In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

The key problem of inductive-learning in Bayes network is the estimator of prior distribution. This paper adopted general native Bayes to handle continuous variables, proposed a kind of kernel function constructed by orthogonal polynomials, which is used to estimate the density function of prior distribution in Bayes network. Paper then made further researches into optimality of kernel density ...

This paper provides a comparison. on three levels. of several promising data-driven methods for selecting the bandwidth of a kernel density estimator. The methods compared are: least squares cross-validation. biased cross-val idation. partitioned cross-val idation. and a plug-in rule. The levels of comparison are: asymptotic rate of convergence to the optimum, explici t calculation in the case ...

This paper presents an unsupervised, density-based approach to anomaly detection. The purpose is to define a smooth yet effective measure of outlierness that can be used to detect anomalies in nonlinear systems. The approach assigns each sample a local outlier score indicating how much one sample deviates from others in its locality. Specifically, the local outlier score is defined as a relativ...

The density capabilities of free-space optical interconnects are analyzed by applying Gabor's theory of information. It is shown that it is possible to increase the space-bandwidth product capabilities of space-variant interconnect schemes if they have symmetry properties. Several examples of such symmetries (locality, separability and smoothness) are discussed in detail, together with some exp...

The structure of non-Gaussian autoregressive schemes is described. Asymptotically efficient methods for the estimation of the coefficients of the models are described under appropriate conditions, some of which relate to smoothness and positivity of the density function f of the independent random variables generating the process. The principal interest is in nonminimum phase models.

In this talk it is shown a way for constructing magnetic surface sources for stationary axisymmetric electrovac spacetimes possessing a non-smooth electromagnetic Ernst potential. The magnetic moment density is related to this lack of smoothness and its calculation involves solving a linear elliptic differential equation. As an application the results are used for constructing a magnetic source...