Functional Form Model Research Articles

Learning thermodynamically constrained equations of state with uncertainty

Numerical simulations of high energy-density experiments require equation of state (EOS) models that relate a material’s thermodynamic state variables—specifically pressure, volume/density, energy, and temperature. EOS models are typically constructed using a semi-empirical parametric methodology, which assumes a physics-informed functional form with many tunable parameters calibrated using experimental/simulation data. Since there are inherent uncertainties in the calibration data (parametric uncertainty) and the assumed functional EOS form (model uncertainty), it is essential to perform uncertainty quantification (UQ) to improve confidence in EOS predictions. Model uncertainty is challenging for UQ studies since it requires exploring the space of all possible physically consistent functional forms. Thus, it is often neglected in favor of parametric uncertainty, which is easier to quantify without violating thermodynamic laws. This work presents a data-driven machine learning approach to constructing EOS models that naturally captures model uncertainty while satisfying the necessary thermodynamic consistency and stability constraints. We propose a novel framework based on physics-informed Gaussian process regression (GPR) that automatically captures total uncertainty in the EOS and can be jointly trained on both simulation and experimental data sources. A GPR model for the shock Hugoniot is derived, and its uncertainties are quantified using the proposed framework. We apply the proposed model to learn the EOS for the diamond solid state of carbon using both density functional theory data and experimental shock Hugoniot data to train the model and show that the prediction uncertainty is reduced by considering thermodynamic constraints.

Tuning the optical properties of molybdenum oxide using electric field: A theoretical and experimental study

Molybdenum Oxide (MoO3) with van der Waals structure can lead to the exotic properties under the action of external physical perturbation. Here, a combined density functional theory and an experimental study were performed to analyze the response of MoO3 under electric field. The electric field with the strength varying from 0.05 V/Å to 0.23 V/Å was applied across the MoO3 cell which induced the splitting in the valence and conduction band and decreases the bandgap. A critical electric field of 0.23 V/Å resulted a closing of the bandgap of MoO3 and led semiconductor to metal transition. The results of DFT regarding decrease in the bandgap of MoO3 were further supported experimentally. For this, MoO3 films were fabricated using thermal evaporation and their chemical and optical properties were analyzed using X-ray photoelectron spectroscopy and Electroreflectance (ER). To analyze the optical response, an ER analysis with external voltage varying from 10 to 50 volts was performed on Aluminum/MoO3/Aluminum heterostructure. The resultant ER spectra revealed three distinct critical points that correspond to the fundamental as well as defect related optical transitions involved in MoO3. The Third derivative functional form model applied on the ER spectra depicted a monotonical decrease in the critical points of MoO3 at lower voltage. At high voltage of about 80 volts, the existence of high built-in electric field results the delocalization in the electrons and hole wave function and gives rise to the Franz-Keldysh oscillations.

Recovering the optical transitions in tin oxide thin films at room temperature using electroreflectance

Observing the optical transitions in Tin Oxide at room temperature is a difficult task because of its forbidden bandgap nature in bulk form. Moreover, it possesses the well know low emission efficiency issue in its reduced dimensional thin film structures . In this work, we use Electroreflectance (ER) method to recover the optical transitions in tin oxide thin films . A metal-oxide-metal geometry, with SnO2 film was sandwiched between two metal electrodes , was illuminated by the light under an external perturbation voltage. This results the well-enhanced critical points in the ER spectra with a suppressed featureless background. The characteristics of observed critical points are found using the third derivative functional form model. The points are identified as defect transition and surface exciton transition originated due to the presence of defect states formed by the oxygen vacancies . In addition to this, the free exciton transition, from deep of the valence band to the conduction band , is explicitly revealed by ER spectra of r-SnO 2 film. A built-in electric field driven by external voltage is supposed to be the main factor for enhancing the critical points associated with optical transitions. • The optical transitions in SnO 2 films were observed at room temperature by using electroreflectance method. • A metal-oxide-metal structure was fabricated to explore the optical transitions in SnO 2. • The electroreflectance method with external perturbation of 10 V was applied across the geometry. • The electroreflectance spectra revealed the defect and exciton transitions within the visible, near UV, and UV region.

