Nonlinear Least-squares Regression Research Articles

Investigation of the effect of the flow rate of coolant on the kinetics of carbon dioxide hydrate growth using sigmoidal growth model

Relaxation time plays a crucial role in studying reaction kinetics and other processes. This study addresses the importance of relaxation time and suggests methods to minimize it. In this article, we adjust the relaxation time by extracting heat from the hydrate formation process through variations in the flow rate of the cooling fluid. It has been demonstrated that heat transfer plays a dominant role in this process. The kinetics of carbon dioxide hydrate growth were evaluated by increasing the flow rate of cooling fluid using modified sigmoidal growth curve equations, including Logistics and Gompertz. It was conducted a nonlinear least-squares regression analysis to fit sigmoidal functions to the cumulative formation curves of hydrate generated from gas uptake in the static reactor over time. The percentage of error between Areal and Amodel shows that the Gompertz model with Q = 14.59 Lit/min at T = 276 K and Q = 20.25 Lit/min at T = 277 K is the best model for predicting the maximum consumption capacity of CO2. The results also showed that increasing the cooling fluid’s flow rate reduces relaxation time at any temperature. Moreover, increasing the flow rate of the cooling fluid decreased the average relaxation time by 2 % to 60 % at T = 276 K and by 7 % to 22 % at T = 277 K compared to the lowest investigated flow rate. Additionally, reducing the experimental temperature while keeping the flow rate of the cooling fluid constant led to a reduction in the relaxation time.

Mirtazapine blood levels and antidepressant response

Objective Therapeutic drug monitoring (TDM) is an important tool for treatment optimisation. Its usefulness has recently been demonstrated for some first-line antidepressants; however, few studies have been reported on the relationship between blood levels of mirtazapine and its antidepressant effects. The aim of this study was to investigate the association between blood concentration of mirtazapine and antidepressant response. Methods 59 outpatients treated with mirtazapine for depression were recruited and followed up for three months in a naturalistic setting. Hamilton Depression Rating Scale-21 (HAMD-21) was administered at baseline, month 1, and month 3 to assess antidepressant response. Mirtazapine serum concentration was measured at steady state. Linear regression analysis and nonlinear least-squares regression were used to estimate association between serum concentration of mirtazapine and antidepressant response. Results Our results showed no overall association between serum concentration of mirtazapine and symptom improvement at month 1 and month 3. A marginally significantly higher serum concentration of mirtazapine was found in responders vs non-responders at month 3. Conclusions The study suggests that serum concentration of mirtazapine is not strongly associated with the antidepressant efficacy of mirtazapine. This is probably attributed to its pharmacodynamic profile, even though higher blood levels seem to be marginally more effective.

Developing the Additive Systems of Stand Basal Area Model for Broad-Leaved Mixed Forests.

Stand basal area (SBA) is an important variable in the prediction of forest growth and harvest yield. However, achieving the additivity of SBA models for multiple tree species in the complex structure of broad-leaved mixed forests is an urgent scientific issue in the study of accurately predicting the SBA of mixed forests. This study used data from 58 sample plots (30 m × 30 m) for Populus davidiana × Betula platyphylla broad-leaved mixed forests to construct the SBA basic model based on nonlinear least squares regression (NLS). Adjustment in proportion (AP) and nonlinear seemingly unrelated regression (NSUR) were used to construct a multi-species additive basal area prediction model. The results identified the Richards model (M6) and Korf model (M1) as optimal for predicting the SBA of P. davidiana and B. platyphylla, respectively. The SBA models incorporate site quality, stand density index, and age at 1.3 m above ground level, which improves the prediction accuracy of basal area. Compared to AP, NSUR is an effective method for addressing the additivity of basal area in multi-species mixed forests. The results of this study can provide a scientific basis for optimizing stand structure and accurately predicting SBA in multi-species mixed forests.

Head growth in patients with myelomeningocele treated with prenatal and postnatal surgery.

