Single Model Parameter Research Articles

Yields of weakly bound light nuclei as a probe of the statistical hadronization model

The statistical hadronization model is a simple and efficient phenomenological framework in which the relative yields for very high energy heavy ion collisions are essentially determined by a single model parameter---the chemical freeze-out temperature. Recent measurements of yields of hadrons and light nuclei covering over 9 orders of magnitudes from the ALICE collaboration at the LHC were described by the model with remarkable accuracy with a chemical freeze-out temperature of 156.5 $\pm$ 1.5 MeV. A key physical question is whether the freeze-out temperature can be understood, literally, as the temperature at which the various species of an equilibrated gas of hadrons (including resonances) and nuclei chemically freeze out as the model assumes, or whether it successfully parametrizes the yield data for a different reason. The yields of weakly-bound light nuclei---the deuteron and the hypertriton---provide insights into this issue. The analysis indicates that a key assumption underlying the model---that hadrons (and nuclei), just prior to chemical freeze-out temperature, are in thermal equilibrium and are sufficiently dilute as to have particle distributions accurately described statistically by a nearly ideal gas of hadrons and nuclei with masses given by their free space values---appears to be inconsistent with the chemical freeze-out temperature output by the model, at least for these weakly-bound nuclei.

Automatic generation of evolutionary hypotheses using mixed Gaussian phylogenetic models

Phylogenetic comparative methods are widely used to understand and quantify the evolution of phenotypic traits, based on phylogenetic trees and trait measurements of extant species. Such analyses depend crucially on the underlying model. Gaussian phylogenetic models like Brownian motion and Ornstein-Uhlenbeck processes are the workhorses of modeling continuous-trait evolution. However, these models fit poorly to big trees, because they neglect the heterogeneity of the evolutionary process in different lineages of the tree. Previous works have addressed this issue by introducing shifts in the evolutionary model occurring at inferred points in the tree. However, for computational reasons, in all current implementations, these shifts are "intramodel," meaning that they allow jumps in 1 or 2 model parameters, keeping all other parameters "global" for the entire tree. There is no biological reason to restrict a shift to a single model parameter or, even, to a single type of model. Mixed Gaussian phylogenetic models (MGPMs) incorporate the idea of jointly inferring different types of Gaussian models associated with different parts of the tree. Here, we propose an approximate maximum-likelihood method for fitting MGPMs to comparative data comprising possibly incomplete measurements for several traits from extant and extinct phylogenetically linked species. We applied the method to the largest published tree of mammal species with body- and brain-mass measurements, showing strong statistical support for an MGPM with 12 distinct evolutionary regimes. Based on this result, we state a hypothesis for the evolution of the brain-body-mass allometry over the past 160 million y.

Squeezed displaced entangled states in the quantum Rabi model

The quantum Rabi model accepts analytical solutions in the so-called degenerate qubit and relativistic regimes with discrete and continuous spectrum, in that order.We show that solutions in the laboratory frame are the superposition of even and odd displaced number states, in the former, and infinitely squeezed coherent states, in the latter, of the boson field correlated to the internal states of the qubit. We propose a single parameter model that interpolates between these discrete and continuous spectrum regimes to study the spectral statistics for first and second neighbor differences before the so-called spectral collapse. We find two central first neighbor differences that interweave and fluctuate keeping a constant second neighbor separation.

Parametric model order reduction for acoustic metamaterials based on local thickness variations

The use of lightweight materials is obligatory in the design of economic structures, but with decreasing mass, the vibro-acoustic properties of the structures become unfavorable. Acoustic metamaterials based on the concept of acoustic black holes (ABH) can improve the vibrational behavior by adding local thickness variations to the host structure. To make computational models of metamaterials also valid for high frequencies, a fine discretization has to be used. This leads to high computation times. A parametric model order reduction (PMOR) approach is presented, which is able to create an efficient reduced model of ABHs. In the first step, one structure preserving reduced model for each parameter is generated using the iterative rational Krylov algorithm (IRKA). The transfer functions of all reduced models are used in the second step to create a single parametric model using the Loewner framework. The resulting model can be used to efficiently evaluate the frequency response of a structure equipped with ABHs for different parameter sets.

