Improved Prediction Model Research Articles

Contrasting terpene emissions from canopy and understory vegetation in response to increases in nitrogen deposition and seasonal changes in precipitation

Given global change and shifts in climate are expected to increase BVOC emissions, the quantification of links between environmental conditions, plant physiology, and terpene emission dynamics is required to improve model predictions of ecosystem responses to increasing nitrogen deposition and changes in precipitation regimes. Here, we conducted a two-factor field experiment in sub-tropical forest plots to determine effects of N addition (N), precipitation change (PC), and NP (N and PC combined treatment) on wet and dry season terpene emissions and leaf photosynthetic parameters from canopy and understory species. Changes of β-ocimene and sabinene under PC and NP in the wet season (0.4–5.6-fold change) were the largest contributor to changes in total terpene emissions. In the dry season, the standardized total terpene emission rate was enhanced by 144.9% under N addition and 185.7% under PC for the understory species, while the total terpene emission rate was lower under NP than N addition and PC, indicating that N addition tended to moderate increases in PC-induced understory total terpene emissions. In the wet season, the total terpene emission rate under N and PC was close to ambient conditions for the canopy species, while the total terpene emission rate was enhanced by 54.6% under NP, indicating that N and PC combined treatment had an additive effect on canopy total terpene emissions. Total terpene emission rates increased with rates of net leaf photosynthesis (Pn) and transpiration (Tr) and there was a decoupling between terpene emission rates and Pn under NP, indicating that complex effects between PC and N decreased the regularity of single-factor effects. We recommend that N and PC interaction effects are included in models for the prediction of terpene emissions, particularly from canopy vegetation during the wet season as a major source of forest ecosystem terpene emissions.

Are infections the missing elements in predicting Alzheimer’s disease?

AbstractBackgroundAlzheimer’s disease (AD) begins many years before its clinical expression. Therefore, an important goal is accurate long‐term prediction, especially for prevention trials and when evaluating the impacts of early intervention. Yet, current efforts still fall short, which is indicative of missing information in the modelling. Recently, the Epstein‐Barr virus has been shown to trigger the development of multiple sclerosis, years after infection. Similarly, some studies have reported odds ratios for AD that were almost as high as age for some chronic infections, such as those caused by either the herpes simplex virus or cytomegalovirus. We aim to review the literature on prediction models to examine whether infection load has been sufficiently studied as an early biomarker of AD.MethodWe used the same strategy employed in previous reviews by Stephen et al. (2010), Tang et al. (2015), and Hou et al. (2018) to perform a systematic review of the literature published between January 2018 to May 2021 for the prediction of AD in cognitively intact individuals from the general population. We examined the type of model and input data as well as the performance of the prediction models in the selected articles with a particular focus on infection load.ResultOur initial search yielded 18,915 articles. Artificial intelligence was found to be the most widely used technique for prediction model computation. Most models included chronological age, and long‐term prediction accuracy was mainly determined by this parameter. Of note, models with a measure of amyloid beta misfolding were highly predictive of the progression to AD. Only one model included data exploring the contribution of infection.ConclusionLong‐term prediction models for AD in the general population of cognitively intact older adults were mostly driven by age. Despite the growing literature associating specific infectious agents with the pathophysiological development of AD, only one model used infection load as a parameter to predict AD. The potential of serological infection status as a parameter to improve prediction models in the general population must therefore be further explored.

An Improved Prediction Model of Pig Price

In many agricultural products, pig price fluctuation has a significant impact on price level and consumer price index, so accurate prediction of pig price is of great significance for pig market research and production. In order to predict the price of pigs more accurately in the short term, Attention-LSTM prediction model (a short-term memory neural network based on attention mechanism) is established. The results show that: compared with the traditional LSTM forecasting model, the Attention-LSTM model has higher prediction accuracy, and this model has a good effect on the short-term prediction of pig prices.

