A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors

We consider multilinear systems of equations whose coefficient tensors are (Formula presented.)-tensors. Multilinear systems of equations have many applications in engineering and scientific computing, such as data mining and numerical partial differential equations. In this paper, we show that solving multilinear systems with (Formula presented.)-tensors is equivalent to solving nonlinear systems of equations where the involving functions are P-functions. Based on this result, we propose a Newton-type method to solve multilinear systems with (Formula presented.)-tensors. For a multilinear system with a nonsingular (Formula presented.)-tensor and a positive right side vector, we prove that the sequence generated by the proposed method converges to the unique solution of the multilinear system and the convergence rate is quadratic. Numerical results are reported to show that the proposed method is promising

Design and in vitro studies of a needle-type glucose sensor for subcutaneous monitoring

International audienceA new miniaturized glucose oxidase based needle-type glu¬ cose mlcrosensor has been developed for subcutaneous glu¬ cose monitoring. The sensor Is equivalent In shape and size to a 26-gauge needle (0.45-mm o.d.) and can be Implanted with ease without any Incision. The novel configuration greatly facilitates the deposition of enzyme and polymer films so that sensors with characteristics suitable for In vivo use (upper limit of linear range > 15 mM, response time 60%). The sensor response is largely Independent of ox¬ ygen tension In the normal physiological range. It also ex¬ hibits good selectivity against common interferences except for the exogenous drug acetaminophen

Stock-Water Harvesting with Wax on the Arizona Strip

From the Proceedings of the 1976 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 29-May 1, 1976, Tucson, ArizonaThis article is part of the Hydrology and Water Resources in Arizona and the Southwest collections. Digital access to this material is made possible by the Arizona-Nevada Academy of Science and the University of Arizona Libraries. For more information about items in this collection, contact [email protected]

Fast higher-order functions for tensor calculus with tensors and subtensors

Tensors analysis has become a popular tool for solving problems in computational neuroscience, pattern recognition and signal processing. Similar to the two-dimensional case, algorithms for multidimensional data consist of basic operations accessing only a subset of tensor data. With multiple offsets and step sizes, basic operations for subtensors require sophisticated implementations even for entrywise operations. In this work, we discuss the design and implementation of optimized higher-order functions that operate entrywise on tensors and subtensors with any non-hierarchical storage format and arbitrary number of dimensions. We propose recursive multi-index algorithms with reduced index computations and additional optimization techniques such as function inlining with partial template specialization. We show that single-index implementations of higher-order functions with subtensors introduce a runtime penalty of an order of magnitude than the recursive and iterative multi-index versions. Including data- and thread-level parallelization, our optimized implementations reach 68% of the maximum throughput of an Intel Core i9-7900X. In comparison with other libraries, the average speedup of our optimized implementations is up to 5x for map-like and more than 9x for reduce-like operations. For symmetric tensors we measured an average speedup of up to 4x