scholarly journals Neutron optical test of completeness of quantum root-mean-square errors

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Stephan Sponar ◽  
Armin Danner ◽  
Masanao Ozawa ◽  
Yuji Hasegawa
Keyword(s):  
Root Mean Square ◽  
Quantum Physics ◽  
Classical Mechanics ◽  
Quantum Measurements ◽  
Mean Square ◽  
Error Measure ◽  
Optical Test ◽  
The Mean ◽  
Noise Operator ◽  
Mean Square Errors

AbstractWhile in classical mechanics the mean error of a measurement is solely caused by the measuring process (or device), in quantum mechanics the operator-based nature of quantum measurements has to be considered in the error measure as well. One of the major problems in quantum physics has been to generalize the classical root-mean-square error to quantum measurements to obtain an error measure satisfying both soundness (to vanish for any accurate measurements) and completeness (to vanish only for accurate measurements). A noise-operator-based error measure has been commonly used for this purpose, but it has turned out incomplete. Recently, Ozawa proposed an improved definition for a noise-operator-based error measure to be both sound and complete. Here, we present a neutron optical demonstration for the completeness of the improved error measure for both projective (or sharp) as well as generalized (or unsharp) measurements.

scholarly journals Histamine Control in Raw and Processed Tuna: A Rapid Tool Based on NIR Spectroscopy

Foods ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 885
Author(s):  
Sergio Ghidini ◽  
Luca Maria Chiesa ◽  
Sara Panseri ◽  
Maria Olga Varrà ◽  
Adriana Ianieri ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Partial Least Square ◽  
Least Square ◽  
Partial Least Square Regression ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Tuna Fish ◽  
Mean Square Errors

The present study was designed to investigate whether near infrared (NIR) spectroscopy with minimal sample processing could be a suitable technique to rapidly measure histamine levels in raw and processed tuna fish. Calibration models based on orthogonal partial least square regression (OPLSR) were built to predict histamine in the range 10–1000 mg kg−1 using the 1000–2500 nm NIR spectra of artificially-contaminated fish. The two models were then validated using a new set of naturally contaminated samples in which histamine content was determined by conventional high-performance liquid chromatography (HPLC) analysis. As for calibration results, coefficient of determination (r2) > 0.98, root mean square of estimation (RMSEE) ≤ 5 mg kg−1 and root mean square of cross-validation (RMSECV) ≤ 6 mg kg−1 were achieved. Both models were optimal also in the validation stage, showing r2 values > 0.97, root mean square errors of prediction (RMSEP) ≤ 10 mg kg−1 and relative range error (RER) ≥ 25, with better results showed by the model for processed fish. The promising results achieved suggest NIR spectroscopy as an implemental analytical solution in fish industries and markets to effectively determine histamine amounts.

scholarly journals Evidence That Supertriangles Exist in Nature from the Vertical Projections of Koelreuteria paniculata Fruit

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 23
Author(s):  
Yuping Li ◽  
Brady K. Quinn ◽  
Johan Gielis ◽  
Yirong Li ◽  
Peijian Shi
Keyword(s):  
Root Mean Square ◽  
Goodness Of Fit ◽  
Mean Square ◽  
Sea Stars ◽  
Different Types ◽  
Koelreuteria Paniculata ◽  
Two Parameters ◽  
Mean Square Errors

Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms.

scholarly journals The Accuracy of Real-Time hmF2 Estimation from Ionosondes

2020 ◽  
Vol 12 (17) ◽  
pp. 2671
Author(s):  
Carlo Scotto ◽  
Dario Sabbagh
Keyword(s):  
Data Analysis ◽  
Real Time ◽  
Root Mean Square ◽  
Magnetic Activity ◽  
Mean Square ◽  
Incoherent Scatter Radar ◽  
Incoherent Scatter ◽  
Scatter Radar ◽  
Mean Square Errors

