Differential Calculi on Some Quantum Prehomogeneous Vector Spaces

This paper is devoted to study of differential calculi over quadratic algebras, which arise in the theory of quantum bounded symmetric domains. We prove that in the quantum case dimensions of the homogeneous components of the graded vector spaces of k-forms are the same as in the classical case. This result is well-known for quantum matrices. The quadratic algebras, which we consider in the present paper, are q-analogues of the polynomial algebras on prehomogeneous vector spaces of commutative parabolic type. This enables us to prove that the de Rham complex is isomorphic to the dual of a quantum analogue of the generalized Bernstein-Gelfand-Gelfand resolution.Comment: LaTeX2e, 51 pages; changed conten

Two dimensional Sen connections in general relativity

The two dimensional version of the Sen connection for spinors and tensors on spacelike 2-surfaces is constructed. A complex metric $\gamma_{AB}$ on the spin spaces is found which characterizes both the algebraic and extrinsic geometrical properties of the 2-surface $\$$. The curvature of the two dimensional Sen operator $\Delta_e$ is the pull back to $\$$ of the anti-self-dual part of the spacetime curvature while its `torsion' is a boost gauge invariant expression of the extrinsic curvatures of $\$$. The difference of the 2 dimensional Sen and the induced spin connections is the anti-self-dual part of the `torsion'. The irreducible parts of $\Delta_e$ are shown to be the familiar 2-surface twistor and the Weyl--Sen--Witten operators. Two Sen--Witten type identities are derived, the first is an identity between the 2 dimensional twistor and the Weyl--Sen--Witten operators and the integrand of Penrose's charge integral, while the second contains the `torsion' as well. For spinor fields satisfying the 2-surface twistor equation the first reduces to Tod's formula for the kinematical twistor.Comment: 14 pages, Plain Tex, no report numbe

The kernel of the edth operators on higher-genus spacelike two-surfaces

The dimension of the kernels of the edth and edth-prime operators on closed, orientable spacelike 2-surfaces with arbitrary genus is calculated, and some of its mathematical and physical consequences are discussed.Comment: 12 page

From 2D conformal to 4D self-dual theories: quaternionic analyticity

It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity (natural in two dimensions) to quaternionic analyticity (natural in four dimensions). To be analytic, conformal transformations should be realized on $CP^3$, which appears as the coset of the complexified conformal group modulo its maximal parabolic subgroup. In this language one visualizes the twistor correspondence of Penrose and Ward and consistently formulates the analyticity of Fueter.Comment: 24 pages, LaTe

3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs

British societies guideline on the management of emergencies in implantable left ventricular assist device recipients in transplant centres

\ua9 The Author(s) 2024.An implantable left ventricular assist device (LVAD) is indicated as a bridge to transplantation or recovery in the United Kingdom (UK). The mechanism of action of the LVAD results in a unique state of haemodynamic stability with diminished arterial pulsatility. The clinical assessment of an LVAD recipient can be challenging because non-invasive blood pressure, pulse and oxygen saturation measurements may be hard to obtain. As a result of this unusual situation and complex interplay between the device and the native circulation, resuscitation of LVAD recipients requires bespoke guidelines. Through collaboration with key UK stakeholders, we assessed the current evidence base and developed guidelines for the recognition of clinical deterioration, inadequate circulation and time-critical interventions. Such guidelines, intended for use in transplant centres, are designed to be deployed by those providing immediate care of LVAD patients under conditions of precipitous clinical deterioration. In summary, the Joint British Societies and Transplant Centres LVAD Working Group present the UK guideline on management of emergencies in implantable LVAD recipients for use in advanced heart failure centres. These recommendations have been made with a UK resuscitation focus but are widely applicable to professionals regularly managing patients with implantable LVADs

Hydroxybenzothiazoles as New Nonsteroidal Inhibitors of 17β-Hydroxysteroid Dehydrogenase Type 1 (17β-HSD1)

17β-estradiol (E2), the most potent estrogen in humans, known to be involved in the development and progession of estrogen-dependent diseases (EDD) like breast cancer and endometriosis. 17β-HSD1, which catalyses the reduction of the weak estrogen estrone (E1) to E2, is often overexpressed in breast cancer and endometriotic tissues. An inhibition of 17β-HSD1 could selectively reduce the local E2-level thus allowing for a novel, targeted approach in the treatment of EDD. Continuing our search for new nonsteroidal 17β-HSD1 inhibitors, a novel pharmacophore model was derived from crystallographic data and used for the virtual screening of a small library of compounds. Subsequent experimental verification of the virtual hits led to the identification of the moderately active compound 5. Rigidification and further structure modifications resulted in the discovery of a novel class of 17β-HSD1 inhibitors bearing a benzothiazole-scaffold linked to a phenyl ring via keto- or amide-bridge. Their putative binding modes were investigated by correlating their biological data with features of the pharmacophore model. The most active keto-derivative 6 shows IC50-values in the nanomolar range for the transformation of E1 to E2 by 17β-HSD1, reasonable selectivity against 17β-HSD2 but pronounced affinity to the estrogen receptors (ERs). On the other hand, the best amide-derivative 21 shows only medium 17β-HSD1 inhibitory activity at the target enzyme as well as fair selectivity against 17β-HSD2 and ERs. The compounds 6 and 21 can be regarded as first benzothiazole-type 17β-HSD1 inhibitors for the development of potential therapeutics

Neurodevelopment Genes in Lampreys Reveal Trends for Forebrain Evolution in Craniates

The forebrain is the brain region which has undergone the most dramatic changes through vertebrate evolution. Analyses conducted in lampreys are essential to gain insight into the broad ancestral characteristics of the forebrain at the dawn of vertebrates, and to understand the molecular basis for the diversifications that have taken place in cyclostomes and gnathostomes following their splitting. Here, we report the embryonic expression patterns of 43 lamprey genes, coding for transcription factors or signaling molecules known to be involved in cell proliferation, stemcellness, neurogenesis, patterning and regionalization in the developing forebrain. Systematic expression patterns comparisons with model organisms highlight conservations likely to reflect shared features present in the vertebrate ancestors. They also point to changes in signaling systems –pathways which control the growth and patterning of the neuroepithelium-, which may have been crucial in the evolution of forebrain anatomy at the origin of vertebrates