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At least 739 records · Page 41

Similarities behind the high- and low- α disc: small intrinsic abundance scatter and migrating stars

The detailed age-chemical abundance relations of stars measure time-dependent chemical evolution. These trends offer strong empirical constraints on nucleosynthetic processes, as well as the homogeneity of star-forming gas. Characterizing chemical abundances of stars across the Milky Way over time has been made possible very recently, thanks to surveys like Gaia , APOGEE, and Kepler . Studies of the low- α disc have shown that individual elements have unique age–abundance trends and the intrinsic dispersion around these relations is small. In this study, we examine and compare the age distribution of stars across both the high and low- α disc and quantify the intrinsic dispersion of 16 elements around their age–abundance relations at [Fe/H] = 0 using APOGEE DR16. Here, we examine the age–metallicity relation and visualize the temporal and spatial distribution of disc stars in small chemical cells. We find: (1) the high- α disc has shallower age–abundance relations compared to the low- α disc, but similar median intrinsic dispersions of ~0.03 dex; (2) turnover points in the age-[Fe/H] relations across radius for both the high- and low- α disc. The former constrains the mechanisms that set similar intrinsic dispersions, regardless of differences in the enrichment history, for stars in both disc, and the latter indicates the presence of radial migration in both disc. Our study is accompanied by an age catalogue for 64 317 stars in APOGEE derived using THE CANNON with a median uncertainty of 1.5 Gyr (26 per cent; APO-CAN stars), and a red clump catalogue of 22 031 stars with a contamination rate of 2.7 per cent.

79 ASTRONOMY AND ASTROPHYSICS↗

The Wolf-Rayet star population in the most massive giant H II regions of M33

Narrow-band images of NGC 604, NGC 595, and NGC 592, the most massive giant H II regions (GHRs) in M33 have been obtained, in order to study their Wolf-Rayet content. These images reveal the presence of nine candidates in NGC 604 (seven WN, two WC), 10 in NGC 595 (nine WN, one WC), and two in NGC 592 (two WN). Precise positions and estimated magnitudes are given for the candidates, half of which have so far been confirmed spectroscopically as genuine W-R stars. The flux in the emission lines of all candidates is comparable to that of normal Galactic W-R stars of similar subtype. A few of the putative superluminous W-R stars are shown to be close visual double or multiple stars; their newly estimated luminosities are now more compatible with those of normal W-R stars. NGC 595 seems to be overabundant in W-R stars for its mass compared to other GHRs, while NGC 604 is normal. Factors influencing the W-R/O number ratio in GHRs are discussed: metallicity and age appear to be the most important.

Drissen, Laurent↗

Iodine 125 Brachytherapy With Vitrectomy and Silicone Oil in the Treatment of Uveal Melanoma: 1-to-1 Matched Case-Control Series

Purpose: We initially reported the radiation-attenuating effect of silicone oil 1000 centistokes for iodine 125. The purpose of this report was to compare the clinical outcomes in case patients who had iodine 125 brachytherapy with vitrectomy and silicone oil 1000 centistokes with the outcomes in matched control patients who underwent brachytherapy alone. Methods and Materials: Consecutive patients with uveal melanoma who were treated with iodine 125 plaque brachytherapy and vitrectomy with silicone oil with minimum 1-year follow-up were included. Control patients who underwent brachytherapy alone were matched for tumor size, location, and sex. Baseline patient and tumor characteristics and tumor response to radiation, final visual acuity, macular status, central macular thickness by ocular coherence tomography (OCT), cataract progression, and metastasis at last follow-up visit were compared. Surgical complications were also determined. Results: Twenty case patients met the inclusion criteria. The average follow-up time was 22.1 months in case patients and 19.4 months in control patients. The final logMAR vision was 0.81 in case patients and 1.1 in control patients (P=.071); 8 case patients and 16 control patients had abnormal macular findings (P=.011); and the average central macular thickness by OCT was 293.2 μm in case patients and 408.5 μm in control patients (P=.016). Eleven case patients (55%) and 1 control patient (5%) had required cataract surgery at last follow-up (P=.002). Four patients in the case group and 1 patient in the control group experienced metastasis (P=.18). Among the cases, intraoperative retinal tear occurred in 3 patients; total serous retinal detachment and macular hole developed in 1 case patient each. There was no case of rhegmatogenous retinal detachment, treatment failure, or local tumor dissemination in case patients or control patients. Conclusions: With up to 3 years of clinical follow-up, silicone oil during brachytherapy for the treatment of uveal melanoma resulted in fewer abnormal maculas, lower central macular thickness on OCT, and a trend toward better final visual acuity in comparison with matched control patients who underwent brachytherapy alone.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Introducing Molecular Hypernetworks for Discovery in Multidimensional Metabolomics Data