Improving generalized models of forest structure in complex forest types using area- and voxel-based approaches from lidar

Modeling forest attributes using lidar data has been a useful tool for forest management but the need to correlate lidar to ground-based measurements creates challenges to modeling in diverse forest landscapes. Many lidar models have been based on metrics derived from summarizations of individual lidar returns over sample plot areas, but more recently, metrics based on summarization by volumetric pixel (voxel) have shown promise to better characterize forest structure and distinguish between diverse forest types. Voxel-based metrics may improve characterization of leaf area distribution and horizontal forest structure, which could help create general models of forest attributes applicable in complex landscapes composed of many distinct forest types. We modeled wood volume in longleaf pine woodlands and associated forests to compare how area- and voxel- based lidar metrics predicted wood volume in forest type specific and general predictive models. We created four area-based and six voxel-based metrics to fit models of wood volume using a multiplicative power function. We selected models and compared metric importance using AIC and evaluated model performance using cross-validated mean prediction error. We found that one area-based metric and four voxel-based metrics consistently improved model predictions We suggest that area-based metrics alone may have limitations for characterizing complex forest structure. Area-based summarizes of lidar returns are more heavily influenced by upper canopy returns because lidar returns attenuate below the canopy. By contrast, summarizing lidar returns into a single value per voxel prior to summarization over plots homogenizes point density, giving added weight to sub-canopy returns. Thus voxel-based metrics may be more sensitive to structural variation that may not be adequately captured by area-based metrics alone. This study highlights the potential of voxel-based metrics for characterizing complex forest structure and model generalization capable of accurate forest attribute prediction across diverse forest types.

Evaluation of Neonatal and Paediatric Vancomycin Pharmacokinetic Models and the Impact of Maturation and Serum Creatinine Covariates in a Large Multicentre Data Set.

Infants and neonates present a clinical challenge for dosing drugs with high interindividual variability due to these patients' rapid growth and the interplay between maturation and organ function. Model-informed precision dosing (MIPD), which can account for interindividual variability via patient characteristics and Bayesian forecasting, promises to improve individualized dosing strategies in this complex population. Here, we assess the predictive performance of published population pharmacokinetic models describing vancomycin in neonates and infants, and analyze the robustness of these models in the face of clinical uncertainty surrounding covariate values. The predictive precision and bias of nine pharmacokinetic models were compared in a large multi-site data set (N = 2061 patients, 5794 drug levels, 28 institutions) of patients aged 0-365 days. The robustness of model predictions to errors in serum creatinine measurements and gestational age was assessed by using recorded values or by replacing covariate values with 0.3, 0.5 or 0.8 mg/dL or with 40 weeks, respectively. Of the nine models, two models (Dao and Jacqz-Aigrain) resulted in predicted concentrations within 2.5 mg/L or 15% of the measured values for at least 60% of population predictions. Within individual models, predictive performance often 2 differed in neonates (0-4 weeks) versus older infants (15-52 weeks). For preterm neonates, imputing gestational age as 40 weeks reduced the accuracy of model predictions. Measured values of serum creatinine improved model predictions compared to using imputed values even in neonates ≤1 week of age. Several available pharmacokinetic models are suitable for MIPD in infants and neonates. Availability and accuracy of model covariates for patients will be important for guiding dose decision-making.

A New Predictive Algorithm for Time Series Forecasting Based on Machine Learning Techniques: Evidence for Decision Making in Agriculture and Tourism Sectors

Accurate time series prediction techniques are becoming fundamental to modern decision support systems. As massive data processing develops in its practicality, machine learning (ML) techniques applied to time series can automate and improve prediction models. The radical novelty of this paper is the development of a hybrid model that combines a new approach to the classical Kalman filter with machine learning techniques, i.e., support vector regression (SVR) and nonlinear autoregressive (NAR) neural networks, to improve the performance of existing predictive models. The proposed hybrid model uses, on the one hand, an improved Kalman filter method that eliminates the convergence problems of time series data with large error variance and, on the other hand, an ML algorithm as a correction factor to predict the model error. The results reveal that our hybrid models obtain accurate predictions, substantially reducing the root mean square and absolute mean errors compared to the classical and alternative Kalman filter models and achieving a goodness of fit greater than 0.95. Furthermore, the generalization of this algorithm was confirmed by its validation in two different scenarios.

