Regularity Result for Quasilinear Elliptic Systems with Super Quadratic Natural Growth Condition

We consider boundary regularity for weak solutions of second-order quasilinear elliptic systems under natural growth condition with super quadratic growth and obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. Combined with existing results on interior partial regularity, this result yields an upper bound on the Hausdorff dimension of the singular set at the boundary

Process-oriented Iterative Multiple Alignment for Medical Process Mining

Adapted from biological sequence alignment, trace alignment is a process mining technique used to visualize and analyze workflow data. Any analysis done with this method, however, is affected by the alignment quality. The best existing trace alignment techniques use progressive guide-trees to heuristically approximate the optimal alignment in O(N2L2) time. These algorithms are heavily dependent on the selected guide-tree metric, often return sum-of-pairs-score-reducing errors that interfere with interpretation, and are computationally intensive for large datasets. To alleviate these issues, we propose process-oriented iterative multiple alignment (PIMA), which contains specialized optimizations to better handle workflow data. We demonstrate that PIMA is a flexible framework capable of achieving better sum-of-pairs score than existing trace alignment algorithms in only O(NL2) time. We applied PIMA to analyzing medical workflow data, showing how iterative alignment can better represent the data and facilitate the extraction of insights from data visualization.Comment: accepted at ICDMW 201

Evaluation of Trace Alignment Quality and its Application in Medical Process Mining

Trace alignment algorithms have been used in process mining for discovering the consensus treatment procedures and process deviations. Different alignment algorithms, however, may produce very different results. No widely-adopted method exists for evaluating the results of trace alignment. Existing reference-free evaluation methods cannot adequately and comprehensively assess the alignment quality. We analyzed and compared the existing evaluation methods, identifying their limitations, and introduced improvements in two reference-free evaluation methods. Our approach assesses the alignment result globally instead of locally, and therefore helps the algorithm to optimize overall alignment quality. We also introduced a novel metric to measure the alignment complexity, which can be used as a constraint on alignment algorithm optimization. We tested our evaluation methods on a trauma resuscitation dataset and provided the medical explanation of the activities and patterns identified as deviations using our proposed evaluation methods.Comment: 10 pages, 6 figures and 5 table