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  • 1.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bernhardsson, Sebastian
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Zipf's law unzipped2011In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 13, p. 043004-Article in journal (Refereed)
    Abstract [en]

    Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be citizens of a country and the groups family names, or the elements can be all the words making up a novel and the groups the unique words, or the elements could be inhabitants and the groups the cities in a country, and so on. A Random Group Formation (RGF) is presented from which a Bayesian estimate is obtained based on minimal information: it provides the best prediction for the number of groups with $k$ elements, given the total number of elements, groups, and the number of elements in the largest group. For each specification of these three values, the RGF predicts a unique group distribution $N(k)\propto \exp(-bk)/k^{\gamma}$, where the power-law index $\gamma$ is a unique function of the same three values. The universality of the result is made possible by the fact that no system specific assumptions are made about the mechanism responsible for the group division. The direct relation between $\gamma$ and the total number of elements, groups, and the number of elements in the largest group, is calculated. The predictive power of the RGF model is demonstrated by direct comparison with data from a variety of systems. It is shown that $\gamma$ usually takes values in the interval $1\leq\gamma\leq 2$ and that the value for a given phenomena depends in a systematic way on the total size of the data set. The results are put in the context of earlier discussions on Zipf's and Gibrat's laws, $N(k)\propto k^{-2}$ and the connection between growth models and RGF is elucidated.

  • 2.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bounds of percolation thresholds in the enhanced binary tree2011In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 390, no 8, p. 1447-1452Article in journal (Refereed)
    Abstract [en]

    It is argued that the lower critical percolation threshold of the enhanced binary tree is bounded as $p_{c1} < 0.355~059$ by studying its subgraphs while the upper threshold is bounded both from above and below by $1/2$ according to renormalization-group arguments. We also review a correlation analysis in an earlier work, which claimed a significantly higher estimate of $p_{c2}$ than $1/2$, to show that this analysis in fact gives a consistent result with this bound. It confirms that the duality relation between critical thresholds does not hold exactly for the EBT and its dual, possibly due to the lack of transitivity.

  • 3.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Hierarchical renormalization-group study on the planar bond-percolation problem2011In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 83, no 5, p. 055601-Article in journal (Refereed)
    Abstract [en]

    For certain hierarchical structures, one can study the percolation problemusing the renormalization-group method in a very precise way.We show that the idea can be alsoapplied to two-dimensional planar lattices by regarding them as hierarchicalstructures. Either a lower bound or an exact critical probability can beobtained with this method and the correlation-length critical exponent isapproximately estimated as $\nu \approx 1$.

  • 4.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Non-Kosterlitz-Thouless transitions for the q-state clock models2010In: 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. 82, no 3, p. 031102-Article in journal (Refereed)
    Abstract [en]

    The $q$-state clock model with the cosine potential has a single phasetransition for $q\leq4$ and two transitions for $q\geq5$. It is shown byMonteCarlo simulations that the helicity modulus for the five-state clock model($q=5$) does not vanish at the high-temperature transition. This is incontrast to the clock models with $q\geq6$ for which the helicity modulusvanishes. This means that the transition for the five-state clock modeldiffers from the Kosterlitz-Thouless (KT) transition. It is also shown thatthis change in the transition is caused by an interplay between the numberof angular directions and the interaction potential: by slightly modifyingthe interaction potential, the KT transition for $q=6$ turns into the samenon-KT transition. Likewise, the KT transition is recovered for $q=5$ whenthe Villain potential is used. Comparisons with other clock-model resultsare made and discussed.

  • 5.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Bernhardsson, Sebastian
    Umeå University, Faculty of Science and Technology, Physics.
    Choi, Kweon
    Gyeonggi Science High School.
    Kim, Beom Jun
    Department of Energy Science and BK21 Physics Research Division, Sungkyunkwan University, Suwon 440-746, Korea.
    Flow improvement caused by agents who ignore traffic rules2009In: 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. 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 ($q=1/2$). The traffic flow, resulting from the interaction between these two types of agents, 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 smallfraction of ignorers are present within a majority of abiders. The characteristic features for the spatial structure of the flow pattern are obtained and discussed.

  • 6.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Kim, Beom Jun
    BK21 Physics Research Division and Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea.
    Comment on `Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees'2009In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 42, p. 478001-Article in journal (Refereed)
    Abstract [en]

    The enhanced binary tree (EBT) is a nontransitive graph which has two percolation thresholds $p_{c1}$ and $p_{c2}$ with $p_{c1}<p_{c2}$. Our Monte Carlo study implies that the second threshold $p_{c2}$ is significantly lower than a recent claim by Nogawa and Hasegawa (J. Phys. A: Math. Theor. {\bf 42} (2009) 145001). This means that $p_{c2}$ for the EBT does not obey the duality relation for the thresholds of dual graphs $p_{c2}+\overline{p}_{c1}=1$ which is a property of a transitive, nonamenable, planar graph with one end. As in regular hyperbolic lattices, this relation instead becomes an inequality $p_{c2}+\overline{p}_{c1}<1$. We also find that the critical behavior is well described by the scaling form previously found for regular hyperbolic lattices.

