Monotonic regression based on Bayesian P-splines: an application to estimating price response functions from store-level scanner data

Generalized additive models have become a widely used instrument for flexible regression analysis. In many practical situations, however, it is desirable to restrict the flexibility of nonparametric estimation in order to accommodate a presumed monotonic relationship between a covariate and the response variable. For example, consumers usually will buy less of a brand if its price increases, and therefore one expects a brand's unit sales to be a decreasing function in own price. We follow a Bayesian approach using penalized B-splines and incorporate the assumption of monotonicity in a natural way by an appropriate specification of the respective prior distributions. We illustrate the methodology in an empirical application modeling demand for a brand of orange juice and show that imposing monotonicity constraints for own- and cross-item price effects improves the predictive validity of the estimated sales response function considerably

Matter-wave interferometer for large molecules

We demonstrate a near-field Talbot-Lau interferometer for C-70 fullerene molecules. Such interferometers are particularly suitable for larger masses. Using three free-standing gold gratings of one micrometer period and a transversally incoherent but velocity-selected molecular beam, we achieve an interference fringe visibility of 40 % with high count rate. Both the high visibility and its velocity dependence are in good agreement with a quantum simulation that takes into account the van der Waals interaction of the molecules with the gratings and are in striking contrast to a classical moire model.Comment: revtex4, 4 pages, 3 figure

Collisional decoherence observed in matter wave interferometry

We study the loss of spatial coherence in the extended wave function of fullerenes due to collisions with background gases. From the gradual suppression of quantum interference with increasing gas pressure we are able to support quantitatively both the predictions of decoherence theory and our picture of the interaction process. We thus explore the practical limits of matter wave interferometry at finite gas pressures and estimate the required experimental vacuum conditions for interferometry with even larger objects.Comment: 4 pages, 3 figure

The wave nature of biomolecules and fluorofullerenes

We demonstrate quantum interference for tetraphenylporphyrin, the first biomolecule exhibiting wave nature, and for the fluorofullerene C60F48 using a near-field Talbot-Lau interferometer. For the porphyrins, which are distinguished by their low symmetry and their abundant occurence in organic systems, we find the theoretically expected maximal interference contrast and its expected dependence on the de Broglie wavelength. For C60F48 the observed fringe visibility is below the expected value, but the high contrast still provides good evidence for the quantum character of the observed fringe pattern. The fluorofullerenes therefore set the new mark in complexity and mass (1632 amu) for de Broglie wave experiments, exceeding the previous mass record by a factor of two.Comment: 5 pages, 4 figure

A scalable optical detection scheme for matter wave interferometry

Imaging of surface adsorbed molecules is investigated as a novel detection method for matter wave interferometry with fluorescent particles. Mechanically magnified fluorescence imaging turns out to be an excellent tool for recording quantum interference patterns. It has a good sensitivity and yields patterns of high visibility. The spatial resolution of this technique is only determined by the Talbot gratings and can exceed the optical resolution limit by an order of magnitude. A unique advantage of this approach is its scalability: for certain classes of nano-sized objects, the detection sensitivity will even increase significantly with increasing size of the particle.Comment: 10 pages, 4 figure

Action principle formulation for motion of extended bodies in General Relativity

We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order coupling to the gravitational field. In particular, a new force due to the octupole moment is obtained. The action also yields the gravitationally induced phase shifts in quantum interference experiments due to the coupling of all multipole moments.Comment: Revised version derives Octupole moment force. Some clarifications and a reference added. To appear in Phys. Rev.

Fast stable direct fitting and smoothness selection for Generalized Additive Models

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of models, with failure being particularly frequent in the presence of concurvity. If smoothness selection is performed by optimizing `whole model' criteria these problems disappear, but until now attempts to do this have employed finite difference based optimization schemes which are computationally inefficient, and can suffer from false convergence. This paper develops the first computationally efficient method for direct GAM smoothness selection. It is highly stable, but by careful structuring achieves a computational efficiency that leads, in simulations, to lower mean computation times than the schemes based on working-model smoothness selection. The method also offers a reliable way of fitting generalized additive mixed models

Concept of an ionizing time-domain matter-wave interferometer

We discuss the concept of an all-optical and ionizing matter-wave interferometer in the time domain. The proposed setup aims at testing the wave nature of highly massive clusters and molecules, and it will enable new precision experiments with a broad class of atoms, using the same laser system. The propagating particles are illuminated by three pulses of a standing ultraviolet laser beam, which detaches an electron via efficient single photon-absorption. Optical gratings may have periods as small as 80 nm, leading to wide diffraction angles for cold atoms and to compact setups even for very massive clusters. Accounting for the coherent and the incoherent parts of the particle-light interaction, we show that the combined effect of phase and amplitude modulation of the matter waves gives rise to a Talbot-Lau-like interference effect with a characteristic dependence on the pulse delay time.Comment: 25 pages, 5 figure

Diffraction of complex molecules by structures made of light

We demonstrate that structures made of light can be used to coherently control the motion of complex molecules. In particular, we show diffraction of the fullerenes C60 and C70 at a thin grating based on a standing light wave. We prove experimentally that the principles of this effect, well known from atom optics, can be successfully extended to massive and large molecules which are internally in a thermodynamic mixed state and which do not exhibit narrow optical resonances. Our results will be important for the observation of quantum interference with even larger and more complex objects.Comment: 4 pages, 3 figure