Review of periodical articles

[First Paragraph] There is only one true city, wrote St Augustine, and it is not of this world. The pessimistic Christian response to the fall of Rome in AD 410, epitomized in Augustine's City of God, affected the development of the later medieval city to a degree which has yet, even now, to be fully appreciated. In the Christian city of the Middle Ages the divinity was normally confined to the sanctuaries of his churches, whose topographical prominence and harmonious proportions made manifest an otherwise hidden spiritual order. Outside the cloister gates, disorder reigned: a general lack of planning revealed the meaninglessness of the outward, secular life. This dichotomy between an inner world of spirit and a public world of transient matter was embodied in the recurrent tensions between spiritual and secular space which ran as a motif throughout the history of medieval towns. Modern studies which have emphasized (not, of course, without reason) the secular political and economic power of ecclesiastical institutions in the medieval city have perhaps distracted attention unduly from the real differences of ethos which, within the town, distinguished religious space from that of the surrounding lay world

Review of periodical articles

One of the attractions of medieval urban history is the fact that major conceptual problems in the field continue to be debated. In a stimulating review article by J.H. Mundy, ’Philip Jones and the medieval Italian city-state‘, J. of European Economic History, 28 (1999), 185–200, one distinguished scholar is taxed for holding views now dismissed by some, but of which he is by no means a unique surviving representative. One of these views assumes a clear distinction between the antique city, supposedly a bureaucratic centre with limited economic functions, and the medieval city, as the home of industrious artisans and nascent capitalism. The image of the non-profit-making ancient town may be overly indebted to the nature of the literary sources and to the prevalent interests of classicists; but, although many would now agree that both the elements in the above equation need qualifying, a more focused comparison is presently lacking, and a fine book is still waiting to be written on the transition from the ancient world to the middle ages in urban history

Generalized Euler constants

We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent monotonicity is investigated. We also prove that a certain property of these numbers is equivalent to the Riemann Hypothesis.Comment: v2. 13 pages. Minor changes suggested by the referee. To appear in Math. Proc. Cambridge Phil. So

Improving the Robustness and Accuracy of Crime Prediction with the Self-Exciting Point Process Through Isotropic Triggering

The self-exciting point process (SEPP) is a model of the spread of crime in space and time, incorporating background and triggering processes. It shows promising predictive performance and forms the basis of a popular commercial software package, however few detailed case studies describing the application of the SEPP to crime data exist in the scientific literature. Using open crime data from the City of Chicago, USA, we apply the SEPP to crime prediction of assaults and burglaries in nine distinct geographical regions of the city. The results indicate that the algorithm is not robust to certain features of the data, generating unrealistic triggering functions in various cases. A simulation study is used to demonstrate that this outcome is associated with a reduction in predictive accuracy. Analysing the second-order spatial properties of the data demonstrates that the failures in the algorithm are correlated with anisotropy. A modified version of the SEPP model is developed in which triggering is non-directional. We show that this provides improved robustness, both in terms of the triggering structure and the predictive accuracy

Novel evaluation metrics for sparse spatio-temporal point process hotspot predictions - a crime case study

Many physical and sociological processes are represented as discrete events in time and space. These spatio-temporal point processes are often sparse, meaning that they cannot be aggregated and treated with conventional regression models. Models based on the point process framework may be employed instead for prediction purposes. Evaluating the predictive performance of these models poses a unique challenge, as the same sparseness prevents the use of popular measures such as the root mean squared error. Statistical likelihood is a valid alternative, but this does not measure absolute performance and is therefore difficult for practitioners and researchers to interpret. Motivated by this limitation, we develop a practical toolkit of evaluation metrics for spatio-temporal point process predictions. The metrics are based around the concept of hotspots, which represent areas of high point density. In addition to measuring predictive accuracy, our evaluation toolkit considers broader aspects of predictive performance, including a characterisation of the spatial and temporal distributions of predicted hotspots and a comparison of the complementarity of different prediction methods. We demonstrate the application of our evaluation metrics using a case study of crime prediction, comparing four varied prediction methods using crime data from two different locations and multiple crime types. The results highlight a previously unseen interplay between predictive accuracy and spatio-temporal dispersion of predicted hotspots. The new evaluation framework may be applied to compare multiple prediction methods in a variety of scenarios, yielding valuable new insight into the predictive performance of point process-based prediction

Electrons in the Earth's Outer Radiation Zone

Electrons in the earths outer radiation bel

Ab-initio molecular dynamics simulation of hydrogen diffusion in α\alpha-iron

First-principles atomistic molecular dynamics simulation in the micro-canonical and canonical ensembles has been used to study the diffusion of interstitial hydrogen in $\alpha$-iron. Hydrogen to Iron ratios between $\theta=1/16 and 1/2 have been considered by locating interstitial hydrogen atoms at random positions in a$2 \times 2 \times 2$ supercell. We find that the average optimum absorption site and the barrier for diffusion depend on the concentration of interestitials. Iron Debye temperature decreases monotonically for increasing concentration of interstitial hydrogen, proving that iron-iron interatomic potential is significantly weakened in the presence of a large number of diffusing hydrogen atoms

The effect of sampling rate on observed statistics in a correlated random walk

Tracking the movement of individual cells or animals can provide important information about their motile behaviour, with key examples including migrating birds, foraging mammals and bacterial chemotaxis. In many experimental protocols, observations are recorded with a fixed sampling interval and the continuous underlying motion is approximated as a series of discrete steps. The size of the sampling interval significantly affects the tracking measurements, the statistics computed from observed trajectories, and the inferences drawn. Despite the widespread use of tracking data to investigate motile behaviour, many open questions remain about these effects. We use a correlated random walk model to study the variation with sampling interval of two key quantities of interest: apparent speed and angle change. Two variants of the model are considered, in which reorientations occur instantaneously and with a stationary pause, respectively. We employ stochastic simulations to study the effect of sampling on the distributions of apparent speeds and angle changes, and present novel mathematical analysis in the case of rapid sampling. Our investigation elucidates the complex nature of sampling effects for sampling intervals ranging over many orders of magnitude. Results show that inclusion of a stationary phase significantly alters the observed distributions of both quantities

Simplified multitarget tracking using the PHD filter for microscopic video data

The probability hypothesis density (PHD) filter from the theory of random finite sets is a well-known method for multitarget tracking. We present the Gaussian mixture (GM) and improved sequential Monte Carlo implementations of the PHD filter for visual tracking. These implementations are shown to provide advantages over previous PHD filter implementations on visual data by removing complications such as clustering and data association and also having beneficial computational characteristics. The GM-PHD filter is deployed on microscopic visual data to extract trajectories of free-swimming bacteria in order to analyze their motion. Using this method, a significantly larger number of tracks are obtained than was previously possible. This permits calculation of reliable distributions for parameters of bacterial motion. The PHD filter output was tested by checking agreement with a careful manual analysis. A comparison between the PHD filter and alternative tracking methods was carried out using simulated data, demonstrating superior performance by the PHD filter in a range of realistic scenarios