New formulas addressing flow resistance of floodplain vegetation from emergent to submerged conditions

ABSTRACT Hydraulic modelling of natural floodplain vegetation using leaf area index (LAI) has been applied successfully for non-submerged conditions whereas its suitability for submerged conditions requires further development. This study investigates the vegetative flow resistance at low relative submergences and extends existing LAI-based approaches building upon new flume data and prior experiences from field-scale applications. We provide advanced LAI-based formulas for modelling the flow resistance from emergent to submerged conditions, with water depth up to three times higher than the vegetation height. Such low relative submergences are highly relevant in hydraulic analyses of riverbank and floodplain flows but not adequately represented in existing formulas. The use of the deflected vegetation height as the characteristic height provided the most accurate modelling results, whereas the use of undeflected height resulted in significant errors. As a new development for submerged conditions, we proposed von Kármán scaling factor for improved model predictions. Overall, the results proved that LAI-based modelling is suitable also at low relative submergences for a wide range of vegetation densities (LAI = 1–5) and mean flow velocities (0.05–1.2 m s−1). For both emergent and slightly overtopped vegetation the JAR and VAS approaches outperformed the BAPmod-LAI approach that does not account for reconfiguration. For modellers, we provide a workflow and guidance on the use of the newly developed LAI-based formulas in 1D/2D hydrodynamic models for both emergent and submerged conditions.

Correction to: An Improved Prediction Model on Fatigue Crack Growth Rate under Variable Amplitude Loads for Metallic Materials

Correction to: An Improved Prediction Model on Fatigue Crack Growth Rate under Variable Amplitude Loads for Metallic Materials

Machine learning with in silico analysis markedly improves survival prediction modeling in colon cancer patients.

Predicting the survival of cancer patients provides prognostic information and therapeutic guidance. However, improved prediction models are needed for use in diagnosis and treatment. This study aimed to identify genomic prognostic biomarkers related to colon cancer (CC) based on computational data and to develop survival prediction models. We performed machine-learning (ML) analysis to screen pathogenic survival-related driver genes related to patient prognosis by integrating copy number variation and gene expression data. Moreover, in silico system analysis was performed to clinically assess data from ML analysis, and we identified RABGAP1L, MYH9, and DRD4 as candidate genes. These three genes and tumor stages were used to generate survival prediction models. Moreover, the genes were validated by experimental and clinical analyses, and the theranostic application of the survival prediction models was assessed. RABGAP1L, MYH9, and DRD4 were identified as survival-related candidate genes by ML and in silico system analysis. The survival prediction model using the expression of the three genes showed higher predictive performance when applied to predict the prognosis of CC patients. A series of functional analyses revealed that each knockdown of three genes reduced the protumor activity of CC cells. In particular, validation with an independent cohort of CC patients confirmed that the coexpression of MYH9 and DRD4 gene expression reflected poorer clinical outcomes in terms of overall survival and disease-free survival. Our survival prediction approach will contribute to providing information on patients and developing a therapeutic strategy for CC patients.

Not from Scratch: Predicting Thermophysical Properties through Model-Based Transfer Learning Using Graph Convolutional Networks.

In this study, a framework for the prediction of thermophysical properties based on transfer learning from existing estimation models is explored. The predictive capabilities of conventional group-contribution methods and traditional machine-learning approaches rely heavily on the availability of experimental datasets and their uncertainty. Through the use of a pretraining scheme, which leverages the knowledge established by other estimation methods, improved prediction models for thermophysical properties can be obtained after fine-tuning networks with more accurate experimental data. As our experiments show, for the case of critical properties of compounds, this pipeline not only improves the performance of the models on commonly found organic structures but can also help these models generalize to less explored areas of chemical space, where experimental data is scarce, such as inorganics and heavier organic compounds. Transfer learning from estimation models data also allows for graph-based deep learning models to create more flexible molecular features over a bigger chemical space, which leads to improved predictive capabilities and can give insights into the relationship between molecular structures and thermophysical properties. The generated molecular features can discriminate behavior discrepancy between isomers without the need of additional parameters. Also, this approach shows better robustness to outliers in experimental datasets.

Improved Prediction Model of Protein and Peptide Toxicity by Integrating Channel Attention into a Convolutional Neural Network and Gated Recurrent Units.

In recent times, the importance of peptides in the biomedical domain has received increasing concern in terms of their effect on multiple disease treatments. However, before successful large-scale implementation in the industry, accurate identification of peptide toxicity is a vital prerequisite. The existing computational methods have reached good results from toxicity prediction, and we present an improved model based on different deep learning architectures. The modification mainly focuses on two aspects: sequence encoding and variational information bottlenecks. Consequently, one of our modified plans shows an obvious increase in sensitivity, while the rest show good performance meanwhile adding novelty in the peptide toxicity prediction domain. In detail, our best model could achieve an accuracy of 97.38 and 95.03% in protein and peptide toxicity predictions, respectively. The performance was superior to previous predictors on the same datasets.