A MODIFIED METHOD FOR MODELLING OF SPREAD FOOTING UNDER UNIFORM DISTRIBUTED LOAD USING WINKLER'S MODEL

Arriving at a realistic model is of importance in foundation analysis by the extreme difficulty of modeling the soil-structure interaction. To this purpose, a plenty of models have been introduced, over the years, range from simple single parameter models to complex mixed models. One of the most popular and simple methods, which is considered as “one-parameter model”, is the Winkler’s model. In this model, the soil continuum is superseded by an infinite number of closely spaced springs, whose stiffness describes the behavior of the elastic foundation. Replacing the soil with a group of springs leads to the model discontinuity and uniform settlement profile of footing, as, every single spring is only responsible for its own vertical load and is not affected by the shear stress or the deformation of the adjacent springs. Two main inborn imperfections of the Winkler’s model include: the necessity of determination of the subgrade reaction modulus (K s ), and uniform settlement of the foundation under distributed load. Actually, the second one is in opposition to the dish-shaped settlement profile of the same footing when considering the soil as continuum using Finite Element Method (FEM). The modulus of subgrade reaction is not a soil property and could have a different value for a specific footing owing to the natural variations in soil properties. The footing dimensions and rigidity, load level, soil condition, and soil model have a direct impact on K s . In the first part of paper, the effect of foundation rigidity on the K s distribution is investigated. Moreover, the commonly-used correlations of K s estimation, i.e. Biot, Vesic and elastic-based correlations, are examined to find the most accurate one, using FEM. In order to amend the Winkler’s model concerning the latter weakness, the foundation is divided into central part as well as side parts and assigning different subgrade modulus to the parts, e.g. a value of K s to the center part and double to the side parts. The settlement profile of the footing with various side-part widths are compared with the corresponding FEM model to find the best case. The results show that with this dividing technique the desired dish-shaped settlement profile could be achieved by error less than 20%.

Simultaneous description of hadron and jet suppression in heavy-ion collisions

We present a global fit to all data on the suppression of high-energy jets and high-energy hadrons in the most central heavy-ion collisions at the CERN Large Hadron Collider (LHC) for two different collision energies, within a hybrid strong-weak coupling quenching model. Even though the measured suppression factors for hadrons and jets differ significantly from one another and appear to asymptote to different values in the high-energy limit, we obtain a simultaneous description of all these data after constraining the value of a single model parameter. We use our model to investigate the origin of the difference between the observed suppression of jets and hadrons and relate it, quantitatively, to the observed modification of the jet fragmentation function in jets that have been modified by passage through the medium produced in heavy-ion collisions. In particular, the observed increase in the fraction of hard fragments in medium-modified jets, which indicates that jets with the fewest hardest fragments lose the least energy, corresponds quantitatively to the observed difference between the suppression of hadrons and jets. We argue that a harder fragmentation pattern for jets with a given energy after quenching is a generic feature of any mechanism for the interaction between jets and the medium that they traverse that yields a larger suppression for wider jets. We also compare the results of our global fit to LHC data to measurements of the suppression of high-energy hadrons in BNL Relativistic Heavy Ion Collider (RHIC) collisions, and find that with its parameter chosen to fit the LHC data, our model is inconsistent with the RHIC data at the $3\ensuremath{\sigma}$ level, suggesting that hard probes interact more strongly with the less hot quark-gluon plasma produced at RHIC.

