Functional Sequential Treatment Allocation

Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present paper we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies

Removing non-stationary, non-harmonic external interference from gravitational wave interferometer data

We describe a procedure to identify and remove a class of non-stationary and non-harmonic interference lines from gravitational wave interferometer data. These lines appear to be associated with the external electricity main supply, but their amplitudes are non-stationary and they do not appear at harmonics of the fundamental supply frequency. We find an empirical model able to represent coherently all the non-harmonic lines we have found in the power spectrum, in terms of an assumed reference signal of the primary supply input signal. If this signal is not available then it can be reconstructed from the same data by making use of the coherent line removal algorithm that we have described elsewhere. All these lines are broadened by frequency changes of the supply signal, and they corrupt significant frequency ranges of the power spectrum. The physical process that generates this interference is so far unknown, but it is highly non-linear and non-stationary. Using our model, we cancel the interference in the time domain by an adaptive procedure that should work regardless of the source of the primary interference. We have applied the method to laser interferometer data from the Glasgow prototype detector, where all the features we describe in this paper were observed. The algorithm has been tuned in such a way that the entire series of wide lines corresponding to the electrical interference are removed, leaving the spectrum clean enough to detect signals previously masked by them. Single-line signals buried in the interference can be recovered with at least 75 % of their original signal amplitude.Comment: 14 pages, 5 figures, Revtex, psfi

Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?

The most promising source of gravitational waves for the planned detectors LIGO and VIRGO are merging compact binaries, i.e., neutron star/neutron star (NS/NS), neutron star/black hole (NS/BH), and black hole/black-hole (BH/BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the gravitational wave signals by the three detector LIGO/VIRGO network using ``advanced detectors'' (those present a few years after initial operation). The combination ${\cal M} \equiv (M_1 M_2)^{3/5}(M_1 +M_2)^{-1/5}$ of the masses of the two bodies is measurable with an accuracy $\approx 0.1\%-1\%$. The reduced mass is measurable to $\sim 10\%-15\%$ for NS/NS and NS/BH binaries, and $\sim 50\%$ for BH/BH binaries (assuming $10M_\odot$ BH's). Measurements of the masses and spins are strongly correlated; there is a combination of $\mu$ and the spin angular momenta that is measured to within $\sim 1\%$. We also estimate that distance measurement accuracies will be $\le 15\%$ for $\sim 8\%$ of the detected signals, and $\le 30\%$ for $\sim 60\%$ of the signals, for the LIGO/VIRGO 3-detector network.Comment: 103 pages, 20 figures, submitted to Phys Rev D, uses revtex macros, Caltech preprint GRP-36

Lagrangian perfect fluids and black hole mechanics

The first law of black hole mechanics (in the form derived by Wald), is expressed in terms of integrals over surfaces, at the horizon and spatial infinity, of a stationary, axisymmetric black hole, in a diffeomorphism invariant Lagrangian theory of gravity. The original statement of the first law given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system contained, in addition, volume integrals of the fluid fields, over a spacelike slice stretching between these two surfaces. When applied to the Einstein-perfect fluid system, however, Wald's methods yield restricted results. The reason is that the fluid fields in the Lagrangian of a gravitating perfect fluid are typically nonstationary. We therefore first derive a first law-like relation for an arbitrary Lagrangian metric theory of gravity coupled to arbitrary Lagrangian matter fields, requiring only that the metric field be stationary. This relation includes a volume integral of matter fields over a spacelike slice between the black hole horizon and spatial infinity, and reduces to the first law originally derived by Bardeen, Carter and Hawking when the theory is general relativity coupled to a perfect fluid. We also consider a specific Lagrangian formulation for an isentropic perfect fluid given by Carter, and directly apply Wald's analysis. The resulting first law contains only surface integrals at the black hole horizon and spatial infinity, but this relation is much more restrictive in its allowed fluid configurations and perturbations than that given by Bardeen, Carter and Hawking. In the Appendix, we use the symplectic structure of the Einstein-perfect fluid system to derive a conserved current for perturbations of this system: this current reduces to one derived ab initio for this system by Chandrasekhar and Ferrari.Comment: 26 pages LaTeX-2

