Simple Functional Form Research Articles

Evaluating the predictive power of an SPF for two-lane rural roads with random parameters on out-of-sample observations

Negative binomial (NB) regression is among the most common statistical modeling methods used to model crash frequencies due to its simple functional form and ability to handle over-dispersion commonly found in crash data. However, a drawback of this approach is that regression parameters are assumed to be the same across observations, which could contribute to biased parameter estimates. To alleviate this concern, the random parameters negative binomial (RPNB) model was recently proposed, which allows regression parameters to differ across observations following some known distribution. The resulting coefficients should be less biased, and thus the RPNB approach is believed to provide a more accurate relationship between independent variables and expected crash frequency. However, the prediction accuracy of the RPNB model relative to the standard NB model has not been thoroughly evaluated, particularly with respect to out-of-sample observations for which unique random parameters cannot be estimated. In this paper, the predictive power of the RPNB and NB models are examined using two-lane rural highway data from three engineering Districts in Pennsylvania. Multiple evaluation metrics are applied—root-mean-square error (RMSE) and mean absolute error (MAE), coefficients from calibration functions and cumulative residual (CURE) plots—to assess each model type. The results show that the RPNB model outperforms the NB model when applied to within sample observations (i.e., those used to estimate the model) by making use of the observation-specific coefficients. However, the predictive power of the RPNB model appears to be similar to or slightly less precise than the traditional NB model when applied to out-of-sample observations. Since the RPNB model is estimated using a simulation-based approach, sensitivity tests were also performed to see how the parameter estimates change with the number of Halton draws used to perform the simulation. For the sample sizes used in this paper, the estimates were fairly insensitive when more than 50 Halton draws were used. The findings suggest that the RPNB model is more reliable when applied to the same set of sites that were used to estimate the model but might not be as robust as the traditional NB model when applied to other sites.

Dynamic adjustments in bankfull width of a braided reach

Remarkable channel degradation has occurred in a braided reach of the Lower Yellow River owing to the recent operation of Xiaolangdi reservoir, and downstream progressive incision has caused a significant process of channel widening. For the 104 km long braided reach, the dynamic adjustments in bankfull channel widths were investigated at both the section scale and reach scale, based on post-flood cross-sectional profiles surveyed annually from 1999 to 2013. It was found that the bankfull width at one section increased by up to 2887 m (296% increase) over 14 years, with an increase in the reach-scale bankfull width of 666 m (59% increase) in the braided reach. Fluvial erosion intensity was identified as a key factor influencing the variation in bankfull width, based on a comparison of various fluvial and non-fluvial factors controlling channel widening. Empirical relationships were developed, in the form of simple power functions, between these bankfull widths and the previous four-year average fluvial erosion intensity during flood seasons at the hydrometric station of Huayuankou. It is concluded that the significant increase in bankfull width was prominent in the channel evolution of the braided reach, which resulted in a major loss of floodplains.

F(Q,\xa0T) gravity

We propose an extension of the symmetric teleparallel gravity, in which the gravitational action L is given by an arbitrary function f of the non-metricity Q and of the trace of the matter-energy-momentum tensor T, so that L=f(Q,T). The field equations of the theory are obtained by varying the gravitational action with respect to both metric and connection. The covariant divergence of the field equations is obtained, with the geometry–matter coupling leading to the nonconservation of the energy-momentum tensor. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of general relativity. We consider several cosmological models by imposing some simple functional forms of the function f(Q, T), corresponding to additive expressions of f(Q, T) of the form f(Q,T)=alpha Q+beta T, f(Q,T)=alpha Q^{n+1}+beta T, and f(Q,T)=-alpha Q-beta T^2. The Hubble function, the deceleration parameter, and the matter-energy density are obtained as a function of the redshift by using analytical and numerical techniques. For all considered cases the Universe experiences an accelerating expansion, ending with a de Sitter type evolution. The theoretical predictions are also compared with the results of the standard Lambda CDM model.

Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid.

