60,837 research outputs found
Higgs Boson in RG running Inflationary Cosmology
An intriguing hypothesis is that gravity may be non-perturbatively
renormalizable via the notion of asymptotic safety. We show that the Higgs
sector of the SM minimally coupled to asymptotically safe gravity can generate
the observed near scale-invariant spectrum of the Cosmic Microwave Background
through the curvaton mechanism. The resulting primordial power spectrum places
an upper bound on the Higgs mass, which for finely tuned values of the curvaton
parameters, is compatible with the recently released Large Hadron Collider
data.Comment: 7 pages, no figur
Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard
State-of-the-art posted-price mechanisms for submodular bidders with
items achieve approximation guarantees of [Assadi and
Singla, 2019]. Their truthfulness, however, requires bidders to compute an
NP-hard demand-query. Some computational complexity of this form is
unavoidable, as it is NP-hard for truthful mechanisms to guarantee even an
-approximation for any [Dobzinski and
Vondr\'ak, 2016]. Together, these establish a stark distinction between
computationally-efficient and communication-efficient truthful mechanisms.
We show that this distinction disappears with a mild relaxation of
truthfulness, which we term implementation in advised strategies, and that has
been previously studied in relation to "Implementation in Undominated
Strategies" [Babaioff et al, 2009]. Specifically, advice maps a tentative
strategy either to that same strategy itself, or one that dominates it. We say
that a player follows advice as long as they never play actions which are
dominated by advice. A poly-time mechanism guarantees an -approximation
in implementation in advised strategies if there exists poly-time advice for
each player such that an -approximation is achieved whenever all
players follow advice. Using an appropriate bicriterion notion of approximate
demand queries (which can be computed in poly-time), we establish that (a
slight modification of) the [Assadi and Singla, 2019] mechanism achieves the
same -approximation in implementation in advised
strategies
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