Woven Graph Codes: Asymptotic Performances and Examples

Constructions of woven graph codes based on constituent block and convolutional codes are studied. It is shown that within the random ensemble of such codes based on $s$-partite, $s$-uniform hypergraphs, where $s$ depends only on the code rate, there exist codes satisfying the Varshamov-Gilbert (VG) and the Costello lower bound on the minimum distance and the free distance, respectively. A connection between regular bipartite graphs and tailbiting codes is shown. Some examples of woven graph codes are presented. Among them an example of a rate $R_{\rm wg}=1/3$ woven graph code with $d_{\rm free}=32$ based on Heawood's bipartite graph and containing $n=7$ constituent rate $R^{c}=2/3$ convolutional codes with overall constraint lengths $\nu^{c}=5$ is given. An encoding procedure for woven graph codes with complexity proportional to the number of constituent codes and their overall constraint length $\nu^{c}$ is presented.Comment: Submitted to IEEE Trans. Inform. Theor

The influence of galaxy surface brightness on the mass-metallicity relation

We study the effect of surface brightness on the mass-metallicity relation using nearby galaxies whose gas content and metallicity profiles are available. Previous studies using fiber spectra indicated that lower surface brightness galaxies have systematically lower metallicity for their stellar mass, but the results were uncertain because of aperture effect. With stellar masses and surface brightnesses measured at WISE W1 and W2 bands, we re-investigate the surface brightness dependence with spatially-resolved metallicity profiles and find the similar result. We further demonstrate that the systematical difference cannot be explained by the gas content of galaxies. For two galaxies with similar stellar and gas masses, the one with lower surface brightness tends to have lower metallicity. Using chemical evolution models, we investigate the inflow and outflow properties of galaxies of different masses and surface brightnesses. We find that, on average, high mass galaxies have lower inflow and outflow rates relative to star formation rate. On the other hand, lower surface brightness galaxies experience stronger inflow than higher surface brightness galaxies of similar mass. The surface brightness effect is more significant for low mass galaxies. We discuss implications on the different inflow properties between low and high surface brightness galaxies, including star formation efficiency, environment and mass assembly history

Momentum dependence of the electron-phonon coupling and self-energy effects in YBa_2Cu_3O_7 within the local density approximation

Using the local density approximation (LDA) and a realistic phonon spectrum we determine the momentum and frequency dependence of $\alpha^2F({\bf k},\omega)$ in YBa$_2$Cu$_3$O$_7$ for the bonding, antibonding, and chain band. The resulting self-energy $\Sigma$ is rather small near the Fermi surface. For instance, for the antibonding band the maximum of $Re \Sigma$ as a function of frequency is about 7 meV at the nodal point in the normal state and the ratio of bare and renormalized Fermi velocities 1.18. These values are a factor 3-5 too small compared to the experiment showing that only a small part of $\Sigma$ can be attributed to phonons. Furthermore, the frequency dependence of the renormalization factor $Z({\bf k},\omega)$ is smooth and has no anomalies at the observed kink frequencies which means that phonons cannot produce well-pronounced kinks in stoichiometric YBa$_2$Cu$_3$O$_7$, at least, within the LDA.Comment: Figure 1 slightly revised, text shortened, accepted as a PR

Composite biasing in Monte Carlo radiative transfer

Biasing or importance sampling is a powerful technique in Monte Carlo radiative transfer, and can be applied in different forms to increase the accuracy and efficiency of simulations. One of the drawbacks of the use of biasing is the potential introduction of large weight factors. We discuss a general strategy, composite biasing, to suppress the appearance of large weight factors. We use this composite biasing approach for two different problems faced by current state-of-the-art Monte Carlo radiative transfer codes: the generation of photon packages from multiple components, and the penetration of radiation through high optical depth barriers. In both cases, the implementation of the relevant algorithms is trivial and does not interfere with any other optimisation techniques. Through simple test models, we demonstrate the general applicability, accuracy and efficiency of the composite biasing approach. In particular, for the penetration of high optical depths, the gain in efficiency is spectacular for the specific problems that we consider: in simulations with composite path length stretching, high accuracy results are obtained even for simulations with modest numbers of photon packages, while simulations without biasing cannot reach convergence, even with a huge number of photon packages.Comment: 12 pages, accepted for publication in A&

The importance of early arthroscopy in athletes with painful cartilage lesions of the ankle: a prospective study of 61 consecutive cases

BACKGROUND Ankle sprains are common in sports and can sometimes result in a persistent pain condition. PURPOSE Primarily to evaluate clinical symptoms, signs, diagnostics and outcomes of surgery for symptomatic chondral injuries of the talo crural joint in athletes. Secondly, in applicable cases, to evaluate the accuracy of MRI in detecting these injuries. Type of study: Prospective consecutive series. METHODS Over around 4 years we studied 61 consecutive athletes with symptomatic chondral lesions to the talocrural joint causing persistent exertion ankle pain. RESULTS 43% were professional full time athletes and 67% were semi-professional, elite or amateur athletes, main sports being soccer (49%) and rugby (14%). The main subjective complaint was exertion ankle pain (93%). Effusion (75%) and joint line tenderness on palpation (92%) were the most common clinical findings. The duration from injury to arthroscopy for 58/61 cases was 7 months (5.7–7.9). 3/61 cases were referred within 3 weeks from injury. There were in total 75 cartilage lesions. Of these, 52 were located on the Talus dome, 17 on the medial malleolus and 6 on the Tibia plafond. Of the Talus dome injuries 18 were anteromedial, 14 anterolateral, 9 posteromedial, 3 posterolateral and 8 affecting mid talus. 50% were grade 4 lesions, 13.3% grade 3, 16.7% grade 2 and 20% grade 1. MRI had been performed pre operatively in 26/61 (39%) and 59% of these had been interpreted as normal. Detection rate of cartilage lesions was only 19%, but subchondral oedema was present in 55%. At clinical follow up average 24 months after surgery (10–48 months), 73% were playing at pre-injury level. The average return to that level of sports after surgery was 16 weeks (3–32 weeks). However 43% still suffered minor symptoms. CONCLUSION Arthroscopy should be considered early when an athlete presents with exertion ankle pain, effusion and joint line tenderness on palpation after a previous sprain. Conventional MRI is not reliable for detecting isolated cartilage lesions, but the presence of subchondral oedema should raise such suspicion