High-frequency asymptotic compression of dense BEM matrices for general geometries without ray tracing

Wave propagation and scattering problems in acoustics are often solved with boundary element methods. They lead to a discretization matrix that is typically dense and large: its size and condition number grow with increasing frequency. Yet, high frequency scattering problems are intrinsically local in nature, which is well represented by highly localized rays bouncing around. Asymptotic methods can be used to reduce the size of the linear system, even making it frequency independent, by explicitly extracting the oscillatory properties from the solution using ray tracing or analogous techniques. However, ray tracing becomes expensive or even intractable in the presence of (multiple) scattering obstacles with complicated geometries. In this paper, we start from the same discretization that constructs the fully resolved large and dense matrix, and achieve asymptotic compression by explicitly localizing the Green's function instead. This results in a large but sparse matrix, with a faster associated matrix-vector product and, as numerical experiments indicate, a much improved condition number. Though an appropriate localisation of the Green's function also depends on asymptotic information unavailable for general geometries, we can construct it adaptively in a frequency sweep from small to large frequencies in a way which automatically takes into account a general incident wave. We show that the approach is robust with respect to non-convex, multiple and even near-trapping domains, though the compression rate is clearly lower in the latter case. Furthermore, in spite of its asymptotic nature, the method is robust with respect to low-order discretizations such as piecewise constants, linears or cubics, commonly used in applications. On the other hand, we do not decrease the total number of degrees of freedom compared to a conventional classical discretization. The combination of the ...Comment: 24 pages, 13 figure

On the eigenmodes of periodic orbits for multiple scattering problems in 2D

Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the oscillatory properties of the solution. However, the high-frequency wave pattern becomes very complicated in the presence of multiple scattering obstacles. We consider a boundary integral equation formulation of the Helmholtz equation in two dimensions involving several obstacles, for which ray tracing schemes have been previously proposed. The existing analysis of ray tracing schemes focuses on periodic orbits between a subset of the obstacles. One observes that the densities on each of the obstacles converge to an equilibrium after a few iterations. In this paper we present an asymptotic approximation of the phases of those densities in equilibrium, in the form of a Taylor series. The densities represent a full cycle of reflections in a periodic orbit. We initially exploit symmetry in the case of two circular scatterers, but also provide an explicit algorithm for an arbitrary number of general 2D obstacles. The coefficients, as well as the time to compute them, are independent of the wavenumber and of the incident wave. The results may be used to accelerate ray tracing schemes after a small number of initial iterations.Comment: 24 pages, 9 figures and the implementation is available on https://github.com/popsomer/asyBEM/release

Resilience in middle-aged partners of patients diagnosed with incurable cancer : a thematic analysis

Background : Providing care for patients with advanced cancer is often the responsibility of the partner. Being confronted with an incurable cancer diagnosis can be highly disruptive for the patient's partner and can be considered a potentially traumatic event. However, most caregivers seem to adapt well during the process of providing care. This finding is in line with the concept of resilience in literature: a dynamic process of adapting well, resulting from the interplay between intrinsic and extrinsic resources and risks. Resilience is age-related, with the elderly population being higher in resilience as compared to the younger generation. However, resilience has been understudied in middle-aged caregivers. Aim : To explore what intrinsic and extrinsic resources facilitate or hamper resilience in the middle-aged partner of a patient with incurable cancer. Methods : Nine middle-aged partners of patients who died at home of cancer were selected and interviewed in depth within the first year following the death of their partner. A thematic analysis utilizing an inductive approach was conducted. Findings : Resilience was challenged by the partner's diagnosis of incurable cancer. All participants made use of a set of interacting, caregiver-specific and context-related resources, facilitating a resilient process and leading to positive feelings and even personal growth. The partners demonstrated individual competences: adaptive flexibility, positivism, a sense of self-initiative and adaptive dependency. Furthermore, they relied on their context: cancer-related professionals and relatives. Context and situation interact continuously. The resulting dynamics were based on the context-availability, meaningful relationships and the patient's role. Conclusion : A resilient trajectory results from an interplay between individual and contextual resources. To build resilience in middle-aged partners of patients with incurable cancer, health care professionals should address all available resources. Moreover, they should be aware of being part of the caregiver's context, a complex adaptive system that can be either resilience-supporting or -threatening

Resilience in advanced cancer caregiving

Background Family caregivers of advanced cancer patients are at risk for developing mental disorders. Despite this risk, the majority seem to adapt well, and throughout the caregiving period, their trajectory is characterised by healthy functioning. However, GPs struggle with making timely assessments of caregivers at risk for mental dysfunction, since they often fail to seek medical help for themselves and the appropriate research about resilience in cancer caregivers is scarce. Moreover, research is hampered by the lack of a universal definition or theoretical framework. Aim To propose a comprehensive definition and framework for further research in family caregiving for advanced cancer patients. Method Inspired by the hermeneutic methodology, reviews and concept analyses on resilience following a potentially traumatic event were searched and analysed. Conforming to the hermeneutic methodology, article collection from PubMed, EMBASE, CINAHL, and PsycInfo was followed by analysis and was stopped when saturation was reached. Elements consistently arising from the definitions of resilience were listed and the theoretical frameworks were compared. Results The APA definition: ‘resilience is the process of adapting well in the face of adversity, trauma or threats’ and Bonanno’s framework ‘temporal elements of resilience’ are proposed. Conclusion There is a need for studies on resilience in caregivers of advanced cancer patients. Resilience is context-dependent, hence, study results cannot be transferred as such from one clinical situation to another. Furthermore, conceptual ambiguities hinder the interpretation and comparison of study results. For further research on resilience in caregivers of advanced cancer patients, we suggest the APA definition of resilience and Bonanno’s framework

