Homogeneous Bundles Research Articles

Thread-based microfluidics: Flow patterns in homogeneous and heterogeneous microfiber bundles

Thread-based microfluidics has recently seen considerable developments in the domain of portable diagnostic systems, smart bandages and tissue engineering. Similarly to paper-based microfluidics, thread-based microfluidics uses the wicking of fibers to move fluids. It has the advantage of confining and guiding the fluid along the yarns in a one, two or three dimensional space.A global approach to the motion of fluids in yarns and fiber bundles has already been reported in the literature based on the Lucas–Washburn–Rideal law. However no detailed investigation of the flow pattern inside the bundle has been conducted, depending on the internal structure of the bundle. Especially when the bundle possesses heterogeneous wetting properties, such as two different wetting regions interior and exterior, different flow patterns may exist.In this work, we perform a theoretical and numerical analysis of the different flow regimes for homogenous and heterogeneous fiber bundles. It is demonstrated that a limited number of fibers is sufficient for thread-based capillary flows, and that a caging of the flow can be achieved by realizing a lyophobic envelope.

Greatest lower bounds on Ricci curvature of homogeneous toric bundles

We derive a formula of the greatest lower bounds on Ricci curvature of Fano homogeneous toric bundles. A criteria for the ampleness of line bundles over general homogeneous toric bundles is also obtained.

Differential inequalities on homogeneous toric bundles

We study the generalized Abreu equation in n-dimensional polytopes and derive some differential inequalities for homogeneous toric bundles.

ALGEBRAIC ANALYSIS OF SCALAR GENERALIZED VERMA MODULES OF HEISENBERG PARABOLIC TYPE I: A n -SERIES

In the present article, we combine some techniques in harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ( $$ \mathcal{D} $$ -modules), and reformulate the composition series and branching problems for objects in the Bernstein–Gelfand–Gelfand parabolic category $$ {\mathcal{O}}^{\mathfrak{p}} $$ geometrically realized on certain orbits in the generalized flag manifolds. The general framework is then applied to the scalar generalized Verma modules supported on the closed Schubert cell of the generalized flag manifold G / P for G = SL(n + 2, ℂ) and P the Heisenberg parabolic subgroup; and algebraic analysis gives a complete classification of $$ {\mathfrak{g}}_r^{\prime } $$ -singular vectors for all $$ {\mathfrak{g}}_r^{\prime }=\mathfrak{s}\mathfrak{l}\left(n-r+2,\mathbb{C}\right)\kern1em \subset \mathfrak{g}=\mathfrak{s}\mathfrak{l}\left(n+2,\mathbb{C}\right),n-r>21 $$ . A consequence of our results is that we classify SL(n − r + 2, ℂ) -covariant differential operators acting on homogeneous line bundles over the complexification of the odd-dimensional CR-sphere S 2n+1 and valued in homogeneous vector bundles over the complexification of the CR-subspheres S 2(n-r)+1.

Orthosymplectic Lie superalgebras, Koszul duality, and a complete intersection analogue of the Eagon–Northcott complex

We study the ideal of maximal minors in Littlewood varieties, a class of quadratic complete intersections in spaces of matrices. We give a geometric construction for a large class of modules, including all powers of this ideal, and show that they have a linear free resolution over the complete intersection and that their Koszul dual is an infinite-dimensional irreducible representation of the orthosymplectic Lie superalgebra. We calculate the algebra of cohomology operators acting on this free resolution. We prove analogous results for powers of the ideals of maximal minors in the variety of length 2 complexes when it is a complete intersection, and show that their Koszul dual is an infinite-dimensional irreducible representation of the general linear Lie superalgebra. This generalizes work of Akin, Józefiak, Pragacz, Weyman, and the author on resolutions of determinantal ideals in polynomial rings to the setting of complete intersections and provides a new connection between representations of classical Lie superalgebras and commutative algebra. As a curious application, we prove that the cohomology of a class of reducible homogeneous bundles on symplectic and orthogonal Grassmannians and 2-step flag varieties can be calculated by an analogue of the Borel–Weil–Bott theorem.

Geometry of G-Structures via the Intrinsic Torsion

We study the geometry of a $G$-structure $P$ inside the oriented orthonormal frame bundle ${\rm SO}(M)$ over an oriented Riemannian manifold $M$. We assume that $G$ is connected and closed, so the quotient ${\rm SO}(n)/G$, where $n=\dim M$, is a normal homogeneous space and we equip ${\rm SO}(M)$ with the natural Riemannian structure induced from the structure on $M$ and the Killing form of ${\rm SO}(n)$. We show, in particular, that minimality of $P$ is equivalent to harmonicity of an induced section of the homogeneous bundle ${\rm SO}(M)\times_{{\rm SO}(n)}{\rm SO}(n)/G$, with a Riemannian metric on $M$ obtained as the pull-back with respect to this section of the Riemannian metric on the considered associated bundle, and to the minimality of the image of this section. We apply obtained results to the case of almost product structures, i.e., structures induced by plane fields.

