The Local Structure of Lie Bialgebroids

We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical $r$-matrices and matched pairs induced by Poisson group actionsComment: 13 page

Manin Triples for Lie Bialgebroids

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does not satisfy the Jacobi identity except on certain subspaces. In this paper we systematize the properties of this bracket in the definition of a Courant algebroid. This structure on a vector bundle $E\rightarrow M$, consists of an antisymmetric bracket on the sections of $E$ whose ``Jacobi anomaly'' has an explicit expression in terms of a bundle map $E\rightarrow TM$ and a field of symmetric bilinear forms on $E$. When $M$ is a point, the definition reduces to that of a Lie algebra carrying an invariant nondegenerate symmetric bilinear form. For any Lie bialgebroid $(A,A^{*})$ over $M$ (a notion defined by Mackenzie and Xu), there is a natural Courant algebroid structure on $A\oplus A^{*}$ which is the Drinfel'd double of a Lie bialgebra when $M$ is a point. Conversely, if $A$ and $A^*$ are complementary isotropic subbundles of a Courant algebroid $E$, closed under the bracket (such a bundle, with dimension half that of $E$, is called a Dirac structure), there is a natural Lie bialgebroid structure on $(A,A^{*})$ whose double is isomorphic to $E$. The theory of Manin triples is thereby extended from Lie algebras to Lie algebroids. Our work gives a new approach to bihamiltonian structures and a new way of combining two Poisson structures to obtain a third one. We also take some tentative steps toward generalizing Drinfel'd's theory of Poisson homogeneous spaces from groups to groupoids.Comment: 24 pages, LaTeX2e (minor corrections, added section at end), final version of paper to appear in J. Diff. Geo

The environments of Type Ia supernovae with different relative equivalent width of Si II feature in their spectra

Although type Ia supernovae are so important in many astrophysical field, e.g. in cosmology, their explosion mechanism and progenitor system are still unclear. In physics, the relative equivalent width (REW) of the Si II 635.5 nm absorption feature reflects the velocity interval of silicon in the supernova ejecta and then may provide constraints on the explosion mechanism of SNe Ia. In this paper, we divide the SNe Ia into broad line (BL) and normal line (NL) subsamples based on their REW of Si II 635.5 nm absorption lines around maximum light, and find that the BL SNe Ia have a dimmer mean brightness than NL ones, which possibly results from their different metallicities. However, based on the pixel statistics study on the environments of two subsamples, we do not find any significant potential difference on the environments between BL and NL SNe Ia, which implies that the explosion mechanism of SNe Ia could be independent of their progenitor populations.Comment: 17 pages, 13 figures, accepted for publication in Ap

Effects of age, sex and pathological type on the risk of multiple polyps: A Chinese teaching hospital study

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/162741/2/cdd12863.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/162741/1/cdd12863_am.pd

Long-term straw incorporation significantly reduced subsoil organic carbon stock in cinnamon soil

peer reviewe

Recurrence and Polya number of general one-dimensional random walks

The recurrence properties of random walks can be characterized by P\'{o}lya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities $l$ and $r$, or remain at the same position with probability $o$ ($l+r+o=1$). We calculate P\'{o}lya number $P$ of this model and find a simple expression for $P$ as, $P=1-\Delta$, where $\Delta$ is the absolute difference of $l$ and $r$ ($\Delta=|l-r|$). We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability $l$ equals to the right-moving probability $r$.Comment: 3 page short pape

Alzheimer’s disease as a causal risk factor for diabetic retinopathy: a Mendelian randomization study

