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1
Lee, Kwang-Ho, and Yong-Hwan Cho. "Simple Breaker Index Formula Using Linear Model." Journal of Marine Science and Engineering 9, no. 7 (2021): 731. http://dx.doi.org/10.3390/jmse9070731.
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Breaking waves generated by wave shoaling in coastal areas have a close relationship with various physical phenomena in coastal regions. Therefore, it is crucial to accurately predict breaker indexes such as breaking wave height and breaking depth when designing coastal structures. Many studies on wave breaking have been carried out, and many experimental data have been documented. Representative studies on wave breaking provide many empirical formulas for the prediction of breaking index, mainly through hydraulic model experiments. However, the existing empirical formulas for breaking index determine the coefficients of the assumed equation through statistical analysis of data under the assumption of a specific equation. This study presents an alternative method to estimate breaker index using representative linear-based supervised machine learning algorithms that show high predictive performance in various research fields related to regression or classification problems. Based on the used machine learning methods, a new simple linear equation for the prediction of breaker index is presented. The newly proposed breaker index formula showed similar predictive performance compared to the existing empirical formula, although it was a simple linear equation.
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Ngô, Trọng Hữu. "Dự đoán khả năng chịu uốn của tiết diện dầm bê tông cốt thép bằng công thức thực hành". Vietnam Institute for Building Science and Technology 2023, vi.vol2 (2023): 14–21. http://dx.doi.org/10.59382/j-ibst.2023.vi.vol2-2.
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This paper presents the process of developing a practical formula for predicting the ultimate bending moment of rectangular reinforced concrete (RC) beams through regression analysis. The data used for regression analysis was generated by using the fiber method to analyze a non-linear batch of commonly encountered RC beam cross-sections. The practical formula was obtained by fitting a linear regression model to the training set and then making predictions on the test set. The coefficient of determination, R2, between the bending moment values calculated from the formula and the results of the non-linear analysis was 0.9948, indicating a good predictive capability of the formula.
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Mohammadi, Mohammad, та Adel Mohammadpour. "On the Prediction of α-Stable Time Series". Fluctuation and Noise Letters 15, № 04 (2016): 1650021. http://dx.doi.org/10.1142/s0219477516500218.
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This paper addresses the point prediction of [Formula: see text]-stable time series. Our key idea is to define a new Hilbert space that contains [Formula: see text]-stable processes. Then, we apply the advantage of Hilbert space theory for finding the best linear prediction. We show how to use the presented predictor practically for [Formula: see text]-stable linear processes. The implementation of the presented method is easier than the implementation of the minimum dispersion method. We reveal the appropriateness of the presented method through an empirical study on predicting the natural logarithms of the volumes of SP500 market.
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Di, Yu, Ying Li, and Yan Luo. "Prediction of Implantable Collamer Lens Vault Based on Preoperative Biometric Factors and Lens Parameters." Journal of Refractive Surgery 39, no. 5 (2023): 332–39. http://dx.doi.org/10.3928/1081597x-20230207-03.
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Purpose: To establish and validate the accuracy of implantable collamer lens (ICL) vault size prediction formula based on preoperative biometric factors and lens parameters. Methods: This study included 300 patients (300 eyes) with Visian ICL V4c (STAAR Surgical) implantation. They were randomly divided into the formula establishment group and formula validation group. Anterior segment measurements, ICL V4c size and power, and vault 1 week postoperatively were collected from all patients. Multiple linear regression analysis was performed to establish the prediction formula. Mean absolute error (MAE), median absolute error (MedAE), root mean square error (RMSE), and Bland-Altman diagrams were used to evaluate the prediction formula. Results: Anterior chamber depth (ACD) had the greatest influence on vault 1 week after ICL V4c implantation, followed by ICL V4c size and angle-to-angle distance (ATA). The prediction formula was obtained according to the partial regression coefficient, which was vault (mm) = −1.279 + 0.291 × ACD (mm) + 0.210 × ICL V4c size (mm) – 0.144 × ATA (mm) ( R 2 = 0.661). In the formula validation group, the mean predictive vault, MAE, MedAE, and RMSE were 628.10, 135.09, 130.42, and 150.46 µm, respectively. The Bland-Altman diagram showed the predictive vault was in good agreement with the actual vault. Conclusions: A novel ICL V4c vault prediction formula was developed and shown to be an effective method for predicting the vault to reduce surgical complications. [ J Refract Surg . 2023;39(5):332–339.]
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HINTON-BAYRE, ANTON. "Reliable Change formula query." Journal of the International Neuropsychological Society 6, no. 3 (2000): 362–63. http://dx.doi.org/10.1017/s1355617700633118.
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In a recent article, Temkin et al. (1999) contrasted four models for detecting significant change in individual performance on neuropsychological tests. Two of these models relied on the calculation of the Reliable Change Index (RCI) by Jacobson and Truax (1991), with and without a correction for practice associated with repeated testing. The other two models were based on simple linear regression and multiple regression, respectively. The models were contrasted based on the width of 90% prediction intervals (PI) and normal-distribution-based prediction accuracy of classifying unusual cases. Participants were tested twice (Time 1 and Time 2), on seven common neuropsychological measures. Prediction accuracy was based on the discrepancy between obtained and predicted Time 2 scores.
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Engel, B., W. G. Buist, P. Walstra, E. Olsen, and G. Daumas. "Accuracy of prediction of percentage lean meat and authorization of carcass measurement instruments: adverse effects of incorrect sampling of carcasses in pig classification." Animal Science 76, no. 2 (2003): 199–209. http://dx.doi.org/10.1017/s1357729800053455.
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AbstractClassification of pig carcasses in the European Community is based on the lean meat percentage of the carcass. The lean meat percentage is predicted from instrumental carcass measurements, such as fat and muscle depth measurements, obtained in the slaughter-line. The prediction formula employed is derived from the data of a dissection experiment and has to meet requirements for authorization as put down in EC regulations. Requirements involve the sampling procedure and sample size for the dissected carcasses and the accuracy of prediction. Formulae are often derived by linear regression. In this paper we look at a particular type of sampling scheme. This involves selection of carcasses on the basis of carcass measurements not all of which are intended to be used as prediction variables. This sampling scheme frequently appears in requests for authorization of carcass measurement instruments and accompanying prediction formulae, despite the fact that it lacks formal statistical justification when used in conjunction with linear regression. The objective of this work was to assess the performance of the prediction formula that follows from this potentially faulty combination of sampling scheme and linear regression in relation to the requirements in the EC regulations. We show that this sampling scheme may produce poor predictions for lean meat percentage compared with proper sampling procedures with selection on prediction variables only or random sampling. We do so by computer simulation. Initially, simulated data were based on recent and historic data from The Netherlands. Prediction variables are fat and muscle depth measurements. The additional variable involved in sampling, but not included in the regression, was carcass weight. We also show that due to this faulty sampling scheme there is a serious risk that a new measurement instrument may not be authorized because performance criteria in the EC-regulations are not met.
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Xie, Liusen, and William W. Hsieh. "Predicting the Return Migration Routes of the Fraser River Sockeye Salmon (Oncorhynchus nerka)." Canadian Journal of Fisheries and Aquatic Sciences 46, no. 8 (1989): 1287–92. http://dx.doi.org/10.1139/f89-165.
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The Johnstone Strait diversion rate (i.e. the percentage of homeward migrating Fraser River sockeye salmon (Oncorhynchus nerka) travelling around Vancouver Island via the northern route of Johnstone Strait) is statistically predicted using the March values of the Kains Island sea surface temperature T and the Fraser River runoff R. The prediction formula incorporates nonlinear terms such as T2 and RT, as well as the diversion rate 2 yr ago. We tested the forecasting performance by constructing a prediction formula using only data from 1953–78, and making predictions for 1979–88. The mean absolute error of our prediction of the diversion rate was 8% which compared favourably with the prediction by a linear temperature scheme and a linear runoff scheme where the errors were respectively 13 and 29%. Unlike the latter two schemes where T and R data from April–June are needed, our scheme with the use of data no later than March allows much earlier forecasts to be made.
