the full multilevel summation calculation speedups of up to 26 using a single GPU and 46 using multiple GPUs, enabling the computation of a high-resolution map of the electrostatic potential for a system of 1.5 million atoms in under 12 s.

A simplified method of four‐dimensional dose accumulation using the mean patient density representation

The purpose of this work was to demonstrate, both in phantom and patient, the feasibility of using an average 4DCT image set (AVG-CT) for 4D cumulative dose estimation. A series of 4DCT numerical phantoms and corresponding AVG-CTs were generated. For full 4D dose summation, static dose was calculated on each phase and cumulative dose was determined by combining each phase's static dose distribution with known tumor displacement. The AVG-CT cumulative dose was calculated similarly, although the same AVG-CT static dose distribution was used for all phases (i.e., tumor displacements). Four lung cancer cases were also evaluated for stereotactic body radiotherapy and conformal treatments; however, deformable image registration of the 4DCTs was used to generate the displacement vector fields (DVFs) describing patient-specific motion. Dose discrepancy between full 4D summation and AVG-CT approach was calculated and compared. For all phantoms, AVG-CT approximation yielded slightly higher cumulative doses compared to full 4D summation, with dose discrepancy increasing with increased tumor excursion. In vivo, using the AVG-CT coupled with deformable registration yielded clinically insignificant differences for all GTV parameters including the minimum, mean, maximum, dose to 99% of target, and dose to 1% of target. Furthermore, analysis of the spinal cord, esophagus, and heart revealed negligible differences in major dosimetric indices and dose coverage between the two dose calculation techniques. Simplifying 4D dose accumulation via the AVG-CT, while fully accounting for tumor deformation due to respiratory motion, has been validated, thereby, introducing the potential to streamline the use of 4D dose calculations in clinical practice, particularly for adaptive planning purposes.

WE-E-AUD A-05: A Simplified Method of Dose Accumulation in 4DCT

Purpose: To demonstrate, both in phantom and patient, the feasibility of approximating the subject's density distribution via an average 4DCT image (AVG-CT), calculate cumulative dose delivered during respiration with this technique, and evaluate the results with a full 4D dose summation. Method and Materials: A series of 4DCT numerical phantoms (9 phases, lung tumor excursions 2, 3, and 4 cm in S-I direction) and their AVG-CT images were generated. For full 4D dose summation, static dose was calculated on each phase, each dose matrix was sampled with known displacement, and dose was accumulated over all phases. Using the same clinical plan, the AVG-CT cumulative dose was calculated by combining the static AVG-CT dose with known tumor displacement, and assuming the dose distribution was the same for all phases. Four lung cancer cases were also evaluated for stereotactic body radiotherapy and conformal treatments. Here, deformable image registration was used to generate the patient-specific motion model from 4DCT. Dose accumulation was analogous to phantom, however, each phase's dose matrix was sampled using the displacement vector field. Dose discrepancy (D) between full 4D summation and AVG-CT approach was calculated and compared. Results: For all phantoms, AVG-CT approximation yielded slightly higher cumulative doses compared to full 4D summation, with dose discrepancy increasing with increased tumor excursion. In vivo, using the AVG-CT coupled with deformable registration yielded a modest increase in cumulative dose relative to full 4D dose summation and not at clinically applicable levels (D < 2%). Even for a patient with substantial tumor motion near the diaphragm, dose discrepancy was within 4%. Conclusion: Simplifying 4D dose accumulation via the AVG-CT, while fully accounting for tumor deformation due to respiratory motion, has been validated, thereby introducing the potential to streamline the use of 4D dose calculations in clinical practice.

Psychophysical evidence for two routes to suppression before binocular summation of signals in human vision

Visual mechanisms in primary visual cortex are suppressed by the superposition of gratings perpendicular to their preferred orientations. A clear picture of this process is needed to (i) inform functional architecture of image-processing models, (ii) identify the pathways available to support binocular rivalry, and (iii) generally advance our understanding of early vision. Here we use monoptic sine-wave gratings and cross-orientation masking (XOM) to reveal two cross-oriented suppressive pathways in humans, both of which occur before full binocular summation of signals. One is a within-eye (ipsiocular) pathway that is spatially broadband, immune to contrast adaptation and has a suppressive weight that tends to decrease with stimulus duration. The other pathway operates between the eyes (interocular), is spatially tuned, desensitizes with contrast adaptation and has a suppressive weight that increases with stimulus duration. When cross-oriented masks are presented to both eyes, masking is enhanced or diminished for conditions in which either ipsiocular or interocular pathways dominate masking, respectively. We propose that ipsiocular suppression precedes the influence of interocular suppression and tentatively associate the two effects with the lateral geniculate nucleus (or retina) and the visual cortex respectively. The interocular route is a good candidate for the initial pathway involved in binocular rivalry and predicts that interocular cross-orientation suppression should be found in cortical cells with predominantly ipsiocular drive.

