When is negativity not a problem for the ultra-discrete limit?

The `ultra-discrete limit' has provided a link between integrable difference equations and cellular automata displaying soliton like solutions. In particular, this procedure generally turns strictly positive solutions of algebraic difference equations with positive coefficients into corresponding solutions to equations involving the "Max" operator. Although it certainly is the case that dropping these positivity conditions creates potential difficulties, it is still possible for solutions to persist under the ultra-discrete limit even in their absence. To recognize when this will occur, one must consider whether a certain expression, involving a measure of the rates of convergence of different terms in the difference equation and their coefficients, is equal to zero. Applications discussed include the solution of elementary ordinary difference equations, a discretization of the Hirota Bilinear Difference Equation and the identification of integrals of motion for ultra-discrete equations

IN THEIR OWN WORDS: EXPLORING THE UNSEEN WOUNDS OF AN OIF/OEF VETERAN & A CIVILIAN WITH TRAUMATIC BRAIN INJURY

In the past, when thinking of injured soldiers returning home from war, pictures of individuals in wheelchairs with amputations might come to mind. It was hard to ignore those visible injuries. Soldiers returning home from Operation Iraqi Freedom (OIF) and Operation Enduring Freedom (OEF) in Afghanistan can have unseen wounds, some in the form of Traumatic Brain Injuries (TBI). In the past individuals with TBI died of their injuries. Currently, advances in technology has drastically change our image of what an injured individual with TBI looks like, whether veterans or civilians. Unseen wounds such as TBIs pose a new set of challenges for an injured individual’s reintegration into society. Objective: The purpose of this study was to gain insight into the experiences and needs of an OIF/OEF veteran and a civilian with TBI from their perspective. Method: A qualitative study was conducted using semi-structured intensive interviews with two participants (one civilian and one veteran) who suffered a traumatic brain injury. The interview information is presented in case study format that allowed for in-depth exploration of each participant’s experience. Findings: Some of the core themes that emerged from the interviews included isolation, depression, somatic complaints, self-medication, and inability to return to work. Conclusion: The findings suggest that the road to recovery after a TBI contains challenges on a personal, familial, and community level. Implications for social work education, practice, policy, and future research are also addressed

Constructing Integrable Third Order Systems:The Gambier Approach

We present a systematic construction of integrable third order systems based on the coupling of an integrable second order equation and a Riccati equation. This approach is the extension of the Gambier method that led to the equation that bears his name. Our study is carried through for both continuous and discrete systems. In both cases the investigation is based on the study of the singularities of the system (the Painlev\'e method for ODE's and the singularity confinement method for mappings).Comment: 14 pages, TEX FIL

Developing Age-Friendly Cities: An evidence-based evaluation tool

Recent years have seen a proliferation of initiatives aimed at enhancing the age-friendliness of urban settings. The World Health Organization's (WHO) global Age-Friendly Cities (AFC) programme has been central to these. Cities seeking to become more age-friendly need reliable ways of assessing their efforts. This article describes an evidence-based evaluation tool for age-friendly initiatives whose development was informed by fieldwork in Liverpool/UK. The tool complements existing assessment frameworks, including those provided by WHO, by paying particular attention to the structures and processes underlying age-friendly initiatives. It reflects the complexity of age-friendliness by reconciling a focus on breadth with detail and depth, and it allows for a highly accessible visual presentation of findings. Using selected examples from Liverpool, the article illustrates how the evaluation tool can be applied to guide policy and practice with an age-friendly focus in different urban contexts. Pilot testing in further settings is underway to refine the tool as a practical method for evaluation and for supporting city-level decision making. Key words: Age-Friendly City; evaluation tool; ageing; urbanisation; complex intervention

Point Symmetries of Generalized Toda Field Theories II Applications of the Symmetries

The Lie symmetries of a large class of generalized Toda field theories are studied and used to perform symmetry reduction. Reductions lead to generalized Toda lattices on one hand, to periodic systems on the other. Boundary conditions are introduced to reduce theories on an infinite lattice to those on semi-infinite, or finite ones.Comment: 26 pages, no figure

Kinematic characteristics of elite men's 50 km race walking.

Race walking is an endurance event which also requires great technical ability, particularly with respect to its two distinguishing rules. The 50 km race walk is the longest event in the athletics programme at the Olympic Games. The aims of this observational study were to identify the important kinematic variables in elite men's 50 km race walking, and to measure variation in those variables at different distances. Thirty men were analysed from video data recorded during a World Race Walking Cup competition. Video data were also recorded at four distances during the European Cup Race Walking and 12 men analysed from these data. Two camcorders (50 Hz) recorded at each race for 3D analysis. The results of this study showed that walking speed was associated with both step length (r=0.54,P=0.002) and cadence (r=0.58,P=0.001). While placing the foot further ahead of the body at heel strike was associated with greater step lengths (r=0.45,P=0.013), it was also negatively associated with cadence (r= -0.62,P<0.001). In the World Cup, knee angles ranged between 175 and 186° at initial contact and between 180 and 195° at midstance. During the European Cup, walking speed decreased significantly (F=9.35,P=0.002), mostly due to a decrease in step length between 38.5 and 48.5 km (t=8.59,P=0.014). From this study, it would appear that the key areas a 50 km race walker must develop and coordinate are step length and cadence, although it is also important to ensure legal walking technique is maintained with the onset of fatigue

Parallel Electromechanical model of the heart

In this paper, we present a high performance computational electromechanical model of the heart, coupling between electrical activation and mechanical deformation and running efficiently in up to thousands of processors. The electrical potential propagation is modelled by FitzHugh-Nagumo or Fenton-Karma models, with fiber orientation. The mechanical deformation is treated using anisotropic hyper-elastic materials in a total Lagrangian formulation. Several material models are assessed, such as models based on biaxial tests on excised myocardium or orthotropic formulations. Coupling is treated using the Cross-Bridges model of Peterson. The scheme is implemented in Alya, which run simulations in parallel with almost linear scalability in a wide range computer sizes, up to thousands of processors. The computational model is assessed through several tests, including those to evaluate its parallel performance.Sociedad Argentina de Informática e Investigación Operativ

Algebraic entropy for algebraic maps

We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Backlund transformations

Point Symmetries of Generalized Toda Field Theories

A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point symmetries of these theories are found for an infinite, semi-infinite and finite number of fields. Special attention is accorded to conformal invariance and its breaking.Comment: 25 pages, no figures, Latex fil