A total of 4991 ionograms recorded from April 1997 to December 2017 by the Millstone Hill Digisonde (42.6°N, 288.5°E) were considered, with simultaneous Ne(h)[ISR] profiles recorded by the co-located Incoherent Scatter Radar (ISR). The entire ionogram dataset was scaled with both the Autoscala and ARTIST programs. The reliability of the hmF2 values obtained by ARTIST and Autoscala was assessed using the corresponding ISR values as a reference. Average errors Δ and the root mean square errors RMSE were computed for the whole dataset. Data analysis shows that both the Autoscala and ARTIST systems tend to underestimate hmF2 values with |Δ| in all cases less than 10 km. For high magnetic activity ARTIST offers better accuracy than Autoscala, as evidenced by RMSE[ARTIST] < RMSE[Autoscala], under both daytime and nighttime conditions, and considering all hours of the day. Conversely, under low and medium magnetic activity Autoscala tends to estimate hmF2 more accurately than the ARTIST system for both daytime and nighttime conditions, when RMSE[Autoscala] < RMSE[ARTIST]. However, RMSE[Autoscala] slightly exceeds RMSE[ARTIST] for the day as a whole. RMSE values are generally substantial (RMSE > 16 km in all cases), which places a limit on the results obtainable with real-time models that ingest ionosonde data.

scholarly journals Validation of ESA Sentinel-2 L2A Aerosol Optical Thickness and Columnar Water Vapour during 2017–2018

2019 ◽  
Vol 11 (14) ◽  
pp. 1649 ◽  
Author(s):  
María Ángeles Obregón ◽  
Gonçalo Rodrigues ◽  
Maria Joao Costa ◽  
Miguel Potes ◽  
Ana Maria Silva
Keyword(s):  
Water Vapour ◽  
Root Mean Square ◽  
Optical Thickness ◽  
Spectral Response ◽  
Aerosol Optical Thickness ◽  
Mean Bias Error ◽  
Mean Square ◽  
Response Functions ◽  
Mean Square Errors ◽  
Sentinel 2

This study presents a validation of aerosol optical thickness (AOT) and integrated water vapour (IWV) products provided by the European Space Agency (ESA) from multi-spectral imager (MSI) measurements on board the Sentinel-2 satellite (ESA-L2A). For that purpose, data from 94 Aerosol Robotic Network (AERONET) stations over Europe and adjacent regions, covering a wide geographical region with a variety of climate and environmental conditions and during the period between March 2017 and December 2018 have been used. The comparison between ESA-L2A and AERONET shows a better agreement for IWV than the AOT, with normalized root mean square errors (NRMSE) of 5.33% and 9.04%, respectively. This conclusion is also reflected in the values of R2, which are 0.99 and 0.65 for IWV and AOT, respectively. The study period was divided into two sub-periods, before and after 15 January 2018, when the Sentinel-2A spectral response functions of bands 1 and 2 (centered at 443 and 492 nm) were updated by ESA, in order to investigate if the lack of agreement in the AOT values was connected to the use of incorrect spectral response functions. The comparison of ESA-L2A AOT with AERONET measurements showed a better agreement for the second sub-period, with root mean square error (RMSE) values of 0.08 in comparison with 0.14 in the first sub-period. This same conclusion was attained considering mean bias error (MBE) values that decreased from 0.09 to 0.01. The ESA-L2A AOT values estimated with the new spectral response functions were closer to the correspondent reference AERONET values than the ones obtained using the previous spectral response functions. IWV was not affected by this change since the retrieval algorithm does not use bands 1 and 2 of Sentinel-2. Additionally, an analysis of potential uncertainty sources to several factors affecting the AOT comparison is presented and recommendations regarding the use of ESA-L2A AOT dataset are given.

scholarly journals Realization of the Primary Terrestrial Reference Frame

1991 ◽  
Vol 127 ◽  
pp. 108-115
Author(s):  
W. Kosek ◽  
B. Kołaczek
Keyword(s):  
Reference Frame ◽  
Geographic Distribution ◽  
Terrestrial Reference Frame ◽  
Mean Square ◽  
Minimum Value ◽  
Collocation Points ◽  
Station Coordinates ◽  
The Mean ◽  
Transformation Parameters ◽  
Mean Square Errors

AbstractThe PTRF is based on 43 sites with 64 SSC collocation points with the optimum geographic distribution, which were selected from all stations of the ITRF89 according to the criterion of the minimum value of the errors of 7 parameters of transformation. The ITRF89 was computed by the IERS Terrestrial Frame Section in Institut Geographique National - IGN and contains 192 VLBI and SLR stations (points) with 119 collocation ones. The PTRF has been compared with the ITRF89. The errors of the 7 parameters of transformation between the PTRF and 18 individual SSC as well as the mean square errors of station coordinates are of the same order as those for the ITRF89. The transformation parameters between the ITRF89 and the PTRF are negligible and their errors are of the order of 3 mm.

