A different view on the vector-valued empirical mode decomposition (VEMD)

The empirical mode decomposition (EMD) has achieved its reputation by providing a multi-scale time-frequency representation of nonlinear and/or nonstationary signals. To extend this method to vector-valued signals (VvS) in multidimensional (multi-D) space, a multivariate EMD (MEMD) has been designed recently, which employs an ensemble projection to extract local extremum locations (LELs) of the given VvS with respect to different projection directions. This idea successfully overcomes the problems of locally defining extrema of VvS. Different from the MEMD, where vector-valued envelopes (VvEs) are interpolated based on LELs extracted from the 1-D projected signal, the vector-valued EMD (VEMD) proposed in this paper employs a novel back projection method to interpolate the VvEs from 1-D envelopes in the projected space. Considering typical 4-D coordinates (3-D location and time), we show by numerical simulations that the VEMD outperforms state-of-art methods.Comment: 7th International Congress on Image and Signal Processing (CISP

Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs

This paper deals with linear-quadratic optimal control problems constrained by a parametric or stochastic elliptic or parabolic PDE. We address the (difficult) case that the state equation depends on a countable number of parameters i.e., on $\sigma_j$ with $j\in\N$, and that the PDE operator may depend non-affinely on the parameters. We consider tracking-type functionals and distributed as well as boundary controls. Building on recent results in [CDS1, CDS2], we show that the state and the control are analytic as functions depending on these parameters $\sigma_j$. We establish sparsity of generalized polynomial chaos (gpc) expansions of both, state and control, in terms of the stochastic coordinate sequence $\sigma = (\sigma_j)_{j\ge 1}$ of the random inputs, and prove convergence rates of best $N$-term truncations of these expansions. Such truncations are the key for subsequent computations since they do {\em not} assume that the stochastic input data has a finite expansion. In the follow-up paper [KS2], we explain two methods how such best $N$-term truncations can practically be computed, by greedy-type algorithms as in [SG, Gi1], or by multilevel Monte-Carlo methods as in [KSS]. The sparsity result allows in conjunction with adaptive wavelet Galerkin schemes for sparse, adaptive tensor discretizations of control problems constrained by linear elliptic and parabolic PDEs developed in [DK, GK, K], see [KS2]

An Optimization Based Empirical Mode Decomposition Scheme for Images

Bidimensional empirical mode decompositions (BEMD) have been developed to decompose any bivariate function or image additively into multiscale components, so-called intrinsic mode functions (IMFs), which are approximately orthogonal to each other with respect to the $\ell_2$ inner product. In this paper, a novel optimization problem is designed to achieve this decomposition which takes into account important features desired of the BEMD. Specifically, we propose a data-adapted iterative method which we call Opt-BEMD which minimizes in each iteration a smoothness functional subject to inequality constraints involving the strictly local extrema of the image. In this way, the method constructs a sparse data-adapted basis for the input function as well as an envelope in a mathematically stringent sense. Moreover, we propose an ensemble version of Opt-BEMD to strengthen its performance when applied to noise-contaminated images or images with only few extrema

A unique polar representation of the hyperanalytic signal

The hyperanalytic signal is the straight forward generalization of the classical analytic signal. It is defined by a complexification of two canonical complex signals, which can be considered as an inverse operation of the Cayley-Dickson form of the quaternion. Inspired by the polar form of an analytic signal where the real instantaneous envelope and phase can be determined, this paper presents a novel method to generate a polar representation of the hyperanalytic signal, in which the continuously complex envelope and phase can be uniquely defined. Comparing to other existing methods, the proposed polar representation does not have sign ambiguity between the envelope and the phase, which makes the definition of the instantaneous complex frequency possible.Comment: 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP

