9,975 research outputs found
Fields and Fusions: Hrushovski constructions and their definable groups
An overview is given of the various expansions of fields and fusions of
strongly minimal sets obtained by means of Hrushovski's amalgamation method, as
well as a characterization of the groups definable in these structures
Dimensional groups and fields
We shall define a general notion of dimension, and study groups and rings
whose interpretable sets carry such a dimensio. In particular, we deduce chain
conditions for groups, definability results for fields and domains, and show
that pseudofinite groups contain big finite-by-abelian subgroups, and
pseudofinite groups of dimension 2 contain big soluble subgroups
The right angle to look at orthogonal sets
If X and Y are orthogonal hyperdefinable sets such that X is simple, then any
group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup
N such that G/N is Y-internal; N is unique up to commensurability. In order to
make sense of this statement, local simplicity theory for hyperdefinable sets
is developped. Moreover, a version of Schlichting's Theorem for hyperdefinable
families of commensurable subgroups is shown
Computational Complexity Results for Genetic Programming and the Sorting Problem
Genetic Programming (GP) has found various applications. Understanding this
type of algorithm from a theoretical point of view is a challenging task. The
first results on the computational complexity of GP have been obtained for
problems with isolated program semantics. With this paper, we push forward the
computational complexity analysis of GP on a problem with dependent program
semantics. We study the well-known sorting problem in this context and analyze
rigorously how GP can deal with different measures of sortedness.Comment: 12 page
Cooperation in a resource extraction game
An exhaustible stock of resources may be exploited by N players. An arbitrarily long duration of the game is only possible, if the utility function satisfies certain restrictions at small values R of extraction. We find that stability against unilateral defection occurs if the elasticity of the marginal utility turns out to be larger than (N - 1 )/N, however independent of the value of the discount factor. Hence we find that cooperation does not depend on the discount factor for a certain range of elasticities. Analogy to phase transitions in statistical physics is discussed.
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