Summary. We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations. Such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation. The paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non-linear differential equations. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. We derive estimates and confidence intervals, and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology. The performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus.Keywords: Differential equation; Dynamic system; Estimating equation; Functional data analysis; Gauss-Newton method; Parameter cascade; Profiled estimation Challenges in dynamic systems estimation Basic properties of dynamic systemsWe have in mind a process that transforms a set of m input functions u.t/ into a set of d output functions x.t/. Dynamic systems model output change directly by linking the output derivativeṡ x.t/ to x.t/ itself, as well as to inputs u:x.t/ = f.x, u, t|θ/, t ∈ [0, T ]:. 1/ Vector θ contains any parameters defining the system whose values are not known from experimental data, theoretical considerations or other sources of information. Systems involving derivatives of x of order n > 1 are reducible to expression (1) by defining new variables, x 1 = x and x 2 =ẋ 1 , . . . , x n =ẋ n−1 : Further generalizations of expression (1) are also candidates for the approach that is developed in this paper but will not be considered. Dependences of f on t other than through x and u arise when, for example, certain quantities defining the system are themselves time varying. Differential equations as a rule do not define their solutions uniquely, but rather as a manifold of solutions of typical dimension d. For example, d2 x=dt 2 = −ω 2 x.t/, reduced toẋ 1 = x 2 anḋ x 2 = −ω 2 x 1 , implies solutions of the form x 1 .t/ = c 1 sin.ωt/ + c 2 cos.ωt/, where coefficients c 1 and c 2 are arbitrary; and at least d = 2 observations are required to identify the solution that Address for correspondence: J. O. Ramsay, 2748 Howe Street, Ottawa, Ontario, K2B 6W9, Canada. E-mail: ramsay@psych.mcgill.ca 742 J. O. Ramsay, G. Hooker, D. Campbell and J. Cao best fits the data. Initial value problems supply x.0/, whereas boundary value problems require d values selected from x(0) and x.T/.However, we assume more generally that only a subset I of the d output variables x may be measured at time point...

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Diffusing capacity of the lung for nitric oxide (), otherwise known as the transfer factor, was first measured in 1983. This document standardises the technique and application of single-breath This panel agrees that 1) pulmonary function systems should allow for mixing and measurement of both nitric oxide (NO) and carbon monoxide (CO) gases directly from an inspiratory reservoir just before use, with expired concentrations measured from an alveolar "collection" or continuously sampled rapid gas analysers; 2) breath-hold time should be 10 s with chemiluminescence NO analysers, or 4-6 s to accommodate the smaller detection range of the NO electrochemical cell; 3) inspired NO and oxygen concentrations should be 40-60 ppm and close to 21%, respectively; 4) the alveolar oxygen tension ( ) should be measured by sampling the expired gas; 5) a finite specific conductance in the blood for NO (θNO) should be assumed as 4.5 mL·min·mmHg·mL of blood; 6) the equation for 1/θCO should be (0.0062· +1.16)·(ideal haemoglobin/measured haemoglobin) based on breath-holding and adjusted to an average haemoglobin concentration (male 14.6 g·dL, female 13.4 g·dL); 7) a membrane diffusing capacity ratio (/) should be 1.97, based on tissue diffusivity.

In this study sample, FLS simulator scores were independently predictive of intraoperative laparoscopic performance as measured by GOALS. More precisely, an FLS cutoff score of 70 optimized sensitivity and specificity for expert intraoperative performance. A larger prospective study is justified to validate these findings.