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Yuan, Shasha, Weidong Zhou, and Liyan Chen. "Epileptic Seizure Prediction Using Diffusion Distance and Bayesian Linear Discriminate Analysis on Intracranial EEG." International Journal of Neural Systems 28, no. 01 (2017): 1750043. http://dx.doi.org/10.1142/s0129065717500435.
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Epilepsy is a chronic neurological disorder characterized by sudden and apparently unpredictable seizures. A system capable of forecasting the occurrence of seizures is crucial and could open new therapeutic possibilities for human health. This paper addresses an algorithm for seizure prediction using a novel feature — diffusion distance (DD) in intracranial Electroencephalograph (iEEG) recordings. Wavelet decomposition is conducted on segmented electroencephalograph (EEG) epochs and subband signals at scales 3, 4 and 5 are utilized to extract the diffusion distance. The features of all channels composing a feature vector are then fed into a Bayesian Linear Discriminant Analysis (BLDA) classifier. Finally, postprocessing procedure is applied to reduce false prediction alarms. The prediction method is evaluated on the public intracranial EEG dataset, which consists of 577.67[Formula: see text]h of intracranial EEG recordings from 21 patients with 87 seizures. We achieved a sensitivity of 85.11% for a seizure occurrence period of 30[Formula: see text]min and a sensitivity of 93.62% for a seizure occurrence period of 50[Formula: see text]min, both with the seizure prediction horizon of 10[Formula: see text]s. Our false prediction rate was 0.08/h. The proposed method yields a high sensitivity as well as a low false prediction rate, which demonstrates its potential for real-time prediction of seizures.
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Castillo-Sanchez, L. E., J. R. Canul-Solís, D. Pozo-Leyva, et al. "Prediction of live weight in beef heifers using a body volume formula." Arquivo Brasileiro de Medicina Veterinária e Zootecnia 74, no. 6 (2022): 1127–33. http://dx.doi.org/10.1590/1678-4162-12886.
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ABSTRACT The objective of this study was to develop and evaluate linear, quadratic, and allometric models to predict live weight (LW) using the body volume formula (BV) in crossbred heifers raised in southeastern Mexico. The LW (426.25±117.49kg) and BV (338.05±95.38 dm3) were measured in 360 heifers aged between 3 and 30 months. Linear and non-linear regression were used to construct prediction models. The goodness-of-fit of the models was evaluated using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), coefficient of determination (R2), mean squared error (MSE), and root MSE (RMSE). In addition, the developed models were evaluated through cross-validation (k-folds). The ability of the fitted models to predict the observed values was evaluated based on the RMSEP, R2, and mean absolute error (MAE). The quadratic model had the lowest values of AIC (2688.39) and BIC (2700.05). On the other hand, the linear model showed the lowest values of MSE (7954.74) and RMSE (89.19), and the highest values of AIC (2709.70) and BIC (2717.51). Despite this, all models presented the same R2 value (0.87). The cross-validation (k-folds) evaluation of fit showed that the quadratic model had better values of MSEP (41.49), R2 (0.85), and MAE (31.95). We recommend the quadratic model to predictive of the crossbred beef heifers' live weight using the body volume as the predictor.
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KARNA, DILLIP KUMAR, ADITYA PRASAD ACHARYA, BHABESH CHANDRA DAS, GANGADHAR NAYAK, and M. R. DIBYADARSHINI. "Comparison of regression methods and Shaeffer’s formula in prediction of Live Body Weight of Ganjam Goats." Indian Journal of Animal Sciences 92, no. 6 (2022): 770–75. http://dx.doi.org/10.56093/ijans.v92i6.108921.
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Linear regression and polynomial regression of order two and three were utilized to predict the live weight ofGanjam goats across five age groups using chest girth as predictor and their accuracies were compared with theprediction of weight made by Shaeffer’s formula. Live body weight of Ganjam goat recorded by electronic weighingbalance was used as standard for calculating the error of prediction. The body weights of 1014 Ganjam goats (329males and 685 females) were estimated by each technique during 2015 to 2017. Compared with electronic weighingscale, the body weight estimates in Ganjam goat exceeded in all age groups for Shaeffer’s formula whereas predicted body weight estimates by linear regression and second order polynomial regression were close to the live body weights. The estimates of linear regression and second order polynomial regression were significantly different from the electronic weighing scale for all age groups. The study concluded that polynomial regression of order two had better predictive value for live body weight of Ganjam goat, followed by third order polynomial regression, linear regression and Shaeffer’s formula, in order
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Shen, Chen, Hui Zhu, and Zhi Gang Yang. "Study on the Aerodynamics Mechanism of Passenger Car under Unsteady Crosswind." Advanced Materials Research 631-632 (January 2013): 809–16. http://dx.doi.org/10.4028/www.scientific.net/amr.631-632.809.
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Regular formulae for lateral aerodynamic force cannot give precise prediction under unsteady crosswind. By generalizing potential flow theory and taking the aerodynamic derivative into consideration, the semi-empirical expression for lateral aerodynamic force is derived. In order to determine the coefficients in the semi-empirical formula, the model of a typical double-deck coach is investigated in a sequence of numerical simulations under pure crosswind condition (i.e. linear crosswind, pseudo-step crosswind, sinusoidal crosswind). Moreover, advantages of the semi-empirical formula over the regular one are revealed. Further inspections into the flow field derived from the theory of vortex motion indicate that the deviation between the prediction given by semi-empirical formulae and that by numerical simulation is caused by the non-viscous assumption in potential flow theory. The lateral aerodynamic force depends linearly on the crosswind aerodynamic derivative. Situations in which the coach is moving in the direction perpendicular to the wind velocity are also studied to find the cause of the error in semi-empirical formula. Furthermore, the semi-empirical formula is revised by introducing the “damping model method”. A relatively complete system of prediction for lateral aerodynamic force on a coach, which is of practical engineering significance, has been constructed.
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Papuga, Jan, Ivona Vízková, Maxim Lutovinov, and Martin Nesládek. "Mean stress effect in stress-life fatigue prediction re-evaluated." MATEC Web of Conferences 165 (2018): 10018. http://dx.doi.org/10.1051/matecconf/201816510018.
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The paper compares various methods for computing the equivalent stress amplitude for stress cycles of non-zero mean value in stress-life fatigue prediction. A set of 11 calculation methods is evaluated. In addition to formulations based on common static or fatigue properties, the Walker formula and the generalized Linear formula are included in the investigation. These two methods use an optimization routine to find the material parameters. The final response of the methods is compared and discussed. The Walker method provides a better solution. The generalized Linear method produces inferior results, i.e. the linear fit of the segment of the Haigh diagram is not an optimal solution.
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Gu, Wenbin, Zhenxiong Wang, Jianqing Liu, Jinglin Xu, Xin Liu, and Tao Cao. "Water-Depth-Based Prediction Formula for the Blasting Vibration Velocity of Lighthouse Caused by Underwater Drilling Blasting." Shock and Vibration 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/7340845.
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Lighthouses are the most important hydraulic structures that should be protected during underwater drilling blasting. Thus, the effect of blasting vibration on lighthouse should be studied. On the basis of the dimensional analysis, we deduced a revised formula for water depth based on Sodev’s empirical formula and established the linear fitting model. During the underwater reef project in the main channel of Shipu Harbor in the Ningbo–Zhoushan Port, the blasting vibration data of the lighthouse near the underwater blasting area were monitored. The undetermined coefficient, resolvable coefficient, and F value of the two formulas were then obtained. The comparison of the data obtained from the two formulas showed that they can effectively predict the blasting vibration on the lighthouse. The correction formula that considers water depth can obviously reduce prediction errors and accurately predict blasting vibration.
