This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutations e.g., transpositions and 3-cycles.
For a certain class of Z²-actions, we provide a proof of a conjecture that the ratio of the Perron eigenvalues of the transfer matrices of the free boundary restrictions converge to the entropy of that action. Also, a novel method for computing the entropy of Z²-actions is conjectured.
We consider the problem of wireless spectrum management in cognitive wireless networks that maximizes the revenue for a spectrum operator. Specifically, we study the problem on how a wireless spectrum operator can optimally allocate its limited spectrum to various classes users/devices who pay differently for their spectrum per unit time....
Pardoxes in voting has been an interest of voting theorists since the 1800's when Condorcet demonstrated the key example of a voting paradox: voters with individually transitive rankings produce an election outcome which is not transitive. With Arrow's Impossibility Theorem, the hope of finding a fair voting method which accurately...
Counting problems are rich in opportunities for students to make meaningful mathematical connections and develop non-algorithmic thinking; their accessible nature and applications to computer science make counting problems a valuable part of mathematics curricula. However, students struggle in various ways with counting, and while previous studies have indicated that listing...