Warped metrics for location-scale models

This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results : i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, ii) the analytic expression of the sectional curvature of this metric, iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms.Comment: preprint of a submission to GSI 2017 conferenc

How Sensitive are Di-Leptons from Rho Mesons to the High Baryon Density Region?

We show that the measurement of di-leptons might provide only a restricted view into the most dense stages of heavy ion reactions. Thus, possible studies of meson and baryon properties at high baryon densities, as e.g. done at GSI-HADES and envisioned for FAIR-CBM, might observe weaker effects than currently expected in certain approaches. We argue that the strong absorption of resonances in the high baryon density region of the heavy ion collision masks information from the early hot and dense phase due to a strong increase of the total decay width because of collisional broadening. To obtain additional information, we also compare the currently used approaches to extract di-leptons from transport simulations - i.e. shining, only vector mesons from final baryon resonance decays and instant emission of di-leptons and find a strong sensitivity on the method employed in particular at FAIR and SPS energies. It is shown explicitly that a restriction to rho meson (and therefore di-lepton) production only in final state baryon resonance decays provide a strong bias towards rather low baryon densities. The results presented are obtained from UrQMD v2.3 calculations using the standard set-up.Comment: 8 pages, 6 figures, expanded versio

Ultrafast Resonant Polarization Interferometry: Towards the First Direct Detection of Vacuum Polarization

Vacuum polarization, an effect predicted nearly 70 years ago, is still yet to be directly detected despite significant experimental effort. Previous attempts have made use of large liquid-helium cooled electromagnets which inadvertently generate spurious signals that mask the desired signal. We present a novel approach for the ultra-sensitive detection of optical birefringence that can be usefully applied to a laboratory detection of vacuum polarization. The new technique has a predicted birefringence measurement sensitivity of $\Delta n \sim 10^{20}$ in a 1 second measurement. When combined with the extreme polarizing fields achievable in this design we predict that a vacuum polarization signal will be seen in a measurement of just a few days in duration.Comment: 9 pages, 2 figures. submitted to PR

On the distribution of career longevity and the evolution of home run prowess in professional baseball

Statistical analysis is a major aspect of baseball, from player averages to historical benchmarks and records. Much of baseball fanfare is based around players exceeding the norm, some in a single game and others over a long career. Career statistics serve as a metric for classifying players and establishing their historical legacy. However, the concept of records and benchmarks assumes that the level of competition in baseball is stationary in time. Here we show that power-law probability density functions, a hallmark of many complex systems that are driven by competition, govern career longevity in baseball. We also find similar power laws in the density functions of all major performance metrics for pitchers and batters. The use of performance-enhancing drugs has a dark history, emerging as a problem for both amateur and professional sports. We find statistical evidence consistent with performance-enhancing drugs in the analysis of home runs hit by players in the last 25 years. This is corroborated by the findings of the Mitchell Report [1], a two-year investigation into the use of illegal steroids in major league baseball, which recently revealed that over 5 percent of major league baseball players tested positive for performance-enhancing drugs in an anonymous 2003 survey.Comment: 5 pages, 5 figures, 2-column revtex4 format. Revision has change of title, a figure added, and minor changes in response to referee comment

An Ultra-Stable Referenced Interrogation System in the Deep Ultraviolet for a Mercury Optical Lattice Clock

We have developed an ultra-stable source in the deep ultraviolet, suitable to fulfill the interrogation requirements of a future fully-operational lattice clock based on neutral mercury. At the core of the system is a Fabry-P\'erot cavity which is highly impervious to temperature and vibrational perturbations. The mirror substrate is made of fused silica in order to exploit the comparatively low thermal noise limits associated with this material. By stabilizing the frequency of a 1062.6 nm Yb-doped fiber laser to the cavity, and including an additional link to LNE-SYRTE's fountain primary frequency standards via an optical frequency comb, we produce a signal which is both stable at the 1E-15 level in fractional terms and referenced to primary frequency standards. The signal is subsequently amplified and frequency-doubled twice to produce several milliwatts of interrogation signal at 265.6 nm in the deep ultraviolet.Comment: 7 pages, 6 figure

Some triviality results for quasi-Einstein manifolds and Einstein warped products

In this paper we prove a number of triviality results for Einstein warped products and quasi-Einstein manifolds using different techniques and under assumptions of various nature. In particular we obtain and exploit gradient estimates for solutions of weighted Poisson-type equations and adaptations to the weighted setting of some Liouville-type theorems.Comment: 15 pages, fixed minor mistakes in Section

Deterministic quantum teleportation between distant atomic objects

Quantum teleportation is a key ingredient of quantum networks and a building block for quantum computation. Teleportation between distant material objects using light as the quantum information carrier has been a particularly exciting goal. Here we demonstrate a new element of the quantum teleportation landscape, the deterministic continuous variable (cv) teleportation between distant material objects. The objects are macroscopic atomic ensembles at room temperature. Entanglement required for teleportation is distributed by light propagating from one ensemble to the other. Quantum states encoded in a collective spin state of one ensemble are teleported onto another ensemble using this entanglement and homodyne measurements on light. By implementing process tomography, we demonstrate that the experimental fidelity of the quantum teleportation is higher than that achievable by any classical process. Furthermore, we demonstrate the benefits of deterministic teleportation by teleporting a dynamically changing sequence of spin states from one distant object onto another