Direct numerical simulation of turbulence in injection-driven three-dimensional cylindrical flows

2011 ◽  
Vol 670 ◽  
pp. 176-203 ◽  
Author(s):  
JU ZHANG ◽  
THOMAS L. JACKSON
Keyword(s):  
Reynolds Number ◽  
Root Mean Square ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Wall Friction ◽  
Mean Square ◽  
The Mean ◽  
Wall Shear ◽  
Strong Injection ◽  
Near Wall

Incompressible turbulent flow in a periodic circular pipe with strong injection is studied as a simplified model for the core flow in a solid-propellant rocket motor and other injection-driven internal flows. The model is based on a multi-scale asymptotic approach. The intended application of the current study is erosive burning of solid propellants. Relevant analysis for easily accessible parameters for this application, such as the magnitudes, main frequencies and wavelengths associated with the near-wall shear, and the assessment of near-wall turbulence viscosity is focused on. It is found that, unlike flows with weak or no injection, the near-wall shear is dominated by the root mean square of the streamwise velocity which is a function of the Reynolds number, while the mean streamwise velocity is only weakly dependent on the Reynolds number. As a result, a new wall-friction velocity $\(u_\tau{\,=\,}\sqrt{\tau_w/\rho}\)$, based on the shear stress derived from the sum of the mean and the root mean square, i.e. $\(\tau_{w,inj} {\,=\,} \mu |{\partial (\bar{u}+u_{rms})}/{\partial r}|_w\)$, is proposed for the scaling of turbulent viscosity for turbulent flows with strong injection. We also show that the mean streamwise velocity profile has an inflection point near the injecting surface.

A STUDY OF MODELS FOR HANDGRIP FORCE PREDICTION FROM SURFACE ELECTROMYOGRAPHY OF EXTENSOR MUSCLE

2009 ◽  
Vol 21 (02) ◽  
pp. 81-88 ◽  
Author(s):  
Wensheng Hou ◽  
Xiaolin Zheng ◽  
Yingtao Jiang ◽  
Jun Zheng ◽  
Chenglin Peng ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Surface Electromyography ◽  
Random Sequence ◽  
Maximum Voluntary Contraction ◽  
Force Production ◽  
Voluntary Contraction ◽  
Mean Square ◽  
Force Level ◽  
Force Output ◽  
Mean Square Errors

Force production involves the coordination of multiple muscles, and the produced force levels can be attributed to the electrophysiology activities of those related muscles. This study is designed to explore the activity modes of extensor carpi radialis longus (ECRL) using surface electromyography (sEMG) at the presence of different handgrip force levels. We attempt to compare the performance of both the linear and nonlinear models for estimating handgrip forces. To achieve this goal, a pseudo-random sequence of handgrip tasks with well controlled force ranges is defined for calibration. Eight subjects (all university students, five males, and three females) have been recruited to conduct both calibration and voluntary trials. In each trial, sEMG signals have been acquired and preprocessed with Root–Mean–Square (RMS) method. The preprocessed signals are then normalized with amplitude value of Maximum Voluntary Contraction (MVC)-related sEMG. With the sEMG data from calibration trials, three models, Linear, Power, and Logarithmic, are developed to correlate the handgrip force output with the sEMG activities of ECRL. These three models are subsequently employed to estimate the handgrip force production of voluntary trials. For different models, the Root–Mean–Square–Errors (RMSEs) of the estimated force output for all the voluntary trials are statistically compared in different force ranges. The results show that the three models have different performance in different force ranges. Linear model is suitable for moderate force level (30%–50% MVC), whereas a nonlinear model is more accurate in the weak force level (Power model, 10%–30% MVC) or the strong force level (Logarithmic model, 50%–80% MVC).

