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  • Journal article
    Sahasranaman A, Jensen HJ, 2017,

    Cooperative dynamics of neighborhood economic status in cities

    , PLoS ONE, Vol: 12, ISSN: 1932-6203

    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
    Goto H, Viegas E, Jensen HJ, Takayasu H, Takayasu Met al., 2017,

    Appearance of unstable monopoly state caused by selective and concentrative mergers in business networks

    , Scientific Reports, Vol: 7, ISSN: 2045-2322

    Recently, growth mechanism of firms in complex business networks became new targets of scientific study owing to increasing availability of high quality business firms’ data. Here, we paid attention to comprehensive data of M&A events for 40 years and derived empirical laws by applying methods and concepts of aggregation dynamics of aerosol physics. It is found that the probability of merger between bigger firms is bigger than that between smaller ones, and such tendency is enhancing year by year. We introduced a numerical model simulating the whole ecosystem of firms and showed that the system is already in an unstable monopoly state in which growth of middle sized firms are suppressed.

  • Journal article
    Brinck KT, Jensen HJJ, 2017,

    The evolution of ecosystem ascendency in a complex systems based model

    , Journal of Theoretical Biology, Vol: 428, Pages: 18-25, ISSN: 1095-8541

    General patterns in ecosystem development can shed light on driving forces behind ecosystem formation and recovery and have been of long interest. In recent years, the need for integrative and process oriented approaches to capture ecosystem growth, development and organisation, as well as the scope of information theory as a descriptive tool has been addressed from various sides. However data collection of ecological network flows is difficult and tedious and comprehensive models are lacking. We use a hierarchical version of the Tangled Nature Model of evolutionary ecology to study the relationship between structure, flow and organisation in model ecosystems, their development over evolutionary time scales and their relation to ecosystem stability. Our findings support the validity of ecosystem ascendency as a meaningful measure of ecosystem organisation, which increases over evolutionary time scales and significantly drops during periods of disturbance. The results suggest a general trend towards both higher integrity and increased stability driven by functional and structural ecosystem coadaptation.

  • Journal article
    Evans TS, Rivers RJ, 2017,

    Was Thebes necessary? Contingency in spatial modeling

    , Frontiers in Digital Humanities, Vol: 4, ISSN: 2297-2668

    When data are poor, we resort to theory modeling. This is a two-step process. We have first to identify the appropriate type of model for the system under consideration and then to tailor it to the specifics of the case. To understand settlement formation, which is the concern of this article, this involves choosing not only input parameter values such as site separations but also input functions that characterizes the ease of travel between sites. Although the generic behavior of the model is understood, the details are not. Different choices will necessarily lead to different outputs (for identical inputs). We can only proceed if choices that are “close” give outcomes that are similar. Where there are local differences, it suggests that there was no compelling reason for one outcome rather than the other. If these differences are important for the historic record, we may interpret this as sensitivity to contingency. We re-examine the rise of Greek city-states as first formulated by Rihll and Wilson in 1979, initially using the same “retail” gravity model. We suggest that, although cities like Athens owe their position to a combination of geography and proximity to other sites, the rise of Thebes is the most contingent, whose success reflects social forces outside the grasp of simple network modeling.

  • Journal article
    Diaz-Ruelas A, Jensen HJ, Piovani D, Robledo Aet al., 2017,

    Relating high dimensional stochastic complex systems to low-dimensional intermittency

    , European Physical Journal - Special Topics, Vol: 226, Pages: 341-351, ISSN: 1951-6355

    We evaluate the implication and outlook of an unanticipatedsimplification in the macroscopic behavior of two high-dimensional stochasticmodels: the Replicator Model with Mutations and the TangledNature Model (TaNa) of evolutionary ecology. This simplification consistsof the apparent display of low-dimensional dynamics in the nonstationaryintermittent time evolution of the model on a coarse-grainedscale. Evolution on this time scale spans generations of individuals,rather than single reproduction, death or mutation events. While a localone-dimensional map close to a tangent bifurcation can be derivedfrom a mean-field version of the TaNa model, a nonlinear dynamicalmodel consisting of successive tangent bifurcations generates time evolutionpatterns resembling those of the full TaNa model. To advancethe interpretation of this finding, here we consider parallel results on agame-theoretic version of the TaNa model that in discrete time yieldsa coupled map lattice. This in turn is represented, a la Langevin, bya one-dimensional nonlinear map. Among various kinds of behaviourswe obtain intermittent evolution associated with tangent bifurcations.We discuss our results.

