Perturbation theory for the Eckart-Young-Mirsky theorem and the constrained total least squares problem

AbstractGolub et al. (Linear Algebra Appl. 88/89 (1987) 317–327), J.Demmel (SIAM J. Numer. Anal. 24 (1987) 199–206), generalized the Eckart-Young-Mirsky (EYM) theorem, which solves the problem of approximating a matrix by one of lower rank with only a specific rectangular subset of the matrix allowed to be changed. Based on their results, this paper presents perturbation analysis for the EYM theorem and the constrained total least squares problem (CTLS)

On solutions of the matrix equations X−AXB=C and X−AXB=C

AbstractThis paper studies the solutions of complex matrix equations X−AXB=C and X−AXB=C, and obtains explicit solutions of the equations by the method of characteristic polynomial and a method of real representation of a complex matrix respectively

Reverse order laws for least squares g-inverses and minimum norm g-inverses of products of two matrices

AbstractIn this paper, we derive equivalent conditions for reverse order laws of least squares g-inverses and minimum norm g-inverses of product of two matrices A and B, by applying the product singular value decomposition (P-SVD)

On solutions of matrix equation AXB + CYD = F

AbstractIn this paper, the matrix equation with two unknown matrices X, Y of form AXB + CYD = F is discussed. By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain expressions of the least-squares solutions of the matrix equation, and sufficient and necessary conditions for the existence and uniqueness of the solutions. We also derive a general form of the solutions. We also study the least-squares Hermitian (skew-Hermitian) solutions of equation AXAH + CYCH = F

A New Double Color Image Watermarking Algorithm Based on the SVD and Arnold Scrambling

We propose a new image watermarking scheme based on the real SVD and Arnold scrambling to embed a color watermarking image into a color host image. Before embedding watermark, the color watermark image W with size of M×M is scrambled by Arnold transformation to obtain a meaningless image W~. Then, the color host image A with size of N×N is divided into nonoverlapping N/M×N/M pixel blocks. In each (i,j) pixel block Ai,j, we form a real matrix Ci,j with the red, green, and blue components of Ai,j and perform the SVD of Ci,j. We then replace the three smallest singular values of Ci,j by the red, green, and blue values of W~ij with scaling factor, to form a new watermarked host image A~ij. With the reserve procedure, we can extract the watermark from the watermarked host image. In the process of the algorithm, we only need to perform real number algebra operations, which have very low computational complexity and are more effective than the one using the quaternion SVD of color image

Regulation of TLR7/9 responses in plasmacytoid dendritic cells by BST2 and ILT7 receptor interaction

Plasmacytoid dendritic cells (pDCs) produce copious type I interferon (IFN) upon sensing nucleic acids through Toll-like receptor (TLR) 7 and TLR9. Uncontrolled pDC activation and IFN production are implicated in lymphopenia and autoimmune diseases; therefore, a mechanism controlling pDC IFN production is essential. Human pDCs specifically express an orphan receptor, immunoglobulin-like transcript 7 (ILT7). Here, we discovered an ILT7 ligand expressed by human cell lines and identified it as bone marrow stromal cell antigen 2 (BST2; CD317). BST2 directly binds to purified ILT7 protein, initiates signaling via the ILT7–FcϵRIγ complex, and strongly inhibits production of IFN and proinflammatory cytokines by pDCs. Readily induced by IFN and other proinflammatory cytokines, BST2 may modulate the human pDC’s IFN responses through ILT7 in a negative feedback fashion

Perturbation of the least squares problem

AbstractConsider the least squares solutions to Ax = b Āx = b̄, where Ā = A + δA and b̄ = b + δb are perturbed from A, b, respectively. In an earlier paper the author deduced the perturbation bounds for the solution when b ∃ R(A). In this paper we extend the results to cover more general cases when b ∉ R(A) and A is not of full rank