Orthogonal separations of data from high-resolution mass spectrometry can provide insight into sample composition and address challenges of complete annotation of molecules in untargeted metabolomics. “Molecular networks” (MNs), as used in the Global Natural Products Social Molecular Networking platform, are a prominent strategy for exploring and visualizing molecular relationships and improving annotation. MNs are mathematical graphs showing the relationships between measured multidimensional data features. MNs also show promise for using network science algorithms to automatically identify targets for annotation candidates and to dereplicate features associated with a single molecular identity. Here, this paper introduces “molecular hypernetworks” (MHNs) as more complex MN models able to natively represent multiway relationships among observations. Compared to MNs, MHNs can more parsimoniously represent the inherent complexity present among groups of observations, initially supporting improved exploratory data analysis and visualization. MHNs also promise to increase confidence in annotation propagation, for both human and analytical processing. We first illustrate MHNs with simple examples, and build them from liquid chromatography- and ion mobility spectrometry-separated MS data. We then describe a method to construct MHNs directly from existing MNs as their “clique reconstructions”, demonstrating their utility by comparing examples of previously published graph-based MNs to their respective MHNs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Nonlinear, Human-Centered Approach to Motion Cueing with a Neurocomputing Solver

This paper discusses the continuation of research into the development of new motion cueing algorithms first reported in 1999. In this earlier work, two viable approaches to motion cueing were identified: the coordinated adaptive washout algorithm or 'adaptive algorithm', and the 'optimal algorithm'. In this study, a novel approach to motion cueing is discussed that would combine features of both algorithms. The new algorithm is formulated as a linear optimal control problem, incorporating improved vestibular models and an integrated visual-vestibular motion perception model previously reported. A control law is generated from the motion platform states, resulting in a set of nonlinear cueing filters. The time-varying control law requires the matrix Riccati equation to be solved in real time. Therefore, in order to meet the real time requirement, a neurocomputing approach is used to solve this computationally challenging problem. Single degree-of-freedom responses for the nonlinear algorithm were generated and compared to the adaptive and optimal algorithms. Results for the heave mode show the nonlinear algorithm producing a motion cue with a time-varying washout, sustaining small cues for a longer duration and washing out larger cues more quickly. The addition of the optokinetic influence from the integrated perception model was shown to improve the response to a surge input, producing a specific force response with no steady-state washout. Improved cues are also observed for responses to a sway input. Yaw mode responses reveal that the nonlinear algorithm improves the motion cues by reducing the magnitude of negative cues. The effectiveness of the nonlinear algorithm as compared to the adaptive and linear optimal algorithms will be evaluated on a motion platform, the NASA Langley Research Center Visual Motion Simulator (VMS), and ultimately the Cockpit Motion Facility (CMF) with a series of pilot controlled maneuvers. A proposed experimental procedure is discussed. The results of this evaluation will be used to assess motion cueing performance.

Telban, Robert J.↗

WarpIV: In situ visualization and analysis of ion accelerator simulations

The generation of short pulses of ion beams through the interaction of an intense laser with a plasma sheath offers the possibility of compact and cheaper ion sources for many applications--from fast ignition and radiography of dense targets to hadron therapy and injection into conventional accelerators. To enable the efficient analysis of large-scale, high-fidelity particle accelerator simulations using the Warp simulation suite, the authors introduce the Warp In situ Visualization Toolkit (WarpIV). WarpIV integrates state-of-the-art in situ visualization and analysis using VisIt with Warp, supports management and control of complex in situ visualization and analysis workflows, and implements integrated analytics to facilitate query- and feature-based data analytics and efficient large-scale data analysis. WarpIV enables for the first time distributed parallel, in situ visualization of the full simulation data using high-performance compute resources as the data is being generated by Warp. The authors describe the application of WarpIV to study and compare large 2D and 3D ion accelerator simulations, demonstrating significant differences in the acceleration process in 2D and 3D simulations. WarpIV is available to the public via https://bitbucket.org/berkeleylab/warpiv. The Warp In situ Visualization Toolkit (WarpIV) supports large-scale, parallel, in situ visualization and analysis and facilitates query- and feature-based analytics, enabling for the first time high-performance analysis of large-scale, high-fidelity particle accelerator simulations while the data is being generated by the Warp simulation suite. Furthermore, this supplemental material https://extras.computer.org/extra/mcg2016030022s1.pdf provides more details regarding the memory profiling and optimization and the Yee grid recentering optimization results discussed in the main article.