  • 7.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Dept. of Physics, Sungkyunkwan University, Suwon, Korea.
    Comment on `Six-state clock model on the square lattice: Fisher zeroapproach with Wang-Landau sampling'2010In: 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. 81, no 6, p. 3101-Article in journal (Other academic)
    Abstract [en]

    Hwang in [Phys. Rev. E {\bf{80}}, 042103 (2009)] suggested that the two transitions of the six-state clock model on the square lattice are\emph{not} of the Kosterlitz-Thouless type. Here we show from simulations thatat the upper transition, the helicity modulus does make a discontinuous jumpto zero. This gives strong evidence for a Kosterlitz-Thoulesstransition.

  • 8.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    Kosterlitz-Thouless transition of magnetic dipoles on thetwo-dimensional plane2011In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 83, no 18, p. 184409-5 pArticle in journal (Refereed)
    Abstract [en]

    The universality class of a phase transition is often determined by factorslike dimensionality and inherent symmetry. We study the magneticdipole system in which the ground-state symmetry and the underlying latticestructure are coupled to each other in an intricate way. A two-dimensional(2D)square-lattice system of magnetic dipoles undergoes an order-disorder phasetransition belonging to the 2D Ising universality class.According to Prakash and Henley [Phys. Rev. B {\bf 42}, 6572 (1990)], this can berelated to the fourfold-symmetric ground states which suggests a similarityto the four-state clock model. Provided that this type ofsymmetry connection holds true, the magnetic dipoles on a honeycomb lattice,which possess sixfold-symmetric ground states, should exhibit aKosterlitz-Thouless transition in accordance with the six-state clock model.This is verified through numerical simulations in the present investigation.However, it is pointed out that this symmetry argument does not alwaysapply, which suggests that factors other than symmetry can be decisive forthe universality class of the magnetic dipole system.

  • 9.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Department of Physics, BK21 Physics Research Division, Sungkyunkwan University, Suwon 440-746, Korea.
    Percolation in hyperbolic lattices2009In: 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. 79, no 1, p. 011124-011130Article in journal (Refereed)
    Abstract [en]

    The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and reaches from the middle to the boundary. This transition is of the same type and has the same finite-size scaling properties as the corresponding transition for the Cayley tree. At the upper threshold, on the other hand, a single unbounded cluster forms which overwhelms all the others and occupies a finite fraction of the volume as well as of the boundary connections. The finite-size scaling properties for this upper threshold are different from those of the Cayley tree and two of the critical exponents are obtained. The results suggest that the percolation transition for the hyperbolic lattices forms a universality class of its own.

  • 10.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Dept. of Physics, Sungkyunkwan University, Suwon, Korea.
    Surface and bulk criticality in midpoint percolation2010In: 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. 81, no 4, p. 1108-6 sidorArticle in journal (Refereed)
    Abstract [en]

    The concept of midpoint percolation has recently been applied tocharacterize the double percolation transitions in negatively curvedstructures. Regular $d$-dimensional hypercubic lattices are in the presentwork investigated using the same concept.Specifically, the site-percolation transitions at the critical thresholds areinvestigated for dimensions up to $d=10$ by means of the Leath algorithm.It is shown that the explicit inclusion of the boundariesprovides a straightforward way to obtain critical indices, both for thebulk and surface parts. At and above the critical dimension $d=6$, it isfound that the percolation cluster contains only a finite number of surfacepoints in the infinite-size limit. This is in accordance with theexpectation from studies of lattices with negative curvature. It is alsofound that the number of surface points, reached by the percolation clusterin the infinite limit, approaches $2d$ for large dimensions $d$. We alsonote that the size dependence in proliferation of percolatingclusters for $d\ge 7$ can be obtained by solely counting surface pointsof the midpoint cluster.

  • 11.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    The Ten Thousand Kims2011In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 13, p. 073036-Article in journal (Refereed)
    Abstract [en]

    In the Korean culture the family members are recorded in special familybooks. This makes it possible to follow the distribution of Korean familynames far back in history. It is here shown that these name distributionsare well described by a simple null model, the random group formation (RGF)model. This model makes it possible to predict how the name distributionschange and these predictions are shown to be borne out. In particular, theRGF model predicts that, for married women entering a collection of familybooks in a certain year, the occurrence of the most common family name``Kim'' should be directly proportional the total number of married womenwith the same proportionality constant for all the years. This prediction isalso borne out to high degree. We speculate that it reflects some inherentsocial stability in the Korean culture. In addition, we obtain an estimate ofthe total population of the Korean culture down to year 500 AD, based on theRGF model and find about ten thousand Kims.

  • 12.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Kim, Beom Jun
    Dept. of Physics, Sungkyunkwan University, Korea.
    True and quasi long-range order in the generalized q-state clock model2009In: 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. 80, p. 060101-Article in journal (Refereed)
    Abstract [en]

    From consideration of the order-parameter distribution,we propose an observable which makes a clear distinction betweentrue and quasi long-range orders in the two-dimensionalgeneralized $q$-state clock model.Measuring this quantity by Monte Carlo simulations for $q=8$, weconstruct a phase diagram and identify critical properties acrossthe phase-separation lines among the true long-range order, quasilong-range order, and disorder. Our result supports the theoreticalprediction that there appears a discontinuous order-disorder transition assoon as the two phase-separation lines merge.

