Cech and de Rham Cohomology of Integral Forms

We present a study on the integral forms and their Cech/de Rham cohomology. We analyze the problem from a general perspective of sheaf theory and we explore examples in superprojective manifolds. Integral forms are fundamental in the theory of integration in supermanifolds. One can define the integral forms introducing a new sheaf containing, among other objects, the new basic forms delta(dtheta) where the symbol delta has the usual formal properties of Dirac's delta distribution and acts on functions and forms as a Dirac measure. They satisfy in addition some new relations on the sheaf. It turns out that the enlarged sheaf of integral and "ordinary" superforms contains also forms of "negative degree" and, moreover, due to the additional relations introduced, its cohomology is, in a non trivial way, different from the usual superform cohomology.Comment: 20 pages, LaTeX, we expanded the introduction, we add a complete analysis of the cohomology and we derive a new duality between cohomology group

Balanced superprojective varieties

We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the geometry of superprojective spaces, we extend Donaldson\u2019s definition of balanced manifolds to supermanifolds and we derive the new conditions of a balanced supermanifold. We apply the construction to superpoints viewed as submanifolds of superprojective spaces. We conclude with a list of open issues and interesting problems that can be addressed in the present context

Inclusion of the phytoalexin trans-resveratrol in native cyclodextrins: a thermal, spectroscopic, and X-ray structural study

The aim of the study was to determine the feasibility of complexation between the antioxidant trans-resveratrol (RSV) and underivatized cyclodextrins (CDs) using a variety of preparative methods, including physical mixing, kneading, microwave irradiation, co-evaporation, and co-precipitation techniques. Products were characterized using differential scanning calorimetry (DSC), simultaneous thermogravimetric/DSC analysis (TGA/DSC), Fourier transform infrared (FT-IR) spectroscopy, and powder X-ray diffraction (PXRD). With alfa-CD and RSV, sample amorphization was revealed by PXRD and FT-IR, but no definitive inclusion complexation was evident. Similar results were obtained in attempts to complex RSV with beta-CD. However, complex formation between gamma-CD and RSV was evident from observation of an endo-/exothermic effect appearing in the DSC trace of the product from kneading and was further corroborated by FT-IR and PXRD methods. The latter technique indicated complexation unequivocally as the diffraction peak profile for the product matched that for known isostructural gamma-CD complexes. Single crystal X-ray analysis followed, confirming the predicted complex between gamma-CD and RSV. A combination of 1H NMR and TGA data yielded the complex formula (g-CD)3(RSV)4(H2O)62. However, severe disorder of the RSV molecules prevented their modeling. In contrast, our previous studies of the inclusion of RSV in methylated CDs yielded crystals with only minor guest disorder

Microenvironment in neuroblastoma: Isolation and characterization of tumor-derived mesenchymal stromal cells

Background: It has been proposed that mesenchymal stromal cells (MSCs) promote tumor progression by interacting with tumor cells and other stroma cells in the complex network of the tumor microenvironment. We characterized MSCs isolated and expanded from tumor tissues of pediatric patients diagnosed with neuroblastomas (NB-MSCs) to define interactions with the tumor microenvironment. Methods: Specimens were obtained from 7 pediatric patients diagnosed with neuroblastoma (NB). Morphology, immunophenotype, differentiation capacity, proliferative growth, expression of stemness and neural differentiation markers were evaluated. Moreover, the ability of cells to modulate the immune response, i.e. inhibition of phytohemagglutinin (PHA) activated peripheral blood mononuclear cells (PBMCs) and natural killer (NK) cytotoxic function, was examined. Gene expression profiles, known to be related to tumor cell stemness, Wnt pathway activation, epithelial-mesenchymal transition (EMT) and tumor metastasis were also evaluated. Healthy donor bone marrow-derived MSCs (BM-MSC) were employed as controls. Results: NB-MSCs presented the typical MSC morphology and phenotype. They showed a proliferative capacity superimposable to BM-MSCs. Stemness marker expression (Sox2, Nanog, Oct3/4) was comparable to BM-MSCs. NB-MSC in vitro osteogenic and chondrogenic differentiation was similar to BM-MSCs, but NB-MSCs lacked adipogenic differentiation capacity. NB-MSCs reached senescence phases at a median passage of P7 (range, P5-P13). NB-MSCs exhibited greater immunosuppressive capacity on activated T lymphocytes at a 1:2 (MSC: PBMC) ratio compared with BM-MSCs (p = 0.018). NK cytotoxic activity was not influenced by co-culture, either with BM-MSCs or NB-MSCs. Flow-cytometry cell cycle analysis showed that NB-MSCs had an increased number of cells in the G0-G1 phase compared to BM-MSCs. Transcriptomic profiling results indicated that NB-MSCs were enriched with EMT genes compared to BM-MSCs. Conclusions: We characterized the biological features, the immunomodulatory capacity and the gene expression profile of NB-MSCs. The NB-MSC gene expression profile and their functional properties suggest a potential role in promoting tumor escape, invasiveness and metastatic traits of NB cancer cells. A better understanding of the complex mechanisms underlying the interactions between NB cells and NB-derived MSCs should shed new light on potential novel therapeutic approaches

