Making big steps in trajectories

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a similar computation time

Parameterized Uniform Complexity in Numerics: from Smooth to Analytic, from NP-hard to Polytime

The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are known to map (even high-order differentiable) polynomial-time computable functions to instances which are `hard' for classical complexity classes NP, #P, and CH; but, restricted to analytic functions, map polynomial-time computable ones to polynomial-time computable ones -- non-uniformly! We investigate the uniform parameterized complexity of the above operators in the setting of Weihrauch's TTE and its second-order extension due to Kawamura&Cook (2010). That is, we explore which (both continuous and discrete, first and second order) information and parameters on some given f is sufficient to obtain similar data on Max(f) and int(f); and within what running time, in terms of these parameters and the guaranteed output precision 2^(-n). It turns out that Gevrey's hierarchy of functions climbing from analytic to smooth corresponds to the computational complexity of maximization growing from polytime to NP-hard. Proof techniques involve mainly the Theory of (discrete) Computation, Hard Analysis, and Information-Based Complexity

Jordan Areas and Grids

AbstractJordan curves can be used to represent special subsets of the Euclidean plane, either the (open) interior of the curve or the (compact) union of the interior and the curve itself. We compare the latter with other representations of compact sets using grids of points and we are able to show that knowing the length of a rectifiable curve is sufficient to translate from the grid representation to the Jordan curve

Computational Complexity of Iterated Maps on the Interval (Extended Abstract)

The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. As a main result, the computational complexity measure considered here is related to the Ljapunow exponent of the dynamical system under consideration

High frequency oscillatory ventilation compared with conventional mechanical ventilation in adult respiratory distress syndrome: a randomized controlled trial [ISRCTN24242669]

INTRODUCTION: To compare the safety and efficacy of high frequency oscillatory ventilation (HFOV) with conventional mechanical ventilation (CV) for early intervention in adult respiratory distress syndrome (ARDS), a multi-centre randomized trial in four intensive care units was conducted. METHODS: Patients with ARDS were randomized to receive either HFOV or CV. In both treatment arms a priority was given to maintain lung volume while minimizing peak pressures. CV ventilation strategy was aimed at reducing tidal volumes. In the HFOV group, an open lung strategy was used. Respiratory and circulatory parameters were recorded and clinical outcome was determined at 30 days of follow up. RESULTS: The study was prematurely stopped. Thirty-seven patients received HFOV and 24 patients CV (average APACHE II score 21 and 20, oxygenation index 25 and 18 and duration of mechanical ventilation prior to randomization 2.1 and 1.5 days, respectively). There were no statistically significant differences in survival without supplemental oxygen or on ventilator, mortality, therapy failure, or crossover. Adjustment by a priori defined baseline characteristics showed an odds ratio of 0.80 (95% CI 0.22–2.97) for survival without oxygen or on ventilator, and an odds ratio for mortality of 1.15 (95% CI 0.43–3.10) for HFOV compared with CV. The response of the oxygenation index (OI) to treatment did not differentiate between survival and death. In the HFOV group the OI response was significantly higher than in the CV group between the first and the second day. A post hoc analysis suggested that there was a relatively better treatment effect of HFOV compared with CV in patients with a higher baseline OI. CONCLUSION: No significant differences were observed, but this trial only had power to detect major differences in survival without oxygen or on ventilator. In patients with ARDS and higher baseline OI, however, there might be a treatment benefit of HFOV over CV. More research is needed to establish the efficacy of HFOV in the treatment of ARDS. We suggest that future studies are designed to allow for informative analysis in patients with higher OI

Group Polarization in the Team Dictator Game reconsidered

While most papers on team decision-making find teams to behave more selfish, less trusting and less altruistic than individuals, Cason and Mui (1997) report that teams are more altruistic than individuals in a dictator game. Using a within-subjects design we re-examine group polarization by letting subjects make individual as well as team decisions in an experimental dictator game. In our experiment teams are more selfish than individuals, and the most selfish team member has the strongest influence on team decisions. Various sources of the different findings in Cason and Mui (1997) and in our paper are discussed

