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This erratum corrects two notational errors and disambiguates a statement in the original article. These corrections apply to equations that follow Equation 9 in the text of the original.
Here, the authors regret they have discovered errors in Eq. (3) and in a spreadsheet used to calculate cosmogenic exposure ages shown in Table 1. Eq. (3) is missing a term. The spreadsheet errors concerned an incorrect cell reference and application of Eq. (3). Correction of these errors results in ~15–20% changes to the exposure ages of all samples, minor (generally <0.2%) changes to the radioisotopic ages of some samples (those that entailed a correction for chlorine-derived 38Ar calculated based on the exposure age; see Section 3.3), and statistically insignificant changes to the inferred trapped components identified through isochron analyses. These modifications have no impact on the modeling, discussions, or conclusions in the paper, nor do the changes to radioisotopic ages exceed the 1 sigma uncertainties.
The various technologies presented herein relate to the determination of and correction of heading error of platform. Knowledge of at least one of a maximum Doppler frequency or a minimum Doppler bandwidth pertaining to a plurality of radar echoes can be utilized to facilitate correction of the heading error. Heading error can occur as a result of component drift. In an ideal situation, a boresight direction of an antenna or the front of an aircraft will have associated therewith at least one of a maximum Doppler frequency or a minimum Doppler bandwidth. As the boresight direction of the antenna strays from a direction of travel at least one of the maximum Doppler frequency or a minimum Doppler bandwidth will shift away, either left or right, from the ideal situation.
We apply a recently developed Wannier-Koopmans method (WKM), based on density functional theory (DFT), to calculate the electronic energy level alignment at an interface between a molecule and metal substrate. We consider two systems: benzenediamine on Au (111), and a bipyridine-Au molecular junction. The WKM calculated level alignment agrees well with the experimental measurements where available, as well as previous GW and DFT + Σ results. These results suggest that the WKM is a general approach that can be used to correct DFT eigenvalue errors, not only in bulk semiconductors and isolated molecules, but also in hybrid interfaces.
There is an exciting opportunity to start a second digital revolution that will supersede the first digital revolution in information technology (IT) as the primary driver of scientific, technological, and economic growth. This new revolution will be digital fabrication technology. Here, the digital IT revolution has been largely driven by digital algorithms such as error detection and correction and Moore's Law which has given us an exponential trend in product capabilities. However, the longstanding trend in improving manufacturing precision which has enabled Moore's Law simply cannot be continued much longer because we are running into the limits imposed by the quantized nature of matter. At this scale, matter can no longer be treated in an analogue fashion i.e. as an infinitely divisible medium, but must be treated as an integer number of discrete atomic distances, i.e. in a digital fashion. By embracing this digital nature of matter, we can conceive of a digital fabrication technology, where the digital processes are the making and breaking of chemical bonds, there is a digital address grid that is spatial in nature, and error detection and correction processes can be developed. This digital fabrication technology will have the similarly huge advantages over analog fabrication that digital IT has over analog IT. We remind the reader that effective digital technologies are not exclusively digital in their operation. Digital electronics is carried out by analog transistors that are embedded in circuitry designed to accept their output in a digital fashion. Digital fabrication technology is not synonymous with Atomically Precise Manufacturing (APM) but should lead to that important capability. Furthermore this digital fabrication technology will start a new exponential manufacturing trend that will replace Moore's law and will not be just for information processing and therefore will have an even larger impact than Moore's Law. Like any exponential trend Digital Fabrication will start slowly in a few niche markets, but the time for investing in the development of this new technology is now.
Ptychography is a powerful imaging technique that is used in a variety of fields, including materials science, biology, and nanotechnology. However, the accuracy of the reconstructed ptychography image is highly dependent on the accuracy of the recorded probe positions which often contain errors. These errors are typically corrected jointly with phase retrieval through numerical optimization approaches. When the error accumulates along the scan path or when the error magnitude is large, these approaches may not converge with satisfactory result. We propose a fundamentally new approach for ptychography probe position prediction for data with large position errors, where a neural network is used to make single-shot phase retrieval on individual diffraction patterns, yielding the object image at each scan point. The pairwise offsets among these images are then found using a robust image registration method, and the results are combined to yield the complete scan path by constructing and solving a linear equation. We show that our method can achieve good position prediction accuracy for data with large and accumulating errors on the order of 10 2 pixels, a magnitude that often makes optimization-based algorithms fail to converge. For ptychography instruments without sophisticated position control equipment such as interferometers, our method is of significant practical potential.