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Naghizadeh, Mostafa, and Mauricio D. Sacchi. "Multistep autoregressive reconstruction of seismic records." GEOPHYSICS 72, no. 6 (2007): V111—V118. http://dx.doi.org/10.1190/1.2771685.
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Linear prediction filters in the [Formula: see text] domain are widely used to interpolate regularly sampled data. We study the problem of reconstructing irregularly missing data on a regular grid using linear prediction filters. We propose a two-stage algorithm. First, we reconstruct the unaliased part of the data spectrum using a Fourier method (minimum-weighted norm interpolation). Then, prediction filters for all the frequencies are extracted from the reconstructed low frequencies. The latter is implemented via a multistep autoregressive (MSAR) algorithm. Finally, these prediction filters are used to reconstruct the complete data in the [Formula: see text] domain. The applicability of the proposed method is examined using synthetic and field data examples.
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GHANBARIAN, BEHZAD, EDMUND PERFECT, and HUI-HAI LIU. "A GEOMETRICAL APERTURE–WIDTH RELATIONSHIP FOR ROCK FRACTURES." Fractals 27, no. 01 (2019): 1940002. http://dx.doi.org/10.1142/s0218348x19400024.
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The relationship between fracture aperture (maximum opening; [Formula: see text]) and fracture width ([Formula: see text]) has been the subject of debate over the past several decades. An empirical power law has been commonly applied to relate these two parameters. Its exponent ([Formula: see text]) is generally determined by fitting the power-law function to experimental observations measured at various scales. Invoking concepts from fractal geometry we theoretically show, as a first-order approximation, that the fracture aperture should be a linear function of its width, meaning that [Formula: see text]. This finding is in agreement with the result of linear elastic fracture mechanics (LEFM) theory. We compare the model predictions with experimental observations available in the literature. This comparison generally supports a linear relationship between fracture aperture and fracture width, although there exists considerable scatter in the data. We also discuss the limitations of the proposed model, and its potential application to the prediction of flow and transport in fractures. Based on more than 170 experimental observations from the literature, we show that such a linear relationship, in combination with the cubic law, is able to scale flow rate with fracture aperture over [Formula: see text]14 orders of magnitude for variations in flow rate and [Formula: see text]5 orders of magnitude for variations in fracture width.
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KARMALKAR, ARUN S., and VASUDHA R. NIKAM. "Prediction of stature from long bones versus hand and foot measurements: A comparative study of the Kolhapur population." National Medical Journal of India 34 (October 22, 2021): 154–57. http://dx.doi.org/10.25259/nmji_79_20.
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Background Estimation of stature is usually done by measurement of the long bones. Although hand and foot dimensions are useful in predicting stature, they are population-specific. Methods We compared the accuracy of predicting stature by hand and foot dimensions, with long bone (tibia and ulna) lengths, and developed a stature predictive regression formula from the parameters used for the sample population in Kolhapur. We recorded hand and foot measurements and long bone measurements of 1000 consenting participants 18–50 years of age using a stadiometer for height and an anthropometric rod compass for other measurements. Correlation between the variables and stature was determined using Pearson’s correlation analysis (p<0.05). A multiple linear regression formula was derived for the prediction of stature. Results A positive correlation was observed between mean stature and foot length (r=0.67, p<0.05), tibia (r=0.66, p<0.05), ulna (r= 0.75, p<0.05) and hand length (r=0.69 left, r=0.72 right, p<0.05). There was no correlation between foot breadth and stature. Multiple linear regression analysis of hand and foot dimensions returned R2=62.96 and standard error of estimate 4.689 with comparable computed and experimental measurements. Conclusion The dimensions of the hand and foot can be used to predict stature. The formula derived from the multiple regression analysis incorporating hand and foot dimensions is a good fit to estimate stature in the study population.
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Sahin, Mustafa, Cem Bilgen, M. Sezai Tasbakan, Rasit Midilli, and Ozen K. Basoglu. "A Clinical Prediction Formula for Apnea-Hypopnea Index." International Journal of Otolaryngology 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/438376.
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Objectives. There are many studies regarding unnecessary polysomnography (PSG) when obstructive sleep apnea syndrome (OSAS) is suspected. In order to reduce unnecessary PSG, this study aims to predict the apnea-hypopnea index (AHI) via simple clinical data for patients who complain of OSAS symptoms.Method. Demographic, anthropometric, physical examination and laboratory data of a total of 390 patients (290 men, average age 50 ± 11) who were subject to diagnostic PSG were obtained and evaluated retrospectively. The relationship between these data and the PSG results was analyzed. A multivariate linear regression analysis was performed step by step to identify independent AHI predictors.Results. Useful parameters were found in this analysis in terms of body mass index (BMI), waist circumference (WC), neck circumference (NC), oxygen saturation measured by pulse oximetry (SpO2), and tonsil size (TS) to predict the AHI. The formula derived from these parameters was the predicted AHI = (0.797 × BMI) + (2.286 × NC) − (1.272 × SpO2) + (5.114 × TS) + (0.314 × WC).Conclusion. This study showed a strong correlation between AHI score and indicators of obesity. This formula, in terms of predicting the AHI for patients who complain about snoring, witnessed apneas, and excessive daytime sleepiness, may be used to predict OSAS prior to PSG and prevent unnecessary PSG.
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Molnar, Sheri, Stan E. Dosso, and John F. Cassidy. "Uncertainty of linear earthquake site amplification via Bayesian inversion of surface seismic data." GEOPHYSICS 78, no. 3 (2013): WB37—WB48. http://dx.doi.org/10.1190/geo2012-0345.1.
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We examine uncertainty in predicted linear 1D site amplification due to uncertainty in shear-wave velocity ([Formula: see text]) structure quantified from Bayesian (probabilistic) inversion of microtremor array dispersion data. Based on a sample of [Formula: see text] profiles drawn from the posterior probability density of the microtremor inversion, probability distributions are computed for common predictors of site amplification including [Formula: see text] (traveltime average [Formula: see text] to a depth [Formula: see text]) and amplification spectra based on seismic impedance variations and full transverse shear-wave effects. These methods are applicable for any site, but the resulting probabilistic site amplification analyses are specific to the two sediment sites studied here with strongly contrasting geology in high population centers of British Columbia, Canada. The site amplification probability distributions for the two sites are shown to be more informative than amplification estimated for a single best-fit [Formula: see text] profile by characterizing the uncertainty and therefore level of confidence in the predictions. The shear-wave amplification probability spectra are evaluated by comparison to empirical earthquake and microtremor spectral ratios, with generally good agreement in resonant peak frequencies and amplification levels, providing confidence that the primary influence of site-specific structure is accounted for appropriately. The wider implication here is that proper characterization of the [Formula: see text] profile uncertainty distribution from inversion of cost-effective surface wave dispersion data is beneficial in the application of said profiles to the prediction of earthquake site response and its uncertainty, as required for probabilistic seismic hazard assessment.
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Simmons, James L., and Milo M. Backus. "Waveform‐based AVO inversion and AVO prediction‐error." GEOPHYSICS 61, no. 6 (1996): 1575–88. http://dx.doi.org/10.1190/1.1444077.
