Cultural Capital: Challenges to New York State’s Competitive Advantages in the Arts and Entertainment Industry

This is a report on the findings of the Cornell University ILR planning process conducted with support of a grant from the Alfred P. Sloan Foundation to investigate trends in the arts and entertainment industry in New York State and assess industry stakeholders’ needs and demand for industry studies and applied research. Building on a track record of research and technical assistance to arts and entertainment organizations, Cornell ILR moved toward a long-term goal of establishing an arts and entertainment research center by forging alliances with faculty from other schools and departments in the university and by establishing an advisory committee of key players in the industry. The outcome of this planning process is a research agenda designed to serve the priority needs and interests of the arts and entertainment industry in New York State

Marshall University Music Department Presents a Senior Recital, featuring, Daniel Gray, baritone

https://mds.marshall.edu/music_perf/1748/thumbnail.jp

Graphical Indices and their Applications

The biochemical community has been using graphical (topological, chemical) indices in the study of Quantitative Structure-Activity Relationships (QSAR) and Quantitative Structure-Property Relationships (QSPR), as they have been shown to have strong correlations with the chemical properties of certain chemical compounds (i.e. boiling point, surface area, etc.). We examine some of these chemical indices and closely related pure graph theoretical indices: the Randić index, the Wiener index, the degree distance, and the number of subtrees. We find which structure will maximize the Randić index of a class of graphs known as cacti, and we find a functional relationship between the Wiener index and the degree distance for several types of graphs. We also develop an algorithm to find the structure that maximizes the number of subtrees of trees, a characterization of the second maximal tree may also follow as an immediate result of this algorithm

Trees with the most subtrees -- an algorithmic approach

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.Comment: 12 pages, 7 figures; Journal of combinatorics, 201