Detecting nodes with erroneous values in real-world graphs re- mains challenging due to the lack of examples and various error scenarios. We demonstrate GEDet, an error detection engine that can detect erroneous nodes in graphs with a few examples. The GEDet framework tackles error detection as a few-shot node classification problem. We invite the attendees to experience the following unique features. (1) Few-shot detection. Users only need to provide a few examples of erroneous nodes to perform error detection with GEDet. GEDet achieves desirable accuracy with (a) a graph augmentation module, which automatically generates synthetic examples to learn the classifier, and (b) an adversarial detection module, which improves classifiers to better distinguish erroneous nodes from both cleaned nodes and synthetic examples. We show that GEDet significantly improves the state-of-the-art error detection methods. (2) Diverse error scenarios. GEDet profiles data errors with a built-in library of transformation functions from correct values to errors. Users can also easily “plug in” new error types or examples. (3) User-centric detection. GEDet supports (a) an active learning mode to engage users to verify detected results, and adapts the error detection process accordingly; and (b) visual interfaces to interpret and track detected errors.
The original version of this Article contained errors in Fig. 2. In Fig. 2d, the label below the blue circle incorrectly read “S i,a (t) < 0” and should have read “S i,a (t) > 0”. Furthermore, the sequence of labels on the side of the bottom three panel in Fig. 2 from top to bottom incorrectly read “S 9,70 > 0, S 9,70 > 0, S 9,70 < 0”, and should have read “S 9,70 < 0, S 9,70 > 0, S 9,70 < 0”. Finally, in the legend to Fig. 2, the scale bar size description “Scale bar: 100 μm” was incorrectly placed in the description of panel c, and should have been placed in the description of panel d. These errors have been corrected in both the PDF and HTML versions of the Article.
Ellipsoidal mirrors, which can efficiently produce a two-dimensional focusing beam with a single mirror, are superior x-ray focusing optics, especially when compared to elliptical-cylinder mirrors in the Kirkpatrick–Baez geometry. However, nano-focusing ellipsoidal mirrors are not commonly used for x-ray optics because achieving the accuracy required for the surface metrology of nano-focusing ellipsoidal mirrors is difficult due to their small radius of curvature along the short ellipsoidal axis. Here, we developed a surface metrology system for nano-focusing ellipsoidal mirrors using stitching interferometric techniques. The developed system simultaneously measures sub-aperture shapes with a microscopic interferometer and the tilt angles of the sub-aperture shapes with a large Fizeau interferometer. After correcting the systematic errors included in the sub-aperture shapes, the entire mirror shape is calculated by stitching the sub-aperture shapes based on the obtained relative angles between partially overlapped sub-apertures. In this study, we developed correction methods for systematic errors in sub-aperture shapes that originated from off-axis aberrations produced in the optics of the microscopic interferometer. The systematic errors on an ellipsoidal mirror were estimated by measuring a series of tilted plane substrates and the ellipsoidal substrate. From measurements of an ellipsoidal mirror with a 3.6-mm radius of curvature at the mirror center, we obtained a measurement repeatability of 0.51 nm (root-mean-square) in an assessment area of 0.5 mm × 99.18 mm. This value satisfies the requirements for surface metrology of nano-focusing x-ray mirrors. Thus, the developed metrology system should be applicable for fabricating nano-focusing ellipsoidal mirrors.