BPX-Preconditioning for isogeometric analysis

We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or Nurbs mapping which we assume to be regular. The numerical solution of the PDE is computed by means of tensor product B-splines mapped onto the physical domain. We construct additive multilevel preconditioners and show that they are asymptotically optimal, i.e., the spectral condition number of the resulting preconditioned stiffness matrix is independent of $h$. Together with a nested iteration scheme, this enables an iterative solution scheme of optimal linear complexity. The theoretical results are substantiated by numerical examples in two and three space dimensions

MULTISCALE ANALYSIS OF MULTIVARIATE DATA

For many applications, nonuniformly distributed functional data is given which lead to large–scale scattered data problems. We wish to represent the data in terms of a sparse representation with a minimal amount of degrees of freedom. For this, an adaptive scheme which operates in a coarse-to-fine fashion using a multiscale basis is proposed. Specifically, we investigate hierarchical bases using B-splines and spline-(pre)wavelets. At each stage a leastsquares approximation of the data is computed. We take into account different requests arising in large-scale scattered data fitting: we discuss the fast iterative solution of the least square systems, regularization of the data, and the treatment of outliers. A particular application concerns the approximate continuation of harmonic functions, an issue arising in geodesy

Пути модернизации канального исследовательского реактора ИВГ1.М

Рассмотрены варианты перевода реактора ИВГ.1М на топливо пониженного обогащения. Приведены результаты оценок основных нейтронно-физических параметров активной зоны модернизированного реактора ИВГ.1М. Сделан вывод о том, что в качестве нового вида топлива могут выступать уран-цирконевые твэлы с повышенной концентрацией урана в сердечнике и с обогащением по 235U до 20 %

An efficient ADI-solver for scattered data problems with global smoothing

For the approximate representation of large data sets over a parameter domain in ℝ2, many geological and other applications require the construction of surfaces which have minimal energy, i.e., minimal curvature. One way to achieve this is by solving a fourth order elliptic partial differential equation. Its discretization by a difference scheme makes it particularly easy to incorporate (appropriate approximations of) known data points. Because of the solution of the resulting symmetric linear system being the most CPU-demanding step, we investigate first the performance of a preconditioned conjugate gradient method with an SSOR and a RILU preconditioner. However, since the partial differential operator does not contain mixed derivatives, using an alternating-direction-implicit scheme (ADI method) which has been employed successfully in the past for second order problems, together with Cholesky factorization of the corresponding one-dimensional operators provides a fast and effective method for the problem at hand. The computational studies show that an instationary ADI method is superior to the above mentioned preconditioned conjugate gradient solvers both with respect to work load and accuracy of the solution. For the fourth order model problem considered in this paper, the instationary ADI method with Wachspress parameters results in a number of iterations that is essentially independent of the number of variables

Hold or sell? How capital gains taxation affects holding decisions

Investments with exit flexibility require decisions regarding both the investment and holding period. Because selling an investment often leads to taxable capital gains, which crucially depend on the duration of an investment, we investigate the impact of capital gains taxation on exit timing under different tax systems. We observed that capital gains taxation delays exit decisions but loses its decision relevance for very long holdings. Often the optimal exit time, which indicates the maximal present value of future cashflows, cannot be determined analytically. However, we identify the breakeven exit time that guarantees present values exceeding those of an immediate sale. While, after-taxes, an immediate sale is often optimal, long holding periods might also be attractive for investors depending on the degree of income and corporate tax integration. A classic corporate tax system often indicates holdings over more than 100 periods. By contrast, a shareholder relief system indicates the earliest breakeven exit time and thus the highest level of exit timing flexibility. Surprisingly, high retention rates are likely to accelerate sales under a classic corporate system. Additionally, the worst exit time, which should be avoided by investors, differs tremendously across tax systems. For an integrated tax system with full imputation, the worst time is reached earlier than under partial or non-integrated systems. These results could help to predict investors' behavior regarding changes in capital gains taxation and thus are of interest for both investors and tax policymakers. Furthermore, the results emphasize the need to control for the underlying tax system in cross-country empirical studies. (authors' abstract)Series: WU International Taxation Research Paper Serie