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Journal articleDiaz-Ruelas A, Jensen HJ, Piovani D, et 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: 1089-7682It 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
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Journal articleSahasranaman A, Jensen HJ, 2016,
Dynamics of Transformation from Segregation to Mixed Wealth Cities
, PLOS One, Vol: 11, ISSN: 1932-6203We 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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Journal articlePiovani D, Grujic J, Jensen HJ, 2016,
Linear stability theory as an early warning sign for transitions in high dimensional complex systems
, Journal of Physics A - Mathematical and Theoretical, Vol: 49, ISSN: 1751-8113We analyse in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems by application to the Tangled Nature model of evolutionary ecology and high dimensional replicator systems with a stochastic element. A high dimensional stability matrix is derived in the mean field approximation to the stochastic dynamics. This allows us to determine the stability spectrum about the observed quasi-stable configurations. From overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation, we are able to construct a good early-warning indicator of the transitions occurring intermittently.
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Journal articleLee CF, Pruessner G, 2016,
Percolation mechanism drives actin gels to the critically connected state
, Physical Review E, Vol: 93, ISSN: 1539-3755Cell motility and tissue morphogenesis depend crucially on the dynamic remodelling of actomyosinnetworks. An actomyosin network consists of an actin polymer network connected by crosslinkerproteins and motor protein myosins that generate internal stresses on the network. A recent discoveryshows that for a range of experimental parameters, actomyosin networks contract to clusterswith a power-law size distribution [Alvarado J. et al. (2013) Nature Physics 9 591]. Here, weargue that actomyosin networks can exhibit robust critical signature without fine-tuning becausethe dynamics of the system can be mapped onto a modified version of percolation with trapping(PT), which is known to show critical behaviour belonging to the static percolation universalityclass without the need of fine-tuning of a control parameter. We further employ our PT model togenerate experimentally testable predictions.
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Journal articlePruessner G, Lee CF, 2016,
Comment on "Anomalous Discontinuity at the Percolation Critical Point of Active Gels"
, Physical Review Letters, Vol: 116, ISSN: 1079-7114 -
Journal articleDhar D, Pruessner G, Expert P, et al., 2016,
Directed Abelian sandpile with multiple downward neighbors
, Physical Review E, Vol: 042107, ISSN: 1539-3755We study the directed Abelian sandpile model on a square lattice, with K downward neighborsper site, K > 2. The K = 3 case is solved exactly, which extends the earlier known solution forthe K = 2 case. For K > 2, the avalanche clusters can have holes and side-branches and are thusqualitatively different from the K = 2 case where avalanche clusters are compact. However, we findthat the critical exponents for K > 2 are identical with those for the K = 2 case, and the largescale structure of the avalanches for K > 2 tends to the K = 2 case.
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Journal articleBroga KM, Viegas E, Jensen HJ, 2016,
Model analysis of the link between interest rates and crashes
, Physica A - Statistical Mechanics and Its Applications, Vol: 457, Pages: 225-238, ISSN: 0378-4371We analyse the effect of distinct levels of interest rates on the stability of the financial network under ourmodelling framework. We demonstrate that banking failures are likely to emerge early on under sustainedhigh interest rates, and at much later stage - with higher probability - under a sustained low interest ratescenario. Moreover, we demonstrate that those bank failures are of a different nature: high interest ratestend to result in significantly more bankruptcies associated to credit losses whereas lack of liquidity tends tobe the primary cause of failures under lower rates.
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Journal articleRochester CC, Kondrat S, Pruessner G, et al., 2016,
Charging Ultra-nanoporous Electrodes with Size-asymmetric Ions Assisted by Apolar Solvent
, The Journal of Physical Chemistry C, Vol: 120, Pages: 16042-16050, ISSN: 1932-7447We develop a statistical theory of charging quasi single-file pores with cations and anions of different sizes as well as solvent molecules or voids. This is done by mapping the charging onto a one-dimensional Blume–Emery–Griffith model with variable coupling constants. The results are supported by three-dimensional Monte Carlo simulations in which many limitations of the theory are lifted. We explore the different ways of enhancing the energy storage which depend on the competitive adsorption of ions and solvent molecules into pores, the degree of ionophilicity and the voltage regimes accessed. We identify new solvent-related charging mechanisms and show that the solvent can play the role of an “ionophobic agent”, effectively controlling the pore ionophobicity. In addition, we demonstrate that the ion-size asymmetry can significantly enhance the energy stored in a nanopore.
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Journal articleYan X, Minnhagen P, Jensen HJ, 2016,
The likely determines the unlikely
, Physica A - Statistical Mechanics and Its Applications, Vol: 456, Pages: 112-119, ISSN: 0378-4371We point out that the functional form describing the frequency of sizes of events in complexsystems (e.g. earthquakes, forest fires, bursts of neuronal activity) can be obtained from maximallikelihood inference, which, remarkably, only involve a few available observed measures such asnumber of events, total event size and extremes. Most importantly, the method is able to predictwith high accuracy the frequency of the rare extreme events. To be able to predict the few, oftenbig impact events, from the frequent small events is of course of great general importance. For adata set of wind speed we are able to predict the frequency of gales with good precision. We analyseseveral examples ranging from the shortest length of a recruit to the number of Chinese characterswhich occur only once in a text.
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Journal articleNekovar S, Pruessner G, 2016,
A field-theoretic approach to the Wiener Sausage
, Journal of Statistical Physics, Vol: 163, Pages: 604-641, ISSN: 0022-4715The Wiener Sausage, the volume traced out by a sphere attachedto a Brownian particle, is a classical problem in statistics and mathematicalphysics. Initially motivated by a range of field-theoretic, technical questions,we present a single loop renormalised perturbation theory of a stochasticprocess closely related to the Wiener Sausage, which, however, proves to beexact for the exponents and some amplitudes. The field-theoretic approach isparticularly elegant and very enjoyable to see at work on such a classic problem.While we recover a number of known, classical results, the field-theoretictechniques deployed provide a particularly versatile framework, which allowseasy calculation with different boundary conditions even of higher momentaand more complicated correlation functions. At the same time, we provide ahighly instructive, non-trivial example for some of the technical particularitiesof the field-theoretic description of stochastic processes, such as excludedvolume, lack of translational invariance and immobile particles. The aim ofthe present work is not to improve upon the well-established results for theWiener Sausage, but to provide a field-theoretic approach to it, in order togain a better understanding of the field-theoretic obstacles to overcome.
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