1,669 research outputs found
Feasible Multivariate Nonparametric Estimation Using Weak Separability
One of the main practical problems of nonparametric regression estimation is the curse of dimensionality. The curse of dimensionality arises because nonparametric regression estimates are dependent variable averages local to the point at which the regression function is to be estimated. The number of observations `local' to the point of estimation decreases exponentially with the number of dimensions. The consequence is that the variance of unconstrained nonparametric regression estimators of multivariate regression functions is often so great that the unconstrained nonparametric regression estimates are of no practical use. In this paper I propose a new estimation method of weakly separable multivariate nonparametric regression functions. Weak separability is a weaker condition than required by other dimension--reduction techniques, although similar asymptotic variance reductions obtain. Indeed, weak separability is weaker than generalized additivity (see Hardle and Linton, 1996 and Horowitz, 1998). The proposed estimator is relatively easy to compute. Theoretical results in this paper include (i) a uniform law of large numbers for marginal integration estimators, (ii) a uniform law of large numbers for marginal summation estimators, (iii) a uniform law of large numbers for my new nonparametric regression estimator for weakly separable regression functions, (iv) both a uniform strong and weak law of large numbers for U-statistics, and (v) three central limit theorems for my nonparametric regression estimator for weakly separable regression functions.
Empirical Implications of Equilibrium Bidding in First-Price, Symmetric, Common Value Auctions
This paper studies federal auctions for wildcat leases on the Outer Continental Shelf from 1954 to 1970. These are leases where bidders privately acquire (at some cost) noisy, but equally informative, signals about the amount of oil and gas that may be present. We develop a test of equilibrium bidding in a common values model that is implemented using data on bids and ex post values. We compute bid markups and rents under the alternative hypotheses of private and common values and find that the data are more consistent with the latter hypothesis. Finally, we use data on tract location and ex post values to test the comparative static prediction in common value auctions that bidders may bid less aggressively when they expect more competition.
Aberrations of the point spread function of a multimode fiber
We investigate the point spread function of a multimode fiber. The distortion
of the focal spot created on the fiber output facet is studied for a variety of
the parameters. We develop a theoretical model of wavefront shaping through a
multimode fiber and use it to confirm our experimental results and analyze the
nature of the focal distortions. We show that aberration-free imaging with a
large field of view can be achieved by using an appropriate number of segments
on the spatial light modulator during the wavefront-shaping procedure. The
results describe aberration limits for imaging with multimode fibers as in,
e.g., microendoscopy.Comment: 10 pages, 6 figure
Programming multi-level quantum gates in disordered computing reservoirs via machine learning and TensorFlow
Novel machine learning computational tools open new perspectives for quantum
information systems. Here we adopt the open-source programming library
TensorFlow to design multi-level quantum gates including a computing reservoir
represented by a random unitary matrix. In optics, the reservoir is a
disordered medium or a multi-modal fiber. We show that trainable operators at
the input and the readout enable one to realize multi-level gates. We study
various qudit gates, including the scaling properties of the algorithms with
the size of the reservoir. Despite an initial low slop learning stage,
TensorFlow turns out to be an extremely versatile resource for designing gates
with complex media, including different models that use spatial light
modulators with quantized modulation levels.Comment: Added a new section and a new figure about implementation of the
gates by a single spatial light modulator. 9 pages and 4 figure
Optical decay from a Fabry-Perot cavity faster than the decay time
The dynamical response of an optical Fabry-Perot cavity is investigated
experimentally. We observe oscillations in the transmitted and reflected light
intensity if the frequency of the incoupled light field is rapidly changed. In
addition, the decay of a cavity-stored light field is accelerated if the phase
and intensity of the incoupled light are switched in an appropriate way. The
theoretical model by M. J. Lawrence em et al, JOSA B 16, 523 (1999) agrees with
our observations.Comment: submitted to Josa
Water vapor at a translational temperature of one kelvin
We report the creation of a confined slow beam of heavy-water (D2O) molecules
with a translational temperature around 1 kelvin. This is achieved by filtering
slow D2O from a thermal ensemble with inhomogeneous static electric fields
exploiting the quadratic Stark shift of D2O. All previous demonstrations of
electric field manipulation of cold dipolar molecules rely on a predominantly
linear Stark shift. Further, on the basis of elementary molecular properties
and our filtering technique we argue that our D2O beam contains molecules in
only a few ro-vibrational states.Comment: 4 pages, 4 figures, 1 tabl
Cavity sideband cooling of trapped molecules
The efficiency of cavity sideband cooling of trapped molecules is
theoretically investigated for the case where the IR transition between two
rovibrational states is used as a cycling transition. The molecules are assumed
to be trapped either by a radio-frequency or optical trapping potential,
depending on whether they are charged or neutral, and confined inside a
high-finesse optical resonator which enhances radiative emission into the
cavity mode. Using realistic experimental parameters and COS as a
representative molecular example, we show that in this setup cooling to the
trap ground state is feasible
Spillovers in Space: Does Geography Matter?
We simultaneously assess the contributions to productivity of three sources of research and development spillovers: geographic, technology and product- market proximity. To do this, we construct a new measure of geographic proximity that is based on the distribution of a firm's inventor locations rather than its headquarters, and we report both parametric and semiparametric estimates of our geographic-distance functions. We find that: i) Geographic space matters even after conditioning on horizontal and technological spillovers; ii) Technological proximity matters; iii) Product-market proximity is less important; iv) Locations of researchers are more important than headquarters but both have explanatory power; and v) Geographic markets are very local.geographic proximity, R&D spillovers, semiparametric and technological proximity
Cavity-Enhanced Rayleigh Scattering
We demonstrate Purcell-like enhancement of Rayleigh scattering into a single
optical mode of a Fabry-Perot resonator for several thermal atomic and
molecular gases. The light is detuned by more than an octave, in this case by
hundreds of nanometers, from any optical transition, making particle excitation
and spontaneous emission negligible. The enhancement of light scattering into
the resonator is explained quantitatively as an interference effect of light
waves emitted by a classical driven dipole oscillator. Applications of our
method include the sensitive, non-destructive in-situ detection of ultracold
molecules.Comment: v2: 13 pages, 7 figures, small changes to the text, extended
description of the theoretical mode
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