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Data analytics using workflows is an iterative process, in which an analyst makes many iterations of changes, such as additions, deletions, and alterations of operators and their links. In many cases, the analyst wants to compare these workflow versions and their execution results to help in deciding the next iterations of changes. Moreover, the analyst needs to know which versions produced undesired results to avoid refining the workflow in those versions. To enable the analyst to get an overview of the workflow versions and their results, we introduce Drove, a framework that manages the end-to-end lifecycle of constructing, refining, and executing workflows on large data sets and provides a dashboard to monitor these execution results. In many cases, the result of an execution is the same as the result of a prior execution. Identifying such equivalence between the execution results of different workflow versions is important for two reasons. First, it can help us reduce the storage cost of the results by storing equivalent results only once. Second, stored results of early executions can be reused for future executions with the same results. Existing tools that track such executions are geared towards small-scale data and lack the means to reuse existing results in future executions. In Drove, we reason the semantic equivalence of the workflow versions to reduce the storage space and reuse the materialized results.
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A local Hopf lemma and unique continuation for elliptic equations
We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations. The work is motivated by and generalizes the main results of X. Huang et al. in [15] and [16], and M.S. Baouendi and L.P. Rothschild in [5].
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- Award ID(s):
- 1855737
- PAR ID:
- 10330509
- Editor(s):
- Yanyan Li
- Date Published:
- Journal Name:
- Advances in mathematics
- Volume:
- 389
- Issue:
- 8
- ISSN:
- 0001-8708
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.aim.2021.107912
