Geometric quantization of completely integrable Hamiltonian systems in the action-angle variables

We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The associated quantum algebra consists of functions affine in action coordinates. We obtain a set of its nonequivalent representations in the separable pre-Hilbert space of smooth complex functions on the torus where action operators and a Hamiltonian are diagonal and have countable spectra.Comment: 8 page

Gene Editing and Genotoxicity: Targeting the Off-Targets

Gene editing technologies show great promise for application to human disease as a result of rapid developments in targeting tools notably based on ZFN, TALEN, and CRISPR-Cas systems. Precise modification of a DNA sequence is now possible in mature human somatic cells including stem and progenitor cells with increasing degrees of efficiency. At the same time new technologies are required to evaluate their safety and genotoxicity before widespread clinical application can be confidently implemented. A number of methodologies have now been developed in an attempt to predict expected and unexpected modifications occurring during gene editing. This review surveys the techniques currently available as state of the art, highlighting benefits and limitations, and discusses approaches that may achieve sufficient accuracy and predictability for application in clinical settings

Transient down-regulation of beta1 integrin subtypes on kidney carcinoma cells is induced by mechanical contact with endothelial cell membranes

Adhesion molecules of the integrin beta1 family are thought to be involved in the malignant progression renal cell carcinoma (RCC). Still, it is not clear how they contribute to this process. Since the hematogenous phase of tumour dissemination is the rate-limiting step in the metastatic process, we explored beta1 integrin alterations on several RCC cell lines (A498, Caki1, KTC26) before and after contacting vascular endothelium in a tumour-endothelium (HUVEC) co-culture assay. Notably, alpha2, alpha3 and alpha5 integrins became down-regulated immediately after the tumour cells attached to HUVEC, followed by re-expression shortly thereafter. Integrin down-regulation on RCC cells was caused by direct contact with endothelial cells, since the isolated endothelial membrane fragments but not the cell culture supernatant contributed to the observed effects. Integrin loss was accompanied by a reduced focal adhesion kinase (FAK) expression, FAK activity and diminished binding of tumour cells to matrix proteins. Furthermore, intracellular signalling proteins RCC cells were altered in the presence of HUVEC membrane fragments, in particular 14-3-3 epsilon, ERK2, PKCdelta, PKCepsilon and RACK1, which are involved in regulating tumour cell motility. We, therefore, speculate that contact of RCC cells with the vascular endothelium converts integrin-dependent adhesion to integrin-independent cell movement. The process of dynamic integrin regulation may be an important part in tumour cell migration strategy, switching the cells from being adhesive to becoming motile and invasive

Theory of Finite Pseudoalgebras

Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional'' analogues of conformal algebras. They are defined as Lie algebras in a certain ``pseudotensor'' category instead of the category of vector spaces. A pseudotensor category (as introduced by Lambek, and by Beilinson and Drinfeld) is a category equipped with ``polylinear maps'' and a way to compose them. This allows for the definition of Lie algebras, representations, cohomology, etc. An instance of such a category can be constructed starting from any cocommutative (or more generally, quasitriangular) Hopf algebra $H$. The Lie algebras in this category are called Lie $H$-pseudoalgebras. The main result of this paper is the classification of all simple and all semisimple Lie $H$-pseudoalgebras which are finitely generated as $H$-modules. We also start developing the representation theory of Lie pseudoalgebras; in particular, we prove analogues of the Lie, Engel, and Cartan-Jacobson Theorems. We show that the cohomology theory of Lie pseudoalgebras describes extensions and deformations and is closely related to Gelfand-Fuchs cohomology. Lie pseudoalgebras are closely related to solutions of the classical Yang-Baxter equation, to differential Lie algebras (introduced by Ritt), and to Hamiltonian formalism in the theory of nonlinear evolution equations. As an application of our results, we derive a classification of simple and semisimple linear Poisson brackets in any finite number of indeterminates.Comment: 102 pages, 7 figures, AMS late

A toolkit of mechanism and context independent widgets

Most human-computer interfaces are designed to run on a static platform (e.g. a workstation with a monitor) in a static environment (e.g. an office). However, with mobile devices becoming ubiquitous and capable of running applications similar to those found on static devices, it is no longer valid to design static interfaces. This paper describes a user-interface architecture which allows interactors to be flexible about the way they are presented. This flexibility is defined by the different input and output mechanisms used. An interactor may use different mechanisms depending upon their suitability in the current context, user preference and the resources available for presentation using that mechanism

P53 is active in murine stem cells and alters the transcriptome in a manner that is reminiscent of mutant p53

Since it was found that p53 is highly expressed in murine embryonic stem cells, it remained a mystery whether p53 is active in this cell type. We show that a significant part of p53 is localised in the nucleus of murine embryonic stem cells and that the majority of this nuclear p53 is bound to DNA. According to its nuclear localisation, we show that p53 alters the transcriptional program of stem cells. Nevertheless, the anti-proliferative activity of p53 is compromised in stem cells, and this control is due, at least in part, to the high amount of MdmX that is present in embryonic stem cells and bound to p53. Instead of the anti-proliferative activity that p53 has in differentiated cells, p53 controls transcription of pro-proliferative genes in embryonic stem cells including c-myc and c-jun. The impeded anti-proliferative activity of p53 and the induction of certain proto-oncogenes by p53 in murine embryonic stem cells can explain why stem cells proliferate efficiently despite having high levels of p53