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  • 1. Baek, Seung Ki
    et al.
    Minnhagen, Petter
    Bernhardsson, Sebastian
    Choi, Kweon
    Kim, Beom Jun
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Flow improvement caused by agents who ignore traffic rules2009In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 80, no 1, p. 016111-Article in journal (Refereed)
    Abstract [en]

    A system of agents moving along a road in both directions is studied numerically within a cellular-automata formulation. An agent steps to the right with probability q or to the left with 1-q when encountering other agents. Our model is restricted to two agent types, traffic-rule abiders (q=1) and traffic-rule ignorers (q=1/2), and the traffic flow, resulting from the interaction between these two types of agents, which is obtained as a function of density and relative fraction. The risk for jamming at a fixed density, when starting from a disordered situation, is smaller when every agent abides by a traffic rule than when all agents ignore the rule. Nevertheless, the absolute minimum occurs when a small fraction of ignorers are present within a majority of abiders. The characteristic features for the spatial structure of the flow pattern are obtained and discussed.

  • 2. Baek, Seung Ki
    et al.
    Minnhagen, Petter
    Shima, Hiroyuki
    Kim, Beom Jun
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Phase transition of q-state clock models on heptagonal lattices2009In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 80, no 1, p. 011133-Article in journal (Refereed)
    Abstract [en]

    We study the q-state clock models on heptagonal lattices assigned on a negatively curved surface. We show that the system exhibits three classes of equilibrium phases; in between ordered and disordered phases, an intermediate phase characterized by a diverging susceptibility with no magnetic order is observed at every q >= 2. The persistence of the third phase for all q is in contrast with the disappearance of the counterpart phase in a planar system for small q, which indicates the significance of nonvanishing surface-volume ratio that is peculiar in the heptagonal lattice. Analytic arguments based on Ginzburg-Landau theory and generalized Cayley trees make clear that the two-stage transition in the present system is attributed to an energy gap of spin-wave excitations and strong boundary-spin contributions. We further demonstrate that boundary effects break the mean-field character in the bulk region, which establishes the consistency with results of clock models on boundary-free hyperbolic lattices.

  • 3. Baek, Seung Ki
    et al.
    Shima, Hiroyuki
    Kim, Beom Jun
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Curvature-induced frustration in the XY model on hyperbolic surfaces2009In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 79, no 6, p. 060106-Article in journal (Refereed)
    Abstract [en]

    We study low-temperature properties of the XY spin model on a negatively curved surface. Geometric curvature of the surface gives rise to frustration in local spin configuration, which results in the formation of high-energy spin clusters scattered over the system. Asymptotic behavior of the spin-glass susceptibility suggests a zero-temperature glass transition, which is attributed to multiple optimal configurations of spin clusters due to nonzero surface curvature of the system. It implies that a constant ferromagnetic spin interaction on a regular lattice can exhibit glasslike behavior without possessing any disorder if the lattice is put on top of a negatively curved space such as a hyperbolic surface.

  • 4. Holme, Petter
    et al.
    Kim, Beom Jun
    Growing scale-free networks with tunable clustering2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 65, no 2, p. 026107-Article in journal (Refereed)
    Abstract [en]

    We extend the standard scale-free network model to include a "triad formation step." We analyze the Geometric properties of networks Generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scale-free networks such as the power-law degree distribution and the small average geodesic length, but with the high clustering at the same time. In our model, the clustering coefficient is also shown to be tunable simply by changing a control parameter-the average number of triad formation trials per time step.

  • 5. Holme, Petter
    et al.
    Kim, Beom Jun
    Vertex overload breakdown in evolving networks2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 65, no 6, p. 066109-Article in journal (Refereed)
    Abstract [en]

    We study evolving networks based on the Barabasi-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to the fact that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanchelike breakdowns for both load limitations are observed. In order to avoid such avalanches we argue that the capacity of the vertices has to grow with the size of the system. An interesting irregular dynamics of the formation of the giant component (for the intrinsic communication activity case) is also studied. Implications on the growth of the Internet are discussed.