Data analysis of gravitational-wave signals from spinning neutron stars. II. Accuracy of estimation of parameters

We examine the accuracy of estimation of parameters of the gravitational-wave signals from spinning neutron stars that can be achieved from observations by Earth-based laser interferometers. We consider a model of the signal consisting of two narrowband components and including both phase and amplitude modulation. We calculate approximate values of the rms errors of the parameter estimators using the Fisher information matrix. We carry out extensive Monte Carlo simulations and obtain cumulative distribution functions of rms errors of astrophysically interesting parameters: amplitude of the signal, wobble angle, position of the source in the sky, frequency, and spindown coefficients. We consider both all-sky searches and directed searches. We also examine the possibility of determination of neutron star proper motion. We perform simulations for all laser-interferometric detectors that are currently under construction and for several possible lengths of the observation time and sizes of the parameter space. We find that observations of continuous gravitational-wave signals from neutron stars by laser-interferometric detectors will provide a very accurate information about their astrophysical properties. We derive several simplified models of the signal that can be used in the theoretical investigations of the data analysis schemes independently of the physical mechanisms generating the gravitational-wave signal.Comment: LaTeX, 34 pages, 15 figures, submitted to Phys. Rev.

A Geometrical Characterization of the Twin Paradox and its Variants

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is also studied.Comment: 22 pages, 3 figure

Quasi-Asimptotically Flat Spacetimes and Their ADM Mass

We define spacetimes that are asymptotically flat, except for a deficit solid angle $\alpha$, and present a definition of their ``ADM'' mass, which is finite for this class of spacetimes, and, in particular, coincides with the value of the parameter $M$ of the global monopole spacetime studied by Vilenkin and Barriola . Moreover, we show that the definition is coordinate independent, and explain why it can, in some cases, be negative.Comment: Late

Angular Resolution of the LISA Gravitational Wave Detector

We calculate the angular resolution of the planned LISA detector, a space-based laser interferometer for measuring low-frequency gravitational waves from galactic and extragalactic sources. LISA is not a pointed instrument; it is an all-sky monitor with a quadrupolar beam pattern. LISA will measure simultaneously both polarization components of incoming gravitational waves, so the data will consist of two time series. All physical properties of the source, including its position, must be extracted from these time series. LISA's angular resolution is therefore not a fixed quantity, but rather depends on the type of signal and on how much other information must be extracted. Information about the source position will be encoded in the measured signal in three ways: 1) through the relative amplitudes and phases of the two polarization components, 2) through the periodic Doppler shift imposed on the signal by the detector's motion around the Sun, and 3) through the further modulation of the signal caused by the detector's time-varying orientation. We derive the basic formulae required to calculate the LISA's angular resolution $\Delta \Omega_S$ for a given source. We then evaluate $\Delta \Omega_S$ for two sources of particular interest: monchromatic sources and mergers of supermassive black holes. For these two types of sources, we calculate (in the high signal-to-noise approximation) the full variance-covariance matrix, which gives the accuracy to which all source parameters can be measured. Since our results on LISA's angular resolution depend mainly on gross features of the detector geometry, orbit, and noise curve, we expect these results to be fairly insensitive to modest changes in detector design that may occur between now and launch. We also expect that our calculations could be easily modified to apply to a modified design.Comment: 15 pages, 5 figures, RevTex 3.0 fil

Optimal Strategies for Sinusoidal Signal Detection

We derive and study optimal and nearly-optimal strategies for the detection of sinusoidal signals hidden in additive (Gaussian and non-Gaussian) noise. Such strategies are an essential part of algorithms for the detection of the gravitational Continuous Wave (CW) signals produced by pulsars. Optimal strategies are derived for the case where the signal phase is not known and the product of the signal frequency and the observation time is non-integral.Comment: 18 pages, REVTEX4, 7 figures, 2 table

Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame

The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivation which is based upon the behavior of free radiation fields and the assumption that the field correlation functions contain but a single correlation time in thermal equilibrium. The work has connections with the thermal effects of acceleration found in relativistic quantum field theory.Comment: 23 page