  • 13.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mäkelä, Harri
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    Critical temperatures of the three- and four-state Potts models on the kagome lattice2011In: 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. 83, no 6, p. 061104-Article in journal (Refereed)
    Abstract [en]

    The value of the internal energy per spin is independent of the strip widthfor a certain class of spin systems on two dimensional infinite strips. Itis verified that the Ising model on the kagome lattice belongs to this classthrough an exact transfer-matrix calculation of the internal energy for thetwo smallest widths. More generally, one can suggest an upper bound forthe critical coupling strength $K_c(q)$ for the $q$-state Potts model fromexact calculations of the internal energy for the two smallest stripwidths. Combining this with the corresponding calculation for the duallattice and using an exact duality relation enables us to conjecture thecritical coupling strengths for the three- and four-state Pottsmodels on the kagome lattice. The values are $K_c(q=3)=1.056~509~426~929~0$and $K_c(q=4) = 1.149~360~587~229~2$,and the values can, in principle, be obtained to an arbitrary precision. Wediscuss the fact that these values are in the middle of earlierapproximate results and furthermore differ from earlier conjecturesfor the exact values.

  • 14.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mäkelä, Harri
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
    Ising model on a hyperbolic plane with a boundary2011In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, p. 032103-Article in journal (Refereed)
    Abstract [en]

    A hyperbolic plane can be modeled by a structure called the enhanced binarytree. We study the ferromagnetic Ising model on top of the enhanced binarytree using the renormalization-group analysis in combination withtransfer-matrix calculations. We find a reasonable agreement with MonteCarlo calculations on the transition point, and the resulting criticalexponents suggest the mean-field surface critical behavior.

  • 15.
    Baek, Seung Ki
    et al.
    KAS Korea.
    Mäkilä, Harry
    QCD Labs, COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 13500, FI-00076 Aalto, Finland.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Physics Research Division and Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea .
    Residual discrete symmetry of the five-state clock model2013In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 88, no 1, article id 012125Article in journal (Refereed)
    Abstract [en]

    It is well known that the q-state clock model can exhibit a Kosterlitz-Thouless (KT) transition if q is equal to or greater than a certain threshold, which has been believed to be five. However, recent numerical studies indicate that helicity modulus does not vanish in the high-temperature phase of the five-state clock model as predicted by the KT scenario. By performing Monte Carlo calculations under the fluctuating twist boundary condition, we show that it is because the five-state clock model does not have the fully continuous U(1) symmetry even in the high-temperature phase while the six-state clock model does. We suggest that the upper transition of the five-state clock model is actually a weaker cousin of the KT transition so that it is q≥6 that exhibits the genuine KT behavior

  • 16.
    Bernhardsson, Sebastian
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Baek, Seung Ki
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    A Paradoxical Property of the Monkey Book2011In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P07013-Article in journal (Refereed)
    Abstract [en]

    A 'monkey book' is a book consisting of a random sequence of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book to real books. It is shown that the word distribution statistics for the monkey book is different and quite distinct from a typical real book. In particular, the monkey book obeys Heaps' power law to an extraordinarily good approximation, in contrast to the word distributions for real books, which deviate from Heaps' law in a characteristic way. This discrepancy is traced to the different properties of a 'spiked' distribution and its smooth envelope. The somewhat counter-intuitive conclusion is that a 'monkey book' obeys Heaps' power law precisely because its word-frequency distribution is not a smooth power law, contrary to the expectation based on simple mathematical arguments that if one is a power law, so is the other.

  • 17.
    Bernhardsson, Sebastian
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Correa da Rocha, Luis Enrique
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    The meta book and size-dependent properties of written language2009In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 11, article id 123015Article in journal (Refereed)
    Abstract [en]

    Evidence is given for a systematic text-length dependence of the power-law index $\gamma$ of a single book. The estimated $\gamma$ values are consistent with a monotonic decrease from 2 to 1 with increasing length of a text. A direct connection to an extended Heap's lawis explored. The infinite book limit is, as a consequence, proposed to be given by $\gamma = 1$ instead of the value $\gamma=2$ expected if the Zipf's law was ubiquitously applicable. In addition we explore the idea that the systematic text-length dependence can be described by a meta book concept, which is an abstract representation reflecting the word-frequency structure of a text. According to this concept the word-frequency distribution of a text, with a certain length written by a single author, has the same characteristics as a text of the same length pulled out from an imaginary complete infinite corpus written by the same author.

  • 18.
    Bernhardsson, Sebastian
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Models and average properties of scale-free directed networks2006In: 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. 74, p. 026104-026104-7Article in journal (Refereed)
    Abstract [en]

    We extend the merging model for undirected networks by Kim et al. [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile merging, give rise to two distinct network types. We uncover that some nontrivial features of these two network types resemble two levels of a certain randomization/nonspecificity in the link reshuffling during network evolution. Furthermore, the same features show up, respectively, in metabolic networks and transcriptional networks. We introduce measures that single out the distinguishing features between the two prototype networks, as well as point out features that are beyond the prototypes.

