Energy bounds for vertex operator algebra extensions

Let V be a simple unitary vertex operator algebra and U be a (polynomially) energy-bounded unitary subalgebra containing the conformal vector of V. We give two sufficient conditions implying that V is energy-bounded. The first condition is that U is a compact orbifold for some compact group G of unitary automorphisms of V. The second condition is that V is exponentially energy-bounded and it is a finite direct sum of simple U-modules. As consequence of the second condition, we prove that if U is a regular energy-bounded unitary subalgebra of a simple unitary vertex operator V, then V is energy-bounded. In particular, every simple unitary extension (with the same conformal vector) of a simple unitary affine vertex operator algebra associated with a semisimple Lie algebra is energy-bounded

Repetitions in beta-integers

Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif occurring in beta-integers -- one dimensional models of quasicrystals. We are interested in beta-integers realizing only a finite number of distinct distances between neighboring elements. In such a case, the problem may be reformulated in terms of combinatorics on words as a study of the index of infinite words coding beta-integers. We will solve a particular case for beta being a quadratic non-simple Parry number.Comment: 11 page

Preclinical models in oncological pharmacology: limits and advantages

A wide range of experimental tumor models, each with distinct advantages and disadvantages, is nowadays available. Due to the inherent differences in their complexity and functionality, the choice of the model is usually dependent on the application. Thus, to advance specific knowledge, one has to choose and use appropriate models, which complexity is largely dependent on the hypotheses to test, that is on the objectives. Whatever the model chosen, the complexity of cancer is such that none of them will be able to fully represent it. In vitro tumor models have provided important tools for cancer research and still serve as low-cost screening platforms for drugs. The improved understanding of cancer as "organ system" has pushed for increased accuracy and physiological relevance of in vitro tumor models that have in parallel increased in complexity, diversifying their output parameters as they progressed in view to recapitulate the most critical aspects such as the dimensionality of cell cultures (2D versus 3D), the mechanical stimuli, the multicellular interactions, the immune interactions and the soluble signaling. Animal models represent the in vivo counterpart to cell lines and are commonly used for studies during the preclinical investigation of cancer therapy to determine the efficacy and safety of novel drugs. They are super to in vitro models in terms of physiological relevance offering imitation of parental tumors and a heterogeneous microenvironment as part of an interacting complex biochemical system. In the present review we describe advantages and limits of major preclinical models used in Oncological Pharmacology

The role of tumour markers in improving the accuracy of conventional chest X-ray and liver echography in the post-operative detection of thoracic and liver metastases from breast cancer

The aim of this retrospective study was to assess the value of a serum tumour marker panel in selecting from among the patients with equivocal chest X-ray (CXR) or liver echography (LE) those with thoracic or liver metastases respectively. Between January 1984 and December 1999, 467 (341 non-relapsed and 126 metastatic) breast cancer patients were followed-up postoperatively. Among the 126 metastatic patients 36 showed thoracic (19 patients) or liver (17 patients) metastases, alone or in conjunction with other organs as the first evidence of distant spread. We focused on this series of 377 patients including 341 non-relapsed plus 36 with liver or thoracic metastases. The patients were followed-up after mastectomy with serial determinations of a panel of CEA-TPA-CA15.3 tumour markers, bone scintigraphy, CXR and LE. Up to December 1999, equivocal CXR occurred in 23 (6.1%) patients of whom 11 (47.8%) developed thoracic metastases; 14 (3.7%) patients showed an equivocal LE of whom 5 developed liver metastases. In the 37 patients with equivocal CXR or equivocal LE prolonged clinical and imaging follow-up over 41 ± 36 months (mean ± SD, range 3–163) was used to ascertain the presence or absence of thoracic or liver metastases. In the 23 patients with equivocal CXR the negative and positive predictive values of the tumour marker panel to predict thoracic metastases were 92% and 100% respectively. In the 14 patients with equivocal LE the negative and positive predictive values of the tumour marker panel for prediction of liver metastases were 90% and 100% respectively. This study shows that in breast cancer patients the CEA-TPA-CA15.3 tumour marker panel has a high value for selecting those patients at high risk of developing clinically evident pulmonary or liver metastases from amongst those subjects with equivocal CXR or equivocal LE. © 2000 Cancer Research Campaign http://www.bjcancer.co

How to add a boundary condition

Given a conformal QFT local net of von Neumann algebras B_2 on the two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A is a completely rational net on the left/right light-ray, we show how to consistently add a boundary to B_2: we provide a procedure to construct a Boundary CFT net B of von Neumann algebras on the half-plane x>0, associated with A, and locally isomorphic to B_2. All such locally isomorphic Boundary CFT nets arise in this way. There are only finitely many locally isomorphic Boundary CFT nets and we get them all together. In essence, we show how to directly redefine the C* representation of the restriction of B_2 to the half-plane by means of subfactors and local conformal nets of von Neumann algebras on S^1.Comment: 20 page

Loop groups and noncommutative geometry

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group $LG$. The construction is based on certain supersymmetric conformal field theory models associated with LG in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.Comment: Revised versio