Sample Points In Space Research Articles

Effective and flexible modeling approach to investigate various 3D Talbot carpets from a spatial finite mask

We present an effective modeling approach for a fast calculation of the Talbot carpet from an initially 2-dimensional mask pattern. The introduced numerical algorithm is based on a modified angular-spectrum method, in which it is possible to consider the border effects of the Talbot region from a mask with a finite aperture. The Bluestein’s fast Fourier transform (FFT) algorithm is applied to speed up the calculation. This approach allows as well to decouple the sampling points in the real space and the spatial frequency domain so that both parameters can be chosen independently. As a result an extended three-dimensional Talbot-carpet can be calculated with a minimized number of numerical steps and computation time, but still with high accuracy. The algorithm was applied to various 2-dimensional mask patterns and illumination setups. The influence of specific mask patterns to the resulting field intensity distribution is discussed.

An Efficient Parameterized Mesh Method for Large Shape Variation in Optimal Designs of Electromagnetic Devices

An algorithm with parameterized mesh generation, refinement and morphing is presented for the optimal design of electromagnetic (EM) devices. The method can do without mesh regeneration when changing design parameters, hence a lot of computation time can be saved in finite element (FE) parameter sweeping analysis. When the design parameters change, a new mesh can be obtained immediately with this proposed technique by simply resetting the coordinates of the nodes in the parameterized mesh. For nonlinear problems, a good initial value can be obtained from the solution on the former mesh to facilitate fast convergence of the nonlinear iterations for subsequent computation. An efficient memory procedure dealing with the design parameters and a practical technique allowing for large shape variation are also presented in the proposed method. Based on the objective function values by post-processing the FE results when sweeping certain sampling points in the design space, an optimization problem can be reconstructed using the response surface methodology. The differential evolution method is used as an optimization solver to search for the optimal solution efficiently. The TEAM Workshop Problem 25 is used as an example to showcase the efficiency and effectiveness of the proposed method.

Atmospheric Tomography: A Bayesian Inversion Technique for Determining the Rate and Location of Fugitive Emissions

A Bayesian inversion technique to determine the location and strength of trace gas emissions from a point source in open air is presented. It was tested using atmospheric measurements of N(2)O and CO(2) released at known rates from a source located within an array of eight evenly spaced sampling points on a 20-m radius circle. The analysis requires knowledge of concentration enhancement downwind of the source and the normalized, three-dimensional distribution (shape) of concentration in the dispersion plume. The influence of varying background concentrations of ∼1% for N(2)O and ∼10% for CO(2) was removed by subtracting upwind concentrations from those downwind of the source to yield only concentration enhancements. Continuous measurements of turbulent wind and temperature statistics were used to model the dispersion plume. The analysis localized the source to within 0.8 m of the true position and the emission rates were determined to better than 3% accuracy. This technique will be useful in assurance monitoring for geological storage of CO(2) and for applications requiring knowledge of the location and rate of fugitive emissions.

SU‐E‐I‐166: Investigation and Development of Point‐Based Image Reconstruction Algorithm Capable of Handling Non‐Rigid Motion

Purpose: To evaluate PET image reconstruction algorithm capable of handling moving, deformable objects, particularly unrestrained conscious rodents. Methods: The proposed point‐based image reconstruction algorithm is based on 2D filtered back‐projection. Reconstruction took place in 2D virtual space filled with dimensionless sampling points. During the backprojection, points acted as spatial count bins, accumulating values of the backprojected LORs. To correct for motion, sampling points in the image space were moved in accord with the scanned object. Thus, motion correction and deformation correction were performed via image bin repositioning. After the backprojection step, images of activity distributions were obtained by fitting a smooth surface over the sampling points. Results: To evaluate the performance of the image reconstruction algorithm, stationary and moving NEMA image quality phantoms were scanned on Siemens Focus 120 microPET scanner, and data was reconstructed using conventional 2D filtered back‐projection and point‐based algorithms. Images obtained using two reconstruction algorithms were in remarkable quantitative agreement, with deviations mostly in the background and on the order of few percent. The location of points during reconstruction had little influence as long as Nyquist sampling criteria was satisfied. For the point‐ based reconstruction, motion‐corrected images preserved quantification and demonstrated good performance in removing the motion artifact. The SNR of motion‐corrected images also improved compared with shorter but motion‐free frames. Conclusions: It had been demonstrated that point reconstruction can provide accurate, quantitative PET images. As opposed to voxels, points can be moved freely relative to one another. By moving points during the backprojection process, almost any kind of deformation can be taken into account. Plans for the future include further method development of the method to enable full 3D list‐mode reconstruction, which could ultimately lead to unrestrained conscious rodent imaging.

