Metric dimension of the intersections of a point set with hyperplanes

AbstractIn this paper we improve the construction of Goto (1993) to obtain the Main Theorem: Let n, m and k be arbitrary integers such that 0 ⩽ m ⩽ n − 1 ⩾ 1 and m ⩽ k ⩽ min{2m, n − 1}. Then there exists a point set Xm,kn in Euclidean n-space Rn such that 1.(i) μdimXm,kn = m and dim Xm,kn = k,2.(ii) μdim(Xm,kn ∩ H) = m for every hyperplane H in Rn, and3.(iii) if either k < n − 1 or k = n − 1 = m, then dim(Xm,kn ∩ H) = k for every hyperplane H in Rn.Here dim (respectively μdim) denotes covering (respectively metric) dimension, and by a hyperplane in Rn we mean an (n − 1)-dimensional affine subspace of Rn

Metric-dependent dimension functions

Thesis (Ph.D. in Science)--University of Tsukuba, (B), no. 800, 1992.7.3

Proteinase-mediated drastic morphological change of peptide-amphiphile to induce supramolecular hydrogelation

We report a novel peptide-amphiphile having a simple molecular structure that can gelate an aqueous solution at a remarkably low concentration and can be designed to be responsive to a disease-related enzyme by undergoing a drastic morphological change

High variability of expression profiles of homeologous genes for Wnt, Hh, Notch, and Hippo signaling pathways in Xenopus laevis

Cell signaling pathways, such as Wnt, Hedgehog (Hh), Notch, and Hippo, are essential for embryogenesis, organogenesis, and tissue homeostasis. In this study, we analyzed 415 genes involved in these pathways in the allotetraploid frog, Xenopus laevis. Most genes are retained in two subgenomes called L and S (193 homeologous gene pairs and 29 singletons). This conservation rate of homeologs is much higher than that of all genes in the X. laevis genome (86.9% vs 60.2%). Among singletons, 24 genes are retained in the L subgenome, a rate similar to the average for all genes (82.8% vs 74.6%). In addition, as general components of signal transduction, we also analyzed 32 heparan sulfate proteoglycan (HSPG)-related genes and eight TLE/Groucho transcriptional corepressors-related genes. In these gene sets, all homeologous pairs have been retained. Transcriptome analysis using RNA-seq data from developmental stages and adult tissues demonstrated that most homeologous pairs of signaling components have variable expression patterns, in contrast to the conservative expression profiles of homeologs for transcription factors. Our results indicate that homeologous gene pairs for cell signaling regulation have tended to become subfunctionalized after allotetraploidization. Diversification of signaling pathways by subfunctionalization of homeologs may enhance environmental adaptability. These results provide insights into the evolution of signaling pathways after polyploidization

The Effectiveness of Combined Medical Therapy and Hemodialysis for Hypercalcemia in Anaplastic Lymphoma Kinase-negative Anaplastic Large Cell Lymphoma

A 71-year-old man with a right lower abdominal quadrant epithelial tumor developed gradually worsening lumbago and dysbasia. He became comatose and was admitted to our hospital. He had swelling of the left axillary lymph nodes and necrosis of the 4.0-cm diameter abdominal tumor, which infiltrated the subcutaneous tissues. He was hypercalcemic (16.7mg/dl), and had elevated levels of soluble interleukin-2 receptor (24,090U/ml) and parathyroid hormone-related protein (5.4pmol/l). Computerized tomography (CT) showed left axillary lymphadenopathy, splenomegaly, and a right abdominal-wall mass that was described as anaplastic large cell lymphoma upon pathology. Brain radiography and CT revealed multiple lesions infiltrating the cranium. Magnetic resonance imaging showed diffuse low signal intensity throughout the vertebral spine. The patient was diagnosed with anaplastic lymphoma kinase (ALK) -negative anaplastic large cell lymphoma with hypercalcemia. Fluid replacement and drug therapies including calcitonin had no effect on the hypercalcemia or the coma. The patient\u27s serum calcium concentration decreased after hemodialysis (calcium dialysate concentration, 5mg/dl) and subsequent zoledronic acid hydrate therapy. His consciousness improved by the fifth day of treatment. This rare case of hypercalcemia in ALK-negative anaplastic large cell lymphoma improved with combined medical and hemodialysis therapy

Evaluation of focal damage in the retinal pigment epithelium layer in serous retinal pigment epithelium detachment

The purpose of this study was to evaluate focal damage in the retinal pigment epithelium (RPE) layer in serous retinal pigment epithelium detachment (PED) with multi-contrast optical coherence tomography (OCT), which is capable of simultaneous measurement of OCT angiography, polarization-sensitive OCT and standard OCT images. We evaluated 37 eyes with age-related macular degeneration that had serous PED. Focal RPE damage was indicated by hyper-transmission beneath the RPE-Bruch’s membrane band in standard OCT images. Distribution of RPE melanin was calculated using the dataset from multi-contrast OCT. Twenty-four points with hyper-transmission were detected in 21 of the 37 eyes. Standard OCT images failed to show disruption of the RPE-Bruch’s membrane band at 5 of the 24 hyper-transmission points. Conversely, multi-contrast OCT images clearly showed melanin defects in the RPE-Bruch’s membrane band at all points. Areas of melanin defects with disruption of the RPE-Bruch’s membrane band were significantly larger than those without disruption. The volume of intraretinal hyper-reflective foci was significantly larger in eyes with hyper-transmission than that in eyes without hyper-transmission. Multi-contrast OCT is more sensitive than standard OCT for displaying changes at the RPE-Bruch’s membrane band when there are small areas of RPE damage