DISORDERED SYSTEMS, RANDOM SPATIAL PROCESSES AND SOME APPLICATIONS

Through a series of sequential steps, driven by statistical-mechanics and graph-theory perspectives and supported by extensive data, we analyze the product diversification for trades in Spain and we link its behavior with the existence of an underlying social network of migrants interacting with natives. We prove that a boost for diversification in the international trade market is (partially) achieved through the underlying interactions among locals and migrants: the latter, providing key information on policies and needs in their native countries, allow firm holders to leverage transactional costs of exports and duties. As a consequence, international trading is allowed to a larger basin of firms and results in an increased number of transactions (extensive margin), which, in turn, implies a larger diversification of international traded products. Further, as a sideline, our theory allows easily to estimate the critical amount of migrants inside the host country before their presence starts to affect international trading and naturally implies that the social organization of Spanish decision makers exhibits small world features.

In this talk I will briefly review the most recent controversies and developments on the state of macroeconomics. There are a number of different ways ahead in macro. I will focus on computational methods, concerning expecially multi-agent models.

The non linear impact of agent's decisions on market prices is one of the main puzzles that arise when it comes to unraveling the price formation mechanism on (non-)financial markets. Supported by strong evidence from the Bitcoin market, we present a physical model that consistently accounts for most empirical facts known so far on price impact, thus resolving the apparent square root law paradox and laying new foundations for addressing the most common impact-related problems.

Imitation and social pressure are usually observed in the aggregate behavior of populations, and they are responsible for the appearance of trends, herd effects, discontinuities and crashes. To account for these phenomena, interactions networks must be included in the modeling of social systems, and measured from data. We present a recent analysis on an extensive dataset from adhesion to cancer screening campaigns, where a modeling, based on statistical mechanics and multi-species mean field spin models, allows for a quantitive estimate of average interaction effects through an inverse problem and leads to a forecast of effective social policies to enhance participation.

This lecture discusses the crisis in the economy and the macroeconomics. Theory appears to be inadequate in its explanation of the origins and the nature of the crisis, because of the classical physic assumptions which in economics are translated into the representative agent assumption, equilibrium and no interaction. DSGE macroeconomic models, however sophisticated have continued to be based on the same foundations shown to be wanting in the 1970s and have the stability and uniqueness problem emphasized by the SMD theorem, which is a powerful warnings by numerous mathematicians and economists as to its unsound foundations. We need to construct models which view the economy as a complex adaptive system, may use some of the tools of statistical physics and do not necessarily use the standard equilibrium approach. The ABM is a most promising way to do it.

Traditional approaches in economics rely on the assumption that economic agents are identical, non-interacting and rational. Within this framework, economic instabilities would require large exogenous shocks, when in fact small local shocks can trigger large systemic effects when heterogeneities and interactions are taken into account. The need to include these effects motivate the development of agent-based models (ABMs), which are extremely versatile and allow to take into account more realistic behavioural rules. In this talk we introduce a simple ABM, explore the possible types of phenomena that it can reproduce and propose a methodology that characterizes a model through its phase diagram. We then generalize the model with the aim of investigating the role and efficacy of the monetary policy of a central bank. We show that the existence of different equilibrium states of the economy can cause the monetary policy itself to trigger instabilities and be counter-productive.

These last years have witnessed a significant rise of papers from physicists using relatively simple models to understand social systems. The basic idea is to use the physicists’ expertise on the emergence of collective phenomena in condensed-matter : as the properties of materials emerge from the interactions between atoms, the characteristics of societies would emerge from interactions between individuals, taken as ‘social atoms’. In this presentation, I claim that these micro-macro models are unfit to unfold the complexity of collective existence and that the priority should instead be the development of new formal tools to exploit the richness of digital data. Specifically, I will argue that micro-macro models have serious methodological and political problems. From a methodological viewpoint, most simulations work only at the price of simplifying the properties of micro-agents, the rules of interaction and the nature of macro-structures so that they conveniently fit each other. A bit like Descartes’ followers who explained the acidity of lemons by postulating the existence of ‘lemon atoms’ with tiny pricking needles. In the absence of empirical confirmation, social models tend to rely exclusively on internal coherence rather than validation or relevance for real social systems. From a political viewpoint, micro-macro models assume by construction that agents at the local level are incapable to understand and control the phenomena at the global level, as in the so-called ‘tragedy of the commons’. Only the modelers can observe collective phenomena. Ironically, a supposedly “bottom-up” approach leads to “top-down” social politics! In a recent collaboration with sociologists, we have argued that collective action does not originate at the micro level of individual atoms and does not end up in a macro level of stable structures. Instead, actions distribute in intricate and heterogeneous networks than fold and deploy creating differences but not discontinuities. Therefore, the time seems ripe to develop the formal techniques necessary to unfold the origami of collective existence and this should be the aim of the renewed alliance between the social and natural sciences. For the next few years, efforts should be shifted from simulating to mapping, from simple explanations to complex observations.

