Higher-order Kernels Research Articles

비간섭 전력 부하 감시용 고차 적률 특징을 갖는 전력 신호 인식

A pattern recognition (PR) system is addressed for non-intrusive load monitoring. To effectively recognize two appliances (for example, an electric iron and a cook top), we propose a novel feature extraction method based on high order moments of power signals. Simulation results confirm that the PR system with the proposed high order moment features and kernel discriminant analysis can effectively separate two appliances.

Obtaining Spectrum Matching Time Series Using a Reweighted Volterra Series Algorithm (RVSA)

In this paper, we introduce a novel algorithm for morphing any accelerogram into a spectrum matching one. First, the seed time series is re-expressed as a discrete Volterra series. The first-order Volterra kernel is estimated by a multilevel wavelet decomposition using the stationary wavelet transform. Second, the higher-order Volterra kernels are estimated using a complete multinomial mixing of the first-order kernel functions. Finally, the weighting of every term in this Volterra series is optimally adapted using a Levenberg–Marquardt algorithm such that the modified time series matches any target response spectrum. Comparisons are made using the SeismoMatch algorithm, and this reweighted Volterra series algorithm is demonstrated to be considerably more robust,matching the target spectrum more faithfully. This is achieved while qualitatively maintaining the original signal’s non-stationary statistics, such as general envelope, time location of large pulses, and variation of frequency content with time.

Non-parametric kernel estimation for the ANOVA decomposition and sensitivity analysis

In this paper, we consider the non-parametric estimation of the analysis of variance (ANOVA) decomposition, which is useful for applications in sensitivity analysis (SA) and in the more general emulation framework. Pursuing the point of view of the state-dependent parameter (SDP) estimation, the non-parametric kernel estimation (including high order kernel estimator) is built for those purposes. On the basis of the kernel technique, the asymptotic convergence rate is theoretically obtained for the estimator of sensitivity indices. It is shown that the kernel estimation can provide a faster convergence rate than the SDP estimation for both the ANOVA decomposition and the sensitivity indices. This would help one to get a more accurate estimation at a smaller computational cost.

Proper orthogonal decomposition-based spectral higher-order stochastic estimation

A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two well-established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis. The latter of these is based on known methods for characterizing nonlinear systems by way of Volterra series. In that, both linear and higher-order kernels are formed to quantify the spectral (nonlinear) transfer of energy between the system's input and output. This reduces essentially to spectral Linear Stochastic Estimation when only first-order terms are considered, and is therefore presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation (HOSE). The trade-off to seeking higher-order transfer kernels is that the increased complexity restricts the analysis to single-input/output systems. Low-dimensional (POD-based) analysis techniques are inserted to alleviate this void as POD coefficients represent the dynamics of the spatial structures (modes) of a multi-degree-of-freedom system. The mathematical framework behind this POD-based HOSE method is first described. The method is then tested in the context of jet aeroacoustics by modeling acoustically efficient large-scale instabilities as combinations of wave packets. The growth, saturation, and decay of these spatially convecting wave packets are shown to couple both linearly and nonlinearly in the near-field to produce waveforms that propagate acoustically to the far-field for different frequency combinations.

Combinations of High Order Gaussian Kernel Estimator with Simulation Historical of Value at Risk (VaR) Return Portfolio Measurement

Financial experts assume that measures the risk of financial asset returns generally have a normal distribution. Reality often shows asset returns are not normally distributed, so that the constraints and make it difficult to estimate the risk of taking the measurements. For it is necessary to develop methods of risk measurement, VaR on asset returns regardless of the form of distribution as a form of financial risk estimation. In this, research the size of the financial risk VaR calculation that will be developed in the form of High-order kernel estimator of VaR with historical simulation method approach. This method implements the VaR measurement and VaR sensitivity of the asset return data are first estimated using a combination of historical simulations and high-order kernel estimators. Test results obtained Portfolio Return value estimate VaR with Historical Simulation estimation methods and the combination of high order kernels increase with increasing order kernel estimates and tend to be larger than the Historical Simulation estimation methods. Statistical properties indicates that the value of symmetry (Skewness) data distribution is generally obtained values close to zero i.e. between values of 0.06 and 1.06, which means the portfolio return data distribution approximates the shape of a symmetrical distribution. Moderate slope values (the kurtosis) showed the highest value of -1.53, which means the value of the distribution of the portfolio return data are within the scope of normal distribution in which the kurtosis value for the normal distribution is 3. Test sensitivity of VaR portfolio return data shows that the assumption of 99% for a confidence level and a one-year time horizon, VaR at 4,396% a year means 252 days of hope in the risk by 11 days on market movements.

On estimation of mean and covariance functions in repeated time series with long-memory errors*

We consider kernel estimation of trend and covariance functions in models typically encountered in functional data analysis (FDA), with the modification that the random curves are perturbed by error processes that exhibit short- or long-range dependence. Uniform convergence of standardized maximal differences between estimated and true (trend and covariance) functions is established. For the covariance function, a transformation based on contrasts is proposed that does not require explicit trend estimation. Improved estimators can be obtained by using higher-order kernels.