Resilience in family caregivers of patients diagnosed with advanced cancer : unravelling the process of bouncing back from difficult experiences : a hermeneutic review

Background Despite the risk for developing mental disorders, most of advanced cancer patients' family caregivers undergo a resilient process throughout the caregiving period. Research on resilience in caregivers of advanced cancer patients is scarce and further hindered by the lack of a univocal definition and a theoretical framework. Objectives To provide clarity on the concept of resilience by proposing an integrative view that can support health care professionals and researchers in conducting and interpreting research on resilience. Methods The review process was inspired by the hermeneutic methodology: a cyclic review process, consisting of repeated searching and analysing until data saturation is reached and focussed on achieving a deeper understanding of ill-defined concepts. The definitions from eighteen reviews on resilience and the theoretical frameworks from eight concept analyses were analysed. The composing elements of resilience were listed and compared. Results The American Psychological Association's definition of resilience and Bonanno's theoretical framework are suggested to guide further research on resilience. Moreover, four knowledge gaps were uncovered: (1) How do resilience resources interact? (2) What are the key predictors for a resilient trajectory? (3) How do the resilient trajectories evolve across the caregiving period? And (4) how does the patient's nearing death influence the caregiver's resilience? Conclusion To address flaws in conceptualisation and the resulting gaps in knowledge, we suggest a definition and a theoretical framework that are suited to allow heterogeneity in the field, but enables the development of sound interventions, as well as facilitate the interpretation of intervention effectiveness

Digital dermatitis in cattle is associated with an excessive innate immune response triggered by the keratinocytes

Background: Digital Dermatitis (DD) is a common disease of dairy cows, the pathogenesis of which is still not clear. This study examined some host responses associated with the typical lesions, in an attempt to further elucidate the pathogenesis of the disease. Twenty four samples representing the 5 different clinical stages of DD (M0-M4) were collected from slaughtered cattle for histopathological and immunological analyses. Results: Significant increases in total epidermal thickness were found in M2, M3, and M4 when compared with M0 and M1. M3 samples, when compared with M0 and M1, were characterized by a significant increase in the thickness of the keratin layer. Counts of both eosinophils and neutrophils were at a maximum in the M2 stage and decreased in the M3 and M4 stage. A significant increase in IL8 expression was observed in the M2-M3 stages of the disease and immunohistochemical staining showed the source as keratinocytes, suggesting an important role for keratinocyte-derived IL8 in the pathogenesis of DD. Conclusion: Results of the present study point to a strong stimulation of the innate immune response at the level of the keratinocytes throughout most of the clinical stages, and a delayed response of the adaptive immune reaction

Feeding Practices and Factors Contributing to Wasting, Stunting, and Iron-deficiency Anaemia Among 3-23-month Old Children in Kilosa District, Rural Tanzania

Infants in Tanzania are particularly vulnerable to under-nutrition during transition from breastmilk (as the only source of nourishment) to solid foods. A cross-sectional study was undertaken in Kilosa district in Tanzania to determine the feeding practices and the extent of wasting, stunting, and iron-deficiency anaemia. The study was done in two stages: in the first stage, a 24-hour dietary assessment was conducted to identify the type of complementary foods given and the eating habits according to age for 378 children aged 3-23 months. In the second stage, a progressive recruitment of 309 infants aged six months was made to measure weight, length, haemoglobin (Hb) concentration, zinc protoporphyrin concentration, and malaria parasitaemia. Birth-weight, the potential contributing factor to under-nutrition and iron-deficiency anaemia, was obtained from the children's clinic cards. The 24-hour dietary assessment revealed that children consumed mainly a thin porridge prepared from maize flour as complementary food. Carbohydrates contributed most energy (on average 69%), followed by fats (18.6%) and protein (on average 12.1%). The complementary food covered only 15%, 20%, and 27% of the recommended iron intake for children aged 6-8, 9-11 and 12-23 months respectively. The mean Hb concentration was 9.3\ub11.9 g/dL, 68% of the infants were moderately anaemic(7-<11 g/dL), and about 11% were severely anaemic with Hb below 7 g/dL, while 21% were non-anaemic Hb ( 6511 g/dL). Equally, the mean zinc protoporphyrin concentration was 10.0\ub16.2 \u3bcg/g Hb, and 76% of the infants were iron-deficient(>5 \u3bcg/g Hb). The prevalence of stunting was 35%, while wasting was only 1.3%. Low birth-weight and low body mass index of mothers were the strong predictors of stunting, whereas low birth-weight and iron-deficiency were the strong predictors of anaemia. The prevalence of malaria parasitaemia was high, affecting 50% of the infants. Having malaria was the only independent predictor associated with stunting, anaemia, and iron-deficiency. There is an urgent need to improve traditional complementary foods in the studied community in terms of energy density, amount of fat in the diet, and bioavailability of macro and micronutrients