Functional maturation during bovine granulopoiesis

Granulocytic precursor cells undergo morphologic changes in the nucleus and the cytoplasm during the process of granulopoiesis, which takes place in the bone marrow. These changes are associated with the development of stage-specific proteins necessary for the highly specialized roles of polymorphonuclear leukocytes in phagocytosis, bacterial killing, and in mediating the inflammatory process. The objective of the current study was to sequence the various events that occur upon functional development of granulocytic bone marrow cells in the bovine species. Cells were obtained from the bone marrow of clinically healthy cows and separated into different stages of maturation using density gradient centrifugation. Three cellular fractions were obtained that were enriched for either early immature, late immature or mature granulocytic cells. Functions and receptor expressions assessed in the three maturation stages were: Fc-IgG(2) receptor and CD11b expression, phagocytosis of Escherichia coli, respiratory burst activity, and cellular myeloperoxidase activity. Immature cells expressed already Fc-IgG(2) receptor and CD11b on their cytoplasma membrane. Phagocytic ability was acquired in the myelocytic stage, but only the more mature forms were readily capable of phagocytosis. Promyelocytes, myelo-cytes and metamyelocytes showed no respiratory burst activity. Only band and segmented cells produced reactive oxygen species. Myeloperoxidase was present at all stages of maturity. Thus, each of the maturation stages was characterized by a selective expression of one or more functions and receptors. Therefore, sequential biochemical maturation is postulated during bovine granulopoiesis

Laplacian spectral characterization of some graph products

This paper studies the Laplacian spectral characterization of some graph products. We consider a class of connected graphs: $\mathscr{G}={G : |EG|\leq|VG|+1}$, and characterize all graphs $G\in\mathscr{G}$ such that the products $G\times K_m$ are $L$-DS graphs. The main result of this paper states that, if $G\in\mathscr{G}$, except for $C_{6}$ and $\Theta_{3,2,5}$, is $L$-DS graph, so is the product $G\times K_{m}$. In addition, the $L$-cospectral graphs with $C_{6}\times K_{m}$ and $\Theta_{3,2,5}\times K_{m}$ have been found.Comment: 19 pages, we showed that several types of graph product are determined by their Laplacian spectr

Immanantal invariants of graphs

AbstractSomething between an expository note and an extended research problem, this article is an invitation to expand the existing literature on a family of graph invariants rooted in linear and multilinear algebra. There are a variety of ways to assign a real n×n matrix K(G) to each n-vertex graph G, so that G and H are isomorphic if and only if K(G) and K(H) are permutation similar. It follows that G and H are isomorphic only if K(G) and K(H) are similar, i.e., that similarity invariants of K(G) are graph theoretic invariants of G, an observation that helps to explain the enormous literature on spectral graph theory. The focus of this article is the permutation part, i.e., on matrix functions that are preserved under permutation similarity if not under all similarity

On the spectra of nonsymmetric Laplacian matrices

A Laplacian matrix is a square real matrix with nonpositive off-diagonal entries and zero row sums. As a matrix associated with a weighted directed graph, it generalizes the Laplacian matrix of an ordinary graph. A standardized Laplacian matrix is a Laplacian matrix with the absolute values of the off-diagonal entries not exceeding 1/n, where n is the order of the matrix. We study the spectra of Laplacian matrices and relations between Laplacian matrices and stochastic matrices. We prove that the standardized Laplacian matrices are semiconvergent. The multiplicities of 0 and 1 as the eigenvalues of a standardized Laplacian matrix are equal to the in-forest dimension of the corresponding digraph and one less than the in-forest dimension of the complementary digraph, respectively. These eigenvalues are semisimple. The spectrum of a standardized Laplacian matrix belongs to the meet of two closed disks, one centered at 1/n, another at 1-1/n, each having radius 1-1/n, and two closed angles, one bounded with two half-lines drawn from 1, another with two half-lines drawn from 0 through certain points. The imaginary parts of the eigenvalues are bounded from above by 1/(2n) cot(pi/2n); this maximum converges to 1/pi as n goes to infinity. Keywords: Laplacian matrix; Laplacian spectrum of graph; Weighted directed graph; Forest dimension of digraph; Stochastic matrixComment: 11 page

A note on unimodular congruence of graphs

AbstractLet Q = Q>(G) be an oriented vertex-edge incidence matrix for the graph G. Then K(G) = QtQ is an “edge version” of the Kirchhoff, or Laplacian, matrix. The purpose of this note is to examine K(G) under (integer) unimodular congruence