Transformation Kernel Research Articles

On the Kernel of a Hemispherical Funk Transformation and its Local Analogs

Functions on a sphere with zero weighted means over all geodesic balls of a fixed radius are studied. We obtain a description of such functions in the form of series in special functions.

A general framework for face reconstruction using single still image based on 2D-to-3D transformation kernel

Face authentication is a biometric classification method that verifies the identity of a user based on image of their face. Accuracy of the authentication is reduced when the pose, illumination and expression of the training face images are different than the testing image. The methods in this paper are designed to improve the accuracy of a features-based face recognition system when the pose between the input images and training images are different. First, an efficient 2D-to-3D integrated face reconstruction approach is introduced to reconstruct a personalized 3D face model from a single frontal face image with neutral expression and normal illumination. Second, realistic virtual faces with different poses are synthesized based on the personalized 3D face to characterize the face subspace. Finally, face recognition is conducted based on these representative virtual faces. Compared with other related works, this framework has the following advantages: (1) only one single frontal face is required for face recognition, which avoids the burdensome enrollment work; and (2) the synthesized face samples provide the capability to conduct recognition under difficult conditions like complex pose, illumination and expression. From the experimental results, we conclude that the proposed method improves the accuracy of face recognition by varying the pose, illumination and expression.

HPC Benchmark Assessment with Statistical Analysis

High-performance computing (HPC) benchmarks are widely used to evaluate and rank system performance. This paper introduces a benchmark assessment tool equipped with a rigorous statistical method to evaluate HPC benchmarks against a set of scientific applications. The method is based on the combination of Variable Clustering (VarCluster) and Principal Component Analysis (PCA). We built the tool upon HPC Challenge (HPCC) benchmark suite and six popular scientific applications of Kraken, a petaflop supercomputer. Experimental results show that HPCC's Fast Fourier Transform (FFT) kernel, rather than the High-Performance Linpack (HPL) on which Top500 is based, is more representative of the HPC workloads on Kraken.

A Hyper-solution SVM Classification Framework: Application to On-line Aircraft Structural Health Monitoring

Support Vector Machines (SVMs) classification learning is a powerful paradigm to investigate inverse input-output relationship of a specific problem according to some available and representative dataset. In particular, SVMs are able to identify even non-linear relationship by mapping non-linearly separable data into potentially linearly separable one through families of spatial transformation (kernel trick). With respect to this, several parameters (i.e., kernel function and its internal parameters) have to be tuned; however the optimal configuration is usually difficult to be defined a-priori.In this paper, a hyper-solution framework for SVM classification is presented. The main idea is to perform, simultaneously, three different SVM-based classification learning tasks: Model Selection, Multiple Kernel Learning and Ensemble Learning. The meta-heuristic known as Genetic Algorithms (GA) has been proposed to search for the most reliable final hyper-classifier (an SVM with a basic kernel, an SVM with a combination of kernel, or an ensemble of different SVMs, respectively), and the corresponding optimal configuration.We have applied the proposed framework on a critical and quite complex problem: the on-line assessment of structural health of aircraft fuselage panels, a crucial task both in military and civilian settings. In particular, the framework has been used to implement a diagnosis task, that is detecting a possible damage and identifying the structural component involved, according to the strain field measured through a monitoring sensor network deployed on the helicopter fuselage panels.Finite Elements (FE) simulation has been configured to simulate the response of a real panel to different damages. The resulting simulated strain fields have been used to build a dataset. Results obtained through 3 folds-cross validation proved the framework is reliable. Finally, when compared to results obtained by the authors in a previous work based on Artificial Neural Networks (ANN) classification learning paradigm, the proposed SVM framework proved to be more effective and reliable.

New approach to Q — P (P — Q) ordering of quantum mechanical operators and its applications

In this paper, we introduce a new way to obtain the Q — P (P — Q) ordering of quantum mechanical operators, i.e., from the classical correspondence of Q — P (P — Q) ordered operators by replacing q and p with coordinate and momentum operators, respectively. Some operator identities are derived concisely. As for its applications, the single (two-) mode squeezed operators and Fresnel operator are examined. It is shown that the classical correspondence of Fresnel operator's Q — P (P — Q) ordering is just the integration kernel of Fresnel transformation. In addition, a new photo-counting formula is constructed by the Q — P ordering of operators.