The need for permanent CSF diversion is lower in patients who have undergone prenatal surgery for myelomeningocele (MMC) than in those who have undergone postnatal closure. Differences in brain development and head growth between treatment groups are not known, particularly for those who do not require surgical treatment for hydrocephalus. The objective of this study was to determine differences in head growth and to generate MMC-specific head circumference (HC) growth curves for patients who underwent either prenatal or postnatal surgery. The authors retrospectively identified patients from St. Louis Children's Hospital who were treated for MMC between 2016 and 2021. HC data were obtained from birth until the most recent follow-up or hydrocephalus treatment. Nonlinear least-squares regression analysis was performed to fit the data into four models: two-term power, Gompertz, West ontogenetic, and Weibull. Subsequently, the curves were assessed for their utility in predicting hydrocephalus treatment. Sixty-one patients (29 females [47.5%], 25 [41%] underwent prenatal surgery, mean gestational age at birth 36.6 weeks) were included in the study. The Weibull model best fit the HC data (prenatal adjusted R2 = 0.95, postnatal adjusted R2 = 0.95), while the Gompertz model had the worst fit (prenatal adjusted R2 = 0.56, postnatal adjusted R2 = 0.39) across both cohorts. Prenatal MMC repair patients had significantly larger HC measurements than their postnatal repair counterparts. The 50th percentile of the Weibull curve was determined as a useful threshold for hydrocephalus treatment: children with HC measurements that crossed and remained above this threshold were significantly more likely to have hydrocephalus treatment regardless of time of MMC repair (prenatal relative risk [RR] 10.0 [95% CI 1.424-70.220], sensitivity 85.7% [95% CI 0.499-0.984], and specificity 82.4% [95% CI 0.600-0.948]; postnatal RR 4.750 [95% CI 1.341-16.822], sensitivity 90.5% [95% CI 0.728-0.980], and specificity 75.0% [95% CI 0.471-0.924]). The HC growth curves of the MMC patients treated prenatally were significantly larger than the WHO HC curves (p < 0.001). The Weibull model was identified as the HC growth curve with the best fit for MMC patients and serves as a useful predictor of hydrocephalus treatment. For MMC patients with hydrocephalus, prenatal repair patients fit the model well but postnatal repair patients did not, potentially indicating different mechanisms of hydrocephalus development. Those treated prenatally had significantly larger HC measurements compared with both the general population and those treated postnatally. Further study is needed to understand the long-term cognitive outcomes and optimal management of clinically asymptomatic patients with large HC measurements who were treated prenatally for MMC.

A Bayesian Approach to Kinetic Modeling of Accelerated Stability Studies and Shelf Life Determination.

Kinetic modeling of accelerated stability data serves an important purpose in the development of pharmaceutical products, providing support for shelf life claims and expediting the path to clinical implementation. In this context, a Bayesian kinetic modeling framework is considered, accommodating different types of nonlinear kinetics with temperature and humidity dependent rates of degradation and accounting for the humidity conditions within the packaging to predict the shelf life. In comparison to kinetic modeling based on nonlinear least-squares regression, the Bayesian approach allows for interpretable posterior inference, flexible error modeling and the opportunity to include prior information based on historical data or expert knowledge. While both frameworks perform comparably for high-quality data from well-designed studies, the Bayesian approach provides additional robustness when the data are sparse or of limited quality. This is illustrated by modeling accelerated stability data from two solid dosage forms and is further examined by means of artificial data subsets and simulated data.

Optimal choice of IHS-type of transformations for log-linear modeling

The widely used log-linear transformation for fitting scattered positive observations to power models can be generalized to zero and negative values by embedding shape parameters into an inverse hyperbolic sine (IHS) function. The most common IHS-type of functions are analyzed and compared for log-linear modeling. In addition, a novel parametrized log-linear (ParLo) transformation is introduced that generalizes not only the ordinary linear and log-linear regressions but as well the most popular IHS type of transformation, since it allows to reduce the regression’s residual for the case of exclusively positive values. Residual computations for a single regressor are used to benchmark the IHS-type of transformations. An optimization of the shape parameter may lead to residuals lower than those that are achievable by nonlinear least-squares (NLLS) regression for mono-exponential models since reverse IHS transformations are bi-exponential. Thus, the NLLS regression and the covariance-invariant mapping are applied to deterministic bi-exponential models for further benchmarking.

