Krylov subspace approximations for the exponential Euler method: error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error

Fast computation of effective diffusivities using a semi-analytical solution of the homogenization boundary value problem for block locally-isotropic heterogeneous media

Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome this difficulty is to homogenize the model by replacing the spatially-varying fine-scale diffusivity with an effective diffusivity calculated from the solution of an appropriate boundary value problem. In this paper, we present a new semi-analytical method for solving this boundary value problem and computing the effective diffusivity for pixellated, locally-isotropic, heterogeneous media. We compare our new solution method to a standard finite volume method and show that equivalent accuracy can be achieved in less computational time for several standard test cases. We also demonstrate how the new solution method can be applied to complex heterogeneous geometries represented by a grid of blocks. These results indicate that our new semi-analytical method has the potential to significantly speed up simulations of diffusion in heterogeneous media.Comment: 29 pages, 4 figures, 5 table

Solution-focused brief therapy from the perspective of clients with long-term physical health conditions

As long-term physical health conditions are becoming increasingly prevalent in our society, interventions are needed to help individuals live as well as possible. The research explores participants' experiences of solution-focused brief therapy (SFBT) with a view to determining helpful aspects of this. Eleven service users were interviewed, and interviews were analysed using inductive thematic analysis. Participants' responsibility for change and the strengths and resources they possessed were highlighted, along with the focus within therapy on goals. A number of specific SFBT techniques that were perceived as helpful during therapy were described such as reframing, competence talk and reflectiveness, as well as other factors that enabled engagement with the psychologist

Irish drug abusers II: their psychological characteristics.

This is the second in a series of 3 articles based on a study of a cohort of Irish drug abusers. This article attempts to identify the psychological traits of drug abusers within the cohort. The cohort consists of 100 drug abusers who attend a drug advisory and treatment centre in Dublin for the first time between November 1977 and February 1979. Three psychosocial, scales (GEFT, NSQ, and PFS) were administered to each subject. Overall, the results indicate that subjects who participated in the study, while of average or above average intelligence, were poorly psychologically adjusted, characterised by a poor sense of identity, a high level of suggestibility and a tendency towards emotional dependence. Their overall level of intelligence was within or above the normal range

Studies on the structure and function of the human adrenal cortex

1. The human adrenal cortex has been studied at death by correlation of plasma hydrocortisone levels with histology. It has been proved that the totally lipid depleted adrenal cortex seen at death is not functionally exhausted. 2. The pattern of cellular replacement in the human adrenal cortex has been studied. Cell replacement in the human adrenal cortex takes place only in the compact cells of the zona reticularis and ACTH stimulated zona fasciculata. The centripetal theory of cell growth does not hold for the adult human adrenal cortex. 3. The distribution of mitochondria and Golgi apparatus in the human adrenal cortex has been studied. Mitochondria are plentiful in the compact cell and the glomerulosa cell, but fewer in the clear cell. True Golgi impregnation has not been demonstrated except as a network in the clear ultrastructure which probably represents impregnation of the endoplasmic reticulum. 4. The ultrastructure of the human adrenal cortex has been studied. Three cell types are founds (i) the compact cell in the zona reticularis and ACTH-stimulated fasciculata, characterised by the presence of frequent mitochondria, prominent vesicular endoplasmic reticulum, microvilli and scanty lipid. The vesicular component has been shown by cell fractionation to be endoplasmic reticulum. (ii) the clear cell characterised by fewer mitochondria, less endoplasmic reticulum, absence of microvilli and preminent lipid globules. (iii) the glomerulosa cell characterised by relatively frequent mitochondria, dense endoplasmic reticulum, a variable lipid content and small or absent microvilli. (iv) ACTH-stimulation has the effect of altering the fine structure of the clear cell to approximately that of the compact cell

