Biomedical subjects
Publications and source records attributed to Thomas Gilbert.
We present numerical evidence supporting the validity of the Gallavotti-Cohen fluctuation theorem applied to the driven Lorentz gas with Nosé-Hoover thermostating. It is moreover argued that the asymptotic form of the fluctuation formula is independent of the amplitude of the driving force in the limit where it is small.
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three systems, the particles typically drift at constant velocity and spread ballistically. These transport properties are analyzed in terms of the spectral properties of the operator evolving the probability densities. For systems (i) and (ii), we explain the drift from the properties of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors.
The purpose of this prospective study was to compare the pseudarthrosis rate after anterior cervical fusion, estimated either with static and dynamic plain radiographs or with two-dimensional CT-scans. There is a plethora of radiographic tools and criteria used to determine pseudarthrosis after cervical spine fusion. However, it is not known to which extent these tools correlate with each other. Forty-seven adult patients were enrolled in this study, about one year after surgery. Four independent blinded observers evaluated the roentgenological data. CT assessment led to higher pseudarthrosis rates than plain radiographs: 13 to 31% according to CT; 2 to 16% according to plain radiographs. The difference averaged 11%. Consistency between reviewers was higher with CT (average agreement: 89%; range 82%-96%) than with plain radiographs (average agreement: 81%; range: 76% to 87%). The need to accurately document pseudarthrosis is critical as it helps direct the postoperative management of the patient. The present study stresses the value of computed tomography. However, surgical exploration continues to be the gold standard.
This communication describes the computation of slow modes in a generic shell model of passive turbulent advection. It is argued that the propagator for the correlation functions possesses a ladder of slow modes associated with each zero mode. These slow modes decay algebraically fast, as opposed to exponential. Using the explicit form of the propagator of the 2-point structure function, we show that the slow modes structure for the generic case is analogous to the case of a Gaussian correlated advecting field, for which the differential structure of the operator allows a direct computation of these modes. Numerical computations of the slow modes are performed and compare very well to our results.
Active turbulent advection is considered in the context of magnetohydrodynamics. In this case, an auxiliary passive field bears no apparent connection to the active field. The scaling properties of the two fields are different. In the framework of a shell model, we show that the two-point structure function of the passive field has a unique zero mode, characterizing the scaling of this field only. In other words, the existence of statistical invariants for the decaying passive field carries no information on the scaling properties of the active field.
Early psychological adjustment (PA) of mothers of children with cancer (MCC) and mothers of children with acute illnesses (MCA) were compared, and predictors and mediators of maternal adjustment were tested. Sixty-nine MCC and 22 MCA completed standardized measures of depression, anxiety, global mental health (GMH), concurrent stress and strains, social support, coping strategies and child behavior. MCC reported greater depressive symptomatology, emotion-focused coping, and social support than did MCA. For MCC, emotion-focused coping and child behavior both predicted depression, anxiety, and GMH; concurrent stress and strain mediated the relationship between child behavior and depression and between emotion-focused coping and each measure of adjustment. For MCA, only emotion-focused coping predicted PA and concurrent stress and strains mediated the relationship between emotion-focused coping and depression. These findings suggest that MCC have more PA difficulties that are uniquely related to their child's behavior than MCA. Concurrent stress and strains seems to be an important mediator of PA for both groups of mothers.
We have recently proposed that the statistics of active fields (which affect the velocity field itself) in well-developed turbulence are also dominated by the statistically preserved structures of auxiliary passive fields which are advected by the same velocity field. The statistically preserved structures are eigenmodes of eigenvalue 1 of an appropriate propagator of the decaying (unforced) passive field, or equivalently, the zero modes of a related operator. In this paper we investigate further this surprising finding via two examples of shell models, one akin to turbulent convection in which the temperature is the active scalar, and the other akin to magnetohydrodynamics in which the magnetic field is the active vector. In the first example, all the even correlation functions of the active and passive fields exhibit identical scaling behavior. The second example appears at first sight to be a counterexample: the statistical objects of the active and passive fields have entirely different scaling exponents. We demonstrate, nevertheless, that the statistically preserved structures of the passive vector dominate again the statistics of the active field, except that due to a dynamical conservation law the amplitude of the leading zero mode cancels exactly. The active vector is then dominated by the subleading zero mode of the passive vector. Our work thus suggests that the statistical properties of active fields in turbulence can be understood with the same generality as those of passive fields.
We consider shell models that display an inverse energy cascade similar to two-dimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasiequilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of an inverse cascade regime with Kolmogorov scaling. The latter regime is found where predicted, offering a useful model to study inverse cascades.
