Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Induction in the timed interval calculus

The Timed Interval Calculus, a timed-trace formalism based on set theory, is introduced. It is extended with an induction law and a unit for concatenation, which facilitates the proof of properties over trace histories. The effectiveness of the extended Timed Interval Calculus is demonstrated via a benchmark case study, the mine pump. Specifically, a safety property relating to the operation of a mine shaft is proved, based on an implementation of the mine pump and assumptions about the environment of the mine. (C) 2002 Elsevier Science B.V. All rights reserved.

Temporal aspects of the VO2 response at the power output associated with VO2peak in well trained cyclists: Implications for interval training prescription

The power output achieved at peak oxygen consumption (VO2 peak) and the time this power can be maintained (i.e., Tmax) have been used in prescribing high-intensity interval training. In this context, the present study examined temporal aspects of the VO2 response to exercise at the cycling power that output well trained cyclists achieve their VO2 peak (i.e., Pmax). Following a progressive exercise test to determine VO2 peak, 43 well trained male cyclists (M age = 25 years, SD = 6; M mass = 75 kg SD = 7; M VO2 peak = 64.8 ml(.)kg(1.)min(-1), SD = 5.2) performed two Tmax tests 1 week apart.1. Values expressed for each participant are means and standard deviations of these two tests. Participants achieved a mean VO2 peak during the Tmax test after 176 s (SD = 40; = 74% of Tmax, SD = 12) and maintained it for 66 s (SD = 39; M = 26% of Tmax, SD = 12). Additionally they obtained mean 95 % of VO2 peak after 147 s (SD = 31; M = 62 % of Tmax, SD = 8) and maintained it for 95 s (SD = 38; M = 38 % of Tmax, SD = 8). These results suggest that 60-70% of Tmax is an appropriate exercise duration for a population of well trained cyclists to attain VO2 peak during exercise at Pmax. However due to intraparticipant variability in the temporal aspects of the VO2 response to exercise at Pmax, future research is needed to examine whether individual high-intensity interval training programs for well trained endurance athletes might best be prescribed according to an athlete's individual VO2 response to exercise at Pmax.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.

Pharmacokinetic-pharmacodynamic modelling of QT interval prolongation following citalopram overdoses

Aims To develop a pharmacokinetic-pharmacodynamic model describing the time-course of QT interval prolongation after citalopram overdose and to evaluate the effect of charcoal on the relative risk of developing abnormal QT and heart-rate combinations. Methods Plasma concentrations and electrocardiograph (ECG) data from 52 patients after 62 citalopram overdose events were analysed in WinBUGS using a Bayesian approach. The reported doses ranged from 20 to 1700 mg and on 17 of the events a single dose of activated charcoal was administered. The developed pharmacokinetic-pharmacodynamic model was used for predicting the probability of having abnormal combinations of QT-RR, which was assumed to be related to an increased risk for torsade de pointes (TdP). Results The absolute QT interval was related to the observed heart rate with an estimated individual heart-rate correction factor [alpha = 0.36, between-subject coefficient of variation (CV) = 29%]. The heart-rate corrected QT interval was linearly dependent on the predicted citalopram concentration (slope = 40 ms l mg(-1), between-subject CV = 70%) in a hypothetical effect-compartment (half-life of effect-delay = 1.4 h). The heart-rate corrected QT was predicted to be higher in women than in men and to increase with age. Administration of activated charcoal resulted in a pronounced reduction of the QT prolongation and was shown to reduce the risk of having abnormal combinations of QT-RR by approximately 60% for citalopram doses above 600 mg. Conclusion Citalopram caused a delayed lengthening of the QT interval. Administration of activated charcoal was shown to reduce the risk that the QT interval exceeds a previously defined threshold and therefore is expected to reduce the risk of TdP.