43 PARTICLE ACCELERATORS↗

MetaboDirect: an analytical pipeline for the processing of FT-ICR MS-based metabolomic data

Background: Microbiomes are now recognized as the main drivers of ecosystem function ranging from the oceans and soils to humans and bioreactors. However, a grand challenge in microbiome science is to characterize and quantify the chemical currencies of organic matter (i.e., metabolites) that microbes respond to and alter. Critical to this has been the development of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), which has drastically increased molecular characterization of complex organic matter samples, but challenges users with hundreds of millions of data points where readily available, user-friendly, and customizable software tools are lacking. Results: Here, we build on years of analytical experience with diverse sample types to develop MetaboDirect, an open-source, command-line-based pipeline for the analysis (e.g., chemodiversity analysis, multivariate statistics), visualization (e.g., Van Krevelen diagrams, elemental and molecular class composition plots), and presentation of direct injection high-resolution FT-ICR MS data sets after molecular formula assignment has been performed. When compared to other available FT-ICR MS software, MetaboDirect is superior in that it requires a single line of code to launch a fully automated framework for the generation and visualization of a wide range of plots, with minimal coding experience required. Among the tools evaluated, MetaboDirect is also uniquely able to automatically generate biochemical transformation networks (ab initio) based on mass differences (mass difference network-based approach) that provide an experimental assessment of metabolite connections within a given sample or a complex metabolic system, thereby providing important information about the nature of the samples and the set of microbial reactions or pathways that gave rise to them. Finally, for more experienced users, MetaboDirect allows users to customize plots, outputs, and analyses. Conclusion: Application of MetaboDirect to FT-ICR MS-based metabolomic data sets from a marine phage-bacterial infection experiment and a Sphagnum leachate microbiome incubation experiment showcase the exploration capabilities of the pipeline that will enable the research community to evaluate and interpret their data in greater depth and in less time. It will further advance our knowledge of how microbial communities influence and are influenced by the chemical makeup of the surrounding system. The source code and User’s guide of MetaboDirect are freely available through (https://github.com/Coayala/MetaboDirect) and (https://metabodirect.readthedocs.io/en/latest/), respectively.

54 ENVIRONMENTAL SCIENCES↗

Proposal to evaluate the use of ERTS-A imagery in mapping and managing soil and range resources in the Sand Hills Region of Nebraska

The author has identified the following significant results. Visual examination of RB-57F color infrared imagery of range sites within Test Site 313 indicates that early season imagery will show significant differences in appearance of sub-irrigated sites as compared to dry valley sites. Differences appear to be significant also when comparing the previous two sites to sands sites. Comparison of existing soil map soils delineations with vegetative growth patterns shows reasonably good agreement between the two patterns over rather broad areas. Visual examination of ERTS-1 imagery has also shown that rangeland burned by prairie fire within the last six months can be distinguished. Three confirmed fire areas have been shown on the imagery. Since only broad estimates of burned acres are available, more accurate acreage measurements will be attempted. Known acreage of burned areas will be of value to those agencies responsible for deferred grazing payments to land owners. The relative speed with which this acreage information would become available to these agencies through ERTS-1 imagery would be of much benefit.