  • 19.
    Bernhardsson, Sebastian
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Selective pressure on metabolic network structures as measured from the random blind-watchmaker network2010In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 12, no 103047Article in journal (Refereed)
    Abstract [en]

    A random null model termed the Blind Watchmaker network (BW) has been shown to reproduce the degree distribution found in metabolic networks. This might suggest that natural selection has had little influence on this particular network property. We here investigate to what extent other structural network properties have evolved under selective pressure from the corresponding ones of the random null model: The clustering coefficient and the assortativity measures are chosen and it is found that these measures for the metabolic network structure are close enough to the BW-network so as to fit inside its reachable random phase space. It is furthermore shown that the use of this null model indicates an evolutionary pressure towards low assortativity and that this pressure is stronger for larger networks. It is also shown that selecting for BW networks with low assortativity causes the BW degree distribution to slightly deviate from its power-law shape in the same way as the metabolic networks. This implies that an equilibrium model with fluctuating degree distribution is more suitable as a null model, when identifying selective pressures, than a randomized counterpart with fixed degree sequence, since the overall degree sequence itself can change under selective pressure on other global network properties.

  • 20.
    Bernhardsson, Sebastian
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rocha, Luis E C
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Size dependent word frequencies and translational invariance of books2010In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 389, no 2, p. 330-341Article in journal (Refereed)
    Abstract [en]

    It is shown that a real novel shares many characteristic features with a null model in which the words are randomly distributed throughout the text. Such a common feature is a certain translational invariance of the text. Another is that the functional form of the word-frequency distribution of a novel depends on the length of the text in the same way as the null model.This means that an approximate power-law tail ascribed to the data will have an exponent which changes with the size of the text-section which is analyzed.A further consequence is that a novel cannot be described by text-evolution models like the Simon model.The size-transformation of a novel is found to be well described by a specific Random Book Transformation.This size transformation in addition enables a more precise determination of the functional form of the word-frequency distribution.The implications of the results are discussed.

  • 21.
    Bokma, Folmer
    et al.
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Baek, Seung Ki
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    50 years of inordinate fondness2014In: Systematic Biology, ISSN 1063-5157, E-ISSN 1076-836X, Vol. 63, no 2, p. 251-256Article in journal (Refereed)
  • 22. Christofano, G.
    et al.
    Marotta, V.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Naddeo, A.
    Niccoli, G.
    CFT description of the fully frustrated XY model and phase diagram analysis2006In: Journal of Statistical Mechanics, p. P11009-Article in journal (Refereed)
  • 23. Do Yi, Su
    et al.
    Noh, Jae Dong
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Song, Mi-Young
    Chon, Tae-Soo
    Kim, Beom Jun
    Human bipedalism and body-mass index2017In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, article id 3688Article in journal (Refereed)
    Abstract [en]

    Body-mass index, abbreviated as BMI and given by M/H2 with the mass M and the height H, has been widely used as a useful proxy to measure a general health status of a human individual. We generalise BMI in the form of M/Hp and pursue to answer the question of the value of p for populations of animal species including human. We compare values of p for several different datasets for human populations with the ones obtained for other animal populations of fish, whales, and land mammals. All animal populations but humans analyzed in our work are shown to have p ≈ 3 unanimously. In contrast, human populations are different: As young infants grow to become toddlers and keep growing, the sudden change of p is observed at about one year after birth. Infants younger than one year old exhibit significantly larger value of p than two, while children between one and five years old show p ≈ 2, sharply different from other animal species. The observation implies the importance of the upright posture of human individuals. We also propose a simple mechanical model for a human body and suggest that standing and walking upright should put a clear division between bipedal human (p ≈ 2) and other animals (p ≈ 3).

  • 24.
    Grönlund, Andreas
    et al.
    Umeå University, Faculty of Science and Technology, Department of Plant Physiology. Umeå University, Faculty of Science and Technology, Umeå Plant Science Centre (UPSC).
    Holme, Petter
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Dynamic scaling regimes of collective decision making2008In: EPL - Europhysics Letters, Vol. 81, no 2, p. 28003-Article in journal (Refereed)
    Abstract [en]

    We investigate a social system of agents faced with a binary choice. We assume there is a correct, or beneficial, outcome of this choice. Furthermore, we assume agents are influenced by others in making their decision, and that the agents can obtain information that may guide them towards making a correct decision. The dynamic model we propose is of nonequilibrium type, converging to a final decision. We run it on random graphs and scale-free networks. On random graphs, we find two distinct regions in terms of the finalizing time —the time until all agents have finalized their decisions. On scale-free networks, on the other hand, there do not seem to be such distinct scaling regions.

