Empirical Linear Model Research Articles

Correlations between airborne and terrestrial gamma-ray spectrometric data in the bitumen deposit area, Ogun State, Nigeria

Abstract Radioelements deposit (uranium, thorium and potassium) were found to be influenced by geological bedrock compositions and their response varies from place to place. In this study, two radiometric surveys (ground and airborne) were carried out to investigate the possible relationship in the response of radioelements deposit to the geological composition of a bitumen rich area in Ogun State, Nigeria. Regression analysis was adopted to establish the empirical mathematical relation that exists between the two surveys. With this, the correlation between the two surveys was deduced and interpreted in conjunction with the geological map of the study area. Coefficient of variation was also utilized to assess the level of homogeneity of the surveys carried out. A linear empirical mathematical model was established for the two surveys. The results revealed the coefficient of correlation (r) of 0.66407, 0.70398 and 0.68792 for thorium, uranium and potassium respectively. The p-values obtained at 95% confidence level for the three radioelements also indicated that there exists a significant relationship (p-value

MAP‑1B, PACS‑2 and AHCYL1 are regulated by miR‑34A/B/C and miR‑449 in neuroplasticity following traumatic spinal cord injury in rats: Preliminary explorative results from microarray data.

Spinal cord injury (SCI) is a specific type of damage to the central nervous system causing temporary or permanent changes in its function. The present aimed to identify the genetic changes in neuroplasticity following SCI in rats. The GSE52763 microarray dataset, which included 15 samples [3 sham (1 week), 4 injury only (1 week), 4 injury only (3 weeks), 4 injury + treadmill (3 weeks)] was downloaded from the Gene Expression Omnibus database. An empirical Bayes linear regression model in limma package was used to identify the differentially expressed genes (DEGs) in injury vs. sham and treadmill vs. non-treadmill comparison groups. Subsequently, time series and enrichment analyses were performed using pheatmap and clusterProfile packages, respectively. Additionally, protein-protein interaction (PPI) and transcription factor (TF)-microRNA (miRNA)-target regulatory networks were constructed using Cytoscape software. In total, 159 and 105 DEGs were identified in injury vs. sham groups and treadmill vs. non-treadmill groups, respectively. There were 40 genes in cluster 1 that presented increased expression levels in the injury (1 week/3 weeks) groups compared with the sham group, and decreased expression levels in the injury + treadmill group compared with the injury only groups; conversely, 52 genes in cluster 2 exhibited decreased expression levels in the injury (1 week/3 weeks) groups compared with the sham group, and increased expression levels in the injury + treadmill group compared with the injury only groups. Enrichment analysis indicated that clusters 1 and 2 were associated with immune response and signal transduction, respectively. Furthermore, microtubule associated protein 1B, phosphofurin acidic cluster sorting protein 2 and adenosylhomocysteinase-like 1 exhibited the highest degrees in the regulatory network, and were regulated by miRNAs including miR-34A, miR-34B, miR-34C and miR-449. These miRNAs and their target genes may serve important roles in neuroplasticity following traumatic SCI in rats. Nevertheless, additional in-depth studies are required to confirm these data.

Effects of Operating Parameters on the Cut Size of Turbo Air Classifier for Particle Size Classification of SAC305 Lead-Free Solder Powder

In the present study, the effects of operating parameters, namely, rotor speed, feed rate, and inlet air velocity, on the cut diameter of a cage-type separator were studied. The design of experiments (DOE) method was used to investigate the relationship between the operating parameters and the cut size. The experimental results were statistically analyzed using MINITAB 16 software. Both the rotor speed and air inlet velocity had significant main effects on the cut size. The feed rate was also significant but had a weak effect with respect to the rotor speed and inlet air velocity effects. The cut size decreased with an increase in rotor speed and increased with an increase in air inlet velocity. However, the cut size slightly decreased with an increase in feed rate. An empirical multiple-variable linear model for predicting the cut size of the classification was created and presented. The results derived from the statistical analysis were in good agreement with those from the experiments, additionally extended from the DOE. The optimal conditions for classification of SAC305 powder with size range 25–40 μm were obtained when the turbo air classifier was operated at rotor speed 406 RPM, the feed rate 4 kg/h, and the air velocity 5 m/s. The smallest cut size of the classifier was about 27.8 μm.

