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Abstract COVID-19-associated respiratory failure offers the unprecedented opportunity to evaluate the differential host response to a uniform pathogenic insult. Understanding whether there are distinct subphenotypes of severe COVID-19 may offer insight into its pathophysiology. Sequential Organ Failure Assessment (SOFA) score is an objective and comprehensive measurement that measures dysfunction severity of six organ systems, i.e., cardiovascular, central nervous system, coagulation, liver, renal, and respiration. Our aim was to identify and characterize distinct subphenotypes of COVID-19 critical illness defined by the post-intubation trajectory of SOFA score. Intubated COVID-19 patients at two hospitals in New York city were leveraged as development and validation cohorts. Patients were grouped into mild, intermediate, and severe strata by their baseline post-intubation SOFA. Hierarchical agglomerative clustering was performed within each stratum to detect subphenotypes based on similarities amongst SOFA score trajectories evaluated by Dynamic Time Warping. Distinct worsening and recovering subphenotypes were identified within each stratum, which had distinct 7-day post-intubation SOFA progression trends. Patients in the worsening suphenotypes had a higher mortality than those in the recovering subphenotypes within each stratum (mild stratum, 29.7% vs. 10.3%, p = 0.033; intermediate stratum, 29.3% vs. 8.0%, p = 0.002; severe stratum, 53.7% vs. 22.2%, p < 0.001). Pathophysiologic biomarkers associated with progression were distinct at each stratum, including findings suggestive of inflammation in low baseline severity of illness versus hemophagocytic lymphohistiocytosis in higher baseline severity of illness. The findings suggest that there are clear worsening and recovering subphenotypes of COVID-19 respiratory failure after intubation, which are more predictive of outcomes than baseline severity of illness. Distinct progression biomarkers at differential baseline severity of illness suggests a heterogeneous pathobiology in the progression of COVID-19 respiratory failure. 

In this paper, we investigate a certain class of tile-based pattern games through a simplified version of a recent game titled Nonads. We prove that Nonads is PSPACE-complete with a reduction from bounded 2-player constraint logic (Bounded 2CL) even when both players share the same target and there is only one type of playable tile. This has application to any grid-based pattern building game.