Rosenfeld proposed two different scaling approaches to model the transport properties of fluids, separated by 22 years, one valid in the dilute gas, and another in the liquid phase. In this work, we demonstrate that these two limiting cases can be connected through the use of a novel approach to scaling transport properties and a bridging function. This approach, which is empirical and not derived from theory, is used to generate reference correlations for the transport properties of the Lennard-Jones 12-6 fluid of viscosity, thermal conductivity, and self-diffusion. This approach, with a very simple functional form, allows for the reproduction of the most accurate simulation data to within nearly their statistical uncertainty. The correlations are used to confirm that for the Lennard-Jones fluid the appropriately scaled transport properties are nearly monovariate functions of the excess entropy from low-density gases into the supercooled phase and up to extreme temperatures. This study represents the most comprehensive metastudy of the transport properties of the Lennard-Jones fluid to date.

A coarse-grain model for entangled polyethylene melts and polyethylene crystallization.

The Shinoda-DeVane-Klein (SDK) model is herein demonstrated to be a viable coarse-grain model for performing molecular simulations of polyethylene (PE), affording new opportunities to advance molecular-level, scientific understanding of PE materials and processes. Both structural and dynamical properties of entangled PE melts are captured by the SDK model, which also recovers important aspects of PE crystallization phenomenology. Importantly, the SDK model can be used to represent a variety of materials beyond PE and has a simple functional form, making it unique among coarse-grain PE models. This study expands the suite of tools for studying PE in silico and paves the way for future work probing PE and PE-based composites at the molecular level.

A Modified Peng–Robinson Equation of State for Heavy Hydrocarbons

A new simple and accurate functional form for an attractive parameter α is introduced for Peng–Robinson equation of state. The modified Peng–Robinson equation of state is applied to calculate the density of different pure heavy hydrocarbons. The performance of this proposed equation of state for density calculations is examined with the corresponding experimental measurements and the results are compared with those obtained from the original Peng–Robinson equation of state. The new alpha function allows significant improvements of prediction of density. The overall average absolute deviation percentage of the calculated density of 12 heavy hydrocarbons obtained by this modified equation of state is 0.35%.

Can Metropolitan Region Not Be Innovative?

One of the qualities of metropolises is their innovativeness. However, when we ask about the qualities of an innovative metropolitan region, the matter becomes somewhat complicated. The tasks of a metropolitan region concentrate around matters of supporting the functioning of its main centre. However, we should not assume that this support is only meant to take place in the form of simple economic functions like workforce accessibility, the providing of food, drinking water or fuel. Technological and industrial subcentres play an important role in a metropolitan region, their operation being directed at goals that the main centre works towards, which shows that if this support is to be efficient, then it has to be adapted to specific needs in a greater manner, in addition to meeting the criteria of innovativeness. In turn, if the subcentres are directed towards competitiveness, then they must tend to the development of their own creativity, which must result in increasing the degree of innovativeness of the activity that takes place inside them in all four types of innovation: product, process, marketing and organisational. From among the most commonly cited indicators of innovativeness, the number of patents is brought up the most frequently. Among Polish research institutions, the highest number of patents are being filed by universities and pharmaceutical companies, while territorially the most innovative region is that of the Warsaw metropolis. Innovation in urban planning and architecture is most often based on striving towards sustainable development, the minimisation of labour associated with transport and improving the quality of life of society, in addition to the adaptation of the latest technological solutions in building construction and the promoting of energy efficiency and the generation of renewable energy.

Short-range combined water model

The short-range combined water model (SRCW model) for the calculation of the hydration free energy of the non-polar solutes is presented. A mixed explicit/implicit representation of the solvent is used in the model. A thermodynamic basis for the boundary potential between explicit and implicit parts of the simulation area is derived. A simple functional form for the boundary potential minimizing the water density fluctuations in the explicit part is found. Hydration free energies of the model solutes are calculated in the frame of the developed model. Obtained values are in the good agreement with results of the Monte Carlo simulation using the periodic boundary conditions.