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A practical approach to linear prestack seismic inversion in the context of a locally 1-D earth is employed to use amplitude variation with offset (AVO) information for the direct detection in hydrocarbons. The inversion is based on the three‐term linearized approximation to the Zoeppritz equations. The normal‐incidence compressional‐wave reflection coefficient [Formula: see text] models the background reflectivity in the absence of hydrocarbons and incorporates the mudrock curve and Gardner’s equation. Prediction‐error parameters, [Formula: see text] and [Formula: see text], represent perturbations in the normal‐incidence shear‐wave reflection coefficient and the density contribution to the normal incidence reflectivity, respectively, from that predicted by the mudrock curve and Gardner’s equation. This prediction‐error approach can detect hydrocarbons in the absence of an overall increase in AVO, and in the absence of bright spots, as expected in theory. Linear inversion is applied to a portion of a young, Tertiary, shallow‐marine data set that contains known hydrocarbon accumulations. Prestack data are in the form of angle stack, or constant offset‐to‐depth ratio, gathers. Prestack synthetic seismograms are obtained by primaries‐only ray tracing using the linearized approximation to the Zoeppritz equations to model the reflection amplitudes. Where the a priori assumptions hold, the data are reproduced with a single parameter [Formula: see text]. Hydrocarbons are detected as low impedance relative to the surrounding shales and the downdip brine‐filled reservoir on [Formula: see text], also as positive perturbations (opposite polarity relative to [Formula: see text]) on [Formula: see text] and [Formula: see text]. The maximum perturbation in [Formula: see text] from the normal‐incidence shear‐wave reflection coefficient predicted by the a priori assumptions is 0.08. Hydrocarbon detection is achieved, although the overall seismic response of a gas‐filled thin layer shows a decrease in amplitude with offset (angle). The angle‐stack data (70 prestack ensembles, 0.504–1.936 s time range) are reproduced with a data residual that is 7 dB down. Reflectivity‐based prestack seismograms properly model a gas/water contact as a strong increase in AVO and a gas‐filled thin layer as a decrease in AVO.
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Yu, Xinliang, Rimeng Zhan, Jiyong Deng, and Xianwei Huang. "Prediction of the maximum nonseizure load of lubricant additives." Journal of Theoretical and Computational Chemistry 16, no. 02 (2017): 1750014. http://dx.doi.org/10.1142/s0219633617500146.
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Lubricating additives can improve the lubricant performance of base oil in reducing friction and wear and minimizing loss of energy. It is of great significance to study the relationship between chemical structures and lubrication properties of lubricant additives. This paper reports a quantitative structure–property relationship (QSPR) model of the maximum nonseizure loads ([Formula: see text]) of 79 lubricant additives by applying artificial neural network (ANN) based on the algorithm of backward propagation of errors. Six molecular descriptors appearing in the multiple linear regression (MLR) model were used as vectors to develop the ANN model. The optimal condition of ANN with network structure of [6-4-1] was obtained by adjusting various parameters by trial-and-error. The root-mean-square (rms) errors from ANN model are [Formula: see text] ([Formula: see text]) for the training set and [Formula: see text] ([Formula: see text]) for the test set, which are superior to the MLR results of [Formula: see text] ([Formula: see text]) for the training set and [Formula: see text] ([Formula: see text]) for the test set. Compared to the existing model for [Formula: see text], our model has better statistical quality. The results indicate that our ANN model can be applied to predict the [Formula: see text] values for lubricant additives.
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Takemoto, H., N. Tomita, K. Murata, et al. "Optimal patient selection for CPT-11 chemotherapy in colorectal cancer: Quantitative prediction of tumor response and overall survival using expression data of novel marker genes." Journal of Clinical Oncology 27, no. 15_suppl (2009): e14529-e14529. http://dx.doi.org/10.1200/jco.2009.27.15_suppl.e14529.
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e14529 Background: Unlike the toxicity, none of the critical prediction markers of CPT-11 efficacy has been validated to date. With a hypothesis that expression analysis of a set of the key drug sensitivity genes could allow us to predict the therapeutic response, we identified potent marker genes for CPT-11 in in vitro, conducted this prospective study attempting to develop a prediction formula of efficacy using the expression data (2006 ASCO, 2006 ESMO), and demonstrated the latest prediction formula of the best tumor response (BTR), time to treatment failure (TTP), and the overall survival after CPT-11 chemotherapy (OS). Methods: Seven genes identified as possible marker genes for CPT-11 (SN-38)- AMD1, CTSC, EIF1AX, FLJ13089 , DDX54, PTPN2, and TBX3-, and 5 other possible marker genes (ABCG2, CYP3A4, MGMT, POR, and TOP2A) that had already been known as drug sensitivity determinants and selected by our in vitro screening process, were studied. CPT-11 was intravenously administered on Days 1, 8, and 15, every 4 weeks in chemo-naive patients with stage IV colorectal cancer after palliative operation. Tumor samples were collected at surgery and tumor response was evaluated by RECIST. Results: All of the 44 enrolled patients were assessable for BTR (% of initial tumor size), TTP (day), and OS (day) in the clinical study, and we successfully developed the best linear model for each, which converted the quantified expression data of the 7 selected genes into objective BTR, TTP, and OS. We used 20, 16, and 15 tumor specimens and constructed potent prediction formulae for BTR (r=0.9420), TTP (r=0.7103), and OS (r=0.8406), respectively. Utility-confirmation analyses using another 16, 10, 13 clinical samples appeared to show that the formulae could predict BTR (r=0.6491, p=0.007) and OS (r=0.7947, p=0.011). We also fixed the best linear models using 5 other known marker genes, but they had less advantage in prediction. Conclusions: Despite limited data, our developed formulae using the 7 novel genes would provide advantages in prediction of individual response to CPT-11. Based on the positive results of this study, we have initiated a large scale validation study of the formula. [Table: see text]
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Lee, Byung Joo, Sang-Mok Lee, Jeong Hun Kim, and Young Suk Yu. "Predictability of formulae for intraocular lens power calculation according to the age of implantation in paediatric cataract." British Journal of Ophthalmology 103, no. 1 (2018): 106–11. http://dx.doi.org/10.1136/bjophthalmol-2017-311706.
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AimsTo analyse the predictability of diverse intraocular lens (IOL) power calculation formulae in paediatric patients with congenital cataract.MethodsThe medical records of patients who underwent cataract surgery and posterior chamber IOL implantation (in-the-bag) for congenital cataract before 17 years of age were reviewed retrospectively. Target refractions calculated by Sanders-Retzlaff-Kraff (SRK)/II, SRK/T and Hoffer-Q formulae were compared with the actual refraction. Patients were subgroup according to the age at IOL implantation (age group 0–24 months, 25–60 months, 61–120 months, 121–203 months), and we compared mean prediction error (PE) and mean absolute error (AE) for each formula. Corrected AE was obtained by linear regression analysis.ResultsTotally 481 eyes were included in the final analysis. Both SRK/II and SRK/T yielded the lowest mean AE in the age group 0–24 months and SRK/II yielded the lowest mean AE in the age group 25–60 months. For every formula, the mean PE was positive during the first five years of age, which converged to zero according to age as IOL implantation increases. The tendency for immediate postoperative overcorrection in younger patients (<6 years) could be improved by corrected formulae based on the linear regression equation.ConclusionsPatients with congenital cataract who underwent IOL implantation within 5 years of age showed higher AE than the older ones did. Among the three formulae evaluated, SRK/II consistently provided the best predictive result in these patients. For patients aged >10 years, all three formulae showed favourable predictive abilities.
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Berger, Andrew J., and Michael S. Feld. "Analytical Method of Estimating Chemometric Prediction Error." Applied Spectroscopy 51, no. 5 (1997): 725–32. http://dx.doi.org/10.1366/0003702971940882.
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We present an analytical formula that estimates the uncertainty in concentrations predicted by linear multivariate calibration, particularly partial least-squares (PLS). We emphasize the analysis of spectroscopic data. The derivation addresses the important limit in which calibration error is negligible in comparison to noise in the prediction spectra. The formula is expressed in terms of standard PLS calibration parameters and the amplitude of spectral noise; it is therefore straightforward to evaluate. To test the formula, we performed PLS analysis upon simulated spectra and upon experimental Raman spectra of dissolved biological analytes in water. In each instance, the root-mean-squared error of prediction was compared to the estimate from the formula. Accurate uncertainty estimates were obtained in cases where calibration noise was lower than prediction noise, and surprisingly good estimates were obtained even when the noise levels were equal. By comparing measured and estimated uncertainties, we assessed the robustness of each PLS calibration model. The scaling of prediction uncertainty with the spectral signal-to-noise ratio is also discussed.
