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Johansson, Anders

Open this publication in new window or tab >>Phase transitions in long-range Ising models and an optimal condition for factors of g-measures### Johansson, Anders

### Öberg, Anders

### Pollicott, Mark

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 39, no 5, p. 1317-1330Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cambridge University Press, 2019
##### National Category

Probability Theory and Statistics Mathematical Analysis
##### Identifiers

urn:nbn:se:hig:diva-24122 (URN)10.1017/etds.2017.66 (DOI)000462581800009 ()2-s2.0-85063586064 (Scopus ID)
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Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2019-11-29Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.

Uppsala University.

University of Warwick, Coventry, UK.

We weaken the assumption of summable variations in a paper by Verbitskiy [On factors of g-measures. Indag. Math. (N.S.) 22 (2011), 315-329] to a weaker condition, Berbee's condition, in order for a one-block factor (a single-site renormalization) of the full shift space on finitely many symbols to have a g-measure with a continuous g-function. But we also prove by means of a counterexample that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is a critical inverse temperature in a one-sided long-range Ising model which is at most eight times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.

Open this publication in new window or tab >>Ergodic Theory of Kusuoka Measures### Johansson, Anders

### Öberg, Anders

### Pollicott, Mark

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Journal of Fractal Geometry, ISSN 2308-1309, Vol. 4, no 2, p. 185-214Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

European Mathematical Society Publishing House, 2017
##### Keywords

Kusuoka measure, energy Laplacian, transfer operator, quasi-compactness, g-measure
##### National Category

Geometry
##### Identifiers

urn:nbn:se:hig:diva-24121 (URN)10.4171/JFG/49 (DOI)000419781400004 ()
#####

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Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2018-06-26Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.

Department of Mathematics, Uppsala University, Uppsala, Sweden.

Mathematics Institute, University of Warwick, Coventry, UK.

In the analysis on self-similar fractal sets, the Kusuoka measure plays an important role. Here we investigate the Kusuoka measure from an ergodic theoretic viewpoint, seen as an invariant measure on a symbolic space. Our investigation shows that the Kusuoka measure generalizes Bernoulli measures and their properties to higher dimensions of an underlying finite dimensional vector space. Our main result is that the transfer operator on functions has a spectral gap when restricted to a certain Banach space that contains the Hölder continuous functions, as well as the highly discontinuous g" role="presentation">g-function associated to the Kusuoka measure. As a consequence, we obtain exponential decay of correlations. In addition, we provide some explicit rates of convergence for a family of generalized Sierpinski gaskets.

Open this publication in new window or tab >>Current-reinforced random walks for constructing transport networks### Ma, Qi

### Johansson, Anders

### Tero, Atsushi

### Nakagaki, Toshiyuki

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); ### Sumpter, David

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_2_j_idt188_j_idt202",{id:"formSmash:j_idt184:2:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2013 (English)In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 10, no 80, p. 20120864-Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

reinforced random walk; shortest path problem; transport networks; ant algorithm; true slime mould; optimization
##### National Category

Other Mathematics
##### Identifiers

urn:nbn:se:hig:diva-15216 (URN)10.1098/rsif.2012.0864 (DOI)000314285400014 ()23269849 (PubMedID)2-s2.0-84873658337 (Scopus ID)
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Available from: 2013-09-12 Created: 2013-09-12 Last updated: 2018-03-13Bibliographically approved

Mathematics Department, Uppsala University, Uppsala, Sweden.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Mathematics Department, Uppsala University, Uppsala, Sweden.

PRESTO, JST, Kawaguchi, Saitama, Japan.

Future University Hakodate, Hakodate, Japan.

Mathematics Department, Uppsala University, Uppsala, Sweden.

Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

Open this publication in new window or tab >>A Slime Mold Solver for Linear Programming Problems### Johansson, Anders

### Zou, James

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: How the World Computes: Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Cambridge, UK, June 18-23, 2012. Proceedings / [ed] S. Barry Cooper , Anuj Dawar and Benedikt Löwe, Springer, 2012, p. 344-354Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2012
##### Series

Lecture notes in Computer Science, ISSN 0302-9743 ; 7318
##### Keywords

Physarum, Linear programming
##### National Category

Computer Sciences
##### Identifiers

urn:nbn:se:hig:diva-12929 (URN)10.1007/978-3-642-30870-3_35 (DOI)978-3-642-30869-7 (ISBN)
##### Conference

Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Cambridge, UK, June 18-23, 2012
#####

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Available from: 2012-09-17 Created: 2012-09-17 Last updated: 2018-03-13Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.

School of Engineering and Applied Sciences, Harvard University.

*Physarum polycephalum* (true slime mold) has recently emerged as a fascinating example of biological computation through morphogenesis. Despite being a single cell organism, experiments have observed that through its growth process, the Physarum is able to solve various minimum cost flow problems. This paper analyzes a mathematical model of the Physarum growth dynamics. We show how to encode general linear programming (LP) problems as instances of the Physarum. We prove that under the growth dynamics, the Physarum is guaranteed to converge to the optimal solution of the LP. We further derive an efficient discrete algorithm based on the Physarum model, and experimentally verify its performance on assignment problems.

Open this publication in new window or tab >>Tuning positive feedback for signal detection in noisy dynamic environments### Johansson, Anders

### Ramsch, Kai

### Middendorf, Martin

### Sumpter, David J. T.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 309, p. 88-95Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Self-organisation, Ant foraging, Bandit problems, Biochemical systems
##### National Category

Biological Sciences Mathematics
##### Identifiers

urn:nbn:se:hig:diva-17870 (URN)10.1016/j.jtbi.2012.05.023 (DOI)000307526200010 ()2-s2.0-84863104976 (Scopus ID)
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Available from: 2014-11-09 Created: 2014-11-09 Last updated: 2018-03-13Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Mathematics Department, Uppsala University, Uppsala, Sweden.

Institut für Informatik, Universität Leipzig, Leipzig, Germany .

Institut für Informatik, Universität Leipzig, Leipzig, Germany .

Mathematics Department, Uppsala University, Uppsala, Sweden .

Learning from previous actions is a key feature of decision-making. Diverse biological systems, from neuronal assemblies to insect societies, use a combination of positive feedback and forgetting of stored memories to process and respond to input signals. Here we look how these systems deal with a dynamic two-armed bandit problem of detecting a very weak signal in the presence of a high degree of noise. We show that by tuning the form of positive feedback and the decay rate to appropriate values, a single tracking variable can effectively detect dynamic inputs even in the presence of a large degree of noise. In particular, we show that when tuned appropriately a simple positive feedback algorithm is Fisher efficient, in that it can track changes in a signal on a time of order L(h)= (vertical bar h vertical bar/sigma)(-2), where vertical bar h vertical bar is the magnitude of the signal and sigma the magnitude of the noise.

Open this publication in new window or tab >>Unique Bernoulli *g*-measures### Johansson, Anders

### Öberg, Anders

### Pollicott, Mark

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 14, no 5, p. 1599-1615Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Bernoulli measure, g-measure, chains with complete connections
##### National Category

Probability Theory and Statistics Mathematical Analysis
##### Identifiers

urn:nbn:se:hig:diva-12919 (URN)10.4171/JEMS/342 (DOI)000308126300009 ()2-s2.0-84866052071 (Scopus ID)
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Available from: 2012-09-18 Created: 2012-09-17 Last updated: 2018-03-13Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Uppsala University, Department of Mathematics.

Uppsala University, Department of Mathematics.

University of Warwick, Mathematics Institute.

We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique g-measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the g-measure.

Open this publication in new window or tab >>A first principles derivation of animal group size distributions### Ma, Qi

### Johansson, Anders

### Sumpter, David

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2011 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 283, no 1, p. 35-43Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2011
##### Keywords

Truncated power law, merge and split dynamics
##### National Category

Biological Sciences
##### Identifiers

urn:nbn:se:hig:diva-12928 (URN)10.1016/j.jtbi.2011.04.031 (DOI)000298526600005 ()
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Available from: 2012-09-17 Created: 2012-09-17 Last updated: 2018-03-13Bibliographically approved

Department of Mathematics, Uppsala University.

