Local Decoders for the 2D and 4D Toric Code

We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a model of independent $X$ and $Z$ errors and faulty syndrome measurements with identical probability we report a threshold of $0.133\%$ for this Harrington decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings arXiv:1312.2546 . Incorporating a method for handling faulty syndromes we estimate a threshold of $1.59\%$ for the same noise model as in the 2D case. We compare the performance of this decoder with a decoder based on a 4D version of Toom's cellular automaton rule as well as the decoding method suggested by Dennis et al. arXiv:quant-ph/0110143 .Comment: 22 pages, 21 figures; fixed typos, updated Figures 6,7,8,

CMB B -mode non-Gaussianity:Optimal bispectrum estimator and Fisher forecasts

Upcoming cosmic microwave background (CMB) data can be used to explore harmonic 3-point functions that involve the B-mode component of the CMB polarization signal. We focus on bispectra describing the non-Gaussian correlation of the B-mode field and the CMB temperature anisotropies (T) and/or E-mode polarization, i.e. , , and . Such bispectra probe violations of the tensor consistency relation: the model-independent behavior of cosmological correlation functions that involve a large-wavelength tensor mode (gravitational wave). An observed violation of the tensor consistency relation would exclude a large number of inflation models. We describe a generalization of the Komatsu-Spergel-Wandelt (KSW) bispectrum estimator that allows statistical inference on this type of primordial non-Gaussianity with data of the CMB temperature and polarization anisotropies. The generalized estimator shares its statistical properties with the existing KSW estimator and retains the favorable numerical scaling with angular resolution. In this paper we derive the estimator and present a set of Fisher forecasts. We show how the forecasts scale with various experimental parameters such as lower and upper angular band-limit, relevant for e.g. the upcoming ground-based Simons Observatory experiment and proposed LiteBIRD satellite experiment. We comment on possible contaminants due to secondary cosmological and astrophysical sources.Comment: 40 pages, 7 figure

Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions

We continue our study of nonperturbative superpotentials of four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, broken to N=1 due to a classical superpotential. In a previous paper, hep-th/0304061, we discussed how the low-energy quantum superpotential can be obtained by substituting the Lax matrix of the underlying integrable system directly into the classical superpotential. In this paper we prove algebraically that this recipe yields the correct factorization of the Seiberg-Witten curves, which is an important check of the conjecture. We will also give an independent proof using the algebraic-geometrical interpretation of the underlying integrable system.Comment: laTeX, 14 pages, uses AMSmat

Minimizing gravitational lensing contributions to the primordial bispectrum covariance

The next generation of ground-based cosmic microwave background (CMB) experiments aim to measure temperature and polarization fluctuations up to ℓmax≈5000 over half of the sky. Combined with Planck data on large scales, this will provide improved constraints on primordial non-Gaussianity. However, the impressive resolution of these experiments will come at a price. Besides signal confusion from galactic foregrounds, extragalactic foregrounds, and late-time gravitational effects, gravitational lensing will introduce large non-Gaussianity that can become the leading contribution to the bispectrum covariance through the connected four-point function. Here, we compute this effect analytically for the first time on the full sky for both temperature and polarization. We compare our analytical results with those obtained directly from map-based simulations of the CMB sky for several levels of instrumental noise. Of the standard shapes considered in the literature, the local shape is most affected, resulting in a 35% increase of the estimator standard deviation for an experiment such as the Simons Observatory (SO) and a 110% increase for a cosmic-variance limited experiment, including both temperature and polarization modes up to ℓmax=3800. Because of the nature of the lensing four-point function, the impact on other shapes is reduced while still non-negligible for the orthogonal shape. Two possible avenues to reduce the non-Gaussian contribution to the covariance are proposed: First by marginalizing over lensing contributions, such as the Integrated Sachs Wolfe (ISW)-lensing three-point function in temperature, and second by delensing the CMB. We show the latter method can remove almost all extra covariance, reducing the effect to below <5% for local bispectra. At the same time, delensing would remove signal biases from secondaries induced by lensing, such as ISW lensing. We aim to apply both techniques directly to the forthcoming SO data when searching for primordial non-Gaussianity

Adverse events and survival after closing- and opening-wedge high tibial osteotomy: a comparative study of 412 patients

Purpose: Varus medial knee osteoarthritis (OA) can be treated with a closing-wedge (CW) or opening-wedge (OW) high tibial osteotomy (HTO). Little is known about the adverse event (AE) rate of these techniques. The purpose of this study was to examine the AE rate and survival rate of a consecutive series of 412 patients undergoing CW- or OW-HTO. Methods: Medical records were retrospectively screened, and all patients who underwent HTO from 1993 to 2012 at the Erasmus University Medical Centre were assessed with a self-administered questionnaire. Patients filled in the intermittent and constant osteoarthritis pain score, knee injury and osteoarthritis outcome score, and a general questionnaire focusing on AE. Results: Medical records of 412 patients (354 CW- and 112 OW-HTOs) were screened. Of the 358 eligible patients, 291 (81 %) returned their questionnaire. A total of 80 AE (17 %) were found in 466 osteotomies. In the CW-group, 47 (13 %) serious adverse events (SAE) and 2 (0.6 %) AE were found. In the OW-group, 17 (15 %) SAE and 14 (13 %) AE were found. The most common AE was in 14 (4 %) patients of the CW-group sensory palsy of the common peroneal nerve. The most common AE in the OW-group was persistent pain at the iliac crest [11 (9.8 %) patients]. Hardware was removed in 48 % of the CW-osteotomies and 71 % of the OW-osteotomies (p < 0.05). The probability of survival was 75 % after 10 years in the CW-group versus 90 % in the OW-group (p < 0.05). In both groups, an equal number of patients were “in need for prosthesis” according to OARSI criteria. Conclusion: OW-HTO was associated with more AE than CW-HTO. OW-HTO resulted in better survival than CW-HTO. However, in both groups an equal number of patients were in need for prosthesis. Level of evidence: Retrospective comparative study, Level III