Applying machine learning to the pharmacokinetic modeling of cyclosporine in adult renal transplant recipients: a multi-method comparison.

Objective: The aim of this study was to identify the important factors affecting cyclosporine (CsA) blood concentration and estimate CsA concentration using seven different machine learning (ML) algorithms. We also assessed the predictability of established ML models and previously built population pharmacokinetic (popPK) model. Finally, the most suitable ML model and popPK model to guide precision dosing were determined. Methods: In total, 3,407 whole-blood trough and peak concentrations of CsA were obtained from 183 patients who underwent initial renal transplantation. These samples were divided into model-building and evaluation sets. The model-building set was analyzed using seven different ML algorithms. The effects of potential covariates were evaluated using the least absolute shrinkage and selection operator algorithms. A separate evaluation set was used to assess the ability of all models to predict CsA blood concentration. R squared (R 2) scores, median prediction error (MDPE), median absolute prediction error (MAPE), and the percentages of PE within 20% (F20) and 30% (F30) were calculated to assess the predictive performance of these models. In addition, previously built popPK model was included for comparison. Results: Sixteen variables were selected as important covariates. Among ML models, the predictive performance of nonlinear-based ML models was superior to that of linear regression (MDPE: 3.27%, MAPE: 34.21%, F20: 30.63%, F30: 45.03%, R 2 score: 0.68). The ML model built with the artificial neural network algorithm was considered the most suitable (MDPE: -0.039%, MAPE: 25.60%, F20: 39.35%, F30: 56.46%, R 2 score: 0.75). Its performance was superior to that of the previously built popPK model (MDPE: 5.26%, MAPE: 29.22%, F20: 33.94%, F30: 51.22%, R 2 score: 0.68). Furthermore, the application of the most suitable model and the popPK model in clinic showed that most dose regimen recommendations were reasonable. Conclusion: The performance of these ML models indicate that a nonlinear relationship for covariates may help to improve model predictability. These results might facilitate the application of ML models in clinic, especially for patients with unstable status or during initial dose optimization.

Population flow based spatial-temporal eigenvector filtering modeling for exploring effects of health risk factors on COVID-19

The COVID-19 pandemic has had great impact on human health and social economy. Several studies examined spatial and temporal patterns of health risk factors associated with COVID-19, but population flow spillover effect has not been sufficiently considered. In this paper, a population flow-based spatial-temporal eigenvector filtering model (FLOW-ESTF) was developed to consider spatial-temporal patterns and population flow connectivity simultaneously. The proposed FLOW-ESTF method efficiently improved model prediction accuracy, which could help the government aware of the infection risk level and to make suitable control policies. The selected population flow spatial-temporal eigenvector contributed most to modeling and the visualization of corresponding eigenvector set helped to explore the underlying spatial-temporal patterns and pandemic transmission nodes. The model coefficients could reflect how health risk factors contribute the modeling of state-level COVID-19 weekly increased cases and how their influence changed through time, which could help people and government to better aware the potential health risks and to adjust control measures at different stage. The extracted population flow spatial-temporal eigenvector not only represents influence of population flow and its spillover effects but also represents some possible omitted health risk factors. This could provide an efficient path to solve the problem of spatial and temporal autocorrelation in COVID-19 modeling and an intuitive way to discover underlying spatial patterns, which will partially compensate for the problems of insufficient consideration of potential risk variables and missing data.

Assessing the contribution of UGT isoforms on raltegravir drug disposition through PBPK modeling

This work aimed to develop a physiologically based pharmacokinetic (PBPK) model for raltegravir accounting for UDP-glucuronosyltransferase (UGT) metabolism to assess the effect of UGT gene polymorphisms. Raltegravir elimination was evaluated using Km and Vmax values from human recombinant systems and UGT tissue scalar considering liver, kidney, and intestine. The predicted/observed ratios for raltegravir PK parameters were within a 2-fold error range in UGT1A1 poor and normal metabolizers, except in Asian UGT1A1 poor metabolizers. This PBPK modeling approach suggests that UGT1A3 is the main contributor to raltegravir's metabolism. UGT1A3 and UGT1A1 gene polymorphisms might have an additive effect on raltegravir's drug disposition and response. The final model accounting for hepatic, renal, and intestinal UGT metabolism, biliary clearance, and renal excretion improved model predictions compared with the previously published models. This PBPK model with the quantitative characterization of raltegravir elimination pathways can support dose adjustments in different clinical scenarios.

