Logarithmic connections on principal bundles over normal varieties

Let $X$ be a normal complex algebraic variety with a reduced Weil divisor $D$. Let $G$ be a complex linear algebraic group. We formalize the notion of a logarithmic connection on a Zariski locally trivial principal $G$-bundle over $X$, which is singular along $D$. The existence of a logarithmic connection on the frame bundle associated to a vector bundle over $X$ is equivalent to the existence of a covariant derivative on the vector bundle. A torus equivariant principal bundle over a toric variety admits an integrable logarithmic connection singular along the boundary divisor. We consider the notion of residue of a logarithmic connection on a vector bundle over a toric variety, and show that for a toric vector bundle, the residue encodes the equivariant structure of the vector bundle.Comment: 30 page

Classification, reduction and stability of toric principal bundles

Let $X$ be a complex toric variety equipped with the action of an algebraic torus $T$, and let $G$ be a complex linear algebraic group. We classify all $T$-equivariant principal $G$-bundles $\mathcal{E}$ over $X$ and the morphisms between them. When $G$ is connected and reductive, we characterize the equivariant automorphism group $\text{Aut}_T(\mathcal{E} )$ of $\mathcal{E}$ as the intersection of certain parabolic subgroups of $G$ that arise naturally from the $T$-action on $\mathcal{E}$. We then give a criterion for the equivariant reduction of the structure group of $\mathcal{E}$ to a Levi subgroup of $G$ in terms of $\text{Aut}_T(\mathcal{E} )$. We use it to prove a principal bundle analogue of Kaneyama's theorem on equivariant splitting of torus equivariant vector bundles of small rank over a projective space. When $X$ is projective and $G$ is connected and reductive, we show that the notions of stability and equivariant stability are equivalent for any $T$-equivariant principal $G$-bundle over $X$.Comment: 47 page

Ultrasound guided platelet rich plasma or corticosteroid for supraspinatus tendonosis or partial tear: an observational study of clinical outcome

Background: The clinical application of platelet rich plasma (PRP) in rotator cuff tears has increased recently. Many studies have found no difference between placebo controls and PRP and corticosteroids (CS) and some have found more rapid benefits with PRP injections. The present study was undertaken with the objectives to observe and assess efficacies of the two different treatment modalities in terms of symptomatic relief and recovery of ROM and to ascertain the duration of symptom free period and functional improvement on follow up. Methods: Observational clinical outcome study, conducted at a tertiary care hospital between September 2020 and March 2022 after institute ethical committee clearance. A total of 100 patients, with a positive clinical test for supraspinatus and magnetic resonance imaging (MRI) suggestive of supraspinatus tendinitis were divided to 2 groups and based on whether they received either intra-articular CS or PRP injection under ultrasonography (USG) guidance All patients were followed up at for assessing the outcomes at 6 weeks, 3 months and 6 months from intervention Results: The clinical outcome of the group receiving the PRP was better than group receiving CS intervention. Conclusions: PRP should therefore be considered as a viable option to treat supraspinatus tendinopathy/partial tear as it is cheap, readily available modality using patients own blood which is more acceptable to patient and also safe to individual where complications related to corticosteroids anticipated. Ultrasound guided procedure were found to enhance the accuracy of injection

Osteological morphometric analysis of instrumentation safe zones of C1 and C2 vertebra in North Indian population: a multicentric study

Background: The complex anatomy and critical functional role of the C1 and C2 vertebrae necessitate precise understanding of safe zones for instrumentation to mitigate risks during surgical interventions. This study aimed to conduct a comprehensive morphometric analysis to identify and characterize safe zones for instrumentation within C1 and C2 vertebrae. Though there are multiple radiological based studies, actual osteological measurements are not available for North Indian population. Methods: 200 atlas and axis vertebrae were measured within an accuracy of 0.01 mm to ascertain various dimensions, distances and angles to guide safe exposure and instrumentation. To the best of our knowledge this observational morphometric study is first to provide actual osteological measurements in large number of C1 and C2 vertebrae in North Indian population. Results: The morphometric analysis revealed precise measurements of pedicle dimensions, transverse foramen parameters, and distances from key anatomical landmarks within C1 and C2 vertebrae. Safe zones for instrumentation were identified based on these measurements, considering the optimal implant size and trajectory to minimize the risk of neural or vascular damage. Differences between the morphology of North Indian, South Indian and Turkish C1 and C2 morphology was also identified. Conclusions: This study provides critical insights into the morphometric parameters which can be used to identify safe zones for instrumentation within the C1 and C2 vertebrae. The identified safe zones and associated measurements are essential for optimizing surgical strategies, enhancing instrumentation accuracy, and ultimately improving patient outcomes during craniovertebral surgical procedures. Spine Surgeons can utilize this data to tailor surgical approaches and implant placements, promoting safer and more effective interventions in the challenging anatomical region of the craniovertebral junction

Nitrogen Content in the Earth\u27s Outer Core

Using first principles molecular dynamic simulations, we explore the effects of nitrogen (N) on the density and sound velocity of liquid iron and evaluate its potential as a light element in the Earth\u27s outer core. Our results suggest that Fe-N melt cannot simultaneously explain the density and seismic velocity of the Earth\u27s outer core. Although ~2.0 wt.% N can explain the bulk sound velocity of the outer core, such N content only lowers the density of liquid Fe by ~3%. Matching both the velocity and density by the other light elements limits the N in the core to ≪2.0 wt.%. Our finding suggests that nitrogen is a minor to trace element in the Earth\u27s core and is consistent with the geochemical mass balance with terrestrial abundance of N and alloy-silicate partitioning data, which suggest that there cannot be significant N in the core

Sex Differences in 20-Hydroxyecdysone Hormone Levels Control Sexual Dimorphism in Bicyclus anynana Wing Patterns

10.1093/molbev/msx301MOLECULAR BIOLOGY AND EVOLUTION352465-47

Mass spectrometry and bioinformatics analysis data

2DE and 2D-DIGE based proteomics analysis of serum from women with endometriosis revealed several proteins to be dysregulated. A complete list of these proteins along with their mass spectrometry data and subsequent bioinformatics analysis are presented here. The data is related to “Investigation of serum proteome alterations in human endometriosis” by Dutta et al. [1]

Investigation of serum proteome alterations in human endometriosis

Endometriosis is a common benign gynecological disease, characterized by proliferation of functional endometrial glands and stroma outside the uterine cavity. The present study involves investigation of alterations in the serum proteome of endometriosis patients compared to healthy controls using 2DE and 2D-DIGE combined with MALDI TOF/TOF-MS. Comparison of serum proteome of endometriosis patients and healthy subjects revealed 25 significant differentially expressed proteins. Gene ontology and network analysis, performed using PANTHER, DAVID, WebGestalt and STRING, revealed that the differentially expressed proteins are majorly involved in response to stimulus, immune system, metabolic, localization and cellular processes. For serum diagnostic marker identification, several robust statistical screening procedures were applied to identify the set of the most significant proteins responsible for successful diagnosis of different endometriosis stages. Partial least squares (PLS) based marker selection tool and orthogonal partial least squares-discriminant analysis (OPLS-DA) were used to identify the most significant proteins for disease prediction. Western blotting validation in a separate cohort of patients revealed that haptoglobin (HP), Ig kappa chain C region (IGKC), alpha-1B-glycoprotein (A1BG) can be considered effective serum protein markers for the diagnosis of Stage II, III and IV endometriosis. For diagnosis of Stage I, only IGKC and HP seemed promising