On uniform edge-n-colorings of tilings.

An edge-n-coloring of a uniform tiling {\cal T} is uniform if for any two vertices of {\cal T} there is a symmetry of {\cal T} that preserves the colors of the edges and maps one vertex onto the other. This paper gives a method based on group theory and color symmetry theory to arrive at uniform edge-n-colorings of uniform tilings. The method is applied to give a complete enumeration of uniform edge-n-colorings of the uniform tilings of the Euclidean plane, for which the results point to a total of 114 colorings, n = 1, 2, 3, 4, 5. Examples of uniform edge-n-colorings of tilings in the hyperbolic plane and two-dimensional sphere are also presented.

Symmetry groups of two-way twofold and three-way threefold fabrics.

This work discusses the symmetry groups of two classes of woven fabrics, two-way twofold fabrics and three-way threefold fabrics. A method to arrive at a design of a fabric is presented, employing methods in color symmetry theory. Geometric representations of all possible layer group or diperiodic symmetry structures of the fabrics are derived. There are 50 layer symmetry groups corresponding to two-way twofold fabrics and 27 layer symmetry groups corresponding to three-way threefold fabrics.

Reduction in transfer of micro-organisms between patients and staff using short-sleeved gowns and hand/arm hygiene in intensive care during the COVID-19 pandemic: A simulation-based randomised trial.

Background: Current personal protective equipment (PPE) practices in UK intensive care units involve "sessional" use of long-sleeved gowns, risking nosocomial infection transmitted via gown sleeves. Data from the first wave of the COVID19 pandemic demonstrated that these changes in infection prevention and control protocols were associated with an increase in healthcare associated bloodstream infections. We therefore explored the use of a protocol using short-sleeved gowns with hand and arm hygiene to reduce this risk. Methods: ICU staff were trained in wearing short-sleeved gowns and using a specific hand and arm washing technique between patients (experimental protocol). They then underwent simulation training, performing COVID-19 intubation and proning tasks using either experimental protocol or the standard (long-sleeved) control protocol. Fluorescent powder was used to simulate microbial contamination, detected using photographs under ultraviolet light. Teams were randomised to use control or experimental PPE first. During the simulation, staff were questioned on their feelings about personal safety, comfort and patient safety. Results: Sixty-eight staff and 17 proning volunteers were studied. Experimental PPE completely prevented staff contamination during COVID-19 intubation, whereas this occurred in 30/67 staff wearing control PPE (p = .003, McNemar). Proning volunteers were contaminated by staff in 15/17 control sessions and in 1/17 with experimental PPE (p = .023 McNemar). Staff comfort was superior with experimental PPE (p< .001, Wilcoxon). Their personal safety perception was initially higher with control PPE, but changed towards neutrality during sessions (p < .001 start, 0.068 end). Their impressions of patient safety were initially similar (p = .87), but finished strongly in favour of experimental PPE (p < .001). Conclusions: Short-sleeved gowns with hand and forearm cleansing appear superior to sessional long-sleeved gowns in preventing cross-contamination between staff and patients.

On the frequency module of the hull of a primitive substitution tiling.

Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitution. A method is presented on how to arrive at the frequency module of the hull of a primitive substitution tiling (the minimal {\bb Z}-module, where {\bb Z} is the set of integers) containing the absolute frequency of each of its patches. The method involves deriving the tiling's edge types and vertex stars; in the process, a new substitution is introduced on a reconstructed set of prototiles.

Child-parent screening for familial hypercholesterolemia.

A pilot study of child-parent screening for familial hypercholesterolemia was undertaken in children aged 1 to 2 years coming for immunization. Of 214 parents asked, 200 agreed to screening (94%). Simultaneous immunization-cholesterol measurement was successful in all children. Population child-parent screening is feasible and acceptable when combined with pediatric immunization.

k-Isocoronal tilings.

In this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s ≤ k. A tiling {\cal T} is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex corona of a vertex x of {\cal T} is used to refer to the tiles that are incident to x. The k-isocoronal tilings include the vertex-k-transitive tilings (k-isogonal) and k-uniform tilings. In a vertex-k-transitive tiling, the vertices form k transitivity classes under its symmetry group. If this tiling consists of regular polygons then it is k-uniform. This article also presents the classification of isocoronal tilings in the Euclidean plane.

