State sum construction of two-dimensional open-closed Topological Quantum Field Theories

We present a state sum construction of two-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, which generalizes the state sum of Fukuma--Hosono--Kawai from triangulations of conventional two-dimensional cobordisms to those of open-closed cobordisms, i.e. smooth compact oriented 2-manifolds with corners that have a particular global structure. This construction reveals the topological interpretation of the associative algebra on which the state sum is based, as the vector space that the TQFT assigns to the unit interval. Extending the notion of a two-dimensional TQFT from cobordisms to suitable manifolds with corners therefore makes the relationship between the global description of the TQFT in terms of a functor into the category of vector spaces and the local description in terms of a state sum fully transparent. We also illustrate the state sum construction of an open-closed TQFT with a finite set of D-branes using the example of the groupoid algebra of a finite groupoid.Comment: 33 pages; LaTeX2e with xypic and pstricks macros; v2: typos correcte

Trace as an alternative decategorification functor

Categorification is a process of lifting structures to a higher categorical level. The original structure can then be recovered by means of the so-called "decategorification" functor. Algebras are typically categorified to additive categories with additional structure and decategorification is usually given by the (split) Grothendieck group. In this expository article we study an alternative decategorification functor given by the trace or the zeroth Hochschild--Mitchell homology. We show that this form of decategorification endows any 2-representation of the categorified quantum sl(n) with an action of the current algebra U(sl(n)[t]) on its center.Comment: 47 pages with tikz figures. arXiv admin note: text overlap with arXiv:1405.5920 by other author

AQFT from n-functorial QFT

There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal. More recently, based on ideas by Baez and Dolan, the latter is being refined to "extended" functorial QFT by Freed, Hopkins, Lurie and others. The first approach uses local nets of operator algebras which assign to each patch an algebra "of observables", the latter uses n-functors which assign to each patch a "propagator of states". In this note we present an observation about how these two axiom systems are naturally related: we demonstrate under mild assumptions that every 2-dimensional extended Minkowskian QFT 2-functor ("parallel surface transport") naturally yields a local net. This is obtained by postcomposing the propagation 2-functor with an operation that mimics the passage from the Schroedinger picture to the Heisenberg picture in quantum mechanics. The argument has a straightforward generalization to general pseudo-Riemannian structure and higher dimensions.Comment: 39 pages; further examples added: Hopf spin chains and asymptotic inclusion of subfactors; references adde

Immunotherapies in neuromyelitis optica spectrum disorder: efficacy and predictors of response

OBJECTIVE: To analyse predictors for relapses and number of attacks under different immunotherapies in patients with neuromyelitis optica spectrum disorder (NMOSD). DESIGN: This is a retrospective cohort study conducted in neurology departments at 21 regional and university hospitals in Germany. Eligible participants were patients with aquaporin-4-antibody-positive or aquaporin-4-antibody-negative NMOSD. Main outcome measures were HRs from Cox proportional hazard regression models adjusted for centre effects, important prognostic factors and repeated treatment episodes. RESULTS: 265 treatment episodes with a mean duration of 442 days (total of 321 treatment years) in 144 patients (mean age at first attack: 40.9 years, 82.6% female, 86.1% aquaporin-4-antibody-positive) were analysed. 191 attacks occurred during any of the treatments (annual relapse rate=0.60). The most common treatments were rituximab (n=77, 111 patient-years), azathioprine (n=52, 68 patient-years), interferon-beta (n=32, 61 patient-years), mitoxantrone (n=34, 32.1 patient-years) and glatiramer acetate (n=17, 10 patient-years). Azathioprine (HR=0.4, 95% CI 0.3 to 0.7, p=0.001) and rituximab (HR=0.6, 95% CI 0.4 to 1.0, p=0.034) reduced the attack risk compared with interferon-beta, whereas mitoxantrone and glatiramer acetate did not. Patients who were aquaporin-4-antibody-positive had a higher risk of attacks (HR=2.5, 95% CI 1.3 to 5.1, p=0.009). Every decade of age was associated with a lower risk for attacks (HR=0.8, 95% CI 0.7 to 1.0, p=0.039). A previous attack under the same treatment tended to be predictive for further attacks (HR=1.5, 95% CI 1.0 to 2.4, p=0.065). CONCLUSIONS: Age, antibody status and possibly previous attacks predict further attacks in patients treated for NMOSD. Azathioprine and rituximab are superior to interferon-beta

Contrasting disease patterns in seropositive and seronegative neuromyelitis optica: A multicentre study of 175 patients

BACKGROUND: The diagnostic and pathophysiological relevance of antibodies to aquaporin-4 (AQP4-Ab) in patients with neuromyelitis optica spectrum disorders (NMOSD) has been intensively studied. However, little is known so far about the clinical impact of AQP4-Ab seropositivity. OBJECTIVE: To analyse systematically the clinical and paraclinical features associated with NMO spectrum disorders in Caucasians in a stratified fashion according to the patients' AQP4-Ab serostatus. METHODS: Retrospective study of 175 Caucasian patients (AQP4-Ab positive in 78.3%). RESULTS: Seropositive patients were found to be predominantly female (p 1 myelitis attacks in the first year were identified as possible predictors of a worse outcome. CONCLUSION: This study provides an overview of the clinical and paraclinical features of NMOSD in Caucasians and demonstrates a number of distinct disease characteristics in seropositive and seronegative patients