An adaptive finite element water column model using the Mellor-Yamada level 2.5 turbulence closure scheme

A one-dimensional water column model using the Mellor and Yamada level 2.5 parameterization of vertical turbulent fluxes is presented. The model equations are discretized with a mixed finite element scheme. Details of the finite element discrete equations are given and adaptive mesh refinement strategies are presented. The refinement criterion is an "a posteriori" error estimator based on stratification, shear and distance to surface. The model performances are assessed by studying the stress driven penetration of a turbulent layer into a stratified fluid. This example illustrates the ability of the presented model to follow some internal structures of the flow and paves the way for truly generalized vertical coordinates. (c) 2005 Elsevier Ltd. All rights reserved.

Adjoint goal-based error norms for adaptive mesh ocean modelling

Flow in the world's oceans occurs at a wide range of spatial scales, from a fraction of a metre up to many thousands of kilometers. In particular, regions of intense flow are often highly localised, for example, western boundary currents, equatorial jets, overflows and convective plumes. Conventional numerical ocean models generally use static meshes. The use of dynamically-adaptive meshes has many potential advantages but needs to be guided by an error measure reflecting the underlying physics. A method of defining an error measure to guide an adaptive meshing algorithm for unstructured tetrahedral finite elements, utilizing an adjoint or goal-based method, is described here. This method is based upon a functional, encompassing important features of the flow structure. The sensitivity of this functional, with respect to the solution variables, is used as the basis from which an error measure is derived. This error measure acts to predict those areas of the domain where resolution should be changed. A barotropic wind driven gyre problem is used to demonstrate the capabilities of the method. The overall objective of this work is to develop robust error measures for use in an oceanographic context which will ensure areas of fine mesh resolution are used only where and when they are required. (c) 2006 Elsevier Ltd. All rights reserved.

Adaptive routing in active networks

New conceptual ideas on network architectures have been proposed in the recent past. Current store-andforward routers are replaced by active intermediate systems, which are able to perform computations on transient packets, in a way that results very helpful for developing and deploying new protocols in a short time. This paper introduces a new routing algorithm, based on a congestion metric, and inspired by the behavior of ants in nature. The use of the Active Networks paradigm associated with a cooperative learning environment produces a robust, decentralized algorithm capable of adapting quickly to changing conditions.

Very short delays prior to escape from potential predators may function efficiently as adaptive risk-assessment periods

Periods between predator detection and an escape response (escape delays) by prey upon attack by a predator often arise because animals trade-off the benefits such a delay gives for assessing risk accurately with the costs of not escaping as quickly as possible. We tested whether freezing behaviour (complete immobility in a previously foraging bird) observed in chaffinches before escaping from an approaching potential threat functions as a period of risk-assessment, and whether information on predator identity is gained even when time available is very short. We flew either a model of a sparrowhawk (predator) or a woodpigeon (no threat) at single chaffinches. Escape delays were significantly shorter with the hawk, except when a model first appeared close to the chaffinch. Chaffinches were significantly more vigilant when they resumed feeding after exposure to the sparrowhawk compared to the woodpigeon showing that they were able to distinguish between threats, and this applied even when time available for assessment was short (an average of 0.29 s). Our results show freezing in chaffinches functions as an effective economic risk assessment period, and that threat information is gained even when very short periods of time are available during an attack.

Evaluating the efficiency of sampling methods in assessing soil macrofauna communities in arable systems

The soil fauna is often a neglected group in many large-scale studies of farmland biodiversity due to difficulties in extracting organisms efficiently from the soil. This study assesses the relative efficiency of the simple and cheap sampling method of handsorting against Berlese-Tullgren funnel and Winkler apparatus extraction. Soil cores were taken from grassy arable field margins and wheat fields in Cambridgeshire, UK, and the efficiencies of the three methods in assessing the abundances and species densities of soil macroinver-tebrates were compared. Handsorting in most cases was as efficient at extracting the majority of the soil macrofauna as the Berlese-Tullgren funnel and Winkler bag methods, although it underestimated the species densities of the woodlice and adult beetles. There were no obvious biases among the three methods for the particular vegetation types sampled and no significant differences in the size distributions of the earthworms and beetles. Proportionally fewer damaged earthworms were recorded in larger (25 x 25 cm) soil cores when compared with smaller ones (15 x 15 cm). Handsorting has many benefits, including targeted extraction, minimum disturbance to the habitat and shorter sampling periods and may be the most appropriate method for studies of farmland biodiversity when a high number of soil cores need to be sampled. (C) 2008 Elsevier Masson SAS. All rights reserved.