In an effort to understand the drivers of the decoupling of finance from the real economy, I will discuss simple models that provide a quantitative measure of unpriced information losses that occur in widespread financial practices.

Whenever customers'choices (e.g. to buy or not a given good) depend on others choices ('bandwagon effect' in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one -- in which case one says that the customers coordinate. This leads to a dilemma for the seller: should he sell at a high price, targeting a small number of buyers, or at low price targeting a large number of buyers? We show that the interaction between demand and supply is even more complex than expected, leading to what we call the curse of coordination: the pricing strategy for the seller which aimed at maximizing his profit corresponds to posting a price which, not only assumes that the customers will coordinate, but also lies very near the critical price value at which such high demand no more exists. This is obtained by the detailed mathematical analysis of a particular model formally related to the Random Field Ising Model and to a model introduced in social sciences by T. C. Schelling in the 70's.

Work with Mirta B. Gordon (LIG, Grenoble), Denis Phan (GEMASS, Paris) and Viktoriya Semeshenko (Instituto Interdisciplinario de Economía Política, Buenos-Aires)

In this talk we survey some recent results on the control of complex socio-economic systems composed by a large number of agents. We focus in particular on constrained opinion models and investigate model predictive control techniques in the mean-field and Boltzmann limits. Connections with continuous control based on Riccati equations are also presented. Finally the presence of random inputs in the system is considered and the need to control instabilities is discussed. Several numerical results illustrate the different approaches. References
[1] G.Albi, M.Herty, and L.Pareschi. Kinetic description of optimal control problems in consensus modeling. Comm. Math. Sci., to appear
[2] G.Albi, L.Pareschi, and M.Zanella. Boltzmann type control of opinion consensus through leaders. Phil. Trans. A Math. Phys. Eng. Sci., 13:372(2028), 2014
[3] M.Herty, L.Pareschi, S.Steffensen. Mean-field control and Riccati equations. Network and Heterogeneous Media, to appear
[4] G.Albi, L.Pareschi, and M.Zanella. Uncertainty quantification in control problems for flocking models, preprint 2014

The purpose of this talk is to discuss some issues related to the analysis of social phenomena from the perspective of sociology. First, I claim that, overall, the sociological analysis of social phenomena still has an uncertain scientific status, due to its being a melting pot of sometimes divergent epistemological and methodological stances. Then, I focus on the quantitative analysis of social phenomena and discuss its current practices, pointing to strengths and weaknesses. Finally, I suggest that a new alliance between sociology and other scientific disciplines, like biology and physics, might contribute to bring about a truly scientific analysis of social phenomena.

The piece of work described in this talk aims to challenging current thinking in IT about the 'Big Data' question, proposing – almost verbatim, with almost no formulas – a program whose goal is to construct an innovative methodology to perform data analytics. We suggest to build a theoretical framework which – directly probing the data space – could enable us to extract the manifold of hidden relations (patterns) that exist among data as correlations. The latter depend on and at the same time generate the semantics underlying the mining context itself. The approach, that exploits recent innovative ways of incorporating data in a topological setting, proposes a Field Theory of Data, transferring and generalizing to the space of data notions inspired by physical (topological) field theories. It harnesses as well the theory of formal languages to define a potential semantics to understand the emerging patterns.

Exploiting recent availability of comprehensive data on all scoring events in recent NBA basketball games, the statistics of scoring and lead changes are investigated. Except for anomalies at the start and the end of the game, basketball scoring is well described by a continuous-time anti-persistent random walk, with essentially no temporal correlations between successive scoring events. We also determine the criterion for when a lead of a specified size is "safe" as a function of the time remaining in the game. Finally, we show that the distribution of times when the last lead change occurs and the distribution of times when the score difference is maximal are both given by the celebrated arcsine law, a prediction that is in excellent agreement with basketball game data.

