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Minnhagen, Petter
Publications (10 of 48) Show all publications
Yan, X. & Minnhagen, P. (2016). Randomness versus specifics for word-frequency distributions. Physica A: Statistical Mechanics and its Applications, 444, 828-837.
Open this publication in new window or tab >>Randomness versus specifics for word-frequency distributions
2016 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 444, 828-837 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
Word-frequency distributions, Zipf's law, Random Group Formation, Maximum entropy
National Category
Probability Theory and Statistics Physical Sciences
Identifiers
urn:nbn:se:umu:diva-114601 (URN)10.1016/j.physa.2015.10.082 (DOI)000366785900075 ()
Available from: 2016-02-11 Created: 2016-01-25 Last updated: 2017-11-30Bibliographically approved
Yan, X., Minnhagen, P. & Jensen, H. J. (2016). The likely determines the unlikely. Physica A: Statistical Mechanics and its Applications, 456, 112-119.
Open this publication in new window or tab >>The likely determines the unlikely
2016 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 456, 112-119 p.Article in journal (Refereed) Published
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.

Keyword
Complex systems, Frequency distributions, Maximum entropy, Predictions, Real data
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-123037 (URN)10.1016/j.physa.2016.03.027 (DOI)000376693500011 ()
Available from: 2016-08-22 Created: 2016-06-27 Last updated: 2017-11-28Bibliographically approved
Yan, X. & Minnhagen, P. (2015). Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings. PLoS ONE, 10(5), Article ID e0125592.
Open this publication in new window or tab >>Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings
2015 (English)In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 10, no 5, e0125592Article in journal (Refereed) Published
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.

National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
urn:nbn:se:umu:diva-106610 (URN)10.1371/journal.pone.0125592 (DOI)000356768100060 ()25955175 (PubMedID)
Available from: 2015-07-28 Created: 2015-07-24 Last updated: 2018-01-11Bibliographically approved
Bokma, F., Baek, S. K. & Minnhagen, P. (2014). 50 years of inordinate fondness. Systematic Biology, 63(2), 251-256.
Open this publication in new window or tab >>50 years of inordinate fondness
2014 (English)In: Systematic Biology, ISSN 1063-5157, E-ISSN 1076-836X, Vol. 63, no 2, 251-256 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Oxford University Press, 2014
Keyword
Taxa, species, distributions, maximum entropy, random group formation
National Category
Evolutionary Biology
Identifiers
urn:nbn:se:umu:diva-81886 (URN)10.1093/sysbio/syt067 (DOI)000332044900010 ()
Available from: 2013-10-22 Created: 2013-10-22 Last updated: 2017-12-06Bibliographically approved
Yi, S. D., Kim, B. J. & Minnhagen, P. (2013). Allometric exponent and randomness. New Journal of Physics, 15, 043001.
Open this publication in new window or tab >>Allometric exponent and randomness
2013 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 15, 043001- p.Article in journal (Refereed) Published
Abstract [en]

An allometric height-mass exponent gamma gives an approximative power-law relation < M > proportional to H-gamma between the average mass < M > and the height H for a sample of individuals. The individuals in the present study are humans but could be any biological organism. The sampling can be for a specific age of the individuals or for an age interval. The body mass index is often used for practical purposes when characterizing humans and it is based on the allometric exponent gamma = 2. It is shown here that the actual value of gamma is to a large extent determined by the degree of correlation between mass and height within the sample studied: no correlation between mass and height means gamma = 0, whereas if there was a precise relation between mass and height such that all individuals had the same shape and density then gamma = 3. The connection is demonstrated by showing that the value of gamma can be obtained directly from three numbers characterizing the spreads of the relevant random Gaussian statistical distributions: the spread of the height and mass distributions together with the spread of the mass distribution for the average height. Possible implications for allometric relations, in general, are discussed.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2013
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-70338 (URN)10.1088/1367-2630/15/4/043001 (DOI)000317035700001 ()
Available from: 2013-05-14 Created: 2013-05-14 Last updated: 2017-12-06Bibliographically approved
Minnhagen, P., Baek, S. K., Kim, B. J. & Mäkilä, H. (2013). Residual discrete symmetry of the five-state clock model. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 88(1), 012125.
Open this publication in new window or tab >>Residual discrete symmetry of the five-state clock model
2013 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 88, no 1, 012125- p.Article in journal (Refereed) Published
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

Keyword
Phase transistions, Kostelitz-Thouless, clock-models, helicity modulus
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-81890 (URN)10.1103/PhysRevE.88.012125 (DOI)
Available from: 2013-10-22 Created: 2013-10-22 Last updated: 2017-12-06Bibliographically approved
Lee, S. H., Bernhardsson, S., Holme, P., Kim, B. J. & Minnhagen, P. (2012). Neutral theory of chemical reaction networks. New Journal of Physics, 14, 033032.
Open this publication in new window or tab >>Neutral theory of chemical reaction networks
Show others...
2012 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 14, 033032- p.Article in journal (Refereed) Published
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.

Keyword
Nertwork, chemical reactions, mettabolism, planets, emergent properties
National Category
Other Physics Topics
Identifiers
urn:nbn:se:umu:diva-53319 (URN)10.1088/1367-2630/14/3/033032 (DOI)000302370400002 ()
Available from: 2012-03-22 Created: 2012-03-20 Last updated: 2017-12-07Bibliographically approved
Bernhardsson, S., Baek, S. K. & Minnhagen, P. (2011). A Paradoxical Property of the Monkey Book. Journal of Statistical Mechanics: Theory and Experiment, P07013.
Open this publication in new window or tab >>A Paradoxical Property of the Monkey Book
2011 (English)In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, P07013- p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Institute of Physics, 2011
Keyword
analysis of algorithms, growth processes
National Category
Natural Sciences
Identifiers
urn:nbn:se:umu:diva-47758 (URN)10.1088/1742-5468/2011/07/P07013 (DOI)
Available from: 2011-09-29 Created: 2011-09-28 Last updated: 2017-12-08Bibliographically approved
Baek, S. K. & Minnhagen, P. (2011). Bounds of percolation thresholds in the enhanced binary tree. Physica A: Statistical Mechanics and its Applications, 390(8), 1447-1452.
Open this publication in new window or tab >>Bounds of percolation thresholds in the enhanced binary tree
2011 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 390, no 8, 1447-1452 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2011
Keyword
percolation threshold, enhanced binary tree, hyperbolic lattice
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-39227 (URN)10.1016/j.physa.2010.12.030 (DOI)
Funder
Swedish Research Council, 621-2002-4135
Available from: 2011-01-18 Created: 2011-01-18 Last updated: 2017-12-11Bibliographically approved
Baek, S. K., Mäkelä, H., Minnhagen, P. & Kim, B. J. (2011). Critical temperatures of the three- and four-state Potts models on the kagome lattice. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 83(6), 061104.
Open this publication in new window or tab >>Critical temperatures of the three- and four-state Potts models on the kagome lattice
2011 (English)In: 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, 061104- p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
American Physical Society, 2011
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-44393 (URN)10.1103/PhysRevE.83.061104 (DOI)
Funder
Swedish Research Council, 621-2008-4449
Available from: 2011-06-09 Created: 2011-06-07 Last updated: 2017-12-11Bibliographically approved
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