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Yuan, Dong-Qing, Chun-Hua Yang, Hui Zhang, et al. "Prediction of SMILE surgical cutting formula based on back propagation neural network." International Journal of Ophthalmology 16, no. 9 (2023): 1424–30. http://dx.doi.org/10.18240/ijo.2023.09.08.
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AIM: To predict cutting formula of small incision lenticule extraction (SMILE) surgery and assist clinicians in identifying candidates by deep learning of back propagation (BP) neural network. METHODS: A prediction program was developed by a BP neural network. There were 13 188 pieces of data selected as training validation. Another 840 eye samples from 425 patients were recruited for reverse verification of training results. Precision of prediction by BP neural network and lenticule thickness error between machine learning and the actual lenticule thickness in the patient data were measured. RESULTS: After training 2313 epochs, the predictive SMILE cutting formula BP neural network models performed best. The values of mean squared error and gradient are 0.248 and 4.23, respectively. The scatterplot with linear regression analysis showed that the regression coefficient in all samples is 0.99994. The final error accuracy of the BP neural network is -0.003791±0.4221102 μm. CONCLUSION: With the help of the BP neural network, the program can calculate the lenticule thickness and residual stromal thickness of SMILE surgery accurately. Combined with corneal parameters and refraction of patients, the program can intelligently and conveniently integrate medical information to identify candidates for SMILE surgery.
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Cao, Bin, Shuang Yang, Ankang Sun, Ziqiang Dong, and Tong-Yi Zhang. "Domain knowledge-guided interpretive machine learning: formula discovery for the oxidation behavior of ferritic-martensitic steels in supercritical water." Journal of Materials Informatics 2, no. 2 (2022): 4. http://dx.doi.org/10.20517/jmi.2022.04.
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A general formula with high generalization and accurate prediction power is highly desirable for science, technology and engineering. In addition to human beings, artificial intelligence algorithms show great promise for the discovery of formulas. In this study, we propose a domain knowledge-guided interpretive machine learning strategy and demonstrate it by studying the oxidation behavior of ferritic-martensitic steels in supercritical water. The oxidation Cr equivalent is, for the first time, proposed in the present work to represent all contributions of alloying elements to oxidation, derived by our domain knowledge and interpretive machine learning algorithms. An open-source tree classifier for linear regression algorithm is also, for the first time, developed to materialize the formula with collected data. This algorithm effectively captures the linear correlation between compositions, testing environments and oxidation behaviors from the data. The sure independence screening and sparsifying operator algorithm finally assembles the information derived from the tree classifier for linear regression algorithm, resulting in a general formula. The general formula with the determined parameters has the power to predict, quantitatively and accurately, the oxidation behavior of ferritic-martensitic steels with multiple alloying elements exposed to various supercritical water environments, thereby providing guidance for the design of anti-oxidation steels and hence promoting the development of power plants with improved safety. The present work demonstrates the power of domain knowledge-guided interpretive machine learning with respect to the data-driven discovery of physics-informed formulas and the acceleration of materials informatics development.
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Bulger, Christopher M., Weihua Gao, Chad Jacobs, and Walter J. McCarthy. "Beyond the Categories: A Formula-Driven Prediction of Carotid Stenosis." Journal for Vascular Ultrasound 29, no. 1 (2005): 15–20. http://dx.doi.org/10.1177/154431670502900102.
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Purpose Current methods to predict carotid stenosis from ultrasound duplex criteria involve assigning a category of stenosis on the basis of an individual laboratory-defined combination of peak systolic velocity (PSV), end diastolic velocity (EDV), and ratio of internal carotid artery velocity to common carotid artery velocity. This study will define a formula by use of regression analysis of the duplex ultrasound criteria compared with the angiographic results. This study will then compare the formula predictions of stenosis with the current means of combining categories to determine whether there is an increase in accuracy and correlation with angiographic findings. Methods A retrospective review of the duplex scans and NASCET-defined angiogram results from 209 patent carotid arteries in 114 patients over the course of 4 yr at a single institution was performed. Regression analysis comparing each of the PSV, EDV, and internal carotid artery/common carotid artery ratios (RATIO) with angiographic stenosis was performed. Simple and multiple linear regression equations were obtained. The equation was tested for validity. The data were then reanalyzed by use of the formulas, and predicted stenoses from the formulas were obtained. The formula-predicted stenoses (F1 and F2), category-based stenoses (READAS), and angiographic stenoses were compared. A determination was then made of their statistically significant difference by use of the Wilcoxon signed rank test and receiver operator curve (ROC) analysis. Results An r2 value of 0.7231, 0.6341, and 0.7262 was obtained, respectively, for the equations comparing PSV, EDV, and ICA/CCA ratio with angiographic stenosis. Limiting the data to stenosis >30% resulted in correlation coefficients between the regression formula predicted data and the angiographic data of 0.71. A statistically significant difference was demonstrated between the category results and angiography ( p < 0.0001). No statistically significant difference was demonstrated between the formula-predicted data and the angiographic data. ROC analysis and Area (AZ) test demonstrated a statistically significant difference and better prediction of a >60% stenosis by the regression equation than by the current category method ( p < 0.05). Conclusion Regression analysis of duplex data versus NASCET-defined angiographic findings allows formation of a model to predict carotid stenosis. This can be done with greater accuracy than the commonly accepted means of categorizing the duplex results.
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Wang, Gui Cheng, Zhong Feng Pan, Jin Yu Zhang, Chong Lue Hua, and Ju Dong Liu. "Finite Element Prediction of Grind-Hardening Layer Thickness." Key Engineering Materials 416 (September 2009): 253–58. http://dx.doi.org/10.4028/www.scientific.net/kem.416.253.
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According to the grind-hardening test and using the multiple linear regression analysis, the empirical formula of the tangential grinding force is established in this paper. Combined with the heat distribution coefficient formula of Rowe and Pettit, the thickness of the grind-hardening layer is predicted by using the finite element method under different grinding parameters. It draws the influence law of the grinding speed, cutting depth and feed rate to the thickness of the grind-hardening layer. It provided the basis to the drawing up, the application and the optimization of the grind-hardening process.
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Ruiz-Medina, M. D., and M. J. Valderrama. "Orthogonal representations of random fields and an application to geophysics data." Journal of Applied Probability 34, no. 2 (1997): 458–76. http://dx.doi.org/10.2307/3215385.
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We present a brief summary of some results related to deriving orthogonal representations of second-order random fields and its application in solving linear prediction problems. In the homogeneous and/or isotropic case, the spectral theory provides an orthogonal expansion in terms of spherical harmonics, called spectral decomposition (Yadrenko 1983). A prediction formula based on this orthogonal representation is shown. Finally, an application of this formula in solving a real-data problem related to prospective geophysics techniques is presented.
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Ruiz-Medina, M. D., and M. J. Valderrama. "Orthogonal representations of random fields and an application to geophysics data." Journal of Applied Probability 34, no. 02 (1997): 458–76. http://dx.doi.org/10.1017/s0021900200101093.
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We present a brief summary of some results related to deriving orthogonal representations of second-order random fields and its application in solving linear prediction problems. In the homogeneous and/or isotropic case, the spectral theory provides an orthogonal expansion in terms of spherical harmonics, called spectral decomposition (Yadrenko 1983). A prediction formula based on this orthogonal representation is shown. Finally, an application of this formula in solving a real-data problem related to prospective geophysics techniques is presented.
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SHUKLA, J., and R. SURYANARAYANA. "Forecasting five-day mean contours of 700 mb using empirical influence coefficients." MAUSAM 19, no. 4 (2022): 407–12. http://dx.doi.org/10.54302/mausam.v19i4.5721.
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With the help of 5-day mean data for the ten-year period (1955-64) for July and August, empirical influence coefficients have been worked out. With these coefficients we derive a linear prediction formula for 700-mb contours at 12 radiosonde stations in India. We assume that the predicted 700-mb contour height is a linear function of the contours in the past pentad. The coefficients in Our prediction formula are evaluated by the method of least squares using past data.
 
 The usefulness of the method was tested with data of 2 years (1965-66) and we find good success in forecasting broad features on 5-day mean charts.