Design of an Insurance Policy Model Applied to Natural Stone Facade Claddings

The insurance market deliberately excludes the buildings’ envelope from their insurance policies, neglecting all the damage that can be caused by the degradation process or ageing of the materials. This stance is mainly due to the lack of knowledge in terms of risk and costs associated to the failure of these elements. Even though the building and its elements are the most valuable asset of any owner, most often homeowners do not adopt effective preventive measures to mitigate the deterioration and obsolescence of their assets. This study proposes an innovative methodology for the design of insurance policies for buildings’ envelopes, applied to natural stone facade claddings. The insurance product is defined based on deterministic and stochastic service life prediction models, established through the past degradation history of 142 natural stone claddings analyzed in service conditions in Portugal. Single-parameter (only analyzing the cladding’s age) and multiparameter (encompassing the relevant variables) models are applied in the calculation of the insurance premium. The expected claims are related with the performance of maintenance actions and established according to three degradation levels. The results obtained reveal that an increased knowledge about the insured cladding leads to a reduction of the risk margin and consequently, to a lower annual value of commercial premium paid by a household. This study proposes an innovative solution for tailoring the insurance products, in terms of the risk of failure of the buildings components, as well as the financial charges related with the maintenance of these elements, channeling the risks to the market.

A theoretical single-parameter model for urbanisation to study infectious disease spread and interventions.

The world is continuously urbanising, resulting in clusters of densely populated urban areas and more sparsely populated rural areas. We propose a method for generating spatial fields with controllable levels of clustering of the population. We build a synthetic country, and use this method to generate versions of the country with different clustering levels. Combined with a metapopulation model for infectious disease spread, this allows us to in silico explore how urbanisation affects infectious disease spread. In a baseline scenario with no interventions, the underlying population clustering seems to have little effect on the final size and timing of the epidemic. Under within-country restrictions on non-commuting travel, the final size decreases with increased population clustering. The effect of travel restrictions on reducing the final size is larger with higher clustering. The reduction is larger in the more rural areas. Within-country travel restrictions delay the epidemic, and the delay is largest for lower clustering levels. We implemented three different vaccination strategies—uniform vaccination (in space), preferentially vaccinating urban locations and preferentially vaccinating rural locations. The urban and uniform vaccination strategies were most effective in reducing the final size, while the rural vaccination strategy was clearly inferior. Visual inspection of some European countries shows that many countries already have high population clustering. In the future, they will likely become even more clustered. Hence, according to our model, within-country travel restrictions are likely to be less and less effective in delaying epidemics, while they will be more effective in decreasing final sizes. In addition, to minimise final sizes, it is important not to neglect urban locations when distributing vaccines. To our knowledge, this is the first study to systematically investigate the effect of urbanisation on infectious disease spread and in particular, to examine effectiveness of prevention measures as a function of urbanisation.

Sedentary behaviour, physical activity, and sarcopenia among older adults in the TSHA: isotemporal substitution model.

