5,401 research outputs found
Profit Sharing and Reciprocity: Theory and Survey Evidence
The 1/n problem potentially limits the effectiveness of profit sharing in motivating workers. While the economic literature suggests that reciprocity can mitigate this problem, it remains silent on the optimal degree of reciprocity. We present a representative model demonstrating that reciprocity may increase productive effort but may also increase unproductive effort such as socializing on the job. The model implies that reciprocity increases profit up to a point but decreases profit beyond that point. Using detailed survey measures of worker reciprocity, we show that the probability of receiving profit sharing takes an inverse U-shape as reciprocity increases. This supports the general implication of the model and is shown to exist for both positive and negative reciprocity and to remain when a series of ability proxies and detailed industry indicators are included.
Near-Optimal Quantum Algorithms for Multivariate Mean Estimation
We propose the first near-optimal quantum algorithm for estimating in
Euclidean norm the mean of a vector-valued random variable with finite mean and
covariance. Our result aims at extending the theory of multivariate
sub-Gaussian estimators to the quantum setting. Unlike classically, where any
univariate estimator can be turned into a multivariate estimator with at most a
logarithmic overhead in the dimension, no similar result can be proved in the
quantum setting. Indeed, Heinrich ruled out the existence of a quantum
advantage for the mean estimation problem when the sample complexity is smaller
than the dimension. Our main result is to show that, outside this low-precision
regime, there is a quantum estimator that outperforms any classical estimator.
Our approach is substantially more involved than in the univariate setting,
where most quantum estimators rely only on phase estimation. We exploit a
variety of additional algorithmic techniques such as amplitude amplification,
the Bernstein-Vazirani algorithm, and quantum singular value transformation.
Our analysis also uses concentration inequalities for multivariate truncated
statistics.
We develop our quantum estimators in two different input models that showed
up in the literature before. The first one provides coherent access to the
binary representation of the random variable and it encompasses the classical
setting. In the second model, the random variable is directly encoded into the
phases of quantum registers. This model arises naturally in many quantum
algorithms but it is often incomparable to having classical samples. We adapt
our techniques to these two settings and we show that the second model is
strictly weaker for solving the mean estimation problem. Finally, we describe
several applications of our algorithms, notably in measuring the expectation
values of commuting observables and in the field of machine learning.Comment: 35 pages, 1 figure; v2: minor change
Auto-oscillation threshold, narrow spectral lines, and line jitter in spin-torque oscillators based on MgO magnetic tunnel junctions
We demonstrate spin torque induced auto-oscillation in MgO-based magnetic
tunnel junctions. At the generation threshold, we observe a strong line
narrowing down to 6 MHz at 300K and a dramatic increase in oscillator power,
yielding spectrally pure oscillations free of flicker noise. Setting the
synthetic antiferromagnet into autooscillation requires the same current
polarity as the one needed to switch the free layer magnetization. The induced
auto-oscillations are observed even at zero applied field, which is believed to
be the acoustic mode of the synthetic antiferromagnet. While the phase
coherence of the auto-oscillation is of the order of microseconds, the power
autocorrelation time is of the order of milliseconds and can be strongly
influenced by the free layer dynamics
Improved Quantum Query Upper Bounds Based on Classical Decision Trees
We consider the following question in query complexity: Given a classical query algorithm in the form of a decision tree, when does there exist a quantum query algorithm with a speed-up (i.e., that makes fewer queries) over the classical one? We provide a general construction based on the structure of the underlying decision tree, and prove that this can give us an up-to-quadratic quantum speed-up in the number of queries. In particular, our results give a bounded-error quantum query algorithm of cost O(?s) to compute a Boolean function (more generally, a relation) that can be computed by a classical (even randomized) decision tree of size s. This recovers an O(?n) algorithm for the Search problem, for example.
Lin and Lin [Theory of Computing\u2716] and Beigi and Taghavi [Quantum\u2720] showed results of a similar flavor. Their upper bounds are in terms of a quantity which we call the "guessing complexity" of a decision tree. We identify that the guessing complexity of a decision tree equals its rank, a notion introduced by Ehrenfeucht and Haussler [Information and Computation\u2789] in the context of learning theory. This answers a question posed by Lin and Lin, who asked whether the guessing complexity of a decision tree is related to any measure studied in classical complexity theory. We also show a polynomial separation between rank and its natural randomized analog for the complete binary AND-OR tree.
Beigi and Taghavi constructed span programs and dual adversary solutions for Boolean functions given classical decision trees computing them and an assignment of non-negative weights to edges of the tree. We explore the effect of changing these weights on the resulting span program complexity and objective value of the dual adversary bound, and capture the best possible weighting scheme by an optimization program. We exhibit a solution to this program and argue its optimality from first principles. We also exhibit decision trees for which our bounds are strictly stronger than those of Lin and Lin, and Beigi and Taghavi. This answers a question of Beigi and Taghavi, who asked whether different weighting schemes in their construction could yield better upper bounds
Stable divisorial gonality is in NP
Divisorial gonality and stable divisorial gonality are graph parameters,
which have an origin in algebraic geometry. Divisorial gonality of a connected
graph can be defined with help of a chip firing game on . The stable
divisorial gonality of is the minimum divisorial gonality over all
subdivisions of edges of .
In this paper we prove that deciding whether a given connected graph has
stable divisorial gonality at most a given integer belongs to the class NP.
Combined with the result that (stable) divisorial gonality is NP-hard by
Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof
consist of a partial certificate that can be verified by solving an Integer
Linear Programming instance. As a corollary, we have that the number of
subdivisions needed for minimum stable divisorial gonality of a graph with
vertices is bounded by for a polynomial
Auto-oscillation threshold and line narrowing in MgO-based spin-torque oscillators
We present an experimental study of the power spectrum of current-driven
magnetization oscillations in MgO tunnel junctions under low bias. We find the
existence of narrow spectral lines, down to 8 MHz in width at a frequency of
10.7 GHz, for small applied fields with clear evidence of an auto-oscillation
threshold. Micromagnetics simulations indicate that the excited mode
corresponds to an edge mode of the synthetic antiferromagnet
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