The mechanisms by which the branching of epithelial tissue occurs and is regulated to generate different organ structures are not well understood. In this work, image analyses of the organ rudiments demonstrate specific epithelial branching patterns for the early lung and kidney; the lung type typically generating several side branches, whereas kidney branching was mainly dichotomous. Parameter...

The Multicommodity Flow Problem (MCFP) considers the efficient routing of commodities from their origins to their destinations, subject to capacity restrictions and edge costs. This paper studies the NP-hard Minimum Cost Multicommodity k-splittable Flow Problem in which each commodity may use at most k paths between its origin and its destination. The problem has applications in transportation ...

Safflower (Carthamustinctorius L.) is an oilseed crop adapted to drought prone arid and semi-arid environments. This study was conducted to evaluate the effects of water deficit stress on antioxidant activity, membrane stability index (MSI), leaf chlorophyll content, leaf area index (LAI) and their relationship with seed yield using 64 safflower genotypes grown under normal and water defici...

Randić index, R, also known as the connectivity or branching index, is an important topological index in chemistry. In order to attack some conjectures concerning Randić index, Dvořák et al. [5] introduced a modification of this index, denoted by R′. In this paper we present some of the basic properties of R′. We determine graphs with minimal and maximal values of R′, as well as graphs with min...

For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...

The postnatal development of the main neuron type in the ectostriatum, the telencephalic station of the tectofugal pathway, was followed in normally reared and monocularly deprived zebra finches by using the Golgi method. Three parameters were investigated: dendritic field radius, branching index, and spine density. The results show that all three exhibit the same developmental trend--namely, a...

Plant branching is a key process in the yield elaboration of winter oilseed rape (WOSR). It is also involved in plant tolerance to flower damage because it allows the setting of new fertile inflorescences. Here we characterize the changes in the branching and distribution of the number of pods between primary and secondary inflorescences in response to floral bud clippings. Then we investigate ...