Deformation quantization with generators and relations

In this paper we prove a conjecture of B. Shoikhet which claims that two quantization procedures arising from Fourier dual constructions actually coincide.Comment: 9 pages; 4 figures; many typos have been corrected; the introduction has been considerably extended and a more detailed exposition of the Koszul theory behind the main idea has been added; the proof of Proposition 2.4 (iii) has been also extended; Subsection 3.2 has been enlarged, and a more detailed exposition of how the Duflo element arises has been adde

A gerbe for the elliptic gamma function

The identities for elliptic gamma functions discovered by A. Varchenko and one of us are generalized to an infinite set of identities for elliptic gamma functions associated to pairs of planes in 3-dimensional space. The language of stacks and gerbes gives a natural framework for a systematic description of these identities and their domain of validity. A triptic curve is the quotient of the complex plane by a subgroup of rank three (it is a stack). Our identities can be summarized by saying that elliptic gamma functions form a meromorphic section of a hermitian holomorphic abelian gerbe over the universal oriented triptic curve.Comment: 54 page

Bimodules and branes in deformation quantization

We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space $X$. The result implies in particular that the Kontsevich deformation quantizations of $\mathrm{S}(X^*)$ and $\wedge(X)$ associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet's recent paper on Koszul duality in deformation quantization.Comment: 40 pages, 15 figures; a small change of notations in the definition of the 4-colored propagators; an Addendum about the appearance of loops in the $L_\infty$-quasi-isomorphism and a corresponding change in the proof of Theorem 7.2; several changes regarding completions, when dealing with general $A_\infty$-structure

A simulation study of the electron cloud in the experimental regions of the LHC

The LHC experimental regions (ATLAS, ALICE, CMS and LHCb) are characterised by having a variable geometry, non-uniform magnetic field, and the presence of two beams that will collide at the Interaction Point (IP). A detailed study of electron multipacting in the experimental chambers is needed to establish the pressure increase due to electron stimulated desorption, especially critical in the experimental regions. Furthermore, knowledge of the predicted electron cloud density all along the experimental regions will allow for an estimation of its possible effects on the beam stability

Bimodules and branes in deformation quantization

We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space X. The result implies, in particular, that the Kontsevich deformation quantizations of S(X*) and (X) associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet's recent paper on Koszul duality in deformation quantizatio

Measurements of vehicle pollutants in a high-traffic urban area by a multiwavelength dial approach: Correlation between two different motor vehicle pollutants

The development and improvement of monitoring techniques to measure the concentration of pollutants in the atmosphere are a starting point to guarantee high levels of human health and environmental safety. The combination of lidar and dial techniques, by measuring backscattering signals and reconstructing the map of their concentrations, can be used to provide detailed information about the presence of aerosols, particulate and pollutions. Moreover, by using a multiwavelength approach, it is possible to increase the measurement accuracy and reliability. In this work, the dial approach is used to monitor the pollution in a very congested urban area with high trac. In order to provide a validation of the results, correlation analyses between the measured pollutants was performed. A new lidar analysis method, based on the least-square minimization technique, was introduced and demonstrated to work properly. The dial capability to detect polluted areas was shown—and by correlation analysis—also the possibility to identify the source of pollutions can be performed

Enhancement of radiosensitivity by the novel anticancer quinolone derivative vosaroxin in preclinical glioblastoma models

Purpose: Glioblastoma multiforme (GBM) is the most aggressive brain tumor. The activity of vosaroxin, a first-in-class anticancer quinolone derivative that intercalates DNA and inhibits topoisomerase II, was investigated in GBM preclinical models as a single agent and combined with radiotherapy (RT). Results: Vosaroxin showed antitumor activity in clonogenic survival assays, with IC50 of 10-100 nM, and demonstrated radiosensitization. Combined treatments exhibited significantly higher γH2Ax levels compared with controls. In xenograft models, vosaroxin reduced tumor growth and showed enhanced activity with RT; vosaroxin/RT combined was more effective than temozolomide/RT. Vosaroxin/ RT triggered rapid and massive cell death with characteristics of necrosis. A minor proportion of treated cells underwent caspase-dependent apoptosis, in agreement with in vitro results. Vosaroxin/RT inhibited RT-induced autophagy, increasing necrosis. This was associated with increased recruitment of granulocytes, monocytes, and undifferentiated bone marrow-derived lymphoid cells. Pharmacokinetic analyses revealed adequate blood-brain penetration of vosaroxin. Vosaroxin/RT increased disease-free survival (DFS) and overall survival (OS) significantly compared with RT, vosaroxin alone, temozolomide, and temozolomide/RT in the U251-luciferase orthotopic model. Materials and Methods: Cellular, molecular, and antiproliferative effects of vosaroxin alone or combined with RT were evaluated in 13 GBM cell lines. Tumor growth delay was determined in U87MG, U251, and T98G xenograft mouse models. (DFS) and (OS) were assessed in orthotopic intrabrain models using luciferasetransfected U251 cells by bioluminescence and magnetic resonance imaging. Conclusions: Vosaroxin demonstrated significant activity in vitro and in vivo in GBM models, and showed additive/synergistic activity when combined with RT in O6- methylguanine methyltransferase-negative and -positive cell lines