On the ground states of the Bernasconi model

The ground states of the Bernasconi model are binary +1/-1 sequences of length N with low autocorrelations. We introduce the notion of perfect sequences, binary sequences with one-valued off-peak correlations of minimum amount. If they exist, they are ground states. Using results from the mathematical theory of cyclic difference sets, we specify all values of N for which perfect sequences do exist and how to construct them. For other values of N, we investigate almost perfect sequences, i.e. sequences with two-valued off-peak correlations of minimum amount. Numerical and analytical results support the conjecture that almost perfect sequences do exist for all values of N, but that they are not always ground states. We present a construction for low-energy configurations that works if N is the product of two odd primes.Comment: 12 pages, LaTeX2e; extended content, added references; submitted to J.Phys.

Ghost-free braneworld bigravity

We consider a generalisation of the DGP model, by adding a second brane with localised curvature, and allowing for a bulk cosmological constant and brane tensions. We study radion and graviton fluctuations in detail, enabling us to check for ghosts and tachyons. By tuning our parameters accordingly, we find bigravity models that are free from ghosts and tachyons. These models will lead to large distance modifications of gravity that could be observable in the near future.Comment: Dedicated to the memory of Ian Kogan. Version to appear in Classical and Quantum Gravit

Complementarity of the Maldacena and Karch-Randall Pictures

We perform a one-loop test of the holographic interpretation of the Karch-Randall model, whereby a massive graviton appears on an AdS_4 brane in an AdS_5 bulk. Within the AdS/CFT framework, we examine the quantum corrections to the graviton propagator on the brane, and demonstrate that they induce a graviton mass in exact agreement with the Karch-Randall result. Interestingly enough, at one loop order, the spin 0, spin 1/2 and spin 1 loops contribute to the dynamically generated (mass)^2 in the same 1: 3: 12 ratio as enters the Weyl anomaly and the 1/r^3 corrections to the Newtonian gravitational potential.Comment: 20 pages, Revtex 3, Discussion on the absence of a scalar ghost clarified; Additional details on the computation give

DNA methylation patterns in bladder cancer and washing cell sediments: a perspective for tumor recurrence detection

<p>Abstract</p> <p>Background</p> <p>Epigenetic alterations are a hallmark of human cancer. In this study, we aimed to investigate whether aberrant DNA methylation of cancer-associated genes is related to urinary bladder cancer recurrence.</p> <p>Methods</p> <p>A set of 4 genes, including <it>CDH1 </it>(E-cadherin), <it>SFN </it>(stratifin), <it>RARB </it>(retinoic acid receptor, beta) and <it>RASSF1A </it>(Ras association (RalGDS/AF-6) domain family 1), had their methylation patterns evaluated by MSP (Methylation-Specific Polymerase Chain Reaction) analysis in 49 fresh urinary bladder carcinoma tissues (including 14 cases paired with adjacent normal bladder epithelium, 3 squamous cell carcinomas and 2 adenocarcinomas) and 24 cell sediment samples from bladder washings of patients classified as cancer-free by cytological analysis (control group). A third set of samples included 39 archived tumor fragments and 23 matched washouts from 20 urinary bladder cancer patients in post-surgical monitoring. After genomic DNA isolation and sodium bisulfite modification, methylation patterns were determined and correlated with standard clinic-histopathological parameters.</p> <p>Results</p> <p><it>CDH1 </it>and <it>SFN </it>genes were methylated at high frequencies in bladder cancer as well as in paired normal adjacent tissue and exfoliated cells from cancer-free patients. Although no statistically significant differences were found between <it>RARB </it>and <it>RASSF1A </it>methylation and the clinical and histopathological parameters in bladder cancer, a sensitivity of 95% and a specificity of 71% were observed for <it>RARB </it>methylation (Fisher's Exact test (p < 0.0001; OR = 48.89) and, 58% and 17% (p < 0.05; OR = 0.29) for <it>RASSF1A </it>gene, respectively, in relation to the control group.</p> <p>Conclusion</p> <p>Indistinct DNA hypermethylation of <it>CDH1 </it>and <it>SFN </it>genes between tumoral and normal urinary bladder samples suggests that these epigenetic features are not suitable biomarkers for urinary bladder cancer. However, <it>RARB </it>and <it>RASSF1A </it>gene methylation appears to be an initial event in urinary bladder carcinogenesis and should be considered as defining a panel of differentially methylated genes in this neoplasia in order to maximize the diagnostic coverage of epigenetic markers, especially in studies aiming at early recurrence detection.</p