Drew, J. V.↗

Advantages of Intraprocedural Unenhanced CT During Adrenal Venous Sampling to Confirm Accurate Catheterization of the Right Adrenal Vein

Purpose: To evaluate the advantages of intraprocedural CT during adrenal venous sampling (AVS) to confirm accurate catheterization of the right adrenal vein (RAV). Materials and Methods: This single-institution study included 106 patients (mean age 52.4 years; range 28–74 years) with primary aldosteronism who performed contrast-enhanced CT (CECT) before AVS following AVS between January 2011 and March 2018. After catheterization of the RAV under fluoroscopic guidance, unenhanced CT images were obtained to confirm catheter position on unified CT angiography system. Catheter repositioning was performed when the catheter was inaccurately positioned. Venography findings were classified into two groups: (1) presumably cannulated in the RAV (presumed RAV group) and (2) obscured visualization of the RAV because of collateral vessels (obscured RAV group). Success rates of AVS were compared using Fisher’s exact test. Results: The overall success of AVS was achieved in 104 patients (98.1%). Catheter was deviated into the IVC during intraprocedural CT in four patients. Fourteen patients (14.0%) required catheter repositioning by intraprocedural CT images, and accurate catheterization in the RAV was eventually accomplished. The success rate of AVS was significantly higher in the presumed RAV group (90.1% [73/81]) than that in the obscured RAV group (68.4% [13/19]) (p = 0.024). If intraprocedural CT was not acquired during AVS, the success rate of AVS would have been significantly lower (84.9% [90/106]) compared with that use of intraprocedural CT (98.1% [104/106]) (p < 0.001). Conclusions: Intraprocedural unenhanced CT by referring to the preprocedural CECT before AVS enables the confirmation of accurate catheterization of the RAV. Level of Evidence: Level 4, case series.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Nanowire growth kinetics in aberration corrected environmental transmission electron microscopy

Here, we visualize atomic level dynamics during Si nanowire growth using aberration corrected environmental transmission electron microscopy, and compare with lower pressure results from ultra-high vacuum microscopy. We discuss the importance of higher pressure observations for understanding growth mechanisms and describe protocols to minimize effects of the higher pressure background gas.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

An apparatus for generation and quantitative measurement of homogeneous isotropic turbulence in He ii

The superfluid phase of helium-4, known as He ii, exhibits extremely small kinematic viscosity and may be a useful tool for economically producing and studying high Reynolds number turbulent flow. Such applications are not currently possible because a comprehensive understanding of the complex two-fluid behavior of He ii is lacking. This situation could be remedied by a systematic investigation of simple, well controlled turbulence that can be directly compared with theoretical models. To this end, we have developed a new apparatus that combines flow visualization with second sound attenuation to study turbulence in the wake of a mesh grid towed through a He ii filled channel. One of three mesh grids (mesh number M = 3, 3.75, or 5 mm) can be pulled at speeds between 0.1 and 60 cm/s through a cast acrylic flow channel which has a 16 mm × 16 mm cross section and measures 330 mm long. The motion of solidified deuterium tracer particles, with diameter of the order 1 μm, in the resulting flow is captured by a high speed camera, and a particle tracking velocimetry algorithm resolves the Lagrangian particle trajectories through the turbulent flow field. A pair of oscillating superleak second sound transducers installed in the channel allows complementary measurement of vortex line density in the superfluid throughout the turbulent decay process. Here, success in early experiments demonstrates the effectiveness of both probes, and preliminary analysis of the data shows that both measurements strongly correlate with each other. Further investigations will provide comprehensive information that can be used to address open questions about turbulence in He ii and move toward the application of this fluid to high Reynolds number fluid research

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimizing Error-Bounded Lossy Compression for Scientific Data With Diverse Constraints

Vast volumes of data are produced by today's scientific simulations and advanced instruments. These data cannot be stored and transferred efficiently because of limited I/O bandwidth, network speed, and storage capacity. Error-bounded lossy compression can be an effective method for addressing these issues: not only can it significantly reduce data size, but it can also control the data distortion based on user-defined error bounds. In practice, many scientific applications have specific requirements or constraints for lossy compression, in order to guarantee that the reconstructed data are valid for post hoc analysis. For example, some datasets contain irrelevant data that should be isolated in particular and users often have intuition regarding value ranges, geospatial regions, and other data subsets that are crucial for subsequent analysis. Existing state-of-the-art error-bounded lossy compressors, however, do not consider these constraints during compression, resulting in inferior compression ratios with respect to user's post hoc analysis, due to the fact that the data itself provides little or no value for post hoc analysis. In this work we address this issue by proposing an optimized framework that can preserve diverse constraints during the error-bounded lossy compression, e.g., cleaning the irrelevant data, efficiently preserving different precision for multiple value intervals, and allowing users to set diverse precision over both regular and irregular regions. We perform our evaluation on a supercomputer with up to 2,100 cores. Experiments with six real-world applications show that our proposed diverse constraints based error-bounded lossy compressor can obtain a higher visual quality or data fidelity on reconstructed data with the same or even higher compression ratios compared with the traditional state-of-the-art compressor SZ. Furthermore, our experiments also demonstrate very good scalability in compression performance compared with the I/O throughput of the parallel file system.

