Survey propagation for the cascading Sourlas code

We investigate how insights from statistical physics, namely survey propagation, can improve decoding of a particular class of sparse error correcting codes. We show that a recently proposed algorithm, time averaged belief propagation, is in fact intimately linked to a specific survey propagation for which Parisi's replica symmetry breaking parameter is set to zero, and that the latter is always superior to belief propagation in the high connectivity limit. We briefly look at further improvements available by going to the second level of replica symmetry breaking.Comment: 14 pages, 5 figure

Finite-Connectivity Spin-Glass Phase Diagrams and Low Density Parity Check Codes

We obtain phase diagrams of regular and irregular finite connectivity spin-glasses. Contact is firstly established between properties of the phase diagram and the performances of low density parity check codes (LDPC) within the Replica Symmetric (RS) ansatz. We then study the location of the dynamical and critical transition of these systems within the one step Replica Symmetry Breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that, away from the Nishimori line, in the low temperature region, the location of the dynamical transition line does change within the RSB theory, in comparison with the (RS) case. For LDPC decoding over the binary erasure channel we find, at zero temperature and rate R=1/4 an RS critical transition point located at p_c = 0.67 while the critical RSB transition point is located at p_c = 0.7450, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel (BSC) we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes within the RSB theory; the location of the dynamical transition point occurring at higher values of the channel noise. Possible practical implications to improve the performances of the state-of-the-art error correcting codes are discussed.Comment: 21 pages, 15 figure

Bicoloring Random Hypergraphs

We study the problem of bicoloring random hypergraphs, both numerically and analytically. We apply the zero-temperature cavity method to find analytical results for the phase transitions (dynamic and static) in the 1RSB approximation. These points appear to be in agreement with the results of the numerical algorithm. In the second part, we implement and test the Survey Propagation algorithm for specific bicoloring instances in the so called HARD-SAT phase.Comment: 14 pages, 10 figure

Inhibition of p70 S6 Kinase (S6K1) Activity by A77 1726 and Its Effect on Cell Proliferation and Cell Cycle Progress

AbstractLeflunomide is a novel immunomodulatory drug prescribed for treating rheumatoid arthritis. It inhibits the activity of protein tyrosine kinases and dihydroorotate dehydrogenase, a rate-limiting enzyme in the pyrimidine nucleotide synthesis pathway. Here, we report that A77 1726, the active metabolite of leflunomide, inhibited the phosphorylation of ribosomal protein S6 and two other substrates of S6K1, insulin receptor substrate-1 and carbamoyl phosphate synthetase 2, in an A375 melanoma cell line. A77 1726 increased the phosphorylation of AKT, p70 S6 (S6K1), ERK1/2, and MEK through the feedback activation of the IGF-1 receptor–mediated signaling pathway. In vitro kinase assay revealed that leflunomide and A77 1726 inhibited S6K1 activity with IC50 values of approximately 55 and 80 μM, respectively. Exogenous uridine partially blocked A77 1726–induced inhibition of A375 cell proliferation. S6K1 knockdown led to the inhibition of A375 cell proliferation but did not potentiate the antiproliferative effect of A77 1726. A77 1726 stimulated bromodeoxyuridine incorporation in A375 cells but arrested the cell cycle in the S phase, which was reversed by addition of exogenous uridine or by MAP kinase pathway inhibitors but not by rapamycin and LY294002 (a phosphoinositide 3-kinase inhibitor). These observations suggest that A77 1726 accelerates cell cycle entry into the S phase through MAP kinase activation and that pyrimidine nucleotide depletion halts the completion of the cell cycle. Our study identified a novel molecular target of A77 1726 and showed that the inhibition of S6K1 activity was in part responsible for its antiproliferative activity. Our study also provides a novel mechanistic insight into A77 1726–induced cell cycle arrest in the S phase