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Full-Text Articles in Physical Sciences and Mathematics
On Elegance, Form, And Function: Exploring The Nexus Between Scientific Research And Movement Research, Naja N. Gordon
On Elegance, Form, And Function: Exploring The Nexus Between Scientific Research And Movement Research, Naja N. Gordon
Senior Projects Fall 2016
Live performance is an inimitable opportunity for a transfer of energy between viewer and performer. Through movement, I attempt to provide a foundation for this transfer. At the heart of my practice is a deep curiosity about movement as it relates to energy, a truly indestructible force. Moreover, systems need energy in order to function. When I think of a dance as a system, or a collection of dancers on stage as a system, the energy that feeds them is the energy that makes a composition .There is kinetic and potential energy within physical practice, incandescent energy from the lights, …
Random Walks On Thompson's Group F, Sarah C. Ghandour
Random Walks On Thompson's Group F, Sarah C. Ghandour
Senior Projects Fall 2016
In this paper we consider the statistical properties of random walks on Thompson’s group F . We use two-way forest diagrams to represent elements of F . First we describe the random walk of F by relating the steps of the walk to the possible interactions between two-way forest diagrams and the elements of {x0,x1}, the finite generating set of F, and their inverses. We then determine the long-term probabilistic and recurrence properties of the walk.
Envy-Free Fair Division With Two Players And Multiple Cakes, Justin J. Shin
Envy-Free Fair Division With Two Players And Multiple Cakes, Justin J. Shin
Senior Projects Fall 2016
When dividing a valuable resource amongst a group of players, it is desirable to have each player believe that their allocation is at least as valuable as everyone else's allocation. This condition, where nobody is envious of anybody else's share in a division, is called envy-freeness. Fair division problems over continuous pools of resources are affectionately known as cake-cutting problems, as they resemble attempts to slice and distribute cake amongst guests as fairly as possible. Previous work in multi-cake fair division problems have attempted to prove that certain conditions do not allow for guaranteed envy-free divisions. In this paper, we …
Exploring Tournament Graphs And Their Win Sequences, Sadiki O. Lewis
Exploring Tournament Graphs And Their Win Sequences, Sadiki O. Lewis
Senior Projects Fall 2016
In this project we will be looking at tournaments on graphs and their win sequences. The main purpose for a tournament is to determine a winner amongst a group of competitors. Usually tournaments are played in an elimination style where the winner of a game advances and the loser is knocked out the tournament. For the purpose of this project I will be focusing on Round Robin Tournaments where all competitors get the opportunity to play against each other once. This style of tournaments gives us a more real life perspective of a fair tournament. We will model these Round …