Dickkopf-3 is upregulated in osteoarthritis and has a chondroprotective role

Objective Dickkopf-3 (Dkk3) is a non-canonical member of the Dkk family of Wnt antagonists and its upregulation has been reported in microarray analysis of cartilage from mouse models of osteoarthritis (OA). In this study we assessed Dkk3 expression in human OA cartilage to ascertain its potential role in chondrocyte signaling and cartilage maintenance. Methods Dkk3 expression was analysed in human adult OA cartilage and synovial tissues and during chondrogenesis of ATDC5 and human mesenchymal stem cells. The role of Dkk3 in cartilage maintenance was analysed by incubation of bovine and human cartilage explants with interleukin-1 (IL1) and oncostatin-M (OSM). Dkk3 expression was measured in cartilage following murine hip avulsion. Whether Dkk3 influenced Wnt, TGF and activin cell signaling was assessed in primary human chondrocytes and SW1353 chondrosarcoma cells using RT-qPCR and luminescence assays. Results Increased gene and protein levels of Dkk3 were detected in human OA cartilage, synovial tissue and synovial fluid. DKK3 expression was decreased during chondrogenesis of both ATDC5 cells and humans MSCs. Dkk3 inhibited IL1 and OSM-mediated proteoglycan loss from human and bovine cartilage explants and collagen loss from bovine cartilage explans. Cartilage DKK3 expression was decreased following hip avulsion injury. TGF signaling was enhanced by Dkk3 and Wnt3a and activin signaling were inhibited. Conclusions We provide evidence that Dkk3 is upregulated in OA and may have a protective effect on cartilage integrity by preventing proteoglycan loss and helping to restore OA-relevant signaling pathway activity. Targeting Dkk3 may be a novel approach in the treatment of OA

The art of travel: forever engaged in the "there" beyond the "here"

It is, of course, the city of this year's "Platea dell'umanita"; part two, one might say, of Harald Szeemann's grand linkage between the then of the twentieth century and the now of the new millennium. I'm here--in another June--to pursue those two thoughtlets of a year ago a little bit further through Janet Cardiff and George Bures Miller's work The Paradise Institute, shown here under the curatorial direction of Wayne Baerwaldt. Taking my cue from Venice itself, I'm interested in pursuing the linkage of time with that of place: in returning to Venice, I am in a place that connects Cardiff and Collyer across time--eight years, 1993 and 2001--through place, the same site--Canada's ambassador pavilion to the biennale. I want to reconsider Collyer's sculpture Kiosk, shown along with four similar works from the early 1990s in the Canadian pavilion that year by curator Philip Monk. In the process, we add then and now to here and there. As with Yonge Street, Willowdale, Robin Collyer's Kiosk in the pavilion in 1993 was clear about its boundaries. The pavilion itself was conceived around the discrete nature of the visual artwork, its historic definitional status as an implicit commentary on, rather than elision with, affairs in the world. To enter the Canadian pavilion that year was to enter into an assembly of five iconic three-dimensional images, each of which, like Kiosk, acted with respect to one another as words in a sentence. I want to insist on this comparison, because I made the point earlier that, with Collyer, the language within signs has been converted to the language of signs--in this case the palpable form of the sign: Kiosk. Language in this mode as both title and object becomes itself palpable, very much here, and assumes an equivalent dimension to the icon to which it refers, to the "there" of the object-image. It is this contiguous relationship of here to there that connects Younge Street, Willowdale and Kiosk to the viewer within the oscillation I have described as a form of travel. Alice ran hard to find herself in the place she never left, about to embark upon a game whose moves were clearly established while their possibilities remained entirely undetermined. Collyer's pavilion in 1993 presented the viewer with a set play of five "moves," like those sketched out for Alice by the Red Queen. Striking about all of them, Kiosk included, was their quotation of suburban culture and the fabrication of interlocking specific objects whose anonymity produces the realm of possibilities out of which are generated the recognitions that provide the viewer the "carnal delight and spiritual ecstasy" experienced when confronted with Collyer's work. The viewer of Kiosk is free to move from their "here" to Collyer's "there" unimpeded. If The Paradise Institute is overdetermined, in both the technical and popular senses of the term, Collyer's Kiosk is underdetermined, indeterminate and open to moves in a game whose evolution is to be determined by the viewer. Delight and ecstasy thrive in an environment of ambiguity where possibility can be both recognized and invented, where the terms at issue are driven neither by deception nor by imposition. With Kiosk, I know where I am, even in a strange land