Determining the germination speed is essential in experiments in the field of seed technology, as it allows the performance evaluation of a seed lot and the creation of predictive models. To this end, the literature addresses several methods and indexes. The objective of this study was to compare the main methods of emergence speed analysis in seeds, namely the non-linear regression models and the Emergence Speed Index (ESI), with the time-to-event models. The research was conducted with peach palm seeds (Bactris gasipaes) that were measured for viability and vigour through daily evaluations for 4 months. Vigour was evaluated by the quantification of the seed emergence speed, which was performed in three ways: ESI, non-linear regression and non-linear regression considering germination as a time-to-event event. From the results obtained, we conclude that the ESI is not a good indicator to evaluate the emergence speed; the non-linear regression model underestimates the errors and, thus, increases the probability of misclassifying treatments; the time-to-event model is more reliable in classifying treatments according to the emergence speed.

Piloting in the Panama Canal is exceptional as, due to its importance, the functions of the captains of vessels are taken over by pilots. Hence, prior to inauguration of the expanded canal, a limited number of pilots experienced on the existing canal were certified for the transit of Neopanamax vessels by means of planned and innovative individual learning. After this organisational training through operative training, with the implementation of the expanded canal in June 2016, the routine training started. Hence the learning curve in the performance of these manoeuvres will represent the growing skill acquired by both the pilots and the organisation. Given that the learning effect is measurable, this paper has the dual objective of determining two curve models: the organisation operative learning curve model and the routine learning curve model for pilots performing transit manoeuvres in the expanded Panama Canal waterways and the Cocolí and Agua Clara locks. Manoeuvre times in locks and transit in the whole of the canal were followed up continuously in the first 42 months of operation.

Dose-response studies are an important tool in weed science. The use of such studies has become especially prevalent following the widespread development of herbicide resistant weeds. In the past, analyses of dose-response studies have utilized various types of transformations and equations which can be validated with several statistical techniques. Most dose-response analysis methods 1) do not accurately describe data at the extremes of doses and 2) do not provide a proper statistical test for the difference(s) between two or more dose-response curves. Consequently, results of dose-response studies are analyzed and reported in a great variety of ways, and comparison of results among various researchers is not possible. The objective of this paper is to review the principles involved in dose-response research and explain the log-logistic analysis of herbicide dose-response relationships. In this paper the log-logistic model is illustrated using a nonlinear computer analysis of experimental data. The log-logistic model is an appropriate method for analyzing most dose-response studies. This model has been used widely and successfully in weed science for many years in Europe. The log-logistic model possesses several clear advantages over other analysis methods and the authors suggest that it should be widely adopted as a standard herbicide dose-response analysis method.

Dynamic models which predict changes in the intensity of schistosome infection with host age are fitted to pre-intervention Schistosoma mansoni data from Kenya. Age-specific post-treatment-reinfection data are used to estimate the force of infection, thus enabling investigation of the rate of worm death. An empirical and statistical approach is taken to the model fitting: where possible, distributional properties and function relationships are obtained from the data rather than assumed from theory. Attempts are made to remove known sources of bias. Maximum likelihood techniques, employed to allow for error in both the pre-intervention and reinfection data, yield confidence intervals for the worm life-span (CI95% = 5·7–10·5 years) and demonstrate that the worm death rate is unlikely to vary with host age. The possibilities and limitations of fitting dynamic models to data are discussed. We conclude that a detailed, quantitative approach will be necessary if progress is to be made with the interpretation of epidemiological data and the models intended to describe them.

While investigating germinability in the new-crop meadowfoam (Limnanthes alba Benth.), it was desired to gain maximum information despite minimal seed material and prior knowledge. Extended use of the Richards function in a factorial germination experiment proved very powerful. The functions yielded estimates of four correlated coefficients, requiring multivariate analysis of variance (MANOVA) to provide valid F-tests among germination profiles. These germination functions provided more rigorous discrimination among treatments than the univariate final germination level. The functions for the imbibants KNO3 and GA4+7, in darkness at 10/5°C, were best, being characterized by high mean absolute germination rate, relatively short duration, and high final germination (upper asymptote). The results provided insights into possible dormancy mechanisms.

The thermal resistance of the lactococcal bacteriophage P008 was investigated between 55 and 80 °C. Inactivation kinetics revealed an order of reaction above 1 and could be determined by a non-1st-order regression model. Phage inactivation was influenced by the medium (milk and Ca-M17-broth). Within the investigated temperature range, milk had a protective effect on phage P008. This was reflected in the rate constant and in the activation energy. Thermal phage inactivation studies reported in literature were re-analysed using non-1st-order regression. The obtained kinetic parameters showed that phage P008 belongs to the most heat resistant lactococcal phages investigated so far.

An in vitro method applying Michaelis–Menten saturation kinetics was developed as an alternative approach for estimating protein degradation rates in the rumen. Non-linear regression (NLR) analysis of the integrated Michaelis–Menten equation yielded fractional degradation rates, kd, from direct estimates of the maximum velocity: Michaelis constant ratio (kd = Vmax: Km). Degradation rates obtained using data from a series of 2 h inhibitor in vitro incubations were respectively 0.989, 0.134, and 0.037 /h for casein, solvent soya-bean meal (SSBM) and expeller soya-bean meal (ESBM). Degradation rates obtained from 2 h incubations had lower standard errors than those obtained using 1 h incubations; 2 h rates were not significantly different from 1 h rates, suggesting end-product inhibition was not significant at 2 h. The NLR Michaelis–Menten method was used to determine degradation rates for twelve protein sources: casein, bovine serum albumin, two samples of lucerne (Medicago sativa) hay, and four samples each of SSBM and ESBM. Statistical analysis of NLR results revealed significant differences among the twelve protein sources. Casein was degraded most rapidly (0.827 /h), and the four ESBM samples most slowly (0.050–0.098 /h). Degradation rate for serum albumin was 0.135 /h; rates for SSBM and lucerne hays ranged from 0.160 to 0.208 /h. Degradation rates estimated using the NLR method were more rapid than those obtained with a limited substrate approach; NLR rates were more consistent with in vivo estimates of rumen protein escape. Greater concentrations of slowly degraded proteins were needed with the NLR method to define curvilinearity of the degradation curve more accurately.

Protein degradation rate: Rumen protein escape: Michaelis–Menten kinetics: Non-linear regression

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j in a subset of Rp and θ is a finite-dimensional parameter. The particular cases of 0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j} are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient.

Contributions of the paper include: study of the Rp case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j} is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.

Wahba (1978) and Weinert et al. (1980), using different models, show that an optimal smoothing spline can be thought of as the conditional expectation of a stochastic process observed with noise. This observation leads to efficient computational algorithms. By going back to the Hilbert space formulation of the spline minimization problem, we provide a framework for linking the two different stochastic models. The last part of the paper reviews some new efficient algorithms for spline smoothing.

Very general forms of the strong law of large numbers and the central limit theorem are proved for estimates of the unknown parameters in a sinusoidal oscillation observed subject to error. In particular when the unknown frequency θ0, is in fact 0 or <it is shown that the estimate, , satisfies for N ≧ N0 (ω) where N0 (ω) is an integer, determined by the realisation, ω, of the process, that is almost surely finite.