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"Jeldtoft Jensen, Henrik"
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Trends of the World Input and Output Network of Global Trade
The international trade naturally maps onto a complex networks. Theoretical analysis of this network gives valuable insights about the global economic system. Although different economic data sets have been investigated from the network perspective, little attention has been paid to its dynamical behaviour. Here we take the World Input Output Data set, which has values of the annual transactions between 40 different countries of 35 different sectors for the period of 15 years, and infer the time interdependence between countries and sectors. As a measure of interdependence we use correlations between various time series of the network characteristics. First we form 15 primary networks for each year of the data we have, where nodes are countries and links are annual exports from one country to the other. Then we calculate the strengths (weighted degree) and PageRank of each country in each of the 15 networks for 15 different years. This leads to sets of time series and by calculating the correlations between these we form a secondary network where the links are the positive correlations between different countries or sectors. Furthermore, we also form a secondary network where the links are negative correlations in order to study the competition between countries and sectors. By analysing this secondary network we obtain a clearer picture of the mutual influences between countries. As one might expect, we find that political and geographical circumstances play an important role. However, the derived correlation network reveals surprising aspects which are hidden in the primary network. Sometimes countries which belong to the same community in the original network are found to be competitors in the secondary networks. E.g. Spain and Portugal are always in the same trade flow community, nevertheless secondary network analysis reveal that they exhibit contrary time evolution.
Journal Article
Group Entropies: From Phase Space Geometry to Entropy Functionals via Group Theory
The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalised entropies crucially depend on the number of allowed degrees of freedom N. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume W on N. We review the ensuing entropies, discuss the composability axiom and explain why group entropies may be particularly relevant from an information-theoretical perspective.
Journal Article
Group Structure as a Foundation for Entropies
Entropy can signify different things. For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced, and it can be difficult to ascertain their respective importance and merits. Here, we consider entropy in an abstract sense, as a functional on a probability space, and we review how being able to handle the trivial case of non-interacting systems, together with the subtle requirement of extensivity, allows for a systematic classification of the functional form.
Journal Article
Ethnicity and wealth: The dynamics of dual segregation
Creating inclusive cities requires meaningful responses to inequality and segregation. We build an agent-based model of interactions between wealth and ethnicity of agents to investigate 'dual' segregations-due to ethnicity and due to wealth. As agents are initially allowed to move into neighbourhoods they cannot afford, we find a regime where there is marginal increase in both wealth segregation and ethnic segregation. However, as more agents are progressively allowed entry into unaffordable neighbourhoods, we find that both wealth and ethnic segregations undergo sharp, non-linear transformations, but in opposite directions-wealth segregation shows a dramatic decline, while ethnic segregation an equally sharp upsurge. We argue that the decrease in wealth segregation does not merely accompany, but actually drives the increase in ethnic segregation. Essentially, as agents are progressively allowed into neighbourhoods in contravention of affordability, they create wealth configurations that enable a sharp decline in wealth segregation, which at the same time allow co-ethnics to spatially congregate despite differences in wealth, resulting in the abrupt worsening of ethnic segregation.
Journal Article
Poverty in the time of epidemic: A modelling perspective
We create a network model to study the spread of an epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for two kinds of agents—poor and non-poor. Under non-intervention, peak caseload is maximised, but no differences are observed in infection rates across poor and non-poor. Introducing interventions to control spread, peak caseloads are reduced, but both cumulative infection rates and current infection rates are systematically higher for the poor than for non-poor, across all scenarios. Larger populations, higher fractions of poor, and longer durations of intervention are found to progressively worsen outcomes for the poor; and these are of particular concern for economically vulnerable populations in cities of the developing world. Addressing these challenges requires a deeper, more rigorous understanding of the relationships between structural poverty and epidemy, as well as effective utilization of extant community level infrastructure for primary care in developing cities. Finally, improving iniquitous outcomes for the poor creates better outcomes for the whole population, including the non-poor.
Journal Article
Quantifying ‘Causality’ in Complex Systems: Understanding Transfer Entropy
'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables. Here we investigate the ability of the Transfer Entropy measure to identify causal relations embedded in emergent coherent correlations. We do this by firstly applying Transfer Entropy to an amended Ising model. In addition we use a simple Random Transition model to test the reliability of Transfer Entropy as a measure of 'causal' direction in the presence of stochastic fluctuations. In particular we systematically study the effect of the finite size of data sets.
Journal Article
Spontaneous emergence of computation in network cascades
Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that computation of complex Boolean functions arises spontaneously in threshold networks as a function of connectivity and antagonism (inhibition), computed by
logic automata (motifs)
in the form of
computational cascades
. We explain the emergent inverse relationship between the computational complexity of the motifs and their rank-ordering by function probabilities due to motifs, and its relationship to symmetry in function space. We also show that the optimal fraction of inhibition observed here supports results in computational neuroscience, relating to optimal information processing.
Journal Article
Dynamics of Transformation from Segregation to Mixed Wealth Cities
We model the dynamics of a variation of the Schelling model for agents described simply by a continuously distributed variable-wealth. Agent movement is not dictated by agent choice as in the classic Schelling model, but by their wealth status. Agents move to neighborhoods where their wealth is not lesser than that of some proportion of their neighbors, the threshold level. As in the case of the classic Schelling model, we find here that wealth-based segregation occurs and persists. However, introducing uncertainty into the decision to move-that is, with some probability, if agents are allowed to move even though the threshold condition is contravened-we find that even for small proportions of such disallowed moves, the dynamics no longer yield segregation but instead sharply transition into a persistent mixed wealth distribution, consistent with empirical findings of Benenson, Hatna, and Or. We investigate the nature of this sharp transformation, and find that it is because of a non-linear relationship between allowed moves (moves where threshold condition is satisfied) and disallowed moves (moves where it is not). For small increases in disallowed moves, there is a rapid corresponding increase in allowed moves (before the rate of increase tapers off and tends to zero), and it is the effect of this non-linearity on the dynamics of the system that causes the rapid transition from a segregated to a mixed wealth state. The contravention of the tolerance condition, sanctioning disallowed moves, could be interpreted as public policy interventions to drive de-segregation. Our finding therefore suggests that it might require limited, but continually implemented, public intervention-just sufficient to enable a small, persistently sustained fraction of disallowed moves so as to trigger the dynamics that drive the transformation from a segregated to mixed equilibrium.
Journal Article
Cooperative dynamics of neighborhood economic status in cities
We significantly extend our earlier variant of the Schelling model, incorporating a neighborhood Potential function as well as an agent wealth gain function to study the long term evolution of the economic status of neighborhoods in cities. We find that the long term patterns of neighborhood relative economic status (RES) simulated by this model reasonably replicate the empirically observed patterns from American cities. Specifically, we find that larger fractions of rich and poor neighborhoods tend to, on average, retain status for longer than lower- and upper-middle wealth neighborhoods. The use of a Potential function that measures the relative wealth of neighborhoods as the basis for agent wealth gain and agent movement appears critical to explaining these emergent patterns of neighborhood RES. This also suggests that the empirically observed RES patterns could indeed be universal and that we would expect to see these patterns repeated for cities around the world. Observing RES behavior over even longer periods of time, the model predicts that the fraction of poor neighborhoods retaining status remains almost constant over extended periods of time, while the fraction of middle-wealth and rich neighborhoods retaining status reduces significantly over time, tending to zero.
Journal Article