A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Extrinsic Analog Synthesis using Piecewise Linear Current-Mode Circuits

A methodology is presented for the synthesis of analog circuits using piecewise linear (PWL) approximations. The function to be synthesized is divided into PWL segments such that each segment can be realized using elementary MOS current-mode programmable-gain circuits. A number of these elementary current-mode circuits when connected in parallel, it is possible to realize piecewise linear approximation of any arbitrary analog function with in the allowed approximation error bounds. Simulation results show a close agreement between the desired function and the synthesized output. The number of PWL segments used for approximation and hence the circuit area is determined by the required accuracy and the smoothness of the resulting function.

Some central limit theorems for doubly restricted partitions

Let P_{K, L}(N) be the number of unordered partitions of a positive integer N into K or fewer positive integer parts, each part not exceeding L. A distribution of the form

Ʃ/N≤x P_K,L(N)

is considered first. For any fixed K, this distribution approaches a piecewise polynomial function as L increases to infinity. As both K and L approach infinity, this distribution is asymptotically normal. These results are proved by studying the convergence of the characteristic function.

The main result is the asymptotic behavior of P_K,K(N) itself, for certain large K and N. This is obtained by studying a contour integral of the generating function taken along the unit circle. The bulk of the estimate comes from integrating along a small arc near the point 1. Diophantine approximation is used to show that the integral along the rest of the circle is much smaller.

基于Stewart平台六维力传感器的分区静态标定方法

基于Stewart平台的六维力传感器具有结构紧凑、刚度大、量程宽等特点,它在工业机器人、空间站对接等领域具有广泛的应用前景。好的标定方法是正确使用传感器的基础。由于基于Stewart平台的六维力传感器是一个复杂的非线性系统,所以采用常规的线性标定方法必将带来较大的标定误差从而影响其使用性能。标定的实质是,由测量值空间到理论值空间的映射函数的确定过程。由函数逼近理论可知,当只在已知点集上给出函数值时,可用多项式或分段多项式等较简单函数逼近待定函数。基于上述思想,本文将整个测量空间划分为若干连续的子测量空间,再对每个子空间进行线性标定,从而提高了整个测量系统的标定精度。实验分析结果表明了该标定方法有效。

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Component reliability estimations without field data

Maintenance activities in a large-scale engineering system are usually scheduled according to the lifetimes of various components in order to ensure the overall reliability of the system. Lifetimes of components can be deduced by the corresponding probability distributions with parameters estimated from past failure data. While failure data of the components is not always readily available, the engineers have to be content with the primitive information from the manufacturers only, such as the mean and standard deviation of lifetime, to plan for the maintenance activities. In this paper, the moment-based piecewise polynomial model (MPPM) are proposed to estimate the parameters of the reliability probability distribution of the products when only the mean and standard deviation of the product lifetime are known. This method employs a group of polynomial functions to estimate the two parameters of the Weibull Distribution according to the mathematical relationship between the shape parameter of two-parameters Weibull Distribution and the ratio of mean and standard deviation. Tests are carried out to evaluate the validity and accuracy of the proposed methods with discussions on its suitability of applications. The proposed method is particularly useful for reliability-critical systems, such as railway and power systems, in which the maintenance activities are scheduled according to the expected lifetimes of the system components.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Transient response of coupled non-linear non-conservative systems

This paper deals with an approximate method of analysis of non-linear, non-conservative systems of two degrees of freedom. The approximate equations for amplitude and phase are obtained by a generalized averaging technique based on the ultraspherical polynomial approximation. The method is illustrated by an example of a spring-mass-damper system.

Efficient probabilistic contingency analysis through a stability measure considering wind perturbation

The integration of stochastic wind power has accentuated a challenge for power system stability assessment. Since the power system is a time-variant system under wind generation fluctuations, pure time-domain simulations are difficult to provide real-time stability assessment. As a result, the worst-case scenario is simulated to give a very conservative assessment of system transient stability. In this study, a probabilistic contingency analysis through a stability measure method is proposed to provide a less conservative contingency analysis which covers 5-min wind fluctuations and a successive fault. This probabilistic approach would estimate the transfer limit of a critical line for a given fault with stochastic wind generation and active control devices in a multi-machine system. This approach achieves a lower computation cost and improved accuracy using a new stability measure and polynomial interpolation, and is feasible for online contingency analysis.

Kernels for large margin time-series classification

In this paper we propose a novel family of kernels for multivariate time-series classification problems. Each time-series is approximated by a linear combination of piecewise polynomial functions in a Reproducing Kernel Hilbert Space by a novel kernel interpolation technique. Using the associated kernel function a large margin classification formulation is proposed which can discriminate between two classes. The formulation leads to kernels, between two multivariate time-series, which can be efficiently computed. The kernels have been successfully applied to writer independent handwritten character recognition.

Can one electrochemically measure the statistical morphology of a rough electrode

We have developed a theory for an electrochemical way of measuring the statistical properties of a nonfractally rough electrode. We obtained the expression for the current transient on a rough electrode which shows three times regions: short and long time limits and the transition region between them. The expressions for these time ranges are exploited to extract morphological information about the surface roughness. In the short and long time regimes, we extract information regarding various morphological features like the roughness factor, average roughness, curvature, correlation length, dimensionality of roughness, and polynomial approximation for the correlation function. The formulas for the surface structure factors (the measure of surface roughness) of rough surfaces in terms of measured reversible and diffusion-limited current transients are also obtained. Finally, we explore the feasibility of making such measurements.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.