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  • 1.
    Gaidashev, Denis
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Zabzina, Natalia
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Fractal dimentions of the conformal diffusion-limited aggregationManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Diffusion-limited aggregation (DLA) is an important and popular mathematical model of random cluster growth. Conformal DLA, in which a cluster is grown by successive applications of conformal maps, is relletavily new and unexplored version of DLA. We implement conformal DLA numerically and compute several fractal dimentions of DLA clusters. To test applicability of the model to biological systems, the dimentions are compared with the experimentally computed fractal dimentions of the slime mould Physarum Polycephalum.

  • 2.
    Zabzina, Natalia
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    A gradient flow approach to the model of positive feedback in decision-making2015Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 77, s. 215-224Artikel i tidskrift (Refereegranskat)
    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.

  • 3.
    Zabzina, Natalia
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Mathematical modelling approach to collective decision-making2017Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    In everyday situations individuals make decisions. For example, a tourist usually chooses a crowded or recommended restaurant to have dinner. Perhaps it is an individual decision, but the observed pattern of decision-making is a collective phenomenon. Collective behaviour emerges from the local interactions that give rise to a complex pattern at the group level. In our example, the recommendations or simple copying the choices of others make a crowded restaurant even more crowded. The rules of interaction between individuals are important to study. Such studies should be complemented by biological experiments. Recent studies of collective phenomena in animal groups help us to understand these rules and develop mathematical models of collective behaviour. The most important communication mechanism is positive feedback between group members, which we observe in our example. In this thesis, we use a generic experimentally validated model of positive feedback to study collective decision-making.

    The first part of the thesis is based on the modelling of decision-making associated to the selection of feeding sites. This has been extensively studied for ants and slime moulds. The main contribution of our research is to demonstrate how such aspects as "irrationality", speed and quality of decisions can be modelled using differential equations. We study bifurcation phenomena and describe collective patterns above critical values of a bifurcation points in mathematical and biological terms. In the second part, we demonstrate how the primitive unicellular slime mould Physarum Polycephalum provides an easy test-bed for theoretical assumptions and model predictions about decision-making. We study its searching strategies and model decision-making associated to the selection of food options. We also consider the aggregation model to investigate the fractal structure of Physarum Polycephalum plasmodia.

    Delarbeten
    1. Collective Irrationality and Positive Feedback
    Öppna denna publikation i ny flik eller fönster >>Collective Irrationality and Positive Feedback
    2011 (Engelska)Ingår i: PLoS ONE, ISSN 1932-6203, Vol. 6, nr 4, s. e18901-Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    Recent experiments on ants and slime moulds have assessed the degree to which they make rational decisions when presented with a number of alternative food sources or shelter. Ants and slime moulds are just two examples of a wide range of species and biological processes that use positive feedback mechanisms to reach decisions. Here we use a generic, experimentally validated model of positive feedback between group members to show that the probability of taking the best of n options depends crucially on the strength of feedback. We show how the probability of choosing the best option can be maximized by applying an optimal feedback strength. Importantly, this optimal value depends on the number of options, so that when we change the number of options the preference of the group changes, producing apparent "irrationalities''. We thus reinterpret the idea that collectives show "rational" or "irrational" preferences as being a necessary consequence of the use of positive feedback. We argue that positive feedback is a heuristic which often produces fast and accurate group decision-making, but is always susceptible to apparent irrationality when studied under particular experimental conditions.

    Nationell ämneskategori
    Biologiska vetenskaper Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-153556 (URN)10.1371/journal.pone.0018901 (DOI)000290018400016 ()21541321 (PubMedID)
    Tillgänglig från: 2011-05-16 Skapad: 2011-05-16 Senast uppdaterad: 2017-02-27Bibliografiskt granskad
    2. Six Predictions about the Decision Making of Animal and Human Groups
    Öppna denna publikation i ny flik eller fönster >>Six Predictions about the Decision Making of Animal and Human Groups
    2012 (Engelska)Ingår i: Managerial and Decision Economics, Vol. 33, nr 5-6, s. 295-309Artikel i tidskrift (Refereegranskat) Published
    Nationell ämneskategori
    Samhällsvetenskap
    Identifikatorer
    urn:nbn:se:uu:diva-192153 (URN)10.1002/mde.2553 (DOI)
    Tillgänglig från: 2013-01-16 Skapad: 2013-01-16 Senast uppdaterad: 2017-02-27
    3. A gradient flow approach to the model of positive feedback in decision-making
    Öppna denna publikation i ny flik eller fönster >>A gradient flow approach to the model of positive feedback in decision-making
    2015 (Engelska)Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 77, s. 215-224Artikel i tidskrift (Refereegranskat) Published
    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.

    Nyckelord
    Mathematical model of positive feedback in decision making, Gradient flow equations, Differential geometry
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-261246 (URN)10.1016/j.chaos.2015.05.027 (DOI)000358970500022 ()
    Tillgänglig från: 2015-09-07 Skapad: 2015-08-31 Senast uppdaterad: 2017-12-04
    4. Symmetry Restoring Bifurcation in Collective Decision-Making
    Öppna denna publikation i ny flik eller fönster >>Symmetry Restoring Bifurcation in Collective Decision-Making
    Visa övriga...
    2014 (Engelska)Ingår i: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 10, nr 12, s. e1003960-Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.

    Nationell ämneskategori
    Matematisk analys
    Identifikatorer
    urn:nbn:se:uu:diva-312747 (URN)
    Forskningsfinansiär
    EU, Europeiska forskningsrådet, IDCAB 220/104702003
    Tillgänglig från: 2017-01-12 Skapad: 2017-01-12 Senast uppdaterad: 2017-11-29
    5. Fractal dimentions of the conformal diffusion-limited aggregation
    Öppna denna publikation i ny flik eller fönster >>Fractal dimentions of the conformal diffusion-limited aggregation
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Diffusion-limited aggregation (DLA) is an important and popular mathematical model of random cluster growth. Conformal DLA, in which a cluster is grown by successive applications of conformal maps, is relletavily new and unexplored version of DLA. We implement conformal DLA numerically and compute several fractal dimentions of DLA clusters. To test applicability of the model to biological systems, the dimentions are compared with the experimentally computed fractal dimentions of the slime mould Physarum Polycephalum.

    Nationell ämneskategori
    Naturvetenskap Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-314796 (URN)
    Tillgänglig från: 2017-02-06 Skapad: 2017-02-06 Senast uppdaterad: 2017-03-01Bibliografiskt granskad
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  • 4.
    Zabzina, Natalia
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Dussutour, Audrey
    Mann, Richard P.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Sumpter, David J. T.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Nicolis, Stamatios C.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Symmetry Restoring Bifurcation in Collective Decision-Making2014Ingår i: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 10, nr 12, s. e1003960-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.

  • 5.
    Zabzina, Natalia
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Dussutour, Audrey
    Mann, Richard P.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Sumpter, David J. T.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Nicolis, Stamatios C.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Symmetry Restoring Bifurcation in Collective Decision-Making2014Ingår i: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 10, nr 12, s. e1003960-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.

    Ladda ner fulltext (pdf)
    fulltext
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