  • 25.
    Holme, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Wu, Zhi-Xi
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Multiscaling in an YX model of networks2009In: 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. 80, p. 036120-Article in journal (Refereed)
    Abstract [en]

    Weinvestigate a Hamiltonian model of networks. The model is amirror formulation of the XY model (hence the name)—instead ofletting the XY spins vary, keeping the coupling topology static,we keep the spins conserved and sample different underlying networks.Our numerical simulations show complex scaling behaviors with various exponentsas the system grows and temperature approaches zero, but nofinite-temperature universal critical behavior. The ground-state and low-order excitations forsparse, finite graphs are a fragmented set of isolated networkclusters. Configurations of higher energy are typically more connected. Theconnected networks of lowest energy are stretched out giving thenetwork large average distances. For the finite sizes we investigate,there are three regions—a low-energy regime of fragmented networks, anintermediate regime of stretched-out networks, and a high-energy regime ofcompact, disordered topologies. Scaling up the system size, the bordersbetween these regimes approach zero temperature algebraically, but different network-structuralquantities approach their T=0 values with different exponents. We arguethis is a, perhaps rare, example of a statistical-physics modelwhere finite sizes show a more interesting behavior than thethermodynamic limit.

  • 26.
    Kim, Beom Jun
    et al.
    Department of Molecular Science and Technology, Ajou University, Suwon, 442-749, Korea.
    Trusina, Ala
    Umeå University, Faculty of Science and Technology, Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Sneppen, Kim
    NORDITA, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
    Self organized scale-free networks from merging and regeneration2005In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 43, no 3, p. 369-372Article in journal (Refereed)
    Abstract [en]

    We propose that the ubiquitous scale free nature of many real world networks may emerge from a steady state process where nodes are created and merged randomly. The merging may be viewed as an optimization of efficiency by minimizing redundancy.

  • 27.
    Lee, Sang Hoon
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bernhardsson, Sebastian
    FOI, Swedish Defence Research Agency, Tumba SE-14725, Sweden.
    Holme, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Neutral theory of chemical reaction networks2012In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 14, p. 033032-Article in journal (Refereed)
    Abstract [en]

    To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex structure. However, specific features may sometimes be neutral and uncorrelated with any system-specific purpose, function or causal chain. Such neutral features are caused by chance and randomness. Here we compare two classes of chemical networks: one that has been subjected to biological evolution (the chemical reaction network of metabolism in living cells) and one that has not (the atmospheric planetary chemical reaction networks). Their degree distributions are shown to share the very same neutral system-independent features. The shape of the broad distributions is to a large extent controlled by a single parameter, the network size. From this perspective, there is little difference between atmospheric and metabolic networks; they are just different sizes of the same random assembling network. In other words, the shape of the degree distribution is a neutral characteristic feature and has no functional or evolutionary implications in itself; it is not a matter of life and death.

  • 28.
    Medvedyeva, K.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Holme, Peter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Department of Molecular Science and Technology, Ajou University, Suwon 442-749, Korea.
    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 P≳0.03.

  • 29.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Just and unjust distributions2011In: Physics today, ISSN 0031-9228, E-ISSN 1945-0699Article in journal (Other (popular science, discussion, etc.))
    Abstract [en]

    A single theory can explain how power-law distributions emerge from such wildly different areas as economy, cultural geography, ecology, linguistics, sociology, and biological chemistry.

    http://www.physicstoday.org/daily_edition/points_of_view/just_and_unjust_distributions

  • 30.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Om rättvisa och orättvisa fördelningar2011In: Fysikaktuellt, ISSN 0283-9148, no 4, p. 18-20Article in journal (Other (popular science, discussion, etc.))
  • 31.
    Minnhagen, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Baek, Seung Ki
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Analytic results for the percolation transitions of the enhancedbinary tree2010In: 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. 82, p. 011113-Article in journal (Refereed)
    Abstract [en]

    Percolation for a planar lattice has a single percolation threshold, whereaspercolation for a negatively curved lattice displays two separate thresholds.The enhanced binary tree (EBT) can be viewed as aprototype model displaying two separate percolation thresholds.We present an analytic result for the EBT model which givestwo critical percolation threshold probabilities,$p_{c1}=\frac{1}{2}\sqrt{13}-\frac{3}{2}$ and $p_{c2}=1/2$,and yields a size-scaling exponent $\Phi =\ln\left[\frac{p(1+p)}{1-p(1-p)}\right]/\ln 2$. It is inferred that the twothresholdvalues give exact upper limits and that $p_{c1}$ is furthermore exact. Inaddition, we argue that $p_{c2}$ is also exact. The physics of the model andthe results are described within themidpoint-percolation concept: Monte Carlo simulations are presented for thenumber of boundary points which are reached from the midpoint, and theresults are compared to the number of routes from the midpoint to theboundary given by the analytic solution. These comparisonsprovide a more precise physical picture of what happens at the transitions.Finally, the results are compared to related works, in particular, the Cayleytree and Monte Carlo results for hyperbolic lattices as well as earlierresults for the EBT model. It disproves a conjecture that the EBT has anexact relation to the thresholds of its dual lattice.

  • 32.
    Minnhagen, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Bernhardsson, Sebastian
    Umeå University, Faculty of Science and Technology, Physics.
    Optimization and scale-freeness for complex networks2007In: Chaos, ISSN 1054-1500, E-ISSN 1089-7682, Vol. 17, no 026117, p. 7-Article in journal (Refereed)
    Abstract [en]

    Complex networks are mapped to a model of boxes and balls where the balls are distinguishable. It is shown that the scale-free size distribution of boxes maximizes the information associated with the boxes provided configurations including boxes containing a finite fraction of the total amount of balls are excluded. It is conjectured that for a connected network with only links between different nodes, the nodes with a finite fraction of links are effectively suppressed. It is hence suggested that for such networks the scale-free node-size distribution maximizes the information encoded on the nodes. The noise associated with the size distributions is also obtained from a maximum entropy principle. Finally, explicit predictions from our least bias approach are found to be borne out by metabolic networks.