A nonlinear convolution scheme to simulate bridge aerodynamics

A linear convolution scheme involving first-order (linear) kernels for linear bridge aerodynamics is first reviewed and the significance of the selection of proper input parameters is emphasized. Following the concept of nonlinear indicial response function, the linear convolution scheme is extended to the nonlinear convolution scheme involving higher-order (nonlinear) kernels for the treatment of nonlinear bridge aerodynamics using a “peeling-an-onion” type procedure. Utilizing an impulse function as input, a comprehensive kernel identification scheme is developed. A numerical example of a long-span suspension bridge is investigated to verify the fidelity of the proposed nonlinear convolution scheme.

SMALL BANDWIDTH ASYMPTOTICS FOR DENSITY-WEIGHTED AVERAGE DERIVATIVES

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (Econometrica 57, 1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels, and the standard errors are “robust” in the sense that they accommodate (but do not require) bandwidths that are smaller than those for which conventional standard errors are valid. Moreover, the results of a Monte Carlo experiment suggest that the finite sample coverage rates of confidence intervals constructed using the standard errors developed in this papercoincide (approximately) with the nominal coverage rates across a nontrivial range of bandwidths.

Higher-order kinetic expansion of quantum dissipative dynamics: Mapping quantum networks to kinetic networks

We apply a new formalism to derive the higher-order quantum kinetic expansion (QKE) for studying dissipative dynamics in a general quantum network coupled with an arbitrary thermal bath. The dynamics of system population is described by a time-convoluted kinetic equation, where the time-nonlocal rate kernel is systematically expanded of the order of off-diagonal elements of the system Hamiltonian. In the second order, the rate kernel recovers the expression of the noninteracting-blip approximation method. The higher-order corrections in the rate kernel account for the effects of the multi-site quantum coherence and the bath relaxation. In a quantum harmonic bath, the rate kernels of different orders are analytically derived. As demonstrated by four examples, the higher-order QKE can reliably predict quantum dissipative dynamics, comparing well with the hierarchic equation approach. More importantly, the higher-order rate kernels can distinguish and quantify distinct nontrivial quantum coherent effects, such as long-range energy transfer from quantum tunneling and quantum interference arising from the phase accumulation of interactions.

Higher-order Gaussian kernel in bootstrap boosting algorithm

The bootstrap boosting algorithm is a bias reduction scheme. The adoption of higher-order Gaussian kernel in a bootstrap boosting algorithm in kernel density estimation was investigated. The algorithm used the higher-order Gaussian kernel instead of the regular fixed kernels. A comparison of the scheme with existing fixed kernel methods indicated the results were better.

A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in \(\mathbb{R }^d\). For two-dimensional surfaces embedded in \(\mathbb{R }^3\), these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that appear in the PDEs are approximated using collocation. The method only requires nodes at “scattered” locations on the surface and the corresponding normal vectors to the surface. Additionally, it does not rely on any surface-based metrics and avoids any intrinsic coordinate systems, and thus does not suffer from any coordinate distortions or singularities. We provide error estimates for the kernel-based approximate surface derivative operators and numerically study the accuracy and stability of the method. Applications to different non-linear systems of PDEs that arise in biology and chemistry are also presented.

Adaptive Digital Predistortion for Wideband High Crest Factor Applications Based on the WACP Optimization Objective: A Conceptual Overview

This paper proposes a method of digital predistortion suitable for wideband high crest factor applications such as those encountered in DAB, DVB-T and WCDMA transmitters. The proposed method is advantageous for four main reasons. Firstly, it utilizes a reliable frequency domain measure of transmitter output nonlinearity, specifically the Weighted Adjacent Channel Power (WACP), as the objective for predistortion filter parameter estimation. This is in direct contrast to traditional approaches which utilize a time domain measure obtained via a full feedback path and potentially corrupted by gain and phase compensation error as well as ADC distortion. Secondly, the method models predistortion filter parameter estimation as a generic nonlinear mathematical optimization problem. This model assumes a nonconvex objective function and therefore utilizes both global and local optimization algorithms to achieve true global convergence. This is once again in direct contrast to traditional approaches which model predistortion filter parameter estimation as a linear regression problem. Such a model incorrectly assumes a convex error surface and therefore restricts itself to inadequate local optimization algorithms which unfortunately cannot guarantee true global convergence. Thirdly, the method's predistortion filter is a pruned Volterra Series with memory which utilizes a hybrid pruning strategy in order to keep high order kernels to a practically manageable size, suitable for optimization parameter estimation. Predistortion filter memory ultimately makes the method highly suited to wideband applications. Finally, predistortion filter parameter estimation does not require known test signals to be injected into the transmitter and therefore the technique is on-air adaptive. This means any transmitter using this method of digital predistortion will be both on-air and optimally linearized for its entire operational life. Preliminary results obtained from actual hardware are presented.

