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  • Journal article
    Palmieri L, Jensen HJ, 2018,

    The emergence of weak criticality in SOC systems

    , EPL, Vol: 123, ISSN: 0295-5075

    Since Self-Organised Criticality (SOC) was introduced in 1987, both the nature of the self-organisation and the criticality have remained controversial. Besides, SOC-like dynamics has recently been observed in many natural processes like brain activity and rain precipitations, making a better understanding of such systems more urgent. Here we focus on the Drossel-Schwabl forest-fire model (FFM) of SOC and show that despite the model is not critical, it nevertheless exhibits a behaviour that justifies the introduction of a new kind of weak criticality. We present a method that allows to quantify the degree of criticality of a system and to introduce a new class of critical systems. This method can be easily adapted to experimental settings and contribute to a better understanding of real systems.

  • Journal article
    Goto H, Viegas E, Jensen HJ, Takayasu H, Takayasu Met al., 2018,

    Smoluchowski equation for networks: merger induced intermittent giant node formation and degree gap

    , Journal of Statistical Physics, Vol: 172, Pages: 1086-1100, ISSN: 1572-9613

    The dynamical phase diagram of a network undergoing annihilation, creation, and coagulation of nodes is found to exhibit two regimes controlled by the combined effect of preferential attachment for initiator and target nodes during coagulation and for link assignment to new nodes. The first regime exhibits smooth dynamics and power law degree distributions. In the second regime, giant degree nodes and gaps in the degree distribution are formed intermittently. Data for the Japanese firm network in 1994 and 2014 suggests that this network is moving towards the intermittent switching region.

  • Journal article
    Piovani 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: 1751-8113

    We 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.

  • Journal article
    Lee CF, Pruessner G, 2016,

    Percolation mechanism drives actin gels to the critically connected state

    , Physical Review E, Vol: 93, ISSN: 1539-3755

    Cell 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.

  • Journal article
    Pruessner 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 article
    Broga 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: 0378-4371

    We 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.

  • Journal article
    Rochester CC, Kondrat S, Pruessner G, Kornyshev AAet 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: 1932-7447

    We 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.

  • Journal article
    Yan X, Minnhagen P, Jensen HJ, 2016,

    The likely determines the unlikely

    , Physica A - Statistical Mechanics and Its Applications, Vol: 456, Pages: 112-119, ISSN: 0378-4371

    We 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.

  • Conference paper
    Piovani D, Grujic J, Jensen HJ, 2015,

    Forecasting systemic transitions in high dimensional stochastic complex systems

    , 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSquare), Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588
  • Journal article
    Jensen HJ, Wan X, Crüts B, 2014,

    The Causal Inference of Cortical Neural Networks during Music Improvisations

    , PLOS One, Vol: 9, ISSN: 1932-6203

    We present an EEG study of two music improvisation experiments. Professional musicians with high level of improvisation skills were asked to perform music either according to notes (composed music) or in improvisation. Each piece of music was performed in two different modes: strict mode and “let-go” mode. Synchronized EEG data was measured from both musicians and listeners. We used one of the most reliable causality measures: conditional Mutual Information from Mixed Embedding (MIME), to analyze directed correlations between different EEG channels, which was combined with network theory to construct both intra-brain and cross-brain networks. Differences were identified in intra-brain neural networks between composed music and improvisation and between strict mode and “let-go” mode. Particular brain regions such as frontal, parietal and temporal regions were found to play a key role in differentiating the brain activities between different playing conditions. By comparing the level of degree centralities in intra-brain neural networks, we found a difference between the response of musicians and the listeners when comparing the different playing conditions.