  • 33.
    Minnhagen, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Physics. Teoretisk fysik.
    Bernhardsson, Sebastian
    Umeå University, Faculty of Science and Technology, Physics.
    The blind watchmaker network: Scale-freeness and evolution2008In: PLoS ONE, ISSN 1932-6203, Vol. 3, no 2, p. e1690-1-e1690-5Article in journal (Other (popular science, discussion, etc.))
    Abstract [en]

    It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects an ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree distribution during evolution. The corresponding random network, here termed the blind watchmaker network has a power-law degree distribution with an exponent gamma >= 2. It is random with respect to a complete set of network states characterized by a description of which links are attached to a node as well as a time-ordering of these links. No a priory assumption of any growth mechanism or evolution process is made. It is found that the degree distribution of the blind watchmaker network agrees very precisely with that of the metabolic networks. This implies that the evolutionary pathway of the cell-metabolism, when projected onto a metabolic network representation, has remained statistically random with respect to a complete set of network states. This suggests that even a biological system, which due to natural selection has developed an enormous specificity like the cellular metabolism, nevertheless can, at the same time, display well defined characteristics emanating from the ubiquitous inherent random element of Darwinian evolution. The fact that also completely random networks may have scale-free node distributions gives a new perspective on the origin of scale-free networks in general.

  • 34.
    Minnhagen, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bernhardsson, Sebastian
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    The groundstates and phases of the two-dimensional fully frustrated XY model2010In: CONDENSED MATTER THEORIES, VOL 24, 2010, p. 3-14Conference paper (Refereed)
    Abstract [en]

    The 2D Fully Frustrated NY(FFXY) class of models is shown to contain a new ground-state in addition to the checkerboard groundstate of the standard 2D NY model. The spin configuration of this additional groundstate is obtained and its connection to a broken Z(2)-symmetry explained. This means that the class of 2D FEXY models belongs within a U(1) circle times Z(2) circle times Z(2)-symmetry phase-transition representation. The phase diagram is reviewed and the central charges of the four multicritical points described. The implications for the standard 2D FFXY-model are discussed and elucidated, in particular with respect to the long standing controversy concerning the phase transitions of the standard 2D FEXY-model.

  • 35.
    Minnhagen, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bernhardsson, Sebastian
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    The groundstates and phases of the two-dimensional fully frustrated XY model2009In: International Journal of Modern Physics B, ISSN 0217-9792, Vol. 23, no 20-21, p. 3939-3950Article in journal (Refereed)
    Abstract [en]

    The 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new groundstate in addition to the checkerboard groundstate of the standard 2D XY model. The spin configuration of this additional groundstate is obtained and its connection to a broken Z2-symmetry explained. This means that the class of 2D FFXY models belongs within a U(1) ⊗ Z2 ⊗ Z2-symmetry phase-transition representation. The phase diagram is reviewed and the central charges of the four multicritical points described. The implications for the standard 2D FFXY-model are discussed and elucidated, in particular with respect to the long standing controversy concerning the phase transitions of the standard 2D FFXY-model.

  • 36.
    Minnhagen, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Bernhardsson, Sebastian
    Umeå University, Faculty of Science and Technology, Physics.
    Kim, Beum Jun
    Department of Physics, BK21 Physics Research Division, and Institute of Basic Science, Sungkyunkwan University - Suwon 440-746, Korea.
    Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation2007In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 78, no 2, p. 28004-1-28004-5Article in journal (Other (popular science, discussion, etc.))
    Abstract [en]

    The origin of scale-free degree distributions in the context of networks is addressed through an analogous non-network model in which the node degree corresponds to the number of balls in a box and the rewiring of links to balls moving between the boxes. A statistical mechanical formulation is presented and the corresponding Hamiltonian is derived. The energy, the entropy, as well as the degree distribution and its fluctuations are investigated at various temperatures. The scale-free distribution is shown to correspond to the degenerate ground state, which has small fluctuations in the degree distribution and yet a large entropy. We suggest an implication of our results from the viewpoint of the stability in evolution of networks.

  • 37.
    Minnhagen, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Norqvist, Patrik
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Wiklund, Krister
    Umeå University, Faculty of Science and Technology, Department of Physics.
    ABC-bok för fysiknyfikna2010Book (Other (popular science, discussion, etc.))
  • 38.
    Minnhagen, Petter
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Physics.
    Sneppen, Kim
    NORDITA, Blegdamsvej 17, DK 2100, Copenhagen, Denmark.
    Trusina, Ala
    Self-organization of structures and networks from merging and small-scale fluctuations2004In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 340, no 4, p. 725-732Article in journal (Refereed)
    Abstract [en]

    We discuss merging-and-creation as a self-organizing process for scale-free topologies in networks. Three power-law classes characterized by the power-law exponents 23 , 2 and 25 are identified and the process is generalized to networks. In the network context the merging can be viewed as a consequence of optimization related to more efficient signaling.

