It is an empirical observation that the Riemann zeta function can be well approximated in its critical strip using the Number-Theoretical Spin Chain. A proof of this would imply the Riemann Hypothesis. Here we relate that question to the one of spectral radii of a family of Markov chains. This in turn leads to the question whether certain graphs are Ramanujan. The general idea is to explain the...

This work is a tutorial on Shor's factoring algorithm by means of a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are reviewed. It is intended for non-specialists which have basic knowledge on undergraduate Linear Algebra.

I Given n students and n colleges, each with preferences over the other. Can we find a stable matching? I Stability: Don’t want to match c with s and c′ with s′ if c and s′ would prefer to switch to being matched with each other. I Yes! Propose and Reject Algorithm. I Algorithm terminates in n2 iterations I Everyone gets matched I Resulting matching is stable! Big-O: Motivation What is the runn...

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The eXtensible Markup Language (XML) is a World Wide Web Consortium (W3C) recommendation which has widely been used in both commerce and research. As the importance of XML documents increase, the need to deal with these documents increases as well. This chapter illustrates the methodology that has been used throughout the research, discussing all its parts and how these parts were adopted in th...