MEAN SQUARE ERRORS OF POINT DETERMINATIONS

1944 ◽  
Vol 7 (53) ◽  
pp. 279-294
Author(s):  
G. H. Menzies
Keyword(s):  
Mean Square ◽  
Mean Square Errors

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 Automatic modelling of human musculoskeletal ligaments – Framework overview and model quality evaluation

2021 ◽  
pp. 1-14
Author(s):  
Noura Hamze ◽  
Lukas Nocker ◽  
Nikolaus Rauch ◽  
Markus Walzthöni ◽  
Matthias Harders ◽  
...  
Keyword(s):  
Statistical Model ◽  
Soft Tissues ◽  
Automatic Generation ◽  
Cadaveric Study ◽  
Patient Specific ◽  
Mean Square ◽  
Shape Modelling ◽  
Morphological Studies ◽  
Insertion Sites ◽  
Mean Square Errors

BACKGROUND: Accurate segmentation of connective soft tissues in medical images is very challenging, hampering the generation of geometric models for bio-mechanical computations. Alternatively, one could predict ligament insertion sites and then approximate the shapes, based on anatomical knowledge and morphological studies. OBJECTIVE: In this work, we describe an integrated framework for automatic modelling of human musculoskeletal ligaments. METHOD: We combine statistical shape modelling with geometric algorithms to automatically identify insertion sites, based on which geometric surface/volume meshes are created. As clinical use case, the framework has been applied to generate models of the forearm interosseous membrane. Ligament insertion sites in the statistical model were defined according to anatomical predictions following a published approach. RESULTS: For evaluation we compared the generated sites, as well as the ligament shapes, to data obtained from a cadaveric study, involving five forearms with 15 ligaments. Our framework permitted the creation of models approximating ligaments’ shapes with good fidelity. However, we found that the statistical model trained with the state-of-the-art prediction of the insertion sites was not always reliable. Average mean square errors as well as Hausdorff distances of the meshes could increase by an order of magnitude, as compared to employing known insertion locations of the cadaveric study. Using those, an average mean square error of 0.59 mm and an average Hausdorff distance of less than 7 mm resulted, for all ligaments. CONCLUSIONS: The presented approach for automatic generation of ligament shapes from insertion points appears to be feasible but the detection of the insertion sites with a SSM is too inaccurate, thus making a patient-specific approach necessary.

scholarly journals Improving a real-time helicopter simulator model with linear input filters

2021 ◽  
Author(s):  
Pavle Šćepanović ◽  
Frederik A. Döring
Keyword(s):  
Feedback Control ◽  
Time Domain ◽  
Flight Test ◽  
Flight Mechanics ◽  
Mean Square ◽  
Qualification Test ◽  
Model Inversion ◽  
Helicopter Flight ◽  
The Time Domain ◽  
Mean Square Errors

AbstractFor a broad range of applications, flight mechanics simulator models have to accurately predict the aircraft dynamics. However, the development and improvement of such models is a difficult and time consuming process. This is especially true for helicopters. In this paper, two rapidly applicable and implementable methods to derive linear input filters that improve the simulator model are presented. The first method is based on model inversion, the second on feedback control. Both methods are evaluated in the time domain, compared to recorded helicopter flight test data, and assessed based on root mean square errors and the Qualification Test Guide bounds. The best results were achieved when using the first method.

scholarly journals A Study on the Generalized Approximation Modeling Method Based on Fitting Sensitivity for Prediction of Engine Performance

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Lin Lin ◽  
Fang Wang ◽  
Shisheng Zhong
Keyword(s):  
Engine Performance ◽  
Grey Model ◽  
Model Parameters ◽  
Bayesian Regularization ◽  
Safety Engineering ◽  
The Novel ◽  
Mean Square ◽  
Approximation Model ◽  
Mean Square Errors ◽  
Fitting Accuracy

Prediction technology for aeroengine performance is significantly important in operational maintenance and safety engineering. In the prediction of engine performance, to address overfitting and underfitting problems with the approximation modeling technique, we derived a generalized approximation model that could be used to adjust fitting precision. Approximation precision was combined with fitting sensitivity to allow the model to obtain excellent fitting accuracy and generalization performance. Taking the Grey model (GM) as an example, we discussed the modeling approach of the novel GM based on fitting sensitivity, analyzed the setting methods and optimization range of model parameters, and solved the model by using a genetic algorithm. By investigating the effect of every model parameter on the prediction precision in experiments, we summarized the change regularities of the root-mean-square errors (RMSEs) varying with the model parameters in novel GM. Also, by analyzing the novel ANN and ANN with Bayesian regularization, it is concluded that the generalized approximation model based on fitting sensitivity can achieve a reasonable fitting degree and generalization ability.

scholarly journals Uncertainties of ground-based microwave radiometer retrievals in zenith and off-zenith observations under snow conditions

2017 ◽  
Vol 10 (1) ◽  
pp. 155-165 ◽  
Author(s):  
Wengang Zhang ◽  
Guirong Xu ◽  
Yuanyuan Liu ◽  
Guopao Yan ◽  
Dejun Li ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Microwave Radiometer ◽  
Retrieval Algorithm ◽  
Mean Square ◽  
Atmospheric Conditions ◽  
Vapor Density ◽  
Heavy Snowfall ◽  
Snow Conditions ◽  
The Impact ◽  
Mean Square Errors

Abstract. This paper is to investigate the uncertainties of microwave radiometer (MWR) retrievals in snow conditions and also explore the discrepancies of MWR retrievals in zenith and off-zenith observations. The MWR retrievals were averaged in a ±15 min period centered at sounding times of 00:00 and 12:00 UTC and compared with radiosonde observations (RAOBs). In general, the MWR retrievals have a better correlation with RAOB profiles in off-zenith observations than in zenith observations, and the biases (MWR observations minus RAOBs) and root mean square errors (RMSEs) between MWR and RAOB are also clearly reduced in off-zenith observations. The biases of temperature, relative humidity, and vapor density decrease from 4.6 K, 9 %, and 1.43 g m−3 in zenith observations to −0.6 K, −2 %, and 0.10 g m−3 in off-zenith observations, respectively. The discrepancies between MWR retrievals and RAOB profiles by altitude present the same situation. Cases studies show that the impact of snow on accuracies of MWR retrievals is more serious in heavy snowfall than in light snowfall, but off-zenith observation can mitigate the impact of snowfall. The MWR measurements become less accurate in snowfall mainly due to the retrieval algorithm, which does not consider the effect of snow, and the accumulated snow on the top of the radome increases the signal noise of MWR measurements. As the snowfall drops away by gravity on the sides of the radome, the off-zenith observations are more representative of the atmospheric conditions for RAOBs.

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 Parameter estimation of qubit states with unknown phase parameter

2015 ◽  
Vol 13 (01) ◽  
pp. 1450044 ◽  
Author(s):  
Jun Suzuki
Keyword(s):  
Parameter Estimation ◽  
Logarithmic Derivative ◽  
Mean Square ◽  
Level System ◽  
Optimal Measurement ◽  
Unknown Phase ◽  
Phase Parameter ◽  
Qubit System ◽  
Mean Square Errors ◽  
Qubit States

We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean square errors (MSEs) when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative (SLD) Cramér–Rao (CR) bound and Hayashi–Gill–Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given n quantum states to estimate the phase parameter. We also discuss the Holevo bound which can be attained asymptotically by a collective measurement.

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.

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