Fitted Density Function Research Articles

Raccoon Vigilance and Activity Patterns When Sympatric with Coyotes

Nonconsumptive effects of predators potentially have negative fitness consequences on prey species through changes in prey behavior. Coyotes (Canis latrans) recently expanded into the eastern United States, and raccoons (Procyon lotor) are a common mesocarnivore that potentially serve as competitors and food for coyotes. We used camera traps at baited sites to quantify vigilance behavior of feeding raccoons and used binomial logistic regression to analyze the effects of social and environmental factors. Additionally, we created raccoon and coyote activity patterns from the camera trap data by fitting density functions based on circular statistics and calculating the coefficient of overlap (Δ). Overall, raccoons were vigilant 46% of the time while foraging at baited sites. Raccoons were more vigilant during full moon and diurnal hours but less vigilant as group size increased and when other species were present. Raccoons and coyotes demonstrated nocturnal activity patterns, with coyotes more likely to be active during daylight hours. Overall, raccoons did not appear to exhibit high levels of vigilance. Activity pattern results provided further evidence that raccoons do not appear to fear coyotes, as both species were active at the same time and showed a high degree of overlap (Δ = 0.75) with little evidence of temporal segregation in activity. Thus, our study indicates that nonconsumptive effects of coyotes on raccoons are unlikely, which calls into question the ability of coyotes to initiate strong trophic cascades through some mesocarnivores.

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.

Nonparametric series density estimation and testing

This paper first establishes consistency of the exponential series density estimator when nuisance parameters are estimated as a preliminary step. Convergence in relative entropy of the density estimator is preserved, which in turn implies that the quantiles of the population density can be consistently estimated. The density estimator can then be employed to provide a test for the specification of fitted density functions. Commonly, this testing problem has utilized statistics based upon the empirical distribution function, such as the Kolmogorov-Smirnov or Cramér von-Mises, type. However, the tests of this paper are shown to be asymptotically pivotal having limiting standard normal distribution, unlike those based on the edf. For comparative purposes with those tests, the numerical properties of both the density estimator and test are explored in a series of experiments. Some general superiority over commonly used edf based tests is evident, whether standard or bootstrap critical values are used.

Mitigating the zonal effect in modeling urban population density functions by Monte Carlo simulation

Most empirical studies indicate that the pattern of declining urban population density with distance from the city center is best captured by a negative exponential function. Such studies usually use aggregated data in census area units that are subject to several criticisms such as modifiable areal unit problem, unfair sampling, and uncertainty in distance measure. In order to mitigate these concerns associated, this paper uses Monte Carlo simulation to generate individual residents that are consistent with known patterns of population distribution. By doing so, we are able to aggregate population back to various uniform area units to examine the scale and zonal effects explicitly. The case study in Chicago area indicates that the best fitting density function remains exponential for data in census tracts or block groups, however, the logarithmic function becomes a better fit when uniform area units such as squares, triangles or hexagons are used. The study also suggests that the scale effect remain to some extent in all area units, and the zonal effect be largely mitigated by uniform area units of regular shape.

Modeling Large Macromolecular Structures Using Promolecular Densities.

A procedure to easily construct fitted density functions is presented. This methodology, based on the promolecule approach, is able to handle large macromolecular systems, such as proteins. The usual procedure dealing with fitted densities has been improved by adding some restrictions, which allow faster calculations. As a main application example, molecular isodensity contours (MIDCOs) are constructed for two proteins, one of them composed of more than 50 000 atoms. MIDCOs, as a visual representation of the molecular density function, and thus an important descriptor of the molecular charge distribution, constitute a powerful tool in the understanding of molecular systems. MIDCOs are presented for both proteins, allowing exploration of their surfaces, as well as analysis of their shapes. Also, as a quantum mechanical calculation example, molecular quantum self-similarity measures are calculated for several proteins.

Modeling large macromolecular structures using promolecular densities.

A procedure to easily construct fitted density functions is presented. This methodology, based on the promolecule approach, is able to handle large macromolecular systems, such as proteins. The usual procedure dealing with fitted densities has been improved by adding some restrictions, which allow faster calculations. As a main application example, molecular isodensity contours (MIDCOs) are constructed for two proteins, one of them composed of more than 50 000 atoms. MIDCOs, as a visual representation of the molecular density function, and thus an important descriptor of the molecular charge distribution, constitute a powerful tool in the understanding of molecular systems. MIDCOs are presented for both proteins, allowing exploration of their surfaces, as well as analysis of their shapes. Also, as a quantum mechanical calculation example, molecular quantum self-similarity measures are calculated for several proteins.

Fitted electronic density functions from H to Rn for use in quantum similarity measures: cis-diamminedichloroplatinum(II) complex as an application example

A consistent set of fitted electronic density functions was generated for the elements from hydrogen to radon using an algorithm based on the elementary Jacobi rotations (EJR) technique. The main distinguishing attribute of this fitting procedure is the production of approximated electronic density functions with positive definite expansion coefficients; in this way, the statistical meaning of the probability distribution is preserved. The methodology, which was fully described previously, was modified in this work to improve and accelerate the fitting procedure. This variation concerns the optimization method employed to obtain the optimal angle of the EJR, implementing an algorithm based on a Taylor series expansion. Additionally, a new 1S-Type Gaussian basis set for atoms H to Rn is presented, that was fitted from a primitive basis set of Huzinaga. Fitted density functions facilitate theoretical calculations over large molecules and may be employed in many areas of computational chemistry, for example, in quantum similarity measures (QSM). To verify the basis set, a sound example related to QSM applications is given. This corresponds to the comparison of experimental structures obtained from X-ray determination for cis-diamminedichloroplatinum(II) complex with optimized molecular geometries using several theoretical methods to quantify the differences between the analyzed levels of theory. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 911–920, 1999

