Towards Rapid Parameter Estimation on Gravitational Waves from Compact Binaries using Interpolated Waveforms

Accurate parameter estimation of gravitational waves from coalescing compact binary sources is a key requirement for gravitational-wave astronomy. Evaluating the posterior probability density function of the binary's parameters (component masses, sky location, distance, etc.) requires computing millions of waveforms. The computational expense of parameter estimation is dominated by waveform generation and scales linearly with the waveform computational cost. Previous work showed that gravitational waveforms from non-spinning compact binary sources are amenable to a truncated singular value decomposition, which allows them to be reconstructed via interpolation at fixed computational cost. However, the accuracy requirement for parameter estimation is typically higher than for searches, so it is crucial to ascertain that interpolation does not lead to significant errors. Here we provide a proof of principle to show that interpolated waveforms can be used to recover posterior probability density functions with negligible loss in accuracy with respect to non-interpolated waveforms. This technique has the potential to significantly increase the efficiency of parameter estimation.Comment: 7 pages, 2 figure

Rapidly evaluating the compact-binary likelihood function via interpolation

Bayesian parameter estimation on gravitational waves from compact-binary coalescences (CBCs) typically requires millions of template waveform computations at different values of the parameters describing the binary. Sampling techniques such as Markov chain Monte Carlo and nested sampling evaluate likelihoods and, hence, compute template waveforms, serially; thus, the total computational time of the analysis scales linearly with that of template generation. Here we address the issue of rapidly computing the likelihood function of CBC sources with nonspinning components. We show how to efficiently compute the continuous likelihood function on the three-dimensional subspace of parameters on which it has a nontrivial dependence—the chirp mass, symmetric mass ratio and coalescence time—via interpolation. Subsequently, sampling this interpolated likelihood function is a significantly cheaper computational process than directly evaluating the likelihood; we report improvements in computational time of two to three orders of magnitude while keeping likelihoods accurate to ≲0.025%. Generating the interpolant of the likelihood function over a significant portion of the CBC mass space is computationally expensive but highly parallelizable, so the wall time can be very small relative to the time of a full parameter-estimation analysis

Spin Susceptibility and Gap Structure of the Fractional-Statistics Gas

This paper establishes and tests procedures which can determine the electron energy gap of the high-temperature superconductors using the $t\!-\!J$ model with spinon and holon quasiparticles obeying fractional statistics. A simpler problem with similar physics, the spin susceptibility spectrum of the spin 1/2 fractional-statistics gas, is studied. Interactions with the density oscillations of the system substantially decrease the spin gap to a value of $(0.2 \pm 0.2)$ $\hbar \omega_c$, much less than the mean-field value of $\hbar\omega_c$. The lower few Landau levels remain visible, though broadened and shifted, in the spin susceptibility. As a check of the methods, the single-particle Green's function of the non-interacting Bose gas viewed in the fermionic representation, as computed by the same approximation scheme, agrees well with the exact results. The same mechanism would reduce the gap of the $t\!-\!J$ model without eliminating it.Comment: 35 pages, written in REVTeX, 16 figures available upon request from [email protected]

Spin Transition in Strongly Correlated Bilayer Two Dimensional Electron Systems

Using a combination of heat pulse and nuclear magnetic resonance techniques we demonstrate that the phase boundary separating the interlayer phase coherent quantum Hall effect at $\nu_T = 1$ in bilayer electron gases from the weakly coupled compressible phase depends upon the spin polarization of the nuclei in the host semiconductor crystal. Our results strongly suggest that, contrary to the usual assumption, the transition is attended by a change in the electronic spin polarization.Comment: 4 pages, 3 postscript figur

Charge Imbalance and Bilayer 2D Electron Systems at νT=1\nu_T = 1

We use interlayer tunneling to study bilayer 2D electron systems at $\nu_T = 1$ over a wide range of charge density imbalance, $\Delta \nu =\nu_1-\nu_2$, between the two layers. We find that the strongly enhanced tunneling associated with the coherent excitonic $\nu_T = 1$ phase at small layer separation can survive at least up to an imbalance of $\Delta \nu$ = 0.5, i.e $(\nu_1, \nu_2)$ = (3/4, 1/4). Phase transitions between the excitonic $\nu_T = 1$ state and bilayer states which lack significant interlayer correlations can be induced in three different ways: by increasing the effective interlayer spacing $d/\ell$, the temperature $T$, or the charge imbalance, $\Delta \nu$. We observe that close to the phase boundary the coherent $\nu_T = 1$ phase can be absent at $\Delta \nu$ = 0, present at intermediate $\Delta \nu$, but then absent again at large $\Delta \nu$, thus indicating an intricate phase competition between it and incoherent quasi-independent layer states. At zero imbalance, the critical $d/\ell$ shifts linearly with temperature, while at $\Delta \nu$ = 1/3 the critical $d/\ell$ is only weakly dependent on $T$. At $\Delta \nu$ = 1/3 we report the first observation of a direct phase transition between the coherent excitonic $\nu_T = 1$ bilayer integer quantum Hall phase and the pair of single layer fractional quantized Hall states at $\nu_1$ = 2/3 and $\nu_2=1/3$.Comment: 13 pages, 8 postscript figures. Final published versio

Seismic Retrofitting Using Micropile Systems Centrifugal Model Studies

A series of centrifuge tests were conducted on micropile group and network systems in order to investigate the response to earthquake loading and soil-micropile interaction behavior. Model tests on group and network systems embedded in loose to medium dry sand are described. Micropile bending moment, deflection, and acceleration were measured during testing. Dynamic p-y curves were derived from the measurements for low and high levels of shaking and were compared with the backbone p-y curves for sand recommended by API and other published data. Group and network effects were investigated for different configurations and at different levels of loading. For the selected frequency of excitation, the results indicate a positive group effect increasing with the number of piles and the batter angle. This paper describes the experimental procedures used to carry out the centrifugal model tests and summarizes the main preliminary results

Pattern of Reaction Diffusion Front in Laminar Flows

Autocatalytic reaction between reacted and unreacted species may propagate as solitary waves, namely at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. The effect of advective flow on the autocatalytic reaction between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is analyzed experimentally and numerically using lattice BGK simulations. We do observe the existence of solitary waves with concentration profiles exhibiting a cusp and we delineate the eikonal and mixing regimes recently predicted.Comment: 4 pages, 3 figures. This paper report on experiments and simulations in different geometries which test the theory of Boyd Edwards on flow advection of chemical reaction front which just appears in PRL (PRL Vol 89,104501, sept2002

Poor oral health including active caries in 187 UK professional male football players: clinical dental examination performed by dentists

The few studies that have assessed oral health in professional/elite football suggest poor oral health with minimal data on impact on performance. The aim of this research was to determine oral health in a representative sample of professional footballers in the UK and investigate possible determinants of oral health and self-reported impact on well-being, training and performance

Mathematical and computer modeling of electro-optic systems using a generic modeling approach

The conventional approach to modelling electro-optic sensor systems is to develop separate models for individual systems or classes of system, depending on the detector technology employed in the sensor and the application. However, this ignores commonality in design and in components of these systems. A generic approach is presented for modelling a variety of sensor systems operating in the infrared waveband that also allows systems to be modelled with different levels of detail and at different stages of the product lifecycle. The provision of different model types (parametric and image-flow descriptions) within the generic framework can allow valuable insights to be gained