Industrial design rights and the market value of firms

This paper studies how investments in design affect the market value of firms, using European Registered Community Designs and national Swedish design rights data combined with R&D, patent and trademark data, for the period 2003–2013. This paper is the first large-scale quantitative study using industrial designs rights to measure design. Nonlinear least-squares regressions are used to investigate the association between these variables and the market value of Swedish firms. The results show that industrial designs rights have a positive and significant relationship to the market value of firms. It provides both new evidence on the effect of industrial design rights on the market value of firms and internationally comparable results for other intangible assets such as patents, trademarks and R&D. Theoretically, the paper contributes to the understanding of design knowledge and the valuation of design rights.

Comprehensive characterization of the adiabatic temperature change and (convection) heat transfer coefficient of a NiTi tube elastocaloric refrigerant

Elastocaloric cooling without global warming substance emission is a promising alternative to the vapor-compression technology. Comprehensive and precise characterization of the adiabatic temperature change of the elastocaloric refrigerant and the heat transfer coefficient between the elastocaloric refrigerant and the surrounding heat transfer fluid/solid is significant for the structural design of elastocaloric coolers. In this article, an analytical solution of the volume-averaged temperature variation in a tubular shape memory alloy elastocaloric refrigerant under cyclic compression was derived using lumped analysis, and a method of comprehensive characterization of the adiabatic temperature change (∆Tad) and (convection) heat transfer coefficient h for the elastocaloric refrigerant based on the analytical solution was proposed. A dimensionless number Ch was defined as the ratio of the latent heat release/absorption rate to the (convection) heat transfer rate, with which the characterization procedure including a series of nonlinear least-square regression tests and data selection criteria were established. The method proposed is applicable to any cross section geometry under both tension and compression, and it was validated using experimental data on a NiTi tube under sinusoidal force-controlled and reverse Brayton cyclic compressions and using existing experimental data of NiTi-based films, strips, and pillars under tension and compression in the literature. The ∆Tad characterized using the proposed method agreed with that using the reverse Brayton cyclic loading method within 5% (absolute value of 1 K). The effect of data selection sequence on the characterization of ∆Tad and h was investigated, and the results showed that proper starting points were significant for the convergence of ∆Tad and h.

On the Short-Term Creep and Recovery Behaviors of Injection Molded and Additive-Manufactured Tough Polylactic Acid Polymer

The creep and recovery behaviors of a tough polylactic acid polymer are investigated experimentally and theoretically. We studied the influence of manufacturing methods and parameters on the viscoelastic responses. Experimental comparisons were carried out on 13 different samples manufactured using fused deposition modeling (FDM) and injection molding methods. The sample variations in the FDM were based on four infill densities (70-100%) and 3 infill directions (0^circ ,45^circ ,90^circ ). Theoretically, the Burgers and Weibull’s models are used to predict the creep and recovery responses of the samples. Our experimental findings suggest that the injection-molded samples perform better in creep for most of the cases. However, at higher stress loadings, the 90 and 100% infill density samples showed excellent creep resistance behaviors at the 90^circ infill direction. On the other hand, the theoretical creep and recovery predictions were based on the nonlinear least-squares regression method. The Burgers model predicted the creep responses with reasonable accuracies. A maximum of 5.83% mean absolute percentage error (MAPE) was found for the 0° infill direction and 80% infill density sample. On the contrary, the model lacks accuracy in recovery strain predictions, showing an average of 173.15% MAPE for all studied samples. Introducing Weibull’s distribution improved the accuracies showing a 3.44% average MAPE for all samples.

On volatile growth: Simple fitting of exponential functions taking into account values of every observation with any signs, applied to readily calculate a novel covariance-invariant CAGR

The commonly used compound annual growth rate does not consider volatility, and its calculation fails for time series beginning or terminating with a zero or negative value, which may be the case for a company’s earnings history. Thus, a modification of the standard definition is proposed, derived from a covariance-invariant mapping of observations to a two-parameter exponential model. The novel growth rate is called “covariance-invariant “, which becomes for the special case of steady growth at a constant rate. It can be obtained using different options such as a chart, look-up table or formula. Further, the extension of the model by an additive constant may be used if negative values dominate. The approach is viewed as easy to apply as the log-linear model but with a superior performance. Compared to nonlinear least-squares regression, unique solutions can be obtained that allow a rather quick calculation.

