Results 111 to 120 of about 226,801 (347)
Lietuvos Matematikos RinkinysIn this article we define the canonical forms on the principal bundle of holonomic frames of order r, give structure equations for these forms and determine the connection of order r.
Kazimeras Navickis
doaj +1 more source
Construction of Categorical Bundles from Local Data [PDF]
arXiv, 2016 A categorical principal bundle is a structure comprised of categories that is analogous to a classical principal bundle; examples arise from geometric contexts involving bundles over path spaces. We show how a categorical principal bundle can be constructed from local data specified through transition functors and natural transformations.
arxiv
Molecular Oncology, EarlyView.The authors analyzed the spatial distributions of gene and metabolite profiles in cervical cancer through spatial transcriptomic and spatially resolved metabolomic techniques. Pivotal genes and metabolites within these cases were then identified and validated.
Lixiu Xu +3 more
wiley +1 more source
An Introduction to Pull-backs of Bundles and Homotopy Invariance [PDF]
arXiv, 2001 We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article is to show that for a principal fibre bundle over a paracompact manifold, there is a principal fibre bundle ...
arxiv
Connections on the path bundle of a principal fiber bundle
Differential Geometry and its Applications, 1994 AbstractLet (P, M, π, G) be a principal fiber bundle. In the first section of this paper, we consider the Fréchet manifold PP of smooth paths in P along with important Fréchet submanifolds such as the space PP of paths in P which emanate from some fixed point u0 ∈ P and the space π∗u0(Lx0M) of paths at u0 in P which project to the set Lx0M of loops of ...
openaire +2 more sources
Crosstalk between gut microbiota and tumor: tumors could cause gut dysbiosis and metabolic imbalance
Molecular Oncology, EarlyView.In this research, we analyzed the relationship between gut microbiota and tumor. We discovered that both subcutaneous and metastatic tumors would alter the composition and metabolic function of gut microbiota. Meanwhile, fecal microbiota transplantation also indicated the anti‐tumor role of the gut microbiota, revealing the crosstalk between tumor and ...
Siyuan Zhang +8 more
wiley +1 more source
A compactification of the moduli space of principal Higgs bundles over singular curves [PDF]
arXiv, 2011 A principal Higgs bundle $(P,\phi)$ over a singular curve $X$ is a pair consisting of a principal bundle $P$ and a morphism $\phi:X\to\text{Ad}P \otimes \Omega^1_X$. We construct the moduli space of principal Higgs G-bundles over an irreducible singular curve $X$ using the theory of decorated vector bundles.
arxiv
Molecular Oncology, EarlyView.VASP was found to be overexpressed in metastatic oral squamous cell carcinoma (OSCC) tissues. Notably, PTTG1‐ and VASP‐deficient OSCC cells demonstrated suppressed metastatic properties by disrupting the interaction between the cytoskeleton and focal adhesion (FAs) in the filopodia region.
Suyeon Park +6 more
wiley +1 more source
Bundles over Quantum RealWeighted Projective Spaces
Axioms, 2012 The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed.
Tomasz Brzeziński, Simon A. Fairfax
doaj +1 more source
Molecular Oncology, EarlyView.Consensus molecular subtypes (CMS1‐4) have been identified to study colorectal cancer heterogeneity and serve as potential biomarkers. In this study, we developed and evaluated NanoCMSer, a NanoString‐based classifier using 55 genes, optimized for FF and FFPE to facilitate the clinical evaluation of CMS subtyping.
Arezo Torang +10 more
wiley +1 more source