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Search Results: 1 - 10 of 123902 matches for " Philip T. Dunwoody "
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Introduction to the special issue
Philip T. Dunwoody
Judgment and Decision Making , 2009,
Abstract: Editor's introduction to the special issue.
Theories of truth as assessment criteria in judgment and decision making
Philip T. Dunwoody
Judgment and Decision Making , 2009,
Abstract: Hammond (1996) argued that much of the research in the field of judgment and decision making (JDM) can be categorized as focused on either coherence or correspondence (CandC) and that, in order to understand the findings of the field, one needs to understand the differences between these two criteria. extit{Hammond's claim} is that conclusions about the competence of judgments and decisions will depend upon the selection of coherence or correspondence as the criterion (Hammond, 2008). First, I provide an overview of the terms coherence and correspondence (CandC) as philosophical theories of truth and relate them to the field of JDM. Second, I provide an example of Hammond's claim by examining literature on base rate neglect. Third, I examine Hammond's claim as it applies to the broader field of JDM. Fourth, I critique Hammond's claim and suggest that refinements to the CandC distinction are needed. Specifically, the CandC distinction 1) is more accurately applied to criteria than to researchers, 2) should be refined to include two important types of coherence (inter and intrapersonal coherence) and 3) neglects the third philosophical theory of truth, pragmatism. Pragmatism, as a class of criteria in JDM, is defined as goal attainment. In order to provide the most complete assessment of human judgment possible, and understand different findings in the field of JDM, all three criteria should be considered.
Planar graphs and covers
M. J. Dunwoody
Mathematics , 2007,
Abstract: Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is well-known. A general result is obtained for such graphs where no restriction is put on the number of ends. It is shown that such a graph can be built up from one ended or finite planar graphs in a precise way. The results give a classification of the finitely generated groups with planar Cayley graphs.
Rectangle groups
M. J. Dunwoody
Mathematics , 2008,
Abstract: A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a homomorphic image any group which is a 2-orbifold group or which is a group of isometries of the reals. However it does have incompatible splittings over subgroups which are not small. This contradicts some ideas I had about universal JSJ decompostions for finitely presented groups over finitely generated subgroups. Such a group also has an unstable action on an R-tree and a cocompact action on a CAT(0) cube complex with finite cyclic point stabilizers, and trivial edge stabilizers.
An Inaccessible Graph
M. J. Dunwoody
Mathematics , 2010,
Abstract: An inaccessible, vertex transitive, locally finite graph is described. This graph is not quasi-isometric to a Cayley graph.
Structure Trees and Networks
M. J. Dunwoody
Mathematics , 2013,
Abstract: In this paper it is shown that for any network there is a uniquely determined network based on a structure tree that provides a convenient way of determining a minimal cut separating a pair $s, t$ where each of $s, t$ is either a vertex or an end in the original network. A Max-Flow Min-Cut Theorem is proved for any network. In the case of a Cayley Graph for a finitely generated group the theory provides another proof of Stallings' Theorem on the structure of groups with more than one end.
Almost Invariant Sets
M. J. Dunwoody
Mathematics , 2014,
Abstract: A short proof of a conjecture of Kropholler is given. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, that gives information about the structure of the Sageev cubing.
Finitely Presented Groups Acting on Trees
M. J. Dunwoody
Mathematics , 2012,
Abstract: It is shown that for any action of a finitely presented group $G$ on an $\R$-tree, there is a decomposition of $G$ as the fundamental group of a graph of groups related to this action. If the action of $G$ on $T$ is non-trivial, i.e. there is no global fixed point, then $G$ has a non-trivial action on a simplcial $\R $-tree.
Folding sequences
M. J. Dunwoody
Mathematics , 1998,
Abstract: Bestvina and Feighn showed that a morphism S --> T between two simplicial trees that commutes with the action of a group G can be written as a product of elementary folding operations. Here a more general morphism between simplicial trees is considered, which allow different groups to act on S and T. It is shown that these morphisms can again be written as a product of elementary operations: the Bestvina-Feighn folds plus the so-called `vertex morphisms'. Applications of this theory are presented. Limits of infinite folding sequences are considered. One application is that a finitely generated inaccessible group must contain an infinite torsion subgroup.
Retracts of vertex sets of trees and the almost stability theorem
Warren Dicks,M. J. Dunwoody
Mathematics , 2005, DOI: 10.1515/JGT.2007.051
Abstract: Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose vertex set is V'. This fact leads to various new consequences of the almost stability theorem. We also give an example of a group G, a G-tree T and a G-retract V' of VT such that no G-tree has vertex set V'.
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