BackgroundThe associations between free‐living physical activity (PA) and sedentary behaviour (SB) and sarcopenia in older people and its determinants are controversial. Self‐reporting, the use of one‐size‐fits‐all cut‐points for intensity categorization when using accelerometers and the absence of a clear sarcopenia definition hampered explorations. The aim of this study is to describe the associations between objectively measured PA patterns and sarcopenia and its determinants.MethodsSubjects aged >65 with valid accelerometry and sarcopenia‐related measures from Toledo Study of Healthy Aging (TSHA) were included. Muscle mass (MM) was estimated by dual‐energy X‐ray absorptiometry. Handgrip strength (HS) was measured by dynamometry. Physical performance assessment relied on gait speed (GS). Sarcopenia presence was ascertained using Foundation for the National Institutes of Health (FNIH) criteria. PA and SB were estimated by ActiTrainer worn for 1 week and classified into time spent in SB and different PA intensity bands [light PA (LPA) and moderate‐to‐vigorous PA (MVPA)] using age‐specific cut‐points. Different multivariate linear and logistic regression models [(i) single‐parameter, (ii) partition, and (iii) isotemporal substitution models] were used for estimating associations between PA, SB, and sarcopenia determinants and sarcopenia rates, respectively. All models adjusted for age, sex, co‐morbidities (Charlson index), and functional ability (Katz and Lawton indexes).ResultsFive hundred twelve subjects from the TSHA had available data (78.08 ± 5.71 years of age; 54.3% women). FNIH sarcopenia assessment was performed in 497 subjects (23.3% were sarcopenic). In the linear regression, the single‐parameter model showed an association between MVPA and all sarcopenia determinants. In the partition model, MVPA was associated with greater MM and GS. The isotemporal substitution showed that reallocating 1 h/day of MVPA displacing SB was associated with greater values in MM [β = 0.014; 95% confidence interval (CI) = 0.004, 0.024; P < 0.01], GS (β = 0.082; 95% CI = 0.054, 0.110; P < 0.001), and HS (β = 0.888; 95% CI = 0.145, 1.631; P < 0.05). In the logistic regression, the single‐parameter model yielded a significant association between 1 h/day increase in MVPA and sarcopenia reduction [odds ratio (OR) = 0.522; 95% CI = 0.367, 0.726; P < 0.001], as did the partition model (OR = 0.555; 95% CI = 0.376, 0.799; P < 0.01). The reallocation of 1 h/day SB only yielded a significant lower sarcopenia risk by almost 50% when it was substituted with MVPA, whereas the substitution of 15 min/day yielded a significant lower sarcopenia risk by 15% (P < 0.001) but did not show any association when it was substituted with LPA.ConclusionsAn increase in MVPA replacing SB and LPA was associated with a reduction in sarcopenia prevalence and better performance across its determinants (MM, GS, and HS). LPA did not show any significant effect.

Matter-Wave Diffraction from a Periodic Array of Half Planes.

We report on reflection and diffraction of beams of He and D_{2} from square-wave gratings of a 400-μm period and strip widths ranging from 10 to 200 μm at grazing-incidence conditions. In each case we observe fully resolved matter-wave diffraction patterns including the specular reflection and diffracted beams up to the second diffraction order. With decreasing strip width, the observed diffraction efficiencies exhibit a transformation from the known regime of quantum reflection from the grating strips to the regime of edge diffraction from a half-plane array. The latter is described by a single-parameter model developed previously to describe phenomena as diverse as quantum billiards, scattering of radio waves in urban areas, and reflection of matter waves from microstructures. Our data provide experimental confirmation of the widespread model. Moreover, our results demonstrate that neither classical reflection nor quantum reflection are essential for reflective diffraction of matter waves from a structured solid, but it can result exclusively from half-plane edge diffraction.

Circulating cell-free DNA in breast cancer: size profiling, levels, and methylation patterns lead to prognostic and predictive classifiers.

Blood circulating cell-free DNA (ccfDNA) is a suggested biosource of valuable clinical information for cancer, meeting the need for a minimally-invasive advancement in the route of precision medicine. In this paper, we evaluated the prognostic and predictive potential of ccfDNA parameters in early and advanced breast cancer. Groups consisted of 150 and 16 breast cancer patients under adjuvant and neoadjuvant therapy respectively, 34 patients with metastatic disease and 35 healthy volunteers. Direct quantification of ccfDNA in plasma revealed elevated concentrations correlated to the incidence of death, shorter PFS, and non-response to pharmacotherapy in the metastatic but not in the other groups. The methylation status of a panel of cancer-related genes chosen based on previous expression and epigenetic data (KLK10, SOX17, WNT5A, MSH2, GATA3) was assessed by quantitative methylation-specific PCR. All but the GATA3 gene was more frequently methylated in all the patient groups than in healthy individuals (all p < 0.05). The methylation of WNT5A was statistically significantly correlated to greater tumor size and poor prognosis characteristics and in advanced stage disease with shorter OS. In the metastatic group, also SOX17 methylation was significantly correlated to the incidence of death, shorter PFS, and OS. KLK10 methylation was significantly correlated to unfavorable clinicopathological characteristics and relapse, whereas in the adjuvant group to shorter DFI. Methylation of at least 3 or 4 genes was significantly correlated to shorter OS and no pharmacotherapy response, respectively. Classification analysis by a fully automated, machine learning software produced a single-parametric linear model using ccfDNA plasma concentration values, with great discriminating power to predict response to chemotherapy (AUC 0.803, 95% CI [0.606, 1.000]) in the metastatic group. Two more multi-parametric signatures were produced for the metastatic group, predicting survival and disease outcome. Finally, a multiple logistic regression model was constructed, discriminating between patient groups and healthy individuals. Overall, ccfDNA emerged as a highly potent predictive classifier in metastatic breast cancer. Upon prospective clinical evaluation, all the signatures produced could aid accurate prognosis.

