The strip entropy approximation of Markov shifts on trees

The strip entropy is studied in this article. We prove that the strip entropy approximation is valid for every ray of a golden-mean tree. This result extends the previous result of [Petersen-Salama, Discrete \& Continuous Dynamical Systems, 2020] on the conventional 2-tree. Lastly, we prove that the strip entropy approximation is valid for eventually periodic rays of a class of Markov-Cayley trees

XRCC1, but not APE1 and hOGG1 gene polymorphisms is a risk factor for pterygium.

PurposeEpidemiological evidence suggests that UV irradiation plays an important role in pterygium pathogenesis. UV irradiation can produce a wide range of DNA damage. The base excision repair (BER) pathway is considered the most important pathway involved in the repair of radiation-induced DNA damage. Based on previous studies, single-nucleotide polymorphisms (SNPs) in 8-oxoguanine glycosylase-1 (OGG1), X-ray repair cross-complementing-1 (XRCC1), and AP-endonuclease-1 (APE1) genes in the BER pathway have been found to affect the individual sensitivity to radiation exposure and induction of DNA damage. Therefore, we hypothesize that the genetic polymorphisms of these repair genes increase the risk of pterygium.MethodsXRCC1, APE1, and hOGG1 polymorphisms were studied using fluorescence-labeled Taq Man probes on 83 pterygial specimens and 206 normal controls.ResultsThere was a significant difference between the case and control groups in the XRCC1 genotype (p=0.038) but not in hOGG1 (p=0.383) and APE1 (p=0.898). The odds ratio of the XRCC1 A/G polymorphism was 2.592 (95% CI=1.225-5.484, p=0.013) and the G/G polymorphism was 1.212 (95% CI=0.914-1.607), compared to the A/A wild-type genotype. Moreover, individuals who carried at least one C-allele (A/G and G/G) had a 1.710 fold increased risk of developing pterygium compared to those who carried the A/A wild type genotype (OR=1.710; 95% CI: 1.015-2.882, p=0.044). The hOGG1 and APE1 polymorphisms did not have an increased odds ratio compared with the wild type.ConclusionsXRCC1 (Arg399 Glu) is correlated with pterygium and might become a potential marker for the prediction of pterygium susceptibility

Thermally-Switchable Metalenses Based on Quasi-Bound States in the Continuum

Dynamic wavefront shaping with optical metasurfaces has presented a major challenge and inspired a large number of highly elaborate solutions. Here, we experimentally demonstrate thermo-optically reconfigurable, nonlocal metasurfaces using simple device architectures and conventional CMOS-compatible dielectric materials. These metasurfaces support quasi-bound states in the continuum (q-BICs) derived from symmetry breaking and encoded with a spatially varying geometric phase, such that they shape optical wavefront exclusively on spectrally narrowband resonances. Due to the enhanced light-matter interaction enabled by the resonant q-BICs, a slight variation of the refractive index introduced by heating and cooling the entire device leads to a substantial shift of the resonant wavelength and a subsequent change to the optical wavefront associated with the resonance. We experimentally demonstrate a metalens modulator, the focusing capability of which can be thermally turned on and off, and reconfigurable metalenses, which can be thermo-optically switched to produce two distinct focal patterns. Our devices offer a pathway to realize reconfigurable, multifunctional meta-optics using established manufacturing processes and widely available dielectric materials that are conventionally not considered "active" materials due to their small thermo-optic or electro-optic coefficients