Automatic solution of integral equations describing electrochemical transients under conditions of internal spherical diffusion

Diffusion of reactants inside spherical spatial domains, in the absence of homogeneous reactions, is characteristic of some electrochemical systems, such as amalgam mercury drop electrodes. Simulation of transient experiments in such systems can be performed by the classical integral equation method [see, for example, R.S. Nicholson, I. Shain, Anal. Chem. 36 (1964) 706]. This requires an accurate computation of a specific integral transformation kernel function and its moment integrals. Based on formerly known series expansions, highly accurate (16 digits) and cost-optimised procedures serving for this purpose have been designed in this work. The procedures have been combined with the adaptive Huber method developed by the present author. The resulting simulation technique has been tested on simple examples of relevant integral equations, including models of potential step chronoamperometry and cyclic voltammetry. The method is shown to provide automatic solutions, with a user-selected target accuracy. Errors corresponding to the range from about 10-2 of the maximum solution value, down to about 10-7 or even smaller, can be easily obtained at a modest computational cost.

Automatic solution of the Singh and Dutt integral equations for channel or tubular electrodes, by the adaptive Huber method

Digital simulation of transient experiments at channel and tubular electrodes can be performed approximately but relatively cheaply, by means of the integral equation based approach introduced by Singh and Dutt [J. Electroanal. Chem. 182 (1985) 259]. Unfortunately, the use of the series expansion for the relevant integral transformation kernel, suggested by Singh and Dutt, makes such calculations overly slow. A new series expansion is proposed in the present study, which, when combined with the former expansion, yields inexpensive approximations to the kernel and its moment integrals. The relative error of these approximations is at the level of 10−16. The approximations are incorporated into the adaptive Huber method, developed by the present author. The method is shown to provide automatic solutions to the representative integral equations describing chronoamperometry for irreversible charge transfer and cyclic voltammetry for irreversible and reversible charge transfer. Desired accuracy of the solutions is selected simply by specifying a value of the error tolerance parameter. Errors corresponding to the range from about 10−2 of the maximum solution value, down to about 10−7 or even smaller, can be easily obtained at a modest computational cost.

Uniformly Consistency of the Cauchy-Transformation Kernel Density Estimation Underlying Strong Mixing

In this paper, one uses the idea of Cauchy-transformation to construct a Cauchy-transformation kernel density estimator underlying the condition of strong mixing. The uniformly strong consistency and convergence rates of the proposed estimator are obtained underlying the papers of Cai and Roussas (1) and Kim and Lee (6). The proposed estimator can improve the boundary effects of the empirical (or uniform)-transformation kernel density estimator in the boundary area. Besides, the proposed estimator can also be applied to estimate the hazard function.

A nonparametric approach to calculating value-at-risk

A method to estimate an extreme quantile that requires no distributional assumptions is presented. The approach is based on transformed kernel estimation of the cumulative distribution function (cdf). The proposed method consists of a double transformation kernel estimation. We derive optimal bandwidth selection methods that have a direct expression for the smoothing parameter. The bandwidth can accommodate to the given quantile level. The procedure is useful for large data sets and improves quantile estimation compared to other methods in heavy tailed distributions. Implementation is straightforward and R programs are available.

2M维矢量余弦整数变换核矩阵

To reduce the computation time of multidimensional data processing,a 2 M-dimensional vector integer Discrete Cosine Transformation(DCT) kernel matrix was proposed and the orthogonality and energy concentration of the integer transform kernel matrix were analyzed.First,according to the theory and properties of original floating-point 2 M-dimensional vector DCT transform kernel matrix,the algorithm for the 2 M-dimensional vector DCT integer transform kernel matrix was introduced and the orthogonality of 2 M-vector integer transform kernel matrix was validated.Then,the basic principles of blocking and reorganizing the *.yuv format video files were given.Finally,by taking the four order and eight order integer transform kernels as examples,the 2 M-dimensional vector integer transform kernel matrix was analyzed,namely,the energy concentration of multidimensional data after integer transform was discussed.The experimental results show that 2 M-vector transform relative floating-point transformation has good energy concentration.The average value of energy concentration for the Y component has reached more than 97.3%,and those for the U component and V component have been more than 99.9%.It concludes that the results will provide a strong basis for compression processing of multi-dimensional data.

