In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by D ij = F ii +F jj −2F ij. When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interes...

The axoneme-the conserved core of eukaryotic cilia and flagella-contains highly specialized doublet microtubules (DMTs). A long-standing question is what protein(s) compose the junctions between two tubules in DMT. Here we identify a highly conserved flagellar-associated protein (FAP), FAP20, as an inner junction (IJ) component. The flagella of Chlamydomonas FAP20 mutants have normal length but...

In this note, we investigate the tree-depth and tree-width in a heterogeneous random graph obtained by including each edge $e_{ij}$ $(i\neq j)$ of complete $K_{n}$ over $n$ vertices independently with probability $p_{n}(e_{ij})$. When sequence probabilities satisfies some density assumptions, show both are linear size high probability. Moreover, extend method to weighted graphs non-identical we...

Two entomopathogenic nematodes, Steinernema riobravis and Steinernema carpocapsae, were compared for their ability to parasitize corn earworm, Helicoverpa zea (Boddie) prepupae and pupae in corn plots at the Lower Rio Grande Valley of Texas. The most effective S. riobravis concentration was 200,000 infective juveniles (IJ)/m(2) (95% parasitism), as compared with 100,000 IJ/m(2) (81%), 50,000 IJ...

Table A. ERGM Notations Network Graph Y, Yij a random network graph matrix, its i,j element Y-ij all elements except i,j y the set of all possible graphs for a fixed set of notes y, yij y, yij a realization of the random network graph and its i,j element zk(y) a statistic of network graph y Network Statistics t total number of edges d2 number of nodes which have at least 2 edges hs number of ed...

1 Roadways, the links of transportation networks, are susceptible to a variety of degradations. 2 Some degradation patterns are severe; they make the network incapable of meeting origin3 destination (OD) demands. Most others are non-severe; they increase the network operational 4 cost while OD demands remain met. In other words, the network structure is resilient to such 5 degradations. It is i...

The elastic behavior and stability of elemental crystals are studied in the neighborhood of a stable equilibrium state, also called a phase, at finite pressure p. It is shown that two kinds of elastic constants are needed to describe elasticity under pressure. One set, designated as c(ij),i,j = 1-6, determines stability or lack of it; another set, designated as c(ij)(p), describes the linear re...

A combination of detailed magnetisation studies and electronic-structure analysis using broken-symmetry DFT is used to explore the electronic structure of a trigonal prismatic Cu(II)(6) cluster. The presence of six paramagnetic metal centres with S = 1/2 gives rise to a maximum multiplicity of S = 3 and a total of 31 broken-symmetry states with M(S) < 3. Computed differences in energy between t...

We continue the study in [11, 14] on the upper Lyapunov exponents for products of matrices. Here the matrix function M(x) is only assumed to be non-negative. In general, the variational formula about Lyapunov exponents we obtained in part I does not hold in this setting. Anyway we focus our interest on a special case where M(x) takes finite values M1, . . ., Mm. In this case we prove the variat...