Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation

Sanderson, Conrad; Curtin, Ryan R.

doi:10.3390/mca24030070

“…whereq(t + ∆t) is the quaternion after an unconstrained time step in ∆t [148]. We implemented these equations using the Armadillo C++ framework for linear algebra [149,150].…”

Section: A14 Soft Nuclear Envelopementioning

confidence: 99%

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

Edelmaier

¹

,

Lamson

²

,

Gergely

³

et al. 2020

eLife

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The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle.

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“…whereq(t + ∆t) is the quaternion after an unconstrained time step in ∆t [149]. We implemented these equations using the Armadillo C++ framework for linear algebra [150,151].…”

Section: A14 Soft Nuclear Envelopementioning

confidence: 99%

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

Edelmaier

¹

,

Lamson

²

,

Gergely

³

et al. 2019

Preprint

View full text Add to dashboard Cite

The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle.

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“…Power consumption is measured with nvidia-smi. For mobile CPU, we use Armadillo library [37], [38] on a 4-core ARM A53 CPU and measure its dynamic power using a powermeter.…”

Section: A Methodologymentioning

confidence: 99%

SpArch: Efficient Architecture for Sparse Matrix Multiplication

Zhang

¹

,

Wang

²

,

Han

³

et al. 2020

2020 IEEE International Symposium on High Performance Computer Architecture (HPCA)

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Generalized Sparse Matrix-Matrix Multiplication (SpGEMM) is a ubiquitous task in various engineering and scientific applications. However, inner product based SpGEMM introduces redundant input fetches for mismatched nonzero operands, while outer product based approach [1] suffers from poor output locality due to numerous partial product matrices. Inefficiency in the reuse of either inputs or outputs data leads to extensive and expensive DRAM access.To address this problem, this paper proposes an efficient sparse matrix multiplication accelerator architecture, SpArch, which jointly optimizes the data locality for both input and output matrices. We first design a highly parallelized streamingbased merger to pipeline the multiply and merge stage of partial matrices so that partial matrices are merged on chip immediately after produced. We then propose a condensed matrix representation that reduces the number of partial matrices by three orders of magnitude and thus reduces DRAM access by 5.4×. We further develop a Huffman tree scheduler to improve the scalability of the merger for larger sparse matrices, which reduces the DRAM access by another 1.8×. We also resolve the increased input matrix read induced by the new representation using a row prefetcher with near-optimal buffer replacement policy, further reducing the DRAM access by 1.5×. Evaluated on 20 benchmarks, SpArch reduces the total DRAM access by 2.8× over previous state-of-the-art. On average, SpArch achieves 4×, 19×, 18×, 17×, 1285× speedup and 6×, 164×, 435×, 307×, 62× energy savings over OuterSPACE, MKL, cuSPARSE, CUSP, and ARM Armadillo, respectively.

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Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation

Cited by 20 publications

References 22 publications

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

SpArch: Efficient Architecture for Sparse Matrix Multiplication

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