Uniform in Bandwidth Law of the Iterated Logarithm for a Transformation Kernel Estimator of Copulas

In this paper, we establish a uniform in bandwidth law of the iterated logarithm for the Transformation kernel estimator of bivariate copulas introduced in Omelka et al. (2009). To this end, we make use of a general empirical process approach inspired by the works in Mason and Swanepoel (2011). We obtain the asymptotic order of the maximal deviation of this estimator from its expectation. Then, we show that the bias converges asymptotically to zero at the same order provided that the second-order partial derivatives of the copula exist and are bounded.We also propose a bandwidth selection method by using a cross-validation approach. Finally, we compare in a simulation study the performances of the Transformation kernel estimator by considering two different methods of selecting the bandwidth. Keywords: Copula function; Kernel estimation; Transformation estimator; Law of the iterated logarithm; Uniform in bandwidth consistency; Cross-validation method

Nonparametric Estimation of Value-at-Risk

A method to estimate an extreme quantile that requires no distributional assumptions is presented. The approach is based on transformed kernel estimation of the cumulative distribution function (cdf). The proposed method consists of a double transformation kernel estimation. We derive optimal bandwidth selection methods that have a direct expression for the smoothing parameter. The bandwidth can accommodate to the given quantile level. The procedure is useful for large data sets and improves quantile estimation compared to other methods in heavy tailed distributions. Implementation is straightforward and R programs are available.

Automatic simulation of electrochemical transients assuming finite diffusion space at planar interfaces, by the adaptive Huber method for Volterra integral equations

Integral equations describing controlled-potential transient experiments at planar interfaces, and under conditions of diffusion in one-dimensional finite space, occur in various areas of electrochemistry. Former simulation methods used to solve such equations were rather crudely approximate and non-automatic. In the present work computationally inexpensive approximations to the integral transformation kernels occurring in these equations are determined, that possess the best accuracy achievable within the standard floating point arithmetic. The approximations are combined with the recently developed adaptive Huber method for solving electrochemical integral equations of the Volterra type. The resulting algorithm is tested on representative examples of transient experiments: potential step chronoamperometry for irreversible electron transfer, and cyclic voltammetry for irreversible and reversible electron transfers. The performance of the method is found similar to that previously reported for integral equations involving kernels specific for semi-infinite diffusion. Desired accuracy of the solutions is achieved automatically, depending on user-selected values of the error tolerance parameter. Errors corresponding to the range from about 10−2 of the maximum solution value, down to about 10−7 or even smaller, can be easily achieved at a modest computational cost.

Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?

This paper analyzes whether the skew-normal and skew-student distributions recently discussed in the finance literature are reasonable models for describing claims in property-liability insurance. We consider two well-known datasets from actuarial science and fit a number of parametric distributions to these data. Also the non-parametric transformation kernel approach is considered as a benchmark model. We find that the skew-normal and skew-student are reasonably competitive compared to other models in the literature when describing insurance data. In addition to goodness-of-fit tests, tail risk measures such as value at risk and tail value at risk are estimated for the datasets under consideration.

Automatic solution of integral equations pertinent to diffusion with first order homogeneous reactions at cylindrical wire electrodes

The application of the integral equation method to the modelling of controlled-potential transient experiments at cylindrical wire or fibre electrodes under conditions of diffusion coupled with (pseudo-) first order homogeneous reactions, was not attempted thus far. One of the reasons is the lack of simple closed-form formulae for the relevant integral transformation kernels. The algorithm presented in this work allows one to compute accurately (at least 13–15 significant digits) moment integrals of the kernel that most frequently occurs in such cases. It is assumed that the cylinder length to radius ratio is very large. The algorithm is combined with the recently developed adaptive Huber method for solving electrochemical integral equations. The resulting method is tested on example integral equations, including the equations of cyclic voltammetry for the catalytic mechanism, for which no former simulation reports have been available. The method provides automatic solutions with an accuracy that can be effectively achieved by choosing an appropriate value of the error tolerance parameter. Errors as small as 10−6 (relative to the maximum solution value) or even smaller, are obtainable, at a moderate computational cost. In this way, a variety of integral equations pertinent to cylindrical wire electrodes can now be solved easily and reliably.

Extension of the adaptive Huber method for Volterra integral equations arising in electroanalytical chemistry, to convolution kernels exp [−α (t-τ)] erex {[β(t-τ)]1/2} and exp [−α(t-τ)] daw {[β(t-τ)]1/2}