Mathematical-Statistical Methods for the Analysis of Aerial Triangulation Adjustment Errors Using a Computer Program

1975 ◽  
Vol 29 (2) ◽  
pp. 175-188
Author(s):  
M. Mosaad Allam
Keyword(s):  
Computer Program ◽  
Frequency Interval ◽  
Mean Square ◽  
Fisher Criterion ◽  
Statistical Parameters ◽  
Sample Distribution ◽  
Development Section ◽  
The Mean ◽  
Kolmogorov Criterion ◽  
Mean Square Errors

In practice, photogrammetrists use a single statistic reliability interval criterion, based on the mean square errors, to judge the accuracy of adjustment of photogrammetric blocks. Even in some cases, if the practical and theoretical distributions of frequency interval agree, such a test does not make it possible to establish the closeness of their convergence nor the degree of their difference. In other words, to get a complete picture of the character of the distribution of errors in the adjusted photogrammetric blocks, it is insufficient to investigate any single statistic. In the Research and Development Section of the Topographical Survey Directorate, a computer program (SABA) has been designed to analyze the errors of photogrammetric block adjustments, compute various statistical parameters and check the sample distribution using Kolmogorov criterion. Based on the decision taken, the correspondence between the empirical and theoretical distribution series are checked using the criterion χ2. The program divides the adjusted block to make a comparative evaluation of accuracies in the different sub-blocks. In this case, in addition to Kolmogorov and χ2 tests, the program checks the reliability intervals of the means and mean square errors of the samples and uses Fisher criterion ‘F’ to check the hypothesis of the equality of dispersion. SABA is coded in Fortran IV and Compass for the CDC CYBER 74 and requires a central memory of 28K decimal works. SABA is the acronym for Statistical Analysis of Block Adjustment.

scholarly journals Prediction of Wheat Grain Protein by Coupling Multisource Remote Sensing Imagery and ECMWF Data

2020 ◽  
Vol 12 (8) ◽  
pp. 1349 ◽  
Author(s):  
Xiaobin Xu ◽  
Cong Teng ◽  
Yu Zhao ◽  
Ying Du ◽  
Chunqi Zhao ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Linear Model ◽  
Root Mean Square ◽  
Vegetation Index ◽  
Meteorological Data ◽  
Hierarchical Linear Model ◽  
Grain Protein ◽  
Landsat 8 ◽  
Mean Square ◽  
Mean Square Errors

Industrialization production with high quality and effect on winter is an important measure for accelerating the shift from increasing agricultural production to improving quality in terms of grain protein content (GPC). Remote sensing technology achieved the GPC prediction. However, large deviations in interannual expansion and regional transfer still exist. The present experiment was carried out in wheat producing areas of Beijing (BJ), Renqiu (RQ), Quzhou, and Jinzhou in Hebei Province. First, the spectral consistency of Landsat 8 Operational Land Imager (LS8) and RapidEye (RE) was compared with Sentinel-2 (S2) satellites at the same ground point in the same period. The GPC prediction model was constructed by coupling the vegetation index with the meteorological data obtained by the European Center for Medium-range Weather Forecasts using hierarchical linear model (HLM) method. The prediction and spatial expansion of regional GPC were validated. Results were as follows: (1) Spectral information calculated from S2 imagery were highly consistent with LS8 (R2 = 1.00) and RE (R2 = 0.99) imagery, which could be jointly used for GPC modeling. (2) The predicted GPC by using the HLM method (R2 = 0.524) demonstrated higher accuracy than the empirical linear model (R2 = 0.286) and showed higher improvements across inter-annual and regional scales. (3) The GPC prediction results of the verification samples in RQ, BJ, Xiaotangshan (XTS) in 2018, and XTS in 2019 were ideal with root mean square errors of 0.61%, 1.13%, 0.91%, and 0.38%, and relative root mean square error of 4.11%, 6.83%, 6.41%, and 2.58%, respectively. This study has great application potential for regional and inter-annual quality prediction.

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