15,370 research outputs found
An accurate, fast, mathematically robust, universal, non-iterative algorithm for computing multi-component diffusion velocities
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 , 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
in finite precision. The key idea involves leveraging the fact
that the matrix of the reciprocal of the binary diffusivities, , is low
rank, with its rank being independent of the number of species involved. The
low rank representation of matrix is computed in a fast manner at a
computational complexity of and the Sherman-Morrison-Woodbury
formula is used to solve for the diffusion velocities at a computational
complexity of . Rigorous proofs and numerical benchmarks
illustrate the low rank property of the matrix 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
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
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
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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