Minimal knotted polygons in cubic lattices

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Confinement of knotted polymers in a slit

We investigate the effect of knot type on the properties of a ring polymer confined to a slit. For relatively wide slits, the more complex the knot, the more the force exerted by the polymer on the walls is decreased compared to an unknotted polymer of the same length. For more narrow slits the opposite is true. The crossover between these two regimes is, to first order, at smaller slit width for more complex knots. However, knot topology can affect these trends in subtle ways. Besides the force exerted by the polymers, we also study other quantities such as the monomer-density distribution across the slit and the anisotropic radius of gyration.Comment: 9 pages, 6 figures, submitted for publicatio

Ultrasound study of the asymptomatic shoulder in patients with a confirmed rotator cuff tear in the opposite shoulder

Objective. To document the incidence of asymptomatic rotator cuff tears in patients with a confirmed symptomatic tear in the opposite shoulder, and to identify ultrasound findings that may distinguish symptomatic from asymptomatic tears. Design. When patients are referred for an ultrasound examination for the confirmation of symptomatic rotator cuff tear the opposite shoulder is often used for comparison. However, patients often have a similar tear on the asymptomatic side. Fifty patients with a confirmed symptomatic rotator cuff tear and an asymptomatic shoulder on the opposite side were chosen for inclusion. The patients were examined using a Siemens Sonoline Elegra 7.5 MHz linear multi-frequency probe. The appearance of the rotator cuff, long head of the biceps and the subacromial-subdeltoid bursa (SASD bursa) were documented. The antero-posterior (AP) dimension of the supraspinatus muscle and fat between the trapezius and supraspinatus muscles were measured, which indicated if a tear was acute or chronic. The width and length of the rotator cuff tear were measured. Setting. Division of Sports Medicine, University of Pretoria. Results. Fifty-four per cent of the asymptomatic shoulders had tears. We found that the symptomatic tears were larger, appeared more chronic and had an associated biceps tendinopathy and glenohumeral joint effusion. Conclusion. As other authors have found, the high incidence of asymptomatic tears indicates that rotator cuff tears can be regarded as a natural correlate of aging and that bilateral tears are common. Initial treatment should be conservative, but larger tears may benefit from early surgery before becoming chronic and causing glenohumeral dysfunction. South African Journal of Sports Medicine Vol. 19 (1) 2007: pp. 23-2

Tuberculosis infection control practices in a high-burden metro in South Africa : a perpetual bane for efficient primary health care service delivery

Background: Tuberculosis (TB) prevention, including infection control, is a key element in the strategy to end the global TB epidemic. While effective infection control requires all health system components to function well, this is an area that has not received sufficient attention in South Africa despite the availability of policy and guidelines. Aim: To describe the state of implementation of TB infection control measures in a high-burden metro in South Africa. Setting: The research was undertaken in a high TB-and HIV-burdened metropolitan area of South Africa. More specifically, the study sites were primary health care facilities (PHC), that among other services also diagnosed TB. Methods: A cross-sectional survey, focusing on the World Health Organization levels of infection control, which included structured interviews with nurses providing TB diagnosis and treatment services as well as observations, at all 41 PHC facilities in a high TB-burdened and HIV-burdened metro of South Africa. Results: Tuberculosis infection control was poorly implemented, with few facilities scoring 80% and above on compliance with infection control measures. Facility controls: 26 facilities (63.4%) had an infection control committee and 12 (29.3%) had a written infection control plan. Administrative controls: 26 facilities (63.4%) reported separating coughing and non-coughing patients, while observations revealed that only 11 facilities (26.8%) had separate waiting areas for (presumptive) TB patients. Environmental controls: most facilities used open windows for ventilation (n = 30; 73.2%); however, on the day of the visit, only 12 facilities (30.3%) had open windows in consulting rooms. Personal protective equipment: 9 facilities (22%) did not have any disposable respirators in stock and only 9 respondents (22%) had undergone fit testing. The most frequently reported barrier to implementing good TB infection control practices was lack of equipment (n = 22; 40%) such as masks and disposable respirators, as well as the structure or layout of the PHC facilities. The main recommendation to improve TB infection control was education for patients and health care workers (n = 18; 33.3%). Conclusion: All levels of the health care system should be engaged to address TB prevention and infection control in PHC facilities. Improved infection control will address the nosocomial spread of TB in health facilities and keep health care workers and patients safe from infection

Collapsing lattice animals and lattice trees in two dimensions

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into two different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees, but the other is {\it not yet} bond driven and does not contain the Derrida-Herrmann model as special point. Instead it ends at a multicritical point $P^*$ where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. The Derrida-Herrmann model is representative for the bond driven collapse, which then forms the fourth universality class on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl

Tricarbon­yl(η6-flavone)chromium(0)

In the title compound, [Cr(C15H10O2)(CO)3], the Cr(CO)3 unit exhibits a three-legged piano-stool conformation. The chromium metal centre is coordinated by the phenyl ring of the flavone ligand [Cr—(phenyl centroid) distance = 1.709 (1) Å]. The ligand is approximately planar, the dihedral angles between the γ-pyrone ring and the phenyl ring and between the γ-pyrone and the phenyl­ene ring being 2.91 (5) and 3.90 (5)°, respectively. The mol­ecular packing shows π–π stacking between the flavone ligands of neighbouring mol­ecules

Simulations of lattice animals and trees

The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. Essentially we start simulating percolation clusters (either site or bond), re-weigh them according to the animal (tree) ensemble, and prune or branch the further growth according to a heuristic fitness function. In contrast to previous applications of PERM, this fitness function is {\it not} the weight with which the actual configuration would contribute to the partition sum, but is closely related to it. We obtain high statistics of animals with up to several thousand sites in all dimension 2 <= d <= 9. In addition to the partition sum (number of different animals) we estimate gyration radii and numbers of perimeter sites. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and >= 8. In addition, we present the hitherto most precise estimates for growth constants in d >= 3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy. Finally, we discuss the collapse of animals and trees, arguing that our present version of the algorithm is also efficient for some of the models studied in this context, but showing that it is {\it not} very efficient for the `classical' model for collapsing animals.Comment: 17 pages RevTeX, 29 figures include