  • 6.
    Holme, Petter
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Kim, Beom Jun
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Fodor, Viktoria
    KTH, School of Electrical Engineering (EES), Communication Networks.
    Heterogeneous attachment strategies optimize the topology of dynamic wireless networks2010In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 73, no 4, p. 597-604Article in journal (Refereed)
    Abstract [en]

    In optimizing the topology of wireless networks built of a dynamic set of spatially embedded agents, there are many trade-offs to be dealt with. The network should preferably be as small (in the sense that the average, or maximal, pathlength is short) as possible, it should be robust to failures, not consume too much power, and so on. In this paper, we investigate simple models of how agents can choose their neighbors in such an environment. In our model of attachment, we can tune from one situation where agents prefer to attach to others in closest proximity, to a situation where agents attach to random others regardless of distance (which thus are, on average, further away than the connections to the spatial neighbors). We evaluate this scenario with several performance measures and find that the optimal topologies, for most of the quantities, is obtained for strategies resulting in a mix of most local and a few random connections.

  • 7. Holme, Petter
    et al.
    Kim, Beom Jun
    Minnhagen, P.
    Phase transitions in the two-dimensional random gauge XY model2003In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 67, no 10Article in journal (Refereed)
    Abstract [en]

    The two-dimensional random gauge XY model, where the quenched random variables are magnetic bond angles uniformly distributed within [(-)rpi,rpi](0less than or equal torless than or equal to1), is studied via Monte Carlo simulations. We investigate the phase diagram in the plane of the temperature T and the disorder strength r and infer, in contrast to a prevailing conclusion in many earlier studies, that the system is superconducting at any disorder strength r for sufficiently low T. It is also argued that the superconducting to normal transition has different nature at weak disorder and strong disorder: termed Kosterlitz-Thouless (KT) type and non-KT type, respectively. The results are compared to earlier works.

  • 8. Holme, Petter
    et al.
    Kim, Beom Jun
    Yoon, C. N.
    Han, S. K.
    Attack vulnerability of complex networks2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 65, no 5, p. 056109-Article in journal (Refereed)
    Abstract [en]

    We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph. For each case of attacks on vertices and edges, four different attacking strategies are used: removals by the descending order of the degree and the betweenness centrality, calculated for either the initial network or the current network during the removal procedure. It is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network, suggesting that the network structure changes as important vertices or edges are removed. Furthermore, the correlation between the betweenness centrality and the degree in complex networks is studied.

  • 9. Holme, Petter
    et al.
    Liljeros, Fredrik
    Edling, Christofer R.
    Kim, Beom Jun
    Network bipartivity2003In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 68, no 5, p. 056107-Article in journal (Refereed)
    Abstract [en]

    Systems with two types of agents with a preference for heterophilous interaction produce networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity. The two measures-one well known and natural, but computationally intractable, and the other computationally less complex, but also less intuitive-are examined on model networks that continuously interpolate between bipartite graphs and graphs with many odd circuits. We find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity, and thus conclude that the measures are quite relevant. We also measure and discuss the values of our bipartivity measures for empirical social networks (constructed from professional collaborations, Internet communities, and field surveys). Here we find, as expected, that networks arising from romantic online interaction have high, and professional collaboration networks have low, bipartivity values. In some other cases, probably due to low average degree of the network, the bipartivity measures cannot distinguish between romantic and friendship oriented interaction.

  • 10. Holme, Petter
    et al.
    Trusina, A.
    Kim, Beom Jun
    Minnhagen, Petter
    Prisoners' dilemma in real-world acquaintance networks: Spikes and quasiequilibria induced by the interplay between structure and dynamics2003In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 68, no 3, p. 030901-Article in journal (Refereed)
    Abstract [en]

    We study Nowak and May's spatial prisoners' dilemma game driven by mutations (random choices of suboptimal strategies) on empirical social networks. The time evolution of the cooperation level is highly complex containing spikes and steps between quasistable levels. A statistical characterization of the quasistable states and a study of the mechanisms behind the steps are given. We argue that the crucial structural ingredients causing the observed behavior is an inhomogeneous degree distribution and that the connections within vertices of highest degree are rather sparse. Based on these observations we construct model networks with a similar complex time evolution of the cooperation level.

  • 11. Kim, Beom Jun
    et al.
    Hong, H.
    Holme, Petter
    Jeon, G. S.
    Minnhagen, Petter
    Choi, M. Y.
    XY model in small-world networks2001In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 64, no 5, p. 056135-Article in journal (Refereed)
    Abstract [en]

    The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally coupled XY model.