Chlamydomonas reinhardtii is a unicellular chlorophyte alga that is widely studied as a reference organism for understanding photosynthesis, sensory and motile cilia, and for development of an algal-based platform for producing biofuels and bio-products. Its highly repetitive, ~205-kbp circular chloroplast genome and ~15.8-kbp linear mitochondrial genome were sequenced prior to the advent of high-throughput sequencing technologies. Here, high coverage shotgun sequencing was used to assemble both organellar genomes de novo. These new genomes correct dozens of errors in the prior genome sequences and annotations. Gen-ome sequencing coverage indicates that each cell contains on average 83 copies of the chloroplast genome and 130 copies of the mitochondrial genome. Using protocols and analyses optimized for organellar tran-scripts, RNA-Seq was used to quantify their relative abundances across 12 different growth conditions. Forty-six percent of total cellular mRNA is attributable to high expression from a few dozen chloroplast genes. RNA-Seq data were used to guide gene annotation, to demonstrate polycistronic gene expression, and to quantify splicing of psaA and psbA introns. In contrast to a conclusion from a recent study, we found that chloroplast transcripts are not edited. Unexpectedly, cytosine-rich polynucleotide tails were observed at the 3’-end of all mitochondrial transcripts. A comparative genomics analysis of eight laboratory strains and 11 wild isolates of C. reinhardtii identified 2658 variants in the organellargenomes, which is 1/10th as much genetic diversity as is found in the nucleus.
Noise-induced gate errors remain one of the main obstacles to realizing a broad range of quantum information technologies. Dynamical error suppression using carefully designed control schemes is critical for overcoming this challenge. Such schemes must be able to correct against multiple noise sources simultaneously afflicting a qubit to reach error-correction thresholds. Here we present a general framework for designing control fields that simultaneously suppress both noise in the fields themselves as well as transverse dephasing noise. Using the recently developed space curve quantum control formalism, in which robust quantum evolution is mapped to closed geometric curves in a multidimensional Euclidean space, we derive the minimal conditions necessary to guarantee the simultaneous cancellation of both types of noise to leading order. In particular, we find that the cancellation of control field noise requires the derivative of the space curve to have zero-area projections, which is a much more subtle property compared to the closed-curve condition needed to suppress transverse dephasing. We present several techniques for solving both these conditions simultaneously and provide explicit examples of error-resistant control fields. Finally, our work also sheds light on the relation between holonomic evolution and the suppression of control field errors.
A typographical error needs to be corrected in the Results section, subsection “2.5. Evaluation of Li + Ion Conduction Properties”, fourth paragraph, where the activation energy barriers derived from PFG-NMR were swapped for components 1 and 2, for both BM-LYC and SS-LYC. The same error should also corrected in the second paragraph of the Discussion section.
Self-gravity computation by multipole expansion is a common approach in problems such as core-collapse and Type Ia supernovae, where single large condensations of mass must be treated. The standard formulation of multipole self-gravity in arbitrary coordinate systems suffers from two significant sources of error, which we correct in the formulation presented in this article. The first source of error is due to the numerical approximation that effectively places grid cell mass at the central point of the cell, then computes the gravitational potential at that point, resulting in a convergence failure of the multipole expansion. We describe a new scheme that avoids this problem by computing gravitational potential at cell faces. The second source of error is due to sub-optimal choice of location for the expansion center, which results in angular power at high multipole l values in the gravitational field, requiring a high—and expensive—value of multipole cutoff l {sub max}. By introducing a global measure of angular power in the gravitational field, we show that the optimal coordinate for the expansion is the square-density-weighted mean location. We subject our new multipole self-gravity algorithm, implemented in the FLASH simulation framework, to two rigorous test problems: MacLaurin spheroids for which exact analytic solutions are known, and core-collapse supernovae. We show that key observables of the core-collapse simulations, particularly shock expansion, proto-neutron star motion, and momentum conservation, are extremely sensitive to the accuracy of the multipole gravity, and the accuracy of their computation is greatly improved by our reformulated solver.
