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  • 1.
    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.

  • 2. Banerjee, Santo
    et al.
    Misra, Amar P
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rondoni, L.
    Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model2012In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 391, no 1-2, p. 107-112Article in journal (Refereed)
    Abstract [en]

    Simulations are performed to investigate the nonlinear dynamics of a (2 + 1)-dimensional chemotaxis model of Keller-Segel (KS) type, with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to steady-states, to divergencies in a finite time as well as to the formation of spatiotemporal irregular patterns. The latter, in particular, appears to be chaotic in part of the range of bounded solutions, as demonstrated by the analysis of wavelet power spectra. Steady-states are achieved with sufficiently large values of the chemotactic coefficient (chi) and/or with growth rates r below a critical value r(c). For r > r(c), the solutions of the differential equations of the model diverge in a finite time. We also report on the pattern formation regime, for different values of chi, r and of the diffusion coefficient D. (C) 2011 Elsevier B.V. All rights reserved.

  • 3. Bech, Morten L
    et al.
    Bergstrom, Carl T
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Garratt, Rodney J
    Mapping change in the overnight money market2015In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 424, p. 44-51Article in journal (Refereed)
    Abstract [en]

    We use an information-theoretic approach to describe changes in lending relationships between financial institutions around the time of the Lehman Brothers failure. Unlike previous work that conducts maximum likelihood estimation on undirected networks our analysis distinguishes between borrowers and lenders and looks for broader lending relationships (multi-bank lending cycles) that extend beyond the immediate counter-parties. We detect significant changes in lending patterns following implementation of the Interest on Required and Excess Reserves policy by the Federal Reserve in October 2008. Analysis of micro-scale rates of change in the data suggests these changes were triggered by the collapse of Lehman Brothers a few weeks before.

  • 4.
    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.

  • 5.
    Karimi, Fariba
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Holme, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics. Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea and Department of Sociology, Stockholm University, 10691 Stockholm, Sweden.
    Threshold model of cascades in empirical temporal networks2013In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 392, no 16, p. 3476-3483Article in journal (Refereed)
    Abstract [en]

    Threshold models try to explain the consequences of social influence like the spread of fads and opinions. Along with models of epidemics, they constitute a major theoretical framework of social spreading processes. In threshold models on static networks, an individual changes her state if a certain fraction of her neighbors has done the same. When there are strong correlations in the temporal aspects of contact patterns, it is useful to represent the system as a temporal network. In such a system, not only contacts but also the time of the contacts are represented explicitly. In many cases, bursty temporal patterns slow down disease spreading. However, as we will see, this is not a universal truth for threshold models. In this work we propose an extension of Watts’s classic threshold model to temporal networks. We do this by assuming that an agent is influenced by contacts which lie a certain time into the past. I.e., the individuals are affected by contacts within a time window. In addition to thresholds in the fraction of contacts, we also investigate the number of contacts within the time window as a basis for influence. To elucidate the model’s behavior, we run the model on real and randomized empirical contact datasets.

  • 6.
    Karimi, Fariba
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Ramenzoni, Verónica
    Donders Institute for Brain, Cognition, and Behavior, Radboud University, The Netherlands.
    Holme, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics. Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Republic of Korea and Department of Sociology, Stockholm University, 10691 Stockholm, Sweden.
    Structural differences between open and direct communication in an online community2014In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 414, no 15 November, p. 263-273Article in journal (Refereed)
    Abstract [en]

    Most research of online communication focuses on modes of communication that are either open (like forums, bulletin boards, Twitter, etc.) or direct (like e-mails). In this work, we study a dataset that has both types of communication channels. We relate our findings to theories of social organization and human dynamics. The data comprises 36,492 users of a movie discussion community. Our results show that there are differences in the way users communicate in the two channels that are reflected in the shape of degree- and interevent time distributions. The open communication that is designed to facilitate conversations with any member shows a broader degree distribution and more of the triangles in the network are primarily formed in this mode of communication. The direct channel is presumably preferred by closer communication and the response time in dialogs is shorter. On a more coarse-grained level, there are common patterns in the two networks. The differences and overlaps between communication networks, thus, provide a unique window into how social and structural aspects of communication establish and evolve.

  • 7.
    Lee, Sang Hoon
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Holme, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Pathlength scaling in graphs with incomplete navigational information2011In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 390, no 21-22, p. 3996-4001Article in journal (Refereed)
    Abstract [en]

    The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1 and the total number of vertices) in a way to aid navigation. This information is too little to ensure errorfree navigation but enough, as we will show, for the agents to do significantly better than a random walk. In our setup, given a graph, we first assign information to the vertices that agents can utilize for their navigation. To evaluate the navigation, we calculate the average distance traveled over random pairs of source and target and different graph realizations. We show that this type of embedding can be made quite efficiently; the more information is embedded, the more efficient it gets. We also investigate the embedded navigational information in a standard graph layout algorithm and find that although this information does not make algorithms as efficient as the above-mentioned schemes, it is significantly helpful.

