Spectral methods have recently emerged as a powerful tool for dimensionality reduction and manifold learning. These methods use information contained in the eigenvectors of a data affinity (i.e., item-item similarity) matrix to reveal low dimensional structure in high dimensional data. The most popular manifold learning algorithms include Locally Linear Embedding, Isomap, and Laplacian Eigenmap...

Spectral methods have recently emerged as a powerful tool for dimensionality reduction and manifold learning. These methods use information contained in the eigenvectors of a data affinity (i.e., item-item similarity) matrix to reveal low dimensional structure in high dimensional data. The most popular manifold learning algorithms include Locally Linear Embedding, Isomap, and Laplacian Eigenmap...

In this paper we study the automorphisms group of some K3 surfaces which are double covers of the projective plane ramified over a smooth sextic plane curve. More precisely, we study the case of a K3 surface of Picard rank two such that there is a rational curve of degree d which is tangent to the sextic in d points. Introduction K3 surfaces which are double covers of the plane ramified over a ...

We investigate some relations between a generic immersion of a graph into the 2-space with small number of double points and the embeddings of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the 2-space. Specifically we prove: (1) An embedding of a graph obtained from a generic immersion of the graph with at most three doub...

The superficial similarity between the Chu construction and the Hyland-Tan double glueing construction G has been observed widely. This paper establishes a more formal mathematical relationship between the two. We show that double glueing on relations subsumes the Chu construction on sets: we present a full monoidal embedding of the category chu(Set,K) of biextensional Chu spaces over K into G(...

The strong embedding conjecture states that every 2-connected graph has a closed 2-cell embedding in some surface , i . e . an embedding that each face is bounded by a circuit in the graph . A graph is called k -crosscap embeddable if it can be embedded in the surface of non-orientable genus k . We confirm the strong embedding conjecture for 5-crosscap embeddable graphs . As a corollary , every...

Despite their relatedness, Dutch and German differ in the interpretation of a particular intonation contour, the hat pattern. In the literature, this contour has been described as neutral forDutch, and as contrastive forGerman. A recent study supports the idea that Dutch listeners interpret this contour neutrally, compared to the contrastive interpretation of a lexically identical utterance rea...

We present a generalised and improved version of the category attack on LSB steganography in JPEG images with straddled embedding path. It detects more reliably low embedding rates and is also less disturbed by double compressed images. The proposed methods are evaluated on several thousand images. The results are compared to both recent blind and specific attacks for JPEG embedding. The propos...

We use recent results on symplectic integration of Hamiltonian systems with constraints to construct symplectic integrators on cotangent bundles of manifolds by embedding the manifold in a linear space. We also prove that these methods are equivariant under cotangent lifts of a symmetry group acting linearly on the ambient space and consequently preserve the corresponding momentum. These result...

R. Thomas proved that the Hodge conjecture is essentially equivalent to the existence of a Thomas hyperplane section having only ordinary double points as singularities and such that the restriction of a given primitive Hodge class to it does not vanish. We show that the relations between the vanishing cycles associated to the ordinary double points of a Thomas hyperplane section have the same ...