478 research outputs found
Overtwisted open books from sobering arcs
We study open books on three manifolds which are compatible with an
overtwisted contact structure. We show that the existence of certain arcs,
called sobering arcs, is a sufficient condition for an open book to be
overtwisted, and is necessary up to stabilization by positive Hopf-bands. Using
these techniques we prove that some open books arising as the boundary of
symplectic configurations are overtwisted, answering a question of Gay in
Algebr. Geom. Topol. 3 (2003) 569--586.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-47.abs.htm
Learning the Preferences of Ignorant, Inconsistent Agents
An important use of machine learning is to learn what people value. What
posts or photos should a user be shown? Which jobs or activities would a person
find rewarding? In each case, observations of people's past choices can inform
our inferences about their likes and preferences. If we assume that choices are
approximately optimal according to some utility function, we can treat
preference inference as Bayesian inverse planning. That is, given a prior on
utility functions and some observed choices, we invert an optimal
decision-making process to infer a posterior distribution on utility functions.
However, people often deviate from approximate optimality. They have false
beliefs, their planning is sub-optimal, and their choices may be temporally
inconsistent due to hyperbolic discounting and other biases. We demonstrate how
to incorporate these deviations into algorithms for preference inference by
constructing generative models of planning for agents who are subject to false
beliefs and time inconsistency. We explore the inferences these models make
about preferences, beliefs, and biases. We present a behavioral experiment in
which human subjects perform preference inference given the same observations
of choices as our model. Results show that human subjects (like our model)
explain choices in terms of systematic deviations from optimal behavior and
suggest that they take such deviations into account when inferring preferences.Comment: AAAI 201
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