15,370 research outputs found

    An accurate, fast, mathematically robust, universal, non-iterative algorithm for computing multi-component diffusion velocities

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    Using accurate multi-component diffusion treatment in numerical combustion studies remains formidable due to the computational cost associated with solving for diffusion velocities. To obtain the diffusion velocities, for low density gases, one needs to solve the Stefan-Maxwell equations along with the zero diffusion flux criteria, which scales as O(N3)\mathcal{O}(N^3), when solved exactly. In this article, we propose an accurate, fast, direct and robust algorithm to compute multi-component diffusion velocities. To our knowledge, this is the first provably accurate algorithm (the solution can be obtained up to an arbitrary degree of precision) scaling at a computational complexity of O(N)\mathcal{O}(N) in finite precision. The key idea involves leveraging the fact that the matrix of the reciprocal of the binary diffusivities, VV, is low rank, with its rank being independent of the number of species involved. The low rank representation of matrix VV is computed in a fast manner at a computational complexity of O(N)\mathcal{O}(N) and the Sherman-Morrison-Woodbury formula is used to solve for the diffusion velocities at a computational complexity of O(N)\mathcal{O}(N). Rigorous proofs and numerical benchmarks illustrate the low rank property of the matrix VV and scaling of the algorithm.Comment: 16 pages, 7 figures, 1 table, 1 algorith

    On the Complexity and Approximation of Binary Evidence in Lifted Inference

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    Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities. The reason is that conditioning on evidence breaks many of the model's symmetries, which can preempt standard lifting techniques. Recent theoretical results show, for example, that conditioning on evidence which corresponds to binary relations is #P-hard, suggesting that no lifting is to be expected in the worst case. In this paper, we balance this negative result by identifying the Boolean rank of the evidence as a key parameter for characterizing the complexity of conditioning in lifted inference. In particular, we show that conditioning on binary evidence with bounded Boolean rank is efficient. This opens up the possibility of approximating evidence by a low-rank Boolean matrix factorization, which we investigate both theoretically and empirically.Comment: To appear in Advances in Neural Information Processing Systems 26 (NIPS), Lake Tahoe, USA, December 201

    A distributed-memory package for dense Hierarchically Semi-Separable matrix computations using randomization

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    We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable representations (HSS). Such matrices appear in many applications, e.g., finite element methods, boundary element methods, etc. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, relies on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. This work is part of a more global effort, the STRUMPACK (STRUctured Matrices PACKage) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver

    A Lightweight McEliece Cryptosystem Co-processor Design

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    Due to the rapid advances in the development of quantum computers and their susceptibility to errors, there is a renewed interest in error correction algorithms. In particular, error correcting code-based cryptosystems have reemerged as a highly desirable coding technique. This is due to the fact that most classical asymmetric cryptosystems will fail in the quantum computing era. Quantum computers can solve many of the integer factorization and discrete logarithm problems efficiently. However, code-based cryptosystems are still secure against quantum computers, since the decoding of linear codes remains as NP-hard even on these computing systems. One such cryptosystem is the McEliece code-based cryptosystem. The original McEliece code-based cryptosystem uses binary Goppa code, which is known for its good code rate and error correction capability. However, its key generation and decoding procedures have a high computation complexity. In this work we propose a design and hardware implementation of an public-key encryption and decryption co-processor based on a new variant of McEliece system. This co-processor takes the advantage of the non-binary Orthogonal Latin Square Codes to achieve much smaller computation complexity, hardware cost, and the key size.Comment: 2019 Boston Area Architecture Workshop (BARC'19
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