We study the simple evolutionary process in which we repeatedly find the least fit agent in a population of agents and give it a new fitness which is chosen independently at random from a specified distribution. We show that many of the average properties of this process can be calculated...

Recent work has demonstrated that many social networks, and indeed many networks of other types also, have broad distributions of vertex degree. Here we show that this has a substantial impact on the shape of ego-centered networks, i.e., sets of network vertices that are within a given distance...

We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three color model, appears to have a dynamic exponent close to zero, making it particularly useful for simulations of critical ice...

Mycoplasma pneumoniae is a major cause of bacterial pneumonia in the United States. Outbreaks of illness due to mycoplasma commonly occur in closed or semi-closed communities. These outbreaks are difficult to contain due to delays in outbreak detection, the long incubation period of the...

Using data drawn from large-scale databases, a number of interesting trends in the fossil record have been observed in recent years. These include the average decline in extinction rates throughout the Phanerozoic, the average increase in standing diversity, correlations between rates of...

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physical and mathematical literature. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/recovered...

We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a divergent correlation length as the degree of randomness...

Recently, it has been shown that the power spectrum of extinction intensity during the Phanerozoic takes a power-law form, which, it is suggested, may indicate the presence of critical phenomena in the dynamics underlying the extinction process. In this paper we reproduce these results using the...

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions...

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of...