With the rise in prominence of high dimensional data, multivariate measures of center have become very important. In this paper we focus on one multivariate measure of center the geometric median, which is defined as the minimizer of the sum of distances to the data points. We study the quantitative robustness of the geometric median. Showing that for a non-degenerate distribution of N points, ...

This paper proposes a holographic blind watermarking algorithm of the three-dimensional mesh model based on QR decomposition. Firstly the three-dimensional model is pre-processed by moving the model center to the coordinate origin and doing PCA analysis. Secondly the model’s geometric feature matrix is constructed by using the distance from the three-dimensional mesh model vortex to the model c...

In the Standard Model (SM), CP violation is described by the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix, V [1]. In particular an irreducible complex phase in the 3 × 3 mixing matrix is the source of all the SM CP violation. Measurements of time-dependent CP asymmetries in the B meson decays, through the interference between decays with and without B −B0 mixing, have provides stringent ...

We usually think of a graph visually, i.e. we see vertices as points on a plane or in space, with edges as lines connecting them. When speci ed algebraically (e.g. by its adjacency matrix), the geometrical association is not present. Can we nd a natural embedding of a graph in the plane or in space given the adjacency matrix? This is the question for the lecture. It will turn out that such an e...

We usually think of a graph visually, i.e. we see vertices as points on a plane or in space, with edges as lines connecting them. When speci ed algebraically (e.g. by its adjacency matrix), the geometrical imagery is lost. Can we nd a natural embedding of a graph in the plane or in space given the adjacency matrix? This is the question for the lecture. It will turn out that such an embedding ca...

Consider I ⊂ C[x1, . . . , xm], a zero dimensional complete intersection ideal, with I = (f1, . . . , fm). Assume that I has clusters of roots, each cluster of radius at most ε in the ∞-norm. We compute the “approximate radical” of I, i.e. an ideal which contains one root for each cluster, corresponding to the center of gravity of the points in the cluster, up to an error term asymptotically bo...

Now a day’s number of medical images are generated in scan center. These are emerging tool to diagnose diseases. The storage of an image is an economical problem of scan center. Hence digital image compression is necessary in order to solve the problem. Normally during compression, loss of data is not acceptable. Hence the scan images have required high resolution and without any loss of data i...

Abstract In this paper, we employ compressive sensing (CS) to design a data gathering scheme for wireless sensor networks (WSNs) with transmit-only nodes, where plenty of transmit-only nodes are activated to perform the sensing task and their data are gathered at a sink center to monitor environment using the CS principle. Typically, in the research published methods based on CS and random chan...

The recently developed self-consistent charge Xa (SCCXa) method has been utilised to investigate various types of point-charge approximations to molecular expectation values. In the first' A A part observables of the structure m 1 (r) r' Y L (r) and a1 (r) r -'1 Y L (r), respectively, are analysed yielding the conclusion that, in general, only certain matrix elements can be treated by point-cha...

When space points and camera optical center lie on a twisted cubic, no matter how many corresponding pairs there are from space points to their image points, camera projection matrix cannot be uniquely determined, in other words, the configuration of camera and space points in this case is critical for camera parameter estimation. In practice, it is important to detect this critical configurati...