A Novel Liquid Water Content Retrieval Method Based on Mass Absorption for Single-Wavelength Cloud Radar

Low-level clouds (LLC), mainly composed of liquid water droplets, cool the climate system by strongly reflecting solar radiation back to space, and thus play an important role in the Earth energy budget. However, the LLC properties and their radiative effects are poorly represented in climate models, leading to the largest source of uncertainty in the climate prediction. Liquid water content (LWC) is a key property of LLC determining cloud extinction characteristics and is a fundamental parameter in the radiative transfer model. To improve the understanding of LWC properties, algorithms have been proposed to retrieve LWC based on millimeter-wavelength radar. However, the traditional retrieval relies on pre-constructed empirical relationship between reflectivity and LWC and have noticeable limitations. Particularly, the retrieval uncertainty is strongly depended on the assumed particle size distribution, the existence of drizzle particle; and on the accuracy of reflectivity measurement. In this study, we develop a new self-consistent algorithm to retrieve LWC by constraining radar reflectivity factor and attenuation in the whole liquid cloud layer. A relationship between the radar measured reflectivity, LWC, and the intrinsic reflectivity is first constructed based on the radiative transfer theory under Rayleigh scattering regime. A nonlinear least-square regression technique is then applied to derive the optimal parameters in the retrieval equations to obtain the LWC. Comparison with the microwave radiometer (MWR) derived liquid water path (LWP) indicates that our proposed method retrieves more accurate LWC products than that from the traditional empirical algorithms.

Height-Diameter Models for Prediction of Teak Stand in Western Nigeria

The Diameter-height relationship has proven to be an important part in growth and yield models which describe stand changes. Ten existing nonlinear height-diameter models were used to fit and evaluate Tectona grandis stand in Oluwa forest reserve (Nigeria) in this study. Three hundred and ninety-seven (397) trees were measured for their stand variables of which diameter at breast height (Dbh) and height (Ht) were paramount. All functions were fitted using weighted nonlinear least square regression (NLLSR), considering hetroscadasticity of variance. Model performance were evaluated using three fit statistics such as root mean squared error (RMSE), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Logistic 3-parameters H-D function as the best fit based on the model’s evaluation statistics and its predictive ability with values of RMSE, AIC and BIC as 2.8925, 1974 and 1990, respectively. Gompertz, Weibull, Chapman-Richards and Michaelis-Menten models also provided good fit results comparable to the observed height-diameter relationship. Logistic function with 3-parameters has been confirmed to provide a secure estimate of total tree height for Tectona grandis in Oluwa Forest Reserve.

Biomass char gasification kinetic rates compared to data, including ash effects

This investigation provides both experimental and theoretical analyses of biomass char gasification kinetics over 1150–1350 °C in the environment of CO2, H2O and combinations of these reactants. The experimental data include continuous measurements of particle mass, external and internal temperatures, shape, and size with periodic but not continuous measurements of char porosity, pore size distribution, and pore surface area. The model describes heterogeneous char gasification for poplar wood, corn stover and switchgrass in different shapes and industrially relevant sizes (12.5 mm and smaller). Nonlinear least-squares regression produces optimized power-law model parameters for global kinetics that describe biomass char gasification with respect to both CO2 and H2O separately and in combination. A single set of kinetic parameters describes reaction rates for all three fuels. Model simulations agree with measured data at all stages of char conversion even though the observed mass loss rates change significantly with conversion. The change in rate with conversion depends strongly on ash content, and this investigation provides a simple and theoretically based reaction rate expression that includes the effect of inert ash occupying an increasing portion of the reactive surface with increased conversion.

HPAEC-PAD analysis for determination of the amino acid profiles in protein fractions from oat flour combined with correction of amino acid loss during hydrolysis

Current derivatization-dependent approaches for amino acid composition analysis of cereal proteins have significant variability due to lack of direct analysis opportunities and loss of amino acids during protein-hydrolysis. To tackle these drawbacks, a novel direct, derivatization-free approach was successfully introduced, using HPAEC-PAD, and applied for analysis of hydrolyzed defatted oat flour and extracted flour protein fractions. The approach ensured reliable detection of amino acids, including L-tryptophan, as well as oxidation products of L-cysteine and L-methionine. A time course study, analysed by nonlinear least-square regression to determine rates of hydrolysis and loss of each amino acid, allowed comparison of the original mass fraction (AA0) of the respective amino acid in the oat flour mixture with the mass fraction obtained after 24 h hydrolysis (AA24). The difference between (AA0) and (AA24) was less than 0.05%, except for L-arginine (0.61%), glycine (0.14%), L-isoleucine (0.27%), and L-tryptophan (0.17%). The (AA0)s obtained corresponded to literature-data, and fitted with the amino acid composition estimated from deduced proteins encoded in the oat genome, except for L-arginine (27%) and L-glutamic acid/L-glutamine (10%). The amino acid composition estimation from sequence data indirectly confirmed that the high presence of L-arginine observed was a result of co-elution with unknown flour components.