A hybrid feature selection approach for Microarray datasets using graph theoretic-based method

The feature selection process plays an important role in different fields, particularly in bioinformatics and microarray gene expression data analysis, for choosing discriminative genes from high-dimensional datasets and selecting a subset of highly relevant features with low redundancy that may lead to build improved prediction models. Consequently, this study proposes a new feature selection method that integrates Preordonnances theory in terms of new Relevance and Complementarity criteria introduced here and also connectivity in undirected Weighted Graphs (PCRWG). The method can handle high-dimensional data. PCRWG retains the relevant and complementary features to select effective features in large scale gene datasets. The proposed algorithm operates in two phases: filtering and wrapping. The strength of the first phase is that it is preceded by a step that further reduces the number of predictors by removing those in disagreement with the target based on the new proposed relevance criterion. Then, the proposed heuristic uses the relevance-complementarity ratio between preordonnances to automatically update the compromise rule between relevance and complementarity. In the wrapping phase, the suggested graph-based approach using maximal clique is based on a powerful relevance-complementarity matrix to consolidate edges, two connected interdependent features are complementary to each other, and it is possible to have high discriminative power when they serve as a group. We highlight the fact that existing graph-based feature selection algorithms do not consider relevance and complementarity simultaneously. The experiments were carried out on three simulated scenarios and the thirteen most popular cancer microarray gene datasets. Formally, they are eight binary and five multi-class microarray data. A 10-fold cross validation was used to evaluate the Support Vector Machine (SVM), Naive Bayes (NB) and artificial Neural Network (NN) classifiers. The empirical results demonstrate the high performance of the proposed hybrid approach when compared to the most recently published articles.

Identification of HLA-E Binding Mycobacterium tuberculosis-Derived Epitopes through Improved Prediction Models.

Tuberculosis (TB) remains one of the deadliest infectious diseases worldwide, posing great social and economic burden to affected countries. Novel vaccine approaches are needed to increase protective immunity against the causative agent Mycobacterium tuberculosis (Mtb) and to reduce the development of active TB disease in latently infected individuals. Donor-unrestricted T cell responses represent such novel potential vaccine targets. HLA-E-restricted T cell responses have been shown to play an important role in protection against TB and other infections, and recent studies have demonstrated that these cells can be primed in vitro. However, the identification of novel pathogen-derived HLA-E binding peptides presented by infected target cells has been limited by the lack of accurate prediction algorithms for HLA-E binding. In this study, we developed an improved HLA-E binding peptide prediction algorithm and implemented it to identify (to our knowledge) novel Mtb-derived peptides with capacity to induce CD8+ T cell activation and that were recognized by specific HLA-E-restricted T cells in Mycobacterium-exposed humans. Altogether, we present a novel algorithm for the identification of pathogen- or self-derived HLA-E-presented peptides.

A novel neural network-based alloy design strategy: Gated recurrent unit machine learning modeling integrated with orthogonal experiment design and data augmentation

Machine learning-aided alloy design has recently attracted broad interest among the materials science community. However, the prediction accuracy of general machine learning models is limited due to a limited number of model hyperparameters and their dedicated application domains. The artificial neural network (ANN) model can significantly improve the prediction accuracy. At the same time, it suffers from the well-known curse of dimensionality issue (i.e., the amount of required training data increases exponentially with input feature dimensions). In this work, a novel alloy design strategy through a Gated recurrent unit (GRU) deep learning model, orthogonal experimental design and data augmentation technique was developed. Under the case of orthogonal experimental design and data augmentation, the GRU model, compared with the regular feed-forward neural network model, reduced the amount of training data required for accurate prediction and dramatically improved model prediction accuracy. The experimental results further verified that the GRU model exhibited the best prediction accuracy in the case of data augmentation and orthogonal experimental sampling. In addition, the prediction trend of GRU model and the analysis results of orthogonal experiment indicated the main factors affecting yield strength were HD (Hot rolling deformation), CD (Cold rolling deformation), AT (Aging temperature), the main factors affecting conductivity were AT (Aging temperature), At (Aging time). Finally, a high strength and high conductivity Cu-Ni-Si alloy with a tensile strength of 923 MPa, a yield strength of 685 MPa, and electrical conductivity of 47.2% IACS was predicted by using 36 experimental data through the strategy. These findings provide a new machine learning method to predict the properties through dozens of experimental data.

