This paper presents a new tool, AshCalc, for the comparison of the three most commonly used models for the calculation of the bulk volume of volcanic tephra fall deposits: the exponential model, the power law model and the Weibull model. AshCalc provides a simple and intuitive tool to speed up the analysis of tephra deposits and compare and contrast the fits for each model. Two improvements in terms of computational performance are implemented in AshCalc for the estimation of the parameters for the Weibull model. The first is an analytic method for reducing the number of free parameters, whilst the second exaggerates the minima in parameter space, leading to a more robust solution. We show that AshCalc provides volume estimates in line with other previously published estimates and hence can be used with a high degree of confidence. We include the open source python code for Ashcalc with the intention that it can be used both as a stand-alone program and integrated into other python projects.

We present new results in the theory of asynchronous convergence for the Distributed Bellman-Ford (DBF) family of routing protocols which includes distance-vector protocols (e.g. RIP) and path-vector protocols (e.g. BGP). We take the "increasing" conditions of Sobrinho and make three main new contributions.First, we show that the conditions are sufficient to guarantee that the protocols will converge to a unique solution from any state. This eliminates the possibility of BGP wedgies. Second, unlike previous work, we decouple the computation from the asynchronous context in which it occurs, allowing us to reason about a more relaxed model of asynchronous computation in which routing messages can be lost, reordered, and duplicated. Third, our theory and results have been fully formalised in the Agda theorem prover and the resulting library is publicly available for others to use and extend. We feel this is in line with the increased emphasis on formal verification of software for critical infrastructure.

In recent decades, the world has experienced rates of urban growth unparalleled in any other period of history and this growth is shaping the environment in which an increasing proportion of us live. In this paper, we use a longitudinal dataset from Foursquare, a location-based social network, to analyse urban growth across 100 major cities worldwide. Initially, we explore how urban growth differs in cities across the world. We show that there exists a strong spatial correlation, with nearby pairs of cities more likely to share similar growth profiles than remote pairs of cities. Subsequently, we investigate how growth varies inside cities and demonstrate that, given the existing local density of places, higher-than-expected growth is highly localized while lower-than-expected growth is more diffuse. Finally, we attempt to use the dataset to characterize competition between new and existing venues. By defining a measure based on the change in throughput of a venue before and after the opening of a new nearby venue, we demonstrate which venue types have a positive effect on venues of the same type and which have a negative effect. For example, our analysis confirms the hypothesis that there is large degree of competition between bookstores, in the sense that existing bookstores normally experience a notable drop in footfall after a new bookstore opens nearby. Other place types, such as museums, are shown to have a cooperative effect and their presence fosters higher traffic volumes to nearby places of the same type.

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