Ruling out coronary heart disease in primary care patients with chest pain: a clinical prediction score

Chest pain raises concern for the possibility of coronary heart disease. Scoring methods have been developed to identify coronary heart disease in emergency settings, but not in primary care. Data were collected from a multicenter Swiss clinical cohort study including 672 consecutive patients with chest pain, who had visited one of 59 family practitioners' offices. Using delayed diagnosis we derived a prediction rule to rule out coronary heart disease by means of a logistic regression model. Known cardiovascular risk factors, pain characteristics, and physical signs associated with coronary heart disease were explored to develop a clinical score. Patients diagnosed with angina or acute myocardial infarction within the year following their initial visit comprised the coronary heart disease group. The coronary heart disease score was derived from eight variables: age, gender, duration of chest pain from 1 to 60 minutes, substernal chest pain location, pain increasing with exertion, absence of tenderness point at palpation, cardiovascular risks factors, and personal history of cardiovascular disease. Area under the receiver operating characteristics curve was of 0.95 with a 95% confidence interval of 0.92; 0.97. From this score, 413 patients were considered as low risk for values of percentile 5 of the coronary heart disease patients. Internal validity was confirmed by bootstrapping. External validation using data from a German cohort (Marburg, n = 774) revealed a receiver operating characteristics curve of 0.75 (95% confidence interval, 0.72; 0.81) with a sensitivity of 85.6% and a specificity of 47.2%. This score, based only on history and physical examination, is a complementary tool for ruling out coronary heart disease in primary care patients complaining of chest pain

In vivo imaging of pancreatic tumours and liver metastases using 7 Tesla MRI in a murine orthotopic pancreatic cancer model and a liver metastases model

<p>Abstract</p> <p>Background</p> <p>Pancreatic cancer is the fourth leading cause of tumour death in the western world. However, appropriate tumour models are scarce. Here we present a syngeneic murine pancreatic cancer model using 7 Tesla MRI and evaluate its clinical relevance and applicability.</p> <p>Methods</p> <p>6606PDA murine pancreatic cancer cells were orthotopically injected into the pancreatic head. Liver metastases were induced through splenic injection. Animals were analyzed by MRI three and five weeks following injection. Tumours were detected using T2-weighted high resolution sequences. Tumour volumes were determined by callipers and MRI. Liver metastases were analyzed using gadolinium-EOB-DTPA and T1-weighted 3D-Flash sequences. Tumour blood flow was measured using low molecular gadobutrol and high molecular gadolinium-DTPA.</p> <p>Results</p> <p>MRI handling and applicability was similar to human systems, resolution as low as 0.1 mm. After 5 weeks tumour volumes differed significantly (p < 0.01) when comparing calliper measurments (n = 5, mean 1065 mm³+/-243 mm³) with MRI (mean 918 mm³+/-193 mm³) with MRI being more precise. Histology (n = 5) confirmed MRI tumour measurements (mean size MRI 38.5 mm²+/-22.8 mm²versus 32.6 mm²+/-22.6 mm²(histology), p < 0,0004) with differences due to fixation and processing of specimens. After splenic injection all mice developed liver metastases with a mean of 8 metastases and a mean volume of 173.8 mm³+/-56.7 mm³after 5 weeks. Lymphnodes were also easily identified. Tumour accumulation of gadobutrol was significantly (p < 0.05) higher than gadolinium-DTPA. All imaging experiments could be done repeatedly to comply with the 3R-principle thus reducing the number of experimental animals.</p> <p>Conclusions</p> <p>This model permits monitoring of tumour growth and metastasis formation in longitudinal non-invasive high-resolution MR studies including using contrast agents comparable to human pancreatic cancer. This multidisciplinary environment enables radiologists, surgeons and physicians to further improve translational research and therapies of pancreatic cancer.</p