Sprouting angiogenesis, crucial for the development of new blood vessels, is a prime example of collective migration in which endothelial cells migrate as a group joined via cadherin-containing adherens junctions (AJ). The actomyosin apparatus is connected to AJ and generates contractile forces, which, depending on their strength and duration, increase or decrease cell cohesion. Thus, appropria...

The paper studies the counting function R2(n, k) = ∑ a1+a2+···+ak=n (ai,aj)=1 i 6=j 1, ai ≥ 1, k ≥ 2 with ai, n and k positive integers and establishes a relationship between R2(n, k) and P2(n, k) where P2(n, k) = ∑ a1+a2+···+ak=n 1≤a1≤a2≤···≤ak≤n (ai,aj)=1 i 6=j 1, ai ≥ 1, k ≥ 2 with ai, n, k positive integers. 1. PRELIMINARIES Gould [4], studied the number-theoretic function R(n, k) = ∑ a1+a2...

Cadherin-based adherens junctions (AJs) mediate cell adhesion and regulate cell shape change. The nectin-afadin complex also localizes to AJs and links to the cytoskeleton. Mammalian afadin has been suggested to be essential for adhesion and polarity establishment, but its mechanism of action is unclear. In contrast, Drosophila melanogaster's afadin homologue Canoe (Cno) has suggested roles in ...

The receptor tyrosine kinase human epidermal growth factor receptor-2 (HER2) is known to regulate pulmonary epithelial barrier function; however, the mechanisms behind this effect remain unidentified. We hypothesized that HER2 signaling alters the epithelial barrier through an interaction with the adherens junction (AJ) protein β-catenin, leading to dissolution of the AJ. In quiescent pulmonary...

Let 0 < 2 and let def = ei : 2 [ ; ] . We show that for generalized (non–negative) polynomials P of degree r and p > 0, we have m X j=1 jP (aj)j aj e aj e + pr + 1 2!1=2 c (pr + 1) Z P e p d ; where a1; a2; :::; am 2 , c is an absolute constant (and, thus, it is independent of , , p, m, r, P , fajg) and is an explicitly determined constant which measures the number of points fajg in a small int...

Let G be a multidigraph with vertices V (G) and arcs A(G). G is balanced if d+G(v) = d − G(v) for every v ∈ V (G). Let ri, rj be the number of cycles in G that include ai, aj ∈ A(G) respectively, and ri ≥ rj. Local quality index of G is defined as the largest ratio ri rj for opposite arcs ai, aj . Global quality index of G is defined as the largest ratio ri rj for distinct arcs ai, aj . In this...

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The affine synthesis operator Sc = ∑j>0 ∑k∈Zd cj,kψj,k is shown to map the coefficient space (Z+ × Zd ) surjectively onto Lp(Rd ), for p ∈ (0, 1]. Here ψj,k(x) = | det aj |ψ(aj x − k) for dilation matrices aj that expand, and the synthesizer ψ ∈ Lp(Rd ) need satisfy only mild restrictions, for example, ψ ∈ L1(Rd ) with nonzero integral or else with periodization that is real-valued, nontrivial ...