Detection of B-mode polarization at degree angular scales by BICEP2

We report results from the BICEP2 experiment, a cosmic microwave background (CMB) polarimeter specifically designed to search for the signal of inflationary gravitational waves in the B-mode power spectrum around ℓ∼80. The telescope comprised a 26 cm aperture all-cold refracting optical system equipped with a focal plane of 512 antenna coupled transition edge sensor 150 GHz bolometers each with temperature sensitivity of ≈300  μKCMB√s . BICEP2 observed from the South Pole for three seasons from 2010 to 2012. A low-foreground region of sky with an effective area of 380 square deg was observed to a depth of 87 nK deg in Stokes Q and U. In this paper we describe the observations, data reduction, maps, simulations, and results. We find an excess of B-mode power over the base lensed-ΛCDM expectation in the range 305σ. Through jackknife tests and simulations based on detailed calibration measurements we show that systematic contamination is much smaller than the observed excess. Cross correlating against WMAP 23 GHz maps we find that Galactic synchrotron makes a negligible contribution to the observed signal. We also examine a number of available models of polarized dust emission and find that at their default parameter values they predict power ∼(5–10)× smaller than the observed excess signal (with no significant cross-correlation with our maps). However, these models are not sufficiently constrained by external public data to exclude the possibility of dust emission bright enough to explain the entire excess signal. Cross correlating BICEP2 against 100 GHz maps from the BICEP1 experiment, the excess signal is confirmed with 3σ significance and its spectral index is found to be consistent with that of the CMB, disfavoring dust at 1.7σ. The observed B-mode power spectrum is well fit by a lensed-ΛCDM+tensor theoretical model with tensor-to-scalar ratio r=0.20 +0.07 −0.05, with r=0 disfavored at 7.0σ. Accounting for the contribution of foreground, dust will shift this value downward by an amount which will be better constrained with upcoming data sets

Exploiting Target Enlargement and Dynamic Abstraction within Mixed BDD and SAT Invariant Checking

In this paper, we propose a methodology to make Binary Decision Diagrams (BDDs) and Boolean Satisfiability (SAT) Solvers cooperate. The underlying idea is simple: We start a verification task with BDDs, we go on with them as long as the problem remains of manageable size, then we switch to SAT, without losing the work done on the BDD domain. We propose target enlargement as an attempt to bring some of the advantages of state set manipulation from BDDs to SAT-based verification. We first, "enlarge" initial and target state sets of a given verification problem by affordable BDD manipulations. This step is carried on with a few breadth-first steps of traversal, or with what we call high-density dynamic abstraction, i.e., a new technique to collect under-approximate reachable state sets. Then, we perform SAT-based verification with the newly computed "enlarged" sets. We experimentally test our methodology within an industrial environment, the Intel BOolean VErifier BOVE. Preliminary results on standard benchmarks (the ISCAS'89, ISCAS'89--addendum, and VIS suites), and industrial ones (the IBM Formal Verification Benchmark Library) are provided. Results show interesting improvements over state-of-the-art techniques: We could decrease CPU time up to a 5x factor, when performing verification with the same depth, or we could increase the verification depth up to 30%, when performing verification within the same time limi