1,002 research outputs found
Mind Your Expectations: Exploring the Roles of Suggestion and Intention in Mindfulness Training
Mindfulness training (MT) has received increasing recognition for its therapeutic benefits in a variety of clinical contexts. Despite acknowledgement that MT effects are predicated upon the development of both mindful attention and intention, research on MT mechanisms has focused chiefly upon attentional effects. By contrast, hypnosis research has focused explicitly on suggestion techniques for cultivating beneficial therapeutic expectations. Comparing similarities between mindfulness and hypnosis techniques, this paper explores mechanisms of suggestion tacitly employed in mindfulness interventions. Distinctions between mindfulness meditation and hypnotic induction are then used to identify a form of intentionality that is unique to MT, including candidate markers of mindful intention that may help to explain mindfulness’ salutary effects. Finally, the idea of changing intentions during MT is discussed, generating suggestions for how best to monitor the interaction between expectation and attentional practice when studying mindfulness interventions. Studies of intention and expectation in MT could help to determine: i) the degree to which MT benefits are driven by expectation effects rather than changes to attention, ii) how to best motivate the development of mindful attention in therapeutic interventions, and iii) what factors predict the generalization of mindfulness techniques to improve emotion regulation. By acknowledging that suggestion may be important for cultivating mindful intentions, it may be possible to deepen our understanding of how to optimally deliver mindfulness training and improve participant well-being
On abstract commensurators of groups
We prove that the abstract commensurator of a nonabelian free group, an
infinite surface group, or more generally of a group that splits appropriately
over a cyclic subgroup, is not finitely generated.
This applies in particular to all torsion-free word-hyperbolic groups with
infinite outer automorphism group and abelianization of rank at least 2.
We also construct a finitely generated, torsion-free group which can be
mapped onto Z and which has a finitely generated commensurator.Comment: 13 pages, no figur
Topological Designs
We give an exponential upper and a quadratic lower bound on the number of
pairwise non-isotopic simple closed curves can be placed on a closed surface of
genus g such that any two of the curves intersects at most once. Although the
gap is large, both bounds are the best known for large genus. In genus one and
two, we solve the problem exactly.
Our methods generalize to variants in which the allowed number of pairwise
intersections is odd, even, or bounded, and to surfaces with boundary
components.Comment: 14 p., 4 Figures. To appear in Geometriae Dedicat
A Combination Theorem for Metric Bundles
We define metric bundles/metric graph bundles which provide a purely
topological/coarse-geometric generalization of the notion of trees of metric
spaces a la Bestvina-Feighn in the special case that the inclusions of the edge
spaces into the vertex spaces are uniform coarsely surjective quasi-isometries.
We prove the existence of quasi-isometric sections in this generality. Then we
prove a combination theorem for metric (graph) bundles (including exact
sequences of groups) that establishes sufficient conditions, particularly
flaring, under which the metric bundles are hyperbolic. We use this to give
examples of surface bundles over hyperbolic disks, whose universal cover is
Gromov-hyperbolic. We also show that in typical situations, flaring is also a
necessary condition.Comment: v3: Major revision: 56 pages 5 figures. Many details added.
Characterization of convex cocompact subgroups of mapping class groups of
surfaces with punctures in terms of relative hyperbolicity given v4: Final
version incorporating referee comments: 63 pages 5 figures. To appear in
Geom. Funct. Ana
Personalising Practice Using Preferences for Meditation Anchor Modality
Many people are starting to establish contemplative practices and Mindfulness-Based Interventions have become quite popular. While Mindfulness-Based Interventions positively impact well-being, drop-out and lack of practice-maintenance plagues these interventions. Such adherence issues may reveal a lack of fit between participant partiality for attentional anchors of meditative practice and the intervention’s use of the breath as the anchor of attention. No study had yet compared partiality towards practices using anchors from different sensory modalities (e.g., auditory and visual) thus the present study examined such individual differences, sharing resources on the Open Science Framework1. Participants (N = 82) engaged 10-min practices within three modalities (somatosensory, auditory, and visual) and partiality towards these meditations was modelled. Partiality differences did exist: 49% preferred the breath, 30% the auditory-phrase, and 21% the visual-image. Pre-practice motivation and anchor-modality predicted partiality while cardiac responses were also positively associated with partiality. Preferences were updated through experience and over half of participants left the experiment partial to a different anchor than their initial meditation-naïve bias. Tangible next-steps are discussed, including integrating additional anchor modalities into existing interventions by offering brief practices with a variety of anchors. Suggestions are made for increasing post-training contact using email-automation to answer central practice-maintenance questions, including whether and which contemplative benefits are predicated on continued practice
Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator
A group obtained from a nontrivial group by adding one generator and one
relator which is a proper power of a word in which the exponent-sum of the
additional generator is one contains the free square of the initial group and
almost always (with one obvious exception) contains a non-abelian free
subgroup. If the initial group is involution-free or the relator is at least
third power, then the obtained group is SQ-universal and relatively hyperbolic
with respect to the initial group.Comment: 11 pages. A Russian version of this paper is at
http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V3:
revised following referee's comment
Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = -1
We prove that the hyperelliptic Torelli group is generated by Dehn twists about
separating curves that are preserved by the hyperelliptic involution. This verifies a
conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel
of the Burau representation evaluated at t = −1 and also the fundamental group of
the branch locus of the period mapping, and so we obtain analogous generating sets
for those. One application is that each component in Torelli space of the locus of
hyperelliptic curves becomes simply connected when curves of compact type are added
Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures
This arXived paper has two independant parts, that are improved and corrected
versions of different parts of a single paper once named "On equations in
relatively hyperbolic groups".
The first part is entitled "Existential questions in (relatively) hyperbolic
groups". We study there the existential theory of torsion free hyperbolic and
relatively hyperbolic groups, in particular those with virtually abelian
parabolic subgroups. We show that the satisfiability of systems of equations
and inequations is decidable in these groups.
In the second part, called "Finding relative hyperbolic structures", we
provide a general algorithm that recognizes the class of groups that are
hyperbolic relative to abelian subgroups.Comment: Two independant parts 23p + 9p, revised. To appear separately in
Israel J. Math, and Bull. London Math. Soc. respectivel
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