Effect of Electrolyte-to-Sulfur Ratio in the Cell on the Li-S Battery Performance

The effect of electrolyte-to-sulfur (E/S) ratio on the electrochemical and cell- and systems-level performance of a Li-S battery is investigated through modeling efforts. A 1-D electrochemical model is proposed predicting the cell voltage at 60% discharge depth. In the model, increasing electrolyte amount improves the cell voltage by linearly increasing the cathode exchange current density, which is the single kinetic model parameter. Moreover, cathode specific capacity is either defined as a linear function of the E/S ratio or taken constant in the performance models. Increasing E/S ratio enhances the cell- and systems-level specific energy and energy density until 9 mL/g S when cathode specific capacity depends on the E/S ratio. However, when the cathode specific capacity is constant at 1200 mAh/g S, battery performance decreases continuously with increasing electrolyte amount. The effect of other critical design parameters -cathode thickness, carbon-to-sulfur ratio, S loading and excess Li%- are also considered in the analysis.

Philip Carter's numerical competency test is graded using the rash model according to the characteristic curve theory of the individual

The current research is designed to test Phillip Carter's numerical efficiency using the Rush model according to the unique curve theory of the individual. To achieve this goal, the researcher relied on the precise steps in the development of the test starting with the translation of the test paragraphs and instructions from English to Arabic, taking into account the accuracy and comprehensiveness of all the ideas in the test, and then presented the instructions and test paragraphs consisting of (30) English to verify the sincerity of the procedure. It was then presented to a group of experts to ascertain the availability of the appropriate characteristics in terms of form and content. All sections of the tool were suitable for measuring what was set for measurement. The test was applied to 250 subjects from the preparatory stage randomly selected by the researcher.&#x0D; The researcher relied on the Rash model (one of the models of the inherent characteristics) as a model for the analysis of the components of the test, and to make sure that the clauses of the tool for the model follow the following:&#x0D; &#x0D; The Unilateral Dimension: To ascertain the procedure, the researcher analyzed the data in a global analysis. He obtained a factor (1) that is meaningful for the instrument. The interpretation of this factor was based on the Gitman criterion, which considered the factor to be statistically significant, Of (1).&#x0D; The researcher adopted the criterion of the value of the square to accept the paragraphs at the level of significance (0.05) and according to what the program showed.&#x0D; The coefficient of discrimination approached (1) for all paragraphs.&#x0D; The researcher realized the local independence through the outputs of the program and the adoption of the single-parameter model.&#x0D; &#x0D; (6) paragraphs of the test were excluded because their values ​​were greater than the value of the square of Kai at the level of significance (0.05), thus the number of remaining paragraphs (24) in the total test

An energy conservative method to predict the erosive aggressiveness of collapsing cavitating structures and cavitating flows from numerical simulations

