Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Does cardiovascular therapy affect the onset and recurrence of preretinal and vitreous haemorrhage in diabetic eye disease?

Aims To review the role of cardiovascular disease and therapy in the onset and recurrence of preretinal/vitreous haemorrhage in diabetic patients. Methods Retrospective case note analysis of diabetic patients with vitreous haemorrhage from the Diabetic Eye Clinic at Birmingham Heartlands Hospital. Results In total, 54 patients (mean age 57.1, 37 males, 20 type I vs34 type II diabetic patients) were included. The mean (SD) duration of diagnosed diabetes at first vitreous haemorrhage was significantly longer, 21.9 (7.6) years for type I and 14.8 (9.3) years for type II diabetic patients (P<0.01, unpaired t-test, two-tailed). Aspirin administration was not associated with a significantly later onset of vitreous haemorrhage. Four episodes were associated with ACE-inhibitor cough. There was a trend towards HMGCoA reductase inhibitor (statin) use being associated with a delayed onset of vitreous haemorrhage: 21.4 years until vitreous haemorrhage (treatment group) vs 16.2 years (nontreatment group) (P=0.09, two-tailed, unpaired t-test, not statistically significant). During follow-up 56 recurrences occurred, making a total of 110 episodes of vitreous haemorrhage in 79 eyes of 54 patients. The mean (range) follow-up post haemorrhage was 1067 (77–3842) days, with an average of 1.02 recurrences. Age, gender, diabetes type (I or II) or control, presence of hypertension or hypercholesterolaemia, and macrovascular complications were not associated with a significant effect on the 1-year recurrence rate. Aspirin (and other antiplatelet or anticoagulant agents) and ACE- inhibitors appeared to neither increase nor decrease the 1-year recurrence rate. However, statin use was significantly associated with a reduction in recurrence (Fisher exact P<0.05; two-tailed) with an odds ratio (95% CI) of 0.25 (0.1–0.95). Conclusion In this retrospective analysis, the onset of preretinal/vitreous haemorrhage was not found to be accelerated by gender, hypertension, hypercholesterolaemia, evidence of macrovascular disease, or HbA1c. Neither aspirin nor ACE-inhibitor administration accelerated the onset or recurrence of first vitreous haemorrhage. Statins may have a protective role, both delaying and reducing the recurrence of haemorrhage.