Urban population size and road traffic collisions in Europe.

Millions of road traffic collisions take place every year, leading to significant knock-on effects. Many of these traffic collisions take place in urban areas, where traffic levels can be elevated. Yet, little is known about the extent to which urban population size impacts road traffic collision rates. Here, we use urban scaling models to analyse geographic and road traffic collision data from over 300 European urban areas in order to study this issue. Our results show that there is no significant change in the number of road traffic collisions per person for urban areas of different sizes. However, we find individual urban locations with traffic collision rates which are remarkably high. These findings have the potential to inform policies for the allocation of resources to prevent road traffic collisions across the different cities.

The effect of dragon-kings on the estimation of scaling law parameters.

Scaling laws are used to model how different quantifiable properties of cities, such as the number of road traffic accidents or average house prices, vary as a function of city population size, with parameters estimated from data. Arcaute et al. raised the issue of whether specific cities with extremely large population sizes, known as dragon-kings, should be considered separately from other smaller cities when estimating the scaling law parameters since the two types of cities tend to display different behaviour. Through the analysis of randomly generated samples, we find that the inclusion of dragon-kings in the scaling analysis does not affect the estimated values for the parameters but only provided that all the data points satisfy the same scaling law. We also analyse randomly generated samples where data corresponding to a particular city deviates from the scaling law followed by the rest of the cities. We then show that deviations corresponding to dragon-king cities have the most significant effect on the estimated values of the scaling parameters. The extent of this effect also depends on which estimation procedure is used. Our results have important implications on the suitability of scaling laws as a model for urban systems.

A Financial Market Model Incorporating Herd Behaviour.

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents' accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents' accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option.

Predicting the Lifetime of Dynamic Networks Experiencing Persistent Random Attacks.

Estimating the critical points at which complex systems abruptly flip from one state to another is one of the remaining challenges in network science. Due to lack of knowledge about the underlying stochastic processes controlling critical transitions, it is widely considered difficult to determine the location of critical points for real-world networks, and it is even more difficult to predict the time at which these potentially catastrophic failures occur. We analyse a class of decaying dynamic networks experiencing persistent failures in which the magnitude of the overall failure is quantified by the probability that a potentially permanent internal failure will occur. When the fraction of active neighbours is reduced to a critical threshold, cascading failures can trigger a total network failure. For this class of network we find that the time to network failure, which is equivalent to network lifetime, is inversely dependent upon the magnitude of the failure and logarithmically dependent on the threshold. We analyse how permanent failures affect network robustness using network lifetime as a measure. These findings provide new methodological insight into system dynamics and, in particular, of the dynamic processes of networks. We illustrate the network model by selected examples from biology, and social science.

Quantifying regional differences in the length of Twitter messages.

The increasing usage of social media for conversations, together with the availability of its data to researchers, provides an opportunity to study human conversations on a large scale. Twitter, which allows its users to post messages of up to a limit of 140 characters, is one such social media. Previous studies of utterances in books, movies and Twitter have shown that most of these utterances, when transcribed, are much shorter than 140 characters. Furthermore, the median length of Twitter messages was found to vary across US states. Here, we investigate whether the length of Twitter messages varies across different regions in the UK. We find that the median message length, depending on grouping, can differ by up to 2 characters.

A spatial model with pulsed releases to compare strategies for the sterile insect technique applied to the mosquito Aedes aegypti.

We present a simple mathematical model to replicate the key features of the sterile insect technique (SIT) for controlling pest species, with particular reference to the mosquito Aedes aegypti, the main vector of dengue fever. The model differs from the majority of those studied previously in that it is simultaneously spatially explicit and involves pulsed, rather than continuous, sterile insect releases. The spatially uniform equilibria of the model are identified and analysed. Simulations are performed to analyse the impact of varying the number of release sites, the interval between pulsed releases and the overall volume of sterile insect releases on the effectiveness of SIT programmes. Results show that, given a fixed volume of available sterile insects, increasing the number of release sites and the frequency of releases increases the effectiveness of SIT programmes. It is also observed that programmes may become completely ineffective if the interval between pulsed releases is greater that a certain threshold value and that, beyond a certain point, increasing the overall volume of sterile insects released does not improve the effectiveness of SIT. It is also noted that insect dispersal drives a rapid recolonisation of areas in which the species has been eradicated and we argue that understanding the density dependent mortality of released insects is necessary to develop efficient, cost-effective SIT programmes.

Quantifying the digital traces of Hurricane Sandy on Flickr.

Society's increasing interactions with technology are creating extensive "digital traces" of our collective human behavior. These new data sources are fuelling the rapid development of the new field of computational social science. To investigate user attention to the Hurricane Sandy disaster in 2012, we analyze data from Flickr, a popular website for sharing personal photographs. In this case study, we find that the number of photos taken and subsequently uploaded to Flickr with titles, descriptions or tags related to Hurricane Sandy bears a striking correlation to the atmospheric pressure in the US state New Jersey during this period. Appropriate leverage of such information could be useful to policy makers and others charged with emergency crisis management.

A mathematical model of the London riots and their policing.

In August 2011, several areas of London experienced episodes of large-scale disorder, comprising looting, rioting and violence. Much subsequent discourse has questioned the adequacy of the police response, in terms of the resources available and strategies used. In this article, we present a mathematical model of the spatial development of the disorder, which can be used to examine the effect of varying policing arrangements. The model is capable of simulating the general emergent patterns of the events and focusses on three fundamental aspects: the apparently-contagious nature of participation; the distances travelled to riot locations; and the deterrent effect of policing. We demonstrate that the spatial configuration of London places some areas at naturally higher risk than others, highlighting the importance of spatial considerations when planning for such events. We also investigate the consequences of varying police numbers and reaction time, which has the potential to guide policy in this area.

Quantifying the advantage of looking forward.

We introduce a future orientation index to quantify the degree to which Internet users worldwide seek more information about years in the future than years in the past. We analyse Google logs and find a striking correlation between the country's GDP and the predisposition of its inhabitants to look forward.

Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems.

Scaling factor characterizes the synchronized dynamics of projective synchronization in partially linear chaotic systems but it is difficult to be estimated. To manipulate projective synchronization of chaotic systems in a favored way, a control algorithm is introduced to direct the scaling factor onto a desired value. The control approach is derived from the Lyapunov stability theory. It allows us to arbitrarily amplify or reduce the scale of the response of the slave system via a feedback control on the master system. In numerical experiments, we illustrate the application to the Lorenz system. (c) 2001 American Institute of Physics.