Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups

We extend each higher Johnson homomorphism to a crossed homomorphism from the automorphism group of a finite-rank free group to a finite-rank abelian group. We also extend each Morita homomorphism to a crossed homomorphism from the mapping class group of once-bounded surface to a finite-rank abelian group. This improves on the author's previous results [Algebr. Geom. Topol. 7 (2007):1297-1326]. To prove the first result, we express the higher Johnson homomorphisms as coboundary maps in group cohomology. Our methods involve the topology of nilpotent homogeneous spaces and lattices in nilpotent Lie algebras. In particular, we develop a notion of the "polynomial straightening" of a singular homology chain in a nilpotent homogeneous space.Comment: 34 page

Phase diagram of the antiferromagnetic XY model in two dimensions in a magnetic field

The phase diagram of the quasi-two-dimensional easy-plane antiferromagnetic model, with a magnetic field applied in the easy plane, is studied using the self-consistent harmonic approximation. We found a linear dependence of the transition temperature as a function of the field for large values of the field. Our results are in agreement with experimental data for the spin-1 honeycomb compound BaNi_2V_2O_3Comment: 3 page

Universality of residence-time distributions in non-adiabatic stochastic resonance

We present mathematically rigorous expressions for the residence-time and first-passage-time distributions of a periodically forced Brownian particle in a bistable potential. For a broad range of forcing frequencies and amplitudes, the distributions are close to periodically modulated exponential ones. Remarkably, the periodic modulations are governed by universal functions, depending on a single parameter related to the forcing period. The behaviour of the distributions and their moments is analysed, in particular in the low- and high-frequency limits.Comment: 8 pages, 1 figure New version includes distinction between first-passage-time and residence-time distribution

Investigation of the Micromechanics of the Microbond Test

The microbond test is a method which is sometimes used for measuring interfacial shear strength. In the analysis of the data it is often assumed that the interfacial shear stress is constant and thus, by implication, that the strain in the fibre along the embedded fibre decreases linearly from the point of entry to the point of exit. In this paper the results of conventional microbond tests and simulated microbond tests performed under a Raman microscope on a Kevlar-49/epoxy system are reported. The conventionally performed tests show that the calculated interfacial shear strength for this system is approximately 16 MPa regardless of the position of the supporting knife edges. The strain distribution along the fibre during simulated microbond tests was studied as a function of knife edge position, interfacial area and level of load by means of Raman spectroscopy. It was found that the interfacial shear stress was not constant, as is frequently assumed, but was strongly dependent upon distance through the droplet, knife-edge position and applied load. At low loads the strain was a maximum at the point where the fibre entered the droplet and then dropped off sharply through the embedded length. This effect was enhanced when the knife-edge separation was reduced. The variation of the shape of the stress distribution was similar to that predicted by a linear finite element analysis. At higher load levels the onset of failure in the region closest to the point where the fibre entered the droplet could be observed

Efimov states and their Fano resonances in a neutron-rich nucleus

Asymmetric resonances in elastic n+$^{19}$C scattering are attributed to Efimov states of such neutron-rich nuclei, that is, three-body bound states of the n+n+$^{18}$C system when none of the pairs is bound or some of them only weakly bound. By fitting to the general resonance shape described by Fano, we extract resonance position, width, and the "Fano profile index". While Efimov states have been discussed extensively in many areas of physics, there is only one very recent experimental observation in trimers of cesium atoms. The conjunction that we present of the Efimov and Fano phenomena may lead to experimental realization in nuclei.Comment: 4 double-column pages, 3 figure

Estimating enrichment of repetitive elements from high-throughput sequence data

We describe computational methods for analysis of repetitive elements from short-read sequencing data, and apply them to study histone modifications associated with the repetitive elements in human and mouse cells. Our results demonstrate that while accurate enrichment estimates can be obtained for individual repeat types and small sets of repeat instances, there are distinct combinatorial patterns of chromatin marks associated with major annotated repeat families, including H3K27me3/H3K9me3 differences among the endogenous retroviral element classes

On the noise-induced passage through an unstable periodic orbit II: General case

Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first exit from the interior of the unstable orbit occurs, typically displays the phenomenon of cycling: The distribution of first-exit locations is translated along the unstable periodic orbit proportionally to the logarithm of the noise intensity as the noise intensity goes to zero. We show that for a large class of such systems, the cycling profile is given, up to a model-dependent change of coordinates, by a universal function given by a periodicised Gumbel distribution. Our techniques combine action-functional or large-deviation results with properties of random Poincar\'e maps described by continuous-space discrete-time Markov chains.Comment: 44 pages, 4 figure

Bridging the second gap in translation: a case study of barriers and facilitators to implementing Patient-initiated Clinics into secondary care

Rationale: Patient-initiated Clinics (PIC) have been found to be safe and have patient and service benefits in terms of satisfaction and cost. This paper reports our experiences of implementing PIC and the practical challenges of translating research into practice.Methods: The Knowledge to Action framework was used to inform the design of implementation plans in three different departments in one secondary healthcare organisation. A focused ethnographic approach was utilised to collect data on barriers and facilitators to implementation which were analysed using iterative qualitative analytic techniques. The Promoting Action on Research Implementation in Health Services framework was used to develop the analysis and data presentation. Results: The success of implementation was mixed across the three departments. Despite evidence of effectiveness, contextual issues at a department level, such as empowered leadership and team members, trust in colleagues and patients and capacity to make changes, impacted on the progress of implementation. Discussion: Patient-initiated Clinics can offer a useful and feasible alternative for follow-up care of some groups of patients with long-term conditions in secondary care and can be implemented through strong leadership and teamwork and a positive attitude to change. Although Implementation Science as an emerging field offers useful tools and theoretical support, its complexity may create additional challenges to implementation of specific interventions and so further contribute to the second gap in translation