Optimum Robust Control for an Oil Cooler System with Variable Speed Drive of Machine Tools

This paper deals with optimum robust control for an inverter driven oil cooler system of machine tools based on a state space model. An empirical linear first-order model of the oil cooler system obtained by experiments was changed into a state space model suitable for multi-input multi-output optimum controller design. An optimum robust controller was designed to ensure asymptotical stability and robustness against stepwise disturbance and system parameter variation. Effects of two weight matrices in a cost function were observed in detail from experimental results to clarify their trade-off relation. Some experiments were conducted to demonstrate control performance of a designed controller. Experimental results showed that the designed controller had good robustness and fairly good control performance even though abrupt stepwise disturbance addition.

Unraveling location-specific and time-dependent interactions between soil water content and environmental factors in cropped sandy soils using Sentinel-1 and moisture probes

Advances in sensor technologies provide the potential for real-time monitoring of soil moisture status. Little work has been conducted to study the spatial and temporal variations of soil water content at the field scale and the interactions between soil water content and environmental controlling factors in cropped fields during the growing season. In this study, we assessed the spatial and temporal variations of surface soil water content (0–0.1 m) using seven in-situ soil moisture probes and Sentinel-1 satellite data over the 2016 and 2017 cropping seasons in irrigated fields of the Central Sands Plains, Wisconsin, USA. An empirical multiple linear regression model was developed between the soil water content with Sentinel-1 backscatter data. The model was evaluated with leave-one-group-out cross-validation, which showed an R2 of 0.60, mean error of –0.00 m3 m−3, root mean square error of 0.02 m3 m−3, and Lin’s concordance correlation coefficient of 0.75. Soil volumetric water content (VWC) and soil water deficit (SWD) were mapped at 30-m resolution every 6–12 days across one field (DU field at the Wallendal farm). Using two statistical metrics (“first metric” and “last metric”) and a bootstrapping approach, the location-specific and time-dependent interactions between estimated soil water content and environmental controlling factors across the DU field during the cropping season were evaluated, and it was found that such interactions were affected by initial soil water content and plant stress status. The robustness of the model needs to be improved in the future by collecting more VWC measurements in different soil and crop conditions. The method has the potential to provide a baseline soil moisture map and can be coupled with mechanistic models and subsoil VWC measurements for improved irrigation management and water use efficiency under a changing climate.

How has empirical monetary policy analysis in the U.S. changed after the financial crisis?

During the Great Recession, the Federal Reserve lowered the federal funds rate nearly to zero and began using unconventional monetary policy. A fed funds rate near zero is no longer a proper representation of policy. Thus, empirical models of monetary policy cannot be estimated as usual. We use a linear empirical model to investigate whether alternative instruments such as the balance sheet or shadow rates can replace the fed funds rate to capture unconventional policy. Our objective is to determine whether adding to or replacing the policy instrument can preserve linearity or whether one must allow structural breaks. We include data for both normal and unconventional periods and find that shadow rates preserve linearity better than using a bounded federal funds rate alone, adding the balance sheet, or adding long rates. When short rates are bounded, shadow rates produce similar responses to the unbounded period and alleviate the need for structural breaks. [JEL codes: E43, E44, E52] Keywords: zero lower bound, affine term structure.

Empirical Linear Seismic Site Amplification in Central and Eastern North America

We present empirical linear site amplification models conditioned on time-averaged shear wave velocity in the upper 30 m ( VS30) for central and eastern North America. The models are derived from ground motion data and site condition information from the NGA-East project and are intended for use with reference rock ground motion models. Site amplification is found to scale with VS30for intermediate to stiff site conditions ( VS30> 300 m/s) in a weaker manner than for active tectonic regions such as the western United States. For stiff sites ( >800 m/s), we find differences in site amplification for previously glaciated and nonglaciated regions, with nonglaciated sites having lower amplification. The models were developed using a combination of least-squares, mixed effects, and Bayesian techniques; the latter show that accounting for predictor uncertainty does not appreciably affect the median model but decreases model dispersion. Our VS30-scaling models are modular and additive to simulation-based models for the nonlinear components of site response. A limitation of the present models is that they do not account for site-specific resonance effects.

