Super-KMS functionals for graded-local conformal nets

Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on translation-covariant nets over R, fundamental objects in chiral algebraic quantum field theory. Although we are able to make a few statements concerning their general structure, most properties will be studied in the setting of specific graded-local (super-) conformal models. In particular, we provide a constructive existence and partial uniqueness proof of super-KMS functionals for the supersymmetric free field, for certain subnets, and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a separate result, we classify bounded super-KMS functionals for graded-local conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare

Thermal States in Conformal QFT. II

We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on the real line. In the first part we have proved the uniqueness of KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U(1)-current net and on the Virasoro net Vir_1 with the central charge c=1, whilst for the Virasoro net Vir_c with c>1 we exhibit a (possibly incomplete) list of continuously many primary KMS states. To this end, we provide a variation of the Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework: if there is an inclusion of split nets A in B and A is the fixed point of B w.r.t. a compact gauge group, then any locally normal, primary KMS state on A extends to a locally normal, primary state on B, KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.Comment: 36 pages, no figure. Dedicated to Rudolf Haag on the occasion of his 90th birthday. The final version is available under Open Access. This paper contains corrections to the Araki-Haag-Kaster-Takesaki theorem (and to a proof of the same theorem in the book by Bratteli-Robinson). v3: a reference correcte

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

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

Ground state representations of loop algebras

Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg.Comment: 22 pages, no figur

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

Autoeficacia y percepción de control en la prevención de la enfermedad cardiovascular

From the Theory of Planed Behaviour (TPB), the aim of this study is to analyse the effect of self-efficacy and perceived control on intention and preventive behaviors of cardiovascular disease. To this end, 359 participants were evaluated in an empirical study. Data were analysed using the statistical package EQS 6.1. The results indicate that self-efficacy has a positive and significant influence on behaviour intentions and on behaviour, while perception of control has a negative and significant influence on intention but not on behaviour. This work has shown the utility to distinguish between self-efficacy and perceived control in the TPB to prevent cardiovascular diseases

A Characterization of Bispecial Sturmian Words

A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian words.Comment: Accepted to MFCS 201