On computing the degree of convexity of polyominoes

In this paper we present an algorithm which has as input a convex polyomino P and computes its degree of convexity, de\ufb01ned as the smallest integer k such that any two cells of P can be joined by a monotone path inside P with at most k changes of direction. The algorithm uses space O(m + n) to represent a polyomino P with n rows and m columns, and has time complexity O(min(m, rk)), where r is the number of corners of P. Moreover, the algorithm leads naturally to a decomposition of P into simpler polyominoes

Spectral properties of quantum NN-body systems versus chaotic properties of their mean field approximations

We present numerical evidence that in a system of interacting bosons there exists a correspondence between the spectral properties of the exact quantum Hamiltonian and the dynamical chaos of the associated mean field evolution. This correspondence, analogous to the usual quantum-classical correspondence, is related to the formal parallel between the second quantization of the mean field, which generates the exact dynamics of the quantum $N$-body system, and the first quantization of classical canonical coordinates. The limit of infinite density and the thermodynamic limit are then briefly discussed.Comment: 15 pages RevTeX, 11 postscript figures included with psfig, uuencoded gz-compressed .tar fil

Constraining the true nature of an exotic binary in the core of NGC 6624

We report on the identification of the optical counterpart to Star1, the exotic object serendipitously discovered by Deutsch et al. in the core of the Galactic globular cluster NGC 6624. Star1 has been classified by Deutsch et al. as either a quiescent Cataclysmic Variable or a low-mass X-ray binary. Deutsch et al. proposed StarA as possible optical counterpart to this object. We used high-resolution images obtained with the Hubble Space Telescope to perform a variability analysis of the stars close to the nominal position of Star1. While no variability was detected for StarA, we found another star, here named COM_Star1, showing a clear sinusoidal light modulation with amplitude \Delta m_F435W~0.7 mag and orbital period of P_orb~98 min. The shape of the light curve is likely caused by strong irradiation by the primary heating one hemisphere of the companion, thus suggesting a quite hot primary.Comment: Accepted for publication by ApJ Letters; 6 pages, 5 figure

L-Convex Polyominoes are Recognizable in Real Time by 2D Cellular Automata

A polyomino is said to be L-convex if any two of its cells are connected by a 4-connected inner path that changes direction at most once. The 2-dimensional language representing such polyominoes has been recently proved to be recognizable by tiling systems by S. Brocchi, A. Frosini, R. Pinzani and S. Rinaldi. In an attempt to compare recognition power of tiling systems and cellular automata, we have proved that this language can be recognized by 2-dimensional cellular automata working on the von Neumann neighborhood in real time. Although the construction uses a characterization of L-convex polyominoes that is similar to the one used for tiling systems, the real time constraint which has no equivalent in terms of tilings requires the use of techniques that are specific to cellular automata

Association of FOBT-assessed faecal Hb content with colonic lesions detected in the Florence screening programme

We assessed the correlation between quantitative results of immunological faecal occult blood testing (I-FOBT) and colonic lesions (191 colorectal cancers, 890 adenomas) detected at colonoscopy in 2597 FOBT+ (cutoff 100 ng ml−1 Hb) subjects. At univariate analysis, a higher average faecal Hb content was significantly associated with male gender (P=0.003), age (P=0.02), and colonoscopy findings (P=0.000). Among adenomas, higher faecal Hb content was significantly associated with size (P=0.0000), presence of severe dysplasia (P=0.0001), presence of villous component (P=0.0002), and location in the left colon (P=0.003). At multivariate analysis adjusting for potential confounders, age (P=0.03), size (P=0.0000), and location in the left colon (P=0.0005) were confirmed as having an independent association with higher faecal Hb content. Immunological FOBT is confirmed to be a specific screening test to detect cancer and adenoma, with a low positivity rate (3.7%) and a high positive predictive value (41.5%). Faecal Hb content is significantly higher for those lesions (cancer and high-risk adenomas) screening is aimed at detecting