In this paper we argue that the pattern of cell movements in the morphogenetic process known as convergent extension can be understood as a energy minimization process, provided the cell-cell adhesive energy has a certain kind of anisotropy. This single simple property is sufficient cause for the type of cell elongation, alignment, and intercalation of a cellular array that is the characteristi...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

We are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres) and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections). The notation and terminology used in this paper have been introduced in the From now on X denotes a non empty set, F denotes a filter of X, and S denotes...

Online identification of sinusoidal components is an important problem that occurs in active noise control, vibration suppression, on line health monitoring, and radar, sonar, and seismic applications. We adopt a new approach to this identification problem which consists of the utilization of the underlying nonlinearlity and an algorithm that is based on the nonlinear parameterization. The algo...

and Applied Analysis 3 where σ s σ σj−1 s . In this case, we write σ − limx . By V 2 σ , we denote the set of all σ-convergent and bounded double sequences. One can see that in contrast to the case for single sequences, a convergent double sequence need not be σ-convergent. But every bounded convergent double sequence is σ-convergent. So, c∞ 2 ⊂ V 2 σ ⊂ ∞ 2 . In the case σ i i 1, σ-convergence ...

Coordinated cell movements contribute to the shaping of developing organisms during morphogenesis. Understanding the molecular basis of these directed movements is a crucial part of understanding the mechanisms in action during development. We present here a cellular description of two morphogenetic processes: dorsal closure of the Drosophila embryo and convergent extension in two vertebrate mo...

Deduplication is a storage saving technique which has been adopted by many cloud storage providers such as Dropbox. The simple principle of deduplication is that duplicate data uploaded by different users are stored only once. Unfortunately, deduplication is not compatible with encryption. As a scheme that allows deduplication of encrypted data segments, we propose ClouDedup, a secure and effic...

The constructive study of metric spaces requires at first an examination of each classical proposition for numerical content. In classical mathematics it is a theorem that sequences in a compact space have convergent subsequences, but this is not constructively true. For compact intervals on the real line it has long been known that this theorem is nonconstructive because it implies the Limited...

We proved uniqueness and instability of the symmetric subsonic– sonic flow solution of the compressible potential flow equation in a surface with convergent areas of cross–sections. Such a surface may be regarded as an approximation of a two–dimensional convergent nozzle in aerodynamics. Mathematically these are uniqueness and nonexistence results of a nonlinear degenerate elliptic equation wit...

Simulations using the Extended Potts Model suggest that anisotropic differential adhesion can account for convergent extension, as observed during embryonic development of the frog Xenopus laevis for example. During gastrulation in these frogs, convergent extension produces longitudinal tissue growth from latitudinal elongation and migration of aligned constituent cells. The Extended Potts Mode...