24 research outputs found
Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets
In the paper, we focus on the connectedness of planar self-affine sets
generated by an integer expanding matrix with and a collinear digit set , where and
such that is linearly independent. We discuss
the domain of the digit to determine the connectedness of
. Especially, a complete characterization is obtained when
we restrict to be an integer. Some results on the general case of are obtained as well.Comment: 15 pages, 10 figure
Boundaries of Disk-like Self-affine Tiles
Let be a disk-like self-affine tile generated by an
integral expanding matrix and a consecutive collinear digit set , and let be the characteristic polynomial of . In the
paper, we identify the boundary with a sofic system by
constructing a neighbor graph and derive equivalent conditions for the pair
to be a number system. Moreover, by using the graph-directed
construction and a device of pseudo-norm , we find the generalized
Hausdorff dimension where
is the spectral radius of certain contact matrix . Especially,
when is a similarity, we obtain the standard Hausdorff dimension where is the largest positive zero of
the cubic polynomial , which is simpler than
the known result.Comment: 26 pages, 11 figure
Meta-analysis Followed by Replication Identifies Loci in or near CDKN1B, TET3, CD80, DRAM1, and ARID5B as Associated with Systemic Lupus Erythematosus in Asians
Systemic lupus erythematosus (SLE) is a prototype autoimmune disease with a strong genetic involvement and ethnic differences. Susceptibility genes identified so far only explain a small portion of the genetic heritability of SLE, suggesting that many more loci are yet to be uncovered for this disease. In this study, we performed a meta-analysis of genome-wide association studies on SLE in Chinese Han populations and followed up the findings by replication in four additional Asian cohorts with a total of 5,365 cases and 10,054 corresponding controls. We identified genetic variants in or near CDKN1B, TET3, CD80, DRAM1, and ARID5B as associated with the disease. These findings point to potential roles of cell-cycle regulation, autophagy, and DNA demethylation in SLE pathogenesis. For the region involving TET3 and that involving CDKN1B, multiple independent SNPs were identified, highlighting a phenomenon that might partially explain the missing heritability of complex diseases
Pre-service teachers' attitudes towards mathematics and mathematics education
published_or_final_versionabstracttocEducationMasterMaster of Educatio
Retinal Nerve Fiber Layer Measurements in Myopia: An Optical Coherence Tomography Study
PURPOSE. To evaluate the relationship between retinal nerve fiber layer (RNFL) thickness measured by optical coherence tomography (OCT) and the axial length/refractive error of the eye. METHODS. A total of 115 eyes of 115 healthy subjects, comprising 75 eyes with high myopia (spherical equivalent [SE] Ͻ Ϫ6.0 D) and 40 eyes with low to moderate myopia (SE between Ϫ6.0 D and Ϫ0.5D), were analyzed in this cross-sectional study. Total average and mean clock hour RNFL thicknesses were measured by OCT and compared between the two myopia groups. Associations between RNFL measurements and axial length and spherical equivalent were evaluated by linear regression analysis. RESULTS. The RNFL measurements were significantly lower in the high myopia group compared with those of the low-tomoderate myopia group at 12, 1, and 7 o'clock (right eye orientation). Apart from the temporal clock hours, significant correlations were evident between RNFL measurements and the axial length and spherical equivalent. The average RNFL thickness decreased with increasing axial length (r ϭ Ϫ0.314, P ϭ 0.001) and negative refractive power (r ϭ 0.291, P ϭ 0.002). A significant proportion of myopic eyes were classified as outside normal limits, with reference to the normative database. The most frequently abnormal sector was at 2 o'clock, where 16.5% of myopic eyes were outside normal limits. CONCLUSIONS. RNFL measurements vary with the axial length/ refractive error of the eye. Analysis of RNFL thickness in the evaluation of glaucoma should always be interpreted with reference to the refractive status. Although the normative database provided by OCT has been helpful in identifying ocular diseases involving the RNFL, it may not be reliable in the analysis of myopic eyes. (Invest Ophthalmol Vis Sci. 2006;47: 5171-5176