Mathematics and Social Sciences Workshop

A workshop sponsored by EHESS, ERC Readi, Imperial College London & the EPSRC

November 16 and 17, 2015 - Imperial College in London, 170 Queen’s Gate, London, UK

Marc Barthelemy - Revisiting urban economics in light of data

Always more data about cities are available which allows to build and to test theories and models. In particular, many urban economics models were developed to describe how cities are organized and I will discuss here their predictions about urban mobility. I will illustrate on various examples such as the total commuting length in cities, or the variation of the commuting length with income, how empirical data force us to reconsider these models in order to reach conclusions that are in agreement with empirical observations.

JP Bouchaud - Exploration-exploitation tradeoffs, optimal taxes and inequalities

Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. We then argue that growth-optimal taxation can be thought of as the ``two-sites'' version of this problem. The exact solution of this problem allows us to conclude that wealth taxes can be beneficial even when the private sector is more ``efficient" than the governement, and conversely that a certain level of inequalities can be -- perhaps paradoxically -- socially beneficial.

Guillaume Carlier - Variational problems and PDEs arising in congested transport models

In this talk, starting from the notion of Wardrop equilibria on congested networks, I ll discuss continuous counterparts, how they appear from limits on dense networks and how they lead to degenerate elliptic PDEs. Based on joint works with Jean-Bernard Baillon, Lorenzo Brasco, Chloé Jimenez and Filippo Santambrogio.

Rama Cont - Feedback effects and endogenous risk in financial markets

Shane D Johnson - From Patterns to Policy – The need to understand and model crime prevention interventions

This talk is in two related parts. The first speaks to the study of crime patterns and how this informs our understanding of problems and how we might prevent them. The second speaks to the effectiveness of crime reduction interventions. Drawing on research concerned with what works to reduce crime being conducted at UCL, I discuss what we know about interventions and what we do not (in broad terms) and how research in crime prevention differs from that in (say) medicine. In closing, I will discuss how simulation models or mathematical analysis might improve understanding about what might work to reduce crime, and how it might do so.

Betrand Maury - Faster is Slower effect and related phenomena in crowd motions through bottlenecks: a challenge to modelling

The actual motion of a dense crowd through a bottleneck present particular features that present challenges in terms of modelling, like the so-called Faster is Slower Effect: when individuals try to move faster upstream the bottleneck, it may actually reduce the global flow. A related phenomenon is phrased as Capacity Drop: beyond a certain density upstream an exit door, the outflow may significantly drop down. Another observable phenomenon pertains to the unsteadiness (oscillatory) character of the motion: Stop-and-Go waves. We shall present some attempts that have been made to reproduce those phenomenon, by integrating ad-hoc principles in the model to mimic them, or by trying to understand the phenomena by an in-depth investigation of interaction between indviduals in competition to reach a common goal. We shall in particular present how the very structure of the neighbor-to-neighbor network sheds some light on the overall behaviour, which explains in particular why macroscopic approachs have trouble to natively recover this type of phenomena.

Jean-Pierre Nadal - 10 years after: modelling the dynamics of the 2005 French riots

I will introduce families of models aiming at describing riot dynamics, taking into account the self-excitment mechanism (after a rioting event the likeliness of a new one is increased) and the process of diffusion or propagation from one place to another. Working on a detailed data base of the events of the 2005 French riots (which started exactly 10 years ago, on October 27 2005, and lasted three weeks), I will discuss a data driven model, taking into account both local and non-local interactions. With less than 10 free parameters, the model reproduces the full dynamics of the riots hitting more than 800 municipalities. This talk is based on works done in collaboration with Laurent Bonnasse-Gahot, Henri Berestycki, Marie-Aude Depuiset, Mirta B Gordon, Sebastian Roche and Nancy Rodriguez

