On the joint analysis of CMB temperature and lensing-reconstruction power spectra

Gravitational lensing provides a significant source of cosmological information in modern CMB parameter analyses. It is measured in both the power spectrum and trispectrum of the temperature fluctuations. These observables are often treated as independent, although as they are both determined from the same map this is impossible. In this paper, we perform a rigorous analysis of the covariance between lensing power spectrum and trispectrum analyses. We find two dominant contributions coming from: (i) correlations between the disconnected noise bias in the trispectrum measurement and sample variance in the temperature power spectrum; and (ii) sample variance of the lenses themselves. The former is naturally removed when the dominant N0 Gaussian bias in the reconstructed deflection spectrum is dealt with via a partially data-dependent correction, as advocated elsewhere for other reasons. The remaining lens-cosmic-variance contribution is easily modeled but can safely be ignored for a Planck-like experiment, justifying treating the two observable spectra as independent. We also test simple likelihood approximations for the deflection power spectrum, finding that a Gaussian with a parameter-independent covariance performs well.Comment: 25+11 pages, 14 figure

Global consensus Monte Carlo

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

Lensed CMB power spectra from all-sky correlation functions

Weak lensing of the CMB changes the unlensed temperature anisotropy and polarization power spectra. Accounting for the lensing effect will be crucial to obtain accurate parameter constraints from sensitive CMB observations. Methods for computing the lensed power spectra using a low-order perturbative expansion are not good enough for percent-level accuracy. Non-perturbative flat-sky methods are more accurate, but curvature effects change the spectra at the 0.3-1% level. We describe a new, accurate and fast, full-sky correlation-function method for computing the lensing effect on CMB power spectra to better than 0.1% at l<2500 (within the approximation that the lensing potential is linear and Gaussian). We also discuss the effect of non-linear evolution of the gravitational potential on the lensed power spectra. Our fast numerical code is publicly available.Comment: 16 pages, 4 figures. Changes to match PRD version including new section on non-linear corrections. CAMB code available at http://camb.info

The 21cm angular-power spectrum from the dark ages

At redshifts z >~ 30 neutral hydrogen gas absorbs CMB radiation at the 21cm spin-flip frequency. In principle this is observable and a high-precision probe of cosmology. We calculate the linear-theory angular power spectrum of this signal and cross-correlation between redshifts on scales much larger than the line width. In addition to the well known redshift-distortion and density perturbation sources a full linear analysis gives additional contributions to the power spectrum. On small scales there is a percent-level linear effect due to perturbations in the 21cm optical depth, and perturbed recombination modifies the gas temperature perturbation evolution (and hence spin temperature and 21cm power spectrum). On large scales there are several post-Newtonian and velocity effects; although negligible on small scales, these additional terms can be significant at l <~ 100 and can be non-zero even when there is no background signal. We also discuss the linear effect of reionization re-scattering, which damps the entire spectrum and gives a very small polarization signal on large scales. On small scales we also model the significant non-linear effects of evolution and gravitational lensing. We include full results for numerical calculation and also various approximate analytic results for the power spectrum and evolution of small scale perturbations.Comment: 29 pages; significant extensions including: self-absorption terms (i.e. change to background radiation due to 21cm absorption); ionization fraction perturbations; estimates of non-linear effects; approximate analytic results; results for sharp redshift window functions. Code available at http://camb.info/sources

Geometry of weak lensing of CMB polarization

Hu [Phys. Rev. D62 (2000) 043007] has presented a harmonic-space method for calculating the effects of weak gravitational lensing on the cosmic microwave background (CMB) over the full sky. Computing the lensed power spectra to first order in the deflection power requires one to formulate the lensing displacement beyond the tangent-space approximation. We point out that for CMB polarization this displacement must undergo geometric corrections on the spherical sky to maintain statistical isotropy of the lensed fields. Although not discussed by Hu, these geometric effects are implicit in his analysis. However, there they are hidden by an overly-compact notation that is both unconventional and rather confusing. Here we aim to ameliorate this deficiency by providing a rigorous derivation of the lensed spherical power spectra.Comment: 3 page

CMB power spectrum parameter degeneracies in the era of precision cosmology

Cosmological parameter constraints from the CMB power spectra alone suffer several well-known degeneracies. These degeneracies can be broken by numerical artefacts and also a variety of physical effects that become quantitatively important with high-accuracy data e.g. from the Planck satellite. We study degeneracies in models with flat and non-flat spatial sections, non-trivial dark energy and massive neutrinos, and investigate the importance of various physical degeneracy-breaking effects. We test the CAMB power spectrum code for numerical accuracy, and demonstrate that the numerical calculations are accurate enough for degeneracies to be broken mainly by true physical effects (the integrated Sachs-Wolfe effect, CMB lensing and geometrical and other effects through recombination) rather than numerical artefacts. We quantify the impact of CMB lensing on the power spectra, which inevitably provides degeneracy-breaking information even without using information in the non-Gaussianity. Finally we check the numerical accuracy of sample-based parameter constraints using CAMB and CosmoMC. In an appendix we document recent changes to CAMB's numerical treatment of massive neutrino perturbations, which are tested along with other recent improvements by our degeneracy exploration results.Comment: 27 pages, 28 figures. Latest CAMB version available from http://camb.info/. Reduced number of figures, plot legend corrected and minor edits to match published versio

Bioresorbable Polylactide Interbody Implants in an Ovine Anterior Cervical Discectomy and Fusion Model: Three-Year Results

Study Design. In vivo study of anterior discectomy and fusion using a bioresorbable 70:30 poly(l-lactide-co-d,l-lactide) interbody implant in an ovine model. Objective. To evaluate the efficacy of the polylactide implant to function as an interbody fusion device, and to assess the tissue reaction to the material during the resorption process. Summary of Background Data. The use of polylactide as a cervical interbody implant has several potential advantages when compared with traditional materials. Having an elastic modulus very similar to bone minimizes the potential for stress shielding, and as the material resorbs additional loading is transferred to the developing fusion mass. Although preclinical and clinical studies have demonstrated the suitability of polylactide implants for lumbar interbody fusion, detailed information on cervical anterior cervical discectomy and fusion (ACDF) with polylactide devices is desirable. Methods. Single level ACDF was performed in 8 skeletally mature ewes. Bioresorbable 70:30 poly (l-lactide-co-d,l-lactide) interbody implants packed with autograft were used with single-level metallic plates. Radiographs were made every 3 months up to 1 year, and yearly thereafter. The animals were killed at 6 months (3 animals), 12 months (3 animals), and 36 months (2 animals). In addition to the serial plain radiographs, the specimens were evaluated by nondestructive biomechanical testing and undecalcified histologic analysis. Results. The bioresorbable polylactide implants were effective in achieving interbody fusion. The 6-month animals appeared fused radiographically and biomechanically, whereas histologic sections demonstrated partial fusion (in 3 of 3 animals). Radiographic fusion was confirmed histologically and biomechanically at 12 months (3 of 3 animals) and 36 months (2 of 2 animals). A mild chronic inflammatory response to the resorbing polylactide implant was observed at both 6 months and 12 months. At 36 months, the operative levels were solidly fused and the implants were completely resorbed. No adverse tissue response was observed in any animal at any time period. Conclusion. Interbody fusion was achieved using bioresorbable polylactide implants, with no evidence of implant collapse, extrusion, or adverse tissue response to the material. The use of polylactide as a cervical interbody device appears both safe and effective based on these ACDF animal model results

Global consensus Monte Carlo

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

CPU-less robotics: distributed control of biomorphs

Traditional robotics revolves around the microprocessor. All well-known demonstrations of sensory guided motor control, such as jugglers and mobile robots, require at least one CPU. Recently, the availability of fast CPUs have made real-time sensory-motor control possible, however, problems with high power consumption and lack of autonomy still remain. In fact, the best examples of real-time robotics are usually tethered or require large batteries. We present a new paradigm for robotics control that uses no explicit CPU. We use computational sensors that are directly interfaced with adaptive actuation units. The units perform motor control and have learning capabilities. This architecture distributes computation over the entire body of the robot, in every sensor and actuator. Clearly, this is similar to biological sensory- motor systems. Some researchers have tried to model the latter in software, again using CPUs. We demonstrate this idea in with an adaptive locomotion controller chip. The locomotory controller for walking, running, swimming and flying animals is based on a Central Pattern Generator (CPG). CPGs are modeled as systems of coupled non-linear oscillators that control muscles responsible for movement. Here we describe an adaptive CPG model, implemented in a custom VLSI chip, which is used to control an under-actuated and asymmetric robotic leg