Parking and the visual perception of space

Using measured data we demonstrate that there is an amazing correspondence among the statistical properties of spacings between parked cars and the distances between birds perching on a power line. We show that this observation is easily explained by the fact that birds and human use the same mechanism of distance estimation. We give a simple mathematical model of this phenomenon and prove its validity using measured data

Vehicular traffic flow at an intersection with the possibility of turning

We have developed a Nagel-Schreckenberg cellular automata model for describing of vehicular traffic flow at a single intersection. A set of traffic lights operating in fixed-time scheme controls the traffic flow. Open boundary condition is applied to the streets each of which conduct a uni-directional flow. Streets are single-lane and cars can turn upon reaching to the intersection with prescribed probabilities. Extensive Monte Carlo simulations are carried out to find the model flow characteristics. In particular, we investigate the flows dependence on the signalisation parameters, turning probabilities and input rates. It is shown that for each set of parameters, there exist a plateau region inside which the total outflow from the intersection remains almost constant. We also compute total waiting time of vehicles per cycle behind red lights for various control parameters.Comment: 8 pages, 17 eps figures, Late

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491