  • 8.
    Lizana, Ludvig
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Lomholt, Michael A.
    Ambjörnsson, Tobias
    Single-file diffusion with non-thermal initial conditions2014In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 395, p. 148-153Article in journal (Refereed)
    Abstract [en]

    Single-file diffusion is a theoretically challenging many-body problem where the calculation of even the simplest observables, e.g. mean square displacement, for a tracer particle requires an elaborate mathematical machinery. There is therefore a need for simple approaches which provide intuitive understandings and predict qualitatively correct behaviours. Here we put forward a scaling-type method which we use to investigate the influence of non-thermal initial conditions on the dynamics of a tracer particle. With our new approach we reproduce, up to scaling, several known long and short time asymptotic results for the tracer particle mean square displacement.

  • 9.
    Lundow, Per-Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Campbell, I. A.
    Hyperscaling breakdown and Ising spin glasses: The Binder cumulant2018In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 492, p. 1838-1852Article in journal (Refereed)
    Abstract [en]

    Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region. 

  • 10.
    Lundow, Per-Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Campbell, I. A.
    The Ising Spin Glass in dimension four2015In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 434, p. 181-193Article in journal (Refereed)
    Abstract [en]

    The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG) models in dimension four are studied through extensive numerical simulations, and from an analysis of high temperature series expansion (HTSE) data of Klein et al. (1991). The simulations include standard finite size scaling measurements, thermodynamic limit regime measurements, and analyses which provide estimates of critical exponents without any consideration of the critical temperature. The higher order HTSE series for the bimodal model provide accurate estimates of the critical temperature and critical exponents. These estimates are independent of and fully consistent with the simulation values. Comparisons between ISG models in dimension four show that the critical exponents and the critical constants for dimensionless observables depend on the form of the interaction distribution of the model.

  • 11.
    Lundow, Per-Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Campbell, I. A.
    The Ising universality class in dimension three: Corrections to scaling2018In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 511, p. 40-53Article in journal (Refereed)
    Abstract [en]

    Simulation data are analyzed for four 3D spin-1/2 Ising models: on the FCC lattice, the BCC lattice, the SC lattice and the Diamond lattice. The observables studied are the susceptibility, the reduced second moment correlation length, and the normalized Binder cumulant. From measurements covering the entire paramagnetic temperature regime the corrections to scaling are estimated. We conclude that a correction term having an exponent which is consistent within the statistics with the bootstrap value of the universal subleading thermal confluent correction exponent, theta(2) similar to 2.454(3), is almost always present with a significant amplitude. In all four models, for the normalized Binder cumulant the leading confluent correction term has zero amplitude. This implies that the universal ratio of leading confluent correction amplitudes a(x4)/a(x) = 2 in the 3D Ising universality class.

  • 12.
    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.

  • 13. Rojdestvenski, I
    et al.
    Cottam, M G
    Oquist, Gunnar
    Umeå University, Faculty of Science and Technology, Department of Plant Physiology. Umeå University, Faculty of Science and Technology, Umeå Plant Science Centre (UPSC).
    Huner, N
    Thermodynamics of complexity2003In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 320, p. 318-328Article in journal (Refereed)
    Abstract [en]

    The definition of complexity, simultaneously introduced by Kolmogorov and Chaitin, has given a numerical measure to what was previously defined only at an intuitive level. This measure, useful as it is, becomes hard to utilise when one deals with the complexity of most real systems, and biological objects in particular. We try to overcome this difficulty by discussing a possible thermodynamic definition of complexity based on energy balance. The Kolmogorov-Chaitin definition of complexity thus relates to our thermodynamic definition in a similar way as the probabilistic definition of entropy relates to the thermodynamic one. In the framework of this intuitive treatment it is discussed how the complexity of a biological system may depend on the variability of the environmental conditions. A specific illustration of this approach is given using some numerical modeling examples. (C) 2002 Elsevier Science B.V. All rights reserved.

  • 14.
    Tang, Xiao-Gai
    et al.
    Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China.
    Wong, Eric W.M.
    Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China.
    Wu, Zhi-Xi
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Integrating network structure and dynamic information for better routing strategy on scale-free networks2009In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 388, no 12, p. 2547-2554Article in journal (Refereed)
    Abstract [en]

    We study information packet routing processes on scale-free networks by mimicking the Internet traffic delivery strategies. We incorporate both the global network structure information and local queuing information in the dynamic processes. We propose several new routing strategies to guide the packet routing. The performance of the routing strategies is measured by the average transit time of the packets as well as their dependence on the traffic amount. We find that the routing strategies which integrate both global network structure information and local dynamic information perform much better than the traditional shortest-path routing protocol which takes into account only the global topological information. Moreover, from comparative studies of these routing strategies, we observe that some of our proposed methods can decrease the average transit time of packets but the performance is closely dependent on the total amount of traffic while some other proposed methods can have good performance independent of the total amount of traffic with hyper-excellent average transit time of packets. Also, numerical results show that our proposed methods integrating network structure information and local dynamic information can work much better than the methods recently proposed in [S. Sreenivasan, R. Cohen, E. López, Z. Toroczkai, H.E. Stanley, Phys. Rev. E 75 (2007) 036105, Zhi-Xi Wu, Gang Peng, Eric W.M. Wong, Kai-Hau Yeung, J. Stat. Mech. (2008) P11002.], which only considered network structure information.

  • 15. 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.

  • 16. 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. 

  • 17. 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.

  • 18. 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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