Identification of Quadratic Volterra System Using Random Multi-Tone Excitation

This paper presents a simplified method for the identification of quadratic Volterra systems. Since the higher order kernels often play a secondary role compared to the linear component of the system, it is worth establishing a balance between the calculation consumption of the higher order kernels and their effect on the model accuracy. The equivalent kernels are used to substitute original quadratic kernels, and therefore both the model complexity and identification computational requirement are significantly reduced. Then the identification algorithm based on least square minimization of model output error and random multi-tone excitation is designed. Simulations show this simplified method is of excellent generalization ability and has robustness against noise in output signals.

A Volterra series approach to the frequency domain analysis of non-linear viscous Burgers’ equation

In this paper, higher order frequency response functions, based on the Volterra series, are employed to characterise the input-output behaviour of the non-linear viscous Burgers’ equation subject to sinusoidal excitation. First, a formal Volterra series representation for each spatial location is derived for the solution of Burgers’ equation with a boundary condition as the input to the system. Then a systematic method is presented to obtain the higher order frequency kernels of the Volterra series at each spatial location by solving a series of ordinary differential equations. It is shown that the convergence region of the individual harmonics with respect to the magnitude of the input excitation can be estimated by using these higher order kernels. The frequency characteristics of Burgers’ equation is investigated and compared with numerical simulation.

Partition functions on the Euclidean plane with compact boundaries in conformal and non-conformal theories

In this paper we calculate the exact partition function for free bosons on the plane with lacunae. First the partition function for a plane with two spherical holes is calculated by matching exactly for the infinite set of Wilson coefficients in an effective world line theory and then performing the ensuing Gaussian integration. The partition is then re-calculated using conformal field theory techniques, and the equality of the two results is made manifest. It is then demonstrated that there is an exact correspondence between the Wilson coefficients (susceptibilities) in the effective field theory and the weights of the individual excitations of the closed string coherent state on the boundary. We calculate the partition function for the case of three holes where CFT techniques necessitate a closed form for the map from the corresponding closed string pants diagrams. Finally, it is shown that the Wilson coefficients for the case of quartic and higher order kernels, where standard CFT techniques are no longer applicable, can also be completely determined. These techniques can also be applied to the case of non-trivial central charges.

Canonical higher-order kernels for density derivative estimation

In this note we present νth-order kernel density derivative estimators using canonical higher-order kernels. These canonical rescalings uncouple the choice of kernel and scale factor. This approach is useful for selection of the order of the kernel in a data-driven procedure as well as for visual comparison of kernel estimates.

Modelling of nonlinear bridge aerodynamics and aeroelasticity: a convolution based approach

Innovative bridge decks exhibit nonlinear behaviour in wind tunnel studies which has placed increasing importance on the nonlinear bridge aerodynamics/aeroelasticity considerations for long-span bridges. The convolution scheme concerning the first-order kernels for linear analysis is reviewed, which is followed by an introduction to higher-order kernels for nonlinear analysis. A numerical example of a long- span suspension bridge is presented that demonstrates the efficacy of the proposed scheme.

Investigation of the temporal properties of the retina using the m-sequence

The mfERG provides a topographic map of function of the retina and has been used in numerous studies to identify macular, paramacular and peripheral retinal dysfunction. This study investigates the changes in response due to the presentation rate of the stimulus. Twenty subjects gave informed consent to take part in the study, which had local regional ethical committee approval. Only a single hexagon of 8° diameter was presented to reduce ambiguity when identifying the higher-order kernels (HOK). Six rates were tested using a 60-Hz CRT monitor by introducing blank (black ~0 cd/m2) filler frames (FF). The rates tested were 0FF; 1FF; 2FF; 4FF; 7FF; and 14FF. The first-order kernel had largest responses to the slower stimuli (4FF and above). HOK had largest amplitudes at faster rates with the second-order kernel peaking at 1FF. At rates with 4FF and slower, the higher-order kernels were indiscernible above the noise.

Second-order response Bethe-Salpeter equation

A Bethe-Salpeter equation for the three-particle correlation function is derived, representing a second-order response generalization of the usual Bethe-Salpeter equation. The equation can be solved formally, giving the three-particle correlation function in terms of the two-particle correlation function and many-body interaction kernels. The similarity to second-order response time-dependent density-functional theory can be used to improve the understanding of the higher-order exchange and correlation kernels of this theory. An exact expression for such a kernel is derived.

Transaction-Pattern-Based Anomaly Detection Algorithm for IP Multimedia Subsystem

The Internet Protocol (IP) multimedia subsystem (IMS) plays an important role when migrating to next-generation networks. Based on the all-IP network architecture, at least an IP address is assigned to user equipment for communication. It thus brings not only value-added services, but also security issues such as attacks and threats from traditional IP networks. This paper proposes a novel scheme to detect the anomaly attempts or attacks in an IMS core network. Our proposed scheme adopts the support vector machines (SVMs) technique as our data-mining module. We also utilize the high-order Markov kernel to enhance the detection and prediction rate in sequence calls. Furthermore, the detection algorithm and feature selection for SVM kernel are designed by utilizing IMS transaction patterns. It is proved that the proposed algorithm can efficiently filter out the anomaly attempts in an IMS core network.