The maximum-likelihood (ML) approach in emission tomography provides images with superior noise characteristics compared to conventional filtered backprojection (FBP) algorithms. The expectation-maximization (EM) algorithm is an iterative algorithm for maximizing the Poisson likelihood in emission computed tomography that became very popular for solving the ML problem because of its attractive theoretical and practical properties. Recently, (Browne and DePierro, 1996 and Hudson and Larkin, 1994) block sequential versions of the EM algorithm that take advantage of the scanner's geometry have been proposed in order to accelerate its convergence. In Hudson and Larkin, 1994, the ordered subsets EM (OS-EM) method was applied to the ML problem and a modification (OS-GP) to the maximum a posteriori (MAP) regularized approach without showing convergence. In Browne and DePierro, 1996, we presented a relaxed version of OS-EM (RAMLA) that converges to an ML solution. In this paper, we present an extension of RAMLA for MAP reconstruction. We show that, if the sequence generated by this method converges, then it must converge to the true MAP solution. Experimental evidence of this convergence is also shown. To illustrate this behavior we apply the algorithm to positron emission tomography simulated data comparing its performance to OS-GP.

This work presents a mathematical model that establishes an interesting connection between nucleotide frequencies in human singlestranded DNA and the famous Fibonacci's numbers. The model relies on two assumptions. First, Chargaff 's second parity rule should be valid, and, second, the nucleotide frequencies should approach limit values when the number of bases is sufficiently large. Under these two hypotheses, it is possible to predict the human nucleotide frequencies with accuracy. It is noteworthy, that the predicted values are solutions of an optimization problem, which is commonplace in many nature's phenomena.

Trans-splicing is a common phenomenon in nematodes and kinetoplastids, and it has also been reported in other organisms, including humans. Up to now, all in silico strategies to find evidence of trans-splicing in humans have required that the candidate sequences follow the consensus splicing site rules (spliceosome-mediated mechanism). However, this criterion is not supported by the best human experimental evidence, which, except in a single case, do not follow canonical splicing sites. Moreover, recent findings describe a novel alternative tRNA mediated trans-splicing mechanism, which prescinds the spliceosome machinery. In order to answer the question, 'Are there hybrid mRNAs in sequence databanks, whose characteristics resemble those of the best human experimental evidence?', we have developed a methodology that successfully identified 16 hybrid mRNAs which might be instances of interchromosomal trans-splicing. Each hybrid mRNA is formed by a trans-spliced region (TSR), which was successfully mapped either onto known genes or onto a human endogenous retrovirus (HERV-K) transcript which supports their transcription. The existence of these hybrid mRNAs indicates that trans-splicing may be more widespread than believed. Furthermore, non-canonical splice site patterns suggest that infrequent splicing sites may occur under special conditions, or that an alternative trans-splicing mechanism is involved. Finally, our candidates are supposedly from normal tissue, and a recent study has reported that trans-splicing may occur not only in malignant tissues, but in normal tissues as well. Our methodology can be applied to 5'-UTR, coding sequences and 3'-UTR in order to find new candidates for a posteriori experimental confirmation.

Whole-genome re-sequencing, alignment and annotation analyses were undertaken for 12 sires representing four important cattle breeds in Brazil: Guzerat (multi-purpose), Gyr, Girolando and Holstein (dairy production). A total of approximately 4.3 billion reads from an Illumina HiSeq 2000 sequencer generated for each animal 10.7 to 16.4-fold genome coverage. A total of 27,441,279 single nucleotide variations (SNVs) and 3,828,041 insertions/deletions (InDels) were detected in the samples, of which 2,557,670 SNVs and 883,219 InDels were novel. The submission of these genetic variants to the dbSNP database significantly increased the number of known variants, particularly for the indicine genome. The concordance rate between genotypes obtained using the Bovine HD BeadChip array and the same variants identified by sequencing was about 99.05%. The annotation of variants identified numerous non-synonymous SNVs and frameshift InDels which could affect phenotypic variation. Functional enrichment analysis was performed and revealed that variants in the olfactory transduction pathway was over represented in all four cattle breeds, while the ECM-receptor interaction pathway was over represented in Girolando and Guzerat breeds, the ABC transporters pathway was over represented only in Holstein breed, and the metabolic pathways was over represented only in Gyr breed. The genetic variants discovered here provide a rich resource to help identify potential genomic markers and their associated molecular mechanisms that impact economically important traits for Gyr, Girolando, Guzerat and Holstein breeding programs.