Skynet Algorithm for Single-dish Radio Mapping. I. Contaminant-cleaning, Mapping, and Photometering Small-scale Structures

Abstract We present a single-dish mapping algorithm with a number of advantages over traditional techniques. (1) Our algorithm makes use of weighted modeling, instead of weighted averaging, to interpolate between signal measurements. This smooths the data, but without blurring the data beyond instrumental resolution. Techniques that rely on weighted averaging blur point sources sometimes by as much as 40%. (2) Our algorithm makes use of local, instead of global, modeling to separate astronomical signal from instrumental and/or environmental signal drift along the telescope’s scans. Other techniques, such as basket weaving, model this drift with simple functional forms (linear, quadratic, etc.) across the entirety of scans, limiting their ability to remove such contaminants. (3) Our algorithm makes use of a similar, local modeling technique to separate astronomical signal from radio-frequency interference (RFI), even if only continuum data are available. (4) Unlike other techniques, our algorithm does not require data to be collected on a rectangular grid or regridded before processing. (5) Data from any number of observations, overlapping or not, may be appended and processed together. (6) Any pixel density may be selected for the final image. We present our algorithm and evaluate it using both simulated and real data. We are integrating it into the image-processing library of the Skynet Robotic Telescope Network, which includes optical telescopes spanning four continents, and now also Green Bank Observatory’s 20 m diameter radio telescope in West Virginia. Skynet serves hundreds of professional users, and additionally tens of thousands of students, of all ages. Default data products are generated on the fly, but will soon be customizable after the fact.

Atomic orbitals revisited: generalized hydrogen-like basis sets for 2nd-row elements

In the present work, we revisit the problem of atomic orbitals from the positions mostly dictated by semiempirical approaches in quantum chemistry. To construct basis set, having proper nodal structure and simple functional form of orbitals and representing atomic properties with reasonable accuracy, authors propose an Ansatz based on gradual improvement of hydrogen atomic orbitals. According to it, several basis sets with different numbers of variable parameters are considered and forms of orbitals are obtained for the 2nd-row elements either by minimization of their ground state energy (direct problem) or by extracting from atomic spectra (inverse problem). It is shown that so-derived three- and four-parametric basis sets provide accurate description of atomic properties, being, however, substantially provident for computational requirements and, what is more important, simple to handle in analytic models of quantum chemistry. Since the discussed Ansatz allows a generalization for heavier atoms, our results may be considered not only as a solution for light elements, but also as a proof of concept with possible further extension to a wider range of elements.

Parametric study of water vapor and water ice particle plumes based on DSMC calculations: Application to the Enceladus geysers

The field parameters – number density, velocity components and temperature – for the Enceladus geysers, and possibly similar jets from other bodies, such as Europa, Ceres or comets, are expensive to obtain using physically correct simulation methods, such as the Direct Simulation Monte Carlo (DSMC) approach. It would be very useful to be able to correctly reproduce all the different states that the flow is undergoing while expanding into vacuum, from a high density and collisional state near the surface to free-molecular and collisionless at high altitude without resorting to expensive DSMC simulations in every case. In this work, we consider a two-phase water vapor/grain mixture exiting a circular vent, assuming a uniform radius of the water ice grains, and study how the field parameters can be fitted at an altitude of 10 km, where the flow is collisionless. To do so, we define simple functional forms for each of these fitted parameters, and we study how their coefficients vary as a function of the vent exit parameters, i.e. the vent radius, the water mixture mass flow, the water vapor/water ice mass ratio, the water ice grain radius, the water vapor and water ice exit speed, the vent exit angle and flow temperature. We define polynomial approximations to model these variations. We show that all the vent parameters have nearly-independent influences on the radial profiles at 10 km, except for the water vapor and water ice exit speed, for which we considered cross-correlations. We finally show that the geyser field parameters can be reconstructed using our parametric study for variations of the vent parameters within the range considered here, and in a time frame of a few milliseconds. The results of the parametrizations presented in this study can now be used to propagate the geyser field parameters using computationally inexpensive free molecular/ballistic codes up to higher altitudes. The DSMC results that have been run for this paper are available at an online repository.

