Quantum statistical properties of the radiation field in a cavity with a movable mirror

A quantum system composed of a cavity radiation field interacting with a movable mirror is considered and quantum statistical properties of the field are studied. Such a system can serve in principle as an idealized meter for detection of a weak classical force coupled to the mirror which is modelled by a quantum harmonic oscillator. It is shown that the standard quantum limit on the measurement of the mirror position arises naturally from the properties of the system during its dynamical evolution. However, the force detection sensitivity of the system falls short of the corresponding standard quantum limit. We also study the effect of the nonlinear interaction between the moving mirror and the radiation pressure on the quadrature fluctuations of the initially coherent cavity field.Comment: REVTeX, 9 pages, 5 figures. More info on http://www.ligo.caltech.edu/~cbrif/science.htm

Rank-based camera spectral sensitivity estimation

In order to accurately predict a digital camera response to spectral stimuli, the spectral sensitivity functions of its sensor need to be known. These functions can be determined by direct measurement in the lab—a difficult and lengthy procedure—or through simple statistical inference. Statistical inference methods are based on the observation that when a camera responds linearly to spectral stimuli, the device spectral sensitivities are linearly related to the camera rgb response values, and so can be found through regression. However, for rendered images, such as the JPEG images taken by a mobile phone, this assumption of linearity is violated. Even small departures from linearity can negatively impact the accuracy of the recovered spectral sensitivities, when a regression method is used. In our work, we develop a novel camera spectral sensitivity estimation technique that can recover the linear device spectral sensitivities from linear images and the effective linear sensitivities from rendered images. According to our method, the rank order of a pair of responses imposes a constraint on the shape of the underlying spectral sensitivity curve (of the sensor). Technically, each rank-pair splits the space where the underlying sensor might lie in two parts (a feasible region and an infeasible region). By intersecting the feasible regions from all the ranked-pairs, we can find a feasible region of sensor space. Experiments demonstrate that using rank orders delivers equal estimation to the prior art. However, the Rank-based method delivers a step-change in estimation performance when the data is not linear and, for the first time, allows for the estimation of the effective sensitivities of devices that may not even have “raw mode.” Experiments validate our method

Cosmic Microwave Background Anisotropy Observing Strategy Assessment

I develop a method for assessing the ability of an instrument, coupled with an observing strategy, to measure the angular power spectrum of the cosmic microwave background (CMB). It allows for efficient calculation of expected parameter uncertainties. Related to this method is a means of graphically presenting, via the ``eigenmode window function'', the sensitivity of an observation to different regions of the spectrum, which is a generalization of the traditional practice of presenting the trace of the window function. I apply these techniques to a balloon-borne bolometric instrument to be flown this summer (MSAM2). I find that a smoothly scanning secondary is better than a chopping one and that, in this case, a very simple analytic formula provides a good (40\% or better) approximation to expected power spectrum uncertainties.Comment: Substantial revisions, LaTeX 15 pages including 3 figure

Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters

The paper develops Newton's method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It computes the nearest value of a parameter vector with a matrix having a multiple eigenvalue of given multiplicity. The method also works in the whole matrix space (in the absence of parameters). The approach is based on the versal deformation theory for matrices. Numerical examples are given. The implementation of the method in MATLAB code is available.Comment: 19 pages, 3 figure

Manifold interpolation and model reduction

One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric structure and thus form so-called matrix manifolds. This work will be featured as a chapter in the upcoming Handbook on Model Order Reduction (P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W.H.A. Schilders, L.M. Silveira, eds, to appear on DE GRUYTER) and reviews the numerical treatment of the most important matrix manifolds that arise in the context of model reduction. Moreover, the principal approaches to data interpolation and Taylor-like extrapolation on matrix manifolds are outlined and complemented by algorithms in pseudo-code.Comment: 37 pages, 4 figures, featured chapter of upcoming "Handbook on Model Order Reduction

M\"obius Invariants of Shapes and Images

Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the M\"obius group $\mathrm{PSL}(2,\mathbb{C})$, which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known M\"obius invariants, and then develop an algorithm by which shapes can be recognised that is M\"obius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a M\"obius-invariant signature of grey-scale images

On recent SFR calibrations and the constant SFR approximation

Star Formation Rate (SFR) inferences are based in the so-called constant SFR approximation, where synthesis models are require to provide a calibration; we aims to study the key points of such approximation to produce accurate SFR inferences. We use the intrinsic algebra used in synthesis models, and we explore how SFR can be inferred from the integrated light without any assumption about the underling Star Formation history (SFH). We show that the constant SFR approximation is actually a simplified expression of more deeper characteristics of synthesis models: It is a characterization of the evolution of single stellar populations (SSPs), acting the SSPs as sensitivity curve over different measures of the SFH can be obtained. As results, we find that (1) the best age to calibrate SFR indices is the age of the observed system (i.e. about 13Gyr for z=0 systems); (2) constant SFR and steady-state luminosities are not requirements to calibrate the SFR; (3) it is not possible to define a SFR single time scale over which the recent SFH is averaged, and we suggest to use typical SFR indices (ionizing flux, UV fluxes) together with no typical ones (optical/IR fluxes) to correct the SFR from the contribution of the old component of the SFH, we show how to use galaxy colors to quote age ranges where the recent component of the SFH is stronger/softer than the older component. Particular values of SFR calibrations are (almost) not affect by this work, but the meaning of what is obtained by SFR inferences does. In our framework, results as the correlation of SFR time scales with galaxy colors, or the sensitivity of different SFR indices to sort and long scale variations in the SFH, fit naturally. In addition, the present framework provides a theoretical guide-line to optimize the available information from data/numerical experiments to improve the accuracy of SFR inferences.Comment: A&A accepted, 13 pages, 4 Figure