Revisiting environmental kuznets curve for carbon dioxide emissions: The role of trade

In the three decades since the environmental Kuznets curve (EKC) hypothesis was proposed, there have been a massive amount of empirical studies on the relationship between per capita income and carbon dioxide (CO2) emissions based on the production accounting approach. International trade has played a critical role in effectively and efficiently allocating resources in the process of economic globalization. Through international trade, part of the responsibilities for CO2 emission mitigation which should have been taken by consumers have been transferred to the producers of traded goods and resources. The focus of this research is on the re-examination of the EKC hypothesis, taking the role of international trade into account. The findings are as follows. In the first stage, we calculated the CO2 emissions of 39 countries using the input-output analysis approach based on production accounting and consumption accounting. Currently, China is the largest CO2 emitter, surpassing the U.S. However, the per capita CO2 emissions of China lag behind those of the U.S. In the second stage, although both an inverted U-shaped curve and an N-shaped curve were obtained, the cubic functional form model is better fitted. In addition, the turning point occurs earlier if adopting the production-based accounting rather than adopting the consumption-based accounting, implying that international trade postpones the peak time of global CO2 emissions. From the above analysis, it follows that when testing for the validity of the EKC for global CO2 emissions, the role of trade cannot be overstated.

Asymptotics and bootstrap for random-effects panel data transformation models

ABSTRACTThis article investigates the asymptotic properties of quasi-maximum likelihood (QML) estimators for random-effects panel data transformation models where both the response and (some of) the covariates are subject to transformations for inducing normality, flexible functional form, homoskedasticity, and simple model structure. We develop a QML-type procedure for model estimation and inference. We prove the consistency and asymptotic normality of the QML estimators, and propose a simple bootstrap procedure that leads to a robust estimate of the variance-covariance (VC) matrix. Monte Carlo results reveal that the QML estimators perform well in finite samples, and that the gains by using the robust VC matrix estimate for inference can be enormous.

Photoreflectance analysis of annealed vanadium-doped GaAs thin films grown by metalorganic vapor phase epitaxy

Abstract In this study, we investigate the optical properties of annealed vanadium-doped GaAs films grown on GaAs substrates by metalorganic vapor phase epitaxy. The temperature dependence of the photoreflectance (PR) of as-grown GaAs:V films has been studied. We used the fit with Third-Derivative Functional Form model to evaluate the physical parameters. The temperature dependence of band gap and spin–orbit energies can be described by the Bose–Einstein statistical expression. The PR spectra of the samples are measured after thermal annealing in order to check any improvement in the optical quality of the material. The PR signal amplitude of GaAs:V samples decreased after thermal annealing. Degradation of the PR signal for annealing temperature at about 850 °C is observed revealing a poor quality of the layer surface states and an important density of the recombination centers. The lock-in phase analysis of PR spectra allows to determine the time constant for GaAs:V sample before and after thermal annealing.

An Analysis of Factors Influencing Household Income: A Case Study of PACT Microfinance in Kyaukpadaung Township of Myanmar

The study investigates factors influencing the household income of both clients and non-clients and effect of microfinance on clients’ socioeconomic characteristics on establishing new enterprises. It uses Cobb-douglas functional form and Logistic regression model with a total sample size of 162 respondents [102 (clients) and 60 (non-clients)]. The empirical results from the model indicate that most common important influencing factor on household income is education. Educational level has a strongly positive impact on household income, suggesting that a client with a higher educational level can generate more income than one with a lower educational level. The results of the pool analysis show that six independent variables—age of the head of household, gender of the head of household, educational level of the head of household, land holding size, number of crops, and established new enterprise—have a significant influence on household income. We found that starting new enterprises is one of the most important factors for increasing the household income of clients. In order to establish new enterprises, the local government should pay more attention to the basic infrastructure requirement, market access facilities in the study area. Private Agency Collaborating Together (PACT) should focus on business training skills, apart from the provision of loans, to create sustainable microenterprises and other economic activities that increase the income of households.

