Dynamic density estimation with diffusive Dirichlet mixtures

We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose sections are continuous or discrete distributions depending on the choice of kernel. The construction exploits the widely used stick-breaking representation of the Dirichlet process and induces the time dependence by replacing the stick-breaking components with one-dimensional Wright-Fisher diffusions. These features combine appealing properties of the model, inherited from the Wright-Fisher diffusions and the Dirichlet mixture structure, with great flexibility and tractability for posterior computation. The construction can be easily extended to multi-parameter GEM marginal states, which include, for example, the Pitman--Yor process. A full inferential strategy is detailed and illustrated on simulated and real data.Comment: Published at http://dx.doi.org/10.3150/14-BEJ681 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Geometric Stick-Breaking Processes for Continuous-Time Nonparametric Modeling

This paper is concerned with the construction of a continuous parameter sequence of random probability measures and its application for modeling random phenomena evolving in continuous time. At each time point we have a random probability measure which is generated by a Bayesian nonparametric hierarchical model, and the dependence structure is induced through a Wright-Fisher diffusion with mutation. The sequence is shown to be a stationary and reversible diffusion taking values on the space of probability measures. A simple estimation procedure for discretely observed data is presented and illustrated with simulated and real data sets.Bayesian non-parametric inference, continuous time dependent random measure, Markov process, measure-valued process, stationary process, stick-breaking process

Light-cone fluctuations and the renormalized stress tensor of a massless scalar field

We investigate the effects of light-cone fluctuations over the renormalized vacuum expectation value of the stress-energy tensor of a real massless minimally coupled scalar field defined in a ($d+1$)-dimensional flat space-time with topology ${\cal R}\times {\cal S}^d$. For modeling the influence of light-cone fluctuations over the quantum field, we consider a random Klein-Gordon equation. We study the case of centered Gaussian processes. After taking into account all the realizations of the random processes, we present the correction caused by random fluctuations. The averaged renormalized vacuum expectation value of the stress-energy associated with the scalar field is presented

Fiber R and D for the CMS HCAL

This paper documents the fiber R and D for the CMS hadron barrel calorimeter (HCAL). The R and D includes measurements of fiber flexibility, splicing, mirror reflectivity, relative light yield, attenuation length, radiation effects, absolute light yield, and transverse tile uniformity. Schematics of the hardware for each measurement are shown. These studies are done for different diameters and kinds of multiclad fiber.Comment: 23 pages, 30 Figures 89 pages, 41 figures, corresponding author: H. Budd, [email protected]

A post-Keplerian parameter to test gravito-magnetic effects in binary pulsar systems

We study the pulsar timing, focusing on the time delay induced by the gravitational field of the binary systems. In particular, we study the gravito-magnetic correction to the Shapiro time delay in terms of Keplerian and post-Keplerian parameters, and we introduce a new post-Keplerian parameter which is related to the intrinsic angular momentum of the stars. Furthermore, we evaluate the magnitude of these effects for the binary pulsar systems known so far. The expected magnitude is indeed small, but the effect is important per se.Comment: 6 pages, RevTeX, 1 eps figure, accepted for publication in Physical Review D; references adde

On the time delay in binary systems

The aim of this paper is to study the time delay on electromagnetic signals propagating across a binary stellar system. We focus on the antisymmetric gravitomagnetic contribution due to the angular momentum of one of the stars of the pair. Considering a pulsar as the source of the signals, the effect would be manifest both in the arrival times of the pulses and in the frequency shift of their Fourier spectra. We derive the appropriate formulas and we discuss the influence of different configurations on the observability of gravitomagnetic effects. We argue that the recently discovered PSR J0737-3039 binary system does not permit the detection of the effects because of the large size of the eclipsed region.Comment: 7 pages, 2 eps figures, RevTex, to appear in Physical Review

Doppler Effects from Bending of Light Rays in Curved Space-Times

We study Doppler effects in curved space-time, i.e. the frequency shifts induced on electromagnetic signals propagating in the gravitational field. In particular, we focus on the frequency shift due to the bending of light rays in weak gravitational fields. We consider, using the PPN formalism, the gravitational field of an axially symmetric distribution of mass. The zeroth order, i.e. the sphere, is studied then passing to the contribution of the quadrupole moment, and finally to the case of a rotating source. We give numerical estimates for situations of physical interest, and by a very preliminary analysis, we argue that analyzing the Doppler effect could lead, in principle, in the foreseeable future, to the measurement of the quadrupole moment of the giant planets of the Solar System.Comment: 16 pages, 2 EPS figures; to appear in the International Journal of Modern Physics

About Gravitomagnetism

The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the electrodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms.Comment: 16 pages, a few amendments have been performed and a new section has been adde

Angular momentum effects in Michelson-Morley type experiments

The effect of the angular momentum density of a gravitational source on the times of flight of light rays in an interferometer is analyzed. The calculation is made imagining that the interferometer is at the equator of the gravity source and, as long as possible, the metric, provided it is stationary and axisymmetric, is not approximated. Finally, in order to evaluate the size of the effect in the case of the Earth a weak field approximation is introduced. For laboratory scales and non-geodesic paths the correction turns out to be comparable with the sensitivity expected in gravitational waves interferometric detectors, whereas it drops under the threshold of detectability when using free (geodesic) light rays.Comment: 12 pages, LaTeX; more about the detection technique, references added; accepted for publication in GR