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Gao, Yanxia, Yiwen Liu, Pengju Tang, and Chunqiao Mi. "Modification of Peck Formula to Predict Surface Settlement of Tunnel Construction in Water-Rich Sandy Cobble Strata and Its Program Implementation." Sustainability 14, no. 21 (2022): 14545. http://dx.doi.org/10.3390/su142114545.
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There are few studies on the land subsidence induced by shield tunneling in the water-rich sandy gravel stratum, which is of high research value. Linear regression and measured data were employed in this study to investigate the land subsidence induced by shield tunneling when crossing the water-rich sandy gravel stratum from Mudan Dadao Station to Longmen Dadao station of Luoyang Metro Line 2. The maximum land subsidence correction coefficient, α, and the settlement trough width correction coefficient, β, were introduced to modify the peck formula to predict land subsidence induced by shield tunneling in Luoyang’s water-rich sandy gravel stratum. It was discovered that the original Peck formula needs to be modified because its prediction result was significantly larger than the actual value. When the value ranges of α and β in the modified Peck formula were 0.379~0.690 and 0.455~0.508, respectively, the modified Peck formula presented a minor error, in terms of the prediction curve, compared with the original formula, and the prediction result was more reliable. The best prediction result could be obtained when α = 0.535 and β = 0.482. In addition, Python could effectively improve the calculation efficiency of the Peck formula modification.
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Wang, Yan, Xinyu Bao, Song Zhang, et al. "Fetal growth prediction: Establishing fetal growth prediction curves in the second trimester." Technology and Health Care 29 (March 25, 2021): 345–50. http://dx.doi.org/10.3233/thc-218032.
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BACKGROUND: Monitoring fetal weight during pregnancy has a guiding role in prenatal care. OBJECTIVE: To establish a personalized fetal growth curve for effectively monitoring fetal growth during pregnancy. METHODS: (1) This study retrospectively analyzed the birth weight database of 2,474 singleton newborns delivered normally at term. The personalized fetal growth curve model was formed by combining the estimating birth weight of newborns with the proportional weight formula. (2) Multiple linear stepwise regression method was used to estimate the birth weight of newborns. RESULTS: (1) Delivery gestational age, weight at first visit, maternal height, pre-pregnancy body mass index, fetal sex, parity had significant effects on birth weight. Based on these parameters, the formula for calculating term optimal weight was obtained (R2= 22.8%, P< 0.001). (2) The personalized fetal growth curve was obtained according to the epidemiological factors input model of each pregnant woman. CONCLUSIONS: A model of personalized fetal growth curve can be established, and be used to evaluate fetal growth and development through estimated fetal weight monitoring.
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CHANG, IKSOO. "WINDING ANGLE DISTRIBUTION OF SELF-AVOIDING WALKS IN TWO DIMENSIONS." International Journal of Modern Physics C 11, no. 04 (2000): 721–29. http://dx.doi.org/10.1142/s012918310000064x.
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Winding angle problem of two-dimensional self-avoiding walks (SAWs) on a square lattice is studied intensively by the scanning Monte Carlo simulation at high, theta (Θ), and low-temperatures. The winding angle distribution PN(θ) and the even moments of winding angle [Formula: see text] are calculated for lengths of SAWs up to N = 300 and compared with the analytical prediction. At the infinite temperature (good solvent regime of linear polymers), PN(θ) is well described by either a Gaussian function or a stretched exponential function which is close to Gaussian, so, it is not incompatible with an analytical prediction that it is a Gaussian function exp [-θ2/ ln N] in terms of a variable [Formula: see text] and that [Formula: see text]. However, the results for SAWs at Θ and low-temperatures (Θ and bad solvent regime of linear polymers) significantly deviate from this analytical prediction. PN(θ) is then described much better by a stretched exponential function exp [-|θ|α/ln N] and [Formula: see text] with α = 1.54 and 1.51 which is far from being a Gaussian. We provide a consistent numerical evidence that the winding angle distribution for SAWs at the finite temperatures may not be a Gaussian function but a nontrivial distribution, possibly a stretched exponential function.
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Tseng, A. A., M. H. Lee, and B. Zhao. "Design and Operation of a Droplet Deposition System for Freeform Fabrication of Metal Parts." Journal of Engineering Materials and Technology 123, no. 1 (1999): 74–84. http://dx.doi.org/10.1115/1.1286187.
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A droplet generator has been designed and built to make wax and tin alloy droplets for freeform fabrication. The linear stability theory of liquid jets for forming droplets is first reviewed. The analytical formula for predicting droplet size and breakup length at optimal conditions are then developed. The suitability of the formulas to be used for the present droplet deposition system is studied by comparing its prediction with the more accurate numerical results and previously published experimental data. Only the suitable formulation is adopted for the design and operation of the droplet generator system. Experiments have been conducted at a wide range of operating conditions including different nozzle sizes, jet velocities, and frequencies. Good agreements are found between the predictions based on the adopted analytical formulation and the experimental results. It has been found that using the present design and procedure recommended, the droplet sizes can be controlled having a size deviation of less than 3 percent and the shape variation of the deposited layer can be managed within 3 percent of its deposited width.
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Maas, John, Francis D. Galey, John R. Peauroi, et al. "The Correlation between Serum Selenium and Blood Selenium in Cattle." Journal of Veterinary Diagnostic Investigation 4, no. 1 (1992): 48–52. http://dx.doi.org/10.1177/104063879200400111.
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The selenium (Se) concentration of paired blood and serum samples from cattle was determined by 2 methods: 1) atomic absorption spectroscopy using hydride generation (HG-AAS), and 2) inductively coupled argon plasma emission spectroscopy using hydride generation (ICP). Samples from 327 cattle were analyzed by HG-AAS, and samples from 344 cattle were analyzed by ICP. The data were examined by linear regression analysis, and the technique of inverse prediction was utilized to determine prediction intervals for estimating blood Se concentration from known serum Se concentration. The correlation coefficients, by simple linear regression of serum Se on blood Se, were 0.79 ( r2 = 0.62) and 0.88 ( r2 = 0.77) for the HG-AAS data and the ICP data, respectively. For the HG-AAS data, the inverse prediction formula for estimating blood Se when serum Se is known, at the 95% prediction interval, was For the ICP data, the inverse prediction formula for estimating blood Se when serum Se is known, at the 95% prediction interval, was The prediction intervals were quite wide, and the accuracy of estimating blood Se from a known serum Se was not useful for diagnostic purposes. The use of serum Se concentration to assess nutritional status of cattle with respect to Se does not appear to be appropriate.
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Li, Ping Kang, Rui Pan, and Chen Chen. "A Novel Neural Network Based Modeling for Control of NOx Emission in Power Plant." Applied Mechanics and Materials 643 (September 2014): 385–90. http://dx.doi.org/10.4028/www.scientific.net/amm.643.385.
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A novel neural network based modeling for non-linear model identification technique is proposed. It combines a nonlinear steady state model with a linear one, to describe the disturbance and dynamics in the coal-fired power plant. The modeling and training algorithm is used to develop a model of nitrogen oxides (NOx) emitted from the process where one-step ahead optimal prediction formula are developed. Two cases show that the resulting model provides a better prediction of NOx and fitting capabilities.
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Kao, Chin Ming, Li Chen, Chih Chiang Wei, and You Rong Fu. "Grammatical Evolution for Total Phosphorus in Reservoir Prediction." Advanced Materials Research 211-212 (February 2011): 369–73. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.369.
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The present study applied genetic programming (GP) to estimate the slump flow of high-performance concrete (HPC) using seven concrete ingredients. GP optimizes functions and their associated coefficients simultaneously and is suitable to automatically discover complex relationships between nonlinear systems. The results demonstrated that GP generates a more accurate formula and has lower estimating errors for predicting the slump flow of HPC than multiple linear regressions (MLRs).