A transformed random effects model with applications

This paper proposes a transformed random effects model for analyzing non-normal panel data where both the response and (some of) the covariates are subject to transformations for inducing flexible functional form, normality, homoscedasticity, and simple model structure. We develop a maximum likelihood procedure for model estimation and inference, along with a computational device which makes the estimation procedure feasible in cases of large panels. We provide model specification tests that take into account the fact that parameter values for error components cannot be negative. We illustrate the model and methods with two applications: state production and wage distribution. The empirical results strongly favor the new model to the standard ones where either linear or log-linear functional form is employed. Monte Carlo simulation shows that maximum likelihood inference is quite robust against mild departure from normality. Copyright © 2009 John Wiley & Sons, Ltd.

Photosynthesis and growth in macroalgae: linking functional-form and power-scaling approaches

Grouping species into functional-form groups and measuring directly their surface area to volume ratio are 2 common approaches to forecast primary production of marine macroalgae. A link between the functional-form model (FFM) and the power-scaling approach (PSA) for a wide vari- ety of marine macroalgae has been attempted for the first time in the present work. To test both approaches, thalli of 44 species of marine benthic macroalgae were collected from intertidal zones adjacent to Cadiz Bay. Metabolic rates, tissue nutrient content, surface area to biomass ratio (SA/B) and specific growth rates were measured for these species. PSA slopes were close to 2/3 power for growth rate, while metabolic rates scaled very close to, or matched, 3/4 power. The FFM descriptive model provided similar results to the PSA when it was transformed to a numerical model through the SA/B ratio. Even though both models appear to be valid, the problems derived from species alloca- tion into morphological groups, and other previous criticisms, make the direct use of SA/B ratios more suitable for representing primary production in macroalgal functional groups in numerical models of coastal ecosystems.

Zinc concentrations in marine macroalgae and a lichen from western Ireland in relation to phylogenetic grouping, habitat and morphology

Zinc concentrations in 19 species of marine macroalgae and a lichen from western Ireland (Spiddal, Co. Galway) were analysed by atomic absorption spectrophotometry. Algae were collected from a single site but occupied different shore levels and belonged to distinct phylogenetic groupings and to different (previously recognised) morphological groups. Concentrations ranged from 15–115 μg g −1 dry weight. The greatest variation in concentration occurred amongst the red algal species, containing both maximum and minimum concentrations. Zn concentrations in brown and green algae were generally lower than those in red algae. When grouped according to thallus morphology, thin, branched sheets (which consisted mainly of red algae) contained the highest Zn concentrations. In filamentous algae, Zn levels were higher than in thick-leathery or coarsely branched algae. However, all green algal species examined had similar Zn concentrations, despite their different morphologies. In brown algae, the highest Zn levels were detected in mid-shore fucoids ( Fucus vesiculosus and Fucus serratus), while thicker, subtidal and low-shore brown algae ( Laminaria digitata, Halydris siliquosa) exhibited lower Zn concentrations. The lowest Zn concentrations were detected in high-intertidal species ( Fucus spiralis, Pelvetia canaliculata), the only marine lichen examined ( Ramalina siliquosa) and a red crustose alga ( Corallina officinalis). In all morphological groups, red algal representatives contained relatively higher levels of Zn, the exception being Corallina officinalis. Zn levels in 4 species from a second, estuarine site in Galway Bay exhibited the same relative differences amongst species, but were all consistently higher than in algae from Spiddal. It is concluded that Zn accumulation in macroalgae is closely related to ecological growth strategies, following a functional-form model. However, the phylogenetic origin of species which determines carbohydrate and phenol composition, and responses to ambient environmental conditions ultimately determine, the availability of binding sites for polyvalent cations.

Thermoreflectance study of the direct energy gap of GaSb

We studied the optical properties of high quality GaSb layers, grown by molecular beam epitaxy, in the region of the fundamental gap E 0 using thermoreflectance spectroscopy in the temperature range between 80 and 300 K. The experimental line-shapes were analyzed with a functional form model including excitonic effects. Taking advantage of the derivative-like nature of the thermoreflectance spectroscopy, an accurate determination of the temperature dependence of the energy gap E 0( T) is obtained, which is well reproduced by the semi-empirical Varshni relation.

