An iterative algorithm for parametrization of shortest length shift registers over finite rings

The construction of shortest feedback shift registers for a finite sequence S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for the sequence of numbers S_1,...,S_N, thus solving an open problem in the literature. The algorithm iteratively processes each number, starting with S_1, and constructs at each step a particular type of minimal Gr\"obner basis. The construction involves a simple update rule at each step which leads to computational efficiency. It is shown that the algorithm simultaneously computes a similar parametrization for the reciprocal sequence S_N,...,S_1.Comment: Submitte

Use of 16S rRNA Gene Based Clone Libraries to Assess Microbial Communities Potentially Involved in Anaerobic Methane Oxidation in a Mediterranean Cold Seep

This study provides data on the diversities of bacterial and archaeal communities in an active methane seep at the Kazan mud volcano in the deep Eastern Mediterranean sea. Layers of varying depths in the Kazan sediments were investigated in terms of (1) chemical parameters and (2) DNA-based microbial population structures. The latter was accomplished by analyzing the sequences of directly amplified 16S rRNA genes, resulting in the phylogenetic analysis of the prokaryotic communities. Sequences of organisms potentially associated with processes such as anaerobic methane oxidation and sulfate reduction were thus identified. Overall, the sediment layers revealed the presence of sequences of quite diverse bacterial and archaeal communities, which varied considerably with depth. Dominant types revealed in these communities are known as key organisms involved in the following processes: (1) anaerobic methane oxidation and sulfate reduction, (2) sulfide oxidation, and (3) a range of (aerobic) heterotrophic processes. In the communities in the lowest sediment layer sampled (22–34 cm), sulfate-reducing bacteria and archaea of the ANME-2 cluster (likely involved in anaerobic methane oxidation) were prevalent, whereas heterotrophic organisms abounded in the top sediment layer (0–6 cm). Communities in the middle layer (6–22 cm) contained organisms that could be linked to either of the aforementioned processes. We discuss how these phylogeny (sequence)-based findings can support the ongoing molecular work aimed at unraveling both the functioning and the functional diversities of the communities under study

Seascape Genetics of a Globally Distributed, Highly Mobile Marine Mammal: The Short-Beaked Common Dolphin (Genus Delphinus)

Identifying which factors shape the distribution of intraspecific genetic diversity is central in evolutionary and conservation biology. In the marine realm, the absence of obvious barriers to dispersal can make this task more difficult. Nevertheless, recent studies have provided valuable insights into which factors may be shaping genetic structure in the world's oceans. These studies were, however, generally conducted on marine organisms with larval dispersal. Here, using a seascape genetics approach, we show that marine productivity and sea surface temperature are correlated with genetic structure in a highly mobile, widely distributed marine mammal species, the short-beaked common dolphin. Isolation by distance also appears to influence population divergence over larger geographical scales (i.e. across different ocean basins). We suggest that the relationship between environmental variables and population structure may be caused by prey behaviour, which is believed to determine common dolphins' movement patterns and preferred associations with certain oceanographic conditions. Our study highlights the role of oceanography in shaping genetic structure of a highly mobile and widely distributed top marine predator. Thus, seascape genetic studies can potentially track the biological effects of ongoing climate-change at oceanographic interfaces and also inform marine reserve design in relation to the distribution and genetic connectivity of charismatic and ecologically important megafauna

Connections between linear systems and convolutional codes

The article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to finite-support systems under Pontryagin duality. In this duality the dual of a controllable system is observable and vice versa. Uncontrollability can occur only if there are bi-infinite support trajectories in the behavior, so finite and half-infinite-support systems must be controllable. Unobservability can occur only if there are finite support trajectories in the behavior, so bi-infinite and half-infinite-support systems must be observable. It is shown that the different definitions for convolutional codes are equivalent if one restricts attention to controllable and observable codes

An algebraic decoding algorithm for convolutional codes

this article to introduce a new iterative algebraic decoding algorithm which is capable of decoding convolutional codes which have a certain underlying algebraic structure. The algorithm exploits the algebraic structure of the convolutional code and it achieves its best performance if some naturally associated block codes can be efficiently decoded in an algebraic manner. In order to achieve this goal we will work with a classical state space description of a so called systematic encoder. Using this description we will derive a general procedure which will allow one to extend known decoding algorithms for block codes (like e.g. the Berlekamp Massey algorithm) to convolutional codes. In the coding literature there exist several decoding algorithms for convolutional codes. Maybe the most prominent one is the Viterbi decoding algorithm which applies the principle of dynamic programming to compute the transmitted message sequence. It was shown by Forney [6] that this algorithm computes the message sequence in a maximum likelihood fashion. The disadvantage of this algorithm is that it becomes computationally infeasible if the degree of the encoder is larger than 20. On the side of the Viterbi algorithm there are several sub-optimal algorithms and we would like to mention Massey's threshold decoding algorithm [9], the sequential decoding algorithm and the feedback decoding algorithm [7, 8, 12]. More recently there has been a significant interest in some iterative decoding algorithms in connection with the decoding of low density parity check codes and other codes defined on general graphs and we refer to [17, 20]. The iterative decoding algorithm which we will present in this paper seems to be different from above ideas. Indeed the algorithm iteratively computes the state vec..