An extension of the continual reassessment method using decision theory

The primary goal of a phase I trial is to find the maximally tolerated dose (MTD) of a treatment. The MTD is usually defined in terms of a tolerable probability, q*, of toxicity. Our objective is to find the highest dose with toxicity risk that does not exceed q*, a criterion that is often desired in designing phase I trials. This criterion differs from that of finding the dose with toxicity risk closest to q*, that is used in methods such as the continual reassessment method. We use the theory of decision processes to find optimal sequential designs that maximize the expected number of patients within the trial allocated to the highest dose with toxicity not exceeding q*, among the doses under consideration. The proposed method is very general in the sense that criteria other than the one considered here can be optimized and that optimal dose assignment can be defined in terms of patients within or outside the trial. It includes as an important special case the continual reassessment method. Numerical study indicates the strategy compares favourably with other phase I designs.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

A maximum-likelihood method for estimating natural mortality and catchability coefficient from catch-and-effort data

A simple stochastic model of a fish population subject to natural and fishing mortalities is described. The fishing effort is assumed to vary over different periods but to be constant within each period. A maximum-likelihood approach is developed for estimating natural mortality (M) and the catchability coefficient (q) simultaneously from catch-and-effort data. If there is not enough contrast in the data to provide reliable estimates of both M and q, as is often the case in practice, the method can be used to obtain the best possible values of q for a range of possible values of M. These techniques are illustrated with tiger prawn (Penaeus semisulcatus) data from the Northern Prawn Fishery of Australia.

An improved Fabens method for estimation of growth parameters in the vonBertalanffy model with individual asymptotes

In the analysis of tagging data, it has been found that the least-squares method, based on the increment function known as the Fabens method, produces biased estimates because individual variability in growth is not allowed for. This paper modifies the Fabens method to account for individual variability in the length asymptote. Significance tests using t-statistics or log-likelihood ratio statistics may be applied to show the level of individual variability. Simulation results indicate that the modified method reduces the biases in the estimates to negligible proportions. Tagging data from tiger prawns (Penaeus esculentus and Penaeus semisulcatus) and rock lobster (Panulirus ornatus) are analysed as an illustration.

Method for comparing the capture efficiency of benthic sampling devices

Traditional comparisons between the capture efficiency of sampling devices have generally looked at the absolute differences between devices. We recommend that the signal-to-noise ratio be used when comparing the capture efficiency of benthic sampling devices. Using the signal-to-noise ratio rather than the absolute difference has the advantages that the variance is taken into account when determining how important the difference is, the hypothesis and minimum detectable difference can be made identical for all taxa, it is independent of the units used for measurement, and the sample-size calculation is independent of the variance. This new technique is illustrated by comparing the capture efficiency of a 0.05 m(2) van Veen grab and an airlift suction device, using samples taken from Heron and One Tree lagoons, Australia.

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

New temperature fluctuation method for direct determination of thermal activation energy of deep levels in semiconductors

A new method is suggested where the thermal activation energy is measured directly and not as a slope of an Arrhenius plot. The sample temperature T is allowed to fluctuate about a temperature T0. The reverse-biased sample diode is repeatedly pulsed towards zero bias and the transient capacitance C1 at time t1 is measured The activation energy is obtained by monitoring the fluctuations in C1 and T. The method has been used to measure the activation energy of the gold acceptor level in silicon.

Promoting articulated action from diverse stakeholders in response to public policy scenarios: A case analysis of the use of ‘scenario improvisation’ method

In this paper we present a novel application of scenario methods to engage a diverse constituency of senior stakeholders, with limited time availability, in debate to inform planning and policy development. Our case study project explores post-carbon futures for the Latrobe Valley region of the Australian state of Victoria. Our approach involved initial deductive development of two ‘extreme scenarios’ by a multi-disciplinary research team, based upon an extensive research programme. Over four workshops with the stakeholder constituency, these initial scenarios were discussed, challenged, refined and expanded through an inductive process, whereby participants took ‘ownership’ of a final set of three scenarios. These were both comfortable and challenging to them. The outcomes of this process subsequently informed public policy development for the region. Whilst this process did not follow a single extant structured, multi-stage scenario approach, neither was it devoid of form. Here, we seek to theorise and codify elements of our process – which we term ‘scenario improvisation’ – such that others may adopt it.

Graphical method to include temperature variation of activation energy in Hall data analysis

A graphical method is presented for Hall data analysis, including the temperature variation of activation energy due to screening. This method removes the discrepancies noted in the analysis of recently reported Hall data on Si(In).

An absolute method for the determination of surface tension of liquids using pendent drop profiles

Drop formation at conical tips which is of relevance to metallurgists is investigated based on the principle of minimization of free energy using the variational approach. The dimensionless governing equations for drop profiles are computer solved using the fourth order Runge-Kutta method. For different cone angles, the theoretical plots of XT and ZT vs their ratio, are statistically analyzed, where XT and ZT are the dimensionless x and z coordinates of the drop profile at a plane at the conical tip, perpendicular to the axis of symmetry. Based on the mathematical description of these curves, an absolute method has been proposed for the determination of surface tension of liquids, which is shown to be preferable in comparison with the earlier pendent-drop profile methods.

An evaluation of the apxIVA based PCR-REA method for differentiation of Actinobacillus pleuropneumoniae

A restriction analysis of PCR (PCR-REA) amplified apxIVA gene has been suggested as an alternative method for serotyping of Actinobacillus pleuropneumoniae by Jaglic et al. [Jaglic, Z., Svastova, P., Rychlik, I., Nedbalcova, K., Kucerova, Z., Pavlik, I., Bartos, M., 2004. Differentiation of Actinobacillus pleuropneumoniae by PCR-REA based on sequence variability of the apxIVA gene and by ribotyping. Vet. Microbiol. 103, 63-69]. The current study investigated whether this alternative method could distinguish between the reference strains of serovars 13-15 and the value of the method when applied to 47 field isolates representing serovars 1-3, 5, 7-9, 12 and 15 as well as non-typable isolates. The reference strains of serovars 13 and 14 had the same sized product after the apxIVA PCR, while the product for serovar 15 was of different size compared to all the other serovar reference strains. The CfoI digest profiles of the reference serovars 13 and 14 strains were different from each other and from all other serovars. The HpaII digest profiles of these two serovars were very similar to each other, but both were distinctively different from the other serovar profiles. The CfoI digest profile of serovar 15 strain was very similar to the serovars 3 and 12 strains except for two faint extra bands for serovar 15. The HpaII digest profiles of serovars 12 and 15 reference strains were identical. The PCR-REA method correctly recognized the serovar of 21 of 43 field isolates. It was concluded that the method was a useful additional tool to support, but could not replace, conventional serotyping.