In this paper we show that there are explicit Yang-Baxter maps with Darboux-Lax representation between Grassmann extensions of algebraic varieties. Motivated by some recent results on noncommutative extensions of Darboux transformations, we first derive a Darboux matrix associated with the Grassmann-extended derivative Nonlinear Schrödinger (DNLS) equation, and then we deduce novel endomorphism...

In this article we study the duals of Grassmann codes, certain codes coming from the Grassmannian variety. Exploiting their structure, we are able to count and classify all their minimum weight codewords. In this classification the lines lying on the Grassmannian variety play a central role. Related codes, namely the affine Grassmann codes, were introduced more recently in [1], while their dual...

Different topics on the differential geometry of the complex Grassmann manifold are surveyed in relation to the coherent states. A calculation of the tangent conjugate locus and conjugate locus in the complex Grassmann manifold is presented. The proofs use the Jordan’s stationary angles. Also various formulas for the distance on the complex Grassmann manifold are furnished.

Let B be a building over a type set I . Suppose J ⊆ I meets every connected component of the diagram of B and let (P,L) be the point-line truncation of the J -Grassmann geometry of B. We present a theorem that allows one to identify shadows of apartments of residues of B in the point-collinearity graph of (P,L). Also, other results related to shadows of apartments of residues and shadows of res...

In this paper, we study the manifold regularization for the Sliced Inverse Regression (SIR). The manifold regularization improves the standard SIR in two aspects: 1) it encodes the local geometry for SIR and 2) it enables SIR to deal with transductive and semi-supervised learning problems. We prove that the proposed graph Laplacian based regularization is convergent at rate root-n. The projecti...

We analyze dynamical systems of general form possessing gradient (symmetric) and Hamiltonian (antisymmetric) flow parts. The relevance of such systems to self-organizing processes is discussed. Coherent structure formation and related gradient flows on matrix Grassmann type manifolds are considered. The corresponding graph model associated with the partition swap neighborhood problem is studied...

This paper presents a generic approach to analyze the singularity of robots with an articulated nacelle like the H4 robot. Using screw theory, the concept of equivalent twist graph is introduced in order to characterize the constraint wrenches and the actuation wrenches applied to the moving platform. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six...

Based on the inclusion matrices of t-cliques with various sizes of Johnson graphs J(n, t) and Grassmann graphs Jq(n, t) respectively, two families of errorcorrecting pooling designs are given, some of their properties including the errorcorrecting capability together with two parameters ed and e≤dare studied. With an interpretation of matchings K2m of as 2-cliques of Johnson graph J(n, 2), this...

This paper characterizes the effect of finite rate channel state feedback on the sum rate of a multi-access multiple-input multiple-output (MIMO) system. We propose to control the users jointly, specifically, we first choose the users jointly and then select the corresponding beamforming vectors jointly. To quantify the sum rate, this paper introduces the composite Grassmann manifold and the co...