110,476 research outputs found
Stability of exponential bases on d- dimensional domains
We find explicit stability bounds for exponential Riesz bases on domains of
R^d. Our results generalize Kadec theorem and other stability theorems in the
literature.Comment: We have discovered an error in Theorem 1.
Rational Proofs with Multiple Provers
Interactive proofs (IP) model a world where a verifier delegates computation
to an untrustworthy prover, verifying the prover's claims before accepting
them. IP protocols have applications in areas such as verifiable computation
outsourcing, computation delegation, cloud computing. In these applications,
the verifier may pay the prover based on the quality of his work. Rational
interactive proofs (RIP), introduced by Azar and Micali (2012), are an
interactive-proof system with payments, in which the prover is rational rather
than untrustworthy---he may lie, but only to increase his payment. Rational
proofs leverage the provers' rationality to obtain simple and efficient
protocols. Azar and Micali show that RIP=IP(=PSAPCE). They leave the question
of whether multiple provers are more powerful than a single prover for rational
and classical proofs as an open problem.
In this paper, we introduce multi-prover rational interactive proofs (MRIP).
Here, a verifier cross-checks the provers' answers with each other and pays
them according to the messages exchanged. The provers are cooperative and
maximize their total expected payment if and only if the verifier learns the
correct answer to the problem. We further refine the model of MRIP to
incorporate utility gap, which is the loss in payment suffered by provers who
mislead the verifier to the wrong answer.
We define the class of MRIP protocols with constant, noticeable and
negligible utility gaps. We give tight characterization for all three MRIP
classes. We show that under standard complexity-theoretic assumptions, MRIP is
more powerful than both RIP and MIP ; and this is true even the utility gap is
required to be constant. Furthermore the full power of each MRIP class can be
achieved using only two provers and three rounds. (A preliminary version of
this paper appeared at ITCS 2016. This is the full version that contains new
results.)Comment: Proceedings of the 2016 ACM Conference on Innovations in Theoretical
Computer Science. ACM, 201
Statistical uncertainty of eddy flux–based estimates of gross ecosystem carbon exchange at Howland Forest, Maine
We present an uncertainty analysis of gross ecosystem carbon exchange (GEE) estimates derived from 7 years of continuous eddy covariance measurements of forest-atmosphere CO2fluxes at Howland Forest, Maine, USA. These data, which have high temporal resolution, can be used to validate process modeling analyses, remote sensing assessments, and field surveys. However, separation of tower-based net ecosystem exchange (NEE) into its components (respiration losses and photosynthetic uptake) requires at least one application of a model, which is usually a regression model fitted to nighttime data and extrapolated for all daytime intervals. In addition, the existence of a significant amount of missing data in eddy flux time series requires a model for daytime NEE as well. Statistical approaches for analytically specifying prediction intervals associated with a regression require, among other things, constant variance of the data, normally distributed residuals, and linearizable regression models. Because the NEE data do not conform to these criteria, we used a Monte Carlo approach (bootstrapping) to quantify the statistical uncertainty of GEE estimates and present this uncertainty in the form of 90% prediction limits. We explore two examples of regression models for modeling respiration and daytime NEE: (1) a simple, physiologically based model from the literature and (2) a nonlinear regression model based on an artificial neural network. We find that uncertainty at the half-hourly timescale is generally on the order of the observations themselves (i.e., ∼100%) but is much less at annual timescales (∼10%). On the other hand, this small absolute uncertainty is commensurate with the interannual variability in estimated GEE. The largest uncertainty is associated with choice of model type, which raises basic questions about the relative roles of models and data
Gaps between logs
We calculate the limiting gap distribution for the fractional parts of log n,
where n runs through all positive integers. By rescaling the sequence, the
proof quickly reduces to an argument used by Barra and Gaspard in the context
of level spacing statistics for quantum graphs. The key ingredient is Weyl
equidistribution of irrational translations on multi-dimensional tori. Our
results extend to logarithms with arbitrary base; we deduce explicit formulas
when the base is transcendental or the r:th root of an integer. If the base is
close to one, the gap distribution is close to the exponential distribution.Comment: 14 page
Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization
In this paper, we consider the problem of sequentially optimizing a black-box
function based on noisy samples and bandit feedback. We assume that is
smooth in the sense of having a bounded norm in some reproducing kernel Hilbert
space (RKHS), yielding a commonly-considered non-Bayesian form of Gaussian
process bandit optimization. We provide algorithm-independent lower bounds on
the simple regret, measuring the suboptimality of a single point reported after
rounds, and on the cumulative regret, measuring the sum of regrets over the
chosen points. For the isotropic squared-exponential kernel in
dimensions, we find that an average simple regret of requires , and the
average cumulative regret is at least , thus matching existing upper bounds up to the replacement of by
in both cases. For the Mat\'ern- kernel, we give analogous
bounds of the form and
, and discuss the resulting
gaps to the existing upper bounds.Comment: Appearing in COLT 2017. This version corrects a few minor mistakes in
Table I, which summarizes the new and existing regret bound
On quantum mean-field models and their quantum annealing
This paper deals with fully-connected mean-field models of quantum spins with
p-body ferromagnetic interactions and a transverse field. For p=2 this
corresponds to the quantum Curie-Weiss model (a special case of the
Lipkin-Meshkov-Glick model) which exhibits a second-order phase transition,
while for p>2 the transition is first order. We provide a refined analytical
description both of the static and of the dynamic properties of these models.
In particular we obtain analytically the exponential rate of decay of the gap
at the first-order transition. We also study the slow annealing from the pure
transverse field to the pure ferromagnet (and vice versa) and discuss the
effect of the first-order transition and of the spinodal limit of metastability
on the residual excitation energy, both for finite and exponentially divergent
annealing times. In the quantum computation perspective this quantity would
assess the efficiency of the quantum adiabatic procedure as an approximation
algorithm.Comment: 44 pages, 23 figure
Infinite games with finite knowledge gaps
Infinite games where several players seek to coordinate under imperfect
information are deemed to be undecidable, unless the information is
hierarchically ordered among the players.
We identify a class of games for which joint winning strategies can be
constructed effectively without restricting the direction of information flow.
Instead, our condition requires that the players attain common knowledge about
the actual state of the game over and over again along every play.
We show that it is decidable whether a given game satisfies the condition,
and prove tight complexity bounds for the strategy synthesis problem under
-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio
Doubly infinite separation of quantum information and communication
We prove the existence of (one-way) communication tasks with a subconstant
versus superconstant asymptotic gap, which we call "doubly infinite," between
their quantum information and communication complexities. We do so by studying
the exclusion game [C. Perry et al., Phys. Rev. Lett. 115, 030504 (2015)] for
which there exist instances where the quantum information complexity tends to
zero as the size of the input increases. By showing that the quantum
communication complexity of these games scales at least logarithmically in ,
we obtain our result. We further show that the established lower bounds and
gaps still hold even if we allow a small probability of error. However in this
case, the -qubit quantum message of the zero-error strategy can be
compressed polynomially.Comment: 16 pages, 2 figures. v4: minor errors fixed; close to published
version; v5: financial support info adde
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