  • 39.
    Rosvall, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Grönlund, Andreas
    Umeå University, Faculty of Science and Technology, Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Sneppen, Kim
    NORDITA, Blegdamsvej 17, Dk 2100, Copenhagen, Denmark.
    Searchability of networks2005In: 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. 72, no 4, p. 046117-046125Article in journal (Refereed)
    Abstract [en]

    We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively difficult to search, and thus that the abundance of scale-free networks in nature and society may reflect an attempt to protect local areas in a highly interconnected network from nonrelated communication. In fact, starting from a random node, real-world networks with higher order organization like modular or hierarchical structure are even more difficult to navigate than random scale-free networks. The searchability at the node level opens the possibility for a generalized hierarchy measure that captures both the hierarchy in the usual terms of trees as in military structures, and the intrinsic hierarchical nature of topological hierarchies for scale-free networks as in the Internet.

  • 40.
    Rosvall, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Sneppen, Kim
    Navigating networks with limited information2005In: 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. 71, no 6, p. 066111-Article in journal (Refereed)
    Abstract [en]

    We study navigation with limited information in networks and demonstrate that many real-world networks have a structure which can be described as favoring communication at short distance at the cost of constraining communication at long distance. This feature, which is robust and more evident with limited than with complete information, reflects both topological and possibly functional design characteristics. For example, the characteristics of the networks studied derived from a city and from the Internet are manifested through modular network designs. We also observe that directed navigation in typical networks requires remarkably little information on the level of individual nodes. By studying navigation or specific signaling, we take a complementary approach to the common studies of information transfer devoted to broadcasting of information in studies of virus spreading and the like.

  • 41.
    Seung Ki, Baek
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Shima, Hiroyuki
    Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan.
    Kim, Beom Jun
    BK21 Physics Research Division and Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea.
    Phase transition of q-state clock models on heptagonal lattices2009In: 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. 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 breaks the mean-field character in the bulk region, which establishes the consistency with results of clock models on boundary-free hyperbolic lattices.

  • 42.
    Sneppen, Kim
    et al.
    NORDITA, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Physics.
    Trusina, Ala
    Umeå University, Faculty of Science and Technology, Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    A simple model for self-organization of bipartite networks2004In: Europhysics Letters, ISSN 1286-4854, Vol. 67, no 3, p. 349-354Article in journal (Refereed)
    Abstract [en]

    We suggest a minimalistic model for directed networks and suggest an application to injection and merging of magnetic field lines. We obtain a network of connected donor and acceptor vertices with degree distribution 1/s2, and with dynamical reconnection events of size Δs occurring with frequency that scales as 1/Δs3. This suggests that the model is in the same universality class as the model with annihilation for self-organization in the solar atmosphere suggested by Hughes et al. (Phys. Rev. Lett. 90 (2003) 131101).

  • 43.
    Trusina, Ala
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Maslow, Sergei
    Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Sneppen, Kim
    NORDITA, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
    Hierarchy measures in complex networks2004In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 92, no 17, p. 178702-Article in journal (Refereed)
    Abstract [en]

    Using each node’s degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with y, the exponent of a degree distribution, reaching its highest possible value for y ≤,2 and quickly approaching zero for y > 3.

  • 44. Um, J.
    et al.
    Kim, B.J.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Physics.
    Choi, M.Y.
    Lee, S.-I.
    Dynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder2006In: Physical Review B, Vol. 74, no 9, p. 094516-Article in journal (Refereed)
  • 45. Um, Jaegon
    et al.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Kim, Beom Jun
    Synchronization in interdependent networks2011In: Chaos, ISSN 1054-1500, E-ISSN 1089-7682, Vol. 21, p. 025106-Article in journal (Refereed)
    Abstract [en]

    We explore the synchronization behavior in interdependent systems, where the one-dimensional (1D) network (the intranetwork coupling strength JI) is ferromagnetically intercoupled (the strength J) to the Watts-Strogatz (WS) small-world network (the intranetwork coupling strength JII). In the absence of the internetwork coupling (J = 0), the former network is well known not to exhibit the synchronized phase at any finite coupling strength, whereas the latter displays the mean-field transition. Through an analytic approach based on the mean-field approximation, it is found that for the weakly coupled 1D network (JI≪1) the increase of J suppresses synchrony, because the nonsynchronized 1D network becomes a heavier burden for the synchronization process of the WS network. As the coupling in the 1D network becomes stronger, it is revealed by the renormalization group (RG) argument that the synchronization is enhanced as JI is increased, implying that the more enhanced partial synchronization in the 1D network makes the burden lighter. Extensive numerical simulations confirm these expected behaviors, while exhibiting a reentrant behavior in the intermediate range of JI. The nonmonotonic change of the critical value of JII is also compared with the result from the numerical RG calculation.