Compartmental model describing the physiological basis for the HepQuant SHUNT test

The HepQuant SHUNT test quantifies hepatic functional impairment from the simultaneous clearance of cholate from the systemic and portal circulations for the purpose of monitoring treatment effects or for predicting risk for clinical outcome. Compartmental models are defined by distribution volumes and transfer rates between volumes to estimate parameters not defined by noncompartmental analyses. Previously, a noncompartmental analysis method, called the minimal model (MM), demonstrated reproducible and reliable measures of liver function (Translational Research 2021). The aim of this study was to compare the reproducibility and reliability of a new physiologically based compartmental model (CM) vs the MM. Data were analyzed from 16 control, 16 nonalcoholic steatohepatitis (NASH), and 16 hepatitis C virus (HCV) subjects, each with 3 replicate tests conducted on 3 separate days. The CM describes transfer of cholates between systemic, portal, and liver compartments with assumptions from measured or literature-derived values and unknown parameters estimated by nonlinear least-squares regression. The CM was compared to the MM for 6 key indices of hepatic disease in terms of intraclass correlation coefficient (ICC) with a lower acceptable limit of 0.7. The CM correlated well with the MM for disease severity index (DSI) with R2 (95% confidence interval) of 0.96 (0.94–0.98, P < 0.001). Acceptable reproducibility (ICC > 0.7) was observed for 6/6 and 5/6 hepatic disease indices for CM and MM, respectively. SHUNT, a measure of the absolute bioavailability, had ICC of 0.73 (0.60–0.83, P = 0.3095) for MM and 0.84 (0.76–0.90, P = 0.0012) for CM. The CM, but not the MM, allowed determination of anatomic shunt and hepatic extraction and improved the within individual reproducibility.

Multi-coupled mass transfer mechanisms during solvent removal of nitrocellulose-based propellant

This work has designed and developed an industrial-scale experiment system for studying the multi-coupled mass transfer mechanisms included in the solvent removal of the propellant grains. In this respect, the propellant grains were subjected to hot air convection for two hours at a temperature of 40.0°C and relative humidity of 85.0%, of which the mass flow rate was 595.0 kg·h−1 (or 720.0 kg·h−1). The measured data of the transient solvent content were analyzed based on the nonlinear least-squares regression. A slop method was used to predict the effective diffusivity of the solvents held in the propellant grains. In addition, the adsorption kinetics behavior and the mechanism of the propellant grains to the water vapor were studied in detail. As a result, both the vaporization of the solvents as well as the adsorption of the water vapor appeared on the surface of the propellant grains at the same time. The ethanol inside the propellant grains has a greater effective diffusivity compared to ether. The mass transfer in the solvent removal of the propellant grains was controlled by both the internal and external resistances. Moreover, the adsorption of the propellant grains to the water vapor was dominated by physical adsorption.

Passive immunization against COVID-19 by anti-SARS-CoV-2 spike IgG in commercially available immunoglobulin preparations in severe antibody deficiency

Passive immunization against COVID-19 by anti-SARS-CoV-2 spike IgG in commercially available immunoglobulin preparations in severe antibody deficiency

Regularized nonlinear regression for simultaneously selecting and estimating key model parameters: Application to head-neck position tracking

In system identification, estimating parameters of a biomechanical model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model parameters while fixing the remaining parameters to a set of typical values. The problem is formulated as a nonlinear least-squares estimator with L1-regularization on the deviation of parameters from a set of typical values. In addition, a modified optimization approach is introduced to find the solution to the formulated problem. As a result, we provided consistency and oracle properties of the proposed estimator as a theoretical foundation. To show the effectiveness of the proposed method, we conducted simulation and experimental studies. In the simulation study, the proposed Lasso performed significantly better than the ordinary L1-regularization methods in terms of the bias and variance of the parameter estimates. The experimental study presented an application identifying a biomechanical parametric model of a head position tracking task for ten human subjects from limited data. Compared with the variance of the parameter estimates from nonlinear ordinary least-squares regression, that of parameter estimates from the proposed Lasso decreased by 96% using the simulated data. Using the real-world data, the variance of estimated parameters decreased by 71%. In addition, the proposed method kept variance accounted for (VAF) at 83% and was 54 times faster than the ordinary Lasso using a standard simplex-based optimization algorithm.