A new technique is proposed in this study to assess the erosive aggressiveness of cavitating flows from numerical flow simulations. The technique is based on the cavitation intensity approach by Leclercq et al. (2017), predicting the instantaneous surface impact power of collapsing cavities from the potential energy hypothesis (see Hammitt, 1963; Vogel and Lauterborn, 1988). The cavitation intensity approach by Leclercq et al. (2017) is further developed and the amount of accumulated surface energy caused by the near wall collapse of idealized cavity types is verified against analytical predictions. Furthermore, two different impact power functions are introduced to compute a weighted time average of the impact power distribution caused by the cavity collapses in cavitating flows. The extreme events are emphasized to an extent specified by a single model parameter. Thus, the impact power functions provide a physical measure of the cavitating flow aggressiveness. This approach is applied to four idealized cavities, as well as to the cavitating flow around a NACA0015 hydrofoil. Areas subjected to aggressive cavity collapse events are identified and the results are compared against experimental paint test results by Van Rijsbergen et al. (2012) and the numerical erosion risk assessment by Li et al. (2014). The model is implemented as a runtime post-processing tool in the open source CFD environment OpenFOAM (2018), employing the inviscid Euler equations and mass transfer source terms to model the cavitating flow.

A QM/MM Derived Polarizable Water Model for Molecular Simulation.

In this work, we propose an improved QM/MM-based strategy to determine condensed-phase polarizabilities and we use this approach to optimize a new and simple polarizable four-site water model for classical molecular simulation. For the determination of the model value for the polarizability from QM/MM, we show that our proposed consensus-fitting strategy significantly reduces the uncertainty in calculated polarizabilities in cases where the size of the local external electric field is small. By fitting electrostatic, polarization and dispersion properties of our water model based on quantum and/or combined QM/MM calculations, only a single model parameter (describing exchange repulsion) is left for empirical calibration. The resulting model performs well in describing relevant pure-liquid thermodynamic and transport properties, which illustrates the merit of our approach to minimize the number of free variables in our model.

Examining the Gas-Particle Partitioning of Organophosphate Esters: How Reliable Are Air Measurements?

Organophosphate esters (OPEs) in air have been found to be captured entirely on filters of typical active air samplers and thus designated as being in the particle phase. However, this particle fraction is unexpected, especially for more volatile tris(2-chloroethyl) phosphate (TCEP) and tris(chloroisopropyl) phosphate (TCIPP). We evaluated gas-particle partitioning in indoor and outdoor air for OPEs and polybrominated diphenyl ethers (PBDEs) using single-parameter models (Junge-Pankow, Harner-Bidleman) and poly-parameter linear free energy relationship (pp-LFER) models. We also used the pp-LFER to estimate filter-air partitioning in active air samplers. We found that all gas-particle partitioning models predicted that TCEP and TCIPP should be in the gas phase, contrary to measurements. The pp-LFER better accounted for OPE measurements than the single-parameter models, except for TCEP and TCIPP. Gas-particle partitioning of PBDEs was reasonably explained by all models. The pp-LFER for filter-air partitioning showed that gas-phase sorption to glass and especially quartz fiber filters used for active air samplers could account for up to 100% of filter capture and explain the high particle fractions reported for TCIPP, tris(1,3-dichloro-2-propyl) phosphate TDCIPP, and triphenyl phosphate TPhP, but not TCEP. The misclassification of gas-particle partitioning can result in erroneous estimates of the fraction of chemical subject to gas-phase reactions and atmospheric scavenging and, hence, atmospheric long-range transport.

Improving Model Parameters in Vibrating Systems Using Neumann Series

A method is presented to improve the estimates of material properties, dimensions, and other model parameters for linear vibrating systems. The method improves the estimates of a single model parameter of interest by finding parameter values that bring model predictions into agreement with experimental measurements. A truncated Neumann series is used to approximate the inverse of the dynamic stiffness matrix. This approximation avoids the need to directly solve the equations of motion for each parameter variation. The Neumman series is shown to be equivalent to a Taylor series expansion about nominal parameter values. A recursive scheme is presented for computing the associated derivatives, which are interpreted as sensitivities of displacements to parameter variations. The convergence of the Neumman series is studied in the context of vibrating systems, and it is found that the spectral radius is strongly dependent on system resonances. A homogeneous viscoelastic bar in longitudinal vibration is chosen as a test specimen, and the complex-valued Young's modulus is chosen as an uncertain parameter. The method is demonstrated on simulated experimental measurements computed from the model. These demonstrations show that parameter values estimated by the method agree with those used to simulate the experiment when enough terms are included in the Neumann series. Similar results are obtained for the case of an elastic plate with clamped boundary conditions. The method is also demonstrated on experimental data, where it produces improved parameter estimates that bring the model predictions into agreement with the measured response to within 1% at a point on the bar across a frequency range that includes three resonance frequencies.

