Generalized Monotonic Regression Based on B-Splines with an Application to Air Pollution Data

In many studies where it is known that one or more of the certain covariates have monotonic effect on the response variable, common fitting methods for generalized additive models (GAM) may be affected by a sparse design and often generate implausible results. A fitting procedure is proposed that incorporates the monotonicity assumptions on one or more smooth components within a GAM framework. The flexible likelihood based boosting algorithm uses the monotonicity restriction for B-spline coefficients and provides componentwise selection of smooth components. Stopping criteria and approximate pointwise confidence bands are derived. The method is applied to data from a study conducted in the metropolitan area of Sao Paulo, Brazil, where the influence of several air pollutants like SO_2 on respiratory mortality of children is investigated

Smoothing with Curvature Constraints based on Boosting Techniques

In many applications it is known that the underlying smooth function is constrained to have a specific form. In the present paper, we propose an estimation method based on the regression spline approach, which allows to include concavity or convexity constraints in an appealing way. Instead of using linear or quadratic programming routines, we handle the required inequality constraints on basis coefficients by boosting techniques. Therefore, recently developed componentwise boosting methods for regression purposes are applied, which allow to control the restrictions in each iteration. The proposed approach is compared to several competitors in a simulation study. We also consider a real world data set

Estimation of Single-Index Models Based on Boosting Techniques

In single-index models the link or response function is not considered as fixed. The data determine the form of the unknown link function. In order to obtain a flexible form of the link function we specify the link function as an expansion in basis function and propose to estimate parameters as well as the link function by weak learners within a boosting framework. It is shown that the method is a strong competitor to existing methods. The method is investigated in simulation studies and applied to real data

Knot selection by boosting techniques

A novel concept for estimating smooth functions by selection techniques based on boosting is developed. It is suggested to put radial basis functions with different spreads at each knot and to do selection and estimation simultaneously by a componentwise boosting algorithm. The methodology of various other smoothing and knot selection procedures (e.g. stepwise selection) is summarized. They are compared to the proposed approach by extensive simulations for various unidimensional settings, including varying spatial variation and heteroskedasticity, as well as on a real world data example. Finally, an extension of the proposed method to surface fitting is evaluated numerically on both, simulation and real data. The proposed knot selection technique is shown to be a strong competitor to existing methods for knot selection

Paraxial Theory of Direct Electro-Optic Sampling of the Quantum Vacuum

Direct detection of vacuum fluctuations and analysis of sub-cycle quantum properties of the electric field are explored by a paraxial quantum theory of ultrafast electro-optic sampling. The feasibility of such experiments is demonstrated by realistic calculations adopting a thin ZnTe electro-optic crystal and stable few-femtosecond laser pulses. We show that nonlinear mixing of a short near-infrared probe pulse with multi-terahertz vacuum field modes leads to an increase of the signal variance with respect to the shot noise level. The vacuum contribution increases significantly for appropriate length of the nonlinear crystal, short probe pulse durations, tight focusing, and sufficiently large number of photons per probe pulse. If the vacuum input is squeezed, the signal variance depends on the probe delay. Temporal positions with noise level below the pure vacuum may be traced with a sub-cycle accuracy.Comment: 10 pages, 6 figure

Spectra of ultrabroadband squeezed pulses and the finite-time Unruh-Davies effect

We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-field driving in a thin nonlinear crystal with second order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. These spectra can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance.Comment: 11 pages, 5 figure

Subcycle squeezing of light from a time flow perspective

Light as a carrier of information and energy plays a fundamental role in both general relativity and quantum physics, linking these areas that are still not fully compliant with each other. Its quantum nature and spatio-temporal structure are exploited in many intriguing applications ranging from novel spectroscopy methods of complex many-body phenomena to quantum information processing and subwavelength lithography. Recent access to subcycle quantum features of electromagnetic radiation promises a new class of time-dependent quantum states of light. Paralleled with the developments in attosecond science, these advances motivate an urgent need for a theoretical framework that treats arbitrary wave packets of quantum light intrinsically in the time domain. Here, we formulate a consistent time domain theory of the generation and sampling of few-cycle and subcycle pulsed squeezed states, allowing for a relativistic interpretation in terms of induced changes in the local flow of time. Our theory enables the use of such states as a resource for novel ultrafast applications in quantum optics and quantum information.Comment: 24 pages, 7 figures (including supplementary information

Assignment of the NV0 575 nm zero-phonon line in diamond to a 2E-2A2 transition

The time-averaged emission spectrum of single nitrogen-vacancy defects in diamond gives zero-phonon lines of both the negative charge state at 637 nm (1.945 eV) and the neutral charge state at 575 nm (2.156 eV). This occurs through photo-conversion between the two charge states. Due to strain in the diamond the zero-phonon lines are split and it is found that the splitting and polarization of the two zero-phonon lines are the same. From this observation and consideration of the electronic structure of the nitrogen-vacancy center it is concluded that the excited state of the neutral center has A2 orbital symmetry. The assignment of the 575 nm transition to a 2E - 2A2 transition has not been established previously.Comment: 5 pages, 5 figure