On optimal extended row distance profile

In this paper, we investigate extended row distances of Unit Memory (UM) convolutional codes. In particular, we derive upper and lower bounds for these distances and moreover present a concrete construction of a UM convolutional code that almost achieves the derived upper bounds. The generator matrix of these codes is built by means of a particular class of matrices, called superregular matrices. We actually conjecture that the construction presented is optimal with respect to the extended row distances as it achieves the maximum extended row distances possible. This in particular implies that the upper bound derived is not completely tight. The results presented in this paper further develop the line of research devoted to the distance properties of convolutional codes which has been mainly focused on the notions of free distance and column distance. Some open problems are left for further research

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

Complexity of Discrete Energy Minimization Problems

Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations. Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding to problems that are solvable, approximable, and inapproximable in polynomial time. Problems in the first two complexity classes can serve as alternative tractable formulations to the inapproximable ones. This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.Comment: ECCV'16 accepte

Between a Rock and a Hard Place: Habitat Selection in Female-Calf Humpback Whale (Megaptera novaeangliae) Pairs on the Hawaiian Breeding Grounds

The Au'au Channel between the islands of Maui and Lanai, Hawaii comprises critical breeding habitat for humpback whales (Megaptera novaeangliae) of the Central North Pacific stock. However, like many regions where marine mega-fauna gather, these waters are also the focus of a flourishing local eco-tourism and whale watching industry. Our aim was to establish current trends in habitat preference in female-calf humpback whale pairs within this region, focusing specifically on the busy, eastern portions of the channel. We used an equally-spaced zigzag transect survey design, compiled our results in a GIS model to identify spatial trends and calculated Neu's Indices to quantify levels of habitat use. Our study revealed that while mysticete female-calf pairs on breeding grounds typically favor shallow, inshore waters, female-calf pairs in the Au'au Channel avoided shallow waters (<20 m) and regions within 2 km of the shoreline. Preferred regions for female-calf pairs comprised water depths between 40–60 m, regions of rugged bottom topography and regions that lay between 4 and 6 km from a small boat harbor (Lahaina Harbor) that fell within the study area. In contrast to other humpback whale breeding grounds, there was only minimal evidence of typical patterns of stratification or segregation according to group composition. A review of habitat use by maternal females across Hawaiian waters indicates that maternal habitat choice varies between localities within the Hawaiian Islands, suggesting that maternal females alter their use of habitat according to locally varying pressures. This ability to respond to varying environments may be the key that allows wildlife species to persist in regions where human activity and critical habitat overlap

Fast bounded-distance decoding of the Nordstrom-Robinson code

Based on the two-level squaring construction of the Reed-Muller code, a bounded-distance decoding algorithm for the Nordstrom-Robinson code is given. This algorithm involves 199 real operations, which is less than one half of the computational complexity of the known maximum-likelihood decoding algorithms for this code. The algorithm also has exactly the same effective error coefficient as the maximum-likelihood decoding, so that its performance is only degraded by a negligible amount