On a classification of fat bundles over compact homogeneous spaces

This article deals with fat bundles. Bérard-Bergery classified all homogeneous bundles of that type. We ask a question of a possibility to generalize his description in the case of arbitrary G-structures over homogeneous spaces. We obtain necessary conditions for the existence of such bundles. These conditions yield a kind of classification of fat bundles associated with G-structures over compact homogeneous spaces provided that the connection in a G-structure is canonical.

Bladder Acellular Matrix Grafts Seeded with Adipose-Derived Stem Cells and Incubated Intraperitoneally Promote the Regeneration of Bladder Smooth Muscle and Nerve in a Rat Model of Bladder Augmentation.

The objective of this study was to investigate the feasibility of bladder acellular matrix grafts (BAMGs) seeded with adipose-derived stem cells (ASCs) followed by intraperitoneal incubation for bladder reconstruction in a rat model of bladder augmentation, and to explore the underlying mechanism. Autologous CM-DiI-labeled ASC-seeded (experimental group) and unseeded (control group) BAMGs were incubated in the peritoneum of male rats for 2 weeks and then harvested for bladder augmentation. Histological analysis of the incubated BAMGs revealed numerous cells growing in homogeneous collagen bundles in both groups. In the control BAMGs, these cells were mesenchyme derived, while in the ASC-seeded BAMGs, myofibroblasts and mesothelial cells were found inside and on the surface of the scaffold, respectively. Immunofluorescence analysis demonstrated that some of the myofibroblasts were transdifferentiated from the ASCs after 2 weeks of intraperitoneal incubation. The greater bladder capacity was found in the experimental group than the control group both 4 and 14 weeks postoperatively. Histological analysis revealed that the entire urothelium regenerated well both in the experimental group and the control group without significant difference 4 weeks and 14 weeks postoperatively. From the quantitative data of immunohistochemical and immunofluorescence staining, the smooth muscle cells (SMCs) regenerated significantly better in the experimental group than the control group both 4 weeks and 14 weeks postoperatively. Also significantly more nerve cells were found in the experimental group 14 weeks postoperatively. At 4 weeks postoperatively, the immunofluorescence double staining revealed that some SMCs in the BAMG were transdifferentiated from the implanted ASCs, but no CM-DiI labeling of ASCs was detected 14 weeks postoperatively. Taken together, our results demonstrate that ASC-seeded and peritoneally incubated BAMGs promote not only the morphological regeneration of the bladder smooth muscle and nerve, but also the bladder capacity, which indicates their potential for bladder regeneration.

Dimensions of some locally analytic representations

Let G G be the group of points of a split reductive group over a finite extension of Q p \mathbb {Q}_p . In this paper, we compute the dimensions of certain classes of locally analytic G G -representations. This includes principal series representations and certain representations coming from homogeneous line bundles on p p -adic symmetric spaces. As an application, we compute the dimensions of the unitary GL 2 ( Q p ) \textrm {GL}_2(\mathbb {Q}_p) -representations appearing in Colmez’ p p -adic local Langlands correspondence.

COHOMOLOGY GROUPS OF SECTIONS OF HOMOGENEOUS LINE BUNDLES OVER A TOROIDAL GROUP

We completely determine cohomology groups of sections of homogeneous line bundles over a toroidal group.

Homogeneous ACM bundles on a Grassmannian

In this paper, we characterize homogeneous arithmetically Cohen–Macaulay (ACM, for short) bundles on Grassmannians Gr(k,n) and we construct irreducible families of indecomposable ACM bundles on a Grassmannian Gr(k,n) of arbitrary high rank and dimension.As a consequence we prove that all Grassmann varieties Gr(k,n) are of wild representation type unless the projective spaces Gr(0,n) and Gr(n−1,n) and the hyperquadric Gr(1,3) in P5 which are of finite representation type.

Homogeneous generalized holomorphic structures

Homogeneous generalized holomorphic structures in the context of homogeneous principal fiber bundles are investigated. They are characterized in terms of Lie algebra data, and the generalized Dolbeault cohomology groups associated to a homogeneous generalized holomorphic vector bundle are identified with certain relative Lie algebra cohomology groups. We also provide some examples, using generalized flag manifolds.

