We perform a multifractal analysis of the evolution of London's street network from 1786 to 2010. First, we show that a single fractal dimension, commonly associated with the morphological description of cities, does not suffice to capture the dynamics of the system. Instead, for a proper characterization of such a dynamics, the multifractal spectrum needs to be considered. Our analysis reveals that London evolves from an inhomogeneous fractal structure, which can be described in terms of a multifractal, to a homogeneous one, which converges to monofractality. We argue that London's multifractal to monofractal evolution might be a special outcome of the constraint imposed on its growth by a green belt. Through a series of simulations, we show that multifractal objects, constructed through diffusion limited aggregation, evolve toward monofractality if their growth is constrained by a nonpermeable boundary.

The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Urban migration to and from cities is characterised as non-random and following non-random pathways. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements. In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy. Our analysis is based on a stochastic urban fractal model, which mimics urban growing settlements and migration waves. The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales.

The COVID-19 pandemic has become a global public health crisis, causing significant morbidity and mortality worldwide. As an early response, different lockdowns were imposed in the UK (and the world) to limit the spread of the disease. Although effective, these measures profoundly impacted mobility patterns across cities, significantly reducing the number of people commuting to work or travelling for leisure. As different governments introduced massive vaccination programs to tackle the pandemic, cities have significantly but slowly increased human mobility, enabling the resumption of travel, work, and social activities. Nevertheless, how much can this return to normal mobility patterns be attributed to vaccines? In this study, we answer this question using a statistical approach, analysing two different open urban mobility datasets to quantify the effect vaccination rollouts have had on increased human activities.

Street networks provide an invaluable source of information about the different temporal and spatial patterns emerging in our cities. These streets are often represented as graphs where intersections are modeled as nodes and streets as edges between them. Previous work has shown that raster representations of the original data can be created through a learning algorithm on low-dimensional representations of the street networks. In contrast, models that capture high-level urban network metrics can be trained through convolutional neural networks. However, the detailed topological data is lost through the rasterization of the street network, and the models cannot recover this information from the image alone, failing to capture complex street network features. This paper proposes a model capable of inferring good representations directly from the street network. Specifically, we use a variational autoencoder with graph convolutional layers and a decoder that generates a probabilistic, fully connected graph to learn latent representations that encode both local network structure and the spatial distribution of nodes. We train the model on thousands of street network segments and use the learned representations to generate synthetic street configurations. Finally, we proposed a possible application to classify the urban morphology of different network segments, investigating their common characteristics in the learned space.

The UK retail landscape has undergone significant changes over the past decade, driven by factors such as the rise of online shopping, economic downturns, and, more recently, the COVID-19 pandemic. Accurately measuring pedestrian flows in retail areas with high spatial and temporal resolution is essential for selecting the most appropriate forecasting model for different retail locations. However, several studies have adopted a one-size-fits-all approach, overlooking important local characteristics that are only occasionally captured by the best global model. In this work, using data generated by the SmartStreetSensor project, a large network of sensors installed across UK cities that collect Wi-Fi probe requests generated by mobile devices, we examine the optimal forecasting method to predict pedestrian footfall in various retail areas across Great Britain. After assessing six representative time series forecasting models, our results show that the LSTM model outperforms traditional methods in most areas. However, pedestrian counts at certain locations with specific spatial characteristics are better forecasted by other algorithms.

This paper studies insurance companies’ optimal reinsurance–investment strategy under the stochastic interest rate and stochastic volatility model, taking the HARA utility function as the optimal criterion. It uses arithmetic Brownian motion as a diffusion approximation of the insurer’s surplus process and the variance premium principle to calculate premiums. In this paper, we assume that insurance companies can invest in risk-free assets, risky assets, and zero-coupon bonds, where the Cox–Ingersoll–Ross model describes the dynamic change in stochastic interest rates and the Heston model describes the price process of risky assets. The analytic solution of the optimal reinsurance–investment strategy is deduced by employing related methods from the stochastic optimal control theory, the stochastic analysis theory, and the dynamic programming principle. Finally, the influence of model parameters on the optimal reinsurance–investment strategy is illustrated using numerical examples.