7,850 research outputs found
Optimal Competitive Auctions
We study the design of truthful auctions for selling identical items in
unlimited supply (e.g., digital goods) to n unit demand buyers. This classic
problem stands out from profit-maximizing auction design literature as it
requires no probabilistic assumptions on buyers' valuations and employs the
framework of competitive analysis. Our objective is to optimize the worst-case
performance of an auction, measured by the ratio between a given benchmark and
revenue generated by the auction.
We establish a sufficient and necessary condition that characterizes
competitive ratios for all monotone benchmarks. The characterization identifies
the worst-case distribution of instances and reveals intrinsic relations
between competitive ratios and benchmarks in the competitive analysis. With the
characterization at hand, we show optimal competitive auctions for two natural
benchmarks.
The most well-studied benchmark measures the
envy-free optimal revenue where at least two buyers win. Goldberg et al. [13]
showed a sequence of lower bounds on the competitive ratio for each number of
buyers n. They conjectured that all these bounds are tight. We show that
optimal competitive auctions match these bounds. Thus, we confirm the
conjecture and settle a central open problem in the design of digital goods
auctions. As one more application we examine another economically meaningful
benchmark, which measures the optimal revenue across all limited-supply Vickrey
auctions. We identify the optimal competitive ratios to be
for each number of buyers n, that is as
approaches infinity
Correlations for subsets of particles in symmetric states: what photons are doing within a beam of light when the rest are ignored
Given a state of light, how do its properties change when only some of the
constituent photons are observed and the rest are neglected (traced out)? By
developing formulae for mode-agnostic removal of photons from a beam, we show
how the expectation value of any operator changes when only photons are
inspected from a beam, ignoring the rest. We use this to reexpress expectation
values of operators in terms of the state obtained by randomly selecting
photons. Remarkably, this only equals the true expectation value for a unique
value of : expressing the operator as a monomial in normally ordered form,
must be equal to the number of photons annihilated by the operator. A
useful corollary is that the coefficients of any -photon state chosen at
random from an arbitrary state are exactly the th order correlations of the
original state; one can inspect the intensity moments to learn what any random
photon will be doing and, conversely, one need only look at the -photon
subspace to discern what all of the th order correlation functions are. The
astute reader will be pleased to find no surprises here, only mathematical
justification for intuition. Our results hold for any completely symmetric
state of any type of particle with any combination of numbers of particles and
can be used wherever bosonic correlations are found.Comment: 11+3 pages, 1 figure, comments always welcom
Teleamplification on the Borealis boson-sampling device
A recent theoretical proposal for teleamplification requires preparation of
Fock states, programmable interferometers, and photon-number resolving
detectors to herald the teleamplification of an input state. These enable
teleportation and heralded noiseless linear amplification of a photonic state
up to an arbitrarily large energy cutoff. We report on adapting this proposal
for Borealis and demonstrating teleamplification of squeezed-vacuum states with
variable amplification factors. The results match the theoretical predictions
and exhibit features of amplification in the teleported mode, with fidelities
from 50 to 93%. This demonstration motivates the continued development of
photonic quantum computing hardware for noiseless linear amplification's
applications across quantum communication, sensing, and error correction.Comment: 9+5 pages, 6+7 figures; close to published versio
Properties of Nucleon Resonances by means of a Genetic Algorithm
We present an optimization scheme that employs a Genetic Algorithm (GA) to
determine the properties of low-lying nucleon excitations within a realistic
photo-pion production model based upon an effective Lagrangian. We show that
with this modern optimization technique it is possible to reliably assess the
parameters of the resonances and the associated error bars as well as to
identify weaknesses in the models. To illustrate the problems the optimization
process may encounter, we provide results obtained for the nucleon resonances
(1230) and (1700). The former can be easily isolated and thus
has been studied in depth, while the latter is not as well known
experimentally.Comment: 12 pages, 10 figures, 3 tables. Minor correction
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