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Tatsumi, Daisuke, and Takashi Tomita. "REAL-TIME TSUNAMI INUNDATION PREDICTION USING OFFSHORE TSUNAMI OBSERVATION." Coastal Engineering Proceedings 1, no. 32 (2011): 3. http://dx.doi.org/10.9753/icce.v32.currents.3.
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The previous real-time tsunami prediction based on the inversion method and the linear superposition can predict the tsunami in near shore area quickly, but it can not predict the tsunami inundation. The present study developed the empirical formula to estimate the overflow rate from the tsunami profile predicted by the previous method. Moreover, the level fill method was applied to predict the tsunami inundation from the estimated overflow rate. Numerical experiments using the actual topography and the historical earthquakes proved that the combination of the previous method, the empirical formula to estimate the overflow rate, and the level fill method can predict the tsunami inundation quickly from the offshore tsunami observation.
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Najibi, Ali Reza, and Mohammad Reza Asef. "Prediction of seismic-wave velocities in rock at various confining pressures based on unconfined data." GEOPHYSICS 79, no. 4 (2014): D235—D242. http://dx.doi.org/10.1190/geo2013-0349.1.
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Laboratory measurement of P- and S-wave velocities ([Formula: see text] and [Formula: see text], respectively) under confining pressure indicates that with an increase in confining pressure, [Formula: see text] and [Formula: see text] will increase. The trend is exponential at low pressures, transitioning to linear above a critical pressure. However, the trend of the velocity-pressure curve for each rock specimen may be determined knowing the coefficients of this curve. We first studied how the coefficients of the velocity-pressure curve were expected to be functions of elastic moduli. Then, four empirical equations were used to estimate four coefficients of the velocity-pressure curve, using the rock density and [Formula: see text] and [Formula: see text] at atmospheric pressure (unconfined conditions). This analysis was carried out based on laboratory experiments on 285 rock specimens of different lithology from around the world, namely the United States, China, Germany, Iran, and deep-sea-drilling projects. For each rock specimen, [Formula: see text] and [Formula: see text] were measured at different confining stress levels, rendering more than 4000 data points. The accuracy of the estimated wave velocities was on the order of 2%–3% of the measured values on average. This methodology is especially valuable for prediction and analysis of the rock behavior at deep well conditions. This is applicable for predicting geophysical properties of the earth’s crust at depth, geomechanical study of hydrocarbon and geothermal reservoirs, wellbore stability analysis, and in situ stress determination.
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Paroka, Daeng, Yuuichi Ohkura, and Naoya Umeda. "Analytical Prediction of Capsizing Probability of a Ship in Beam Wind and Waves." Journal of Ship Research 50, no. 02 (2006): 187–95. http://dx.doi.org/10.5957/jsr.2006.50.2.187.
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This paper presents a set of formulae to evaluate capsizing probability of a ship in both beam wind and waves based on a piece-wise linear approximation of roll restoring moment with and without simplifications as an extension of the work by Belenky (1993). The new simplified formula is also proposed on the basis of sto-chastic properties of roll motion near the angle of vanishing stability. These formulae are applied to a car carrier having a large windage area. As a result, it was pointed out that Belenky's simplified method could overestimate capsizing probability if the apparent roll angle model is used. The capsizing probability in both wind and waves is definitely larger than that in waves on their own. It was remarked that steeper waves or narrower wave spectrum do not always provide larger capsizing probability.
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Shanbhag, Sachin, and Yogesh M. Joshi. "Kramers–Kronig relations for nonlinear rheology. Part I: General expression and implications." Journal of Rheology 66, no. 5 (2022): 973–82. http://dx.doi.org/10.1122/8.0000480.
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The principle of causality leads to linear Kramers–Kronig relations (KKR) that relate the real and imaginary parts of the complex modulus [Formula: see text] through integral transforms. Using the multiple integral generalization of the Boltzmann superposition principle for nonlinear rheology, and the principle of causality, we derived nonlinear KKR, which relate the real and imaginary parts of the [Formula: see text] order complex modulus [Formula: see text]. For [Formula: see text], we obtained nonlinear KKR for medium amplitude parallel superposition (MAPS) rheology. A special case of MAPS is medium amplitude oscillatory shear (MAOS); we obtained MAOS KKR for the third-harmonic MAOS modulus [Formula: see text]; however, no such KKR exists for the first harmonic MAOS modulus [Formula: see text]. We verified MAPS and MAOS KKR for the single mode Giesekus model. We also probed the sensitivity of MAOS KKR when the domain of integration is truncated to a finite frequency window. We found that (i) inferring [Formula: see text] from [Formula: see text] is more reliable than vice versa, (ii) predictions over a particular frequency range require approximately an excess of one decade of data beyond the frequency range of prediction, and (iii) [Formula: see text] is particularly susceptible to errors at large frequencies.
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Malozovsky, Yuriy, Lashounda Franklin, Chinedu Ekuma, and Diola Bagayoko. "Ab initio prediction of electronic, transport and bulk properties of Li2S." International Journal of Modern Physics B 29, no. 25n26 (2015): 1542006. http://dx.doi.org/10.1142/s0217979215420060.
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In this paper, we present results from ab initio, self-consistent, local density approximation (LDA) calculations of electronic and related properties of cubic antifluorite (anti-[Formula: see text]) lithium sulfide [Formula: see text]. Our nonrelativistic computations implemented the linear combination of atomic orbital (LCAO) formalism following the Bagayoko, Zhao and Williams method, as enhanced by Ekuma and Franklin (BZW–EF). Consequently, using several self-consistent calculations with increasing basis sets, we searched for the smallest basis set that yields the absolute minima of the occupied energies. The outcomes of the calculation with this basis set, called the optimal basis set, have the full physical content of density functional theory (DFT). Our calculated indirect band gap, from [Formula: see text] to [Formula: see text], is 3.723 eV, for the low temperature experimental lattice constant of 5.689 Å. The predicted indirect band gap of 3.702 eV is obtained for the computationally determined equilibrium lattice constant of 5.651 Å. We have also calculated the total density of states (DOS) and partial densities of states (pDOS), electron and hole effective masses and the bulk modulus of [Formula: see text]. Due to a lack of experimental results, most of the calculated ones reported here are predictions for this material suspected of exhibiting a high temperature superconductivity similar to that of [Formula: see text].
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Yu, Xinliang, and Xianwei Huang. "Prediction of glass transition temperatures of polyacrylates from the structures of motion units." Journal of Theoretical and Computational Chemistry 15, no. 02 (2016): 1650011. http://dx.doi.org/10.1142/s0219633616500115.
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The glass transition temperature [Formula: see text] is the most important parameter of an amorphous polymer. A quantitative structure-property relationship (QSPR) was developed for [Formula: see text]s of 82 polyacrylates, by applying stepwise multiple linear regression (MLR) analysis. Molecular descriptors used to describe polymer structures were, for the first time, calculated from the motion units of polymer backbones, which are chain segments with 20 carbons in length (10 repeating units). After internal validation with leave-one-out (LOO) method, external validation was carried out to test the stability of the MLR model of [Formula: see text]s. Compared to the models already published in the literature, the MLR model in this paper was accurate and acceptable, although our model was based on bigger data sets. The feasibility of calculating molecular descriptors from the motion units of polymer backbones for developing [Formula: see text] models of polyacrylates has been demonstrated.
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Minami, Daichi, Tokuteru Uesugi, Yorinobu Takigawa, and Kenji Higashi. "Artificial neural network assisted by first-principles calculations for predicting transformation temperatures in shape memory alloys." International Journal of Modern Physics B 33, no. 08 (2019): 1950055. http://dx.doi.org/10.1142/s0217979219500553.