97 MATHEMATICS AND COMPUTING↗

SU-E-T-234: Daily Quality Assurance for a Six Degrees of Freedom Couch Using a Novel Phantom

Purpose: To test the accuracy and reproducibility of both translational and rotational movements for a couch with six degrees of freedom (6DoF) using a novel phantom design Methods: An end-to-end test was carried out using two different phantoms. A 6 cm3 cube with a central fiducial BB (WL-QA Sun Nuclear) and a custom fabricated rectangular prism (31 cm x 8 cm x 8 cm), placed on a baseplate with known angular offsets for pitch, roll and yaw with a central fiducial BB and unique surface structures for registration purposes, were used. The end-to-end test included an initial CT simulation for a reference study, setup to an offset mark on each phantom, registration of the reference CT to the acquired cone-beam CT, and final Winston-Lutz delivery at four cardinal gantry angles. Results for both translational and rotational movements were recorded and compared for both phantoms. Results: Translational and rotational measurements were performed with a PerfectPitch (Varian) couch for 10 trials for both phantoms. Distinct translational shifts were [−5.372±0.384mm, −10.183±0.137mm, 14.028±0.155mm] for the cube and [7.520±0.159mm, −9.117±0.101mm, 16.273±0.115mm] for the prototype phantom for lateral, longitudinal, and vertical shifts, respectively. Distinct rotational adjustments were [1.121±0.102o, −1.067±0.235o, −2.662±0.380o] for the cube and [2.534±0.059o, 1.994±0.025o, 2.094±0.076o] for the prototype for pitch, roll, and yaw, respectively. Winston-Lutz test results performed after 6DoF couch correction from each cardinal gantry angle ranged from 0.26–0.72mm for the cube and 0.55–0.86mm for the prototype. Conclusion: The prototype phantom is more precise for both translational and rotational adjustments compared to a commercial phantom. The design of the prototype phantom allows for a more discernible visual confirmation of correct translational and rotational adjustments with the prototype phantom. Winston-Lutz results are more accurate for the commercial phantom but are still within tolerance for the prototype phantom.

60 APPLIED LIFE SCIENCES↗

Conceptual Model Update of Mercury Sources and Flux at Y-12 and Upper East Fork Poplar Creek, Oak Ridge,Tennessee

