Integrable models for shallow water with energy dependent spectral problems

We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependance on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup-Bousinesq equation. We formulate the inverse problem as a Riemann-Hilbert problem with a Z2 reduction group. The soliton solutions are explicitly obtained.Comment: 17 pages, 3 figure

Safer healthcare at home: Detecting, correcting and learning from incidents involving infusion devices

OBJECTIVE: Complex medical devices such as infusion pumps are increasingly being used in patients’ homes with little known about the impact on patient safety. Our aim was to better understand the risks to patient safety in this situation and how these risks might be minimised, by reference to incident reports. DESIGN: We identified 606 records of incidents associated with infusion devices that had occurred in a private home and were reported to the UK National Reporting and Learning Service (2005–2015 inclusive). We used thematic analysis to identify key themes. RESULTS: In this paper we focus on two emergent themes: detecting and diagnosing incidents; and locating the patient, lay caregivers and their family in incident reports. The majority of incidents were attributed to device malfunction, and resulted in the patient being under-dosed. Delays in recognising and responding to problems were identified, alongside challenges in identifying the cause. We propose a process model for fault diagnosis and correction. Patients and caregivers did not feature strongly in reports; we highlight how the device is in the home but of the care system, and propose an agent model to describe this; we also identify ways of mitigating this disjoint. CONCLUSION: Devices need to be appropriately tailored to the setting in which they are employed, and within a system of care that ensures they are used optimally and safely. Suggested features to improve patient safety include devices that can provide better feedback to identify problems and support resolution, alongside greater monitoring and technical support by care providers for both patients and frontline professionals. The proposed process and agent models provide a structure for reviewing safety and learning from incidents in home health care

Critical percolation of free product of groups

In this article we study percolation on the Cayley graph of a free product of groups. The critical probability $p_c$ of a free product $G_1*G_2*...*G_n$ of groups is found as a solution of an equation involving only the expected subcritical cluster size of factor groups $G_1,G_2,...,G_n$. For finite groups these equations are polynomial and can be explicitly written down. The expected subcritical cluster size of the free product is also found in terms of the subcritical cluster sizes of the factors. In particular, we prove that $p_c$ for the Cayley graph of the modular group $\hbox{PSL}_2(\mathbb Z)$ (with the standard generators) is $.5199...$, the unique root of the polynomial $2p^5-6p^4+2p^3+4p^2-1$ in the interval $(0,1)$. In the case when groups $G_i$ can be "well approximated" by a sequence of quotient groups, we show that the critical probabilities of the free product of these approximations converge to the critical probability of $G_1*G_2*...*G_n$ and the speed of convergence is exponential. Thus for residually finite groups, for example, one can restrict oneself to the case when each free factor is finite. We show that the critical point, introduced by Schonmann, $p_{\mathrm{exp}}$ of the free product is just the minimum of $p_{\mathrm{exp}}$ for the factors

A socio-ecological model of agency: The role of structure and agency in shaping education and employment transitions in England

This study examines the role of structural and agentic resources in shaping school-to-work transitions in England. We ask to what extent are young people able to steer the course of their lives despite the constraining forces of social structure, and how satisfied are they with their lives following the completion of compulsory schooling. Drawing on data from the Longitudinal Study of Young People in England we use sequence analysis of monthly activity data to identify differences in the timing and sequencing of education and employment transitions. We identified six distinct pathways, differentiating between an academic track, three pathways involving further education and training, as well as a work-focused transition and a group of young people who were over a long period not in education or training (NEET). The findings suggest that not all young people are inclined to follow an academic track and instead select into pathways involving vocational training or further education, enabling them to experience competence and life satisfaction. For others (about one in 10), however, the lack of socioeconomic and psycho-social resources is too overwhelming and they encounter long-term experience of NEET or are not able to transform their educational credentials into employment opportunities. The findings highlight that in addition to considering structural constraints it is important to conceptualise the role of the agent for a better understanding of variations in youth transitions

Microwave properties of DyBa_2Cu_3O_(7-x) monodomains and related compounds in magnetic fields

We present a microwave characterization of a DyBa$_{2}$Cu$_{3}$O$_{7-x}$ single domain, grown by the top-seeded melt-textured technique. We report the (a,b) plane field-induced surface resistance, $\Delta R_s(H)$, at 48.3 GHz, measured by means of a cylindrical metal cavity in the end-wall-replacement configuration. Changes in the cavity quality factor Q against the applied magnetic field yield $\Delta R_s(H)$ at fixed temperatures. The temperature range [70 K ; T_c] was explored. The magnetic field $\mu_0 H <$ 0.8 T was applied along the c axis. The field dependence of $\Delta R_s(H)$ does not exhibit the steep, step-like increase at low fields typical of weak-links. This result indicates the single-domain character of the sample under investigation. $\Delta R_s(H)$ exhibits a nearly square-root dependence on H, as expected for fluxon motion. From the analysis of the data in terms of motion of Abrikosov vortices we estimate the temperature dependences of the London penetration depth $\lambda$ and the vortex viscosity $\eta$, and their zero-temperature values $\lambda(0)=$165 nm and $\eta(0)=$ 3 10$^{-7}$ Nsm$^{-2}$, which are found in excellent agreement with reported data in YBa$_{2}$Cu$_{3}$O$_{7-x}$ single crystals. Comparison of microwave properties with those of related samples indicate the need for reporting data as a function of T/T_c in order to obtain universal laws.Comment: 6 pages, 4 figures, LaTeX, submitted to Journal of Applied Physic

Future mobility in an ageing society:Where are we heading?