Assessing the application of a geographic presence-only model for land suitability mapping

Recent advances in ecological modeling have focused on novel methods for characterizing the environment that use presence-only data and machine-learning algorithms to predict the likelihood of species occurrence. These novel methods may have great potential for land suitability applications in the developing world where detailed land cover information is often unavailable or incomplete. This paper assesses the adaptation and application of the presence-only geographic species distribution model, MaxEnt, for agricultural crop suitability mapping in a rural Thailand where lowland paddy rice and upland field crops predominant. To assess this modeling approach, three independent crop presence datasets were used including a social-demographic survey of farm households, a remote sensing classification of land use/land cover, and ground control points, used for geodetic and thematic reference that vary in their geographic distribution and sample size. Disparate environmental data were integrated to characterize environmental settings across Nang Rong District, a region of approximately 1300 sq. km in size. Results indicate that the MaxEnt model is capable of modeling crop suitability for upland and lowland crops, including rice varieties, although model results varied between datasets due to the high sensitivity of the model to the distribution of observed crop locations in geographic and environmental space. Accuracy assessments indicate that model outcomes were influenced by the sample size and the distribution of sample points in geographic and environmental space. The need for further research into accuracy assessments of presence-only models lacking true absence data is discussed. We conclude that the MaxEnt model can provide good estimates of crop suitability, but many areas need to be carefully scrutinized including geographic distribution of input data and assessment methods to ensure realistic modeling results.

Lattice Point Sets for Deterministic Learning and Approximate Optimization Problems

In this brief, the use of lattice point sets (LPSs) is investigated in the context of general learning problems (including function estimation and dynamic optimization), in the case where the classic empirical risk minimization (ERM) principle is considered and there is freedom to choose the sampling points of the input space. Here it is proved that convergence of the ERM principle is guaranteed when LPSs are employed as training sets for the learning procedure, yielding up to a superlinear convergence rate under some regularity hypotheses on the involved functions. Preliminary simulation results are also provided.

Multivariate irregular sampling theorem

In this paper, we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result, we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.

Edge Detection Based on Density Gradient

This paper proposes a new image edge detection algorithm based on the density gradient.The image pixels are taken as some sample points in the image sample space,and the image can be transformed into the density gradient field by density gradient estimation.In the density gradient field,all the density gradients point against the image edge.According this property,the new algorithm selects the points around which all the gradients point against them as the edge points.Comparing with other detectors,the edges detected by the new algorithm are invariant to the detection scales,and the object's boundary can be directly selected out by the new detector as their size.

A novel computational paradigm for creating a Triangular Irregular Network (TIN) from LiDAR data

The Triangular Irregular Network (TIN) model is an alternative to the grid-based representation of the terrain surface adopted in numerous digital mapping and geographic information systems. In TIN, irregularly spaced sample points model the terrain in such a way that more points represent the areas with rough terrain and there are fewer in smooth terrain. Despite its simplicity, creating a TIN model for an area involves (a) picking sample points, (b) connecting points into triangles, and (c) modeling the surface within each triangle. Most of the available algorithms for picking sample points use either a dense Digital Elevation Model (DEM) or a set of digitized contours as input. Now, the availability and popularity of Light Detection And Ranging (LiDAR) devices, which produce clouds of points, require the development of a new computational paradigm for picking sample points from the new data. This article presents a novel computational framework for picking sample points to create a TIN model from LiDAR data.