Selectivity and Maximum Response of Vibegron and Mirabegron for β3-Adrenergic Receptors

BackgroundThe β3-adrenergic agonists vibegron and mirabegron have shown favorable safety profiles and efficacy for the treatment of overactive bladder. However, β-adrenergic receptors are also found outside the bladder, which could lead to off-target activity.ObjectiveThis study assessed the selectivity of vibegron and mirabegron for β-adrenergic receptors and the maximal effect and potency for β3-adrenergic receptors.MethodsFunctional cellular assays were performed using Chinese hamster ovary-K1 cells expressing β1-, Chinese hamster ovary cells expressing β2-, and human embryonic kidney 293 cells expressing β3-adrenergic receptors. Cells were incubated with vibegron, mirabegron, or control (β1 and β3, isoproterenol; β2, procaterol). Responses were quantified using homogeneous time-resolved fluorescence of cyclic adenosine monophosphate and were normalized to the respective control. Half-maximal effective concentration and maximum response values were determined by nonlinear least-squares regression analysis.ResultsActivation of β3-adrenergic receptors with vibegron or mirabegron resulted in concentration-dependent β3-adrenergic receptor responses. Mean (SEM) half-maximal effective concentration values at β3-adrenergic receptors were 2.13 (0.25) nM for vibegron and 10.0 (0.56) nM for mirabegron. At a concentration of 10 µM, β3-adrenergic activity relative to isoproterenol was 104% for vibegron and 88% for mirabegron. Maximum response at β3-adrenergic receptors was 99.2% for vibegron and 80.4% for mirabegron. β1-adrenergic activity was 0% and 3% for vibegron and mirabegron, respectively; β2-adrenergic activity was 2% and 15%, respectively.ConclusionsVibegron showed no measurable β1 and low β2 activity compared with mirabegron, which showed low β1 and some β2 activity. Both showed considerable selectivity at β3-adrenergic receptors; however, vibegron demonstrated near-exclusive β3 activity and a higher maximum β3 response.

Convergence of Levenberg-Marquardt Estimates of Nonlinear Parameters in EIS Analysis of Coated Aluminum Panels

Equivalent circuit models are frequently employed to analyze electrochemical impedance spectroscopy (EIS) data. However, aside from some simple cases in which the equivalent circuit element parameters can be estimated directly from a plot of the data, the parameters for each of the equivalent circuit elements must often be estimated through the implementation of a nonlinear least-squares regression method. One frequently-used approach is the powerful Levenberg-Marquardt algorithm. This algorithm functions as a damped least-squares method that performs an interpolation between the steepest-descent and the Gauss-Newton methods for estimating nonlinear parameters. However, there are several challenges to using a Levenberg-Marquardt algorithm to model EIS data. The nonlinear nature of the impedance equations along with the difference in the magnitude of the parameter values can result in the algorithm failing to converge to a local minimum in the parameter space. This convergence challenge can be seen in determining equivalent circuit values for undamaged coating systems that have a high pore resistance, a small capacitance, as well as contributions from the underlying metal substrate. A Levenberg-Marquardt algorithm, along with a heuristic approach to use the raw data to improve the initial parameter estimates, is implemented that provides an improved approach for nonlinear regression fits of equivalent circuit models. A comparison of three equivalent circuit models fits, with residuals, for a two-layer coating system on an aluminum substrate is shown in the attached figure.Figure caption: Plot of EIS data (+ symbols) from a cured coating system prior to any environmental exposures compared with 3 equivalent circuit model fits (solid lines). The model fits were obtained using an NRL-developed Levenberg-Marquardt nonlinear regression fitting routine.The Department of Defense Strategic Environmental Research and Development Program (SERDP) sponsored this project under work unit 5399. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Office of Naval Research, the U.S. Navy, the Department of Defense, or the U.S. government. Figure 1