Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Speech-like and non-speech lip kinematics and coordination in aphasia

Background and aims: In addition to the well-known linguistic processing impairments in aphasia, oro-motor skills and articulatory implementation of speech segments are reported to be compromised to some degree in most types of aphasia. This study aimed to identify differences in the characteristics and coordination of lip movements in the production of a bilabial closure gesture between speech-like and nonspeech tasks in individuals with aphasia and healthy control subjects. Method and procedure: Upper and lower lip movement data were collected for a speech-like and a nonspeech task using an AG 100 EMMA system from five individuals with aphasia and five age and gender matched control subjects. Each task was produced at two rate conditions (normal and fast), and in a familiar and a less-familiar manner. Single articulator kinematic parameters (peak velocity, amplitude, duration, and cyclic spatio-temporal index) and multi-articulator coordination indices (average relative phase and variability of relative phase) were measured to characterize lip movements. Outcome and results: The results showed that when the two lips had similar task goals (bilabial closure) in speech-like versus nonspeech task, kinematic and coordination characteristics were not found to be different. However, when changes in rate were imposed on the bilabial gesture, only speech-like task showed functional adaptations, indicated by a greater decrease in amplitude and duration at fast rates. In terms of group differences, individuals with aphasia showed smaller amplitudes and longer movement durations for upper lip, higher spatio-temporal variability for both lips, and higher variability in lip coordination than the control speakers. Rate was an important factor in distinguishing the two groups, and individuals with aphasia were limited in implementing the rate changes. Conclusion and implications: The findings support the notion of subtle but robust differences in motor control characteristics between individuals with aphasia and the control participants, even in the context of producing bilabial closing gestures for a relatively simple speech-like task. The findings also highlight the functional differences between speech-like and nonspeech tasks, despite a common movement coordination goal for bilabial closure.

A method for incorporating climate variability in climate change impact assessments: sensitivity of river flows in the Eden catchment to precipitation scenarios

Interest in the impacts of climate change is ever increasing. This is particularly true of the water sector where understanding potential changes in the occurrence of both floods and droughts is important for strategic planning. Climate variability has been shown to have a significant impact on UK climate and accounting for this in future climate cahgne projections is essential to fully anticipate potential future impacts. In this paper a new resampling methodology is developed which includes the variability of both baseline and future precipitation. The resampling methodology is applied to 13 CMIP3 climate models for the 2080s, resulting in an ensemble of monthly precipitation change factors. The change factors are applied to the Eden catchment in eastern Scotland with analysis undertaken for the sensitivity of future river flows to the changes in precipitation. Climate variability is shown to influence the magnitude and direction of change of both precipitation and in turn river flow, which are not apparent without the use of the resampling methodology. The transformation of precipitation changes to river flow changes display a degree of non-linearity due to the catchment's role in buffering the response. The resampling methodology developed in this paper provides a new technique for creating climate change scenarios which incorporate the important issue of climate variability.

Stated attribute non-attendance in successive choice experiments

Attribute non-attendance in choice experiments affects WTP estimates and therefore the validity of the method. A recent strand of literature uses attenuated estimates of marginal utilities of ignored attributes. Following this approach, we propose a generalisation of the mixed logit model whereby the distribution of marginal utility coefficients of a stated non-attender has a potentially lower mean and lower variance than those of a stated attender. Model comparison shows that our shrinkage approach fits the data better and produces more reliable WTP estimates. We further find that while reliability of stated attribute non-attendance increases in successive choice experiments, it does not increase when respondents report having ignored the same attribute twice.