Quantum similarity measures under atomic shell approximation: First order density fitting using elementary Jacobi rotations

The elementary Jacobi rotations technique is proposed as a useful tool to obtain fitted electronic density functions expressed as linear combinations of atomic spherical shells, with the additional constraint that all coefficients are kept positive. Moreover, a Newton algorithm has been implemented to optimize atomic shell exponents, minimizing the quadratic error integral function between ab initio and fitted electronic density functions. Although the procedure is completely general, as an application example both techniques have been used to compute a 1S-type Gaussian basis for atoms H through Kr, fitted from a 3-21G basis set. Subsequently, molecular electronic densities are modeled in a promolecular approximation, as a simple sum of parameterized atomic contributions. This simple molecular approximation has been employed to show, in practice, its usefulness to some computational examples in the field of molecular quantum similarity measures. © 1997 John Wiley & Sons, Inc. J Comput Chem18: 2023–2039, 1997

A method to estimate icing loads on overhead lines

Probabilistic design methods for overhead lines, such as IEC 826, set the question of statistical behaviour of weather-related loads, especially icing on cables. Two physical models concerning wet snow and in-cloud icing have been developed by EDF; they can reconstruct icing events from standard meteorological data. In France, consistent weather records have been currently available since 1949, so the events can be recalculated on a 40 year approximately period. In regions already treated by the mentioned models, some locations have been selected for a statistical analysis: 1. - histograms, 2. - search for fitted density functions (Weibull, γ, Gumbel) 3. - establishing return period values to be used by the IEC 826 probabilistic method. The results showed a peculiar pattern and also suggested a simplified density function. Simple prediction rules could be derived from this distribution. This probabilistic analysis will be integrated in a nationwide mapping of in-cloud icing.

Fitting Density Functions with Polynomials

A robust procedure is developed for estimating density functions from data. It requires the existence of a parametric function, called the key function, to give a first approximation to the density and then improves the fit using polynomial adjustments. When the key function is the normal density, Hermite polynomials may be used; similarly, Laguerre polynomials might be preferred if the key is negative exponential. However, adequacy of fit is little affected by choice of polynomials, and it is more straightforward to use simple polynomials whatever the form of the key. Short examples illustrate the wide applicability of the technique. The methodology was developed to allow valid analysis of migration count data for the California grey whale, and this example is considered in detail.

An Empirical Fitting-Adaptive Approach to Importance Sampling in Reliability Analysis

This paper presents a fitting-adaptive approach to importance sampling, in which a fitting density function is introduced to calculate the failure probability instead of the importance sampling density function. The approach improves the accuracy of the importance sampling technique when the sample size is relatively small. Therefore, it is very useful to problems that have high reliability and consume much CPU time in a single Monte Carlo run. Furthermore, the adaptive operation is performed if the fitting density function is not satisfactory. When the design point is used, the proposed approach yields even better results. Numerical examples demonstrate that a significant reduction in variance of the failure probability can be achieved by use of this approach.

Fitting Density Functions and Diffusion Tensors to Three-Dimensional Drug Transport within Brain Tissue

In the research on drug transport within brain tissue, typical data sets consist of a collection of volume integrals from various locations in the brain, with each datum measuring the total amount of drug in a sample of tissue. These samples contain medically useful information about the extent and orientation of the distribution of the drug, but extracting this information requires some mathematical analysis. The method of analysis presented here performs a nonlinear regression on the data to fit a multivariate density function (for example, a Gaussian density) to model such transport processes as diffusion and dispersion. The principal components of that density then characterize the size and shape of the distribution of drug.

Fitting density functions and diffusion tensors to three-dimensional drug transport within brain tissue

A common method for researching how the brain works consists in injecting a drug into a part of an animal's brain, and then observing how the subject's behaviour changes. Besides information about how the brain works, such experiments may provide means for understanding, treating, and perhaps curing certain brain disorders. Yet, correlating the drug, the brain, and the behavioural changes requires a quantitative procedure for assessing accurately the location, extent, and orientation of the region of the brain affected by the drug. Such a quantitative estimate must usually rely upon additional assumptions, because the data available from the experiment often fail to cover the entire region of interest. In the present context, the additional assumptions may specify the nature of the transport processes undergone by the drug, for example diffusion and absorption. The solution of the diffusion-absorption equation thus gives a theoretical model for the spatial distribution of the drug in the brain tissue, in effect, a combination of multivariate Gaussian density functions. Then a non-linear least-squares regression may fit a diffusion tensor (the covariance matrix) to the data, whose eigenvalues and eigenvectors yield the required quantitative estimates of extent and orientation. Finally, the residuals of the regression provide confidence regions for the fitted parameters and give a global evaluation of the quality of the model.This work was entirely supported by a grant from the Northwest Institute for Advanced Study, an organ of Eastern Washington University.

Estimation of linear functionals by maximum likelihood*

SUMMARYA classical problem of stereology is estimation of linear functionals of particle size distributions from intersections on planar probes. The maximum likelihood method of estimation is outlined and compared with classical linear methods and with numerical interpolation methods.A population of spherical particles is distributed in an infinite matrix with position defined by a Poisson field. Diameters of circular intersections on a planar probe constitute a generalized Poisson process. Maximum likelihood theory fits a parametric family of planar density functions to observed diameter frequency data. The integral of an appropriate kernel with respect to the fitted density function is the linear functional estimate.The approach can handle composite data involving observation at several magnifications. Estimation of complementary cumulative density of pores in uranium oxide fuel pellets illustrates the maximum likelihood method of data collected with two microscopes at four magnifications.