Finite connectivity systems as error-correcting codes

We investigate the performance of parity check codes using the mapping onto spin glasses proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C parity checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for K?8 when the code rate K/C is finite. We then examine the finite temperature case to asses the use of simulated annealing methods for decoding, study the performance of the finite K case and extend the analysis to accommodate different types of noisy channels. The analogy between statistical physics methods and decoding by belief propagation is also discussed.

The metabolism of n-methyl compounds

The metabolism of compounds containing the N-methyl group is discussed with particular consideration being made to the possible role of the product of oxidative metabolism, the N-hydroxymethyl moiety, in the generation of potentially toxic, reactive electrophiles. Particular pathways which are considered are: (i), the production of formaldehyde; (ii), the generation of iminium ions or imines; and (iii), the formation of N-formyl compounds which might act as formylating agents. 4-Chloro-N-(hydroxymethyl)benzamide and 3-(4-chlorophenyl)-1-hydroxy-methyl-1-methylurea (the product of oxidative metabolism of 3-(4-chlorophenyl)-1,1-dimethylurea) are model carbinolamides which do not readily release formaldehyde. The electrophilic properties of these model carbinolamides were investigated: neither reacted with nucleophiles such as cyanide or glutathione under physiological conditions. In contrast, N-(acetoxymethyl)-4-chlorobenzamide yielded the cyanomethylamide with potassium cyanide and S-(4-chlorobenzamidomethyl)glutathione with glutathione. 4-Chloro-N-(hydroxymethyl)benzamide and 3-(4-chlorophenyl)-1,1-dimethylurea were not biotransformed to electrophilic moieties when incubated with mouse hepatic 9000 x g supernatant and Acetyl-CoA or PAPS-generating system. N-(Acetoxymethyl)-4-chlorobenzamide was non-mutagenic to Salmonella typhimurium in the short term bacterial assay; but toxicity to the bacteria was observed. 4-Chloro-N-(hydroxymethyl)benzamide and 3-(4-chlorophenyl)-1,1-dimethylurea showed no mutagenicity or toxicity in the mutagenicity assay including an Aroclor-induced rat hepatic 9000 x g supernatant. Addition of Acetyl-CoA or a PAPS-generating system did not produce a mutagenic response. 4-Chloro-N-formlbenzamide did not act as a formylating agent towards the weak nucleophile aniline. However, 4-chloro-N-formylbenzamide, N-formylbenzamide, 3-(4-chlorophenyl)-1-formyl-1-methylurea and 3-(4-chlorophenyl)-1-formylurea are all metabolised by mouse hepatic mirosomes and post-microsomal supernatant. The results demonstrate the potential for N-hydroxymethyl compounds to generate highly reactive species if these are substrates for conjugation with sulphate (or acetate). The model compounds employed here, apparently do not show any ability to be conjugated themselves, however, other N-hydroxymethyl compounds might be readily conjugated. The formation of N-formyl compounds does not appear to be toxicologically significant, as adjudged on limited experiments performed, but rather represent a detoxification pathway.

Conversion of a chirped Gaussian pulse to a soliton or a bound multisoliton state in quasi-lossless and lossy optical fiber spans

The formation of single-soliton or bound-multisoliton states from a single linearly chirped Gaussian pulse in quasi-lossless and lossy fiber spans is examined. The conversion of an input-chirped pulse into soliton states is carried out by virtue of the so-called direct Zakharov-Shabat spectral problem, the solution of which allows one to single out the radiative (dispersive) and soliton constituents of the beam and determine the parameters of the emerging bound state(s). We describe here how the emerging pulse characteristics (the number of bound solitons, the relative soliton power) depend on the input pulse chirp and amplitude. © 2007 Optical Society of America.