Remodelling the evolution of grain size distribution in galaxies

We revisit the evolution model of grain size distribution in a galaxy for the ultimate purpose of implementing it in hydrodynamical simulations. We simplify the previous model in such a way that some model-dependent assumptions are replaced with simpler functional forms. For the first test of the developed framework, we apply it to a one-zone chemical evolution model of a galaxy, confirming that our new model satisfactorily reproduces the previous results and that efficient coagulation of small grains produced by shattering and accretion is essential in reproducing the so-called MRN grain size distribution. For the next step, in order to test if our model can be treated together with the hydrodynamical evolution of the interstellar medium (ISM), we post-process a hydrodynamical simulation of an isolated disc galaxy using the new grain evolution model. We sample hydrodynamical particles representing each of the dense and diffuse ISM phases. By this post-processing, we find that the processes occurring in the dense gas (grain growth by accretion and coagulation) are important in reproducing the grain size distribution consistent with the Milky Way extinction curve. In our model, the grain size distributions are similar between the dense and diffuse ISM, although we observe a larger dispersion in the dense ISM. Moreover, we also show that even if we degrade the grain radius resolution (with 16 grid points), the overall shape of grain size distribution (and of resulting extinction curve) can be captured.

Analytical Approximations for American Options: The Binary Power Option Approach

This study proposes an innovative approach to value American options. Using a portfolio of binary power options to replicate the early exercise premium, we modify Medvedev and Scaillet (2010) to derive an analytical approximation of American option values under the Black-Scholes framework. Compared with Medvedev and Scaillet (2010), our approach provides a much simpler functional form of the early exercise premium that can be easily extended to high-order series expansions. The numerical results show that the pricing performance of our method is closely comparable to that of Medvedev and Scaillet (2010) and superior to that of Barone-Adesi and Whaley (1987). Key words: American option, binary power option, early exercise premium

Expansion of Preisach density in magnetic hysteresis using general basis functions

The Preisach model of hysteresis has two parts: a geometrical staircase and a density or weighting function. In typical applications, the underlying density function of hysteresis operators is estimated through partial derivatives of first order reversal curves, or a priori assumed to obey simple functional forms like Gaussian, Lorenzian etc. Here we take a more agnostic and empirical approach, and expand the density in a general form using the spectrum of the Laplace operator on a bounded triangular domain. Transforming the input to the same bounded domain, we have a nonlinear parameter fitting problem. We fit parameters to our own magnetic hysteresis data directly using complex waveforms, for both soft and hard loops. For hard loops, if the Preisach density is to be kept strictly nonnegative (as is usual), a nonlinear transformation of the Preisach output is needed. Additionally, the Preisach density is consists of a single hump for soft loops and three distinct humps for hard loops. Our fitted density function, based on a general expansion, contains several coefficients, but subsequent simulation is quick. The main contribution of this paper is a direct demonstration of fitting the density function without making a priori assumptions about the functional form.

Investigating dependence between frequency and severity via simple generalized linear models

Recently, a body of literature proposed new models relaxing a widely-used but controversial assumption of independence between claim frequency and severity in non-life insurance rate making. This paper critically reviews a generalized linear model approach, where a dependence between claim frequency and severity is introduced by treating frequency as a covariate in a regression model for severity. As an extension of this approach, we propose a dispersion model for severity. For this model, the information loss caused by using average severity rather than individual severity is examined in detail and the parameter estimators suffering from low efficiency are identified. We also provide analytical solutions for the aggregate sum to help rate making. We show that the simple functional form used in current research may not properly reflect the real underlying dependence structure. A real data analysis is given to explain our analytical findings.

Relationship between Computed Rate Constants and the Variability in Maturity-Based Strength Predictions

Abstract ASTM C1074-11, Standard Practice for Estimating Concrete Strength by the Maturity Method, provides instructions for applying the Nurse-Saul and Freiesleben-Hansen Pedersen maturity methods, including ways to obtain the key parameters of datum temperature (T0) or the Arrhenius activation energy (Ea). Default values are provided along with three alternative computational methods for determining a mixture-specific value of T0 or Ea from experimental data, as detailed in C1074-11 Annex A1. This paper demonstrates via examples that the accuracy of the resulting strength estimates can vary considerably depending on which of the three alternatives is selected, potentially masking the more intrinsic variability of these parameters as influenced by composition or temperature. One source of this observed variability is the statistical bias known to characterize the “double reciprocal linearization” regression technique, which is utilized in two of the three ASTM methods. While recommending the deletion of these statistically biased estimators, the authors support the more rigorous nonlinear regression method (A1.1.8.1) as well as simpler functional forms; they affirm the reasonableness of the ASTM default values for T0 and Ea.

