Multifractality applied to the study of spatial inequality in urban systems

This thesis investigates multifractality as a tool to analyse the spatial patterns emerging from urban inequality. In our context, inequality is defined as a difference between individuals in economic welfare (in the tradition of Dalton and Sen). As such, it considers the typical household income distribution, but also variables such as real estate and energy consumption. These variables can be transformed into mathematical measures which present diverse extent of self-similarities explained by the self-organisation processes resulting from an intense competition for space. The multifractal methodology can exploit these self-similarities to produce precise local statistical information even when the usual tools fail due to an excessive complexity. The analysis is performed on large geographical datasets for London, Paris, New-York and Kyoto. The main results are a decrease in multifractality with modernisation that can be understood as an arguably positive homogenisation, but also a negative loss of diversity; striking similarities in the independent evolution of the spatial repartition of land and housing prices across the globe during the 20th century; and discrepancies between income and the other measures, in accordance with the idea that income alone is not enough to fully characterize inequality. The most important result, however, is the validation after comparison with the traditional inequality and segregation measures that multifractality is a high-performing spatial inequality indicator. It is in particular able to extend the exposure and clustering dimensions of segregation to ordinal continuous variables

Explainability in Practice: Estimating Electrification Rates from Mobile Phone Data in Senegal

Explainable artificial intelligence (XAI) provides explanations for not interpretable machine learning (ML) models. While many technical approaches exist, there is a lack of validation of these techniques on real-world datasets. In this work, we present a use-case of XAI: an ML model which is trained to estimate electrification rates based on mobile phone data in Senegal. The data originate from the Data for Development challenge by Orange in 2014/15. We apply two model-agnostic, local explanation techniques and find that while the model can be verified, it is biased with respect to the population density. We conclude our paper by pointing to the two main challenges we encountered during our work: data processing and model design that might be restricted by currently available XAI methods, and the importance of domain knowledge to interpret explanations.Comment: The 1st World Conference on eXplainable Artificial Intelligence (xAI 2023

Synthetic Population Catalyst : a micro-simulated population of England with circadian activities

Funding: This work was supported by Wave 1 of The UKRI Strategic Priorities Fund under the EPSRC Grant EP/W006022/1, particularly the “Ecosystem of Digital Twin” and “Shocks and Resilience” themes within that grant & The Alan Turing Institute.The Synthetic Population Catalyst (SPC) is an open-source tool for the simulation of populations. Building on previous efforts, synthetic populations can be created for any area in England, from a small geographical unit to the entire country, and linked to geolocalised daily activities. In contrast to most transport models, the output is focussed on the population itself and the way people socially interact together, rather than on a precise modelling of the volume of transport trips from one area to another. SPC is therefore particularly well suited, for example, to study the spread of a pandemic within a population. Other applications include identifying segregation patterns and potential causes of inequality of opportunity amongst individuals. It is fast, thanks to its Rust codebase. The outputs for each lieutenancy area in England are directly available without having to run the code.PostprintPeer reviewe

Alternative method for Hamilton-Jacobi PDEs in image processing

International audienceMultiscale signal analysis has been used since the early 1990s as a powerful tool for image processing, notably in the linear case. However, nonlinear PDEs and associated nonlinear operators have advantages over linear operators, notably preserving important features such as edges in images. In this paper, we focus on nonlinear Hamilton-Jacobi PDEs defined with adaptive speeds or, alternatively, on adaptive morphological fiters also called semi-flat morphological operators. Semi-flat morphology were instroduced by H. Heijmans and studied only in the case where the speed (or equivalently the filtering parameter) is a decreasing function of the luminance. It is proposed to extend the definition suggested by H. Heijmans in the case of non decreasing speeds. We also prove that a central property for defining morphological filters, that is the adjunction property, is preserved while dealing with our extended definitions. Finally experimental applications are presented on actual images, including connection of thin lines by semi-flat dilations and image filtering by semi-flat openings

A method to estimate population densities and electricity consumption from mobile phone data in developing countries.

High quality census data are not always available in developing countries. Instead, mobile phone data are becoming a popular proxy to evaluate the density, activity and social characteristics of a population. They offer additional advantages: they are updated in real-time, include mobility information and record visitors' activity. However, we show with the example of Senegal that the direct correlation between the average phone activity and both the population density and the nighttime lights intensity may be insufficiently high to provide an accurate representation of the situation. There are reasons to expect this, such as the heterogeneity of the market share or the particular granularity of the distribution of cell towers. In contrast, we present a method based on the daily, weekly and yearly phone activity curves and on the network characteristics of the mobile phone data, that allows to estimate more accurately such information without compromising people's privacy. This information can be vital for development and infrastructure planning. In particular, this method could help to reduce significantly the logistic costs of data collection in the particularly budget-constrained context of developing countries