Boundaries of Disk-like Self-affine Tiles

Let $T:= T(A, {\mathcal D})$ be a disk-like self-affine tile generated by an integral expanding matrix $A$ and a consecutive collinear digit set ${\mathcal D}$, and let $f(x)=x^{2}+px+q$ be the characteristic polynomial of $A$. In the paper, we identify the boundary $\partial T$ with a sofic system by constructing a neighbor graph and derive equivalent conditions for the pair $(A,{\mathcal D})$ to be a number system. Moreover, by using the graph-directed construction and a device of pseudo-norm $\omega$, we find the generalized Hausdorff dimension $\dim_H^{\omega} (\partial T)=2\log \rho(M)/\log |q|$ where $\rho(M)$ is the spectral radius of certain contact matrix $M$. Especially, when $A$ is a similarity, we obtain the standard Hausdorff dimension $\dim_H (\partial T)=2\log \rho/\log |q|$ where $\rho$ is the largest positive zero of the cubic polynomial $x^{3}-(|p|-1)x^{2}-(|q|-|p|)x-|q|$, which is simpler than the known result.Comment: 26 pages, 11 figure

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

A survey on position-based routing for vehicular ad hoc networks

Position-based routing is considered to be a very promising routing strategy for communication within vehicular ad hoc networks (VANETs), due to the fact that vehicular nodes can obtain position information from onboard global positioning system receivers and acquire global road layout information from an onboard digital map. Position-based routing protocols, which are based mostly on greedy forwarding, are well-suited to the highly dynamic and rapid-changing network topology of VANETs. In this paper, we outline the background and the latest development in VANETs and survey the state-of-the-art routing protocols previously used in VANETs. We present the pros and cons for each routing protocol, and make a detailed comparison. We also discuss open issues, challenges and future research directions. It is observed that a hybrid routing protocol is the best choice for VANETs in both urban and highway environments.Position-based routing is considered to be a very promising routing strategy for communication within vehicular ad hoc networks (VANETs), due to the fact that vehicular nodes can obtain position information from onboard global positioning system receivers and acquire global road layout information from an onboard digital map. Position-based routing protocols, which are based mostly on greedy forwarding, are well-suited to the highly dynamic and rapid-changing network topology of VANETs. In this paper, we outline the background and the latest development in VANETs and survey the state-of-the-art routing protocols previously used in VANETs. We present the pros and cons for each routing protocol, and make a detailed comparison. We also discuss open issues, challenges and future research directions. It is observed that a hybrid routing protocol is the best choice for VANETs in both urban and highway environments

Estrogen Receptor α Gene Polymorphisms and Peak Bone Density in Chinese Nuclear Families

PBD is an important determinant of osteoporotic fractures. Few studies were performed to search for genes underlying PBD variation in Chinese populations. We tested linkage and/or association of the estrogen receptor α gene polymorphism with PBD in 401 Chinese nuclear families. This study suggests the ER-α gene may have some minor effects on PBM variation in the Chinese population. Low peak bone density (PBD) in adulthood is an important determinant of osteoporotic fractures in the elderly. PBD variation is mainly regulated by genetic factors. Extensive molecular genetics studies have been performed to search for genes underlying PBD variation, largely in whites. Few studies were performed in Chinese populations. In this study, we simultaneously test linkage and/or association of the estrogen receptor α (ER-α) gene polymorphism with PBD in 401 Chinese nuclear families (both parents plus their female children) of 1260 subjects, with the 458 children generally between 20 and 40 years of age. All the subjects were genotyped by polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) at polymorphic PvuII and XbaI sites inside the ER-α gene. Bone mineral density was measured at the lumbar spine (L1-L4) and hip (femoral neck, trochanter, and intertrochanteric region). Raw bone mineral density values were adjusted by age, height, and weight as covariates. We detected marginally significant results for within-family association (transmission disequilibrium; p = 0.054) between the spine bone mineral density variation and the ER-α XbaI genotypes. For the hip bone mineral density variation, significant (p < 0.05) linkage results were generally found for the two intragenic markers. Analyses of the haplotypes defined by the two markers confer further evidence for linkage of the ER-α with the hip PBD variation. In conclusion, this study suggests that the ER-α gene may have minor effects on PBD variation in our Chinese population.link_to_subscribed_fulltex

Polymorphisms of four bone mineral density candidate genes in Chinese populations and comparison with other populations of different ethnicity

Studies on polymorphisms of candidate genes and their association with bone mineral density (BMD) have been reported in many populations, but few have been reported in Chinese populations. We investigated polymorphisms of the following five commonly used markers of four prominent BMD candidate genes with the purpose of identifying useful genetic markers for osteoporosis genetic research in Chinese: the Sp1 and RsaI polymorphisms of the collagen type 1 alpha 1 (Col1a1) gene, the -174G/C promoter polymorphism of the interleukin 6 (IL-6) gene, the Asn363Ser polymorphism of the glucocorticoid receptor (GR) gene, and the T → C polymorphism in intron 5 of the transforming growth factor β 1 (TGF-β 1) gene. We evaluated these polymorphisms using PCR-RFLP in samples of at least 124 random individuals. We compared the polymorphisms of these five markers with other populations using the χ 2 test and Fisher's exact two-tailed test. For the RsaI polymorphism, only three heterozygotes but no variant homozygote were identified. For the -174G/C polymorphic site, only one GC heterozygote and no CC homozygote were found. Alleles s, Ser, and A 1 at the Sp1, Asn363Ser, and T → C marker sites that have been found to be polymorphic in other populations were not found in Chinese. Significant differences of allele and genotype frequency distributions were observed at these polymorphisms (P < 0.001) after comparing with other populations. Our results suggest that variant alleles of the five markers are absent or too rare to be useful genetic makers in Chinese, despite the fact that they have been commonly used as polymorphic markers in osteoporosis genetic research in other populations. © Springer-Verlag 2003.link_to_subscribed_fulltex

Differentiation of Caucasians and Chinese at bone mass candidate genes: Implication for ethnic difference of bone mass

Bone mineral density (BMD) is an important risk factor for osteoporosis and has strong genetic determination. While average BMD differs among major ethnic groups, several important candidate genes have been shown to underlie BMD variation within populations of the same ethnicity. To investigate whether important candidate genes may contribute to ethnic differences in BMD, we studied the degree of genetic differentiation among several important candidate genes between two major ethnic groups: Caucasians and Chinese. The genetic variability of these two populations (1131 randomly selected individuals) was studied at six restriction sites exhibiting polymorphisms of five important candidate genes for BMD: the BsaHI polymorphism of the calcium-sensing receptor (CASR) gene, the SacI polymorphism of the α 2HS-glycoprotein (AHSG) gene, the PvuII and XbaI polymorphisms of the estrogen receptor α (ESR1) gene, the ApaI polymorphism of the vitamin D receptor (VDR) gene, and the BstBI polymorphism of the parathyroid hormone (PTH) gene. The two ethnic groups showed significant allelic and genotypic differentiation of all the polymorphisms studied. The mean F ST was 0.103, which significantly differed from zero (P < 0.01). The Chinese population had lower mean heterozygosity (0.331) than the Caucasian one (0.444); the CASR-BsaHI and PTH-BstBI polymorphisms contributed most significantly to this difference. Analysis of the intra- and inter-population variability suggests that various types of natural selection may affect the observed patterns of variation at some loci. If some of the candidate genes we studied indeed underlie variation in BMD, their population differentiation revealed here between ethnic groups may contribute to understanding ethnic difference in BMD. © University College London 2003.link_to_subscribed_fulltex