62,261 research outputs found
First-Order Provenance Games
We propose a new model of provenance, based on a game-theoretic approach to
query evaluation. First, we study games G in their own right, and ask how to
explain that a position x in G is won, lost, or drawn. The resulting notion of
game provenance is closely related to winning strategies, and excludes from
provenance all "bad moves", i.e., those which unnecessarily allow the opponent
to improve the outcome of a play. In this way, the value of a position is
determined by its game provenance. We then define provenance games by viewing
the evaluation of a first-order query as a game between two players who argue
whether a tuple is in the query answer. For RA+ queries, we show that game
provenance is equivalent to the most general semiring of provenance polynomials
N[X]. Variants of our game yield other known semirings. However, unlike
semiring provenance, game provenance also provides a "built-in" way to handle
negation and thus to answer why-not questions: In (provenance) games, the
reason why x is not won, is the same as why x is lost or drawn (the latter is
possible for games with draws). Since first-order provenance games are
draw-free, they yield a new provenance model that combines how- and why-not
provenance
‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation
In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal
The Axelrod model for the dissemination of culture revisited
This article is concerned with the Axelrod model, a stochastic process which
similarly to the voter model includes social influence, but unlike the voter
model also accounts for homophily. Each vertex of the network of interactions
is characterized by a set of cultural features, each of which can assume
states. Pairs of adjacent vertices interact at a rate proportional to the
number of features they share, which results in the interacting pair having one
more cultural feature in common. The Axelrod model has been extensively studied
during the past ten years, based on numerical simulations and simple mean-field
treatments, while there is a total lack of analytical results for the spatial
model itself. Simulation results for the one-dimensional system led physicists
to formulate the following conjectures. When the number of features and the
number of states both equal two, or when the number of features exceeds the
number of states, the system converges to a monocultural equilibrium in the
sense that the number of cultural domains rescaled by the population size
converges to zero as the population goes to infinity. In contrast, when the
number of states exceeds the number of features, the system freezes in a highly
fragmented configuration in which the ultimate number of cultural domains
scales like the population size. In this article, we prove analytically for the
one-dimensional system convergence to a monocultural equilibrium in terms of
clustering when , as well as fixation to a highly fragmented
configuration when the number of states is sufficiently larger than the number
of features. Our first result also implies clustering of the one-dimensional
constrained voter model.Comment: Published in at http://dx.doi.org/10.1214/11-AAP790 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Exploring narrativity in data visualization in journalism
Many news stories are based on data visualization, and storytelling with data has become a buzzword in journalism. But what exactly does storytelling with data mean? When does a data visualization tell a story? And what are narrative constituents in data visualization? This chapter first defines the key terms in this context: story, narrative, narrativity, showing and telling. Then, it sheds light on the various forms of narrativity in data visualization and, based on a corpus analysis of 73 data visualizations, describes the basic visual elements that constitute narrativity: the instance of a narrator, sequentiality, temporal dimension, and tellability. The paper concludes that understanding how data are transformed into visual stories is key to understanding how facts are shaped and communicated in society
Eigenvector localization as a tool to study small communities in online social networks
We present and discuss a mathematical procedure for identification of small
"communities" or segments within large bipartite networks. The procedure is
based on spectral analysis of the matrix encoding network structure. The
principal tool here is localization of eigenvectors of the matrix, by means of
which the relevant network segments become visible. We exemplified our approach
by analyzing the data related to product reviewing on Amazon.com. We found
several segments, a kind of hybrid communities of densely interlinked reviewers
and products, which we were able to meaningfully interpret in terms of the type
and thematic categorization of reviewed items. The method provides a
complementary approach to other ways of community detection, typically aiming
at identification of large network modules
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