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A key property for the design of new shape memory alloys is their working temperature range that depends on their transformation temperature T0. In previous works, T0 was predicted using a simple linear regression with respect to the energy difference between the parent and the martensitic phases, [Formula: see text]E[Formula: see text]. In this paper, we developed an accurate method to predict T0 based on machine learning assisted by the first-principles calculations. First-principles calculations were performed on 15 shape memory alloys; then, we proposed an artificial neural network method that used not only computed [Formula: see text]E[Formula: see text] but also bulk moduli as input variables to predict T0. The prediction error of T0 was improved to 49 K for the proposed artificial neural network compared with 188 K for simple linear regression.
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Wang, Lingqian, Hui Zhou, Yufeng Wang, et al. "Three-parameter prestack seismic inversion based on L1-2 minimization." GEOPHYSICS 84, no. 5 (2019): R753—R766. http://dx.doi.org/10.1190/geo2018-0730.1.
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Prestack inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is the estimation of elastic parameters in the thin layers and weak reflectors. To improve the resolution and the accuracy of the inversion results, we introduced the difference of [Formula: see text] and [Formula: see text] norms as a nearly unbiased approximation of the sparsity of a vector, denoted as the [Formula: see text] norm, to the prestack inversion. The nonconvex penalty function of the [Formula: see text] norm can be decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem can be solved efficiently by the alternating direction method of multipliers. Compared with the [Formula: see text] norm regularization, the [Formula: see text] minimization can reconstruct reflectivities more accurately. In addition, the [Formula: see text]-[Formula: see text] predictive filtering was introduced to guarantee the lateral continuity of the location and the amplitude of the reflectivity series. The generalized linear inversion and [Formula: see text]-[Formula: see text] predictive filtering are combined for stable elastic impedance inversion results, and three parameters of P-wave velocity, S-wave velocity, and density can be inverted with the Bayesian linearized amplitude variation with offset inversion. The inversion results of synthetic and real seismic data demonstrate that the proposed method can effectively improve the resolution and accuracy of the inversion results.
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Jefferson, M. F., N. Pendleton, S. Mohamed, et al. "Prediction of hemorrhagic blood loss with a genetic algorithm neural network." Journal of Applied Physiology 84, no. 1 (1998): 357–61. http://dx.doi.org/10.1152/jappl.1998.84.1.357.
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Jefferson, M. F., N. Pendleton, S. Mohamed, E. Kirkman, R. A. Little, S. B. Lucas, and M. A. Horan. Prediction of hemorrhagic blood loss with a genetic algorithm neural network. J. Appl. Physiol. 84(1): 357–361, 1998.—There is no established method for accurately predicting how much blood loss has occurred during hemorrhage. In the present study, we examine whether a genetic algorithm neural network (GANN) can predict volume of hemorrhage in an experimental model in rats and we compare its accuracy to stepwise linear regression (SLR). Serial measurements of heart period; diastolic, systolic, and mean blood pressures; hemoglobin; pH; arterial[Formula: see text]; arterial[Formula: see text]; bicarbonate; base deficit; and blood loss as percent of total estimated blood volume were made in 33 male Wistar rats during a stepwise hemorrhage. The GANN and SLR used a randomly assigned training set to predict actual volume of hemorrhage in a test set. Diastolic blood pressure, arterial[Formula: see text], and base deficit were selected by the GANN as the optimal predictors set. Root mean square error in prediction of estimated blood volume by GANN was significantly lower than by SLR (2.63%, SD 1.44, and 4.22%, SD 3.48, respectively; P < 0.001). A GANN can predict highly accurately and significantly better than SLR volume of hemorrhage without knowledge of prehemorrhage status, rate of blood loss, or trend in physiological variables.
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Zheng, Wei Feng, Jing Quan Wu, Can Liu, Guang Hui Li, and Guang Yu Tan. "Study on Prediction Model and Experiments of High-Speed Milling Force for Stainless Steel 316." Applied Mechanics and Materials 33 (October 2010): 6–10. http://dx.doi.org/10.4028/www.scientific.net/amm.33.6.
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Through the orthogonal test in which stainless steel 316 was milled with high speed by solid cemented carbide end cutter, the milling force was measured. By multiple linear regression method, the prediction formula of the milling forces of stainless steel 316 was found. In addition, this study validates to significant degree of the formula meeting the actual condition, which can provide a reference to better selection of cutting parameter in advance and the design of high-speed milling cutter.
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Djebli, Abdelkader, Mostefa Bendouba, and Aid Abdelkarim. "Fatigue Life Prediction under Variable Loading Based a Non-Linear Energy Model." International Journal of Engineering Research in Africa 22 (February 2016): 14–21. http://dx.doi.org/10.4028/www.scientific.net/jera.22.14.
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A method of fatigue damage accumulation based upon application of energy parameters of the fatigue process is proposed in the paper. Using this model is simple, it has no parameter to be determined, it requires only the knowledge of the curve W–N (W: strain energy density N: number of cycles at failure) determined from the experimental Wöhler curve. To examine the performance of nonlinear models proposed in the estimation of fatigue damage and fatigue life of components under random loading, a batch of specimens made of 6082 T6 aluminium alloy has been studied and some of the results are reported in the present paper. The paper describes an algorithm and suggests a fatigue cumulative damage model, especially when random loading is considered. This work contains the results of uni-axial random load fatigue tests with different mean and amplitude values performed on 6082 T6 aluminium alloy specimens. The proposed model has been formulated to take into account the damage evolution at different load levels and it allows the effect of the loading sequence to be included by means of a recurrence formula derived for multilevel loading, considering complex load sequences. It is concluded that a ‘damaged stress interaction damage rule’ proposed here allows a better fatigue damage prediction than the widely used Palmgren–Miner rule, and a formula derived in random fatigue could be used to predict the fatigue damage and fatigue lifetime very easily. The results obtained by the model are compared with the experimental results and those calculated by the most fatigue damage model used in fatigue (Miner’s model). The comparison shows that the proposed model, presents a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner’s model.
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Hare, Jenna, and Alex E. Hay. "On the concentration dependence of sound attenuation in aqueous suspensions of silt- and sand-sized sediment: A compilation and analysis of the available data." JASA Express Letters 2, no. 3 (2022): 036002. http://dx.doi.org/10.1121/10.0009830.
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The available measurements of the acoustic attenuation coefficient, α, in aqueous suspensions of glass beads and sand are investigated for [Formula: see text] (where k is the acoustic wavenumber and a the grain radius) and volume concentrations, [Formula: see text], up to 0.65. The data are found to collapse substantially when dividing by volume concentration, consistent with the expected first-order linear dependence. Equations of the form [Formula: see text], with ka-dependent coefficients, provide a prediction that is within a factor of 2 for low and intermediate values of ka.
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Salazar-Cuytun, R., R. Portillo-Salgado, R. A. García-Herrera, et al. "Prediction of live weight in growing hair sheep using the body volume formula." Arquivo Brasileiro de Medicina Veterinária e Zootecnia 74, no. 3 (2022): 483–89. http://dx.doi.org/10.1590/1678-4162-12624.
Full textAbstract:
ABSTRACT Due to the conditions in which traditional sheep production systems operate, the evaluation of animal growth from live weight (LW) is limited by the high cost of the livestock scale as well as the sophisticated maintenance required. In this scenario, in recent years, biometric measurements have been investigated as an accurate indirect method to predict the LW of farm animals. Therefore, the present study was undertaken to examine different models for predicting the body weight of growing lambs using the body volume (BV) formula. Body volume, heart girth (HG) and body length (BL) data of 290 lambs aged between two and eight months were recorded. Body volume was calculated from HG and BL data using a formula that calculates the volume of a cylinder. The estimation of LW from the BV formula was achieved through regression equations using three mathematical models (linear, quadratic and exponential). The mean values of LW, HG, BL and BV of the lambs were 29.12±12.04kg, 70.00±11.69cm, 38.40±6.43cm and 23.93±9.90dm3, respectively. The correlation coefficient between LW and BV was r = 0.96 (P<0.001). The quadratic model showed the highest coefficient of determination (0.93) and the lowest prediction error (3.29kg). Under the experimental conditions adopted in this study, it is possible to predict the live weight of growing lambs using the body volume formula.