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  • 1.
    Bask, Mikael
    Department of Economics, Umeå University.
    A Positive Lyapunov Exponent in Swedish Exchange Rates?2002In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 14, p. 1295-1304Article in journal (Refereed)
  • 2.
    Bask, Mikael
    Department of Economics, Umeå University.
    Dimensions and Lyapunov Exponents from Exchange Rate Series1996In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 7, p. 2199-2214Article in journal (Refereed)
  • 3. Dussutour, Audrey
    et al.
    Nicolis, Stamatios C.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Flexibility in collective decision-making by ant colonies: Tracking food across space and time2013In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 50, no SI, p. 32-38Article in journal (Refereed)
    Abstract [en]

    Deciding which of many available resources to exploit is a problem faced by a range of decentralized biological systems. For example, ants are able to choose between food sources that vary in quality using a chemical trail. This communication system characterized by a strong positive feedback allows a rapid transfer of information and the selection of the best food source. This is true in static environment, where a single, unchanging solution exists. In dynamic environments however such recruitment often 'lock' groups into suboptimal decisions, preventing a response to changes in available resources. Here, we investigate decision-making in a dynamic environment for the greenhead ants (Rhytidoponera metallica) which use a non-chemical recruitment. To experimentally test our study species' ability to adapt to changes in their foraging environment, we offered three feeders that changed in quality. At any given time, only one feeder provided high quality food, while the others provided low quality food. Every two hours, the quality of the feeders changed such that the previously high quality feeder became a low quality feeder, and vice versa. We showed that ants were able to track changes in food quality across space and time. By coupling behavioral observations to computer simulations, we demonstrate that selection of food sources relies uniquely on a retention effect of feeding individuals on newcomers without comparison between available opportunities. The elegance of these parsimonious foraging systems is that the collective decision arises from the perception of conspecifics without the need for a leader having a synoptic overall view of the situation and knowing all the available options.

  • 4. Rossi, Luca
    et al.
    Magnani, Matteo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    Towards effective visual analytics on multiplex and multilayer networks2015In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 72, p. 68-76Article in journal (Refereed)
    Abstract [en]

    In this article we discuss visualisation strategies for multiplex networks. Since Moreno's early works on network analysis, visualisation has been one of the main ways to understand networks thanks to its ability to summarise a complex structure into a single representation highlighting multiple properties of the data. However, despite the large renewed interest in the analysis of multiplex networks, no study has proposed specialised visualisation approaches for this context and traditional methods are typically applied instead. In this paper we initiate a critical and structured discussion of this topic, and claim that the development of specific visualisation methods for multiplex networks will be one of the main drivers pushing current research results into daily practice.

  • 5. Salehi, Mostafa
    et al.
    Siyari, Payam
    Magnani, Matteo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    Montesi, Danilo
    Multidimensional epidemic thresholds in diffusion processes over interdependent networks2015In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 72, p. 59-67Article in journal (Refereed)
    Abstract [en]

    Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring over such coupled networks. In this paper we propose a new concept of multidimensional epidemic threshold characterizing diffusion processes over interdependent networks, allowing different diffusion rates on the different networks and arbitrary degree distributions. We analytically derive and numerically illustrate the conditions for multilayer epidemics, i.e., the appearance of a giant connected component spanning all the networks. Furthermore, we study the evolution of infection density and diffusion dynamics with extensive simulation experiments on synthetic and real networks.

  • 6. Viana, Matheus P.
    et al.
    Fourcassie, Vincent
    Perna, Andrea
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Costa, Luciano da F.
    Jost, Christian
    Accessibility in networks: A useful measure for understanding social insect nest architecture2013In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 46, p. 38-45Article in journal (Refereed)
    Abstract [en]

    Networks and the associated tools from graph theory have now become well-established approaches to study natural as well as human-made systems. While early studies focused on topology and connectivity, the recent literature has acknowledged the importance of the dynamical properties of these networks. Here we focus on such a dynamic measure: accessibility. It characterizes for any given movement dynamics (such as random walks) the average number of nodes that can be reached in exactly h steps (out-accessibility), or the average number of nodes from which a given node can be reached (in-accessibility). This focus on dynamics makes accessibility particularly appropriate to study movement on networks and to detect complementary properties with respect to topology-based measurements such as betweenness centrality. We apply this measure to six nests of Cubitermes termites. Their mushroom-like 3D architectures consist of chambers and connecting tunnels that can be associated to nodes and edges in a communication network. Accessibilities turn out to be particularly low in the bottom part of the nests that link them to their underground tunneling network. We interpret this result in the context of anti-predator (ants) behavior and/or as a side effect of the global nest shape.

  • 7.
    Zabzina, Natalia
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    A gradient flow approach to the model of positive feedback in decision-making2015In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 77, p. 215-224Article in journal (Refereed)
    Abstract [en]

    Recent studies on social dynamics have been done by using tools and methods of physics and economics.. The main idea is that the regularity observed on a global scale arises out of local interactions between the group members. We consider the model describing one of the major interaction mechanism, the model of positive feedback. We propose a geometrical reformulation of this model in terms of gradient flow equations on a Riemannian manifold. The benefit of this reformulation is that we introduce an alternative method to study phenomena of the well known model. We suggest the analogy with a particle moving on curved manifold. We believe that this analogy will allow us to extend powerful mathematical tools from analytical mechanics to the biological systems.

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