The Computational Complexity of Generating Random Fractals

In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation that can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.Comment: 28 pages, LATEX, 8 Postscript figures available from [email protected]

Rethinking the definition of major trauma: The need for trauma intervention outperforms Injury Severity Score and Revised Trauma Score in 38 adult and pediatric trauma centers

BACKGROUND Patients\u27 trauma burdens are a combination of anatomic damage, physiologic derangement, and the resultant depletion of reserve. Typically, Injury Severity Score (ISS) \u3e15 defines major anatomic injury and Revised Trauma Score (RTS) \u3c7.84 defines major physiologic derangement, but there is no standard definition for reserve. The Need For Trauma Intervention (NFTI) identifies severely depleted reserves (NFTI+) with emergent interventions and/or early mortality. We hypothesized NFTI would have stronger associations with outcomes and better model fit than ISS and RTS. METHODS Thirty-eight adult and pediatric U.S. trauma centers submitted data for 88,488 encounters. Mixed models tested ISS greater than 15, RTS less than 7.84, and NFTI\u27s associations with complications, survivors\u27 discharge to continuing care, and survivors\u27 length of stay (LOS). RESULTS The NFTI had stronger associations with complications and LOS than ISS and RTS (odds ratios [99.5% confidence interval]: NFTI = 9.44 [8.46-10.53]; ISS = 5.94 [5.36-6.60], RTS = 4.79 [4.29-5.34]; LOS incidence rate ratios (99.5% confidence interval): NFTI = 3.15 [3.08-3.22], ISS = 2.87 [2.80-2.94], RTS = 2.37 [2.30-2.45]). NFTI was more strongly associated with continuing care discharge but not significantly more than ISS (relative risk [99.5% confidence interval]: NFTI = 2.59 [2.52-2.66], ISS = 2.51 [2.44-2.59], RTS = 2.37 [2.28-2.46]). Cross-validation revealed that in all cases NFTI\u27s model provided a much better fit than ISS greater than 15 or RTS less than 7.84. CONCLUSION In this multicenter study, NFTI had better model fit and stronger associations with the outcomes than ISS and RTS. By determining depletion of reserve via resource consumption, NFTI+ may be a better definition of major trauma than the standard definitions of ISS greater than 15 and RTS less than 7.84. Using NFTI may improve retrospective triage monitoring and statistical risk adjustments. LEVEL OF EVIDENCE Prognostic, level IV