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Purpose: This study explores novel methods to address two significant challenges affecting measurement of patient-specific quality assurance (QA) with IBA’s Matrixx Evolution™ ionization chamber array. First, dose calculation algorithms often struggle to accurately determine dose to the chamber array due to CT artifact and algorithm limitations. Second, finite chamber size and volume averaging effects cause additional deviation from the calculated dose. Methods: QA measurements were taken with the Matrixx positioned on the treatment table in a solid-water Multi-Cube™ phantom. To reduce the effect of CT artifact, the Matrixx CT image set was masked with appropriate materials and densities. Individual ionization chambers were masked as air, while the high-z electronic backplane and remaining solid-water material were masked as aluminum and water, respectively. Dose calculation was done using Varian’s Acuros XB™ (V11) algorithm, which is capable of predicting dose more accurately in non-biologic materials due to its consideration of each material’s atomic properties. Finally, the exported TPS dose was processed using an in-house algorithm (MATLAB) to assign the volume averaged TPS dose to each element of a corresponding 2-D matrix. This matrix was used for comparison with the measured dose. Square fields at regularly-spaced gantry angles, as well as selected patient plans were analyzed. Results: Analyzed plans showed improved agreement, with the average gamma passing rate increasing from 94 to 98%. Correction factors necessary for chamber angular dependence were reduced by 67% compared to factors measured previously, indicating that previously measured factors corrected for dose calculation errors in addition to true chamber angular dependence. Conclusion: By comparing volume averaged dose, calculated with a capable dose engine, on a phantom masked with correct materials and densities, QA results obtained with the Matrixx Evolution™ can be significantly improved. In addition, necessary correction factors are reduced, allowing for more reliable and meaningful patient-specific QA measurements.
We propose a systematic approach that can empirically correct three major errors typically found in a density functional theory (DFT) calculation within the local density approximation (LDA) simultaneously for a set of common cation binary semiconductors, such as III-V compounds, (Ga or In)X with X = N,P,As,Sb, and II-VI compounds, (Zn or Cd)X, with X = O,S,Se,Te. By correcting (1) the binary band gaps at high-symmetry points , L, X, (2) the separation of p-and d-orbital-derived valence bands, and (3) conduction band effective masses to experimental values and doing so simultaneously for common cation binaries, the resulting DFT-LDA-based quasi-first-principles method can be used to predict the electronic structure of complex materials involving multiple binaries with comparable accuracy but much less computational cost than a GW level theory. This approach provides an efficient way to evaluate the electronic structures and other material properties of complex systems, much needed for material discovery and design.
In the version of this article originally published, the present address for Petr Popov was incorrectly listed as ‘Koltech Institute of Science & Technology, Moscow, Russia’. The correct present address is ‘Skolkovo Institute of Science and Technology, Moscow, Russia’. The error has been corrected in the HTML and PDF versions of the paper.
Purpose: In carbon-ion radiotherapy treatment planning, the planar integrated dose (PID) measured in water is applied to the patient dose calculation with density scaling using the stopping power ratio. Since body tissues are chemically different from water, this dose calculation can be subject to errors, particularly due to differences in inelastic nuclear interactions. In recent studies, the authors proposed and validated a PID correction method for these errors. In the present study, the authors used this correction method to assess the influence of these nuclear interactions in body tissues on tumor dose in various clinical cases. Methods: Using 10–20 cases each of prostate, head and neck (HN), bone and soft tissue (BS), lung, liver, pancreas, and uterine neoplasms, the authors first used treatment plans for carbon-ion radiotherapy without nuclear interaction correction to derive uncorrected dose distributions. The authors then compared these distributions with recalculated distributions using the nuclear interaction correction (corrected dose distributions). Results: Median (25%/75% quartiles) differences between the target mean uncorrected doses and corrected doses were 0.2% (0.1%/0.2%), 0.0% (0.0%/0.0%), −0.3% (−0.4%/−0.2%), −0.1% (−0.2%/−0.1%), −0.1% (−0.2%/0.0%), −0.4% (−0.5%/−0.1%), and −0.3% (−0.4%/0.0%) for the prostate, HN, BS, lung, liver, pancreas, and uterine cases, respectively. The largest difference of −1.6% in target mean and −2.5% at maximum were observed in a uterine case. Conclusions: For most clinical cases, dose calculation errors due to the water nonequivalence of the tissues in nuclear interactions would be marginal compared to intrinsic uncertainties in treatment planning, patient setup, beam delivery, and clinical response. In some extreme cases, however, these errors can be substantial. Accordingly, this correction method should be routinely applied to treatment planning in clinical practice.