Mason Alexander Porter - Multilayer Networks and Applications

Networks provided a powerful representation of complex systems of interacting entities. One of the most active areas of network science, with an explosion of publications during the last few years, is the study of "multilayer networks," in which heterogeneous types of entities can be connected via multiple social ties that change in time. Multilayer networks include multiple subsystems and "layers" of connectivity, and it is important to take such multilayer features into account to try to improve our understanding of complex systems. In this talk, I'll give an overview of multilayer networks. I will introduce some ideas for how to find dense sets of nodes known as "communities" in multilayer networks and how this can lead to insights in applications such as political party realignment in voting networks. Time-permitting, I will also discuss how to measure important nodes in multilayer networks, with an example describing the measurement of the quality of mathematics programs over time. Throughout the talk, I'll discuss challenges in the study of multilayer networks.

Camille Roth - Calibration and validation of interaction models

The design and empirical understanding of interaction processes plays a key role in mathematical social modeling. At the individual level, sophisticated statistical methods have been introduced to appraise interaction dynamics and preferences. At a higher level, social network models rely on empirical or normative assumptions on tie formation in order to reconstruct global interaction structures. Put shortly, individual interaction behavior is either the target or the support of such models. After providing a structured overview of the state-of-the-art relevant to the calibration and validation of social network models, we present a technique aiming at addressing both issues, using symbolic regression to jointly comprehend global and local interaction dynamics.

Filippo Santambrogio - Urban equilibria and displacement convexity

I will present some equilibrium problems for the population density in urban areas, and their connection with optimality conditions for minimization problems in the space of probability densities. In most cases the energy to be minimized is not convex, which makes it difficult to prove uniqueness of the equilibrium and equivalence between equilibrium and optimization. We will see how the notion of displacement convexity, introduced by McCann in optimal transport, allows to get an alternative point of view on convexity and obtain the desired results. Also, we will see examples where there are multiple equilibria because of the lack of displacement convexity. The talk will be mainly based on a joint work with A. Blanchet (Toulouse) and P. Mossay (Newcastle).

Andreas Schadschneider - The physics of pedestrian and evacuation dynamics

We will give an introduction to empirical and theoretical approaches for pedestrian dynamics and the motion of large crowds. A variety of collective effects and self-organisation phenomena can be observed, like the formation of lanes or oscillations of the flow direction at bottlenecks. An overview of the various modeling approaches that have been suggested will be given. In controlled laboratory experiments with up to 1000 participants have provided quantitative and reproducible data that forms that basis for validation and calibration of these models. As an example for a practical application, an evacuation assistent for a large sports arena, will be described.

Alberto Tesei - A model for the nexus between economic and political changes

We study in some detail a model proposed by F. Caselli, concerning the impact of natural resource rents on government policy. A major result of the analysis is that a reduction in resource rents can give rise to a political transition, from autocracy to democracy. It is also shown that incumbent governments under the threat of a coup may decide not to make productive investments, when the resource rents and the probability of success of a coup are very high. Both facts are in agreement with well-established empirical observations. In the model the government chooses how to divide its budget, partly consisting of the natural resources income, between productive investments and repression of political opponents. On the other hand, potential political challengers decide whether to try to unseat the government, or dedicate themselves to productive activities. Depending on some exogenous parameters, among which the efficiency of counter-insurgency structures plays an important role, the game gives rise to a variety of situations which correspond to democratic or autocratic policies. References: Caselli, F. (2006) Power struggles and the natural resource curse, mimeo, London School of Economics, London.

Alan Wilson - The mathematics of cities and regions: the state of the science and its challenges

Building effective mathematical models of cities and regions is a major task of twenty-first century science. Much progress has been made but there are challenges that are attractive to the mathematics community both in terms of the science and its applications. To fix ideas, examples of core models are described covering how people live in cities, urban economies, sustainability, urban form and the evolution of infrastructure. These elements are strongly interdependent. This provides the basis for articulating the mathematical challenges in the context of the ‘real’ challenges: how these models can contribute to the development of ‘good’ future cities.