A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data

We present a new Monte Carlo Markov Chain algorithm for CMB analysis in the low signal-to-noise regime. This method builds on and complements the previously described CMB Gibbs sampler, and effectively solves the low signal-to-noise inefficiency problem of the direct Gibbs sampler. The new algorithm is a simple Metropolis-Hastings sampler with a general proposal rule for the power spectrum, C_l, followed by a particular deterministic rescaling operation of the sky signal. The acceptance probability for this joint move depends on the sky map only through the difference of chi-squared between the original and proposed sky sample, which is close to unity in the low signal-to-noise regime. The algorithm is completed by alternating this move with a standard Gibbs move. Together, these two proposals constitute a computationally efficient algorithm for mapping out the full joint CMB posterior, both in the high and low signal-to-noise regimes.Comment: Submitted to Ap

Constraints on mode couplings and modulation of the CMB with WMAP data

We investigate a possible asymmetry in the statistical properties of the cosmic microwave background temperature field and to do so we construct an estimator aiming at detecting a dipolar modulation. Such a modulation is found to induce correlations between multipoles with $\Delta\ell=1$. Applying this estimator, to the V and W bands of the WMAP data, we found a significant detection in the V band. We argue however that foregrounds and in particular point sources are the origin of this signal.Comment: 14 pages, 14 figure

Evidence of vorticity and shear at large angular scales in the WMAP data: a violation of cosmological isotropy?

Motivated by the large-scale asymmetry observed in the cosmic microwave background sky, we consider a specific class of anisotropic cosmological models -- Bianchi type VII_h -- and compare them to the WMAP first-year data on large angular scales. Remarkably, we find evidence of a correlation which is ruled out as a chance alignment at the 3sigma level. The best fit Bianchi model corresponds to x=0.55, Omega_0=0.5, a rotation axis in the direction (l,b)=(222degr,-62degr), shear (sigma/H)_0=2.4e-10 and a right--handed vorticity (omega/H)_0=6.1e-10. Correcting for this component greatly reduces the significance of the large-scale power asymmetry, resolves several anomalies detected on large angular scales (ie. the low quadrupole amplitude and quadrupole/octopole planarity and alignment), and can account for a non--Gaussian "cold spot" on the sky. Despite the apparent inconsistency with the best-fit parameters required in inflationary models to account for the acoustic peaks, we consider the results sufficiently provocative to merit further consideration.Comment: 4 pages, 3 figures; emulateapj.cls; ApJL accepted version plus fixed error in vorticity calculation (sqrt(2) off in Table 1, abstract, and conclusions); basic conclusions unchange

Real space tests of the statistical isotropy and Gaussianity of the WMAP CMB data

ABRIDGED: We introduce and analyze a method for testing statistical isotropy and Gaussianity and apply it to the WMAP CMB foreground reduced, temperature maps, and cross-channel difference maps. We divide the sky into regions of varying size and shape and measure the first four moments of the one-point distribution within these regions, and using their simulated spatial distributions we test the statistical isotropy and Gaussianity hypotheses. By randomly varying orientations of these regions, we sample the underlying CMB field in a new manner, that offers a richer exploration of the data content, and avoids possible biasing due to a single choice of sky division. The statistical significance is assessed via comparison with realistic Monte-Carlo simulations. We find the three-year WMAP maps to agree well with the isotropic, Gaussian random field simulations as probed by regions corresponding to the angular scales ranging from 6 deg to 30 deg at 68% confidence level. We report a strong, anomalous (99.8% CL) dipole ``excess'' in the V band of the three-year WMAP data and also in the V band of the WMAP five-year data (99.3% CL). We notice the large scale hemispherical power asymmetry, and find that it is not highly statistically significant in the WMAP three-year data (<~ 97%) at scales l <= 40. The significance is even smaller if multipoles up to l=1024 are considered (~90% CL). We give constraints on the amplitude of the previously-proposed CMB dipole modulation field parameter. We easily detect the residual foregrounds in cross-band difference maps at rms level <~ 7 \mu K (at scales >~ 6 deg) and limit the systematical uncertainties to <~ 1.7 \mu K (at scales >~ 30 deg).Comment: 20 pages, 20 figures; more tests added; updated to match the version to be published in JCA