It was conjectured recently that statiscally preserved structures underlie the statistical physics of turbulent transport processes. We analyze here in detail the time-dependent (noncompact) linear operator that governs the dynamics of correlation functions in the case of shell models of passive scalar advection. The problem is generic in the sense that the driving velocity field is neither Gaussian nor delta correlated in time. We show how to naturally discuss the dynamics in terms of an effective compact operator that displays "zero modes," which determine the anomalous scaling of the correlation functions. Since shell models have neither a Lagrangian structure nor "shape dynamics," this example differs significantly from standard passive scalar advection. Nevertheless, with the necessary modifications, the generality and efficacy of the concept of statistically preserved structures are further exemplified. In passing we point out a bonus of the present approach, in providing analytic predictions for the time-dependent correlation functions in decaying turbulent transport.
For a class of dynamical systems, called the axiom-A systems, Sinai, Ruelle and Bowen showed the existence of an invariant measure (SRB measure) weakly attracting the temporal average of any initial distribution that is absolutely continuous with respect to the Lebesgue measure. Recently, the SRB measures were found to be related to the nonequilibrium stationary state distribution functions for thermostated or open systems. Inspite of the importance of these SRB measures, it is difficult to handle them analytically because they are often singular functions. In this article, for three kinds of Baker-type maps, the SRB measures are analytically constructed with the aid of a functional equation, which was proposed by de Rham in order to deal with a class of singular functions. We first briefly review the properties of singular functions including those of de Rham. Then, the Baker-type maps are described, one of which is nonconservative but time reversible, the second has a Cantor-like invariant set, and the third is a model of a simple chemical reaction R<-->I<-->P. For the second example, the cases with and without escape are considered. For the last example, we consider the reaction processes in a closed system and in an open system under a flux boundary condition. In all cases, we show that the evolution equation of the distribution functions partially integrated over the unstable direction is very similar to de Rham's functional equation and, employing this analogy, we explicitly construct the SRB measures. (c) 1998 American Institute of Physics.
BACKGROUND: Ensuring the appropriate use of migraine therapies is an important consideration for care providers, patients, employers, and managed care organizations (MCOs) because of the high cost of treatment for this fairly prevalent disabling disease. A review of utilization of serotonin 5-HT1 receptor agonists (triptans) in an MCO determined that about 24% of the patients who received triptan therapy exceeded the manufacturers. recommendations regarding the maximum daily dose and safe treatment guidelines in a 30-day period. An initiative was designed to manage the coverage of migraine abortive therapies with the anticipated outcome of decreasing potential misuse or overuse of the medications. OBJECTIVE: The objective of this retrospective, observational study was to determine the impact of a monthly drug-specific milligram coverage maximum (quantity limit) on serotonin 5-HT1 receptor agonists (triptans) and dihydroergotamine (DHE) nasal spray on the utilization and costs of migraine care in an MCO with approximately 600000 covered members. METHODS: A longitudinal, retrospective cohort analysis was conducted. All migraine-related services were analyzed, including outpatient medical visits, emergency department utilization, inpatient hospitalizations, and outpatient prescription drug use. The analysis was conducted using medical and pharmacy administrative claims. Analysis of data was performed for the period 12 months prior (October 1999 to September 2000) and 18 months postimplementation of the monthly drug-specific milligram coverage maximum (October 2000 through March 2002). RESULTS: Imposition of a monthly coverage maximum for migraine-abortive therapies was associated with a 26.1% reduction in overall per- patient-per-month (PPPM) medical costs for migraine care, from US dollars 55.52 PPPM to US dollars 41.02 PPPM (P<0.01). Utilization of serotonin 5-HT1 receptor agonists and DHE nasal spray declined by 16.7%, from 0.18 prescriptions PPPM to 0.15 prescriptions PPPM (P=0.039), and direct drug costs declined by 28.8%, from US dollars 29.18 PPPM to US dollars 20.78 PPPM (P<0.001). Utilization and costs of outpatient and inpatient migraine-related medical services declined by 40% from US dollars 16.58 PPPM in the preperiod to US dollars 9.94 PPPM in the postperiod (P<0.001). CONCLUSION: A monthly drug-specific milligram coverage maximum was associated with significant reduction in drug costs and utilization of serotonin 5-HT1 receptor agonists (triptans) and DHE nasal spray. Utilization and costs of migraine-related medical services also declined after implementation of the coverage maximum for triptans and DHE nasal spray. The monthly drug-specific milligram coverage maximum appeared to have been successful in managing utilization of triptans and DHE nasal spray, including reduction of overall costs of migraine-related medical services and direct drug costs.