Vortices ans Polynomials: Nonuniqueness of the Adler-Moser polynomials for the Tkachenko equation

Stationary and translating relative equilibria of point vortices in the plane are studied. It is shown that stationary equilibria of a system containing point vortices with arbitrary choice of circulations can be described with the help of the Tkachenko equation. It is obtained that the Adler - Moser polynomial are not unique polynomial solutions of the Tkachenko equation. A generalization of the Tkachenko equation to the case of translating relative equilibria is derived. It is shown that the generalization of the Tkachenko equation possesses polynomial solutions with degrees that are not triangular numbers.Comment: 15 pages, 2 figure

Investigating possible ethnicity and sex bias in clinical examiners: an analysis of data from the MRCP(UK) PACES and nPACES examinations

Bias of clinical examiners against some types of candidate, based on characteristics such as sex or ethnicity, would represent a threat to the validity of an examination, since sex or ethnicity are 'construct-irrelevant' characteristics. In this paper we report a novel method for assessing sex and ethnic bias in over 2000 examiners who had taken part in the PACES and nPACES (new PACES) examinations of the MRCP(UK)

Point vortices and classical orthogonal polynomials

Stationary equilibria of point vortices with arbitrary choice of circulations in a background flow are studied. Differential equations satisfied by generating polynomials of vortex configurations are derived. It is shown that these equations can be reduced to a single one. It is found that polynomials that are Wronskians of classical orthogonal polynomials solve the latter equation. As a consequence vortex equilibria at a certain choice of background flows can be described with the help of Wronskians of classical orthogonal polynomials.Comment: 20 pages, 12 figure

Epigenetic regulation of mucin genes in human cancers

Mucins are high molecular weight glycoproteins that play important roles in diagnostic and prognostic prediction and in carcinogenesis and tumor invasion. Regulation of expression of mucin genes has been studied extensively, and signaling pathways, transcriptional regulators, and epigenetic modification in promoter regions have been described. Detection of the epigenetic status of cancer-related mucin genes is important for early diagnosis of cancer and for monitoring of tumor behavior and response to targeted therapy. Effects of micro-RNAs on mucin gene expression have also started to emerge. In this review, we discuss the current views on epigenetic mechanisms of regulation of mucin genes (MUC1, MUC2, MUC3A, MUC4, MUC5AC, MUC5B, MUC6, MUC16, and MUC17) and the possible clinical applications of this epigenetic information