Static search games played over graphs and general metric spaces

We define a general game which forms a basis for modelling situations of static search and concealment over regions with spatial structure. The game involves two players, the searching player and the concealing player, and is played over a metric space. Each player simultaneously chooses to deploy at a point in the space; the searching player receiving a payoff of 1 if his opponent lies within a predetermined radius r of his position, the concealing player receiving a payoff of 1 otherwise. The concepts of dominance and equivalence of strategies are examined in the context of this game, before focusing on the more specific case of the game played over a graph. Methods are presented to simplify the analysis of such games, both by means of the iterated elimination of dominated strategies and through consideration of automorphisms of the graph. Lower and upper bounds on the value of the game are presented and optimal mixed strategies are calculated for games played over a particular family of graphs

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 diferent quantifable properties of cities, such as the number of road trafc 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 specifc 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 diferent behaviour. Through the analysis of randomly generated samples, we fnd that the inclusion of dragon-kings in the scaling analysis does not afect 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 signifcant efect on the estimated values of the scaling parameters. The extent of this efect 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

Scaling Beyond Cities

City population size is a crucial measure when trying to understand urban life. Many socio-economic indicators scale superlinearly with city size, whilst some infrastructure indicators scale sublinearly with city size. However, the impact of size also extends beyond the city’s limits. Here, we analyse the scaling behaviour of cities beyond their boundaries by considering the emergence and growth of nearby cities. Based on an urban network from African continental cities, we construct an algorithm to create the region of influence of cities. The number of cities and the population within a region of influence are then analysed in the context of urban scaling. Our results are compared against a random permutation of the network, showing that the observed scaling power of cities to enhance the emergence and growth of cities is not the result of randomness. By altering the radius of influence of cities, we observe three regimes. Large cities tend to be surrounded by many small towns for small distances. For medium distances (above 114 km), large cities are surrounded by many other cities containing large populations. Large cities boost urban emergence and growth (even more than 190 km away), but their scaling power decays with distance

FuturICT: Participatory computing to understand and manage our complex world in a more sustainable and resilient way

We have built particle accelerators to understand the forces that make up our physical world. Yet, we do not understand the princi-ples underlying our strongly connected, techno-socio-economic systems. We have enabled ubiquitous Internet connectivity and instant, global information access. Yet we do not understand how it impacts our be-havior and the evolution of society. To fill the knowledge gaps and keep up with the fast pace at which our world is changing, a Knowledge Accelerator must urgently be cre-ated. The financial crisis, international wars, global terror, the spread-ing of diseases and cyber-crime as well as demographic, technological and environmental change demonstrate that humanity is facing seri-ous challenges. These problems cannot be solved within the traditional paradigms. Moving our attention from a component-oriented view of the world to an interaction-oriented view will allow us to understand the com-plex systems we have created and the emergent collective phenomena characterising them. This paradigm shift will enable new solutions to long-standing problems, very much as the shift from a geocentric to a heliocentric worldview has facilitated modern physics and the ability to launch satellites. The FuturICT flagship project will develop new science and technology to manage our future in a complex, strongly connected world. For this, it will combine the power of information and communication technol-ogy (ICT) with knowledge from the social and complexity sciences. ICT will provide the data to boost the social sciences into a new era. Complexity science will shed new light on the emergent phenomena in socially interactive systems, and the social sciences will provide a better understanding of the opportunities and risks of strongly net-worked systems, in particular future ICT systems. Hence, the envisaged FuturICT flagship will create new methods and instruments to tackle the challenges of the 21 st century. FuturICT could indeed become one of the most important scientific endeavours ever, by revealing the principles that make socially inter-active systems work well, by inspiring the creation of new platforms to explore our possible futures, and by initiating an era of social and socio-inspired innovations

A dynamic spatial model of conflict escalation

In both historical and modern conflicts, space plays a critical role in how interactions occur over time. Despite its importance, the spatial distribution of adversaries has often been neglected in mathematical models of conflict. In this paper, we propose an entropy-maximising spatial interaction method for disaggregating the impact of space, employing a general notion of ‘threat’ between two adversaries. This approach addresses a number of limitations that are associated with partial differential equation approaches to spatial disaggregation. We use this method to spatially disaggregate the Richardson model of conflict escalation, and then explore the resulting model with both analytical and numerical treatments. A bifurcation is identified that dramatically influences the resulting spatial distribution of conflict and is shown to persist under a range of model specifications. Implications of this finding for real-world conflicts are discussed

Modelling patterns of burglary on street networks

A fundamental issue in crime prevention is the efficient deployment of resources and the effective targeting of interventions, both of which require some form of prediction of future crime. One crime for which this is feasible is burglary, the distinctive spatio-temporal signatures of which can be exploited to inform predictions. Mathematical models in particular are capable of both encoding concisely the theoretical foundations of criminal behaviour and allowing the quantitative analysis of specific scenarios, and their capacity to reproduce the general patterns of burglary suggests that the approach has considerable potential. Previous models, however, are situated on simplified representations of space and do not reflect realistically the built environment in which crime takes place; specifically, they do not incorporate urban street networks. Such networks are fundamental to situational theories of crime, in the sense that they determine the configuration of urban space and, therefore, shape those human activity patterns which are thought to give rise to crime. Furthermore, streets are the natural domain for many policing activities, and their structure is determined by planning decisions, so that insight into their relationship with crime is likely to be of immediate practical use. With this in mind, this paper presents a mathematical model of crime which is explicitly situated on a street network. After discussing theoretical considerations and specifying the model itself, examples of typical networks are explored

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

A novel rare event approach to measure the randomness and concentration of road accidents

BACKGROUND: Road accidents are one of the main causes of death around the world and yet, from a timespace perspective, they are a rare event. To help us prevent accidents, a metric to determine the level of concentration of road accidents in a city could aid us to determine whether most of the accidents are constrained in a small number of places (hence, the environment plays a leading role) or whether accidents are dispersed over a city as a whole (hence, the driver has the biggest influence). METHODS: Here, we apply a new metric, the Rare Event Concentration Coefficient (RECC), to measure the concentration of road accidents based on a mixture model applied to the counts of road accidents over a discretised space. A test application of a tessellation of the space and mixture model is shown using two types of road accident data: an urban environment recorded in London between 2005 and 2014 and a motorway environment recorded in Mexico between 2015 and 2016. FINDINGS: In terms of their concentration, about 5% of the road junctions are the site of 50% of the accidents while around 80% of the road junctions expect close to zero accidents. Accidents which occur in regions with a high accident rate can be considered to have a strong component related to the environment and therefore changes, such as a road intervention or a change in the speed limit, might be introduced and their impact measured by changes to the RECC metric. This new procedure helps us identify regions with a high accident rate and determine whether the observed number of road accidents at a road junction has decreased over time and hence track structural changes in the road accident settings

Comparative Evaluation of Action Recognition Methods via Riemannian Manifolds, Fisher Vectors and GMMs: Ideal and Challenging Conditions

We present a comparative evaluation of various techniques for action recognition while keeping as many variables as possible controlled. We employ two categories of Riemannian manifolds: symmetric positive definite matrices and linear subspaces. For both categories we use their corresponding nearest neighbour classifiers, kernels, and recent kernelised sparse representations. We compare against traditional action recognition techniques based on Gaussian mixture models and Fisher vectors (FVs). We evaluate these action recognition techniques under ideal conditions, as well as their sensitivity in more challenging conditions (variations in scale and translation). Despite recent advancements for handling manifolds, manifold based techniques obtain the lowest performance and their kernel representations are more unstable in the presence of challenging conditions. The FV approach obtains the highest accuracy under ideal conditions. Moreover, FV best deals with moderate scale and translation changes