Optimization of Dissolution Conditions During Fractionation of Corn-cob in ZnCl2.4H2O/Urea Solvent System: A Statistical Approach

Background and Objectives: The choice of a suitable pretreatment method and the adjustment of the pretreatment parameters for efficient conversion of biomass to value-added products is crucial to a successful biorefinery concept. Pretreatment of corn cob using ZnCl2.4H2O/ Urea was carried out and optimized in this study. Methods: Effect of pretreatment conditions on cellulose recovery, hemicellulose recovery during the pretreatment of corn cob using ZnCl2.4H2O/ Urea was investigated via response surface methodology approach and optimized in this study. Experimental results were analysed and appropriate predictive empirical linear models were developed for each response. Results: For cellulose recovery, time and temperature, and solvent concentration were significant factors. Hemicellulose recovery in the liquid fraction is impacted by time and solvent concentration, while lignin recovery is affected by time and temperature. Using numerical optimization by desirability function, optimum pretreatment conditions obtained were: 90 min, 120°C and concentration of 71.32%/28.68 (w/w) ZnCl2.4H2O/ Urea. At these conditions, the predicted recovery for cellulose, hemicellulose and lignin were 99.03%, 27.18% and 72.43%, respectively, with a desirability of 0.902. The actual recovery was 91%, 29% and 68% for cellulose, hemicellulose and lignin, respectively, at the same conditions. Conclusion: These results indicate that the investigated variables have pronounced effect on the pretreatment of corn cob. Therefore, optimum conditions are required for recovery of desired composition before conversion to value-added products.

Valuing Equities: Discounting Growth Opportunities, Fearing Inflation

Over the last century (Eretained/P)mean ~ constant while D/P has experienced a long secular decline. If investors cannot simultaneously discount both Eretained and D, examination of the relationships between Eretained/P, D/P and the payoff ratio Eretained/D offers support to the hypothesis that Eretained/P is the priced valuation ratio. A linear Empirical Model (EM) identifies two data variables, the trailing earnings growth (EG) and inflation (cpi), that explain R2 ~ 50% of the variance of Eretained/P. The investor’s decision to sell or hold the shares is governed by the investor’s resistance to Intertemporal Substitution, R = γµ, so the MF-Gordon becomes Eretained/P = γµ - µ . A dynamic Model is obtained using Taylor expansions of the functional relationships µ = µ(EG(t)) and γ = γ(cpi(t)). The Model is calibrated using the EM. The MF-Gordon Model is used to explain the quasi-equality of equities and the long bond (1970:2000), the equity/long bond equity premium and the effect of sentiment on equity prices. The Shiller price volatility puzzle is explained by the adaptive growth expectation which is heavily loaded on the highly volatile trailing earnings growth rate.

Potential Predictability and Forecasting of the State of the Field of Anomalies of the Total Electron Concentration from Observational Data

An attempt is made in this study to evaluate the potential predictability of the TEC field (its deviation from the weekly average) at hourly time scales based on observational data. The method is based on the calculation of the distance between the group of observations and its subsample (group of analogues) contaning pairs of points separated in time but at minimum distance from each other. The time of potential predictability is defined as the time at which the distance between the two groups becomes close to the root-mean-square distance over the archive of observations. Calculations performed for the TEC SDDIS NASA data archive give the predictability time for anomalies within 6–12 h. Strong anomalies of the TEC field are characterized by the highest predictability; the predictability is maximal for the winter hemispheres and in years of high solar activity (1999–2004 and 2011–2015). These conclusions are confirmed by the forecasts based on the simplest empirical linear dynamic stochastic model. The forecasting calculations also show that there are statistical relationships between the predictability time and the minima/maxima of daily values of the F10.7 and ap indices.

A linear algebra controller based on reduced order models applied to trajectory tracking for mobile robots: an experimental validation

A linear algebra controller (LACr) based on an empirical linear model of the system is presented in this paper. The controller design is based on a first order plus dead time (FOPDT) model and can be tuned using the characteristic parameters obtained from the reaction curve. In previous studies, the versatility of this proposed controller was tested by simulations, proving be an alternative to control many kinds of processes. In this paper, the proposed controller is implemented for trajectory tracking using a real mobile robot platform. The performance results are compared against a PI controller using the ISE performance index to measure it.