Intraperitoneal incubation of bladder acellular matrix grafts improves bladder smooth muscle regeneration via neovascularization

The objective of this study was to investigate whether intraperitoneal incubation improves the regenerative capacity of bladder acellular matrix grafts (BAMGs) in a rat model of bladder augmentation. After 2 weeks of incubation in the peritoneum of male rats, BAMG flaps with vascular pedicles were harvested for autologous bladder augmentation. As the control, BAMGs were directly used for bladder augmentation without intraperitoneal incubation. Histological analyses of the incubated BAMGs demonstrated extensive cell growth and vasculature in homogeneous collagen bundles. The cells were positive for vimentin and negative for α-smooth muscle actin and pan-cytokeratin AE1/AE3. Cystography revealed smoother contours of the augmented bladders in the incubated group at 4 and 12 weeks postoperatively. However, the bladder capacity was not significantly different between the two groups. In both groups, the entire urothelium regenerated well without obvious differences. At both time points, compared with the control group, increased numbers of smooth muscle cells (SMCs) and blood vessels were found in the incubated group. At 12 weeks, the SMCs in the incubated group were more similar to those in the native smooth muscle fiber bundles of the bladder. Taken together, our results demonstrated that BAMGs preincubated in the peritoneum promote the regeneration of bladder smooth muscle via neovascularization in a rat bladder augmentation model.

Influence of packing on the vibrations of homogeneous bundles of C60 peapods

The non-resonant Raman spectra of homogeneous bundles of C60 peapods (C60 inserted in single-walled carbon nanotubes) are calculated in the framework of spectral moment method, together with a bond-polarizability model. The evolutions of the low wavenumber range of the Raman spectrum of homogeneous bundles of C60 peapods as a function of the nanotube diameter and the size of bundles are discussed. The effect of the C60 filling factor is investigated in detail. The results are compared to experimental Raman data measured on various samples of C60 peapods.

Automated multi-subject fiber clustering of mouse brain using dominant sets.

Mapping of structural and functional connectivity may provide deeper understanding of brain function and disfunction. Diffusion Magnetic Resonance Imaging (DMRI) is a powerful technique to non-invasively delineate white matter (WM) tracts and to obtain a three-dimensional description of the structural architecture of the brain. However, DMRI tractography methods produce highly multi-dimensional datasets whose interpretation requires advanced analytical tools. Indeed, manual identification of specific neuroanatomical tracts based on prior anatomical knowledge is time-consuming and prone to operator-induced bias. Here we propose an automatic multi-subject fiber clustering method that enables retrieval of group-wise WM fiber bundles. In order to account for variance across subjects, we developed a multi-subject approach based on a method known as Dominant Sets algorithm, via an intra- and cross-subject clustering. The intra-subject step allows us to reduce the complexity of the raw tractography data, thus obtaining homogeneous neuroanatomically-plausible bundles in each diffusion space. The cross-subject step, characterized by a proper space-invariant metric in the original diffusion space, enables the identification of the same WM bundles across multiple subjects without any prior neuroanatomical knowledge. Quantitative analysis was conducted comparing our algorithm with spectral clustering and affinity propagation methods on synthetic dataset. We also performed qualitative analysis on mouse brain tractography retrieving significant WM structures. The approach serves the final goal of detecting WM bundles at a population level, thus paving the way to the study of the WM organization across groups.

Analysis of the Hodge Laplacian on the Heisenberg group

Introduction Differential forms and the Hodge Laplacian on Hn Bargmann representations and sections of homogeneous bundles Cores, domains and self-adjoint extensions First properties of D k exact and closed forms A decomposition of L2 L kh related to the i?½ and i?½ complexes Intertwining operators and different scalar forms for D k Unitary intertwining operators and projections Decomposition of L2 L k Lp-multipliers Decomposition of Lp L k and boundedness of the Riesz transforms Applications Appendix Bibliography

Special values for conformally invariant systems associated to maximal parabolics of quasi-Heisenberg type

In this paper we construct conformally invariant systems of first order and second order differential operators associated to a homogeneous line bundle $\Cal{L}_{s} \to G_0/Q_0$ with $Q_0$ a maximal parabolic subgroup of quasi-Heisenberg type. This generalizes the results by Barchini, Kable, and Zierau.To do so we use techniques different from ones used by them.

Homogeneous projective bundles over abelian varieties

We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of commutative algebraic groups; the irreducible bundles correspond to Heisenberg groups and their standard representations. Our results extend those of Mukai on semi-homogeneous vector bundles, and yield a geometric view of the Brauer group of abelian varieties.

Conformally invariant systems of differential operators associated to maximal parabolics of quasi-Heisenberg type

Let $G_{0}$ be a simple Lie group and $Q_{0}$ a maximal parabolic subgroup of quasi-Heisenberg type. In this paper we construct conformally invariant systems of differential operators associated to a homogeneous line bundle $\mathcal{L}_{s} \to G_{0}/Q_{0}$. The systems that we construct yield explicit homomorphisms between appropriate generalized Verma modules. We also determine whether or not these homomorphisms are standard.

Classification of homogeneous holomorphic hermitian principal bundles over G/K

Abstract We give a complete classification of isomorphism classes of homogeneous holomorphic hermitian principal bundles over an irreducible hermitian symmetric space of noncompact type. This generalizes the results of our earlier work [Kyoto J. Math. 50 (2010), 325–363] where homogeneous holomorphic hermitian principal bundles over the upper half-plane were considered.