Interface Problems for Dispersive equations

The interface problem for the linear Schr\"odinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the wave function and a jump in their derivative at the interface are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. The problem and the method considered here extend that of an earlier paper by Deconinck, Pelloni and Sheils (2014). The dispersive nature of the problem presents additional difficulties that are addressed here.Comment: 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:1402.3007, Studies in Applied Mathematics 201

A Fair Exchange: The Reciprocal Relationship Between Universities and Clinical Placement Supervisors

Clinical psychology training in the UK relies heavily upon supervised clinical practice placements. Placement supervisors have a significant responsibility for providing trainees with the learning experiences required for qualification. The role is demanding and whilst the university benefits greatly, it is less clear what supervisors receive in return. This is important when one considers how positive relationships and social action are influenced by reciprocity and a sense of belongingness. Despite its importance, no research has directly explored the relationship between supervisors and the university in a clinical psychology training context. This novel study sought to explore how supervisors perceive their role and their connectedness / belongingness to the university, and whether technology utilized by other areas of pedagogy led to improvements. Access to electronic resources was sent to clinical placement supervisors (n=100). A subset of these (n=7) signed up to complete a semi-structured interview. The interviews were analysed using template analysis. Common themes emerged, including perceived benefits of the supervisor role, such as feeling connected to the training course, despite significant challenges and demands. The provision of electronic resources was found to have the potential to enhance connectedness for all stakeholders. The implications of these findings are discussed

Expression microarray analysis of papillary thyroid carcinoma and benign thyroid tissue: emphasis on the follicular variant and potential markers of malignancy

The most common sub-variant of papillary thyroid carcinoma (PTC) is the so-called follicular variant (FVPTC), which is a particularly problematic lesion and can be challenging from a diagnostic viewpoint even in resected lesions. Although fine needle aspiration cytology is very useful in the diagnosis of PTC, its accuracy and utility would be greatly facilitated by the development of specific markers for PTC and its common variants. We used the recently developed Applied Biosystems 1700 microarray system to interrogate a series of 11 benign thyroid lesions and conditions and 14 samples of PTC (six with classic morphology and eight with follicular variant morphology). TaqMan® reverse transcriptase-polymerase chain reaction was used to validate the expression portfolios of 50 selected transcripts. Our data corroborates potential biomarkers previously identified in the literature, such as LGALS3, S100A11, LYN, BAX, and cluster of differentiation 44 (CD44). However, we have also identified numerous transcripts never previously implicated in thyroid carcinogenesis, and many of which are not represented on other microarray platforms. Diminished expression of metallothioneins featured strongly among these and suggests a possible role for this family as tumour suppressors in PTC. Fifteen transcripts were significantly associated with FVPTC morphology. Surprisingly, these genes were associated with an extremely narrow repertoire of functions, including the major histocompatibility complex and cathepsin families

Platelet adhesion and degranulation induce pro-survival and pro-angiogenic signalling in ovarian cancer cells

Thrombosis is common in ovarian cancer. However, the interaction of platelets with ovarian cancer cells has not been critically examined. To address this, we investigated platelet interactions in a range of ovarian cancer cell lines with different metastatic potentials [HIO-80, 59M, SK-OV-3, A2780, A2780cis]. Platelets adhered to ovarian cancer cells with the most significant adhesion to the 59M cell line. Ovarian cancer cells induced platelet activation [P-selectin expression] in a dose dependent manner, with the most significant activation seen in response to the 59M cell line. The platelet antagonists [cangrelor, MRS2179, and apyrase] inhibited 59M cell induced activation suggesting a P2Y12 and P2Y1 receptor mediated mechanism of platelet activation dependent on the release of ADP by 59M cells. A2780 and 59M cells potentiated PAR-1, PAR-4, and TxA2 receptor mediated platelet activation, but had no effect on ADP, epinephrine, or collagen induced activation. Analysis of gene expression changes in ovarian cancer cells following treatment with washed platelets or platelet releasate showed a subtle but valid upregulation of anti-apoptotic, anti-autophagy pro-angiogenic, pro-cell cycle and metabolic genes. Thus, ovarian cancer cells with different metastatic potential adhere and activate platelets differentially while both platelets and platelet releasate mediate pro-survival and pro-angiogenic signals in ovarian cancer cells