Primordial statistical anisotropy generated at the end of inflation

We present a new mechanism for generating primordial statistical anisotropy of curvature perturbations. We introduce a vector field which has a non-minimal kinetic term and couples with a waterfall field in hybrid inflation model. In such a system, the vector field gives fluctuations of the end of inflation and hence induces a subcomponent of curvature perturbations. Since the vector has a preferred direction, the statistical anisotropy could appear in the fluctuations. We present the explicit formula for the statistical anisotropy in the primordial power spectrum and the bispectrum of curvature perturbations. Interestingly, there is the possibility that the statistical anisotropy does not appear in the power spectrum but does appear in the bispectrum. We also find that the statistical anisotropy provides the shape dependence to the bispectrum.Comment: 9 pages, This version supersedes the JCAP version. Minor revision

Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results

One-dimensional multi-component Fermi or Bose systems with strong zero-range interactions can be described in terms of local exchange coefficients and mapping the problem into a spin model is thus possible. For arbitrary external confining potentials the local exchanges are given by highly non-trivial geometric factors that depend solely on the geometry of the confinement through the single-particle eigenstates of the external potential. To obtain accurate effective Hamiltonians to describe such systems one needs to be able to compute these geometric factors with high precision which is difficult due to the computational complexity of the high-dimensional integrals involved. An approach using the local density approximation would therefore be a most welcome approximation due to its simplicity. Here we assess the accuracy of the local density approximation by going beyond the simple harmonic oscillator that has been the focus of previous studies and consider some double-wells of current experimental interest. We find that the local density approximation works quite well as long as the potentials resemble harmonic wells but break down for larger barriers. In order to explore the consequences of applying the local density approximation in a concrete setup we consider quantum state transfer in the effective spin models that one obtains. Here we find that even minute deviations in the local exchange coefficients between the exact and the local density approximation can induce large deviations in the fidelity of state transfer for four, five, and six particles.Comment: 12 pages, 7 figures, 1 table, final versio

Biogas production by co-ensiling catch crops and straw, effect of substrate blend and microbial communities

The combination of catch crop (CC) and barley straw(S) for biogas production was investigated in order to evaluate the ensiling process in batch assay and in continuous process. Based on two new agriculture strategies designed to produce energy and improve nutrient cycling in organic farming are being evaluated, one of them consisting on the harvest of straw and catch crop in different periods whereas the other strategy consists on harvesting them at the same time. Catch crops is promoted to reduce nutrient leaching during rainy season and straw that is not used for animal feeding or bedding is generally left in the field. Mixtures of CC and S provides several advantages: 1) Provides adequate TS for silage, 2) Absorbs the silage effluent, 3) Produces high LAB activity, and 4) Provides an optimal C/N for anaerobic digestion (AD). The effect of feeding compositions (straw or manurea ddition) on the microbial community structures were also investigated

Rigid motion revisited: rigid quasilocal frames

We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a "system" in general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is expansion-free (constant size) and shear-free (constant shape). This definition of a system is anticipated to yield simple, exact geometrical insights into the problem of motion in general relativity. It begins by answering the questions what is in motion (a rigid two-dimensional system boundary), and what motions of this rigid boundary are possible. Nearly a century ago Herglotz and Noether showed that a three-parameter family of timelike worldlines in Minkowski space satisfying Born's 1909 rigidity conditions has only three degrees of freedom instead of the six we are familiar with from Newtonian mechanics. We argue that in fact we can implement Born's notion of rigid motion in both flat spacetime (this paper) and arbitrary curved spacetimes containing sources (subsequent papers) - with precisely the expected three translational and three rotational degrees of freedom - provided the system is defined quasilocally as the two-dimensional set of points comprising the boundary of a finite spatial volume, rather than the three-dimensional set of points within the volume.Comment: 10 pages (two column), 24 pages (preprint), 1 figur

Matrix Factorizations, Minimal Models and Massey Products

We present a method to compute the full non-linear deformations of matrix factorizations for ADE minimal models. This method is based on the calculation of higher products in the cohomology, called Massey products. The algorithm yields a polynomial ring whose vanishing relations encode the obstructions of the deformations of the D-branes characterized by these matrix factorizations. This coincides with the critical locus of the effective superpotential which can be computed by integrating these relations. Our results for the effective superpotential are in agreement with those obtained from solving the A-infinity relations. We point out a relation to the superpotentials of Kazama-Suzuki models. We will illustrate our findings by various examples, putting emphasis on the E_6 minimal model.Comment: 32 pages, v2: typos corrected, v3: additional comments concerning the bulk-boundary crossing constraint, some small clarifications, typo

New evidence for lack of CMB power on large scales

A digitalized temperature map is recovered from the first light sky survey image published by the Planck team, from which an angular power spectrum is derived. The amplitudes of the low multipoles measured from the preliminary Planck power spectrum are significantly lower than that reported by the WMAP team. Possible systematical effects are far from enough to explain the observed low-l differences.Comment: 9 pages, 3 figure