Highly demanding resistive vibration exercise program is tolerated during 56 days of strict bed-rest

Several studies have tried to find countermeasures against musculoskeletal de-conditioning during bed-rest, but none of them yielded decisive results. We hypothesised that resistive vibration exercise (RVE) might be a suitable training modality. We have therefore carried out a bed-rest study to evaluate its feasibility and efficacy during 56 days of bed-rest. Twenty healthy male volunteers aged 24 to 43 years were recruited and, after medical check-ups, randomised to a non-exercising control (Ctrl) group or a group that performed RVE 11 times per week. Strict bed-rest was controlled by video surveillance. The diet was controlled. RVE was performed in supine position, with a static force component of about twice the body weight and a smaller dynamic force component. RVE comprised four different units (squats, heel raises, toe raises, kicks), each of which lasted 60 - 100 seconds. Pre and post exercise levels of lactate were measured once weekly. Body weight was measured daily on a bed scale. Pain questionnaires were obtained in regular intervals during and after the bed-rest. Vibration frequency was set to 19 Hz at the beginning and progressed to 25.9 Hz (SD 1.9) at the end of the study, suggesting that the dynamic force component increased by 90%. The maximum sustainable exercise time for squat exercise increased from 86 s (SD 21) on day 11 of the BR to 176 s (SD 73) on day 53 (p = 0.006). On the same days, post-exercise lactate levels increased from 6.9 mmol/l (SD2.3) to 9.2 mmol/l (SD 3.5, p = 0.01). On average, body weight was unchanged in both groups during bed-rest, but single individuals in both groups depicted significant weight changes ranging from -10% to + d10% (p < 0.001). Lower limb pain was more frequent during bed-rest in the RVE subjects than in Ctrl (p = 0.035). During early recovery, subjects of both groups suffered from muscle pain to a comparable extent, but foot pain was more common in Ctrl than in RVE (p = 0.013 for plantar pain, p = 0.074 for dorsal foot pain). Our results indicate that RVE is feasible twice daily during bed-rest in young healthy males, provided that one afternoon and one entire day per week are free. Exercise progression, mainly by progression of vibration frequency, yielded increases in maximum sustainable exercise time and blood lactate. In conclusion, RVE as performed in this study, appears to be safe.

Sigmoidal cosine series on the interval

We construct a set of functions, say, psi([r])(n) composed of a cosine function and a sigmoidal transformation gamma(r) of order r > 0. The present functions are orthonormal with respect to a proper weight function on the interval [-1, 1]. It is proven that if a function f is continuous and piecewise smooth on [-1, 1] then its series expansion based on psi([r])(n) converges uniformly to f so long as the order of the sigmoidal transformation employed is 0 < r

Recurrence interval statistics of cellular automaton seismicity models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.

Relative predictive value of intraventricular dysynchrony in determining long-term outcome in patients with known or suspected coronary disease

Improvement of intra-ventricular dysynchrony (IVD) in pts undergoing bi-ventricular pacing is associated with clinical improvementbut little isknownabout the relationship between IVD and prognosis.We sought whether IVD influences long-term outcome in pts with known or suspected coronary disease (CAD). Tissue Doppler imaging was performed in 184 pts (aged 61±10 years, 67% male) prior to dobutamine echo. From velocity curves the interval between QRS onset and max systolic velocity (Ts) was measured in basal septal, lateral, inferior and anterior segments. The maximal difference in Ts between segments (TsMax) was used as a measure of IVD. The standard deviation (TsSD) between all segments and the septal-lateral difference (TsSL) were also calculated. Pts were followed up for a median interval of 5 years and a Cox model used for survival analysis. The medianwall motion index (WMI) was 1.3 (IQR 1.0–1.8) at rest and 1.4 (IQR 1.3–1.9) at stress. The table shows IVD parameters. Forty-one deaths occurred during follow-up. Pts who died during follow-up, compared to survivors, showed greater IVD. WMI at rest (p = 0.03) and peak stress (p = 0.02), TsSD (p = 0.06), TsSL (p = 0.02) and TsMax (p = 0.05) but not QRS width were univariate predictors of mortality. TsSL was the only independent predictor of death (p = 0.01). Therefore, IVD is common in pts with known or suspected CAD. Pts with more IVD have reduced long-term survival, independent of WMI.

Axiomatisation of an Interval Calculus for Theorem Proving

We provide an axiomatisation of the Timed Interval Calculus, a set-theoretic notation for expressing properties of time intervals. We implement the axiomatisation in the Ergo theorem prover in order to allow the machine-checked proof of laws for reasoning about predicates expressed using interval operators. These laws can be then used in the machine-assisted verification of real-time applications.