The kth power of a cycle is obtained by adding an edge between all pairs of vertices whose distance on the cycle is at most k. In 1962, Pósa conjectured that a graph G on n vertices contains a square of a Hamilton cycle if it has minimum degree δ(G) ≥ 3 n, and, 11 years later, Seymour claimed that δ(G) ≥ k k+1 n is sufficient for the appearance of a kth power of a Hamilton cycle for any k ≥ 2. ...

Cluster analysis is the name for a group of multivariate techniques whose primary purpose is to group objects based on the characteristics they possess. Clustering has been applied in many contexts and by researchers in many disciplines. This reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. In this thesis I explore cluster analysis as a means to investi...

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We study the well known vertex cover problem in various data streaming settings. Our first result considers a special family of graphs, the Vertex-Disjoint Paths (V DP ) family. We say that a graph G is in the V DP family if the edges of G are a union of vertex disjoint paths. For a V DP graph with n vertices given in a dynamic stream, in which both insertions and deletions are allowed, we prov...

We present a new method for score-informedsource separation, combining ideas from twoprevious approaches: one based on paramet-ric modeling of the score which constrains theNMF updating process, the other based onPLCA that uses synthesized scores as priorprobability distributions. We experimentallyshow improved separation results using theBSS EVAL and PEASS toolk...

At present, corporate social responsibility has become an important area of modern corporate research theory, and the development of CSR activities all over the world is remarkable. While the relationship between corporate social responsibility and corporate financial performance is still ambiguous. This study reviewed the development of corporate social responsibility and literatures which foc...