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Register a new userInterdisciplinarity in Socio-economics, mathematical analysis and predictability of complex systems
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D. Sornette
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In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology presented by Hollingworth and Mueller (2008). First, I review a personal highlight of my own scientific path that illustrates the power of interdisciplinarity as well as unity of the mathematical description of natural and social processes. I also argue against the claim that complex systems are in general `not susceptible to mathematical analysis, but must be understood by letting them evolve over time or with simulation analysis. Moreover, I present evidence of the limits of the claim that scientists working within Science II do not make predictions about the future because it is too complex. I stress the potentials for a third `Quantum Science and its associated conceptual and philosophical revolutions, and finally point out some limits of the `new theory of networks.
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Using a large database (~ 215 000 records) of relevant articles, we empirically study the complex systems field and its claims to find universal principles applying to systems in general. The study of references shared by the papers allows us to obtain a global point of view on the structure of this highly interdisciplinary field. We show that its overall coherence does not arise from a universal theory but instead from computational techniques and fruitful adaptations of the idea of self-organization to specific systems. We also find that communication between different disciplines goes through specific trading zones, ie sub-communities that create an interface around specific tools (a DNA microchip) or concepts (a network).
Understanding cities is central to addressing major global challenges from climate and health to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is only now accessible to comprehensive analyses with the availability of large datasets. Here, we study abundances of business categories across U.S. metropolitan statistical areas to investigate how diversity of economic activities depends on city size. A universal structure common to all cities is revealed, manifesting self-similarity in internal economic structure as well as aggregated metrics (GDP, patents, crime). A derivation is presented that explains universality and the observed empirical distribution. The model incorporates a generalized preferential attachment process with ceaseless introduction of new business types. Combined with scaling analyses for individual categories, the theory quantitatively predicts how individual business types systematically change rank with city size, thereby providing a quantitative means for estimating their expected abundances as a function of city size. These results shed light on processes of economic differentiation with scale, suggesting a general structure for the growth of national economies as integrated urban systems.
We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network density and the degree distri- bution as a function of the size of the initial subset of nodes. Moreover, we also study the resilience of the network to distress propagation. We first test the method on ensembles of synthetic networks generated with the Exponential Random Graph model which allows to apply common tools from statistical mechanics. We then test it on the empirical case of the World Trade Web. In both cases, we find that a subset of 10 % of nodes is enough to reconstruct the main features of the network along with its resilience with an error of 5%.
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Many models of market dynamics make use of the idea of conservative wealth exchanges among economic agents. A few years ago an exchange model using extremal dynamics was developed and a very interesting result was obtained: a self-generated minimum wealth or poverty line. On the other hand, the wealth distribution exhibited an exponential shape as a function of the square of the wealth. These results have been obtained both considering exchanges between nearest neighbors or in a mean field scheme. In the present paper we study the effect of distributing the agents on a complex network. We have considered archetypical complex networks: Erd{o}s-Renyi random networks and scale-free networks. The presence of a poverty line with finite wealth is preserved but spatial correlations are important, particularly between the degree of the node and the wealth. We present a detailed study of the correlations, as well as the changes in the Gini coefficient, that measures the inequality, as a function of the type and average degree of the considered networks.
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