A variant of the Mukai pairing via deformation quantization

We give a new method to prove a formula computing a variant of Caldararu's Mukai pairing \cite{Cal1}. Our method is based on some important results in the area of deformation quantization. In particular, part of the work of Kashiwara and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler, Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped that our method is useful for generalization to settings involving certain singular varieties.Comment: 8 pages. Comments and suggestions welcom

Experience paper on the operation of pilot project on oyster culture at Tuticorin

The technology of oyster culture was developed in India at the Central Marine Fisheries Research Institute. An experimental farm was established at Tuticorin bay in an area of 0.25 hectares. Different growout methods have been tried and it has been assessed that the shell string method could be practised with relatively low cost inputs with a production rate comparable to highly efficient systems such as rack and tray method or raft culture

Larval and Post-Larval Stages of Pacific Oyster (Crassostrea gigas) Are Resistant to Elevated CO2

published_or_final_versio

Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's

It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface Y of degree n. We provide several definitions of this form - via the Abel-Jacobi map, via Hochschild homology, and via the linkage class, and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Y we show that the Fano scheme is birational to a certain moduli space of sheaves on a p-dimensional Calabi--Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual Calabi-Yau becomes non commutative.Comment: 34 pages; exposition of Hochschild homology expanded; references added; introduction re-written; some imrecisions, typos and the orbit diagram in the last section correcte

Periodic Solutions Averaging Methods in Nonlinear Ordinary Differential Equations

A nonstandard approach to averaging theory for ordinary differential equations and functional differential equations is developed. We define a notion of perturbation and we obtain averaging results under weaker conditions than the results in the literature. The classical averaging theorems approximate the solutions of the system by the solutions of the averaged system, for Lipschitz continuous vector fields, and when the solutions exist on the same interval as the solutions of the averaged system. We extend these results to perturbations of vector fields which are uniformly continuous in the spatial variable with respect to the time variable and without any restriction on the interval of existence of the solution

From Atiyah Classes to Homotopy Leibniz Algebras

A celebrated theorem of Kapranov states that the Atiyah class of the tangent bundle of a complex manifold $X$ makes $T_X[-1]$ into a Lie algebra object in $D^+(X)$, the bounded below derived category of coherent sheaves on $X$. Furthermore Kapranov proved that, for a K\"ahler manifold $X$, the Dolbeault resolution $\Omega^{\bullet-1}(T_X^{1,0})$ of $T_X[-1]$ is an $L_\infty$ algebra. In this paper, we prove that Kapranov's theorem holds in much wider generality for vector bundles over Lie pairs. Given a Lie pair $(L,A)$, i.e. a Lie algebroid $L$ together with a Lie subalgebroid $A$, we define the Atiyah class $\alpha_E$ of an $A$-module $E$ (relative to $L$) as the obstruction to the existence of an $A$-compatible $L$-connection on $E$. We prove that the Atiyah classes $\alpha_{L/A}$ and $\alpha_E$ respectively make $L/A[-1]$ and $E[-1]$ into a Lie algebra and a Lie algebra module in the bounded below derived category $D^+(\mathcal{A})$, where $\mathcal{A}$ is the abelian category of left $\mathcal{U}(A)$-modules and $\mathcal{U}(A)$ is the universal enveloping algebra of $A$. Moreover, we produce a homotopy Leibniz algebra and a homotopy Leibniz module stemming from the Atiyah classes of $L/A$ and $E$, and inducing the aforesaid Lie structures in $D^+(\mathcal{A})$.Comment: 36 page

Grey Relational Analysis-Based Optimisation of Input Parameters of Incremental Forming Process Applied to the AA6061 Alloy

Incremental forming is mainly based on the deformation occurring locally on sheet metal. A hemispherical head tool deforms the sheet metal progressively, and its path is controlled by means of a CNC machine. Even though the process is a time-consuming one, the cost reduction connected with punches and dies makes this process attractive for rapid prototyping. In single point incremental forming, the quality of formability mainly depends on the forming parameters and the tool path generated. In this study, cone-shaped components were formed from AA6061 alloy sheets with a thickness of 1.15 mm. Factors, such as feed rate, spindle speed, and step depth are considered as input parameters to determine the output response in terms of surface roughness and wall thickness. Taguchi’s technique was used for conducting the experiments with the smallest number of repetitions to evaluate the output. Grey relational analysis was introduced to determine the optimal forming parameters with respect to the output response. The experiments conducted with the optimised parameters show a minimal deviation of 0.15% in the grade value compared to the predicted grade which is acceptable