An adaptive approach to implementing bivariate group sequential clinical trial designs

In clinical trials, situations often arise where more than one response from each patient is of interest; and it is required that any decision to stop the study be based upon some or all of these measures simultaneously. Theory for the design of sequential experiments with simultaneous bivariate responses is described by Jennison and Turnbull (Jennison, C., Turnbull, B. W. (1993). Group sequential tests for bivariate response: interim analyses of clinical trials with both efficacy and safety endpoints. Biometrics 49:741-752) and Cook and Farewell (Cook, R. J., Farewell, V. T. (1994). Guidelines for monitoring efficacy and toxicity responses in clinical trials. Biometrics 50:1146-1152) in the context of one efficacy and one safety response. These expositions are in terms of normally distributed data with known covariance. The methods proposed require specification of the correlation, ρ between test statistics monitored as part of the sequential test. It can be difficult to quantify ρ and previous authors have suggested simply taking the lowest plausible value, as this will guarantee power. This paper begins with an illustration of the effect that inappropriate specification of ρ can have on the preservation of trial error rates. It is shown that both the type I error and the power can be adversely affected. As a possible solution to this problem, formulas are provided for the calculation of correlation from data collected as part of the trial. An adaptive approach is proposed and evaluated that makes use of these formulas and an example is provided to illustrate the method. Attention is restricted to the bivariate case for ease of computation, although the formulas derived are applicable in the general multivariate case.

An adaptive group sequential design for phase II/III clinical trials that select a single treatment from several

There is increasing interest in combining Phases II and III of clinical development into a single trial in which one of a small number of competing experimental treatments is ultimately selected and where a valid comparison is made between this treatment and the control treatment. Such a trial usually proceeds in stages, with the least promising experimental treatments dropped as soon as possible. In this paper we present a highly flexible design that uses adaptive group sequential methodology to monitor an order statistic. By using this approach, it is possible to design a trial which can have any number of stages, begins with any number of experimental treatments, and permits any number of these to continue at any stage. The test statistic used is based upon efficient scores, so the method can be easily applied to binary, ordinal, failure time, or normally distributed outcomes. The method is illustrated with an example, and simulations are conducted to investigate its type I error rate and power under a range of scenarios.

A practical comparison of group-sequential and adaptive designs

Sequential methods provide a formal framework by which clinical trial data can be monitored as they accumulate. The results from interim analyses can be used either to modify the design of the remainder of the trial or to stop the trial as soon as sufficient evidence of either the presence or absence of a treatment effect is available. The circumstances under which the trial will be stopped with a claim of superiority for the experimental treatment, must, however, be determined in advance so as to control the overall type I error rate. One approach to calculating the stopping rule is the group-sequential method. A relatively recent alternative to group-sequential approaches is the adaptive design method. This latter approach provides considerable flexibility in changes to the design of a clinical trial at an interim point. However, a criticism is that the method by which evidence from different parts of the trial is combined means that a final comparison of treatments is not based on a sufficient statistic for the treatment difference, suggesting that the method may lack power. The aim of this paper is to compare two adaptive design approaches with the group-sequential approach. We first compare the form of the stopping boundaries obtained using the different methods. We then focus on a comparison of the power of the different trials when they are designed so as to be as similar as possible. We conclude that all methods acceptably control type I error rate and power when the sample size is modified based on a variance estimate, provided no interim analysis is so small that the asymptotic properties of the test statistic no longer hold. In the latter case, the group-sequential approach is to be preferred. Provided that asymptotic assumptions hold, the adaptive design approaches control the type I error rate even if the sample size is adjusted on the basis of an estimate of the treatment effect, showing that the adaptive designs allow more modifications than the group-sequential method.

A jackknife variance estimator for unequal probability sampling

The jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs.We propose a jackknife variance estimator which is defined for any without-replacement unequal probability sampling design. We demonstrate design consistency of this estimator for a broad class of point estimators. A Monte Carlo study shows how the proposed estimator may improve on existing estimators.

Variance estimation with highly stratified sampling designs with unequal probabilities

It is common practice to design a survey with a large number of strata. However, in this case the usual techniques for variance estimation can be inaccurate. This paper proposes a variance estimator for estimators of totals. The method proposed can be implemented with standard statistical packages without any specific programming, as it involves simple techniques of estimation, such as regression fitting.

Variance estimation for systematic sampling from deliberately ordered populations

The systematic sampling (SYS) design (Madow and Madow, 1944) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982) and usual variance estimators (Yates and Grundy, 1953) are inadequate and can overestimate the variance significantly (Särndal et al., 1992). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.