Spatial Pattern Oriented Multicriteria Sensitivity Analysis of a Distributed Hydrologic Model

Hydrologic models are conventionally constrained and evaluated using point measurements of streamflow, which represent an aggregated catchment measure. As a consequence of this single objective focus, model parametrization and model parameter sensitivity typically do not reflect other aspects of catchment behavior. Specifically for distributed models, the spatial pattern aspect is often overlooked. Our paper examines the utility of multiple performance measures in a spatial sensitivity analysis framework to determine the key parameters governing the spatial variability of predicted actual evapotranspiration (AET). The Latin hypercube one-at-a-time (LHS-OAT) sampling strategy with multiple initial parameter sets was applied using the mesoscale hydrologic model (mHM) and a total of 17 model parameters were identified as sensitive. The results indicate different parameter sensitivities for different performance measures focusing on temporal hydrograph dynamics and spatial variability of actual evapotranspiration. While spatial patterns were found to be sensitive to vegetation parameters, streamflow dynamics were sensitive to pedo-transfer function (PTF) parameters. Above all, our results show that behavioral model definitions based only on streamflow metrics in the generalized likelihood uncertainty estimation (GLUE) type methods require reformulation by incorporating spatial patterns into the definition of threshold values to reveal robust hydrologic behavior in the analysis.

Accelerated Evaluation of Automated Vehicles Using Piecewise Mixture Models

The process to certify highly automated vehicles has not yet been defined by any country in the world. Currently, companies test automated vehicles on public roads, which is time-consuming and inefficient. We proposed the accelerated evaluation concept, which uses a modified statistics of the surrounding vehicles and the importance sampling theory to reduce the evaluation time by several orders of magnitude, while ensuring the evaluation results are statistically accurate. In this paper, we further improve the accelerated evaluation concept by using piecewise mixture distribution models, instead of single parametric distribution models. We developed and applied this idea to forward collision control system reacting to vehicles making cutin lane changes. The behavior of the cutin vehicles was modeled based on more than 403,581 lane changes collected by the University of Michigan Safety Pilot Model Deployment Program. Simulation results confirm that the accuracy and efficiency of the piecewise mixture distribution method outperformed single parametric distribution methods in accuracy and efficiency, and accelerated the evaluation process by almost four orders of magnitude.

Unified representation of the C3, C4, and CAM photosynthetic pathways with the Photo3 model

Recent interest in crassulacean acid metabolism (CAM) photosynthesis has resulted in new, physiologically based CAM models. These models show promise, yet typically are not developed with a basis that is compatible with widely used models of C3 and C4 photosynthesis. Indeed, most efforts to assess the potential of CAM still rely on empirically based environmental productivity indices, which makes uniform comparisons between CAM and non-CAM species difficult. In order to represent C3, C4, and CAM photosynthesis in a consistent, physiologically based manner, we introduce the Photo3 model. Photo3 unites a common photosynthetic and hydraulic core with components depicting the circadian rhythm of CAM photosynthesis and the carbon-concentrating mechanism of C4 photosynthesis. This work allows consistent comparisons of the three photosynthetic types for the first time. It also allows the representation of intermediate C3-CAM behavior through the adjustment of a single model parameter. Model simulations of Opuntia ficus-indica (CAM), Sorghum bicolor (C4), and Triticum aestivum (C3) capture the diurnal behavior of each species as well as the cumulative effects of long-term water limitation. These results show the model's potential for evaluating the tradeoffs between C3, C4, and CAM photosynthesis, and for better understanding CAM productivity, ecology, and climate feedbacks.