Pharmacological levels of withaferin A (Withania somnifera) trigger clinically relevant anticancer effects specific to triple negative breast cancer cells

Withaferin A (WA) isolated from Withania somnifera (Ashwagandha) has recently become an attractive phytochemical under investigation in various preclinical studies for treatment of different cancer types. In the present study, a comparative pathway-based transcriptome analysis was applied in epithelial-like MCF-7 and triple negative mesenchymal MDA-MB-231 breast cancer cells exposed to different concentrations of WA which can be detected systemically in in vivo experiments. Whereas WA treatment demonstrated attenuation of multiple cancer hallmarks, the withanolide analogue Withanone (WN) did not exert any of the described effects at comparable concentrations. Pathway enrichment analysis revealed that WA targets specific cancer processes related to cell death, cell cycle and proliferation, which could be functionally validated by flow cytometry and real-time cell proliferation assays. WA also strongly decreased MDA-MB-231 invasion as determined by single-cell collagen invasion assay. This was further supported by decreased gene expression of extracellular matrix-degrading proteases (uPA, PLAT, ADAM8), cell adhesion molecules (integrins, laminins), pro-inflammatory mediators of the metastasis-promoting tumor microenvironment (TNFSF12, IL6, ANGPTL2, CSF1R) and concomitant increased expression of the validated breast cancer metastasis suppressor gene (BRMS1). In line with the transcriptional changes, nanomolar concentrations of WA significantly decreased protein levels and corresponding activity of uPA in MDA-MB-231 cell supernatant, further supporting its anti-metastatic properties. Finally, hierarchical clustering analysis of 84 chromatin writer-reader-eraser enzymes revealed that WA treatment of invasive mesenchymal MDA-MB-231 cells reprogrammed their transcription levels more similarly towards the pattern observed in non-invasive MCF-7 cells. In conclusion, taking into account that sub-cytotoxic concentrations of WA target multiple metastatic effectors in therapy-resistant triple negative breast cancer, WA-based therapeutic strategies targeting the uPA pathway hold promise for further (pre)clinical development to defeat aggressive metastatic breast cancer

Oceanic squids - their distribution, abundance and potential in the EEZ of India and contiguous seas

FORV Sagar Sampada collected a good number of oceanic squids belonging to several families from the Indian EEZ and contiguous seas. Of these, the most important species was the purpleback flying squid Symplectoteuthis oualaniensis which forms a potential oceanic squid resource. This species was caught in pelagic trawl at depths up to.200-250 m from surface in the oceanic areas. Though the squid is known to be distributed throughout India's oceanic waters, it frequently occurred in comparatively more abundance, up to 318 squids per haul, in the northneastem Arabian Sea. There was wide variation in the size of this squid (from 20 mm to 472 mm), the largest individual weighing 4.5 kg. The diamondback squid Thysanoteuthis rhombus, the largest specimen of which measured 585 mm in length and 5.3 kg in weight, was also caught from a few stations. Besides these large species, several others belonging to families such as Onychoteuthidae, Histioteuthidae, Enoploteuthidae and Cranchiidae are also distributed in the EEZ. A large number of oceanic squids were collected at night, which is indicative of their diel vertical migration towards surface layers during night hours

Impact of e-cigarette vaping aerosol exposure in pregnancy on mTOR signaling in rat fetal hippocampus

Electronic cigarette (e-cig) use during pregnancy has become a major health concern in recent years and many view them as less harmful and may help quit or reduce combustible cigarettes. Implementing a state-of-the-art engineered vaping system, comprising an atomizer similar to those sold in vape shops, we aimed to utilize a translational e-cig inhalation delivery method to provide crucial information on the impact of prenatal e-cig aerosols on the developing brain hippocampal mTOR system in a rat model system. Gestational e-cig vaping significantly increased P-mTOR levels (p < 0.05) in the rat fetal hippocampi in the nicotine group (comprising of VG/PG + nicotine) compared to the control and the juice (comprising of VG/PG) groups. Total mTOR expression was not different among groups. Immunofluorescence imaging demonstrated P-mTOR was detected exclusively in the granule cells of the dentate gyrus of the fetal hippocampus. E-cig did not alter DEPTOR, but RAPTOR and RICTOR were higher (p < 0.05) in the Nicotine group. Gestational e-cig vaping with nicotine increased (p < 0.05) the activity and expression of 4EBP1, p70S6K, but decreased (p < 0.05) P-PKCα in the fetal hippocampi. In summary, dysregulation of mTORC1 and the related mTORC2, their activity, and downstream proteins together may play a critical role in e-cig-vaping-induced neurobiological phenotypes during development