scholarly journals Evaluation of peak functions on ultra-coarse grids

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120665 ◽  
Author(s):  
Natalia Petrovskaya ◽  
Nina Embleton
Keyword(s):  
Random Variable ◽  
Spatial Density ◽  
Pest Species ◽  
Sampled Data ◽  
Monitoring And Control ◽  
Density Distributions ◽  
Integration Error ◽  
Peak Functions ◽  
Coarse Grids ◽  
Integrand Function

Integration of sampled data arises in many practical applications, where the integrand function is available from experimental measurements only. One extensive field of research is the problem of pest monitoring and control where an accurate evaluation of the population size from the spatial density distribution is required for a given pest species. High aggregation population density distributions (peak functions) are an important class of data that often appear in this problem. The main difficulty associated with the integration of such functions is that the function values are usually only available at a few locations; therefore, new techniques are required to evaluate the accuracy of integration as the standard approach based on convergence analysis does not work when the data are sparse. Thus, in this paper, we introduce the new concept of ultra-coarse grids for high aggregation density distributions. Integration of the density function on ultra-coarse grids cannot provide the prescribed accuracy because of insufficient information (uncertainty) about the integrand function. Instead, the results of the integration should be treated probabilistically by considering the integration error as a random variable, and we show how the corresponding probabilities can be calculated. Handling the integration error as a random variable allows us to evaluate the accuracy of integration on very coarse grids where asymptotic error estimates cannot be applied.

The 4He Trimer: Structure and Energetics of a Very Unusual Molecule

2003 ◽  
Vol 68 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Cono Di Paola ◽  
Franco A. Gianturco ◽  
Gerardo Delgado-Barrio ◽  
Salvador Miret-Artés ◽  
Pablo Villarreal
Keyword(s):  
Monte Carlo ◽  
Stochastic Analysis ◽  
Binding Energies ◽  
Geometric Constraints ◽  
Spatial Density ◽  
Spatial Distributions ◽  
Diffusion Monte Carlo ◽  
Density Distributions ◽  
Total Binding ◽  
Full Interaction

The 4He3 weakly interacting system is analysed by constructing the full interaction as a sum of two-body (2B) potentials chosen among the most recent proposals from the literature. The spatial density distributions of the three bound atoms are obtained using a diffusion Monte Carlo (DMC) algorithm and a stochastic analysis under specific geometric constraints is carried out with the resulting densities in order to recover a more conventional structural picture for such floppy system. The total binding energies were obtained with the chosen potentials analysed in the present work, using the DMC algorithm, and are compared with previous published results. The ensuing spatial distributions are analysed in some detail to select the dominant structures from a conventional triangular description of this very floppy molecule.

scholarly journals New Families of Bivariate Copulas via Unit Lomax Distortion

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 106
Author(s):  
Fadal Abdullah-A Aldhufairi ◽  
Ranadeera G.M. Samanthi ◽  
Jungsywan H. Sepanski
Keyword(s):  
Random Variable ◽  
Copula Function ◽  
Unit Interval ◽  
Copula Model ◽  
Copula Models ◽  
Density Distributions ◽  
New Family ◽  
Concordance Order ◽  
Bivariate Copula

This article studies a new family of bivariate copulas constructed using the unit-Lomax distortion derived from a transformation of the non-negative Lomax random variable into a variable whose support is the unit interval. Existing copulas play the role of the base copulas that are distorted into new families of copulas with additional parameters, allowing more flexibility and better fit to data. We present general forms for the new bivariate copula function and its conditional and density distributions. The properties of the new family of the unit-Lomax induced copulas, including the tail behaviors, limiting cases in parameters, Kendall’s tau, and concordance order, are investigated for cases when the base copulas are Archimedean, such as the Clayton, Gumbel, and Frank copulas. An empirical application of the proposed copula model is presented. The unit-Lomax distorted copula models outperform the base copulas.

scholarly journals Asymptotically accurate error estimates of exponential convergence for the trapezoidal rule

2021 ◽  
Vol 29 (3) ◽  
pp. 251-259
Author(s):  
Aleksandr A. Belov ◽  
Valentin S. Khokhlachev
Keyword(s):  
Error Estimates ◽  
Complex Plane ◽  
Special Functions ◽  
Integral Form ◽  
Rounding Errors ◽  
Efficient Calculation ◽  
Full Period ◽  
Laplace Transformations ◽  
Coarse Grids ◽  
Integrand Function

In many applied problems, efficient calculation of quadratures with high accuracy is required. The examples are: calculation of special functions of mathematical physics, calculation of Fourier coefficients of a given function, Fourier and Laplace transformations, numerical solution of integral equations, solution of boundary value problems for partial differential equations in integral form, etc. For grid calculation of quadratures, the trapezoidal, the mean and the Simpson methods are usually used. Commonly, the error of these methods depends quadratically on the grid step, and a large number of steps are required to obtain good accuracy. However, there are some cases when the error of the trapezoidal method depends on the step value not quadratically, but exponentially. Such cases are integral of a periodic function over the full period and the integral over the entire real axis of a function that decreases rapidly enough at infinity. If the integrand has poles of the first order on the complex plane, then the Trefethen-Weidemann majorant accuracy estimates are valid for such quadratures. In the present paper, new error estimates of exponentially converging quadratures from periodic functions over the full period are constructed. The integrand function can have an arbitrary number of poles of an integer order on the complex plane. If the grid is sufficiently detailed, i.e., it resolves the profile of the integrand function, then the proposed estimates are not majorant, but asymptotically sharp. Extrapolating, i.e., excluding this error from the numerical quadrature, it is possible to calculate the integrals of these classes with the accuracy of rounding errors already on extremely coarse grids containing only 10 steps.