  • 12. Kim, Beom Jun
    et al.
    Trusina, A
    Holme, Petter
    Minnhagen, Petter
    Chung, S
    Choi, M.Y.
    Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game in small-world networks2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 66, no 2, p. 021907-Article in journal (Refereed)
    Abstract [en]

    A two-dimensional small-world-type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node, with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium-type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, its recovery requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long-range connections.

  • 13. Medvedyeva, Kateryna
    et al.
    Holme, Petter
    Minnhagen, Petter
    Kim, Beom Jun
    Dynamic critical behavior of the XY model in small-world networks2003In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 67, no 3, p. 036118-Article in journal (Refereed)
    Abstract [en]

    The critical behavior of the XY model on small-world network is investigated by means of dynamic Monte Carlo simulations. We use the short-time relaxation scheme, i.e., the critical behavior is studied from the nonequilibrium relaxation to equilibrium. Static and dynamic critical exponents are extracted through the use of the dynamic finite-size scaling analysis. It is concluded that the dynamic universality class at the transition is of the mean-field nature. We also confirm numerically that the value of dynamic critical exponent is independent of the rewiring probability P for Pgreater than or similar to0.03.

  • 14. Wang, B.
    et al.
    Aihara, K.
    Kim, Beom Jun
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB. Sungkyunkwan University, South Korea .
    Immunization of geographical networks2009In: Complex Sciences: First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2, Springer Berlin/Heidelberg, 2009, no PART 2, p. 2388-2395Conference paper (Refereed)
    Abstract [en]

    We numerically investigate the epidemic spread phenomena and efficient immunization strategies on complex networks embedded in geometry. It is assumed that there exists an unavoidable time delay (we call it the detection time) between the actual infection and the beginning of immunization, and we implement two different immunization strategies: one is based on topological connection neighbors (CN) of the infected vertex and the other on geographical spatial neighbors (SN). It is found that the decrease of the detection time is very important for a successful immunization. Our results suggest that within the limitation of the network models considered here, in which the infection probability is assumed to decrease with the geographic distance, the simple SN strategy works almost equally or better than the CN strategy, especially when the detection time is longer.

  • 15. Wang, Bing
    et al.
    Aihara, Kazuyuki
    Kim, Beom Jun
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Comparison of immunization strategies in geographical networks2009In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 373, no 42, p. 3877-3882Article in journal (Refereed)
    Abstract [en]

    The epidemic spread and immunizations in geographically embedded scale-free (SF) and Watts-Strogatz (WS) networks are numerically investigated. We make a realistic assumption that it takes time which we call the detection time. for a vertex to be identified as infected, and implement two different immunization strategies: one is based on connection neighbors (CN) of the infected vertex with the exact information of the network structure utilized and the other is based on spatial neighbors (SN) with only geographical distances taken into account. We find that the decrease of the detection time is crucial for a successful immunization in general. Simulation results show that for both SF networks and WS networks, the SN strategy always performs better than the CN strategy. especially for more heterogeneous SF networks at long detection time. The observation is verified by checking the number of the infected nodes being immunized. We found that in geographical space, the distance preferences in the network construction process and the geographically decaying infection rate are key factors that make the SN immunization strategy outperforms the CN strategy. It indicates that even in the absence of the full knowledge of network connectivity we can still stop the epidemic spread efficiently only by using geographical information as in the SN strategy. which may have potential applications for preventing the real epidemic spread.

  • 16. Zhou, T.
    et al.
    Kiet, H. A. T.
    Kim, Beom Jun
    Wang, B. H.
    Holme, Petter
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Role of activity in human dynamics2008In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 82, no 2Article in journal (Refereed)
    Abstract [en]

    The human society is a very complex system; still, there are several non-trivial, features. One type of them is the presence of power-law-distributed quantities in temporal statistics. In this letter, we focus on the origin of power laws in rating of movies. We present a systematic empirical exploration of the time between two consecutive ratings of movies ( the interevent time). At an aggregate level, we find a monotonous relation between the activity of individuals and the power law exponent of the interevent time distribution. At an individual level, we observe a heavy-tailed distribution for each user, as well as a negative correlation between the activity and the width of the distribution. We support these findings by a similar data set from mobile phone text-message communication. Our results demonstrate a significant role of the activity of individuals on the society-level patterns of human behavior. We believe this is a common character in the interest-driven human dynamics, corresponding to (but different from) the universality classes of task-driven dynamics.

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