The Stationary State of Epithelial Tissues

Author(s):  
Nicolas Rivier ◽  
Benoit Dubertret ◽  
Gudrun Schliecker
Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1134
Author(s):  
Kenta Higuchi ◽  
Takashi Komatsu ◽  
Norio Konno ◽  
Hisashi Morioka ◽  
Etsuo Segawa

We consider the discrete-time quantum walk whose local dynamics is denoted by a common unitary matrix C at the perturbed region {0,1,⋯,M−1} and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ωn at time n(|ω|=1). From this expression, we compute the scattering on the surface of −1 and M and also compute the quantity how quantum walker accumulates in the perturbed region; namely, the energy of the quantum walk, in the long time limit. The frequency of the initial state of the influence to the energy is symmetric on the unit circle in the complex plain. We find a discontinuity of the energy with respect to the frequency of the inflow.


Genetics ◽  
1997 ◽  
Vol 147 (1) ◽  
pp. 243-253 ◽  
Author(s):  
Joseph Jack ◽  
Guy Myette

Abstract The products of two genes, raw and ribbon (rib), are required for the proper morphogenesis of a variety of tissues. Malpighian tubules mutant for raw or rib are wider and shorter than normal tubules, which are only two cells in circumference when they are fully formed. The mutations alter the shape of the tubules beginning early in their formation and block cell rearrangement late in development, which normally lengthens and narrows the tubes. Mutations of both genes affect a number of other tissues as well. Both genes are required for dorsal closure and retraction of the CNS during embryonic development. In addition, rib mutations block head involution, and broaden and shorten other tubular epithelia (salivary glands, tracheae, and hindgut) in much same manner as they alter the shape of the Malpighian tubules. In tissues in which the shape of cells can be observed readily, rib mutations alter cell shape, which probably causes the change in shape of the organs that are affected. In double mutants raw enhances the phenotypes of all the tissues that are affected by rib but unaffected by raw alone, indicating that raw is also active in these tissues.


1985 ◽  
Vol 38 (5-6) ◽  
pp. 1051-1070 ◽  
Author(s):  
R. Artuso ◽  
V. Benza ◽  
A. Frigerio ◽  
V. Gorini ◽  
E. Montaldi

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