Probabilistic Selection of Ship-Ship Collision Scenarios

2013 ◽  
Author(s):  
Samy A. M. Youssef ◽  
Jeom K. Paik ◽  
Yang Seop Kim ◽  
Min Soo Kim ◽  
Fai Cheng
Keyword(s):  
Sampling Technique ◽  
Random Variable ◽  
Quantitative Risk Assessment ◽  
Design Stage ◽  
Density Distributions ◽  
Design Loads ◽  
Ship Collision ◽  
Accident Scenarios ◽  
Probability Density Distributions ◽  
Double Hull

Within the framework of quantitative risk assessment and management in the design stage, it is essential to select relevant sets of accidental scenarios, while a huge number of possible scenarios are obvious. The current industry practices are likely based on prescriptive approaches for the most unfavorable accidental scenarios. However, these approaches are often inadequate for obvious reasons because they may result in too large values of design loads in some cases but they may underestimate design loads in other cases. In the present study, an innovative method using probabilistic approaches is suggested to select relevant sets of ship-ship collision accident scenarios which represent all possible ones. Historical database for each of individual collision parameters which is dealt with as a random variable have been collated and are analyzed by statistical methods to characterize the probability density distributions. A sampling technique is then applied to select collision scenarios. Applied examples to a double hull oil tanker are presented to demonstrate the applicability of the developed method.

scholarly journals Risk of exposure of farms and subsistence nurseries to contact with wild boar in southern Mato Grosso do Sul

2019 ◽  
Vol 39 (2) ◽  
pp. 148-154 ◽  
Author(s):  
Paulo H. Braz ◽  
Maxwell R. Oliveira ◽  
Virgínia S. Silva ◽  
Walfrido M. Tomas ◽  
Raquel S. Juliano ◽  
...  
Keyword(s):  
Wild Boar ◽  
Production Systems ◽  
High Reliability ◽  
Classical Swine Fever ◽  
The State ◽  
Pest Species ◽  
Monitoring And Control ◽  
Mato Grosso ◽  
Commercial Farms ◽  
Mato Grosso Do Sul

ABSTRACT: With the advancement of wild boar distribution in the rural environment, its impacts are not limited to health in the pig sector, but the requirements for monitoring and control of the species are requirements laid down by the OIE for the recognition of classical swine fever free zone status. The construction of ecological models of favorability or suitability for the occurrence of pest species are necessary tools for the decision making on priority areas of management aiming at risk management. This work aims to map the level of suitability for the occurrence of wild boar in the southern state of Mato Grosso do Sul, as well as to identify the main risk variables for contact with the wild boar and evaluate the biosecurity measures adopted by commercial farms integrated in the south of the State of Mato Grosso do Sul. To evaluate the risk potential of wild boar for commercial and subsistence swine farming in southern Mato Grosso do Sul, a model of environmental suitability was constructed for this species in the swine producing region. This model considered different environmental strata, being the selection of the layers considered the physiological and behavioral characteristics of the species. In parallel, interviews were carried out in a sample of commercial farms integrating the region to survey the perception of the presence of the invasive species and the biosafety measures adopted. The results of this work indicate that the risk of contact among wild boars and animals reared in closed production systems may be high in the study area and only establishment of appropriate biosecurity measures that consider the characteristics and habits of the boar may prevent the intrusion of this species and contact with domestic swine. The built model can be considered of high reliability and it is recommended to apply it to other areas of the state, being a useful tool for the productive sector, environmental agencies and decision makers.

A generalized Potts model for confocal microscopy images

2015 ◽  
Vol 29 (08) ◽  
pp. 1550048
Author(s):  
Gabriell Máté ◽  
Dieter W. Heermann
Keyword(s):  
Confocal Microscopy ◽  
Potts Model ◽  
Ground Truth ◽  
Spatial Density ◽  
Model Parameters ◽  
Generative Process ◽  
Density Distributions ◽  
Real Cell ◽  
Microscopy Images

Much as being among the least invasive mainstream imaging technologies in life sciences, the resolution of confocal microscopy is limited. Imaged structures, e.g., chromatin-fiber loops, have diameters around or beyond the diffraction limit, and microscopy images show seemingly random spatial density distributions only. While such images are important because the organization of the chromosomes influences different cell mechanisms, many interesting questions can also be related to the observed patterns. These concern their spatial aspects, the role of randomness, the possibility of modeling these images with a random generative process, the interaction between the densities of adjacent loci, the length-scales of these influences, etc. We answer these questions by implementing a generalization of the Potts model. We show how to estimate the model parameters, test the performance of the estimation process and numerically prove that the obtained values converge to the ground truth. Finally, we generate images with a trained model and show that they compare well to real cell images.

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