A new approach for data partitioning through high dimensional model representation

A multivariate function f(x ₁, …, x _N ) can be evaluated via interpolation if its values are given at a finite number nodes of a hyperprismatic grid in the space of independent variables x ₁, x ₂, …, x _N . Interpolation is a way to characterize an infinite data structure (function) by a finite number of data approximately. Hence it leaves an infinite arbitrariness unless a mathematical structure with finite number of flexibilities is imposed for the unknown function. Imposed structure has finite dimensionality. When the dimensionality increases unboundedly, the complexities grow rapidly in the standard methods. The main purpose here is to partition the given multivariate data into a set of low-variate data by using high dimensional model representation (HDMR) and then, to interpolate each individual data in the set via Lagrange interpolation formula. As a result, computational complexity of the given problem and needed CPU time to obtain the results through a series of programs in computers decrease.     

Finding better weight functions for generalized Shepard's operator on infinite intervals

In this paper, we investigate the difference of Shepard's generalized operators S _σ from the approximated set of data for various weight functions σ. Bounds are given for the sizes of the ‘bumps’ shown on the graph of S _σ for σ(d)=1/d in dimension N=1, and the best weight function σ for practical use is proposed.     

3D image interpolation based on anisotropic diffusion of feature point correspondence

An automatic method has been developed to interpolate between neighboring slices in a gray‐scale data set by anisotropic diffusion of feature point correspondence. The feature point extracted is registered to form the feature vector. Thus a three dimensional (3D) weight anisotropic vector diffusion is introduced to spread the feature vector to the correspondence vector, which estimates spatial correspondence between adjacent slices. Bilinear interpolation is made along the direction of correspondence vector. Experiments are performed on medical data sets to evaluate the proposed method, showing that the new algorithm achieves good quality and improvement in efficiency relative to the traditional methods. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 338–345, 2013     

Ribbon-based transfinite surfaces

One major issue in CAGD is to model complex objects using free-form surfaces of general topology. A natural approach is curvenet-based design, where designers directly create and modify feature curves. These are interpolated by smoothly connected, multi-sided patches, which can be represented by transfinite surfaces, defined as a combination of side interpolants or ribbons. A ribbon embeds Hermite data, i.e., prescribed positional and cross-derivative functions along boundary curves.The paper focuses on two transfinite schemes: the first is an enhanced and extended variant of a multi-sided generalization of the classical Coons patch (Várady et al., 2011); the second one is based on a new concept of combining doubly curved composite ribbons, each one interpolating three adjacent sides. Main contributions include various ribbon parameterizations that surpass former methods in quality and computational efficiency. It is proven that these surfaces smoothly interpolate the prescribed ribbon data. Both formulations are based on non-regular convex polygonal domains and distance-based, rational blending functions. A few examples illustrate the results.     

Computationally feasible narrow‐band antenna modeling using response features

Accurate and low‐cost models of input characteristics are of primary importance from the point of view of efficient design of antenna structures. Yet, the modeling problem is difficult because reflection responses are highly nonlinear functions of frequency and change considerably when adjusting antenna dimensions. Conventional approximation‐based models require massive datasets and often fail to provide required accuracy. This work demonstrates a possibility of dramatic reduction of the number of training samples, which is achieved by reformulating the modeling problem in a space of appropriately defined response features. The key factor is that dependence of feature point coordinates (both frequency and level) on antenna dimensions is less nonlinear than for the standard responses (S‐parameters vs. frequency). Our methodology permits construction of reliable surrogates using much smaller datasets than those required by conventional approaches. Experimental validation indicates that our models provide accuracy that is sufficient for practical antenna design.     

一种基于信息扩散理论的降雨空间插值方法

根据有限的雨量站观测资料进行空间插值是获取精确降雨空间分布信息的有效手段,基于信息扩散理论,建立了一种降雨量空间插值方法,并分别采用窗宽经验公式法、最优窗宽迭代法和粒子群优化3种算法对信息扩散函数中窗宽这一关键参数进行估计。以浙江省临安市雨量站月降雨量的插值计算为例,将3种算法应用于月降雨量资料的插值计算中,并将其插值效果与普通克里金方法进行比较。结果表明,使用粒子群优化算法估计窗宽参数的信息扩散函数插值方法显著优于其他方法,经验公式估计窗宽参数的信息扩散函数插值方法与普通克里金方法插值效果相当,使用最优窗宽迭代估计窗宽参数的信息扩散函数插值效果最差。     

An updated version of BoltzWann: A code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis

BoltzWann is a code to evaluate thermoelectric and electronic transport properties of extended systems with a maximally-localized Wannier function basis set. The semiclassical Boltzmann transport equations for the homogeneous infinite system are solved in the constant relaxation-time approximation and band energies and band derivatives are obtained via Wannier interpolations. Thanks to the exponential localization of the Wannier functions obtained, very high accuracy in the Brillouin zone integrals can be achieved with very moderate computational costs. Moreover, the analytical expression for the band derivatives in the Wannier basis resolves any issues that may occur when evaluating derivatives near band crossings. We present here an updated version of the BoltzWann code, which is now fully integrated within Wannier90 version 2.0, with minor bug fixes and the possibility to study also two-dimensional systems.     

基于多周循环步进式插值扫描轨迹的工业CT柔性检测技术研究

为了在一次CT检测过程中同时实现被检工件的精细检测与内部缺陷快速发现的两种检测需求，提出了一种新型CT检测方案。该方案将一种改进的圆形CT投影扫描轨迹与不完全投影插值算法有效融合，实现了投影采集与最优图像实时重建的同步进行。为验证该技术的可行性，设计了相应的扇束CT仿真平台及试验模体，仿真试验结果表明，该检测技术在CT扫描过程中可及时发现被检工件的内部缺陷，扫描结束后可获得工件的精细CT图像，有效满足了工业CT用户在多种检测目的之间自由切换的柔性检测需求。