Fourier transform over finite groups for error detection and error correction in computation channels

We consider the methods of error detection and correction in devices and programs calculating functions f: G → K where G is a finite group and K is a field. For error detection and correction we use linear checks generated by convolutions in the field K of the original function f and some checking idempotent function δ: G → , 1 For the construction of the optimal checking function δ we use methods of harmonic analysis over the group G in the field K. Since these methods will be the main tools for the construction of optimal checks, we consider the algorithms for the fast computation of Fourier Transforms over the group G in the field K. We solve the problem of error detecting and correcting capability for our methods for two important classes of decoding procedures (memoryless and memory-aided decoding) and consider the question of syndrome computation for these methods. We describe also properties of error correcting codes generated by convolution checks

Potential asphyxia and brainstem abnormalities in sudden and unexpected death in infants

Objective: Sudden and unexplained death is a leading cause of infant mortality. Certain characteristics of the sleep environment increase the risk for sleep-related sudden and unexplained infant death. These characteristics have the potential to generate asphyxial conditions. We tested the hypothesis that infants may be exposed to differing degrees of asphyxia in sleep environments, such that vulnerable infants with a severe underlying brainstem deficiency in serotonergic, γ-aminobutyric acid-ergic, or 14-3-3 transduction proteins succumb even without asphyxial triggers (e.g., supine), whereas infants with intermediate or borderline brainstem deficiencies require asphyxial stressors to precipitate death. Methods: We classified cases of sudden infant death into categories relative to a "potential asphyxia" schema in a cohort autopsied at the San Diego County Medical Examiner's Office. Controls were infants who died with known causes of death established at autopsy. Analysis of covariance tested for differences between groups. Results: Medullary neurochemical abnormalities were present in both infants dying suddenly in circumstances consistent with asphyxia and infants dying suddenly without obvious asphyxia-generating circumstances. There were no differences in the mean neurochemical measures between these 2 groups, although mean measures were both significantly lower (P < .05) than those of controls dying of known causes. Conclusions: We found no direct relationship between the presence of potentially asphyxia conditions in the sleep environment and brainstem abnormalities in infants dying suddenly and unexpectedly. Brainstem abnormalities were associated with both asphyxia-generating and non-asphyxia generating conditions. Heeding safe sleep messages is essential for all infants, especially given our current inability to detect underlying vulnerabilities.Bradley B. Randall, David S. Paterson, Elisabeth A. Haas, Kevin G. Broadbelt, Jhodie R. Duncan, Othon J. Mena, Henry F. Krous, Felicia L. Trachtenberg and Hannah C. Kinne

HLA analysis of Sri Lankan Sinhalese predicts North Indian origin.

The origin of the Sinhalese population of Sri Lanka is debated. We subtyped HLA-A*02 in 101 Sinhalese and observed a preponderance of the rare allele HLA-A*0211 which was similar to reported frequencies in northern India. Taken with low-resolution typing for the remaining A, B, C, DR and DQ alleles, these data suggest a North Indian origin for the Sri Lankan Sinhalese