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