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• Journal article
Duarte D, Amarteifio S, Ang H, Kong IY, Ruivo N, Pruessner G, Hawkins ED, Lo Celso Cet al., 2019,

### Defining the in vivo characteristics of acute myeloid leukemia cells behavior by intravital imaging

, Immunology and Cell Biology, Vol: 97, Pages: 229-235, ISSN: 1440-1711

The majority of acute myeloid leukemia (AML) patients have a poor response to conventional chemotherapy. The survival of chemoresistant cells is thought to depend on leukemia-bone marrow (BM) microenvironment interactions, which are not well understood. The CXCL12/CXCR4 axis has been proposed to support AML growth but was not studied at the single AML cell level. We recently showed that T-cell acute lymphoblastic leukemia (T-ALL) cells are highly motile in the BM; however, the characteristics of AML cell migration within the BM remain undefined. Here, we characterize the in vivo migratory behavior of AML cells and their response to chemotherapy and CXCR4 antagonism, using high-resolution 2-photon and confocal intravital microscopy of mouse calvarium BM and the well-established MLL-AF9-driven AML mouse model. We used the Notch1-driven T-ALL model as a benchmark comparison and AMD3100 for CXCR4 antagonism experiments. We show that AML cells are migratory, and in contrast with T-ALL, chemoresistant AML cells become less motile. Moreover, and in contrast with T-ALL, the in vivo exploratory behavior of expanding and chemoresistant AML cells is unaffected by AMD3100. These results expand our understanding of AML cells-BM microenvironment interactions, highlighting unique traits of leukemia of different lineages.

• Journal article
Garcia Millan R, Pausch J, Walter B, Pruessner Get al., 2018,

### Field-theoretic approach to the universality of branching processes

, Physical Review E, Vol: 98, ISSN: 1539-3755

Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival probability, expected avalanche duration, the so-called avalanche shape, the n-point correlation function, and the probability density function of the total avalanche size. Previous studies have shown universality in certain observables of branching processes using probabilistic arguments; however, a comprehensive description is lacking. We derive the field theory that describes the process and demonstrate how to use it to calculate the relevant observables and their scaling to leading order in time, revealing the universality of the moments of the population size. Our results explain why the first and second moment of the offspring distribution are sufficient to fully characterize the process in the vicinity of criticality, regardless of the underlying offspring distribution. This finding implies that branching processes are universal. We illustrate our analytical results with computer simulations.

• Journal article
Jensen H, Tempesta P, 2018,

### Group entropies: from phase space geometry to entropy functionals via group theory

, Entropy, Vol: 20, ISSN: 1099-4300

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
Rosas De Andraca FE, Martinez Mediano P, Ugarte M, Jensen Het al., 2018,

### An information-theoretic approach to self-organisation: Emergence of complex interdependencies in coupled dynamical systems

, Entropy, Vol: 20, ISSN: 1099-4300

Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures.

• Journal article
Sahasranaman A, Jensen HJ, 2018,

### Ethnicity and wealth: the dynamics of dual segregation

, PLoS ONE, Vol: 13, ISSN: 1932-6203

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
Dolan D, Jensen H, Martinez Mediano P, Molina-Solana MJ, Rajpal H, Rosas De Andraca F, Sloboda JAet al., 2018,

### The improvisational state of mind: a multidisciplinary study of an improvisatory approach to classical music repertoire performance

, Frontiers in Psychology, Vol: 9, ISSN: 1664-1078

The recent re-introduction of improvisation as a professional practice within classical music, however cautious and still rare, allows direct and detailed contemporary comparison between improvised and “standard” approaches to performances of the same composition, comparisons which hitherto could only be inferred from impressionistic historical accounts. This study takes an interdisciplinary multi-method approach to discovering the contrasting nature and effects of prepared and improvised approaches during live chamber-music concert performances of a movement from Franz Schubert’s “Shepherd on the Rock”, given by a professional trio consisting of voice, flute, and piano, in the presence of an invited audience of 22 adults with varying levels of musical experience and training. The improvised performances were found to be differ systematically from prepared performances in their timing, dynamic, and timbral features as well as in the degree of risk-taking and “mind reading” between performers including during moments of added extemporised notes. Post-performance critical reflection by the performers characterised distinct mental states underlying the two modes of performance. The amount of overall body movements was reduced in the improvised performances, which showed less unco-ordinated movements between performers when compared to the prepared performance. Audience members, who were told only that the two performances would be different, but not how, rated the improvised version as more emotionally compelling and musically convincing than the prepared version. The size of this effect was not affected by whether or not the audience could see the performers, or by levels of musical training. EEG measurements from 19 scalp locations showed higher levels of Lempel-Ziv complexity (associated with awareness and alertness) in the improvised version in both performers and audience. Results are discussed in terms of their potential

• Journal article
Jensen HJ, Pazuki RH, Pruessner G, Tempesta Pet al., 2018,

### Statistical mechanics of exploding phase spaces: ontic open systems

, Journal of Physics A: Mathematical and Theoretical, Vol: 51, ISSN: 1751-8113

The volume of phase space may grow super-exponentially ('explosively') with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. Standard ensemble theory can break down as we demonstrate in a simple model reminiscent of complex systems where new collective states emerge. We present an axiomatically defined entropy and argue that it is extensive in the micro-canonical, equal probability, and canonical (max-entropy) ensemble for super-exponentially growing phase spaces. This entropy may be useful in determining probability measures in analogy with how statistical mechanics establishes statistical ensembles by maximising entropy.