Integral transformation kernels having convolution forms exp[-α(t -τ)]erex{[β(t - τ)]1/2} and exp[-α(t- τ)]daw{⌊β(t - τ)⌋1/2}, where erex(z) = exp(z2)erfc(z), daw(z) is the Dawson integral, and α ≥ 0 and β ≥ 0, occur in integral equations of Volterra type, pertinent to electroanalytical chemistry. An ability to solve this sort of integral equations has been added to the recently developed adaptive Huber method. Relevant formulae for the method coefficients are reported, and computational tests of the convergence and numerical stability of the method for these kernels are presented. Practical accuracy orders are close to 2. In cases when integral equations contain contributions from the kernel exp⌊- α(t - τ)⌋daw{[β(t - τ)]1/2}, such that the total kernels are increasing functions of t -τ, the method may become unstable. In cases when α > 0, β > 0, β/α ≫ 1 and integration steps are very small, β/α cannot exceed a certain threshold due to machine precision. Similarly, in the case of kernel exp[-α(t - τ)]erex{⌊β(t -τ)⌋l/2}, when α > 0, β > 0, α ≠ β, but α is very close to β, |β/α -1| cannot be smaller than a certain threshold.

Solution of the unitarity equation in cone variables on the SO(2,1) group in the approximation for small transverse momentum

A known mechanism of description of spatial characteristics of elastic and quasi-elastic processes in terms of irreducible representations of the SO(2,1) group is modified in cone variables. It takes place in the region where transverse momentum is small in comparison with the total momentum. The transformation kernel from the transverse momentum space to the escape parameter space is a Shapiro function. In the mentioned case, this kernel is substantially simplified, assuming exponential form. In spite of some approximations, the physical interpretation of amplitude expansion coefficients and the geometrical interpretation of the escape parameter space are completely retained. This allows us to solve the unitarity equation in a simple analytical form, but we do not confine our solution to the region of large impact parameters which is typical of the eikonal approximation.

Automatic simulation of electrochemical transients by the adaptive Huber method for Volterra integral equations involving Kernel terms exp[−α(t − τ)]erex{[β(t − τ)]1/2} and exp[−α(t − τ)]daw {[β(t − τ)]1/2}

Development of fully automatic methods for the simulation of transient experiments in electroanalytical chemistry is a desirable element of the contemporary trends of laboratory automation in electrochemistry. In accord with this idea, the adaptive Huber method, elaborated by the present author, is intended to solve automatically integral equations of Volterra type, encountered in the theory of controlled-potential transients. The coefficients of the method have been recently obtained for integral transformation kernels involving terms K(t, τ) = exp[−α(t − τ)]erex{[β(t − τ)]1/2} and K(t, τ) = exp[−α(t − τ)]daw{[β(t − τ)]1/2} with α ≥ 0 and β ≥ 0, which are known to occur in the above integral equations. In this work the validity of the resulting method, for electrochemical simulations, is examined using representative examples of electroanalytical models involving integral equations with various special cases of such kernel terms. The performance of the method is found similar to that previously reported for integral equations involving exclusively kernels K(t, τ) = 1, K(t, τ) = (t − τ)−1/2, and K(t, τ) = exp[−λ (t − τ)](t − τ)−1/2 with λ > 0.

A highly accurate, inexpensive procedure for computing integral transformation kernel and its moment integrals for cylindrical wire electrodes

Cylindrical wire or fiber electrodes are attractive for electro-analytical applications, but the theory of transient methods at such electrodes is complicated, necessitating approximate expressions or procedures for computing various special functions occurring in the theory. One of such functions is the integral transformation kernel function corresponding to semi-infinite pure diffusion conditions. In the present work a highly accurate and computationally inexpensive procedure for computing the cylindrical contribution to this kernel function is presented. The procedure relies on local polynomial approximations covering the entire argument domain, and it provides at least 14–15 significant digits. The procedure also computes qth order moment integrals of the kernel function (where q ⩾ 0 is a real number). The relative accuracy of 14–15 digits, of the moment integrals, has been verified for q = 0, 1 and 2. The procedure can be used in conjunction with numerical algorithms for the solution of integral equations or for the convolution analysis of experimental transients. It can also be used for the computation of chronopotentiometric responses to the programmed current density following the power-time dependence i( t) = i 0 t q with integer q ⩾ 0, which is shown as an example application.

Extension of the Adaptive Huber Method for Solving Integral Equations Occurring in Electroanalysis, onto Kernel Function Representing Fractional Diffusion

AbstractElectroanalytical transient experiments performed under conditions of anomalous diffusion have recently attracted some attention. In order to enable automatic simulation of such experiments in the framework of the formalism of integral equations, the adaptive Huber method, recently elaborated by the present author, is extended onto integral transformation kernel function K(t,τ)=(t−τ)α/2−1 (where 0<α≤1), representing fractional diffusion. The extended method is tested on a model integral equation describing cyclic voltammetry for a reversible charge transfer reaction. The performance of the method is found similar to the case of ordinary diffusion.