Modified geometric truncation of the scattering phase function

Phase function of light scattering on large atmospheric particles has very strong peak in forward direction constituting a challenge for accurate numerical calculations of radiance required in remote sensing problems. Scaling transformation replaces original phase function with a sum of the delta function and a new regular smooth phase function. Geometric truncation is one of the ways to construct such a smooth function. The replacement phase function coincides with the original one outside the forward cone and preserves the asymmetry parameter. It has discontinuity at the cone.Another simple functional form of the replacement phase function within the cone is suggested. It enables continuity and allows for a number of modifications. Three of them are considered in this study: preserving asymmetry parameter, providing continuity of the 1st derivative of the phase function, and preserving mean scattering angle.Yet another problem addressed in this study is objective selection of the width of the forward cone. That angle affects truncation fraction and values of the phase function within the cone. A heuristic approach providing unambiguous criterion of selection of the truncation angle is proposed. The approach has easy numerical implementation.Suggested modifications were tested on cloud phase function using discrete ordinates and Monte Carlo methods. It was shown that the modifications provide better accuracy of the radiance computation compare to the original geometric truncation with discrete ordinates while continuous derivative approach provides significant gain in computer time with Monte Carlo simulations.

The amenity cost of road noise

This paper reports a complete two stage hedonic analysis for road noise. It is based on a large and detailed administrative data set covering 100,000 housing transactions in Copenhagen, Denmark including data on the individual households occupying the transacted homes. For the estimation of the hedonic price function I develop a spatial research design which simultaneously reduces the risk of omitted variable bias and addresses the risk of measurement error in the noise measure. The preference parameters are locally identified by approximating utility through a simple functional form. The recovered preference parameters reveal a great deal of heterogeneity across households. Observable demographic characteristics explain up to 40 percent of the variation in taste for quiet. Results are used to discuss willingness to pay for noise reductions from two policy measures: A European standard on noise emissions for tires, and the partial closure of a busy road in central Copenhagen.

Quantifying the impact of simple DNA parameters on the cyclization J-factor for single-basepair-addition families

We use Monte Carlo simulation to quantify the change in cyclization J-factor within a dramatically simplified model of DNA that involves parameters for uniform stiffnesses, intrinsic twist, and intrinsic bending (including nonplanar bending). Plots of J versus DNA length over multiple periods of helical repeat are fit to a simple functional form in order to project the behavior of J over a broad range of these model parameters. In some instances, this process allows us to find families of DNA molecules (within our model) with quite different material properties, but very similar plots of J versus length, so similar as to likely to be indistinguishable by experiments. This effect is seen both for the parameter-pair of bend angle and stiffness scaling, as well as for the parameter-trio of helical repeat, bend angle, and bend non-planarity.

A population genetic interpretation of GWAS findings for human quantitative traits.

Human genome-wide association studies (GWASs) are revealing the genetic architecture of anthropomorphic and biomedical traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architecture is shaped by basic population genetics processes—notably, by mutation, natural selection, and genetic drift. Because many quantitative traits are subject to stabilizing selection and because genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabilizing selection in a multidimensional trait space. We solve the model for the phenotypic distribution and allelic dynamics at steady state and derive robust, closed-form solutions for summary statistics of the genetic architecture. Our results provide a simple interpretation for missing heritability and why it varies among traits. They predict that the distribution of variances contributed by loci identified in GWASs is well approximated by a simple functional form that depends on a single parameter: the expected contribution to genetic variance of a strongly selected site affecting the trait. We test this prediction against the results of GWASs for height and body mass index (BMI) and find that it fits the data well, allowing us to make inferences about the degree of pleiotropy and mutational target size for these traits. Our findings help to explain why the GWAS for height explains more of the heritable variance than the similarly sized GWAS for BMI and to predict the increase in explained heritability with study sample size. Considering the demographic history of European populations, in which these GWASs were performed, we further find that most of the associations they identified likely involve mutations that arose shortly before or during the Out-of-Africa bottleneck at sites with selection coefficients around s = 10−3.