Functional Form Model Specification: An Application to Hedonic Pricing

A combination of conceptual analysis and empirical analysis—partial regression and residuals analysis—was used to derive an appropriate functional form hedonic price model. These procedures are illustrated in the derivation of a functional form hedonic model for an automated, econometric daily cotton price reporting system for the Texas-Oklahoma cotton market. Following conceptualization to deduce the general shapes of relationships, the appropriate specific functional form was found by testing particular attribute transformations identified from partial regression analysis. Minimizing structural errors across attribute levels and estimation accuracy were used in determining when an appropriate functional form for both implicit and explicit prices was found.

Depreciation Patterns for Agricultural Machinery

AbstractA flexible functional form model is used to estimate remaining‐value equations for eleven major types of farm machinery. Data used in estimation were obtained from ten years of machinery auctions. Remaining values were found to be influenced by machinery condition, use, manufacturer, and age. Macroeconomic variables were significant explanatory variables for most types of machinery. Estimated depreciation patterns varied by machinery type, demonstrating the need for updated machinery‐specific remaining‐value equations. Reduced‐form equations are presented for use in applied economic analysis.

The Box-coxVs. modulus power family of response transformations

Economic theory provides researchers little guidance when selecting the appropriate estimating functional form model, given the data. The flexible Box and Cox [J. Roy. Stat. Soc., 1964] power transformation model is one relatively simple device for minimizing functional approximation errors in single-equation, least-squares models. However, the Box-Cox may induce heteroscedastic residuals [Sarkar, Comm. Stats.Theory and Methods, 1985] and is only operational for strictly positive data values. Dynamic econometric models often involve variables calibrated in differences--not levels. Difference data containing negative values incapacitate Box-Cox transformations. Therefore, John and Draper [Appl. Stats., 1980] proposed the modulus alternative power family of transformations. Currently, implementation of the Modulus for econometric modelling does not exist in the literature. The purpose of this note is to increase the awareness of the Modulus and point out its usefulness when the Box-Cox is incapacitated. Consider the general linear model:

Application of the functional-form model to the culture of seaweeds

Application of the functional-form model to the culture of seaweeds

Linear and generalized functional form market models for electric utility firms

The capital asset pricing model's (CAPM) linear form assumes that the investor's holding period implied by the return data is correct. Lee's (1976a,b) generalized functional form model makes no such holding period assumption. Using a sample of electric utility industry firms, the authors find that neither CAPM linearity nor log-linearity, implied in Jensen's (1969) instantaneous horizon, are usually borne out. It is also shown that the use of the generalized model does not ameliorate the “beta reduction” problem in this industry. Analysis of variance confirms that beta estimates can be significantly different across firms and models.

Significance of macroalgal polymorphism: intraspecific tests of the functional-form model

The functional-form model, developed for comparisons among species in a diverse macroalgal community, was used to examine the functional significance of macroalgal polymorphism (i.e., the existence of genetically distinct morphotypes within a single species). Four predictions of this model were examined along a continuum of morphotypes represented by eight clones of the red alga Gracilaria tikvahiae McLachlan. These clones had significant differences in calorific contnet, percentage of photosynthetic tissue, net photosynthesis, and specific growth rate. All of these functional attributes were a function of the surface area:volume ratios. Consistent with the predictions of the functional-form model, clones near opposite ends of the surface area:volume continuum had significant differences for these attributes. A cluster analysis of these attributes identified three clusters of clones that agreed well with their surface:volume ratios. Polymorphism in G. tikvahiae increases the ecological and physiological fitness of this species in an estuarine system where spatial and temporal changes in the environment occur. Each morphotype possesses concomitant, ecologically meaningful combinations of benefits and costs which collectively spread the risk from different sources of mortality and thus increase the overall survival of the population.

