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

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

Bright light therapy versus physical exercise to prevent co-morbid depression and obesity in adolescents and young adults with attention-deficit/hyperactivity disorder: study protocol for a randomized controlled trial

Background: The risk for major depression and obesity is increased in adolescents and adults with attention-deficit / hyperactivity disorder (ADHD) and adolescent ADHD predicts adult depression and obesity. Non-pharmacological interventions to treat and prevent these co-morbidities are urgently needed. Bright light therapy (BLT) improves day– night rhythm and is an emerging therapy for major depression. Exercise intervention (EI) reduces obesity and improves depressive symptoms. To date, no randomized controlled trial (RCT) has been performed to establish feasibility and efficacy of these interventions targeting the prevention of co-morbid depression and obesity in ADHD. We hypothesize that the two manualized interventions in combination with mobile health-based monitoring and reinforcement will result in less depressive symptoms and obesity compared to treatment as usual in adolescents and young adults with ADHD. Methods: This trial is a prospective, pilot phase-IIa, parallel-group RCT with three arms (two add-on treatment groups [BLT, EI] and one treatment as usual [TAU] control group). The primary outcome variable is change in the Inventory of Depressive Symptomatology total score (observer-blinded assessment) between baseline and ten weeks of intervention. This variable is analyzed with a mixed model for repeated measures approach investigating the treatment effect with respect to all three groups. A total of 330 participants with ADHD, aged 14 – < 30 years, will be screened at the four study centers. To establish effect sizes, the sample size was planned at the liberal significance level of α = 0.10 (two-sided) and the power of 1-β = 80% in order to find medium effects. Secondary outcomes measures including change in obesity, ADHD symptoms, general psychopathology, health-related quality of life, neurocognitive function, chronotype, and physical fitness are explored after the end of the intervention and at the 12-week follow-up. This is the first pilot RCT on the use of BLT and EI in combination with mobile health-based monitoring and reinforcement targeting the prevention of co-morbid depression and obesity in adolescents and young adults with ADHD. If at least medium effects can be established with regard to the prevention of depressive symptoms and obesity, a larger scale confirmatory phase-III trial may be warranted.The trial is funded by the EU Framework Programme for Research and Innovation, Horizon 2020 (Project no. 667302). Funding period: January 2016–December 2020. This funding source had no role in the design of this study and will not have any role during its execution, analyses, interpretation of the data, or decision to submit results. Some local funds additionally contributed to carry out this study, especially for the preparation of the interventions: FBO research activity is by the Spanish Ministry of Economy and Competitiveness – MINECO (RYC-2011-09011) and by the University of Granada, Plan Propio de Investigación 2016, Excellence actions: Unit of Excellence on Exercise and Health (UCEES)