M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is explicitly described. This result has applications to deformation quantization and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber operad. They are parameterized by grt_1, up to one class (or two, depending on the definitions). More generally, the homotopy derivations of the (non-unital) E_n operads may be expressed through the cohomology of a suitable graph complex. Our methods also give a second proof of a result of H. Furusho, stating that the pentagon equation for grt_1-elements implies the hexagon equation

Formality theorems for Hochschild chains in the Lie algebroid setting

In this paper we prove Lie algebroid versions of Tsygan's formality conjecture for Hochschild chains both in the smooth and holomorphic settings. In the holomorphic setting our result implies a version of Tsygan's formality conjecture for Hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary Poisson Lie algebroid. The proofs are based on the use of Kontsevich's quasi-isomorphism for Hochschild cochains of R[[y_1,...,y_d]], Shoikhet's quasi-isomorphism for Hochschild chains of R[[y_1,...,y_d]], and Fedosov's resolutions of the natural analogues of Hochschild (co)chain complexes associated with a Lie algebroid.Comment: 40 pages, no figure

One-dimensional Chern-Simons theory

We study a one-dimensional toy version of the Chern-Simons theory. We construct its simplicial version which comprises features of a low-energy effective gauge theory and of a topological quantum field theory in the sense of Atiyah.Comment: 37 page

Hypercommutative operad as a homotopy quotient of BV

We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/$\Delta$ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive an equivalence of Hycomm-algebras and BV-algebras enhanced with a homotopy that trivializes the BV-operator. These formulas are given in terms of the Givental graphs, and are proved in two different ways. One proof uses the Givental group action, and the other proof goes through a chain of explicit formulas on resolutions of Hycomm and BV. The second approach gives, in particular, a homological explanation of the Givental group action on Hycomm-algebras.Comment: minor corrections added, to appear in Comm.Math.Phy

Formality theorems for Hochschild complexes and their applications

We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.Comment: Submitted to proceedings of Poisson 200

a prospective ‘before/after’ cohort study

Objectives Antibiotic resistance has risen dramatically over the past years. For individual patients, adequate initial antibiotic therapy is essential for clinical outcome. Computer-assisted decision support systems (CDSSs) are advocated to support implementation of rational anti-infective treatment strategies based on guidelines. The aim of this study was to evaluate long- term effects after implementation of a CDSS. Design This prospective ‘before/after’ cohort study was conducted over four observation periods within 5 years. One preinterventional period (pre) was compared with three postinterventional periods: directly after intensive implementation efforts (post1), 2 years (post2) and 3 years (post3) after implementation. Setting Five anaesthesiological-managed intensive care units (ICU) (one cardiosurgical, one neurosurgical, two interdisciplinary and one intermediate care) at a university hospital. Participants Adult patients with an ICU stay of >48 h were included in the analysis. 1316 patients were included in the analysis for a total of 12 965 ICU days. Intervention Implementation of a CDSS. Outcome measures The primary end point was percentage of days with guideline adherence during ICU treatment. Secondary end points were antibiotic-free days and all-cause mortality compared for patients with low versus high guideline adherence. Main results Adherence to guidelines increased from 61% prior to implementation to 92% in post1, decreased in post2 to 76% and remained significantly higher compared with baseline in post3, with 71% (p=0.178). Additionally, antibiotic-free days increased over study periods. At all time periods, mortality for patients with low guideline adherence was higher with 12.3% versus 8% (p=0.014) and an adjusted OR of 1.56 (95% CI 1.05 to 2.31). Conclusions Implementation of computerised regional adapted guidelines for antibiotic therapy is paralleled with improved adherence. Even without further measures, adherence stayed high for a longer period and was paralleled by reduced antibiotic exposure. Improved guideline adherence was associated with reduced ICU mortality

Morita Equivalence, Picard Groupoids and Noncommutative Field Theories

In this article we review recent developments on Morita equivalence of star products and their Picard groups. We point out the relations between noncommutative field theories and deformed vector bundles which give the Morita equivalence bimodules.Comment: Latex2e, 10 pages. Conference Proceeding for the Sendai Meeting 2002. Some typos fixe

On the Open-Closed B-Model

We study the coupling of the closed string to the open string in the topological B-model. These couplings can be viewed as gauge invariant observables in the open string field theory, or as deformations of the differential graded algebra describing the OSFT. This is interpreted as an intertwining map from the closed string sector to the deformation (Hochschild) complex of the open string algebra. By an explicit calculation we show that this map induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Reversely, this can be used to derive the closed string from the open string. We shortly comment on generalizations to other models, such as the A-model.Comment: LaTeX, 48 pages. Citation adde