The Translog Utility Function and the Demand for Money in the United States

IN RECENT YEARS considerable effort has been directed towards establishing the nature of the relationship between and nearmonies but with mixed success. The approaches vary from multi-interest-rate single equation studies to the careful simultaneous equations studies summarized (and amended) by Feige and Pearce (1977) and extended recently by Donovan (1978), Offenbacher (1979), and Barnett (1980). The empirical results also vary, with numerous studies favoring only one interest rate (see the surveys in Fisher 1978, 1983), some claiming that a variety of entities are close substitutes for money (e.g., Chetty 1969), and others showing that weak substitution or even complementarity may be the result of the measurement of elasticities of substitution between money and a number of other assets (e.g., Feige and Pearce 1977, Offenbacher 1979, and Barnett 1980). The debate seems to have overshadowed a second and equally intriguing issue which centers on the establishment of an acceptable definition of money. The basic idea of this study is to take an approach that takes account of the different degrees of moneyness possessed by the various monetary assets. This paper produces quantitative estimates of the degree of substitutability of other monetary assets for money in the context of a flexible functional form model (with a

Relationships between macroalgal functional form groups and substrata stability in a subtropical rocky-intertidal system

The general hypothesis that morphological, physiological, and ecological adaptations of macro algal functional-form groups can be related to the level of disturbance encountered in a natural environment was examined. Two articulated calcareous coralline algae ( Amphiroa van-bosseae Lemoine, 24% cover and Corallina frondescens Post. & Rupr. 20%) and one non-articulated coralline alga ( Lithophyllum sp., 16%), all late-successional predation-tolerant strategists, comprise most of the community cover on stable bedrock substrata at Punta Las Cuevitas, Sonora, Mexico. Conversely, Ulva rigida C. ag. (26% cover) and a ralfsioid crust (23%), shows to be early-successional opportunistic strategists, cover more of the disturbed boulder habitat. Porolithon sonorense Daws., a stress-tolerant strategist, is uniquely abundant on both substratum types (13% cover on boulders, 10% on bedrock). The sheet-like and filamentous algae, prevalent in the temporally unstable habitat, generally show greater productivity (>2×) than the thicker and calcareous forms conspicuous in the more constant environment. It appears that selection for delicate thalli with high productivities, as well as selection for tougher morphologies having lower photosynthetic rates due to greater proportions of structural tissues, are widespread, divergent evolutionary forces among marine algae. Experiments with captive sea urchins ( Echinometra vanbrunti Agassiz), in conjunction with fish-preference data published for some of the same algae studied here, offer strong support for the functional-form model. Parrotfishes, rudderfishes, surgeonfishes, damselfishes and E. vanbrunti, in the Gulf of California, preferentially feed on delicate, early-successional, sheet-like, and filamentous algae, while rejecting or ignoring the more structured, late-successional and calcareous algae. There is no significant ( P > 0.05) gradation in calorific content between the first four of the six functional groups (i.e., Sheet-, Filamentous-, Coarsely Branched- and Thick Leathery-Groups), but the mean value for these fleshy forms (2.6 kcal · g ash-free dry wt −1) is significantly greater than that for the last two groups (0.3 kcal, Jointed Calcareous- and Crustose-Groups). The approach used in this study demonstrates a realistic technique for predicting macrophyte community composition from knowledge of the disturbance levels in a given habitat or the reverse. The form group-disturbance relationship has important implications for future biological monitoring of rocky-inter-tidal and subtidal systems.

Functional Forms and the Capital Asset Pricing Model

the functional form model in the context of the returns for 85 mutual funds. Their findings document the presence of significant transformation parameters; how? ever, the impact on estimates of systematic risk does not appear to be substantial. The purposes of this paper are twofold. The first purpose is to derive and test a more generalized form of the CAPM?more general with respect to functional form and also within the context of investment horizons. The second purpose is to investigate nonlinearities, as in [4], and to extend the analysis to a large sam? ple of individual securities. The functional form models to be empirically tested are derived in Section II. Section III discusses the estimation techniques applied to the proposed models and describes the data used in the study. The results are presented in Section IV, along with a discussion of their implications for the horizon problem and the estimation of systematic risk. A summary of the pertinent findings of the study appears in Section V.