Finding zeros of the Riemann zeta function by periodic driving of cold atoms

The Riemann hypothesis, which states that the non-trivial zeros of the Riemann zeta function all lie on a certain line in the complex plane, is one of the most important unresolved problems in mathematics. Inspired by the P\'olya-Hilbert conjecture, we propose a new approach to finding a physical system to study the Riemann zeros, which in contrast to previous examples, is based on applying a time-periodic driving field. This driving allows us to mould the quasienergies of the system (the analogue of the eigenenergies in the absence of driving), so that they are directly governed by the zeta function. We further show by numerical simulations that this allows the Riemann zeros to be measured in currently accessible cold atom experiments.Comment: 6 pages, accepted for publication in Phys. Rev.

Using Similarity Criteria to Make Negotiation Trade-Offs

This paper addresses the issues involved in software agents making trade-offs during automated negotiations in which they have information uncertainty and resource limitations. In particular, the importance of being able to make trade-offs in real-world applications is highlighted and a novel algorithm for performing trade-offs for multi-dimensional goods is developed. The algorithm uses the notion of fuzzy similarity in order to find negotiation solutions that are beneficial to both parties. Empirical results indicate the benefits and effectiveness of the trade-off algorithm in a range of negotiation situations