Delocalization and scaling properties of low-dimensional quasiperiodic systems

In this paper, we explore the localization transition and the scaling properties of both quasi-one-dimensional and two-dimensional quasiperiodic systems, which are constituted from coupling several Aubry-Andr\'{e} (AA) chains along the transverse direction, in the presence of next-nearest-neighbor (NNN) hopping. The localization length, two-terminal conductance, and participation ratio are calculated within the tight-binding Hamiltonian. Our results reveal that a metal-insulator transition could be driven in these systems not only by changing the NNN hopping integral but also by the dimensionality effects. These results are general and hold by coupling distinct AA chains with various model parameters. Furthermore, we show from finite-size scaling that the transport properties of the two-dimensional quasiperiodic system can be described by a single parameter and the scaling function can reach the value 1, contrary to the scaling theory of localization of disordered systems. The underlying physical mechanism is discussed.Comment: 9 pages, 8 figure

Using the Xenopus Developmental Eye Regrowth Stystem to Distinguish the Role of Developmental Versus Regenerative Mechanisms

A longstanding challenge in regeneration biology is to understand the role of developmental mechanisms in restoring lost or damaged tissues and organs. As these body structures were built during embryogenesis, it is not surprising that a number of developmental mechanisms are also active during regeneration. However, it remains unclear whether developmental mechanisms act similarly or differently during regeneration as compared to development. Since regeneration is studied in the context of mature, differentiated tissues, it is difficult to evaluate comparative studies with developmental processes due to the latter’s highly proliferative environment. We have taken a more direct approach to study regeneration in a developmental context (regrowth). Xenopus laevis, the African clawed frog, is a well-established model for both embryology and regeneration studies, especially for the eye. Xenopus eye development is well-defined. Xenopus is also an established model for retinal and lens regeneration studies. Previously, we demonstrated that Xenopus tailbud embryo can successfully regrow a functional eye that is morphologically indistinguishable from an age-matched control eye. In this study, we assessed the temporal regulation of retinal differentiation and patterning restoration during eye regrowth. Our findings showed that during regrowth, cellular patterning and retinal layer formation was delayed by approximately 1 day but was restored by 3 days when compared to eye development. An assessment of the differentiation of ganglion cells, photoreceptor cells, and Müller glia indicated that the retinal birth order generated during regrowth was consistent with that observed for eye development. Thus, retina differentiation and patterning during regrowth is similar to endogenous eye development. We used this eye regrowth model to assess the role of known mechanisms in development versus regrowth. Loss-of-function studies showed that Pax6 was required for both eye development and regrowth whereas apoptosis was only required for regrowth. Together, these results revealed that the mechanisms required for both development and regrowth can be distinguished from regrowth-specific ones. Our study highlights this developmental model of eye regrowth as a robust platform to systematically and efficiently define the molecular mechanisms that are required for regeneration versus development

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization

We study Andreev bound states (ABS) and resulting charge transport of Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures is sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode similar to that in spinless chiral p-wave pairing in topological phase (TP). We clarify that two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether ABS exists at QCP or not. In the former type, ABS has a energy gap and does not cross at zero energy in non-topological phase (NTP). These complex properties can be detected by tunneling conductance between normal metal / RSC junctions.Comment: 5 pages, 6 figure

Universal scheme to generate metal-insulator transition in disordered systems

We propose a scheme to generate metal-insulator transition in random binary layer (RBL) model, which is constructed by randomly assigning two types of layers. Based on a tight-binding Hamiltonian, the localization length is calculated for a variety of RBLs with different cross section geometries by using the transfer-matrix method. Both analytical and numerical results show that a band of extended states could appear in the RBLs and the systems behave as metals by properly tuning the model parameters, due to the existence of a completely ordered subband, leading to a metal-insulator transition in parameter space. Furthermore, the extended states are irrespective of the diagonal and off-diagonal disorder strengths. Our results can be generalized to two- and three-dimensional disordered systems with arbitrary layer structures, and may be realized in Bose-Einstein condensates.Comment: 5 ages, 4 figure

A Model for Investigating Developmental Eye Repair in Xenopus Laevis

Vertebrate eye development is complex and requires early interactions between neuroectoderm and surface ectoderm during embryogenesis. In the African clawed frog, Xenopus laevis, individual eye tissues such as the retina and lens can undergo regeneration. However, it has been reported that removal of either the specified eye field at the neurula stage or the eye during tadpole stage does not induce replacement. Here we describe a model for investigating Xenopus developmental eye repair. We found that tailbud embryos can readily regrow eyes after surgical removal of over 83% of the specified eye and lens tissues. The regrown eye reached a comparable size to the contralateral control by 5 days and overall animal development was normal. It contained the expected complement of eye cell types (including the pigmented epithelium, retina and lens), and is connected to the brain. Our data also demonstrate that apoptosis, an early mechanism that regulates appendage regeneration, is also required for eye regrowth. Treatment with apoptosis inhibitors (M50054 or NS3694) blocked eye regrowth by inhibiting caspase activation. Together, our findings indicate that frog embryos can undergo successful eye repair after considerable tissue loss and reveals a required role for apoptosis in this process. Furthermore, this Xenopus model allows for rapid comparisons of productive eye repair and developmental pathways. It can also facilitate the molecular dissection of signaling mechanisms necessary for initiating repair