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Simulation of Lottery Games: Maximum Time Until a Number Appears
CS-A-01
Yaron Iluz; yaroniluz6@gmail.com
Advisor: Dr. Dina Barak-Pelleg
SCE - Shamoon College of Engineering, Be’er-Sheva
This project simulated a lottery game, where a player randomly draws r distinct numbers from a set of s numbers. We explored the waiting time until a specific number appeared, with a focus on the maximum waiting time among all numbers. The study included designing and verifying simulation of the process, analyzing its efficiency, and comparing naive and improved algorithms. We also estimated theoretical values, such as the expected maximum waiting time, and compared them with the simulated results. Finally, we studied the asymptotic distribution of the waiting time for a fixed number.
Keywords: applied probability, lottery tickets, simulations
Efficiency Comparison of Algorithms for Reducing Brauer Tree Algebras
CS-A-02
Nuzha Enadin; nuzhaem@ac.sce.ac.il
Advisor: Dr. Zehava Zvi
SCE - Shamoon College of Engineering, Be’er-Sheva
Brauer tree algebras are important fundamental building blocks in the modular representation theory of groups. Aihara developed an algorithm, referred to as mutation reduction, for transforming a Brauer tree algebra into the simpler Brauer star algebra by using a sequence of edge-centered mutations. Zvi developed a separate algorithm that assigns a natural numbering to the Brauer star algebra. In this project, we applied computer science tools to test both of these algorithms, in order to determine which is more efficient. The comparison was based on two criteria: the naturalness of the numbering, and the minimal number of steps required to reach the Brauer star.
Keywords: Brauer tree algebras, efficiency algorithm, mutations on Brauer trees