Estimation following selection of the largest of two normal means

This paper considers the problem of estimation when one of a number of populations, assumed normal with known common variance, is selected on the basis of it having the largest observed mean. Conditional on selection of the population, the observed mean is a biased estimate of the true mean. This problem arises in the analysis of clinical trials in which selection is made between a number of experimental treatments that are compared with each other either with or without an additional control treatment. Attempts to obtain approximately unbiased estimates in this setting have been proposed by Shen [2001. An improved method of evaluating drug effect in a multiple dose clinical trial. Statist. Medicine 20, 1913–1929] and Stallard and Todd [2005. Point estimates and confidence regions for sequential trials involving selection. J. Statist. Plann. Inference 135, 402–419]. This paper explores the problem in the simple setting in which two experimental treatments are compared in a single analysis. It is shown that in this case the estimate of Stallard and Todd is the maximum-likelihood estimate (m.l.e.), and this is compared with the estimate proposed by Shen. In particular, it is shown that the m.l.e. has infinite expectation whatever the true value of the mean being estimated. We show that there is no conditionally unbiased estimator, and propose a new family of approximately conditionally unbiased estimators, comparing these with the estimators suggested by Shen.

Estimation of population growth or decline in genetically monitored populations

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.

Chromatographic alignment of LC-MS and LC-MS/MS datasets by genetic algorithm feature extraction

Liquid chromatography-mass spectrometry (LC-MS) datasets can be compared or combined following chromatographic alignment. Here we describe a simple solution to the specific problem of aligning one LC-MS dataset and one LC-MS/MS dataset, acquired on separate instruments from an enzymatic digest of a protein mixture, using feature extraction and a genetic algorithm. First, the LC-MS dataset is searched within a few ppm of the calculated theoretical masses of peptides confidently identified by LC-MS/MS. A piecewise linear function is then fitted to these matched peptides using a genetic algorithm with a fitness function that is insensitive to incorrect matches but sufficiently flexible to adapt to the discrete shifts common when comparing LC datasets. We demonstrate the utility of this method by aligning ion trap LC-MS/MS data with accurate LC-MS data from an FTICR mass spectrometer and show how hybrid datasets can improve peptide and protein identification by combining the speed of the ion trap with the mass accuracy of the FTICR, similar to using a hybrid ion trap-FTICR instrument. We also show that the high resolving power of FTICR can improve precision and linear dynamic range in quantitative proteomics. The alignment software, msalign, is freely available as open source.

Enhancing dominant modes in nonstationary time series by means of the symbolic resonance analysis

We present the symbolic resonance analysis (SRA) as a viable method for addressing the problem of enhancing a weakly dominant mode in a mixture of impulse responses obtained from a nonlinear dynamical system. We demonstrate this using results from a numerical simulation with Duffing oscillators in different domains of their parameter space, and by analyzing event-related brain potentials (ERPs) from a language processing experiment in German as a representative application. In this paradigm, the averaged ERPs exhibit an N400 followed by a sentence final negativity. Contemporary sentence processing models predict a late positivity (P600) as well. We show that the SRA is able to unveil the P600 evoked by the critical stimuli as a weakly dominant mode from the covering sentence final negativity. (c) 2007 American Institute of Physics. (c) 2007 American Institute of Physics.

Use of auditory cues for wayfinding assistance in virtual environment: music aids route decision

This paper addresses the crucial problem of wayfinding assistance in the Virtual Environments (VEs). A number of navigation aids such as maps, agents, trails and acoustic landmarks are available to support the user for navigation in VEs, however it is evident that most of the aids are visually dominated. This work-in-progress describes a sound based approach that intends to assist the task of 'route decision' during navigation in a VE using music. Furthermore, with use of musical sounds it aims to reduce the cognitive load associated with other visually as well as physically dominated tasks. To achieve these goals, the approach exploits the benefits provided by music to ease and enhance the task of wayfinding, whilst making the user experience in the VE smooth and enjoyable.

Performance of asynchronous channel assignment scheme in non-uniform and dynamic topology WLANs

Dense deployments of wireless local area networks (WLANs) are fast becoming a permanent feature of all developed cities around the world. While this increases capacity and coverage, the problem of increased interference, which is exacerbated by the limited number of channels available, can severely degrade the performance of WLANs if an effective channel assignment scheme is not employed. In an earlier work, an asynchronous, distributed and dynamic channel assignment scheme has been proposed that (1) is simple to implement, (2) does not require any knowledge of the throughput function, and (3) allows asynchronous channel switching by each access point (AP). In this paper, we present extensive performance evaluation of this scheme when it is deployed in the more practical non-uniform and dynamic topology scenarios. Specifically, we investigate its effectiveness (1) when APs are deployed in a nonuniform fashion resulting in some APs suffering from higher levels of interference than others and (2) when APs are effectively switched `on/off' due to the availability/lack of traffic at different times, which creates a dynamically changing network topology. Simulation results based on actual WLAN topologies show that robust performance gains over other channel assignment schemes can still be achieved even in these realistic scenarios.

Effectiveness of asynchronous channel assignment scheme in heterogeneous WLANs

Due to their popularity, dense deployments of wireless local area networks (WLANs) are becoming a common feature of many cities around the world. However, with only a limited number of channels available, the problem of increased interference can severely degrade the performance of WLANs if an effective channel assignment scheme is not employed. Previous studies on channel assignment in WLANs almost always assume that all access points (AP) employ the same channel assignment scheme which is clearly unrealistic. On the other hand, to the best of our knowledge, the interaction between different channel assignment schemes has also not been studied before. Therefore, in this paper, we investigate the effectiveness of our earlier proposed asynchronous channel assignment scheme in these heterogeneous WLANs scenarios. Simulation results show that our proposed scheme is still able to provide robust performance gains even in these scenarios.

Impact of interference on throughput in dense WLANs with multiple APs

The popularity of wireless local area networks (WLANs) has resulted in their dense deployments around the world. While this increases capacity and coverage, the problem of increased interference can severely degrade the performance of WLANs. However, the impact of interference on throughput in dense WLANs with multiple access points (APs) has had very limited prior research. This is believed to be due to 1) the inaccurate assumption that throughput is always a monotonically decreasing function of interference and 2) the prohibitively high complexity of an accurate analytical model. In this work, firstly we provide a useful classification of commonly found interference scenarios. Secondly, we investigate the impact of interference on throughput for each class based on an approach that determines the possibility of parallel transmissions. Extensive packet-level simulations using OPNET have been performed to support the observations made. Interestingly, results have shown that in some topologies, increased interference can lead to higher throughput and vice versa.

An analysis of arithmetic averaging in approximate Riemann solvers with an application to steady, supercritical flows

An analysis of various arithmetic averaging procedures for approximate Riemann solvers is made with a specific emphasis on efficiency and a jump capturing property. The various alternatives discussed are intended for future work, as well as the more immediate problem of steady, supercritical free-surface flows. Numerical results are shown for two test problems.

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

Experimental model of the interfacial instability in aluminium reduction cells

A solution has been found to the long-standing problem of experimental modelling of the interfacial instability in aluminium reduction cells. The idea is to replace the electrolyte overlaying molten aluminium with a mesh of thin rods supplying current down directly into the liquid metal layer. This eliminates electrolysis altogether and all the problems associated with it, such as high temperature, chemical aggressiveness of media, products of electrolysis, the necessity for electrolyte renewal, high power demands, etc. The result is a room temperature, versatile laboratory model which simulates Sele-type, rolling pad interfacial instability. Our new, safe laboratory model enables detailed experimental investigations to test the existing theoretical models for the first time.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.