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Functional ectodermal organ regeneration based on epithelial and mesenchymal interactions
Published in David M. Gardiner, Regenerative Engineering and Developmental Biology, 2017
Masamitsu Oshima, Takashi Tsuji
Organogenesis is accomplished through a complex process comprising tissue self-organization, cell-to-cell interactions, spatiotemporal gene expressions, and cell movement (Takeichi 2011, Sasai 2013a, 2013b). During embryonic development, organ-forming fields are generated in an orderly, specific process known as embryonic pattern formation (Sasai 2013b). Almost all organs originate from their respective organ germs through reciprocal epithelial–mesenchymal interactions between the immature epithelium and the mesenchyme in each organ-forming field (Pispa and Thesleff 2003, Thesleff 2003, Tucker and Sharpe 2004, Sharpe and Young 2005). Organ development, which relies on inductive properties such as regional and genetic specificity, is regulated by a developmental mechanism based on epithelial–mesenchymal interactions, based on signaling molecules and transcription factor pathways (Gilbert 2013). Ectodermal organs such as the teeth, salivary glands, lacrimal glands, and hair follicles demonstrate extremely similar developmental processes and develop from their respective germ layers through reciprocal interactions based on the epithelium and mesenchyme in the developing embryo. The principal interactions of ectodermal organ development are common to those of other organs. They allow for the organization of a 3D structure consisting of various tissues and cell populations that coordinate with surrounding tissues such as blood vessels and peripheral nerves to achieve the respective physiological organ functions (Jahoda et al. 2003, Pispa and Thesleff 2003, Thesleff 2003, Nishimura et al. 2005, Schechter et al. 2010, Tucker and Miletich 2010).
Anticipation: learning from the past. The Russian/Soviet contributions to the science of anticipation
Published in International Journal of General Systems, 2018
The history of science – and this book is an important contribution to it – is important not only as information about a past as a discontinuous moment definitively relegate to the museum of knowledge, but also – and rather – as an illustration of the process of creativity that allows for the development of scientific paradigms and essential concepts and theories. The emphasis is on the continuity of knowledge which, however, dialectically interwoven with discontinuity, helps us to understand the objective necessity that has supported the formation of similar concepts, having a “family likeness”, but with the new aspects included within them. We can grasp a link between the already “old” cortical activation patterns and the dynamic pattern formation as the means of the self-organization of the living, which preceded the different types of cooperative actions of neurons (Scott Kelso 1995) or of coordination dynamics of complementary pairs (in the same self-organizing patterns) (Scott Kelso and Engstrøm 2006).
An efficient computational approach for solving two-dimensional extended Fisher–Kolmogorov equation
Published in Applicable Analysis, 2022
Kaouther Ismail, Mohamed Rahmeni, Khaled Omrani
In this article, we consider the following initial value problem of the two-dimensional extended Fisher–Kolmogorov (EFK) equation subject to the boundary conditions and the initial condition where is a real-valued function which defined on , is a bounded domain in with boundary , T>0, γ is a positive constant and φ is a given valued function regular enough. The standard Fisher–Kolmogorov problem is obtained by inserting in Equation (1). However, by adding a stabilizing fourth-order derivative term to the Fisher–Kolmogorov equation, Coullet et al. [1] proposed Equation (1) and called it as the EFK equation. Problem (1) arises in a variety of applications such as pattern formation in bi-stable systems [2], propagation of domain walls in liquid crystals [3], travelling waves in reaction diffusion system [4,5] mezoscopic model of a phase transition in a binary system near Lipschitz point [6]. In the recent years, several numerical methods for the solution of the EFK equation have been developed, including -conforming finite element method [7]. An -Galerkin mixed finite element method is applied to the EFK equation by employing a splitting technique and optimal order error estimates are obtained without any restriction on the mesh [8]. A finite pointset method for EFK equation based on mixed formulation was considered in [9]. A Fourier pseudo-spectral method for solving two-dimensional EFK equation was constructed in [10], quintic B-spline collocation technique for one-dimensional EFK model [11], operational matrices of integration of Gegenbauer wavelets [12], a wavelet collocation technique [13], interpolating element free Galerkin method [14], a local boundary integral equation method based on generalized moving least squares [15], a local meshless method called radial basis function-finite difference method [16], a nonlinear finite difference scheme for 1D [17], a difference scheme for two-dimensional EFK model [18], a fourth-order accurate nonlinear finite difference scheme [19], a high-order linearized difference scheme [20]. In [21], He constructed a three-level linearly implicit finite difference method for solving two-dimensional EFK equation, however in his work, we do not find numerical results. In this article, we establish a linearized difference scheme for the two-dimensional EFK equation and prove that the scheme is convergent with the convergence of in the discrete norm.