Gap‐phase dynamics and coexistence of a long‐lived pioneer and shade‐tolerant tree species in the canopy of an old‐growth coastal temperate rain forest of Chiloé Island, Chile

SummaryAim A major question with regard to the ecology of temperate rain forests in south‐central Chile is how pioneer and shade‐tolerant tree species coexist in old‐growth forests. We explored the correspondence between tree regeneration dynamics and life‐history traits to explain the coexistence of these two functional types in stands apparently representing a non‐equilibrium mixture.Location This study was conducted in northern Chiloé Island, Chile (41.6° S, 73.9° W) in a temperate coastal rain forest with no evidence of stand disruption by human impact.Methods We assessed stand structure by sampling all stems within two 50 × 20 m and four 5 × 100 m plots. A 600‐m long transect, with 20 uniformly spaced sampling points, was used to quantify seedling and sapling densities, obtain increment cores, and randomly select 10 tree‐fall gaps. We used tree‐ring analysis to assess establishment periods and to relate the influences of disturbances to the regeneration dynamics of the main canopy species.Results Canopy emergent tree species were the long‐lived pioneer Eucryphia cordifolia and the shade‐tolerant Aextoxicon punctatum. Shade‐tolerant species such as Laureliopsis philippiana and several species of Myrtaceae occupied the main canopy. The stem diameter distribution for E. cordifolia was distinctly unimodal, while for A. punctatum it was multi‐modal, with all age classes represented. Myrtaceae accounted for most of the small trees. Most tree seedlings and saplings occurred beneath canopy gaps. Based on tree‐ring counts, the largest individuals of A. punctatum and E. cordifolia had minimum ages estimated to be > 350 years and > 286 years, respectively. Shade‐tolerant Myrtaceae species and L. philippiana had shorter life spans (< 200 years). Most growth releases, regardless of tree species, were moderate and have occurred continuously since 1750.Main conclusions We suggest that this coastal forest has remained largely free of stand‐disrupting disturbances for at least 450 years, without substantial changes in canopy composition. Release patterns are consistent with this hypothesis and suggest that the disturbance regime is dominated by individual tree‐fall gaps, with sporadic multiple tree falls. Long life spans, maximum height and differences in shade tolerance provide a basis for understanding the long‐term coexistence of pioneer and shade‐tolerant tree species in this coastal, old‐growth rain forest, despite the rarity of major disturbances.

Point and interval estimation of accuracies of a binary medical diagnostic test following group sequential testing

When hypotheses concerning the sensitivity and specificity of a binary medical diagnostic test are simultaneously tested using a group sequential procedure, constructing point and interval estimates of the parameters is challenging because there is no unique way to order sample points in the two-dimensional space. In this paper, upon termination of a group sequential procedure, we compare the bias and mean squared errors of the maximum-likelihood and Rao-Blackwell unbiased estimators of sensitivity and specificity. Confidence intervals (CIs) of the two parameters were constructed using normal approximation and Woodroofe's pivot methods based on maximum-likelihood and Rao-Blackwell unbiased estimates. The coverage probability and the expected length of CIs for the parameters were compared by simulation studies.

Converting CSG models into meshed B-Rep models using euler operators and propagation based marching cubes

The purpose of this work is to define a new algorithm for converting a CSG representation into a B-Rep representation. Usually this conversion is done determining the union, intersection or difference from two B-Rep represented solids. Due to the lack of explicit representation of surface boundaries, CSG models must be converted into B-Rep solid models when a description based on polygonal mesh is required. A potential solution is to convert a CSG model into a voxel based volume representation and then construct a B-Rep solid model. This method is called CSG voxelization, conceptually it is a set membership classification problem with respect to the CSG object for all sampling points in a volume space. Marching cubes algorithms create a simple mesh that is enough for visualization purposes. However, when engineering processes are involved, a solid model is necessary. A solid ensures that all triangles in the mesh are consistently oriented and define a closed surface. It is proposed in this work an algorithm for converting CSG models into triangulated solid models through propagation based marching cubes algorithm. Three main new concepts are used in the algorithm: open boundary, B-Rep/CSG Voxelization mapping and constructive triangulation of active cells. The triangles supplied by the marching cubes algorithm need not be coherently oriented; the algorithm itself finds the correct orientation for the supplied triangles. The proposed algorithm restricts the exploration to the space occupied by the solid's boundary. Differently from normal marching cubes algorithms that explore the complete sampled space.