ObjectivesThis study aims to investigate the causal relationship between Alzheimer’s Disease (AD) and Diabetic Retinopathy (DR).MethodsEmploying Mendelian Randomization (MR), Generalized Summary-data-based Mendelian Randomization (GSMR), and the MR-Steiger test, this study scrutinizes the genetic underpinnings of the hypothesized causal association between AD and DR, as well as its Proliferative DR (PDR) and Non-Proliferative DR (NPDR) subtypes. Comprehensive data from Genome-Wide Association Studies (GWAS) were analyzed, specifically AD data from the Psychiatric Genomics Consortium (71,880 cases/383,378 controls), and DR, PDR, and NPDR data from both the FinnGen consortium (FinnGen release R8, DR: 5,988 cases/314,042 controls; PDR: 8,383 cases/329,756 controls; NPDR: 3,446 cases/314,042 controls) and the IEU OpenGWAS (DR: 14,584 cases/176,010 controls; PDR: 8,681 cases/204,208 controls; NPDR: 2,026 cases/204,208 controls). The study also incorporated Functional Mapping and Annotation (FUMA) for an in-depth analysis of the GWAS results.ResultsThe MR analyses revealed that genetic susceptibility to AD significantly increases the risk of DR, as evidenced by GWAS data from the FinnGen consortium (OR: 2.5090; 95% confidence interval (CI):1.2102-5.2018, false discovery rate P-value (PFDR)=0.0201; GSMR: bxy=0.8936, bxy_se=0.3759, P=0.0174), NPDR (OR: 2.7455; 95% CI: 1.3178-5.7197, PFDR=0.0166; GSMR: bxy=0.9682, bxy_se=0.3802, P=0.0126), and PDR (OR: 2.3098; 95% CI: 1.2411-4.2986, PFDR=0.0164; GSMR: bxy=0.7962, bxy_se=0.3205, P=0.0129) using DR GWAS from FinnGen consortium. These results were corroborated by DR GWAS datasets from IEU OpenGWAS. The MR-Steiger test confirmed a significant association of all identified instrumental variables (IVs) with AD. While a potential causal effect of DR and its subtypes on AD was identified, the robustness of these results was constrained by a low power value. FUMA analysis identified OARD1, NFYA, TREM1 as shared risk genes between DR and AD, suggesting a potential genetic overlap between these complex diseases.DiscussionThis study underscores the contribution of AD to an increased risk of DR, as well as NPDR and PDR subtypes, underscoring the necessity of a holistic approach in the management of patients affected by these conditions

AI protein structure prediction-based modeling and mutagenesis of a protostome receptor and peptide ligands reveal key residues for their interaction

The protostome leucokinin (LK) signaling system, including LK peptides and their G protein-coupled receptors, has been characterized in several species. Despite the progress, molecular mechanisms governing LK peptide–receptor interactions remain to be elucidated. Previously, we identified a precursor protein for Aplysia leucokinin-like peptides (ALKs) that contains the greatest number of amidated peptides among LK precursors in all species identified so far. Here, we identified the first ALK receptor from Aplysia, ALKR. We used cell-based IP1 activation assays to demonstrate that two ALK peptides with the most copies, ALK1 and ALK2, activated ALKR with high potencies. Other endogenous ALK-derived peptides bearing the FXXWX-amide motif also activated ALKR to various degrees. Our examination of cross-species activity of ALKs with the Anopheles LK receptor was consistent with a critical role for the FXXWX-amide motif in receptor activity. Furthermore, we showed, through alanine substitution of ALK1, the highly conserved phenylalanine (F), tryptophan (W), and C-terminal amidation were each essential for receptor activation. Finally, we used an artificial intelligence– based protein structure prediction server (Robetta) and Autodock Vina to predict the ligand-bound conformation of ALKR. Our model predicted several interactions (i.e., hydrophobic interactions, hydrogen bonds, and amide-pi stacking) between ALK peptides and ALKR, and several of our substitution and mutagenesis experiments were consistent with the predicted model. In conclusion, our results provide important information defining possible interactions between ALK peptides and their receptors. The workflow utilized here may be useful for studying other ligand–receptor interactions for a neuropeptide signaling system, particularly in protostomes

Egorov's theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow

The main result of the paper is Egorov's theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.Comment: 23 pages, no figures. Completely revised and improved version of dg-ga/970301