Bott-Samelson varieties factor the flag variety G/B into a product of CP’s with a map into G/B. These varieties are mostly studied in the case in which the map into G/B is birational; however in this paper we study fibers of this map when it is not birational. We will see that in some cases this fiber is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to tran...

This paper describes a new approach for extending MUltiple SIgnal Classification (MUSIC) to underdetermined direction-of-arrival (DOA) estimation with high resolution by exploiting higher-order moments. The proposed method maps the observed signals nonlinearly onto a space of expanded dimensions, in which signal statistics are analyzed. The covariance matrix in the higher-dimensional space corr...

In this paper we introduce the Extended Method of Moments (XMM) estimator. This estimator accommodates a more general set of moment restrictions than the standard Generalized Method of Moments (GMM) estimator. More specifically, the XMM differs from the GMM in that it can handle not only uniform conditional moment restrictions (i.e. valid for any value of the conditioning variable), but also lo...

A classical result of Schur and Horn [Sc, Ho] states that the set of diagonal elements of all n x n Hermitian matrices with fixed eigenvalues is a convex set in IRn. Kostant [Kt] has generalized this result to the case of any semisimple Lie group. This is often referred to as the linear convexity theorem of Kostant: picking up the diagonal of a Hermitian matrix is a linear operation. This resul...

We study, in type A, the algebraic cycles (MV-cycles) discovered by I. Mirkovi´c and K. Vilonen [MV]. In particular, we partition the loop Grassmannian into smooth pieces such that the MV-cycles are their closures. We explicitly describe the points in each piece using the lattice model of the loop Grassmannian in type A. The partition is invariant under the action of the coweights and, up to th...

We study, in type A, the algebraic cycles (MV-cycles) discovered by I. Mirkovi´c and K. Vilonen [MV]. In particular, we partition the loop Grassmannian into smooth pieces such that the MV-cycles are their closures. We explicitly describe the points in each piece using the lattice model of the loop Grassmannian in type A. The partition is invariant under the action of the coweights and, up to th...

In type A, Bott-Samelson varieties are posets in which ascending chains are flags of vector spaces. They come equipped with a map into the flag variety G/B. These varieties are mostly studied in the case in which the map into G/B is birational to the image. In this paper we study Bott-Samelsons for general types, more precisely, we study the combinatorics a fiber of the map into G/B when it is ...

A new visual navigation method for a mobile robot is proposed in this paper. Its originality lies in integrating a sketched map with a semantic map together for the robot’s navigation and in using unified tags to help recognize landmarks. In this sketched semantic map, the outline and semantic information of key referenced objects are used to represent thems...

The present article focuses on the evaluation of a first-moment closure model applicable to film cooling flow and heat transfer computations. The present first-moment closure model consists of a higher level of turbulent heat flux modeling in which two additional transport equations for temperature variance kθ and its dissipation rate εθ are ...

We show that our earlierwork in [LT05] extends to the twisted case, that is, we defined a notion of moment map and reduction in both twisted generalized complex geometry and twisted generalized Kähler geometry. This is a short note to show that our results in our previously posted paper, Symmetries in generalized Kähler geometry [LT05], can be easily extended to the case of twisted generalized ...