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BackgroundSince biological systems are complex and often involve multiple types of genomic relationships, tensor analysis methods can be utilized to elucidate these hidden complex relationships. There is a pressing need for this, as the interpretation of the results of high‐throughput experiments has advanced at a much slower pace than the accumulation of data. ResultsIn this review we provide an overview of some tensor analysis methods for biological systems. ConclusionsTensors are natural and powerful generalizations of vectors and matrices to higher dimensions and play a fundamental role in physics, mathematics and many other areas. Tensor analysis methods can be used to provide the foundations of systematic approaches to distinguish significant higher order correlations among the elements of a complex systems via finding ensembles of a small number of reduced systems that provide a concise and representative summary of these correlations.
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A Hybrid Regularization for the Navier–Stokes Equations
ABSTRACT In 1991 Ramshaw and Mesina proposed a novel synthesis of penalty methods and artificial compression methods. When the two were balanced they found the combination was 3–4 orders more accurate than either alone. This report begins developing a mathematical foundation addressing the reliability of their interesting method. We perform stability analysis, semi‐discrete error analysis, and tests of the algorithm.
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- Award ID(s):
- 2110379
- PAR ID:
- 10577003
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Numerical Methods for Partial Differential Equations
- Volume:
- 41
- Issue:
- 2
- ISSN:
- 0749-159X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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