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Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded networks, distributed storage systems, and caching systems, can be posed as polyhedral projections. These problems are demonstrated to exhibit multiple types of polyhedral symmetries. It is shown how these symmetries can be exploited to reduce the complexity of solving these problems through polyhedral projection., Comment: 23 pages, 15 figures

Off-the-shelf natural language processing software performs poorly when parsing patent claims owing to their use of irregular language relative to the corpora built from news articles and the web typically utilized to train this software. Stopping short of the extensive and expensive process of accumulating a large enough dataset to completely retrain parsers for patent claims, a method of adapting existing natural language processing software towards patent claims via forced part of speech tag correction is proposed. An Amazon Mechanical Turk collection campaign organized to generate a public corpus to train such an improved claim parsing system is discussed, identifying lessons learned during the campaign that can be of use in future NLP dataset collection campaigns with AMT. Experiments utilizing this corpus and other patent claim sets measure the parsing performance improvement garnered via the claim parsing system. Finally, the utility of the improved claim parsing system within other patent processing applications is demonstrated via experiments showing improved automated patent subject classification when the new claim parsing system is utilized to generate the features.

The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer to test whether a certain rate vector is achievable with vector linear network codes for a multi-source network coding instance and whether there exists a multi-linear secret sharing scheme achieving a specified information ratio for a given secret sharing instance are shown to be special cases of CLRP. Methods for solving CLRP built from group theoretic techniques for combinatorial generation are developed and described. These techniques form the core of an information theoretic achievability prover, an implementation accompanies the article, and several computational experiments with interesting instances of network coding and secret sharing demonstrating the utility of the method are provided., Comment: submitted to IEEE Transactions on Information Theory, (this version: corrected figure 9)

The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be non-polyhedral for four or more random variables, however its boundary remains unknown for four or more discrete random variables. Methods for specifying probability distributions that are in faces and on the boundary of the convex cone are derived, then utilized to map optimized inner bounds to the unknown part of the entropy region. The first method utilizes tools and algorithms from abstract algebra to efficiently determine those supports for the joint probability mass functions for four or more random variables that can, for some appropriate set of non-zero probabilities, yield entropic vectors in the gap between the best known inner and outer bounds. These supports are utilized, together with numerical optimization over non-zero probabilities, to provide inner bounds to the unknown part of the entropy region. Next, information geometry is utilized to parameterize and study the structure of probability distributions on these supports yielding entropic vectors in the faces of entropy and in the unknown part of the entropy region.