Some general comparative points on Chao's and Zelterman's estimators of the population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

Dilettantes, discipline and discourse: requirements management for construction

Requirements management (RM), as practised in the aerospace and defence sectors, attracts interest from construction researchers in response to longstanding problems of project definition. Doubts are expressed whether RM offers a new discipline for construction practitioners or whether it repeats previous exhortations to adopt a more disciplined way of working. Whilst systems engineering has an established track record of addressing complex technical problems, its extension to socially complex problems has been challenged. The dominant storyline of RM is one of procedural rationality and RM is commonly presented as a means of controlling dilettante behaviour. Interviews with RM practitioners suggest a considerable gulf between the dominant storyline in the literature and how practitioners operate in practice. The paper challenges construction researchers interested in RM to reflect more upon the theoretical debates that underpin current equivalent practices in construction and the disparity between espoused and enacted practice.

Urea-N,N-dimethylacetamide (1/1)

Urea forms a 1:1 solvate with N,N-dimethylacetamide (DMA) [systematic name: diaminomethanal- N,N-dimethylacetamide (1/1), C4H9NO center dot CH4N2O] with both molecules positioned on a twofold axis, giving rise to rotational disorder of the DMA molecule. The molecules display a layered structure in which urea molecules form hydrogen-bonded ribbons bounded by molecules of solvent.

From base-rate to cumulative respect

The tendency to neglect base-rates in judgment under uncertainty may be "notorious," as Barbey & Sloman (B&S) suggest, but it is neither inevitable (as they document; see also Koehler 1996) nor unique. Here we would like to point out another line of evidence connecting ecological rationality to dual processes, the failure of individuals to appropriately judge cumulative probability.

Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

What Monte Carlo models can do and cannot do efficiently?

The question "what Monte Carlo models can do and cannot do efficiently" is discussed for some functional spaces that define the regularity of the input data. Data classes important for practical computations are considered: classes of functions with bounded derivatives and Holder type conditions, as well as Korobov-like spaces. Theoretical performance analysis of some algorithms with unimprovable rate of convergence is given. Estimates of computational complexity of two classes of algorithms - deterministic and randomized for both problems - numerical multidimensional integration and calculation of linear functionals of the solution of a class of integral equations are presented. (c) 2007 Elsevier Inc. All rights reserved.

Fourier transform, null variety, and Laplacian's eigenvalues

We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians.

Transport in the low-latitude tropopause zone diagnosed using particle trajectories

Recent literature has described a “transition zone” between the average top of deep convection in the Tropics and the stratosphere. Here transport across this zone is investigated using an offline trajectory model. Particles were advected by the resolved winds from the European Centre for Medium-Range Weather Forecasts reanalyses. For each boreal winter clusters of particles were released in the upper troposphere over the four main regions of tropical deep convection (Indonesia, central Pacific, South America, and Africa). Most particles remain in the troposphere, descending on average for every cluster. The horizontal components of 5-day trajectories are strongly influenced by the El Niño–Southern Oscillation (ENSO), but the Lagrangian average descent does not have a clear ENSO signature. Tropopause crossing locations are first identified by recording events when trajectories from the same release regions cross the World Meteorological Organization lapse rate tropopause. Most crossing events occur 5–15 days after release, and 30-day trajectories are sufficiently long to estimate crossing number densities. In a further two experiments slight excursions across the lapse rate tropopause are differentiated from the drift deeper into the stratosphere by defining the “tropopause zone” as a layer bounded by the average potential temperature of the lapse rate tropopause and the profile temperature minimum. Transport upward across this zone is studied using forward trajectories released from the lower bound and back trajectories arriving at the upper bound. Histograms of particle potential temperature (θ) show marked differences between the transition zone, where there is a slow spread in θ values about a peak that shifts slowly upward, and the troposphere below 350 K. There forward trajectories experience slow radiative cooling interspersed with bursts of convective heating resulting in a well-mixed distribution. In contrast θ histograms for back trajectories arriving in the stratosphere have two distinct peaks just above 300 and 350 K, indicating the sharp change from rapid convective heating in the well-mixed troposphere to slow ascent in the transition zone. Although trajectories slowly cross the tropopause zone throughout the Tropics, all three experiments show that most trajectories reaching the stratosphere from the lower troposphere within 30 days do so over the west Pacific warm pool. This preferred location moves about 30°–50° farther east in an El Niño year (1982/83) and about 30° farther west in a La Niña year (1988/89). These results could have important implications for upper-troposphere–lower-stratosphere pollution and chemistry studies.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Neural network enhanced generalised minimum variance self-tuning controller for nonlinear discrete-time systems

A neural network enhanced self-tuning controller is presented, which combines the attributes of neural network mapping with a generalised minimum variance self-tuning control (STC) strategy. In this way the controller can deal with nonlinear plants, which exhibit features such as uncertainties, nonminimum phase behaviour, coupling effects and may have unmodelled dynamics, and whose nonlinearities are assumed to be globally bounded. The unknown nonlinear plants to be controlled are approximated by an equivalent model composed of a simple linear submodel plus a nonlinear submodel. A generalised recursive least squares algorithm is used to identify the linear submodel and a layered neural network is used to detect the unknown nonlinear submodel in which the weights are updated based on the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model therefore the nonlinear submodel is naturally accommodated within the control law. Two simulation studies are provided to demonstrate the effectiveness of the control algorithm.

Identification of linear systems in the presence of piecewise polynomial disturbances

The paper proposes a method of performing system identification of a linear system in the presence of bounded disturbances. The disturbances may be piecewise parabolic or periodic functions. The method is demonstrated effectively on two example systems with a range of disturbances.

Autonomous ship collision free trajectory navigation and control algorithms

A new autonomous ship collision free (ASCF) trajectory navigation and control system has been introduced with a new recursive navigation algorithm based on analytic geometry and convex set theory for ship collision free guidance. The underlying assumption is that the geometric information of ship environment is available in the form of a polygon shaped free space, which may be easily generated from a 2D image or plots relating to physical hazards or other constraints such as collision avoidance regulations. The navigation command is given as a heading command sequence based on generating a way point which falls within a small neighborhood of the current position, and the sequence of the way points along the trajectory are guaranteed to lie within a bounded obstacle free region using convex set theory. A neurofuzzy network predictor which in practice uses only observed input/output data generated by on board sensors or external sensors (or a sensor fusion algorithm), based on using rudder deflection angle for the control of ship heading angle, is utilised in the simulation of an ESSO 190000 dwt tanker model to demonstrate the effectiveness of the system.

Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.