Older Peoples’ views of choice and decision-making in chronic kidney disease: a grounded theory study of access to the social world of renal care

Chronic kidney disease (CKD) is increasing in prevalence worldwide, with the largest increase occurring in individuals over the age of 65 years. Providing renal replacement therapy (RRT) to this older population will challenge health care systems, in terms of resources needed, as well as healthcare staff caring for this highly dependent group, who frequently have multiple co-morbidities. This study aimed to develop a theory that adequately accounts for the social processes involved when older people, with CKD stages 4 and 5 access treatment. The study sought to explore the concerns they had with CKD when making treatment decisions and identified how their concerns were resolved. This study employed grounded theory using the full complement of coding, categorisation, and theoretical development. Data was collected from interviews and observations of clinic consultations between patients and healthcare practitioners, from 21 older people who were at the point of making treatment decisions. The main concerns for older people in this study focused upon achieving safe care. This led to the development of the theory ‘Negotiating a Safe Existence’, which explains the processes older people encountered during their treatment decision-making journey. The basic social process of negotiation enabled them to use strategies and tactics to secure a place of safe care. This process involved transitioning through three stages represented by the sub-categories ‘Confronting a Deteriorating Self’, ‘Sourcing Information’, and ‘Traversing Disruption’. This grounded theory identified the importance of information to older people with differing awareness levels concerning the seriousness of their CKD. Varying degrees of negotiation were evident reflecting the differences in information awareness, their role in treatment decision-making, and their perceptions of risk and harm from dialysis. The theory represented an insight into the status passage of these individuals as they entered a critical phase of their CKD. The structural processes of the renal clinic, doctors, existing patients, and families all influenced older people’s status passage. The findings highlighted older people’s perception of self-care dialysis, with the majority of patients in this study employing risk-aversion strategies to ensure they received care in a place of perceived safety, which was mainly hospital based dialysis

High-precision Monte Carlo study of directed percolation in (d+1) dimensions

We present a Monte Carlo study of the bond and site directed (oriented) percolation models in $(d+1)$ dimensions on simple-cubic and body-centered-cubic lattices, with $2 \leq d \leq 7$. A dimensionless ratio is defined, and an analysis of its finite-size scaling produces improved estimates of percolation thresholds. We also report improved estimates for the standard critical exponents. In addition, we study the probability distributions of the number of wet sites and radius of gyration, for $1 \leq d \leq 7$.Comment: 11 pages, 21 figure

Phase transition for cutting-plane approach to vertex-cover problem

We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g, for the ER ensemble at connectivity c=e=2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, also the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, change close to this phase transition from "easy" to "hard". In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach, hence the algorithm operates in a space OUTSIDE the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an "easy-hard" transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.Comment: 4 pages, 3 figure

A Search for Instantons at HERA

A search for QCD instanton (I) induced events in deep-inelastic scattering (DIS) at HERA is presented in the kinematic range of low x and low Q^2. After cutting into three characteristic variables for I-induced events yielding a maximum suppression of standard DIS background to the 0.1% level while still preserving 10% of the I-induced events, 549 data events are found while 363^{+22}_{-26} (CDM) and 435^{+36}_{-22} (MEPS) standard DIS events are expected. More events than expected by the standard DIS Monte Carlo models are found in the data. However, the systematic uncertainty between the two different models is of the order of the expected signal, so that a discovery of instantons can not be claimed. An outlook is given on the prospect to search for QCD instanton events using a discriminant based on range searching in the kinematical region Q^2\gtrsim100\GeV^2 where the I-theory makes safer predictions and the QCD Monte Carlos are expected to better describe the inclusive data.Comment: Invited talk given at the Ringberg Workshop on HERA Physics on June 19th, 2001 on behalf of the H1 collaboratio

Efficient Monte Carlo algorithm and high-precision results for percolation

We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at occupation probability 0.59274621(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.Comment: 8 pages, including 3 postscript figures, minor corrections in this version, plus updated figures for the position of the percolation transitio

Staircase polygons: moments of diagonal lengths and column heights

We consider staircase polygons, counted by perimeter and sums of k-th powers of their diagonal lengths, k being a positive integer. We derive limit distributions for these parameters in the limit of large perimeter and compare the results to Monte-Carlo simulations of self-avoiding polygons. We also analyse staircase polygons, counted by width and sums of powers of their column heights, and we apply our methods to related models of directed walks.Comment: 24 pages, 7 figures; to appear in proceedings of Counting Complexity: An International Workshop On Statistical Mechanics And Combinatorics, 10-15 July 2005, Queensland, Australi

Phase Transition in the Aldous-Shields Model of Growing Trees

We study analytically the late time statistics of the number of particles in a growing tree model introduced by Aldous and Shields. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by absorbing new particles at the empty perimeter sites at a rate proportional to c^{-l} where c is a positive parameter and l is the distance of the perimeter site from the root. For c=1, this model corresponds to random binary search trees and for c=2 it corresponds to digital search trees in computer science. By introducing a backward Fokker-Planck approach, we calculate the mean and the variance of the number of particles at large times and show that the variance undergoes a `phase transition' at a critical value c=sqrt{2}. While for c>sqrt{2} the variance is proportional to the mean and the distribution is normal, for c<sqrt{2} the variance is anomalously large and the distribution is non-Gaussian due to the appearance of extreme fluctuations. The model is generalized to one where growth occurs on a tree with $m$ branches and, in this more general case, we show that the critical point occurs at c=sqrt{m}.Comment: Latex 17 pages, 6 figure

Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid

The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as an underlying description of order has branched out to include topological band insulators, and certain featureless gapped Mott insulators with a topological degeneracy in the groundstate wavefunction. Despite intense focus, very few candidates for these topologically ordered "spin liquids" exist. The main difficulty in finding systems that harbour spin liquid states is the very fact that they violate the Landau paradigm, making conventional order parameters non-existent. Here, we uncover a spin liquid phase in a Bose-Hubbard model on the kagome lattice, and measure its topological order directly via the topological entanglement entropy. This is the first smoking-gun demonstration of a non-trivial spin liquid, identified through its entanglement entropy as a gapped groundstate with emergent Z2 gauge symmetry.Comment: 4+ pages, 3 figure

Two-Dimensional Quantum XY Model with Ring Exchange and External Field

We present the zero-temperature phase diagram of a square lattice quantum spin 1/2 XY model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the XY-order, striped or valence bond solid, staggered Neel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.Comment: 4 pages, 4 figure