  • Journal article
    Gastner MT, Markou N, Pruessner G, Draief Met al., 2014,

    Opinion Formation Models on a Gradient

    , PLOS One, Vol: 9, ISSN: 1932-6203

    Statistical physicists have become interested in models of collective social behaviorsuch as opinion formation, where individuals change their inherently preferredopinion if their friends disagree. Real preferences often depend on regional culturaldifferences, which we model here as a spatial gradient g in the initial opinion. Thegradient does not only add reality to the model. It can also reveal that opinionclusters in two dimensions are typically in the standard (i.e., independent)percolation universality class, thus settling a recent controversy about a nonconsensusmodel. However, using analytical and numerical tools, we also present amodel where the width of the transition between opinions scales !g{1=4, not!g{4=7 as in independent percolation, and the cluster size distribution isconsistent with first-order percolation.

  • Journal article
    Pruessner G, Cheang S, Jensen HJ, 2014,

    Synchronization by small time delays

    , Physica A: Statistical Mechanics and its Applications, Vol: 420, Pages: 8-13, ISSN: 1873-2119

    Synchronization is a phenomenon observed in all of the living and in much of the nonliving world, for example in the heart beat, Huygens’ clocks, the flashing of fireflies and the clapping of audiences. Depending on the number of degrees of freedom involved, different mathematical approaches have been used to describe it, most prominently integrateand-fire oscillators and the Kuramoto model of coupled oscillators. In the present work, we study a very simple and general system of smoothly evolving oscillators, which continue to interact even in the synchronized state. We find that under very general circumstances, synchronization generically occurs in the presence of a (small) time delay. Strikingly, the synchronization time is inversely proportional to the time delay.

  • Journal article
    Jensen HJ, Viegas E, Cockburn SP, West GBet al., 2014,

    The dynamics of mergers and acquisitions: ancestry as the seminal determinant

    , Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 470, ISSN: 1471-2946
  • Journal article
    Razak FA, Jensen HJ, 2014,

    Quantifying 'causality' in complex systems: understanding transfer entropy

    , PLOS One, Vol: 9, ISSN: 1932-6203

    ‘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
    Rubin KJ, Pruessner G, Pavliotis GA, 2014,

    Mapping multiplicative to additive noise

  • Journal article
    Evans TS, Rivers RJ, 2014,

    New approaches to Archaic Greek Settlement Structure

    , Les Nouvelles de l'archéologie, Vol: 135, Pages: 21-27, ISSN: 0242-7702

    Recent developments in network theory have led to the creation of new Spatial Interaction Models (SIMs) and a reappraisal of existing models. Although not directed at the archaeology community, these models generalise the familiar gravitational models and Proximal Point Analysis (PPA) used by archaeologists for many years to help explain the archaeological record. However, a problem arises in archaeology that, with the increasing suite of plausible models that now exist, it is unclear how to choose one model over another. This can lead to the criticism that, if we hunt hard enough, we may be doing no more than finding a model which can be manipulated to conform to our preconceptions. In recent articles we have begun to address this criticism (Evans 2014, in press) with particular reference to the maritime networks of the MBA Aegean (Rivers 2014, in press). Different historical periods require different approaches and in this paper we continue this analysis by re-examining the onset of centralisation in mainland Greek city states of the 9th and 8th centuries BCE. Pioneering work on this archaic settlement structure was performed in 1987 by Rihll and Wilson (Rihll & Wilson 1987, 2: 5-32; 1991: 59-95), adapting a 'retail' model devised originally for urban planning. One alternative approach is given by a recent cost-benefit model termed ariadne, developed by ourselves (Evans, Knappett & Rivers 2009, 7: 451-79; Knappett, Evans & Rivers 2008, 82: 1009-84; 2011, 85: 1008-23), initially designed for Bronze Age maritime networks. A comparison of these models and other simpler SIMs for archaic settlements highlights the problems of modelling archaeological data. In particular we examine what constitutes model 'robustness' and the way in which different models handle 'contingency' when handling periods of rapid change.

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Note to staff: Publications will appear here automatically if you link your publications under the College's Sympletic Elements system.  This is done under "link to funding" under which you will find an option to find one or more papers which can be paired with an "organisational unit" where you should find the Centre for Complexity Science as one option. Any problems, talk to Tim Evans or the Faculty Web Team.