Parallelization of the NASA Goddard Cumulus Ensemble Model for Massively Parallel Computing

Massively parallel computing, using a message passing interface (MPI), has been implemented into a three-dimensional version of the Goddard Cumulus Ensemble (GCE) model. The implementation uses the domainresemble concept to design a code structure for both the whole domain and sub-domains after decomposition. Instead of inserting a group of MPI related statements into the model routine, these statements are packed into a single routine. In other words, only a single call statement to the model code is utilized once in a place, thus there is minimal impact on the original code. Therefore, the model is easily modified and/or managed by the model developers and/or users, who have little knowledge of massively parallel computing. The model decomposition is highly flexible such that the entire model domain can be sliced into any number of partial domains in one- or twodimensional decomposition. Data exchange is through a halo-region, which is overlaid with neighboring partial domains. A halo-region is also known as a ghost-cell region. For reproducibility purposes, transposing data among tasks into different decompositions is required, such as Fourier transform and full domain summation.

Self-energy of a nodal fermion in ad-wave superconductor

We re-consider the self-energy of a nodal (Dirac) fermion in a 2D d-wave superconductor. A conventional belief is that Im \Sigma (\omega, T) \sim max (\omega^3, T^3). We show that \Sigma (\omega, k, T) for k along the nodal direction is actually a complex function of \omega, T, and the deviation from the mass shell. In particular, the second-order self-energy diverges at a finite T when either \omega or k-k_F vanish. We show that the full summation of infinite diagrammatic series recovers a finite result for \Sigma, but the full ARPES spectral function is non-monotonic and has a kink whose location compared to the mass shell differs qualitatively for spin-and charge-mediated interactions.

The Binocular Combination of Chromatic Contrast

How is chromatic contrast combined binocularly? One index of binocularity is the binocular contrast summation ratio (BCSR), which is the improvement in contrast sensitivity with binocular rather than monocular presentation. Simmons and Kingdom (1998, Vision Research 38 1063-1071) noted that BCSRs with some red-green isoluminant stimuli were suggestive of full linear summation. This suggestion was investigated further in four subjects by measuring binocular and monocular contrast thresholds for the detection of 0.5 cycle deg(1) isoluminant (red-green) and isochromatic (yellow-black) Gabor patches. These Gabor patches had either vertically or horizontally oriented carrier gratings and were either dichoptically in phase (same coloured bars in binocular correspondence) or in dichoptic anti-phase (opposite coloured bars in binocular correspondence). Full linear summation would be indicated by BCSRs of 2 for the in-phase and close to 0 for the anti-phase conditions. Mean BCSRs at isoluminance were 1.93 and 0.90, respectively, for the in-phase and anti-phase stimuli with horizontal carriers, the former being consistent with full linear summation, but the latter not. Despite these results, BCSRs obtained with isoluminant and isochromatic stimuli under similar conditions were not statistically distinguishable from each other, although there was a tendency for summation at isoluminance with in-phase stimuli to be higher and anti-phase stimuli to be lower. These data fall short of demonstrating full linear summation of chromatic contrast between the eyes under all presentation conditions, but they do indicate that there are strong binocular interactions at red-green isoluminance, which are similar to, and possibly even stronger than, those obtained with luminance stimuli.

Ewald summation of electrostatic multipole interactions up to the quadrupolar level

Ewald summation expressions are derived for the energy, interatomic forces, pressure tensor, electric fields, and electric field gradients in a periodic computer simulation system of molecules with charges, induced dipoles, and quadrupoles. The full expressions including quadrupolar multipole interactions are given; those involving dipoles are included for completeness. The expressions apply not only to molecules with permanent multipoles, but also to systems of polarizable ions where the multipoles are induced by the interionic interactions. The expressions which allow for this generalization consider the ions to be spherically polarizable, but include the consequences of the coupling between dipolar and quadrupolar induction. The phonon dispersion curves of MgO and the structural lattice constants of Al2O3 in its corundum phase are discussed as specific examples. In simulations with a dipole- and quadrupole-polarizable interaction model, a full Ewald summation of quadrupolar interactions is shown to have a significant effect.