We argue that energy minimization can explain the pattern of cell movements in the morphogenetic process known as convergent extension provided that the cell-cell adhesive energy has a certain type of anisotropy, which we describe. This single simple property suffices to cause the cell elongation, cell alignment, and lengthening of a cellular array that characterize convergent extension. We sho...

During development, vertebrate embryos undergo dramatic changes in shape. The lengthening and narrowing of a field of cells, termed convergent extension, contributes to a variety of morphogenetic processes. Focusing on frogs and fish, we review the different cellular mechanisms and the well-conserved signaling pathways that underlie this process.

Let (Ω,F ,P) be a probability space and S = {S1, . . . , SK} a discrete-topological space that consists of K real d-by-d matrices, where K and d both ≥ 2. In this paper, we study the pointwise stabilizability of a discrete-time, time-homogeneous, stationary (p, P)-Markovian jump linear system Ξ = (ξn) n=1 where ξn : Ω → S. Precisely, Ξ is called “pointwise convergent”, if to any initial state x...

Let (Ω,F ,P) be a probability space and S = {S1, . . . , SK} a discrete-topological space that consists of K real d-by-d matrices, where K and d both ≥ 2. In this paper, we study the pointwise stabilizability of a discrete-time, time-homogeneous, stationary (p, P)-Markovian jump linear system Ξ = (ξn) n=1 where ξn : Ω → S. Precisely, Ξ is called “pointwise convergent”, if to any initial state x...

This paper concerns a duality between conditionally convergent real series and permutations of their indices. It is widely known that if one is given a series E ^ which is conditionally convergent but not absolutely convergent, then there is a permutation n such that £«< # £#*(*)• Various authors have studied extensions of this result of Riemann (for example, Smith [8], Steinitz [9], Threlfall ...

Let φ(n) be any function which grows more slowly than exponentially in n, i.e., limsup n→∞ φ(n)1/n ≤ 1. There is a double trigonometric series whose coefficients grow like φ(n), and which is everywhere convergent in the square, restricted rectangular, and one-way iterative senses. Given any preassigned rate, there is a one dimensional trigonometric series whose coefficients grow at that rate, b...

In this article, we introduce the lacunary difference sequence spaces w0(M , θ,∆ n m, p, q), w1(M , θ,∆ n m, p, q) and w∞(M , θ,∆ n m, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define and study the notion of qlacunary ∆nm-statistical convergent sequences. Further, we study the relationship between q-lacunary ∆nm-statis...

Wnt genes play important roles in regulating patterning and morphogenesis during vertebrate gastrulation. In zebrafish, slb/wnt11 is required for convergence and extension movements, but not cell fate specification during gastrulation. To determine if other Wnt genes functionally interact with slb/wnt11, we analysed the role of ppt/wnt5 during zebrafish gastrulation. ppt/wnt5 is maternally prov...

The notation and terminology used here are introduced in the following papers: [17], [19], [20], [3], [4], [2], [16], [5], [1], [18], [9], [11], [12], [8], [6], [7], [13], [10], [21], [14], and [15]. For simplicity, we use the following convention: X denotes a Banach algebra, p denotes a real number, w, z, z1, z2 denote elements of X, k, l, m, n denote natural numbers, s1, s2, s3, s, s ′ denote...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...