Improvement in the method for borehole caliper measurement based on azimuthal gamma-gamma density well logging

Accurate characterization of the size and shape of the borehole is critical to the effective borehole correction for logging while drilling (LWD) measurements. It is also necessary for the real-time evaluation of geomechanical wellbore stability and for optimizing drilling operation and determining proper completion strategies. The pseudo-caliper measurement can be derived from LWD azimuthal density measurement, where a linear empirical model is employed to calculate the tool standoffs. However, we found that as the tool standoff continues to increase, the model could no longer describe the variation in borehole size accurately. In this paper, the responses of LWD azimuthal density measurement under different logging conditions are studied using the Monte Carlo modeling method. To improve the estimation of borehole geometry, a new model is proposed to determine tool standoffs and measure the borehole caliper. Simulation models with different degrees of borehole enlargement are built to investigate the performance of the model. Compared with the currently used method, the wellbore caliper values calculated using the new method are more consistent with the actual values. A field example with mechanical caliper measured from wireline logs is also presented to validate the effectiveness of the proposed method.

Estimating the fractional cover of photosynthetic vegetation, non-photosynthetic vegetation and bare soil from MODIS data: Assessing the applicability of the NDVI-DFI model in the typical Xilingol grasslands

Quantitative estimations of the fractional cover of photosynthetic vegetation (fPV), non-photosynthetic vegetation (fNPV) and bare soil (fBS) are critical for soil wind erosion, desertification, grassland grazing, grassland fire, and grassland carbon storage studies. At present, regional and large-scale fPV, fNPV and fBS estimations have been carried out in many areas. However, few studies have used moderate resolution imaging spectroradiometer (MODIS) data to perform large-scale, long-term fPV, fNPV and fBS estimations in the Xilingol grassland of China. The objective of this study was to quantitatively estimate the time series of fPV, fNPV and fBS in the typical grassland region of Xilingol from MODIS image data. Field measurement spectral and coverage data from May and September 2017 were combined with the 8-day composite product (MOD09A1) acquired during 2017. We established an empirical linear model of different non-photosynthetic vegetation indices (NPVIs) and fNPV based on the sample scale. The linear correlation between the dead fuel index (DFI) and fNPV was best (R2 = 0.60, RMSE = 0.15). A normalized difference vegetation index (NDVI)-DFI model based on MODIS data was proposed to accurately estimate the fPV, fNPV and fBS (estimation accuracies of 44%, 71%, and 74%, respectively) in the typical grasslands of Xilingol in China. The fPV, fNPV and fBS values for the typical grassland time series estimated by the NDVI-DFI model were consistent with the phenological characteristics of the grassland vegetation. The results show that the application of the NDVI-DFI model to the Xilingol grassland is reasonable and appropriate, and it is of great significance to the monitoring of soil wind erosion and fires in grasslands.

An attempt to inverse the ionospheric sporadic-E layer critical frequency based on the COSMIC radio occultation data

Ionospheric sporadic E layer refers to localized thin irregularity with enhanced plasma density appearing in the height range of ionospheric E layer (∼90–130 km). The much higher electron density in the sporadic E layer than the background ionosphere would cause sudden TEC enhancement in the occultation TEC profile. A wavelet decomposition and reconstruction method is applied to extract the TEC fluctuation in this paper, and then Smax index is defined to represent the intensity of the sudden TEC enhancement. Smax index is compared with sporadic E critical frequency (foEs) observed by the ionosonde. The results show a well linear correlation between them with mean correlation coefficient about 0.7. Thus, an empirical linear model is established to inverse the foEs. The monthly/hourly mean values and global distribution of sporadic E intensity and occurrence ratio are calculated using this method based on the COSMIC occultation data from 2007 to 2011. The statistical analysis results indicate that it is feasible to inverse the foEs based on the occultation TEC profile data and the inversion results can be applied to the long-term global variations of sporadic E investigations.