Optimized cascaded CNN for intelligent rainfall prediction model: a research towards statistic-based machine learning

Using artificial intelligence to anticipate weather conditions, according to prior research, can provide positive results. Forecasts of meteorological time series can aid disaster-prevention personnel in making more informed judgments. Deep learning has recently been shown to be a viable technique for solving complicated issues and analyzing large amounts of data. Statistical learning theory is a type of machine learning that combines statistics and functional analysis. To answer the problem of rainfall forecasting, this study employs a statistically-based machine learning technique. The benchmark meteorological data is first pre-processed using data augmentation and data normalization. The machine learning is then given statistical characteristics such as "first order and second order statistical information" for prediction. The Adaptive Searched Scaling factor-based Elephant Herding Optimization (ASS-EHO)is used to optimize the Cascaded Convolutional Neural Network (CNN) for rainfall prediction as an improved prediction model, with parameter tuning such as cascaded CNN count, hidden neuron count, and activation function optimized. The new prediction model is a statistical-based machine learning model in which the aim function is the reduction of the cross entropy loss function. The results are compared to established statistical methodologies, demonstrating that the model may be used to estimate daily rainfall quickly and accurately.

Oxygen availability regulates the quality of soil dissolved organic matter by mediating microbial metabolism and iron oxidation

Dissolved organic matter (DOM) plays a vital role in biogeochemical processes and in determining the responses of soil organic matter (SOM) to global change. Although the quantity of soil DOM has been inventoried across diverse spatio-temporal scales, the underlying mechanisms accounting for variability in DOM dynamics remain unclear especially in upland ecosystems. Here, a gradient of SOM storage across 12 croplands in northeast China was used to understand links between DOM dynamics, microbial metabolism, and abiotic conditions. We assessed the composition, biodegradability, and key biodegradable components of DOM. In addition, SOM and mineral-associated organic matter (MAOM) composition, soil enzyme activities, oxygen availability, soil texture, and iron (Fe), Fe-bound organic matter, and nutrient concentrations were quantified to clarify the drivers of DOM quality (composition and biodegradability). The proportion of biodegradable DOM increased exponentially with decreasing initial DOM concentration due to larger fractions of depolymerized DOM that was rich in small-molecular phenols and proteinaceous components. Unexpectedly, the composition of DOM was decoupled from that of SOM or MAOM, but significantly related to enzymatic properties. These results indicate that microbial metabolism exhibited a dominant role in DOM generation. As DOM concentration declined, increased soil oxygen availability regulated DOM composition and enhanced its biodegradability mainly through mediating microbial metabolism and Fe oxidation. The oxygen-induced oxidation of Fe(II) to Fe(III) removed complex DOM compounds with large molecular weight. Moreover, increased oxygen availability stimulated oxidase-catalyzed depolymerization of aromatic substances, and promoted production of protein-like DOM components due to lower enzymatic C/N acquisition ratio. As global changes in temperature and moisture will have large impacts on soil oxygen availability, the role of oxygen in regulating DOM dynamics highlights the importance of integrating soil oxygen supply with microbial metabolism and Fe redox status to improve model predictions of soil carbon under climate change.

Analytical prediction of the formation factor for isotropic mono-sized unconsolidated porous media

Analytical expressions are derived for the formation factor as a function of porosity based on the Representative Unit Cell model for unconsolidated media by applying volume averaging to Ohm’s law. Three arrays are considered, namely an over-staggered, fully staggered and regular array. Numerical simulations are performed to compute the formation factor for two-dimensional versions of the arrays by solving the Laplace equation. The absolute relative percentage difference between the numerical data and corresponding model predictions obtained for the over-staggered array is less than 20% and that for both the fully staggered and regular arrays are less than 10%. Two weighted isotropic models are introduced and a percolation threshold porosity incorporated. The models have been validated against experimental data and models from the literature. The improvement in model prediction with the percolation threshold porosity included is between 100 and 200% at the average porosity of the data set considered.