Publications
179 results found
Goto 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: 2045-2322
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.
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.
Diaz-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: 1951-6355
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.
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.
Diaz-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: 1089-7682
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
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.
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.
Loe CW, Jensen HJ, 2016, Revisiting interval graphs for Network Science, Journal of Complex Networks, Vol: 4, Pages: 224-244, ISSN: 2051-1310
The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear structure in the system. The higher-dimensional analogue is an embedding of a graph onto a multi-dimensional Euclidean space and it was used by scientists to study the multi-relational complexity of ecology. However, the research went out of fashion in the 1980s and was not revisited when Network Science recently expressed interests with multi-relational networks known as multiplexes. This paper studies interval graphs from the perspective of Network Science.
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.
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.
Watkins NW, Pruessner G, Chapman SC, et al., 2016, Erratum to: 25 Years of Self-organized Criticality:Concepts and Controversies, Space Science Reviews, Vol: 198, Pages: 45-45, ISSN: 1572-9672
Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers.
Watkins NW, Pruessner G, Chapman SC, et al., 2016, 25 Years of Self-organized Criticality: Concepts and Controversies, Space Science Reviews, Vol: 198, Pages: 3-44, ISSN: 1572-9672
Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers.
Zand J, Tirnakli U, Jensen HJ, 2015, On the relevance of q-distribution functions: The return time distribution of restricted random walker, Journal of Physics A - Mathematical and Theoretical, Vol: 48, ISSN: 1751-8113
There exist a large literature on the application of q-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, PR(0; t), of a random walk on the set of integers {0, 1, 2, ..., L} with a position dependent transition probability given by |n/L|^a. We find that for all values of a ∈ [0, 2] P_R(0, t) can be fitted by q-exponentials, but only for a = 1 is P_R(0, t) given exactly by a q-exponential in the limit L → ∞. This is a remarkable result since the exact analytical solution of the corresponding continuum model represents P_R(0, t) as a sum of Bessel functions witha smooth dependence on a from which we are unable to identify a = 1 as of special significance. However, from the high precision numerical iteration of the discrete Master Equation, we do verify that only for a = 1 is P_R(0, t) exactly a q-exponential and that a tiny departure from this parameter value makes the distribution deviate from q-exponential. Further research is certainly required to identify the reason for this result and also the applicability of q-statistics and its domain.
Vázquez P, Del Río JA, Cedano KG, et al., 2015, An Entangled Model for Sustainability Indicators., PLOS One, Vol: 10, Pages: e0135250-e0135250, ISSN: 1932-6203
Nowadays the challenge for humanity is to find pathways towards sustainable development. Decision makers require a set of sustainability indicators to know if the sustainability strategies are following those pathways. There are more than one hundred sustainability indicators but they differ on their relative importance according to the size of the locality and change on time. The resources needed to follow these sustainability indicators are scarce and in some instances finite, especially in smaller regions. Therefore strategies to select set of these indicators are useful for decision makers responsible for monitoring sustainability. In this paper we propose a model for the identification and selection of a set of sustainability indicators that adequately represents human systems. In developing this model, we applied evolutionary dynamics in a space where sustainability indicators are fundamental entities interconnected by an interaction matrix. we used a fixed interaction that simulates the current context for the city of Cuernavaca, México as an example. We were able to identify and define relevant sets indicators for the system by using the Pareto principle. In this case we identified a set of sixteen sustainability indicators with more than 80% of the total strength. This set presents resilience to perturbations. For the Tangled Nature framework we provided a manner of treating different contexts (i.e., cities, counties, states, regions, countries, continents or the whole planet), dealing with small dimensions. This model provides decision makers with a valuable tool to select sustainability indicators set for towns, cities, regions, countries, continents or the entire planet according to a coevolutionary framework. The social legitimacy can arise from the fact that each individual indicator must be selected from those that are most important for the subject community.
Loe CW, Jensen HJ, 2015, Bibliographic search with Mark-and-Recapture, Physica A - Statistical Mechanics and Its Applications, Vol: 434, Pages: 246-256, ISSN: 0378-4371
Mark-and-Recapture is a methodology from Population Biology to estimate the population of a species without counting every individual. This is done by multiple samplings of the species using traps and discounting the instances that were caught repeated. In this paper we show that this methodology is applicable for bibliographic analysis as it is also not feasible to count all the relevant publications of a research topic. In addition this estimation also allows us to propose a stopping rule for researchers to decide how far one should extend their search for relevant literature.
Kawamoto H, Takayasu H, Jensen HJ, et al., 2015, Precise calculation of a bond percolation transition and survival rates of nodes in a complex network, PLOS One, Vol: 10, ISSN: 1932-6203
Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition.
Loe CW, Jensen HJ, 2015, Comparison of communities detection algorithms for multiplex, Physica A - Statistical Mechanics and Its Applications, Vol: 431, Pages: 29-45, ISSN: 0378-4371
Multiplex is a set of graphs on the same vertex set, i.e. {G(V,E1),…,G(V,Em)}{G(V,E1),…,G(V,Em)}. It is a type of generalized graph to model the multiple relationships in a system with parallel edges between vertices. An important application in Network Science is to capture community structures in multiplex as a way to modularize the system. This paper is a literature review and comparative analysis on the existing communities detection algorithms for multiplex. The conclusion is that many of the algorithms deviate in the concept of multi-relational communities and the wrong choice of algorithm can deviate one from his intended concept.
Massobrio P, de Arcangelis L, Pasquale V, et al., 2015, Criticality as a signature of healthy neural systems, Frontiers in Systems Neuroscience, Vol: 9, ISSN: 1662-5137
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
Cairoli A, Piovani D, Jensen HJ, 2014, Forecasting transitions in systems with high-dimensional stochastic complex dynamics: A linear stability analysis of the tangled nature model, Physical Review Letters, Vol: 113, ISSN: 0031-9007
We propose a new procedure to monitor and forecast the onset of transitions in high-dimensional complex systems. We describe our procedure by an application to the tangled nature model of evolutionary ecology. The quasistable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean-field equations. Numerical analysis of the high-dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with a positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean-field approximation is found to be a good early warning of the transitions occurring intermittently.
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.
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.
Jensen HJ, Viegas E, Cockburn SP, et 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
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.
Jensen HJ, 2014, Forecasting transitions in systems with high dimensional stochastic complex dynamics: A Linear Stability Analysis of the Tangled Nature Model, Phys Rev Lett
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean field equations. Numerical analysis of the high dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation is found to be a good early-warning of the transitions occurring intermittently.
Razak FA, Jensen HJ, 2014, Estimation of Information Theoretic Measures on the Ising Model, 3rd International Conference on Mathematical Sciences, Publisher: AMER INST PHYSICS, Pages: 56-61, ISSN: 0094-243X
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Jensen HJ, 2013, Forecasting transitions in systems with high dimensional stochastic complex dynamics: A Linear Stability Analysis of the Tangled Nature Model, Phys Rev Lett
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean field equations. Numerical analysis of the high dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation is found to be a good early-warning of the transitions occurring intermittently.
Viegas E, Takayasu M, Miura W, et al., 2013, Ecosystems Perspective on Financial Networks: Diagnostic Tools, COMPLEXITY, Vol: 19, Pages: 22-36, ISSN: 1076-2787
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Jensen HJ, 2013, Mathematics and painting, INTERDISCIPLINARY SCIENCE REVIEWS, Vol: 27, Pages: 45-49, ISSN: 0308-0188
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Loe CW, Jensen HJ, 2013, Edge union of networks on the same vertex set, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 46, ISSN: 1751-8113
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