A Practical Routing and MAC Framework for Maximum Lifetime Sensor Telemetry

The recent progress in sensor and wireless communication technologies has enabled the design and implementation of new applications such as sensor telemetry which is the use of wireless sensors to gather more fine-grained information from products, people and places. In this work, we consider a realistic telemetry application in which a large 2-dimensional area is periodically monitored by a sensor network which gathers data from equally spaced sample points. The objective is to maximize the lifetime of the network by jointly selecting the sensing nodes, the node transmission powers and the route to the base station from each sensing node. We develop an optimization-based algorithm OPT-RE, and a low complexity algorithm SP-RE for this purpose, and analyze their dynamics through extensive numerical studies. Our results indicate that SP-RE is a promising algorithm which has comparable performance to that of the more computationally intensive OPT-RE algorithm. The energy consumption is significantly affected by the channel access method, and in this paper, we also compare the effects of the collision-free TDMA, and contention-based CSMA/CA methods.

Efficient sampling in approximate dynamic programming algorithms

Dynamic Programming (DP) is known to be a standard optimization tool for solving Stochastic Optimal Control (SOC) problems, either over a finite or an infinite horizon of stages. Under very general assumptions, commonly employed numerical algorithms are based on approximations of the cost-to-go functions, by means of suitable parametric models built from a set of sampling points in the d-dimensional state space. Here the problem of sample complexity, i.e., how "fast" the number of points must grow with the input dimension in order to have an accurate estimate of the cost-to-go functions in typical DP approaches such as value iteration and policy iteration, is discussed. It is shown that a choice of the sampling based on low-discrepancy sequences, commonly used for efficient numerical integration, permits to achieve, under suitable hypotheses, an almost linear sample complexity, thus contributing to mitigate the curse of dimensionality of the approximate DP procedure.

Multivariate Control Charts for Monitoring the Process Mean and Variability Using Sequential Sampling

Traditional control charts for process monitoring are based on taking samples of fixed size at equally spaced sampling points. As an alternative to these traditional fixed sampling rate (FSR) control charts, variable sampling rate (VSR) control charts change the sampling rate as a function of the data from the process. With VSR control charts the sampling rate is increased whenever there is some indication of a problem with the process, and decreased when there is no indication of a problem. This paper investigates a type of VSR control chart based on sequential sampling in which the sample size used at a sampling point is a function of the data from the current and past sampling points. Sequential sampling is investigated in the context of simultaneously monitoring both the mean and variability of a multivariate normal process. Multivariate exponentially weighted moving average (MEWMA) control charts based on sample means and on the sum of the squared deviations from the target are considered. When sequential sampling is used in a combination of the MEWMA charts based on sample means and on squared deviations from the target, the average performance is much better than that of the standard FSR multivariate control charts that have traditionally been used.

Fast methods for determining the evolution of uncertain parameters in reaction-diffusion equations

