# tree

Monday, April 28, 2014 - 9:00am - 9:50am

Naoki Saito (University of California)

I will start describing some basics of the graph Laplacian eigenvectors of a given graph and their properties. In particular, I will describe the peculiar phase transition/localization phenomena of such eigenvectors observed on a certain type of graphs (e.g., dendritic trees of neurons). Then, I will describe how to construct wavelet packets on a given graph including the Haar-Walsh basis dictionary using the graph Laplacian eigenvectors. As an application of such basis dictionaries, I will discuss efficient approximation of functions given on graphs.

Tuesday, September 9, 2014 - 3:15pm - 4:05pm

The Turan number ex(n,H) of an r-graph H is the largest size of an n-vertex

r-graph that does not contain H. The famous Erdos-Sos conjectrure concerns the

Turan number of a tree T of k vertices. The difficulty lies in the fact that

there could be very different extremal families, disjoint cliques of sizes k-1

or in some cases a graph with (k-2)/2 vertices of degree n-1.

A hypergraph H is a hypergraph forest if its edges can be ordered as

r-graph that does not contain H. The famous Erdos-Sos conjectrure concerns the

Turan number of a tree T of k vertices. The difficulty lies in the fact that

there could be very different extremal families, disjoint cliques of sizes k-1

or in some cases a graph with (k-2)/2 vertices of degree n-1.

A hypergraph H is a hypergraph forest if its edges can be ordered as