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 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

Interpolating Coherent States for Heisenberg-Weyl and Single-Photon SU(1,1) Algebras

New quantal states which interpolate between the coherent states of the Heisenberg_Weyl and SU(1,1) algebras are introduced. The interpolating states are obtained as the coherent states of a closed and symmetric algebra which interpolates between the two algebras. The overcompleteness of the interpolating coherent states is established. Differential operator representations in suitable spaces of entire functions are given for the generators of the algebra. A nonsymmetric set of operators to realize the Heisenberg-Weyl algebra is provided and the relevant coherent states are studied.Comment: 13 pages nd 5 ps figure

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

Notes on factorization algebras, factorization homology and applications

These notes are an expanded version of two series of lectures given at the winter school in mathematical physics at les Houches and at the Vietnamese Institute for Mathematical Sciences. They are an introduction to factorization algebras, factorization homology and some of their applications, notably for studying $E_n$-algebras. We give an account of homology theory for manifolds (and spaces), which give invariant of manifolds but also invariant of $E_n$-algebras. We particularly emphasize the point of view of factorization algebras (a structure originating from quantum field theory) which plays, with respect to homology theory for manifolds, the role of sheaves with respect to singular cohomology. We mention some applications to the study of mapping spaces and study several examples, including some over stratified spaces.Comment: 122 pages. A few examples adde

Melatonin the "light of night" in human biology and adolescent idiopathic scoliosis

Melatonin "the light of night" is secreted from the pineal gland principally at night. The hormone is involved in sleep regulation, as well as in a number of other cyclical bodily activities and circadian rhythm in humans. Melatonin is exclusively involved in signalling the 'time of day' and 'time of year' (hence considered to help both clock and calendar functions) to all tissues and is thus considered to be the body's chronological pacemaker or 'Zeitgeber'. The last decades melatonin has been used as a therapeutic chemical in a large spectrum of diseases, mainly in sleep disturbances and tumours and may play a role in the biologic regulation of mood, affective disorders, cardiovascular system, reproduction and aging. There are few papers regarding melatonin and its role in adolescent idiopathic scoliosis (AIS). Melatonin may play a role in the pathogenesis of scoliosis (neuroendocrine hypothesis) but at present, the data available cannot clearly support this hypothesis. Uncertainties and doubts still surround the role of melatonin in human physiology and pathophysiology and future research is needed

Preventive and curative effect of melatonin on mammary carcinogenesis induced by dimethylbenz[a]anthracene in the female Sprague–Dawley rat

INTRODUCTION: It has been well documented that the pineal hormone, melatonin, which plays a major role in the control of reproduction in mammals, also plays a role in the incidence and growth of breast and mammary cancer. The curative effect of melatonin on the growth of dimethylbenz [a]anthracene-induced (DMBA-induced) mammary adenocarcinoma (ADK) has been previously well documented in the female Sprague–Dawley rat. However, the preventive effect of melatonin in limiting the frequency of cancer initiation has not been well documented. METHODS: The aim of this study was to compare the potency of melatonin to limit the frequency of mammary cancer initiation with its potency to inhibit tumor progression once initiation, at 55 days of age, was achieved. The present study compared the effect of preventive treatment with melatonin (10 mg/kg daily) administered for only 15 days before the administration of DMBA with the effect of long-term (6-month) curative treatment with the same dose of melatonin starting the day after DMBA administration. The rats were followed up for a year after the administration of the DMBA. RESULTS: The results clearly showed almost identical preventive and curative effects of melatonin on the growth of DMBA-induced mammary ADK. Many hypotheses have been proposed to explain the inhibitory effects of melatonin. However, the mechanisms responsible for its strong preventive effect are still a matter of debate. At least, it can be envisaged that the artificial amplification of the intensity of the circadian rhythm of melatonin could markedly reduce the DNA damage provoked by DMBA and therefore the frequency of cancer initiation. CONCLUSION: In view of the present results, obtained in the female Sprague–Dawley rat, it can be envisaged that the long-term inhibition of mammary ADK promotion by a brief, preventive treatment with melatonin could also reduce the risk of breast cancer induced in women by unidentified environmental factors