The demographic profile of UK society is changing as people live longer. Maintaining the wellbeing and quality of life of an ageing society is set to be extremely challenging. To what extent can the state afford to meet a potentially burgeoning demand for social care? What expectations will be placed upon informal carers to enable the system to cope? In what ways and to what extent might assistive technologies have a part to play in supporting people both in terms of active ageing and in relation to coping with failing health? Beyond these questions is one which is more explicitly pertinent to transport policy: how and where will older people live and how will this affect patterns of mobility and levels of travel demand? This paper reports on a scenario planning exercise which has examined four different futures for living in later life, defined by considering two critical uncertainties: the extent to which older people in society engage with new healthcare technologies; and the extent to which the state provides care for people living in later life. The scenarios, explored with transport, ageing and assistive technology experts, serve to highlight how social practices may be shaped in very different ways both for older people and for those with whom they interact. The paper goes on to examine the implications for future mobility – such as the role of the home as a trip attractor as well as a trip generator – as well as to explore the extent to which transport policymakers are equipped to address the uncertainties for the transport system of an ageing society

Major features and forcing of high‐latitude northern hemisphere atmospheric circulation using a 110,000‐year‐long glaciochemical series

The Greenland Ice Sheet Project 2 glaciochemical series (sodium, potassium, ammonium, calcium, magnesium, sulfate, nitrate, and chloride) provides a unique view of the chemistry of the atmosphere and the history of atmospheric circulation over both the high latitudes and mid‐low latitudes of the northern hemisphere. Interpretation of this record reveals a diverse array of environmental signatures that include the documentation of anthropogenically derived pollutants, volcanic and biomass burning events, storminess over marine surfaces, continental aridity and biogenic source strength plus information related to the controls on both high‐ and low‐frequency climate events of the last 110,000 years. Climate forcings investigated include changes in insolation of the order of the major orbital cycles that control the long‐term behavior of atmospheric circulation patterns through changes in ice volume (sea level), events such as the Heinrich events (massive discharges of icebergs first identified in the marine record) that are found to operate on a 6100‐year cycle due largely to the lagged response of ice sheets to changes in insolation and consequent glacier dynamics, and rapid climate change events (massive reorganizations of atmospheric circulation) that are demonstrated to operate on 1450‐year cycles. Changes in insolation and associated positive feedbacks related to ice sheets may assist in explaining favorable time periods and controls on the amplitude of massive rapid climate change events. Explanation for the exact timing and global synchroneity of these events is, however, more complicated. Preliminary evidence points to possible solar variability‐climate associations for these events and perhaps others that are embedded in our ice‐core‐derived atmospheric circulation records

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field

Arterial pathology in canine mucopolysaccharidosis-I and response to therapy.

Mucopolysaccharidosis-I (MPS-I) is an inherited deficiency of α-L-iduronidase (IdU) that causes lysosomal accumulation of glycosaminoglycans (GAG) in a variety of parenchymal cell types and connective tissues. The fundamental link between genetic mutation and tissue GAG accumulation is clear, but relatively little attention has been given to the morphology or pathogenesis of associated lesions, particularly those affecting the vascular system. The terminal parietal branches of the abdominal aorta were examined from a colony of dogs homozygous (MPS-I affected) or heterozygous (unaffected carrier) for an IdU mutation that eliminated all enzyme activity, and in affected animals treated with human recombinant IdU. High-resolution computed tomography showed that vascular wall thickenings occurred in affected animals near branch points, and associated with low endothelial shear stress. Histologically these asymmetric 'plaques' entailed extensive intimal thickening with disruption of the internal elastic lamina, occluding more than 50% of the vascular lumen in some cases. Immunohistochemistry was used to show that areas of sclerosis contained foamy (GAG laden) macrophages, fibroblasts and smooth muscle cells, with loss of overlying endothelial basement membrane and claudin-5 expression. Lesions contained scattered cells expressing nuclear factor-κβ (p65), increased fibronectin and transforming growth factor β-1 signaling (with nuclear Smad3 accumulation) in comparison to unaffected vessels. Intimal lesion development and morphology was improved by intravenous recombinant enzyme treatment, particularly with immune tolerance to this exogenous protein. The progressive sclerotic vasculopathy of MPS-I shares some morphological and molecular similarities to atherosclerosis, including formation in areas of low shear stress near branch points, and can be reduced or inhibited by intravenous administration of recombinant IdU