Abstract-In this paper we show that the (co)chain complex associated with a decomposition of the computational domain, commonly called a mesh in computational science and engineering, can be represented by a block-bidiagonal matrix that we call the Hasse matrix. Moreover, we show that topology-preserving mesh refinements, produced by the action of (the simplest) Euler operators, can be reduced to multilinear transformations of the Hasse matrix representing the complex. Our main result is a new representation of the (co)chain complex underlying field computations, a representation that provides new insights into the transformations induced by local mesh refinements. Our approach is based on first principles and is general in that it applies to most representational domains that can be characterized as cell complexes, without any restrictions on their type, dimension, codimension, orientability, manifoldness, connectedness.
Motivation
Oxford Nanopore technologies (ONT) add miniaturization and real-time to high-throughput sequencing. All available software for ONT data analytics run on cloud/clusters or personal computers. Instead, a linchpin to true portability is software that works on mobile devices of internet connections. Smartphones’ and tablets’ chipset/memory/operating systems differ from desktop computers, but software can be recompiled. We sought to understand how portable current ONT analysis methods are.
Results
Several tools, from base-calling to genome assembly, were ported and benchmarked on an Android smartphone. Out of 23 programs, 11 succeeded. Recompilation failures included lack of standard headers and unsupported instruction sets. Only DSK, BCALM2 and Kraken were able to process files up to 16GB, with linearly scaling CPU-times. However, peak CPU temperatures were high. In conclusion, the portability scenario is not favorable. Given the fast market growth, attention of developers to ARM chipsets and Android/iOS is warranted, as well as initiatives to implement mobile-specific libraries.
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