An important problem in mathematical modeling in science and engineering is the determination of the effects of uncertainty or variation in parameters and data on the output of a deterministic nonlinear operator. For example, such variations may describe the effect of experimental error in measured parameter values or may arise as part of a sensitivity analysis of the model. The Monte-Carlo method is a widely used tool for determining such effects. It employs random sampling of the input space in order to produce a pointwise representation of the output. It is a robust and easily implemented tool with relatively low dependence on the number of parameters. Unfortunately, it generally requires sampling the operator very many times at a significant cost, especially when the model is expensive to evaluate. Moreover, standard analysis provides only asymptotic or distributional information about the error computed from a particular realization. In this paper, we present an alternative approach for ascertaining the effects of variations and uncertainty in parameters in a reaction-diffusion equation on the solution. The approach is based on techniques borrowed from a posteriori error analysis for finite element methods. The generalized Green’s function solving the adjoint problem is used to efficiently compute the gradient of a quantity of interest with respect to parameters at sample points in the parameter space. This derivative information is used in turn to produce an error estimate for the information computed from the sample points. The error estimate provides the basis for both deterministic and probabilistic adaptive sampling algorithms. The deterministic adaptive sampling method can be orders of magnitude faster than Monte-Carlo sampling in case of a moderate number of parameters. The gradient can also be used to compute useful information that cannot be obtained easily from a Monte-Carlo sample. For example, the adaptive algorithm yields a natural dimensional reduction in the parameter space where applicable. After describing the new methodology in detail, we apply the new method to analyze the parameter sensitivity of a predator–prey model with a Holling II functional response that has six parameters.

보간법을 이용한 수치적분법의 평균 오차에 관한 연구

이 논문에서는 정적분의 근사 값을 계산하는 여러 적분 문제 중에서 보간 법을 사용하는 수치적분법의 평균오차에 대해서 연구한다. 특히 가장 널리 쓰이고 있는 방법 중의 하나인 복합 Newton-Cotes 구적법의 평균오차에 대해서 연구한다. 주어진 구간을 등 간격으로 나누었을 때, 각 점에서의 함수 값을 information으로 사용할 경우, 복합 Newton-Cotes 구적법의 평균오차를 계산하였으며, 이 때 이 오차는 가장 최소임을 이 논문에서 증명한다. Among many algorithms for the integration problems in which one wants to compute the approximation to the definite integral in the average case setting, we study the average case errors of numerical integration rules using interpolation. In particular, we choose the composite Newton-Cotes quadratures and the function values at equally spaced sample points on the given interval as information. We compute the average case error of composite Newton-Cotes quadratures and show that it is minimal(modulo a multiplicative constant).

Numerical estimation of densities

[Abridged] We present a novel technique, dubbed FiEstAS, to estimate the underlying density field from a discrete set of sample points in an arbitrary multidimensional space. FiEstAS assigns a volume to each point by means of a binary tree. Density is then computed by integrating over an adaptive kernel. As a first test, we construct several Monte Carlo realizations of a Hernquist profile and recover the particle density in both real and phase space. At a given point, Poisson noise causes the unsmoothed estimates to fluctuate by a factor ~2 regardless of the number of particles. This spread can be reduced to about 1 dex (~26 per cent) by our smoothing procedure. [...] We conclude that our algorithm accurately measure the phase-space density up to the limit where discreteness effects render the simulation itself unreliable. Computationally, FiEstAS is orders of magnitude faster than the method based on Delaunay tessellation that Arad et al. employed, making it practicable to recover smoothed density estimates for sets of 10^9 points in 6 dimensions.

Perfectly matched layer in numerical wave propagation: factors that affect its performance

The perfectly matched layer (PML) boundary condition is generally employed to prevent spurious reflections from numerical boundaries in wave propagation methods. However, PML requires additional computational resources. We have examined the performance of the PML by changing the distribution of sampling points and the PML's absorption profile with a view to optimizing the PML's efficiency. We used the collocation method in our study. We found that equally spaced field sampling points give better absorption of beams under both optimal and nonoptimal conditions for low PML widths. At high PML widths, unequally spaced basis points may be equally efficient. The efficiency of various PML absorption profiles, including new ones, has been studied, and we conclude that for better numerical efficiency it is important to choose an appropriate profile.

A study on the average case error of composite Newton-Cotes quadratures

We study the integration problem in which one wants to compute the approximation to the definite integral in the average case setting. We choose the composite Newton-Cotes quadratures as our algorithm and the function values at equally spaced sample points on the given interval [0,1] as information. We compute the average case error of composite Newton-Cotes quadratures and show that it is minimal (modulo a multiplicative constant).