Simple algebras of Weyl type

Over a field $F$ of any characteristic, for a commutative associative algebra $A$ with an identity element and for the polynomial algebra $F[D]$ of a commutative derivation subalgebra $D$ of $A$, the associative and the Lie algebras of Weyl type on the same vector space $A[D]=A\otimes F[D]$ are defined. It is proved that $A[D]$, as a Lie algebra (modular its center) or as an associative algebra, is simple if and only if $A$ is $D$-simple and $A[D]$ acts faithfully on $A$. Thus a lot of simple algebras are obtained.Comment: 9 pages, Late

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page

Del Pezzo surfaces of degree 1 and jacobians

We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.Comment: 24 page

The Ideal Intersection Property for Groupoid Graded Rings

We show that if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio

Noncommutative Geometry of Finite Groups

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more generally for Hopf algebras including quantum groups. A differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and, moreover, for the formulation of field theories and dynamics on finite sets. Associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures. For a covariant calculus, there are notions of invariance for linear connections and tensors. All these concepts are explored for finite groups and illustrated with examples. Some results are formulated more generally for arbitrary associative (Hopf) algebras. In particular, the problem of extension of a connection on a bimodule (over an associative algebra) to tensor products is investigated, leading to the class of `extensible connections'. It is shown that invariance properties of an extensible connection on a bimodule over a Hopf algebra are carried over to the extension. Furthermore, an invariance property of a connection is also shared by a `dual connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late

How often should we monitor for reliable detection of atrial fibrillation recurrence? Efficiency considerations and implications for study design

OBJECTIVE: Although atrial fibrillation (AF) recurrence is unpredictable in terms of onset and duration, current intermittent rhythm monitoring (IRM) diagnostic modalities are short-termed and discontinuous. The aim of the present study was to investigate the necessary IRM frequency required to reliably detect recurrence of various AF recurrence patterns. METHODS: The rhythm histories of 647 patients (mean AF burden: 12±22% of monitored time; 687 patient-years) with implantable continuous monitoring devices were reconstructed and analyzed. With the use of computationally intensive simulation, we evaluated the necessary IRM frequency to reliably detect AF recurrence of various AF phenotypes using IRM of various durations. RESULTS: The IRM frequency required for reliable AF detection depends on the amount and temporal aggregation of the AF recurrence (p<0.0001) as well as the duration of the IRM (p<0.001). Reliable detection (>95% sensitivity) of AF recurrence required higher IRM frequencies (>12 24-hour; >6 7-day; >4 14-day; >3 30-day IRM per year; p<0.0001) than currently recommended. Lower IRM frequencies will under-detect AF recurrence and introduce significant bias in the evaluation of therapeutic interventions. More frequent but of shorter duration, IRMs (24-hour) are significantly more time effective (sensitivity per monitored time) than a fewer number of longer IRM durations (p<0.0001). CONCLUSIONS: Reliable AF recurrence detection requires higher IRM frequencies than currently recommended. Current IRM frequency recommendations will fail to diagnose a significant proportion of patients. Shorter duration but more frequent IRM strategies are significantly more efficient than longer IRM durations. CLINICAL TRIAL REGISTRATION URL: Unique identifier: NCT00806689

Activation of PyMT in β Cells Induces Irreversible Hyperplasia, but Oncogene-Dependent Acinar Cell Carcinomas When Activated in Pancreatic Progenitors

It is unclear whether the cellular origin of various forms of pancreatic cancer involves transformation or transdifferentiation of different target cells or whether tumors arise from common precursors, with tumor types determined by the specific genetic alterations. Previous studies suggested that pancreatic ductal carcinomas might be induced by polyoma middle T antigen (PyMT) expressed in non-ductal cells. To ask whether PyMT transforms and transdifferentiates endocrine cells toward exocrine tumor phenotypes, we generated transgenic mice that carry tetracycline-inducible PyMT and a linked luciferase reporter. Induction of PyMT in β cells causes β-cell hyperplastic lesions that do not progress to malignant neoplasms. When PyMT is de-induced, β cell proliferation and growth cease; however, regression does not occur, suggesting that continued production of PyMT is not required to maintain the viable expanded β cell population. In contrast, induction of PyMT in early pancreatic progenitor cells under the control of Pdx1 produces acinar cell carcinomas and β-cell hyperplasia. The survival of acinar tumor cells is dependent on continued expression of PyMT. Our findings indicate that PyMT can induce exocrine tumors from pancreatic progenitor cells, but cells in the β cell lineage are not transdifferentiated toward exocrine cell types by PyMT; instead, they undergo oncogene-dependent hyperplastic growth, but do not require PyMT for survival

Vascular Wall-Resident CD44+ Multipotent Stem Cells Give Rise to Pericytes and Smooth Muscle Cells and Contribute to New Vessel Maturation

Here, we identify CD44(+)CD90(+)CD73(+)CD34(−)CD45(−) cells within the adult human arterial adventitia with properties of multipotency which were named vascular wall-resident multipotent stem cells (VW-MPSCs). VW-MPSCs exhibit typical mesenchymal stem cell characteristics including cell surface markers in immunostaining and flow cytometric analyses, and differentiation into adipocytes, chondrocytes and osteocytes under culture conditions. Particularly, TGFß1 stimulation up-regulates smooth muscle cell markers in VW-MPSCs. Using fluorescent cell labelling and co-localisation studies we show that VW-MPSCs differentiate to pericytes/smooth muscle cells which cover the wall of newly formed endothelial capillary-like structures in vitro. Co-implantation of EGFP-labelled VW-MPSCs and human umbilical vein endothelial cells into SCID mice subcutaneously via Matrigel results in new vessels formation which were covered by pericyte- or smooth muscle-like cells generated from implanted VW-MPSCs. Our results suggest that VW-MPSCs are of relevance for vascular morphogenesis, repair and self-renewal of vascular wall cells and for local capacity of neovascularization in disease processes

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy