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.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

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.

Cognitive emotion regulation as a mediator between posttraumatic stress symptoms and hypomanic personality within a non-clinical population

Background: There is a high prevalence of traumatic life events within individuals diagnosed with bipolar disorder. However, currently there is limited theoretical understanding of this relationship. Aims: To explore whether non-clinical symptoms of posttraumatic stress have a direct effect on the non-clinical symptoms of bipolar disorder, or whether this relationship is mediated by cognitive emotion regulation strategies. Method: A cross-sectional design within non-clinical participants completing an online survey including the Impact of Events Scale, Cognitive Emotion Regulation Questionnaire and the Hypomanic Personality Scale. Results: Posttraumatic stress symptoms were associated with hypomanic personality. Intrusive memories contributed a small but significant proportion of the variance between these two measures. Rumination of negative emotions mediated the relationship between posttraumatic stress and hypomanic personality. Conclusions: The relationship between traumatic events and an increased prevalence of bipolar disorder remains poorly understood. Further research should explore rumination as a potential target for treatment within those suffering from both posttraumatic stress and bipolar disorder.

Targeting medication non-adherence behavior in selected autoimmune diseases: a systematic approach to digital health program development

Background 29 autoimmune diseases, including Rheumatoid Arthritis, gout, Crohn’s Disease, and Systematic Lupus Erythematosus affect 7.6-9.4% of the population. While effective therapy is available, many patients do not follow treatment or use medications as directed. Digital health and Web 2.0 interventions have demonstrated much promise in increasing medication and treatment adherence, but to date many Internet tools have proven disappointing. In fact, most digital interventions continue to suffer from high attrition in patient populations, are burdensome for healthcare professionals, and have relatively short life spans. Objective Digital health tools have traditionally centered on the transformation of existing interventions (such as diaries, trackers, stage-based or cognitive behavioral therapy programs, coupons, or symptom checklists) to electronic format. Advanced digital interventions have also incorporated attributes of Web 2.0 such as social networking, text messaging, and the use of video. Despite these efforts, there has not been little measurable impact in non-adherence for illnesses that require medical interventions, and research must look to other strategies or development methodologies. As a first step in investigating the feasibility of developing such a tool, the objective of the current study is to systematically rate factors of non-adherence that have been reported in past research studies. Methods Grounded Theory, recognized as a rigorous method that facilitates the emergence of new themes through systematic analysis, data collection and coding, was used to analyze quantitative, qualitative and mixed method studies addressing the following autoimmune diseases: Rheumatoid Arthritis, gout, Crohn’s Disease, Systematic Lupus Erythematosus, and inflammatory bowel disease. Studies were only included if they contained primary data addressing the relationship with non-adherence. Results Out of the 27 studies, four non-modifiable and 11 modifiable risk factors were discovered. Over one third of articles identified the following risk factors as common contributors to medication non-adherence (percent of studies reporting): patients not understanding treatment (44%), side effects (41%), age (37%), dose regimen (33%), and perceived medication ineffectiveness (33%). An unanticipated finding that emerged was the need for risk stratification tools (81%) with patient-centric approaches (67%). Conclusions This study systematically identifies and categorizes medication non-adherence risk factors in select autoimmune diseases. Findings indicate that patients understanding of their disease and the role of medication are paramount. An unexpected finding was that the majority of research articles called for the creation of tailored, patient-centric interventions that dispel personal misconceptions about disease, pharmacotherapy, and how the body responds to treatment. To our knowledge, these interventions do not yet exist in digital format. Rather than adopting a systems level approach, digital health programs should focus on cohorts with heterogeneous needs, and develop tailored interventions based on individual non-adherence patterns.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Joint use of attribute importance rankings and non-attendance data in choice experiments

The joint and alternative uses of attribute non-attendance and importance ranking data within discrete choice experiments are investigated using data from Lebanon examining consumers’ preferences for safety certification in food. We find that both types of information; attribute non-attendance and importance rankings, improve estimates of respondent utility. We introduce a method of integrating both types of information simultaneously and find that this outperforms models where either importance ranking or non-attendance data are used alone. As in previous studies, stated non-attendance of attributes was not found to be consistent with respondents having zero marginal utility for those attributes