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Journal articleClough JR, Evans TS, 2017,
Embedding graphs in Lorentzian spacetime
, PLOS ONE, Vol: 12, ISSN: 1932-6203Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG) into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature. We then use this general method to develop an algorithm which exploits the causal structure of a DAG to assign space and time coordinates in a Minkowski spacetime to each vertex. As in the causal set approach to quantum gravity, causal connections in the discrete graph correspond to timelike separation in the continuous spacetime. The method is demonstrated by calculating embeddings for simple models of causal sets and random DAGs, as well as real citation networks. We find that the citation networks we test yield significantly more accurate embeddings that random DAGs of the same size. Finally we suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.
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Journal articleRochester C, Sartor A, Pruessner G, et al., 2017,
"One dimensional" double layer. The effect of size asymmetry of cations and anions on charge-storage in ultranarrow nanopores-an Ising model theory
, RUSSIAN JOURNAL OF ELECTROCHEMISTRY, Vol: 53, Pages: 1165-1170, ISSN: 1023-1935We develop a statistical mechanical theory of charge storage in quasi-single-file ionophilic nanopores with pure room temperature ionic liquid cations and anions of different size. The theory is mapped to an extension of the Ising model exploited earlier for the case of cations and anions of the same size. We calculate the differential capacitance and the stored energy density per unit surface area of the pore. Both show asymmetry in the dependence on electrode potential with respect to the potential of zero charge, related to the difference in the size of the ions, which will be interesting to investigate experimentally. It also approves the increase of charge storage capacity via obstructed charging, which in these systems emerges for charging nanopores with smaller ions.
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Journal articleSahasranaman A, Jensen HJ, 2017,
Cooperative dynamics of neighborhood economic status in cities
, PLoS ONE, Vol: 12, ISSN: 1932-6203We 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.
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Journal articleGoto H, Viegas E, Jensen HJ, et al., 2017,
Appearance of unstable monopoly state caused by selective and concentrative mergers in business networks
, Scientific Reports, Vol: 7, ISSN: 2045-2322Recently, 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.
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Journal articleBrinck 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: 1095-8541General 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.
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Journal articleEvans TS, Rivers RJ, 2017,
Was Thebes necessary? Contingency in spatial modeling
, Frontiers in Digital Humanities, Vol: 4, ISSN: 2297-2668When 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.
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Journal articleDiaz-Ruelas A, Jensen HJ, Piovani D, et al., 2017,
Relating high dimensional stochastic complex systems to low-dimensional intermittency
, European Physical Journal - Special Topics, Vol: 226, Pages: 341-351, ISSN: 1951-6355We 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.
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Journal articleJensen HJ, del Rio-Chanona RM, Grujic J, 2017,
Trends of the world input and output network of global trade
, PLOS One, Vol: 12, ISSN: 1932-6203The 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.
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Book chapterAchurra Gonzalez PE, Angeloudis P, Zavitsas K, et 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 articleWei 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: 2470-0045R. 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.
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