The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A si...

In this paper, we describe our model designed for automatic prediction of emotional impact of movies. Specifically, a two-stage learning framework is proposed. First, the dimensionality reduction techniques are employed to discover the key emotion information embedded in the original feature space. Specifically, we use a classical method principal component analysis (PCA) and a new algorithm bi...

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...

In this paper we present a semi-supervised sub-manifold discriminant analysis algorithm. To separate each sub-manifold constructed by each class, we define the within-manifold scatter, between-manifold scatter and total-manifold scatter matrices. The scatter matrices are robust to outlier and diverse-density clusters. Kernelization and direct non-linear embedding are also developed. Experimenta...

In this paper we address the question of representing the discriminant of an imaginary quadratic field with respect to the basis of a cyclotomic field. This representation allows us to parameterize new families of ordinary elliptic curves over finite prime fields suitable for pairing applications. In particular these curves have small discriminants greater than four and arbitrary embedding degr...

We further analyze the solutions to the Diophantine equations from which prime-order elliptic curves of embedding degrees k = 3, 4 or 6 (MNT curves) may be obtained. We give an explicit algorithm to generate such curves. We derive a heuristic lower bound for the number E(z) of MNT curves with k = 6 and discriminant D ≤ z, and compare this lower bound with experimental data.

numerical analyses have shown that successful flow simulations and the accuracy of solution noticeably depend on the number of nodes used in computational meshing. a suitable meshing should have the capability of adapting with main flow parameters. because the number of total nodes that can be used in numerical simulation is limited, making such grid for complex flows is almost difficult, if it...

A closed 2-cell embedding of a graph embedded in some surface is an embedding such that each face is bounded by a cycle in the graph. The strong embedding conjecture says that every 2-connected graph has a closed 2-cell embedding in some surface. In this paper, we prove that any 2-connected graph without V8 (the M obius 4-ladder) as a minor has a closed 2-cell embedding in some surface. As a c...

Network embedding is a classical task which aims to map the nodes of a network to lowdimensional vectors. Most of the previous network embedding methods are trained in an unsupervised scheme. Then the learned node embeddings can be used as inputs of many machine learning tasks such as node classification, attribute inference. However, the discriminant power of the node embeddings maybe improved...