900 research outputs found
Mass media destabilizes the cultural homogeneous regime in Axelrod's model
An important feature of Axelrod's model for culture dissemination or social
influence is the emergence of many multicultural absorbing states, despite the
fact that the local rules that specify the agents interactions are explicitly
designed to decrease the cultural differences between agents. Here we
re-examine the problem of introducing an external, global interaction -- the
mass media -- in the rules of Axelrod's model: in addition to their
nearest-neighbors, each agent has a certain probability to interact with a
virtual neighbor whose cultural features are fixed from the outset. Most
surprisingly, this apparently homogenizing effect actually increases the
cultural diversity of the population. We show that, contrary to previous claims
in the literature, even a vanishingly small value of is sufficient to
destabilize the homogeneous regime for very large lattice sizes
Accelerating consensus on co-evolving networks: the effect of committed individuals
Social networks are not static but rather constantly evolve in time. One of
the elements thought to drive the evolution of social network structure is
homophily - the need for individuals to connect with others who are similar to
them. In this paper, we study how the spread of a new opinion, idea, or
behavior on such a homophily-driven social network is affected by the changing
network structure. In particular, using simulations, we study a variant of the
Axelrod model on a network with a homophilic rewiring rule imposed. First, we
find that the presence of homophilic rewiring within the network, in general,
impedes the reaching of consensus in opinion, as the time to reach consensus
diverges exponentially with network size . We then investigate whether the
introduction of committed individuals who are rigid in their opinion on a
particular issue, can speed up the convergence to consensus on that issue. We
demonstrate that as committed agents are added, beyond a critical value of the
committed fraction, the consensus time growth becomes logarithmic in network
size . Furthermore, we show that slight changes in the interaction rule can
produce strikingly different results in the scaling behavior of . However,
the benefit gained by introducing committed agents is qualitatively preserved
across all the interaction rules we consider
Network dynamics with a nested node set: sociability in seven villages in Senegal
We propose two complementary ways to deal with a nesting structure in the node set of a network—such a structure may be called a multilevel network, with a node set consisting of several groups. First, within‐group ties are distinguished from between‐group ties by considering them as two distinct but interrelated networks. Second, effects of nodal variables are differentiated according to the levels of the nesting structure, to prevent ecological fallacies. This is elaborated in a study of two repeated observations of a sociability network in seven villages in Senegal, analyzed using the Stochastic Actor‐oriented Model
On the classification of OADP varieties
The main purpose of this paper is to show that OADP varieties stand at an
important crossroad of various main streets in different disciplines like
projective geometry, birational geometry and algebra. This is a good reason for
studying and classifying them. Main specific results are: (a) the
classification of all OADP surfaces (regardless to their smoothness); (b) the
classification of a relevant class of normal OADP varieties of any dimension,
which includes interesting examples like lagrangian grassmannians. Following
[PR], the equivalence of the classification in (b) with the one of
quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan
algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th
birthday. To appear in a special issue of Science in China Series A:
Mathematic
The media effect in Axelrod's model explained
We revisit the problem of introducing an external global field -- the mass
media -- in Axelrod's model of social dynamics, where in addition to their
nearest neighbors, the agents can interact with a virtual neighbor whose
cultural features are fixed from the outset. The finding that this apparently
homogenizing field actually increases the cultural diversity has been
considered a puzzle since the phenomenon was first reported more than a decade
ago. Here we offer a simple explanation for it, which is based on the
pedestrian observation that Axelrod's model exhibits more cultural diversity,
i.e., more distinct cultural domains, when the agents are allowed to interact
solely with the media field than when they can interact with their neighbors as
well. In this perspective, it is the local homogenizing interactions that work
towards making the absorbing configurations less fragmented as compared with
the extreme situation in which the agents interact with the media only
Three embeddings of the Klein simple group into the Cremona group of rank three
We study the action of the Klein simple group G consisting of 168 elements on
two rational threefolds: the three-dimensional projective space and a smooth
Fano threefold X of anticanonical degree 22 and index 1. We show that the
Cremona group of rank three has at least three non-conjugate subgroups
isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein
metric, and we construct a smooth polarized K3 surface of degree 22 with an
action of the group G.Comment: 43 page
Human group formation in online guilds and offline gangs driven by common team dynamic
Quantifying human group dynamics represents a unique challenge. Unlike
animals and other biological systems, humans form groups in both real (offline)
and virtual (online) spaces -- from potentially dangerous street gangs
populated mostly by disaffected male youths, through to the massive global
guilds in online role-playing games for which membership currently exceeds tens
of millions of people from all possible backgrounds, age-groups and genders. We
have compiled and analyzed data for these two seemingly unrelated offline and
online human activities, and have uncovered an unexpected quantitative link
between them. Although their overall dynamics differ visibly, we find that a
common team-based model can accurately reproduce the quantitative features of
each simply by adjusting the average tolerance level and attribute range for
each population. By contrast, we find no evidence to support a version of the
model based on like-seeking-like (i.e. kinship or `homophily')
Triangulations and Severi varieties
We consider the problem of constructing triangulations of projective planes
over Hurwitz algebras with minimal numbers of vertices. We observe that the
numbers of faces of each dimension must be equal to the dimensions of certain
representations of the automorphism groups of the corresponding Severi
varieties. We construct a complex involving these representations, which should
be considered as a geometric version of the (putative) triangulations
Critical Values for Yen’s Q3: Identification of Local Dependence in the Rasch model using Residual Correlations
The assumption of local independence is central to all IRT models. Violations can lead to inflated estimates of reliability and problems with construct validity. For the most widely used fit statistic Q3 there are currently no well-documented suggestions of the critical values which should be used to indicate local dependence, and for this reason a variety of arbitrary rules of thumb are used. In this study, we used an empirical data example and Monte Carlo simulation to investigate the different factors that can influence the null distribution of residual correlations, with the objective of proposing guidelines that researchers and practitioners can follow when making decisions about local dependence during scale development and validation. We propose that a parametric bootstrapping procedure should be implemented in each separate situation in order to obtain the critical value of local dependence applicable to the data set, and provide example critical values for a number of data structure situations. The results show that for the Q3 fit statistic no single critical value is appropriate for all situations, as the percentiles in the empirical null distribution are influenced by the number of items, the sample size, and the number of response categories. Furthermore, our results show that local dependence should be considered relative to the average observed residual correlation, rather than to a uniform value, as this results in more stable percentiles for the null distribution of an adjusted fit statistic
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