Error-correcting code on a cactus: a solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.Comment: 7 pages, 3 figures, with minor correction

Statistical Physics of Irregular Low-Density Parity-Check Codes

Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulations. We compare the performance of irregular with that of regular codes and discuss the factors that contribute to the improvement in performance.Comment: 20 pages, 9 figures, revised version submitted to JP

Irradiation of the secondary star in X-ray Nova Scorpii 1994 (=GRO J1655--40)

We have obtained intermediate resolution optical spectra of the black-hole candidate Nova Sco 1994 in June 1996, when the source was in an X-ray/optical active state (R~15.05). We measure the radial velocity curve of the secondary star and obtain a semi-amplitude of 279+/-10 km/s; a value which is 30 per cent larger than the value obtained when the source is in quiescence. Our large value for K_2 is consistent with 60 +9,-7 per cent of the secondary star's surface being heated; compared to 35 per cent, which is what one would expect if only the inner face of the secondary star were irradiated. Effects such as irradiation-induced flows on the secondary star may be important in explaining the observed large value for K_2.Comment: 5 pages, 2 figures, accepted by MNRA

Spotting the diffusion of New Psychoactive Substances over the Internet

Online availability and diffusion of New Psychoactive Substances (NPS) represent an emerging threat to healthcare systems. In this work, we analyse drugs forums, online shops, and Twitter. By mining the data from these sources, it is possible to understand the dynamics of drugs diffusion and their endorsement, as well as timely detecting new substances. We propose a set of visual analytics tools to support analysts in tackling NPS spreading and provide a better insight about drugs market and analysis

The Far-Ultraviolet Spectrum and Short Timescale Variability of AM Herculis from Observations with the Hopkins Ultraviolet Telescope

Using the Hopkins Ultraviolet Telescope (HUT), we have obtained 850-1850 angstrom spectra of the magnetic cataclysmic variable star AM Her in the high state. These observations provide high time resolution spectra of AM Her in the FUV and sample much of the orbital period of the system. The spectra are not well-modelled in terms of simple white dwarf (WD) atmospheres, especially at wavelengths shortward of Lyman alpha. The continuum flux changes by a factor of 2 near the Lyman limit as a function of orbital phase; the peak fluxes are observed near magnetic phase 0.6 when the accreting pole of the WD is most clearly visible. The spectrum of the hotspot can be modelled in terms of a 100 000 K WD atmosphere covering 2% of the WD surface. The high time resolution of the HUT data allows an analysis of the short term variability and shows the UV luminosity to change by as much as 50% on timescales as short as 10 s. This rapid variability is shown to be inconsistent with the clumpy accretion model proposed to account for the soft X-ray excess in polars. We see an increase in narrow line emission during these flares when the heated face of the secondary is in view. The He II narrow line flux is partially eclipsed at secondary conjunction, implying that the inclination of the system is greater than 45 degrees. We also present results from models of the heated face of the secondary. These models show that reprocessing on the face of the secondary star of X-ray/EUV emission from the accretion region near the WD can account for the intensities and kinematics of most of the narrow line components observed.Comment: 19 pp., 12 fig., 3 tbl. To appear in The Astrophysical Journal. Also available at http://greeley.pha.jhu.edu/papers/amherpp.ps.g

Integrable Generalisations of the 2-dimensional Born Infeld Equation

The Born-Infeld equation in two dimensions is generalised to higher dimensions whilst retaining Lorentz Invariance and complete integrability. This generalisation retains homogeneity in second derivatives of the field.Comment: 11 pages, Latex, DTP/93/3

The mass of the neutron star in Cyg X-2 (V1341 Cyg)

Cygnus X-2 is one of the brightest and longest known X-ray sources. We present high resolution optical spectroscopy of Cyg X-2 obtained over 4 years which gives an improved mass function of 0.69 +/- 0.03 Msun (1 sigma error). In addition, we resolve the rotationally broadened absorption features of the secondary star for the first time, deriving a rotation speed of vsin(i) = 34.2 +/- 2.5 km per s (1 sigma error) which leads to a mass ratio of q = M_c/M_x = 0.34 +/- 0.04 (1 sigma error), assuming a tidally-locked and Roche lobe-filling secondary). Hence with the lack of X-ray eclipses (i.e. i <~ 73 degrees) we can set firm 95% confidence lower limits to the neutron star mass of M_x > 1.27 Msun and to the companion star mass of M_c > 0.39 Msun. However, by additionally requiring that the companion must exceed 0.75 Msun (as required theoretically to produce a steady low-mass X-ray binary), then M_x > 1.88 Msun and i < 61 degrees (95% confidence lower and upper limit, respectively), thereby making Cyg X-2 the highest mass neutron star measured to date. If confirmed this would set significant constraints on the equation of state of nuclear matter.Comment: 16 pages, 4 figures, ApJ Letters, accepted, LaTeX, aasms4.st