The full impact of the era of internet and the informatics revolution is probably still not fully apprehensible. The informatics revolution no doubt means far reaching changes for just about any science. The increased computer capacity, the speed of calculations, the storage capacity, implies that we can do things that were impossible just a few years ago. For the social sciences the changes are extremely important. The revolution has brought “big data” do the desktop of the researcher. This drastically changes the scope of social research. From being a science foremost engaged with philosophical reasoning of about human and collective behaviour, or from being survey driven, sociology and other social sciences have recently been exposed to large or very large data sets recorded in continues time. The complexity and wealth of this “new” data invites to a different analytical approach than the traditional. In this talk I’ll dissect the mind of the sociologists, show what they are looking out for, and the tools, primitive and advanced, used to produce frontier sociological science. I’ll show the sociologist limitations in dealing with systemic data, and argue for a more close collaboration between social scientists and in particular physicists and mathematicians. Making out with the hard sciences may bring social sciences closer to the reality that it is trying so hard to understand.

Winner selection by majority, in an election between two candidates, is the only rule compatible with democratic principles. Instead, when the candidates are three or more and the voters rank candidates in order of preference, there are no univocal criteria for the selection of the winning (consensus) ranking and the outcome is known to depend sensibly on the adopted rule. Building upon XVIII century Condorcet theory, whose idea was to maximize total voter satisfaction, we propose here the addition of a new basic principle (dimension) to guide the selection: satisfaction should be distributed among voters as equally as possible. With this new criterion we identify an optimal set of rankings. They range from the Condorcet solution to the one which is the most egalitarian with respect to the voters. We show that highly egalitarian rankings have the important property to be more stable with respect to fluctuations and that classical consensus rankings (Copeland, Tideman, Schulze) often turn out to be non optimal. The new dimension we have introduced provides, when used together with that of Condorcet, a clear classification of all the possible rankings. By increasing awareness in selecting a consensus ranking our method may lead to social choices which are more egalitarian compared to those achieved by presently available voting systems.

Growing economic inequalities are observed in several countries throughout the world. Following Pareto, the power-law structure of these inequalities has been the subject of much theoretical and empirical work. But their nonequilibrium dynamics, e.g. after a policy change, remains incompletely understood. I will introduce a thermodynamical theory of inequalities based on the analogy between economic stratification and statistical entropy. Within this framework the combination of upward mobility with precariousness is identified as a fundamental driver of inequality. I will formalize this statement by a "second-law" inequality displaying upward mobility and precariousness as thermodynamic conjugate variables. I will also estimate the time scale for the "relaxation" of the wealth distribution after a sudden change of the after-tax return on capital. My method can be generalized to gain insight into the dynamics of inequalities in any Markovian model of socioeconomic interactions.

In recent years, the distribution of wealth in a multi-agent society has been investigated by resorting to classical methods of kinetic theory of rarefied gases. In analogy with the Boltzmann equation, the change of wealth in these models is due to microscopic binary trades among agents. Surprisingly, other important aspects linked to different types of human wealth, like the role of personal knowledge (information), have not been taken into consideration. In this lecture, we introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through binary trades. The trades, which include both saving propensity and the risks of the market, are here modified in the risk and saving parameters, which now are assumed to depend on the personal degree of knowledge. The numerical simulations show that the presence of knowledge has the potential to produce a class of wealthy agents and to account for a larger proportion of wealth inequality.

In this talk we deal with a classical problem in sociology which is the phenomena of isolation and individual alienation in large urban areas. More specifically, we study the structure of a social network of trust investigating its property of connectedness versus fragmentation. To this purpose we analyse two extensive sets of census data on immigration, concerning social and economic integration quantifiers collected in Spain and in Italy. The study is based on a novel approach that uses data analysis methods and mathematical models inspired by statistical physics. We show that integration quantifiers may exhibit linear or non-linear growth on immigration density. We explain these differences by means of a properly defined social interaction component, and we illustrate how this leads to quantitative estimates of integration across different socioeconomic contexts.