Nahm Transform and Moduli Spaces of CPn Models on the Torus

There is a Nahm transform for two-dimensional gauge fields which establishes a one-to-one correspondence between the orbit space of U(N) gauge fields with topological charge k defined on a torus and that of U(k) gauge fields with charge N on the dual torus. The main result of this paper is to show that a similar duality transform cannot exist for CPn instantons. This fact establishes a significative difference between 4-D gauge theories and CPn models. The result follows from the global analysis of the moduli space of instantons based on a complete and explicit parametrization of all self-dual solutions on the two-dimensional torus. The boundary of the space of regular instantons is shown to coincide with the space of singular instantons. This identification provides a new approach to analyzing the role of overlapping instantons in the infrared sector of CPn sigma models.Comment: 28 pages, 5 eps-figure

Ultrarelativistic circular orbits of spinning particles in a Schwarzschild field

Ultrarelativistic circular orbits of spinning particles in a Schwarzschild field described by the Mathisson-Papapetrou equations are considered. The preliminary estimates of the possible synchrotron electromagnetic radiation of highly relativistic protons and electrons on these orbits in the gravitational field of a black hole are presentedComment: 9 page

On gauge/string correspondence and mirror symmetry

We consider a mirror dual of the Berkovits-Vafa A-model for the BPS superstring on $AdS_5\times S^5$ in the form of a deformed superconifold. Via geometric transition, the theory has a dual description as the hermitian gaussian one-matrix model. We show that the A-model amplitudes of generic $AdS_2\times S^4$ branes, breaking the superconformal symmetry as $U(2,2|4)\to OSp(4^*|4)$, are evaluated in terms of observables in the matrix model. As such, upon the usual identification $g_{YM}^2=g_s$, these can be expanded as Drukker-Gross circular 1/2-BPS Wilson loops in the perturbative regime of ${\cal N}=4$ SYM.Comment: 1+13 pages, minor changes, added refrences, version to appear in JHE

First-in-Man Phase I Trial of the Selective MET Inhibitor Tepotinib in Patients with Advanced Solid Tumors.

PurposeTepotinib is an oral, potent, highly selective MET inhibitor. This first-in-man phase I trial investigated the MTD of tepotinib to determine the recommended phase II dose (RP2D).Patients and methodsPatients received tepotinib orally according to one of three dose escalation regimens (R) on a 21-day cycle: R1, 30-400 mg once daily for 14 days; R2, 30-315 mg once daily 3 times/week; or R3, 300-1,400 mg once daily. After two cycles, treatment could continue in patients with stable disease until disease progression or unacceptable toxicity. The primary endpoint was incidence of dose-limiting toxicity (DLT) and treatment-emergent adverse events (TEAE). Secondary endpoints included safety, tolerability, pharmacokinetics, pharmacodynamics, and antitumor effects.ResultsOne hundred and forty-nine patients received tepotinib (R1: n = 42; R2: n = 45; R3: n = 62). Although six patients reported DLTs [one patient in R1 (115 mg), three patients in R2 (60, 100, 130 mg), two patients in R3 (1,000, 1,400 mg)], the MTD was not reached at the highest tested dose of 1,400 mg daily. The RP2D of tepotinib was established as 500 mg once daily, supported by translational modeling data as sufficient to achieve ≥95% MET inhibition in ≥90% of patients. Treatment-related TEAEs were mostly grade 1 or 2 fatigue, peripheral edema, decreased appetite, nausea, vomiting, and lipase increase. The best overall response in R3 was partial response in two patients, both with MET overexpression.ConclusionsTepotinib was well tolerated with clinical activity in MET-dysregulated tumors. The RP2D of tepotinib was established as 500 mg once daily. MET abnormalities can drive tumorigenesis. This first-in-man trial demonstrated that the potent, highly selective MET inhibitor tepotinib can reduce or stabilize tumor burden and is well tolerated at doses up to 1,400 mg once daily. An RP2D of 500 mg once daily, as determined from translational modeling and simulation integrating human population pharmacokinetic and pharmacodynamic data in tumor biopsies, is being used in ongoing clinical trials