Every first countable pseudocompact Tychonoff space X has the property that every pseudocompact subspace of X is a closed subset of X (denoted herein by “FCC”). We study the property FCC and several closely related ones, and focus on the behavior of extension and other spaces which have one or more of these properties. Characterization, embedding and product theorems are obtained, and some exam...

In this paper, the necessary embedding dimension for electroencephologram(EEG) data is calculated. The tools used include a 1981 theorem from Floris Takens, and a subsequent extension of that theorem in 1991 given by Casdagli, Sauer and Yorke. These theorems give a method of reconstructing the phase space of the original system up to diffeomorphism using time-delays. If d is the original dimens...

The embedding dimension and the number of nearest neighbors are very important parameters in the prediction of a chaotic time series. In order to reduce the uncertainties in the determination of the forgoing two parameters, a new adaptive local linear prediction method is proposed in this study. In the new method, the embedding dimension and the number of nearest neighbors are combined as a par...

Record linkage is the problem of identifying similar records across different data sources. The similarity between two records is defined based on domain-specific similarity functions over several attributes. In this paper, a novel approach is proposed that uses a two level matching based on double embedding. First, records are embedded into a metric space of dimension K, then they are embedded...

We suggest an algorithm for determining the proper delay time and the minimum embedding dimension for Takens’ delay-time embedding procedure. This method resorts to the rate of change of the spatial distribution of points on a reconstructed attractor with respect to the delay time, and can be successfully applied to a noisy time series which is too noisy to be discriminated from a structureless...

1 Definitions An orbifold is a Hausdorff space X0 along with an open cover {Ui} that is closed under finite intersection with the following properties. For each Ui there is an open set Ũi ⊆ R and a finite group Γi which acts on Ũi. In addition there is a homeomorphism φi : Ui ≈ Ũi/Γi and whenever Ui ⊂ Uj there is an injective homomorphism fij : Γi ↪→ Γj and Ũi can be embedded in Ũj such that th...

Based on the principle that the selection of delay time and embedding dimension has no correlation in the process of phase space reconstruction, this paper puts forward a new method of identifying the embedding dimension by Cao Liangyue Theory (CAO Theory) after the delay time is identified by Mutual Information Function. By means of the numerical verification of a few typical examples of chaot...

In this paper, two significant weaknesses of locally linear embedding (LLE) applied to computer vision are addressed: ‘‘intrinsic dimension’’ and ‘‘eigenvector meanings’’. ‘‘Topological embedding’’ and ‘‘multi-resolution nonlinearity capture’’ are introduced based on mathematical analysis of topological manifolds and LLE. The manifold topological analysis (MTA) method is described and is based ...

We suggest an algorithm for determining the proper delay time and the minimum embedding dimension for Takens’ delay-time embedding procedure. This method resorts to the rate of change of the spatial distribution of points on a reconstructed attractor with respect to the delay time, and can be successfully applied to a noisy time series which is too noisy to be discriminated from a structureless...

We investigate the asymptotic behavior, as N grows, of the largest minimal pairwise distance of N points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal configurations. For this purpose, we compare best-packing configurations with minimal Riesz s-energy configurations and determine the s-th root asymptotic behavi...