  • Journal article
    Jensen HJ, del Rio-Chanona RM, Grujic J, 2017,

    Trends of the world input and output network of global trade

    , PLOS One, Vol: 12, ISSN: 1932-6203

    The international trade naturally maps onto a complex networks. Theoretical analysisof this network gives valuable insights about the global economic system. Althoughdifferent economic data sets have been investigated from the network perspective,little attention has been paid to its dynamical behaviour. Here we take the WorldInput Output Data set, which has values of the annual transactions between 40different countries of 35 different sectors for the period of 15 years, and infer the timeinterdependence between countries and sectors. As a measure of interdependence weuse correlations between various time series of the network characteristics. First weform 15 primary networks for each year of the data we have, where nodes are countriesand links are annual exports from one country to the other. Thenwe calculate thestrengths (weighted degree) and PageRank of each country in each of the 15 networksfor 15 different years. This leads to sets of time series and by calculating thecorrelations between these we form a secondary network where the links are thepositive correlations between different countries or sectors. Furthermore, we also forma secondary network where the links are negative correlations in order to study thecompetition between countries and sectors. By analysing this secondary network weobtain a clearer picture of the mutual influences between countries. As one mightexpect, we find that political and geographical circumstances playan important role.However, the derived correlation network reveals surprising aspects which are hiddenin the primary network. Sometimes countries which belong to the same community inthe original network are found to be competitors in the secondarynetworks. E.g.Spain and Portugal are always in the same trade flow community, neverthelesssecondary network analysis reveal that they exhibit contrary time evolution.

  • Book chapter
    Achurra Gonzalez PE, Angeloudis P, Zavitsas K, Niknejad, Graham Det al., 2017,

    Attacker-defender assessment of vulnerability in maritime logistics corridors

    , Advances in Shipping Data Analysis and Modeling. Tracking and Mapping Maritime Flows in the Age of Big Data, Editors: Ducruet, Publisher: Routledge
  • Journal article
    Wei N, Pruessner G, 2016,

    Comment on “Finite-size scaling of survival probability in branching processes”

    , Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol: 94, ISSN: 2470-0045

    R. Garcia-Millan et al. [Phys. Rev. E 91, 042122 (2015)] reported a universal finite-size scaling form of the survival probability in discrete time branching processes. In this comment, we generalize the argument to a wide range of continuous time branching processes. Owing to the continuity, the resulting differential (rather than difference) equations can be solved in closed form, rendering some approximations by R. Garcia-Millan et al. superfluous, although we work along similar lines. In the case of binary branching, our results are in fact exact. Demonstrating that discrete time and continuous time models have their leading order asymptotics in common, raises the question to what extent corrections are identical.

  • Journal article
    Diaz-Ruelas A, Jensen HJ, Piovani D, Robledo Aet al., 2016,

    Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model

    , Chaos, Vol: 26, ISSN: 1089-7682

    It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g. by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of Punctuated Equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, that entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low-dime

  • Journal article
    Sahasranaman A, Jensen HJ, 2016,

    Dynamics of Transformation from Segregation to Mixed Wealth Cities

    , PLOS One, Vol: 11, ISSN: 1932-6203

    We model the dynamics of a variation of the Schelling model for agents described simply bya continuously distributed variable—wealth. Agent movement is not dictated by agentchoice as in the classic Schelling model, but by their wealth status. Agents move to neighborhoodswhere 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 wealthbasedsegregation occurs and persists. However, introducing uncertainty into the decisionto move—that is, with some probability, if agents are allowed to move even though thethreshold condition is contravened—we find that even for small proportions of such disallowedmoves, the dynamics no longer yield segregation but instead sharply transition into apersistent 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 ofa non-linear relationship between allowed moves (moves where threshold condition is satisfied)and disallowed moves (moves where it is not). For small increases in disallowedmoves, there is a rapid corresponding increase in allowed moves (before the rate ofincrease tapers off and tends to zero), and it is the effect of this non-linearity on the dynamicsof 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 interpretedas public policy interventions to drive de-segregation. Our finding therefore suggeststhat it might require limited, but continually implemented, public intervention—just sufficientto enable a small, persistently sustained fraction of disallowed moves so as to trigger thedynamics that drive the transformation from a segregated to mixed equilibrium.

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