736 research outputs found
Metaplectic-c Quantomorphisms
In the classical Kostant-Souriau prequantization procedure, the Poisson
algebra of a symplectic manifold is realized as the space of
infinitesimal quantomorphisms of the prequantization circle bundle. Robinson
and Rawnsley developed an alternative to the Kostant-Souriau quantization
process in which the prequantization circle bundle and metaplectic structure
for are replaced by a metaplectic-c prequantization. They proved
that metaplectic-c quantization can be applied to a larger class of manifolds
than the classical recipe. This paper presents a definition for a metaplectic-c
quantomorphism, which is a diffeomorphism of metaplectic-c prequantizations
that preserves all of their structures. Since the structure of a metaplectic-c
prequantization is more complicated than that of a circle bundle, we find that
the definition must include an extra condition that does not have an analogue
in the Kostant-Souriau case. We then define an infinitesimal quantomorphism to
be a vector field whose flow consists of metaplectic-c quantomorphisms, and
prove that the space of infinitesimal metaplectic-c quantomorphisms exhibits
all of the same properties that are seen for the infinitesimal quantomorphisms
of a prequantization circle bundle. In particular, this space is isomorphic to
the Poisson algebra
Conflict mediation and the news media
There is a plethora of studies about the role that news media plays in conflict escalation, and studies about conflict mediation processes. However, there is comparatively less work that has focused on news media and conflict mediation; and the communication strategies that can be employed by mediators to encourage the media to frame the conflict in a manner that is more conducive to the mediator. Mediators need to learn to use news media more effectively. Drawing on interviews with 15 people with extensive experience, this paper outlines the variables that may affect a mediation process, mentions notable contradictions between the job of a media professional and that of a mediator; recalls some framing considerations; and notes the benefits and risks of some communication strategies
The Hobbit Redemption: Christian Heroism & Humility in the Work of J.R.R. Tolkien
This article takes a look at the Christian themes in J.R.R. Tolkien\u27s book, The Lord of the Rings. It notes that Tolkien\u27s books were endorsed by Christian writer C.S. Lewis for its anti-romantic and revolutionary appeal. It cites that Tolkien not only reflected the sentiments of the persecuted hero, but applied his Christian imagination to express elements of war such as suffering and death. It analyzes the humility and obedience reflected in the character of Frodo the Hobbit
Adaptive Contract Design for Crowdsourcing Markets: Bandit Algorithms for Repeated Principal-Agent Problems
Crowdsourcing markets have emerged as a popular platform for matching
available workers with tasks to complete. The payment for a particular task is
typically set by the task's requester, and may be adjusted based on the quality
of the completed work, for example, through the use of "bonus" payments. In
this paper, we study the requester's problem of dynamically adjusting
quality-contingent payments for tasks. We consider a multi-round version of the
well-known principal-agent model, whereby in each round a worker makes a
strategic choice of the effort level which is not directly observable by the
requester. In particular, our formulation significantly generalizes the
budget-free online task pricing problems studied in prior work.
We treat this problem as a multi-armed bandit problem, with each "arm"
representing a potential contract. To cope with the large (and in fact,
infinite) number of arms, we propose a new algorithm, AgnosticZooming, which
discretizes the contract space into a finite number of regions, effectively
treating each region as a single arm. This discretization is adaptively
refined, so that more promising regions of the contract space are eventually
discretized more finely. We analyze this algorithm, showing that it achieves
regret sublinear in the time horizon and substantially improves over
non-adaptive discretization (which is the only competing approach in the
literature).
Our results advance the state of art on several different topics: the theory
of crowdsourcing markets, principal-agent problems, multi-armed bandits, and
dynamic pricing.Comment: This is the full version of a paper in the ACM Conference on
Economics and Computation (ACM-EC), 201
Evolution with Drifting Targets
We consider the question of the stability of evolutionary algorithms to
gradual changes, or drift, in the target concept. We define an algorithm to be
resistant to drift if, for some inverse polynomial drift rate in the target
function, it converges to accuracy 1 -- \epsilon , with polynomial resources,
and then stays within that accuracy indefinitely, except with probability
\epsilon , at any one time. We show that every evolution algorithm, in the
sense of Valiant (2007; 2009), can be converted using the Correlational Query
technique of Feldman (2008), into such a drift resistant algorithm. For certain
evolutionary algorithms, such as for Boolean conjunctions, we give bounds on
the rates of drift that they can resist. We develop some new evolution
algorithms that are resistant to significant drift. In particular, we give an
algorithm for evolving linear separators over the spherically symmetric
distribution that is resistant to a drift rate of O(\epsilon /n), and another
algorithm over the more general product normal distributions that resists a
smaller drift rate.
The above translation result can be also interpreted as one on the robustness
of the notion of evolvability itself under changes of definition. As a second
result in that direction we show that every evolution algorithm can be
converted to a quasi-monotonic one that can evolve from any starting point
without the performance ever dipping significantly below that of the starting
point. This permits the somewhat unnatural feature of arbitrary performance
degradations to be removed from several known robustness translations
- …