Maximum distance profile (MDP) convolutional codes have been proven to be very suitable for transmission over an erasure channel. In addition, the subclass of complete MDP convolutional codes has the ability to restart decoding after a burst of erasures. However, there is a lack of constructions of these codes over fields of small size. In this paper, we introduce the notion of complete j-MDP convolutional codes, which are a generalization of complete MDP convolutional codes, and describe their decoding properties. In particular, we present a decoding algorithm for decoding erasures within a given time delay T and show that complete T-MDP convolutional codes are optimal for this algorithm. Moreover, using a computer search with the MAPLE software, we determine the minimal binary and non-binary field size for the existence of (2, 1, 2) complete j-MDP convolutional codes and provide corresponding constructions. We give a description of all (2, 1, 2) complete MDP convolutional codes over the smallest possible fields, namely 픽13 and 픽16 and we also give constructions for (2, 1, 3) complete 4-MDP convolutional codes over 픽128 obtained by a randomized computer search.

Because extinctions are not random across taxa, it is important for conservation biologists to identify the traits that make some species more vulnerable. Factors associated with vulnerability include small geographical ranges, low densities, high trophic level, "slow" life histories, body size, and tolerance to altered habitats. In this study we examined the relationship of body size, reproductive output, longevity, and extinction risk for carnivores occurring in Brazil. We used generalized linear models analyses on phylogenetically independent contrasts to test the effect of body size alone, and the combined effect of body size, litter size and longevity on extinction risk. Body size appeared in the two best models according to the selection criteria (AIC), and it was the most plausible bionomic variable associated with extinction risk. Litter size and longevity, bionomic traits previously associated with threat risk of Brazilian carnivores, were implausible. The higher extinction risk for larger species could result from body size influencing vulnerability to different human activities, such as killing, habitat destruction and fragmentation, and the small size of natural reserves.

In 1704, the French priest Sébastien Truchet published a paper where he explored and counted patterns made up from a square divided by a diagonal line into two coloured parts, , now known as a Truchet tile. A few years later, Father Dominique Doüat continued Truchet's work and published a book in 1722 containing many more patterns and further counts of configurations. In this paper, we extend the work introduced by Truchet and Doüat by considering all possible rosettes made up of an $m\times n$ array of square or non-square Truchet tiles, or . We then classify the rosettes according to their symmetry group and count all the distinct rosettes in each group, for all possible sizes. The results are summarized in a separate section where we further analyse the asymptotic behaviour of the counts for square arrays. Finally, some applications are shown using two types of square flexagons.