12,690 research outputs found
Approximation Schemes for a Unit-Demand Buyer with Independent Items via Symmetries
We consider a revenue-maximizing seller with items facing a single buyer.
We introduce the notion of symmetric menu complexity of a mechanism, which
counts the number of distinct options the buyer may purchase, up to
permutations of the items. Our main result is that a mechanism of
quasi-polynomial symmetric menu complexity suffices to guarantee a
-approximation when the buyer is unit-demand over independent
items, even when the value distribution is unbounded, and that this mechanism
can be found in quasi-polynomial time.
Our key technical result is a polynomial time, (symmetric)
menu-complexity-preserving black-box reduction from achieving a
-approximation for unbounded valuations that are subadditive
over independent items to achieving a -approximation when
the values are bounded (and still subadditive over independent items). We
further apply this reduction to deduce approximation schemes for a suite of
valuation classes beyond our main result.
Finally, we show that selling separately (which has exponential menu
complexity) can be approximated up to a factor with a menu of
efficient-linear symmetric menu complexity.Comment: FOCS 201
Experimental observation of chimera and cluster states in a minimal globally coupled network
A "chimera state" is a dynamical pattern that occurs in a network of coupled
identical oscillators when the symmetry of the oscillator population is broken
into synchronous and asynchronous parts. We report the experimental observation
of chimera and cluster states in a network of four globally coupled chaotic
opto-electronic oscillators. This is the minimal network that can support
chimera states, and our study provides new insight into the fundamental
mechanisms underlying their formation. We use a unified approach to determine
the stability of all the observed partially synchronous patterns, highlighting
the close relationship between chimera and cluster states as belonging to the
broader phenomenon of partial synchronization. Our approach is general in terms
of network size and connectivity. We also find that chimera states often appear
in regions of multistability between global, cluster, and desynchronized
states
Factoring the Strong CP Problem
We present a new mechanism to solve the strong CP problem using
axions, each dynamically relaxing part of the parameter. At high
energies the group becomes the diagonal
subgroup of an gauge group, and the non-perturbative effects in
each individual factor generate a potential for the corresponding
axion. The vacuum is naturally aligned to ensure at low
energies, and the masses of these axions can be much larger than for the
standard QCD axion. This mechanism avoids the introduction of a discrete
symmetry and associated 'mirror' copies of the SM fermions, and also avoids the
introduction and stabilization of new light colored states to modify the
running of the QCD gauge coupling found in other heavy axion models. This
strengthens the motivation for axion-like particles solving the strong CP
problem at points beyond the standard QCD axion curve in the
plane.Comment: 14 pages, 5 figure
Constant-Competitive Prior-Free Auction with Ordered Bidders
A central problem in Microeconomics is to design auctions with good revenue
properties. In this setting, the bidders' valuations for the items are private
knowledge, but they are drawn from publicly known prior distributions. The goal
is to find a truthful auction (no bidder can gain in utility by misreporting
her valuation) that maximizes the expected revenue.
Naturally, the optimal-auction is sensitive to the prior distributions. An
intriguing question is to design a truthful auction that is oblivious to these
priors, and yet manages to get a constant factor of the optimal revenue. Such
auctions are called prior-free.
Goldberg et al. presented a constant-approximate prior-free auction when
there are identical copies of an item available in unlimited supply, bidders
are unit-demand, and their valuations are drawn from i.i.d. distributions. The
recent work of Leonardi et al. [STOC 2012] generalized this problem to non
i.i.d. bidders, assuming that the auctioneer knows the ordering of their
reserve prices. Leonardi et al. proposed a prior-free auction that achieves a
approximation. We improve upon this result, by giving the first
prior-free auction with constant approximation guarantee.Comment: The same result has been obtained independently by E. Koutsoupias, S.
Leonardi and T. Roughgarde
Sampling and Representation Complexity of Revenue Maximization
We consider (approximate) revenue maximization in auctions where the
distribution on input valuations is given via "black box" access to samples
from the distribution. We observe that the number of samples required -- the
sample complexity -- is tightly related to the representation complexity of an
approximately revenue-maximizing auction. Our main results are upper bounds and
an exponential lower bound on these complexities
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