  • 46. Yan, Xiaoyong
    et al.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings2015In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 10, no 5, article id e0125592Article in journal (Refereed)
    Abstract [en]

    The word-frequency distribution of a text written by an author is well accounted for by a maximum entropy distribution, the RGF (random group formation)-prediction. The RGF-distribution is completely determined by the a priori values of the total number of words in the text (M), the number of distinct words (N) and the number of repetitions of the most common word (k(max)). It is here shown that this maximum entropy prediction also describes a text written in Chinese characters. In particular it is shown that although the same Chinese text written in words and Chinese characters have quite differently shaped distributions, they are nevertheless both well predicted by their respective three a priori characteristic values. It is pointed out that this is analogous to the change in the shape of the distribution when translating a given text to another language. Another consequence of the RGF-prediction is that taking a part of a long text will change the input parameters (M, N, k(max)) and consequently also the shape of the frequency distribution. This is explicitly confirmed for texts written in Chinese characters. Since the RGF-prediction has no system-specific information beyond the three a priori values (M, N, k(max)), any specific language characteristic has to be sought in systematic deviations from the RGF-prediction and the measured frequencies. One such systematic deviation is identified and, through a statistical information theoretical argument and an extended RGF-model, it is proposed that this deviation is caused by multiple meanings of Chinese characters. The effect is stronger for Chinese characters than for Chinese words. The relation between Zipf's law, the Simon-model for texts and the present results are discussed.

  • 47. Yan, Xiaoyong
    et al.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Randomness versus specifics for word-frequency distributions2016In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 444, p. 828-837Article in journal (Refereed)
    Abstract [en]

    The text-length-dependence of real word-frequency distributions can be connected to the general properties of a random book. It is pointed out that this finding has strong implications, when deciding between two conceptually different views on word-frequency distributions, i.e. the specific 'Zipf's-view' and the non-specific 'Randomness-view', as is discussed. It is also noticed that the text-length transformation of a random book does have an exact scaling property precisely for the power-law index gamma = 1, as opposed to the Zipf's exponent gamma = 2 and the implication of this exact scaling property is discussed. However a real text has gamma > 1 and as a consequence gamma increases when shortening a real text. The connections to the predictions from the RGF (Random Group Formation) and to the infinite length-limit of a meta-book are also discussed. The difference between 'curve-fitting' and 'predicting' word-frequency distributions is stressed. It is pointed out that the question of randomness versus specifics for the distribution of outcomes in case of sufficiently complex systems has a much wider relevance than just the word-frequency example analyzed in the present work.

  • 48. Yan, Xiaoyong
    et al.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    The Dependence of Frequency Distributions on Multiple Meanings of Words, Codes and Signs2018In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 490, p. 554-564Article in journal (Refereed)
    Abstract [en]

    The dependence of the frequency distributions due to multiple meanings of words in a text is investigated by deleting letters. By coding the words with fewer letters the number of meanings per coded word increases. This increase is measured and used as an input in a predictive theory. For a text written in English, the word-frequency distribution is broad and fat-tailed, whereas if the words are only represented by their first letter the distribution becomes exponential. Both distribution are well predicted by the theory, as is the whole sequence obtained by consecutively representing the words by the first L = 6, 5, 4, 3, 2, 1 letters. Comparisons of texts written by Chinese characters and the same texts written by letter-codes are made and the similarity of the corresponding frequency-distributions are interpreted as a consequence of the multiple meanings of Chinese characters. This further implies that the difference of the shape for word-frequencies for an English text written by letters and a Chinese text written by Chinese characters is due to the coding and not to the language per se. 

  • 49. Yan, Xiaoyong
    et al.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Jensen, Henrik Jeldtoft
    The likely determines the unlikely2016In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 456, p. 112-119Article in journal (Refereed)
    Abstract [en]

    We point out that the functional form describing the frequency of sizes of events in complex systems (e.g. earthquakes, forest fires, bursts of neuronal activity) can be obtained from maximal likelihood inference, which, remarkably, only involve a few available observed measures such as number of events, total event size and extremes. Most importantly, the method is able to predict with high accuracy the frequency of the rare extreme events. To be able to predict the few, often big impact events, from the frequent small events is of course of great general importance. For a data set of wind speed we are able to predict the frequency of gales with good precision. We analyse several examples ranging from the shortest length of a recruit to the number of Chinese characters which occur only once in a text. (C) 2016 Elsevier B.V. All rights reserved.

  • 50. Yan, Xiaoyong
    et al.
    Yang, Seong.Gyu
    Kim, Beom Jun
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Benford's Law and the First Letter of Words2018In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 512, p. 305-315Article in journal (Other academic)
    Abstract [en]

    A universal First-Letter Law (FLL) is derived and described. It predicts the percentages of first letters for words in novels. The FLL is akin to Benford’s law (BL) of first digits, which predicts the percentages of first digits in a data collection of numbers. Both are universal in the sense that FLL only depends on the numbers of letters in the alphabet, whereas BL only depends on the number of digits in the base of the number system. The existence of these types of universal laws appears counter-intuitive. Nonetheless both describe data very well. Relations to some earlier works are given. FLL predicts that an English author on the average starts about 16 out of 100 words with the English letter ‘t’. This is corroborated by data, yet an author can freely write anything. Fuller implications and the applicability of FLL remain for the future.

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