Local and global color symmetries of a symmetrical pattern.

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99-108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.

Primitive substitution tilings with rotational symmetries.

This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are given of the substitutions σ6 and σ7 which give rise to aperiodic primitive substitution tilings with dense tile orientations and which are invariant under six- and sevenfold rotations, respectively; the derivation of the symmetry orders of their hulls is also presented.

Body Surface Area and Baseline Blood Pressure Predict Subclinical Anthracycline Cardiotoxicity in Women Treated for Early Breast Cancer.

BACKGROUND AND AIMS: Anthracyclines are highly effective chemotherapeutic agents which may cause long-term cardiac damage (chronic anthracycline cardiotoxicity) and heart failure. The pathogenesis of anthracycline cardiotoxicity remains incompletely understood and individual susceptibility difficult to predict. We sought clinical features which might contribute to improved risk assessment. METHODS: Subjects were women with early breast cancer, free of pre-existing cardiac disease. Left ventricular ejection fraction was measured using cardiovascular magnetic resonance before and >12 months after anthracycline-based chemotherapy (>3 months post-Trastuzumab). Variables associated with subclinical cardiotoxicity (defined as a fall in left ventricular ejection fraction of ≥5%) were identified by logistic regression. RESULTS: One hundred and sixty-five women (mean age 48.3 years at enrollment) completed the study 21.7 months [IQR 18.0-26.8] after starting chemotherapy. All received anthracyclines (98.8% epirubicin, cumulative dose 400 [300-450] mg/m2); 18% Trastuzumab. Baseline blood pressure was elevated (≥140/90mmHg, mean 147.3/86.1mmHg) in 18 subjects. Thirty-four subjects (20.7%) were identified with subclinical cardiotoxicity, independent predictors of which were the number of anthracycline cycles (odds ratio, OR 1.64 [1.17-2.30] per cycle), blood pressure ≥140/90mmHg (OR 5.36 [1.73-17.61]), body surface area (OR 2.08 [1.36-3.20] per standard deviation (0.16m2) increase), and Trastuzumab therapy (OR 3.35 [1.18-9.51]). The resultant predictive-model had an area under the receiver operating characteristics curve of 0.78 [0.70-0.86]. CONCLUSIONS: We found subclinical cardiotoxicity to be common even within this low risk cohort. Risk of cardiotoxicity was associated with modestly elevated baseline blood pressure-indicating that close attention should be paid to blood pressure in patients considered for anthracycline based chemotherapy. The association with higher body surface area suggests that indexing of anthracycline doses to surface area may not be appropriate for all, and points to the need for additional research in this area.

Symmetry groups associated with tilings on a flat torus.

This work investigates symmetry and color symmetry properties of Kepler, Heesch and Laves tilings embedded on a flat torus and their geometric realizations as tilings on a round torus in Euclidean 3-space. The symmetry group of the tiling on the round torus is determined by analyzing relevant symmetries of the planar tiling that are transformed to axial symmetries of the three-dimensional tiling. The focus on studying tilings on a round torus is motivated by applications in the geometric modeling of nanotori and the determination of their symmetry groups.

Symmetry groups of single-wall nanotubes.

This work investigates the symmetry properties of single-wall carbon nanotubes and their structural analogs, which are nanotubes consisting of different kinds of atoms. The symmetry group of a nanotube is studied by looking at symmetries and color fixing symmetries associated with a coloring of the tiling by hexagons in the Euclidean plane which, when rolled, gives rise to a geometric model of the nanotube. The approach is also applied to nanotubes with non-hexagonal symmetry arising from other isogonal tilings of the plane.

On subgroups of crystallographic Coxeter groups.

A framework is presented based on color symmetry theory that will facilitate the determination of the subgroup structure of a crystallographic Coxeter group. It is shown that the method may be extended to characterize torsion-free subgroups. The approach is to treat these groups as groups of symmetries of tessellations in space by fundamental polyhedra.