Restrictions of generalized Verma modules to symmetric pairs

We initiate a new line of investigation on branching problems for generalized Verma modules with respect to complex reductive symmetric pairs (g,k). Here we note that Verma modules of g may not contain any simple module when restricted to a reductive subalgebra k in general. In this article, using the geometry of K_C orbits on the generalized flag variety G_C/P_C, we give a necessary and sufficient condition on the triple (g,k, p) such that the restriction X|_k always contains simple k-modules for any g-module $X$ lying in the parabolic BGG category O^p attached to a parabolic subalgebra p of g. Formulas are derived for the Gelfand-Kirillov dimension of any simple k-module occurring in a simple generalized Verma module of g. We then prove that the restriction X|_k is multiplicity-free for any generic g-module X \in O if and only if (g,k) is isomorphic to a direct sum of (A_n,A_{n-1}), (B_n,D_n), or (D_{n+1},B_n). We also see that the restriction X|_k is multiplicity-free for any symmetric pair (g, k) and any parabolic subalgebra p with abelian nilradical and for any generic g-module X \in O^p. Explicit branching laws are also presented.Comment: 31 pages, To appear in Transformation Group

From scene flow to visual odometry through local and global regularisation in markov random fields

We revisit pairwise Markov Random Field (MRF) formulations for RGB-D scene flow and leverage novel advances in processor design for real-time implementations. We consider scene flow approaches which consist of data terms enforcing intensity consistency between consecutive images, together with regularisation terms which impose smoothness over the flow field. To achieve real-time operation, previous systems leveraged GPUs and implemented regularisation only between variables corresponding to neighbouring pixels. Such systems could estimate continuously deforming flow fields but the lack of global regularisation over the whole field made them ineffective for visual odometry. We leverage the GraphCore Intelligence Processing Unit (IPU) graph processor chip, which consists of 1216 independent cores called tiles, each with 256 kB local memory. The tiles are connected to an ultrafast all-to-all communication fabric which enables efficient data transmission between the tiles in an arbitrary communication pattern. We propose a distributed formulation for dense RGB-D scene flow based on Gaussian Belief Propagation which leverages the architecture of this processor to implement both local and global regularisation. Local regularisation is enforced for pairs of flow estimates whose corresponding pixels are neighbours, while global regularisation is defined for flow estimate pairs whose corresponding pixels are far from each other on the image plane. Using both types of regularisation allows our algorithm to handle a variety of in-scene motion and makes it suitable for estimating deforming scene flow, piece-wise rigid scene flow and visual odometry within the same system

Model independent approach to studies of the confining dual Abrikosov vortex in SU(2) lattice gauge theory

We address the problem of determining the type I, type II or borderline dual superconductor behavior in maximal Abelian gauge SU(2) through the study of the dual Abrikosov vortex. We find that significant electric currents in the simulation data call into question the use of the dual Ginzburg Landau Higgs model in interpreting the data. Further, two definitions of the penetration depth parameter take two different values. The splitting of this parameter into two is intricately connected to the existence of electric currents. It is important in our approach that we employ definitions of flux and electric and magnetic currents that respect Maxwell equations exactly for lattice averages independent of lattice spacings. Applied to specific Wilson loop sizes, our conclusions differ from those that use the dual GLH model.Comment: 18 pages, 14 figures, change title, new anaylysis with more figure

Thermal one- and two-graviton Green's functions in the temporal gauge

The thermal one- and two-graviton Green's function are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading T^4 as well as the subleading T^2 and log(T) contributions to the graviton self-energy. The gauge fixing independence of the leading T^4 terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the 't Hooft identities for the subleading T^2 terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading T^2 contributions.Comment: 17 pages, 5 figures. Revised version to be published in Phys. Rev.

Motion of individual red blood cells in a concentrated suspension flowing through micro-channels

In this study, we use a confocal micro-PIV (Particle Image Velocimetry) system to investigate red blood cell motions flowing in micro-channels. This system enables us to visualize the individual RBCs even in the high Hct blood by exciting the labeled RBCs by the laser. We measure individual trajectories of RBCs in a micro-channel with stenosis or bifurcation under high Hct conditions. Our results clearly demonstrate that the trajectories of RBCs strongly depend on the hematocrit, the RBC property and the position in the micro-channel. This information is important for a better understanding of mass transport in the microcirculation

Blood-on-chips: flow through complex geometries

Blood is a complex body fluid, composed of cells and plasma, which holds a massive amount of information about several physiological and pathologic events happening throughout the body. Hence, blood sampling and analysis are used extensively in traditional clinical laboratories for the diagnosis of several diseases. Since the inception of microfluidics, there has been a growing interest, by both microfluidic and biomedical communities, to develop blood-on-chip devices as an alternative tool for the diagnosis of major diseases, such as cancer and cardiovascular diseases. Therefore, it is essential to understand the blood flow behaviour involved in this kind of microfluidic channels in order to design reliable blood-on-a-chip devices able to efficiently treat and diagnose a variety of diseases. The present experimental study shows the effect of micro-scale contractions and expansions, such as those found in an artificial stenosis, on the blood flow and cell behaviour. The micro-channels were fabricated in PDMS using softlithography and the experiments were carried out by using dextran 40 containing different fractions of human erythrocytes. The in vitro blood flow was measured by means of a high-speed video microscopy system composed with an inverted microscope, a high-speed camera and a thermo plate to control the surrounding temperature

Exceptional Sequences of Line Bundles and Spherical Twists - a Toric Example

Exceptional sequences of line bundles on a smooth projective toric surface are automatically full when they can be constructed via augmentation. By using spherical twists, we give examples that there are also exceptional sequences which can not be constructed this way but are nevertheless full.Comment: 12 pages, 3 figure