Evaluation of 3D point cloud-based models for the prediction of grassland biomass

Farmers, as well as agronomists, are intrigued by efficient quantification of grassland biomass at field-scale. Canopy surface height (CSH) based non-destructive grassland biomass estimation over a larger area has important advantages compared to destructive methods. 3D point clouds generated from remote sensing (RS) data offer a systematic methodology to derive CSH and estimate grassland biomass. This study evaluated 3D point clouds derived from a terrestrial laser scanner (TLS) and an unmanned aerial vehicle (UAV)-borne structure from motion (SFM) approach for grassland biomass estimation over three grasslands with different composition and management practice in northern Hesse, Germany. TLS data, UAV-borne images and reference biomass data were collected two days before each harvest from the selected grasslands in 2017. Three levels of linear empirical models (i.e. sampling date-specific, grassland-specific and global) were developed to estimate grasslands fresh and dry biomass using CSH derived from TLS and SFM 3D point clouds. The aforementioned three level models resulted in an average nRMSE of 17.2%, 25.3%, and 28.7% respectively for the grassland dry biomass estimation based on CSH from TLS data. Similarly, models based on CSH from SFM data estimated dry biomass with somewhat higher average nRMSE of 19.5%, 27.1%, and, 36.2% respectively. In general, models with 3D point clouds from UAV-borne SFM was slightly outperformed by models with TLS point cloud data. This study also identified that the utilisation of UAV-borne SFM developed digital terrain model as a reference layer to derive CSH could enhance the performance of the models with SFM data. Furthermore, the performance of the biomass estimation models was affected by both species richness and sward heterogeneity of the grasslands. Overall, these results disclosed the potential of 3D point cloud derived from RS for estimating field-scale grassland biomass.

Estimation of reservoir properties from seismic data through a Markov Chain Monte Carlo-AVA inversion algorithm

We formulate the amplitude versus angle (AVA) inversion in terms of a Markov Chain Monte Carlo (MCMC) algorithm and apply it for reservoir characterisation and litho-fluid facies prediction in offshore Nile Delta. A linear empirical rock physics model is used to link the petrophysical properties (porosity, water saturation and shaliness) to the elastic attributes (P-wave velocity, S-wave velocity and density), whereas the exact Zoeppritz equations are used to convert the elastic properties into AVA responses. The exact Zoeppritz equations allow us to take advantage of the long offset seismic acquisition and thus to consider a wide range of incidence angles in the inversion. The proposed algorithm reliably estimates the non-uniqueness of the solution that is the uncertainties affecting the estimated subsurface characteristics (both in terms of litho-fluid facies and petrophysical properties), taking into consideration the uncertainties in the prior information, the uncertainties in the estimated rock-physics model and the errors affecting the observed AVA responses. A blind test, based on available well log information, demonstrates the applicability of the proposed method and the reliability of the results. In addition, comparisons between the results provided by the implemented MCMC algorithm with those yielded by a linear AVA inversion and an analytical approach to facies prediction, show the benefits introduced by wide-angle reflections in better constraining the inverted parameters and in attenuating the noise in the predicted subsurface models.

A Subband Radiometric Calibration Method for UAV-Based Multispectral Remote Sensing

In recent years, the use of unmanned aerial vehicles (UAVs) to obtain high-resolution multispectral images has received increasing attention. When using reflectance data for quantitative remote sensing, radiometric calibration is needed that converts digital number to reflectance. Empirical linear radiometric calibration models with large calibration sites are feasible and convenient for remote sensing satellite wide-band sensors, but problems may exist with using this method directly in a UAV high-resolution remote sensing application. In this paper, we proposed a high precision, low cost subband empirical line (SEL) radiometric calibration method with two targets composed of black and white nonwoven fabric. To verify the results of the calibration model, analyses were performed by examining the influence of function selection, calibration materials, and the number of calibration panels. Next, the method was applied to natural field targets. The results show that the black and white panels have good spectral, Lambertian, and contrast characteristics; the power equation was more suitable for the visible bands, whereas the linear equation was more suitable for red-edge and near-infrared bands. The average absolute errors between the predicted reflectance and the measured reflectance were at around 10%. The proposed method had smaller errors and higher accuracy than the other function method, and a high correlation between the predicted and measured reflectance of the maize samples was observed. The SEL method developed in this study provides a reference for studying the radiometric calibration of other multispectral sensors.

