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Johansson, Anders
Publications (10 of 14) Show all publications
Johansson, A., Öberg, A. & Pollicott, M. (2019). Phase transitions in long-range Ising models and an optimal condition for factors of g-measures. Ergodic Theory and Dynamical Systems, 39(5), 1317-1330
Open this publication in new window or tab >>Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
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]

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.

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)
Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2019-11-29Bibliographically approved
Johansson, A., Öberg, A. & Pollicott, M. (2017). Ergodic Theory of Kusuoka Measures. Journal of Fractal Geometry, 4(2), 185-214
Open this publication in new window or tab >>Ergodic Theory of Kusuoka Measures
2017 (English)In: Journal of Fractal Geometry, ISSN 2308-1309, Vol. 4, no 2, p. 185-214Article in journal (Refereed) Published
Abstract [en]

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.

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 ()
Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2018-06-26Bibliographically approved
Ma, Q., Johansson, A., Tero, A., Nakagaki, T. & Sumpter, D. (2013). Current-reinforced random walks for constructing transport networks. Journal of the Royal Society Interface, 10(80), 20120864
Open this publication in new window or tab >>Current-reinforced random walks for constructing transport networks
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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]

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.

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)
Available from: 2013-09-12 Created: 2013-09-12 Last updated: 2018-03-13Bibliographically approved
Johansson, A. & Zou, J. (2012). A Slime Mold Solver for Linear Programming Problems. In: S. Barry Cooper , Anuj Dawar and Benedikt Löwe (Ed.), S. Barry Cooper , Anuj Dawar and Benedikt Löwe (Ed.), How the World Computes: Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Cambridge, UK, June 18-23, 2012. Proceedings. Paper presented at Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Cambridge, UK, June 18-23, 2012 (pp. 344-354). Springer
Open this publication in new window or tab >>A Slime Mold Solver for Linear Programming Problems
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]

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.

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
Available from: 2012-09-17 Created: 2012-09-17 Last updated: 2018-03-13Bibliographically approved
Johansson, A., Ramsch, K., Middendorf, M. & Sumpter, D. J. T. (2012). Tuning positive feedback for signal detection in noisy dynamic environments. Journal of Theoretical Biology, 309, 88-95
Open this publication in new window or tab >>Tuning positive feedback for signal detection in noisy dynamic environments
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]

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.

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)
Available from: 2014-11-09 Created: 2014-11-09 Last updated: 2018-03-13Bibliographically approved
Johansson, A., Öberg, A. & Pollicott, M. (2012). Unique Bernoulli g-measures. Journal of the European Mathematical Society (Print), 14(5), 1599-1615
Open this publication in new window or tab >>Unique Bernoulli g-measures
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]

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.

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)
Available from: 2012-09-18 Created: 2012-09-17 Last updated: 2018-03-13Bibliographically approved
Ma, Q., Johansson, A. & Sumpter, D. (2011). A first principles derivation of animal group size distributions. Journal of Theoretical Biology, 283(1), 35-43
Open this publication in new window or tab >>A first principles derivation of animal group size distributions
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]

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.

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 ()
Available from: 2012-09-17 Created: 2012-09-17 Last updated: 2018-03-13Bibliographically approved
Johansson, A., Johansson, R. & Marklund, K. (2010). Factors of r-partite graphs and bounds for the strong chromatic number. Ars combinatoria, 95, 277-287
Open this publication in new window or tab >>Factors of r-partite graphs and bounds for the strong chromatic number
2010 (English)In: Ars combinatoria, ISSN 0381-7032, Vol. 95, p. 277-287Article in journal (Refereed) Published
Abstract [en]

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.

National Category
Discrete Mathematics
Identifiers
urn:nbn:se:hig:diva-12924 (URN)000276676500025 ()
Available from: 2012-09-17 Created: 2012-09-17 Last updated: 2018-09-07Bibliographically approved
Johansson, A., Jordan, T., Öberg, A. & Pollicott, M. (2010). Multifractal analysis of non-uniformly hyperbolic systems. Israel Journal of Mathematics, 177(1), 125-144
Open this publication in new window or tab >>Multifractal analysis of non-uniformly hyperbolic systems
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]

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.

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)
Available from: 2009-09-17 Created: 2009-09-17 Last updated: 2018-03-13Bibliographically approved
Johansson, A., Kahn, J. & Vu, V. (2008). Factors in random graphs. Random structures & algorithms (Print), 33(1), 1-28
Open this publication in new window or tab >>Factors in random graphs
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]

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.

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)
Available from: 2008-06-19 Created: 2008-06-19 Last updated: 2018-03-13Bibliographically approved
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