Impact of serving method on the consumption of nutritional supplement drinks: randomised trial in older adults with cognitive impairment

Aim: To analyse the influence of serving method on compliance and consumption of nutritional supplement drinks in older adults with cognitive impairment. Background: Oral nutritional supplement drinks have positive benefits on increasing nutritional status within undernourished elderly people leading to weight gain. However, consumption of these drinks is low and therefore limits their effectiveness. Design: This study was a non blind randomised control trial where participants either consumed nutritional supplement drinks in a glass/beaker or consumed them through a straw inserted directly into the container. Method: Participants with longstanding cognitive impairment were recruited from nursing homes (n=31) and hospitals (n=14). Participants were randomised to serving method. Nursing and care staff were instructed to give the supplement drinks three times per day on alternate days over a week by the allocated serving method. The researcher weighed the amount of supplement drink remaining after consumption. Data were collected over 12 months in 2011-2012. Results: 45 people participated in this study mean age 86.7 (SD 7.5 ) years. After randomisation there was no significant difference between the baseline characteristics of the two groups. Participants randomised to consume nutritional drinks from a glass / beaker drank significantly more than those who consumed them via a straw inserted directly into the container. However, supplements allocated to be given in a glass/beaker were more frequently omitted. Conclusion: Nutritional supplement drinks should be given to people with dementia who are able to feed themselves in a glass or a beaker if staffing resources allow (NIHR CSP ref 31101).

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

Non-steady state heat conduction in composite walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

Brief communication: a proposed method for the assessment of pubertal stage in human skeletal remains using cervical vertebrae maturation.

The assessment of age-at-death in non-adult skeletal remains is under constant review. However, in many past societies an individual's physical maturation may have been more important in social terms than their exact age, particularly during the period of adolescence. In a recent article (Shapland and Lewis: Am J Phys Anthropol 151 (2013) 302–310) highlighted a set of dental and skeletal indicators that may be useful in mapping the progress of the pubertal growth spurt. This article presents a further skeletal indicator of adolescent development commonly used by modern clinicians: cervical vertebrae maturation (CVM). This method is applied to a collection of 594 adolescents from the medieval cemetery of St. Mary Spital, London. Analysis reveals a potential delay in ages of attainment of the later CVM stages compared with modern adolescents, presumably reflecting negative environmental conditions for growth and development. The data gathered on CVM is compared to other skeletal indicators of pubertal maturity and long bone growth from this site to ascertain the usefulness of this method on archaeological collections.

A novel transport assimilation method for the Atlantic meridional overturning circulation at 26°N

One of the prerequisites for achieving skill in decadal climate prediction is to initialize and predict the circulation in the Atlantic Ocean successfully. The RAPID array measures the Atlantic Meridional Overturning Circulation (MOC) at 26°N. Here we develop a method to include these observations in the Met Office Decadal Prediction System (DePreSys). The proposed method uses covariances of overturning transport anomalies at 26°N with ocean temperature and salinity anomalies throughout the ocean to create the density structure necessary to reproduce the observed transport anomaly. Assimilating transport alone in this way effectively reproduces the observed transport anomalies at 26°N and is better than using basin-wide temperature and salinity observations alone. However, when the transport observations are combined with in situ temperature and salinity observations in the analysis, the transport is not currently reproduced so well. The reasons for this are investigated using pseudo-observations in a twin experiment framework. Sensitivity experiments show that the MOC on monthly time-scales, at least in the HadCM3 model, is modulated by a mechanism where non-local density anomalies appear to be more important for transport variability at 26°N than local density gradients.

Non-replication of the association between 5HTTLPR and response to psychological therapy for child anxiety disorders

Background We previously reported an association between 5HTTLPR genotype and outcome following cognitive–behavioural therapy (CBT) in child anxiety (Cohort 1). Children homozygous for the low-expression short-allele showed more positive outcomes. Other similar studies have produced mixed results, with most reporting no association between genotype and CBT outcome. Aims To replicate the association between 5HTTLPR and CBT outcome in child anxiety from the Genes for Treatment study (GxT Cohort 2, n = 829). Method Logistic and linear mixed effects models were used to examine the relationship between 5HTTLPR and CBT outcomes. Mega-analyses using both cohorts were performed. Results There was no significant effect of 5HTTLPR on CBT outcomes in Cohort 2. Mega-analyses identified a significant association between 5HTTLPR and remission from all anxiety disorders at follow-up (odds ratio 0.45, P = 0.014), but not primary anxiety disorder outcomes. Conclusions The association between 5HTTLPR genotype and CBT outcome did not replicate. Short-allele homozygotes showed more positive treatment outcomes, but with small, non-significant effects. Future studies would benefit from utilising whole genome approaches and large, homogenous samples.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.