The interactions between the key processes that control the fate and transport of mercury (Hg) in the sediments, groundwater, and stream water within the Y-12 National Security Complex (Y-12) in Oak Ridge, Tennessee are complex, and many aspects are not well understood. In contaminated environments such as Y-12, conceptual models are frequently developed to aid in visualizing and understanding the dynamic nature of the hydrologic, geochemical, and physical environment. These conceptual models integrate data in an internally consistent manner to understand processes that control the fate and transport of contaminants. Over the past few decades of environmental investigation at Y-12, a number of conceptual models have been developed to identify and define various technical processes at various scales. The main purpose of the activities described in this report is to update the 2011 conceptual model for Upper East Fork Poplar Creek using the most recent Hg concentration and flux data and informed scientific interpretation. Emphasis was placed on improving the previous model by implementing a more detailed spatial and temporal approach to visualize transport pathways in the watershed and trends in flux and concentration over time, and to compare baseflow and stormflow system dynamics. Detailed descriptions of historical and current Hg sources and transport pathways are also provided for the east and west ends of the facility. This conceptual model will allow the US Department of Energy to evaluate past and present remedial activities and provide a strong technical basis for prioritizing and optimizing remedial responses in a cost-effective and efficient manner. Twenty years ago, Hg flux from Outfall (OF) 200 at the headwaters of East Fork Poplar Creek represented approximately 20% of the overall flux leaving Y-12. By the time of the 2011 conceptual model report, that percentage had increased to 70%–80%. Flux estimates compiled for this report using data from 2009 to 2018 show that OF200 accounted for roughly 60% of the flux leaving Y-12. The relative role of the four storm drain conduits to OF200 appeared similar to 2011, with OF163 being the greatest contributor to downstream flux. An increase in Hg concentrations and flux occurred throughout and downstream of west end storm drains in 2011 in response to a storm drain cleanout. Leading up to the 2011 storm drain cleanout, annual baseflow flux was higher at OF200A6 than at Station 17. From 2011 to 2018, the trend reversed with concentrations and flux being higher at Station 17 than at OF200A6. A spike in concentrations occurred in July 2018, potentially due to a one-time influx of Hg that occurred during COLEX decontamination and decommissioning activities at Y-12. This report includes recommendations for improving our conceptual understanding of Hg sources, transport pathways, and flux at Y-12. Important recommendations include further evaluation of transport pathways, concurrent measurement of Hg concentration and flux under baseflow and stormflow conditions at multiple sites, and research to understand the connections among periphyton and methylmercury concentration, bioavailability, and bioaccumulation. Ongoing facility decontamination and decommissioning efforts, site characterization, remedial actions, and research are facilitating the collection of new Hg data at Y-12. The conceptual model update provided herein takes advantage of the extensive recent Hg sampling to provide an updated assessment of Hg mass balance and support a refined understanding of Hg behavior at or near Y-12. This assessment should assist in future environmental management decisions and in mitigating the impacts of Hg on the surrounding environment.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Conditional Generative Adversarial Networks (cGANs) for Near Real-Time Precipitation Estimation from Multispectral GOES-16 Satellite Imageries—PERSIANN-cGAN

In this paper, we present a state-of-the-art precipitation estimation framework which leverages advances in satellite remote sensing as well as Deep Learning (DL). The framework takes advantage of the improvements in spatial, spectral and temporal resolutions of the Advanced Baseline Imager (ABI) onboard the GOES-16 platform along with elevation information to improve the precipitation estimates. The procedure begins by first deriving a Rain/No Rain (R/NR) binary mask through classification of the pixels and then applying regression to estimate the amount of rainfall for rainy pixels. A Fully Convolutional Network is used as a regressor to predict precipitation estimates. The network is trained using the non-saturating conditional Generative Adversarial Network (cGAN) and Mean Squared Error (MSE) loss terms to generate results that better learn the complex distribution of precipitation in the observed data. Common verification metrics such as Probability Of Detection (POD), False Alarm Ratio (FAR), Critical Success Index (CSI), Bias, Correlation and MSE are used to evaluate the accuracy of both R/NR classification and real-valued precipitation estimates. Statistics and visualizations of the evaluation measures show improvements in the precipitation retrieval accuracy in the proposed framework compared to the baseline models trained using conventional MSE loss terms. This framework is proposed as an augmentation for PERSIANN-CCS (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network- Cloud Classification System) algorithm for estimating global precipitation.

42 ENGINEERING↗

A shuttle and space station manipulator system for assembly, docking, maintenance, cargo handling and spacecraft retrieval (preliminary design). Volume 2: Concept development and selection

The overall program background, the various system concepts considered, and the rationale for the selected design are described. The concepts for each subsystem are also described and compared. Details are given for the requirements, boom configuration and dynamics, actuators, man/machine interface and control, visual system, control system, environmental control and life support, data processing, and materials.

Source record↗

Error detection and data smoothing based on local procedures

An algorithm is presented which is able to locate isolated bad points and correct them without contaminating the rest of the good data. This work has been greatly influenced and motivated by what is currently done in the manual loft. It is not within the scope of this work to handle small random errors characteristic of a noisy system, and it is therefore assumed that the bad points are isolated and relatively few when compared with the total number of points. Motivated by the desire to imitate the loftsman a visual experiment was conducted to determine what is considered smooth data. This criterion is used to determine how much the data should be smoothed and to prove that this method produces such data. The method utimately converges to a set of points that lies on the polynomial that interpolates the first and last points; however convergence to such a set is definitely not the purpose of our algorithm. The proof of convergence is necessary to demonstrate that oscillation does not take place and that in a finite number of steps the method produces a set as smooth as desired.

Guerra, V. M.↗