• 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
Garcia Millan R, Pruessner G, Pickering L, Christensen Ket al., 2018,

### Correlations and hyperuniformity in the avalanche size of the Oslo Model

, Europhysics Letters: a letters journal exploring the frontiers of physics, Vol: 122, ISSN: 1286-4854

Certain random processes display anticorrelations resulting in local Poisson-like disorder and global order, where correlations suppress fluctuations. Such processes are called hyperuniform. Using a map to an interface picture we show via analytic calculations that a sequence of avalanche sizes of the Oslo model is hyperuniform in the temporal domain with the minimal exponent $\lambda=0$ . We identify the conserved quantity in the interface picture that gives rise to the hyperuniformity in the avalanche size. We further discuss the fluctuations of the avalanche size in two variants of the Oslo model. We support our findings with numerical results.

• Journal article
Siddiqui M, Wedemann RS, Jensen HJ, 2018,

### Avalanches and generalized memory associativity in a network model for conscious and unconscious mental functioning

, Physica A: Statistical Mechanics and its Applications, Vol: 490, Pages: 127-138, ISSN: 0378-4371

We explore statistical characteristics of avalanches associated with the dynamics of a complex-network model, where two modules corresponding to sensorial and symbolic memories interact, representing unconscious and conscious mental processes. The model illustrates Freud’s ideas regarding the neuroses and that consciousness is related with symbolic and linguistic memory activity in the brain. It incorporates the Stariolo–Tsallis generalization of the Boltzmann Machine in order to model memory retrieval and associativity. In the present work, we define and measure avalanche size distributions during memory retrieval, in order to gain insight regarding basic aspects of the functioning of these complex networks. The avalanche sizes defined for our model should be related to the time consumed and also to the size of the neuronal region which is activated, during memory retrieval. This allows the qualitative comparison of the behaviour of the distribution of cluster sizes, obtained during fMRI measurements of the propagation of signals in the brain, with the distribution of avalanche sizes obtained in our simulation experiments. This comparison corroborates the indication that the Nonextensive Statistical Mechanics formalism may indeed be more well suited to model the complex networks which constitute brain and mental structure.

• Journal article
Nesbitt D, Pruessner G, Lee C, 2017,

### Edge instability in incompressible planar active fluids

, Physical Review E, Vol: 96, ISSN: 1539-3755

Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used by Zimmermann, Basan, and Levine [Eur. Phys. J.: Spec. Top. 223, 1259 (2014)], we perform a linear stability analysis on a two-dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorize the stability of the model and find that for experimentally relevant parameters, fingering instability is always absent in this minimal model. Our results point to the crucial role of density variation in the fingering instability in tissue regeneration.

• Journal article
Willis G, Pruessner G, 2017,

### Spatio-temporal correlations in the Manna model in one, three and five dimensions

, International Journal of Modern Physics B, Vol: 32, ISSN: 0217-9792

Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in d

• Journal article
Fallesen T, Roostalu J, Duellberg C, Pruessner G, Surrey Tet al., 2017,

### Ensembles of Bidirectional Kinesin Cin8 Produce Additive Forces in Both Directions of Movement

, Biophysical Journal, Vol: 113, Pages: 2055-2067, ISSN: 0006-3495

Most kinesin motors move in only one direction along microtubules. Members of the kinesin-5 subfamily were initially described as unidirectional plus-end-directed motors and shown to produce piconewton forces. However, some fungal kinesin-5 motors are bidirectional. The force production of a bidirectional kinesin-5 has not yet been measured. Therefore, it remains unknown whether the mechanism of the unconventional minus-end-directed motility differs fundamentally from that of plus-end-directed stepping. Using force spectroscopy, we have measured here the forces that ensembles of purified budding yeast kinesin-5 Cin8 produce in microtubule gliding assays in both plus- and minus-end direction. Correlation analysis of pause forces demonstrated that individual Cin8 molecules produce additive forces in both directions of movement. In ensembles, Cin8 motors were able to produce single-motor forces up to a magnitude of ∼1.5 pN. Hence, these properties appear to be conserved within the kinesin-5 subfamily. Force production was largely independent of the directionality of movement, indicating similarities between the motility mechanisms for both directions. These results provide constraints for the development of models for the bidirectional motility mechanism of fission yeast kinesin-5 and provide insight into the function of this mitotic motor.

• Journal article
Clough JR, Evans TS, 2017,

### Embedding graphs in Lorentzian spacetime

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

Geometric 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.

• Journal article
Rochester C, Sartor A, Pruessner G, Kornyshev AAet 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: 1023-1935

We 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.

• 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.

• 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
Dhar D, Pruessner G, Expert P, Christensen K, Zachariou Net al., 2016,

### Directed Abelian sandpile with multiple downward neighbors

, Physical Review E, Vol: 042107, ISSN: 1539-3755

We 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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## Publications

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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.