994 resultados para Raducanu-Orhan differential operator


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DIN (diabetic nephropathy) is the leading cause of end-stage renal disease worldwide and develops in 25-40% of patients with Type 1 or Type 2 diabetes mellitus. Elevated blood glucose over long periods together with glomerular hypertension leads to progressive glomerulosclerosis and tubulointerstitial fibrosis in susceptible individuals. Central to the pathology of DIN are cytokines and growth factors such as TGF-beta (transforming growth factor beta) superfamily members, including BMPs (bone morphogenetic protein) and TGF-beta 1, which play key roles in fibrogenic responses of the kidney, including podocyte loss, mesangial cell hypertrophy, matrix accumulation and tubulointerstitial fibrosis. Many of these responses can be mimicked in in vitro models of cells cultured in high glucose. We have applied differential gene expression technologies to identify novel genes expressed in in vitro and in vivo models of DN and, importantly, in human renal tissue. By mining these datasets and probing the regulation of expression and actions of specific molecules, we have identified novel roles for molecules such as Gremlin, IHG-1 (induced in high glucose-1) and CTGF (connective tissue growth factor) in DIN and potential regulators of their bioactions.

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Motivation: Microarray experiments generate a high data volume. However, often due to financial or experimental considerations, e.g. lack of sample, there is little or no replication of the experiments or hybridizations. These factors combined with the intrinsic variability associated with the measurement of gene expression can result in an unsatisfactory detection rate of differential gene expression (DGE). Our motivation was to provide an easy to use measure of the success rate of DGE detection that could find routine use in the design of microarray experiments or in post-experiment assessment.

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We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product of A with itself labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved.

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We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

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We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar