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  • 1. Enquist, Magnus
    et al.
    Strimling, Pontus
    Eriksson, Kimmo
    Laland, Kevin
    Sjöstrand, Jonas
    Mälardalens högskola.
    One cultural parent makes no culture2010In: Animal Behaviour, ISSN 0003-3472, E-ISSN 1095-8282, Vol. 79, no 6, p. 1135-1162Article in journal (Refereed)
    Abstract [en]

    The ability to acquire knowledge and skills from others is widespread in animals and is commonly thought to be responsible for the behavioural traditions observed in many species. However, in spite of the extensive literature on theoretical analyses and empirical studies of social learning, little attention has been given to whether individuals acquire knowledge from a single individual or multiple models. Researchers commonly refer to instances of sons learning from fathers, or daughters from mothers, while theoreticians have constructed models of uniparental transmission, with little consideration of whether such restricted modes of transmission are actually feasible. We used mathematical models to demonstrate that the conditions under which learning from a single cultural parent can lead to stable culture are surprisingly restricted (the same reasoning applies to a single social-learning event). Conversely, we demonstrate how learning from more than one cultural parent can establish culture, and find that cultural traits will reach a nonzero equilibrium in the population provided the product of the fidelity of social learning and the number of cultural parents exceeds 1. We discuss the implications of the analysis for interpreting various findings in the animal social-learning literature, as well as the unique features of human culture.

  • 2.
    Eriksson, Henrik
    et al.
    KTH, School of Computer Science and Communication (CSC).
    Eriksson, Kimmo
    Words with intervening neighbours in infinite Coxeter groups are reduced2010In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 17, no 1, p. N9-Article in journal (Refereed)
    Abstract [en]

    Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighbours. For a Coxeter graph, words represent group elements. Speyer recently proved that words with the intervening neighbours property are reduced if the group is infinite and irreducible. We present a new and shorter proof using the root automaton for recognition of reduced words.

  • 3. Eriksson, Kimmo
    et al.
    Jansson, Fredrik
    Sjöstrand, Jonas
    Stockholms universitet.
    Bentley's conjecture on popularity toplist turnover under random copying2010In: The Ramanujan journal, ISSN 1382-4090, E-ISSN 1572-9303, Vol. 23, p. 371-396Article in journal (Refereed)
    Abstract [en]

    Bentley et al studied the turnover rate in popularity toplists in a ’random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ√μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.

  • 4.
    Eriksson, Kimmo
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Sjöstrand, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Limiting shapes of birth-and-death processes on Young diagrams2012In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 48, no 4, p. 575-602Article in journal (Refereed)
    Abstract [en]

    We consider a family of birth processes and birth-and-death processes on Young diagrams of integer partitions of n. This family incorporates three famous models from very different fields: Rost's totally asymmetric particle model (in discrete time), Simon's urban growth model, and Moran's infinite alleles model. We study stationary distributions and limit shapes as n tends to infinity, and present a number of results and conjectures.

  • 5. Eriksson, Kimmo
    et al.
    Sjöstrand, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On two theorems of Quinzii and rent controlled housing allocation in Sweden2007In: International Journal of Game Theory, ISSN 0020-7276, E-ISSN 1432-1270, Vol. 3, no 9, p. 515-526Article in journal (Refereed)
    Abstract [en]

    The Swedish rent control system creates a white market for swapping rental contracts and a black market for selling rental contracts. Empirical data suggests that in this black-and-white market some people act according to utility functions that are both discontinuous and locally decreasing in money. We discuss Quinzii's theorem for the nonemptiness of the core of generalized house-swapping games, and show how it can be extended to cover the Swedish game. In a second part, we show how this theorem of Quinzii and her second theorem on nonemptiness of the core in two-sided models are both special cases of a more general theorem.

  • 6.
    Eriksson, Kimmo
    et al.
    Malardalen Univ, Dept Math & Phys.
    Sjöstrand, Jonas
    Malardalen Univ, Dept Math & Phys.
    Strimling, Pontus
    Malardalen Univ, Dept Math & Phys.
    Optimal expected rank in a two-sided secretary problem2007In: Operations Research, ISSN 0030-364X, E-ISSN 1526-5463, Vol. 55, no 5, p. 921-931Article in journal (Refereed)
    Abstract [en]

    In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.

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