A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction. It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to determine the time delay, which efficiently depresses the computing error caused by tracing arbitrarily the slop variation of average displacement (AD) in AD algorithm. Thereafter, ...

The Johnson-Lindenstrauss Lemma shows that any set of n points in Euclidean space can be mapped linearly down to O((log n)/ǫ) dimensions such that all pairwise distances are distorted by at most 1 + ǫ. We study the following basic question: Does there exist an analogue of the JohnsonLindenstrauss Lemma for the l1 norm? Note that Johnson-Lindenstrauss Lemma gives a linear embedding which is inde...

This paper considers the embeddability of general concept classes in Euclidean half spaces. By embedding in half spaces we refer to a mapping from some concept class to half spaces so that the labeling given to points in the instance space is retained. The existence of an embedding for some class may be used to learn it using an algorithm for the class it is embedded into. The Support Vector Ma...

introduction:in this study, ecg signals have been embedded into medical images to create a novel blind watermarking method. the embedding is done when the original image is compressed using the ezw algorithm. the extraction process is performed at the decompression time of the watermarked image. materials and methods: the multi-resolution watermarking with a secret key algorithm developed in th...

Suppose that we have the unit Euclidean ball in R and construct new bodies using three operations linear transformations, closure in the radial metric and multiplicative summation defined by ‖x‖K+0L = p ‖x‖K‖x‖L. We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of ...

Pursuing a line of work begun by Whitney, Nash showed that every C manifold of dimension d can be embedded in R in such a manner that the local structure at each point is preserved isometrically. We provide an analog of this result for discrete subsets of Euclidean space. For perfect preservation of infinitesimal neighborhoods we substitute near-isometric embedding of neighborhoods of bounded c...

Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have comparatively small dimension and the positive largest Lyapunov exponent

This paper proves that the self-similar set satisfying the strong separation condition can be bilipschitz embedded into self-similar set with larger Hausdorff dimension, and it can be embedded into a self-similar set with the same Hausdorff dimension if and only if these two self-similar sets are bilipschitz equivalent.

Suppose that we have the unit Euclidean ball in R and construct new bodies using three operations linear transformations, closure in the radial metric and multiplicative summation defined by ‖x‖K+0L = p ‖x‖K‖x‖L. We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of ...

O. Wyler [Notices Amer. Math. Soc. 15 (1968), 169. Abstract #653-306.] has given a Stone-Cech compactification for limit spaces. However, his is not necessarily an embedding. Here, it is shown that any Hausdorff limit space (X, t) can be embedded as a dense subspace of a compact, Hausdorff, limit space (Xi, ri) with the following property: any continuous function from (X, t) into a compact, Hau...