Department of Mathematics, Uppsala University.

Department of Mathematics, Uppsala University.

Several empirical studies have shown that the animal group size distribution of many species can be well fit by power laws with exponential truncation. A striking empirical result due to Niwa is that the exponent in these power laws is one and the truncation is determined by the average group size experienced by an individual. This distribution is known as the logarithmic distribution. In this paper we provide first principles derivation of the logarithmic distribution and other truncated power laws using a site-based merge and split framework. In particular, we investigate two such models. Firstly, we look at a model in which groups merge whenever they meet but split with a constant probability per time step. This generates a distribution similar, but not identical to the logarithmic distribution. Secondly, we propose a model, based on preferential attachment, that produces the logarithmic distribution exactly. Our derivation helps explain why logarithmic distributions are so widely observed in nature. The derivation also allows us to link splitting and joining behavior to the exponent and truncation parameters in power laws.

Open this publication in new window or tab >>Factors of r-partite graphs and bounds for the strong chromatic number### Johansson, Anders

### Johansson, Robert

### Marklund, Klas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2010 (English)In: Ars combinatoria, ISSN 0381-7032, Vol. 95, p. 277-287Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:hig:diva-12924 (URN)000276676500025 ()
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Available from: 2012-09-17 Created: 2012-09-17 Last updated: 2018-09-07Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.

Institutionen för matematik och matematisk statistik, Umeå univeristet.

Institutionen för matematik och matematisk statistik, Umeå univeristet.

We give an optimal degree condition for a tripartite graph to have a spanning subgraph consisting of complete graphs of order 3. This result is used to give an upper bound of 2 Delta for the strong chromatic number of n vertex graphs with Delta >= n/6.

Open this publication in new window or tab >>Multifractal analysis of non-uniformly hyperbolic systems### Johansson, Anders

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.### Jordan, Thomas

### Öberg, Anders

### Pollicott, Mark

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2010 (English)In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 177, no 1, p. 125-144Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

hyperbolic maps, Multifractal analysis, non-uniformly hyperbolic systems
##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:hig:diva-5469 (URN)10.1007/s11856-010-0040-y (DOI)000281396700005 ()2-s2.0-77956123226 (Scopus ID)
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Available from: 2009-09-17 Created: 2009-09-17 Last updated: 2018-03-13Bibliographically approved

Department of Mathematics, University of Bristol, Bristol, United Kingdom.

Department of Mathematics, Uppsala Universitet, Uppsala, Sweden.

Mathematics Institute, University of Warwick, Coventry, United Kingdom.

We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.

Open this publication in new window or tab >>Factors in random graphs### Johansson, Anders

### Kahn, Jeff

### Vu, Van

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2008 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 33, no 1, p. 1-28Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Combinatorics, random hypergraphs
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:hig:diva-2056 (URN)10.1002/rsa.20224 (DOI)000257500200001 ()2-s2.0-52349115939 (Scopus ID)
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Available from: 2008-06-19 Created: 2008-06-19 Last updated: 2018-03-13Bibliographically approved

University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.

Department of Mathematics, Rutgers University, Piscataway, NJ, United States.

Department of Mathematics, Rutgers University, Piscataway, NJ, United States.

Let H be a fixed graph on v vertices. For an n-vertex graph G with n divisible by v, an H-factor of G is a collection of n/v copies of H whose vertex sets partition V (G).

In this work, we consider the threshold thH(n) of the property that an Erds-Rényi random graph (on n points) contains an H-factor. Our results determine thH(n) for all strictly balanced H.

The method here extends with no difficulty to hypergraphs. As a corollary, we obtain the threshold for a perfect matching in random k-uniform hypergraph, solving the well-known Shamir's problem.