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Minnhagen, Petter
##### Publications (10 of 45) Show all publications
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, article id 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, p. 251-256Article 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, p. 043001-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
Baek, S. K., Mäkilä, H., Minnhagen, P. & Kim, B. J. (2013). Residual discrete symmetry of the five-state clock model. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 88(1), Article ID 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, article id 012125Article 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)000322084800002 ()23944432 (PubMedID)
Available from: 2013-10-22 Created: 2013-10-22 Last updated: 2018-02-09Bibliographically 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
2012 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 14, p. 033032-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, p. P07013-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
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: 2018-03-15Bibliographically 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, p. 1447-1452Article 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.

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, p. 061104-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
Baek, S. K. & Minnhagen, P. (2011). Hierarchical renormalization-group study on the planar bond-percolation problem. Physica Scripta, 83(5), 055601
Open this publication in new window or tab >>Hierarchical renormalization-group study on the planar bond-percolation problem
2011 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 83, no 5, p. 055601-Article in journal (Refereed) Published
##### 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 $\nu \approx 1$.

##### Place, publisher, year, edition, pages
IOP Publishing, 2011
##### Keyword
Percolation, Critical point phenomena, Renormalization-group theory
##### National Category
Condensed Matter Physics
##### Research subject
Theoretical Physics
##### Identifiers
urn:nbn:se:umu:diva-43641 (URN)10.1088/0031-8949/83/05/055601 (DOI)
##### Funder
Swedish Research Council, 621-2008-4449 Available from: 2011-05-10 Created: 2011-05-05 Last updated: 2017-12-11Bibliographically approved
Baek, S. K., Mäkelä, H., Minnhagen, P. & Kim, B. J. (2011). Ising model on a hyperbolic plane with a boundary. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 84, 032103
Open this publication in new window or tab >>Ising model on a hyperbolic plane with a boundary
2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, p. 032103-Article in journal (Refereed) Published
##### 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.

##### Place, publisher, year, edition, pages
American Physical Society, 2011
##### National Category
Condensed Matter Physics
##### Identifiers
urn:nbn:se:umu:diva-47877 (URN)10.1103/PhysRevE.84.032103 (DOI)
##### Funder
Swedish Research Council, 621-2008-4449 Available from: 2011-10-03 Created: 2011-10-02 Last updated: 2017-12-08Bibliographically approved

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