Two-stage and single-stage seismic-petrophysical inversions applied in the Nile Delta

We discuss two Bayesian seismic-petrophysical inversion techniques, the two-stage and single-stage approach, which estimate petrophysical properties from prestack seismic data. Both approaches are developed considering linear approximations and are applied for reservoir appraisal studies in the Nile Delta. The two-stage approach first uses an amplitude-variation-with-angle (AVA) inversion to infer P-wave velocity, S-wave velocity, and density. Then, a linear empirical rock-physics model, properly calibrated for the investigated area, is used to transform the estimated elastic parameters into the petrophysical properties of interest under the assumption of Gaussian mixture distributed petrophysical properties. The single-stage approach uses the linear rock-physics model to rewrite the time-continuous P-wave reflectivity equation as a function of the petrophysical contrasts instead of the elastic constants. This reformulation, together with the assumption of a Gaussian prior model, allows us to directly derive (in a single-stage inversion) the petrophysical properties from AVA data. Despite the differences in the forward-model parameterization and in the assumed a priori distribution for the petrophysical properties, the two inversion methods yield comparable predictions that are consistent with borehole data. For the investigated zone, this work demonstrates that, although neglecting the facies-dependent behavior of petrophysical properties, the a priori Gaussian assumption for the petrophysical properties can provide reliable predictions with a very limited computational effort. In addition, the good match between predicted and logged properties proves the suitability of the linear rock-physics model for reservoir characterization in the Nile Delta.

Machine learning algorithms to predict core, skin, and hair-coat temperatures of piglets

Internal-body (core) and surface temperatures of livestock are important information that indicate heat stress status and comfort of animals. Previous studies focused on developing mechanistic and empirical models to predict these temperatures. Mechanistic models based on bioenergetics of animals often require parameters that may be difficult to obtain (e.g., thickness of internal tissues). Empirical models, on the other hand, are data-based and often assume linear relationships between predictor (e.g., air temperature) and response (e.g., internal-body temperature) variables although, from the theory of bioenergetics, the relationship between the predictor and the response variables is non-linear. One alternative to consider non-linearity is to use machine learning algorithms to predict physiological temperatures. Unlike mechanistic models, machine learning algorithms do not depend on biophysical parameters, and, unlike linear empirical models, machine learning algorithms automatically select the predictor variables and find non-linear functions between predictor and response variables. In this paper, we tested four different machine learning algorithms to predict rectal (Tr), skin-surface (Ts), and hair-coat surface (Th) temperatures of piglets based on environmental data. From the four algorithms considered, deep neural networks provided the best prediction for Tr with an error of 0.36%, gradient boosted machines provided the best prediction for Ts with an error of 0.62%, and random forests provided the best predictions for Th with an error of 1.35%. These three algorithms were robust for a wide range of inputs. The fourth algorithm, generalized linear regression, predicted at higher errors and was not robust for a wide range of inputs. This study supports the use of machine learning algorithms (specifically deep neural networks, gradient boosted machines, and random forests) to predict physiological temperature responses of piglets.

A Non-Linear Model for Censored and Mismeasured Time Varying Covariates in Survival Models, with Applications in Human Immunodeficiency Virus and Acquired Immune Deficiency Syndrome Studies

Summary In survival regression analysis, when the time-dependent covariates are censored and measured with errors, a joint model is often considered for the longitudinal covariate data and the survival data. Typically, an empirical linear (mixed) model is assumed for the time-dependent covariates. However, such an empirical linear covariate model may be inappropriate for the (unobserved) censored covariate values that may behave quite differently from the observed covariate process. In applications such as human immunodeficiency virus–acquired immune deficiency syndrome studies, a mechanistic non-linear model can be derived for the covariate process on the basis of the underlying data generation mechanisms and such a non-linear covariate model may provide better ‘predictions’ for the censored and mismeasured covariate values. We propose a joint Cox and non-linear mixed effect model to model survival data with censored and mismeasured time varying covariates. We use likelihood methods for inference, implemented by the Monte Carlo EM algorithm. The models and methods are evaluated by simulations. An acquired immune deficiency syndrome data set is analysed in detail, where the time-dependent covariate is a viral load which may be censored because of a lower detection limit and may also be measured with errors. The results based on linear and non-linear covariate models are compared and new insights are gained.