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

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

Derived coisotropic structures II: stacks and quantization

We extend results about $n$-shifted coisotropic structures from part I of this work to the setting of derived Artin stacks. We show that an intersection of coisotropic morphisms carries a Poisson structure of shift one less. We also compare non-degenerate shifted coisotropic structures and shifted Lagrangian structures and show that there is a natural equivalence between the two spaces in agreement with the classical result. Finally, we define quantizations of $n$-shifted coisotropic structures and show that they exist for $n>1$.Comment: 45 pages. Contains the second half of arXiv:1608.01482v1 with new material 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

Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation

We review the definition of hypergeometric coherent states, discussing some representative examples. Then we study mathematical and statistical properties of hypergeometric Schr\"odinger cat states, defined as orthonormalized eigenstates of $k$-th powers of nonlinear $f$-oscillator annihilation operators, with $f$ of hypergeometric type. These "$k$-hypercats" can be written as an equally weighted superposition of hypergeometric coherent states $|z_l\rangle, l=0,1,\dots,k-1$, with $z_l=z e^{2\pi i l/k}$ a $k$-th root of $z^k$, and they interpolate between number and coherent states. This fact motivates a continuous circle representation for high $k$. We also extend our study to truncated hypergeometric functions (finite dimensional Hilbert spaces) and a discrete exact circle representation is provided. We also show how to generate $k$-hypercats by amplitude dispersion in a Kerr medium and analyze their generalized Husimi $Q$-function in the super- and sub-Poissonian cases at different fractions of the revival time.Comment: 21 pages, 15 figure

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

Dynamic changes in eIF4F-mRNA interactions revealed by global analyses of environmental stress responses

BACKGROUND: Translation factors eIF4E and eIF4G form eIF4F, which interacts with the messenger RNA (mRNA) 5' cap to promote ribosome recruitment and translation initiation. Variations in the association of eIF4F with individual mRNAs likely contribute to differences in translation initiation frequencies between mRNAs. As translation initiation is globally reprogrammed by environmental stresses, we were interested in determining whether eIF4F interactions with individual mRNAs are reprogrammed and how this may contribute to global environmental stress responses. RESULTS: Using a tagged-factor protein capture and RNA-sequencing (RNA-seq) approach, we have assessed how mRNA associations with eIF4E, eIF4G1 and eIF4G2 change globally in response to three defined stresses that each cause a rapid attenuation of protein synthesis: oxidative stress induced by hydrogen peroxide and nutrient stresses caused by amino acid or glucose withdrawal. We find that acute stress leads to dynamic and unexpected changes in eIF4F-mRNA interactions that are shared among each factor and across the stresses imposed. eIF4F-mRNA interactions stabilised by stress are predominantly associated with translational repression, while more actively initiating mRNAs become relatively depleted for eIF4F. Simultaneously, other mRNAs are insulated from these stress-induced changes in eIF4F association. CONCLUSION: Dynamic eIF4F-mRNA interaction changes are part of a coordinated early translational control response shared across environmental stresses. Our data are compatible with a model where multiple mRNA closed-loop complexes form with differing stability. Hence, unexpectedly, in the absence of other stabilising factors, rapid translation initiation on mRNAs correlates with less stable eIF4F interactions

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)