Quasicentral modulus and self-similar sets: a supplementary result to Voiculescu's work

In his recent work, Voiculescu generalized his remarkable formula for the quasicentral modulus of a commuting $n$-tuple of hermitian operators with respect to the $(n,1)$-Lorentz ideal to the case where its spectrum is contained in a Cantor-like self-similar set in a certain class. In this note, we treat general self-similar sets satisfying the open set condition, and obtain lower and upper bounds of the quasicentral modulus. Our proof shows that Voiculescu's formula holds for a class of self-similar sets including the Sierpinski gasket and the Sierpinski carpet.Comment: Condition (A1) is relaxed, and Remark 1 and the proof of Lemma 3.4 are changed. Minor corrections.To appear in Integral Equations and Operator Theor

Histopathological Change of Oral Malignant Tumour and Epithelial Dysplasia Subjected to Photodynamic Therapy

Objectives: The purpose of this study is to analyze the morphological change of cell nuclei and the change of proliferating activity of oral malignancy and epithelial dysplasia between before and after photodynamic therapy in order to predict recurrence.Material and Methods: We experienced 14 cases of oral squamous cell carcinoma, one case of verrucous carcinoma and seven cases of epithelial dysplasia treated by photodynamic therapy (PDT). The mean nuclear area (NA) and coefficient of variation of the nuclear area (NACV) of 100 nuclei per slide were calculated using computer-assisted image analysis in hematoxylin and eosin stained biopsy specimens before and after PDT. Additionally, proliferating cell nuclear antigen (PCNA) immunohistochemistry was carried out in each specimen.Results: The mean NA after PDT was significantly lower than that before PDT in the nonrecurrent group. However, there was no significant difference in mean NA before and after PDT in the recurrent group. There were no significance differences in NACV before and after PDT in either the nonrecurrent or recurrent group. Furthermore, the PCNA labelling indices of the specimens after PDT was significantly lower than that before PDT in both the nonrecurrent and the recurrent group.Conclusions: Mean nuclear area in the biopsy specimen after photodynamic therapy is likely to be a predictive marker for the recurrence of oral squamous cell carcinoma or epithelial dysplasia subjected to photodynamic therapy, while coefficient of variation of the nuclear area and proliferating cell nuclear antigen labelling indices are less helpful in predicting the recurrence of such lesions

The correlation between the 500 pc scale molecular gas masses and AGN powers for massive elliptical galaxies

Massive molecular clouds have been discovered in massive elliptical galaxies at the center of galaxy clusters. Some of this cold gas is expected to flow in the central supermassive black holes and activate galactic nucleus (AGN) feedback. In this study, we analyze archival ALMA data of 9 massive elliptical galaxies, focusing on CO line emissions, to explore the circumnuclear gas. We show that the mass of the molecular gas within a fixed radius (500 pc) from the AGNs (M_mol ~ 10^7-10^8 M_sun) is correlated with the jet power estimated from X-ray cavities (P_cav ~ 10^42-10^45 erg/s). The mass accretion rate of the circumnuclear gas \dot{M} also has a correlation with P_cav. On the other hand, the continuum luminosities at ~1.4 GHz and ~100-300 GHz have no correlation with M_mol. These results indicate that the circumnuclear gas is sustaining the long-term AGN activities (~10^7 yr) rather than the current ones. The circumnuclear gas mass is a better indicator of the jet power than the continuum luminosity, which probably changes on a shorter time scale. We also study the origin of the continuum emission from the AGNs at ~100-300 GHz and find that it is mostly synchrotron radiation. For low-luminosity AGNs, however, dust emission appears to contaminate the continuum.Comment: Accepted for publication in PAS

On Haagerup's list of potential principal graphs of subfactors

We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.Comment: 19 page

Engineering Bone Formation from Human Dental Pulp- and Periodontal Ligament-Derived Cells.

A robust method for inducing bone formation from cultured dental mesenchymal cells has not been established. In this study, a method for generating bone tissue in vivo from cultured human dental pulp- and periodontal ligament-derived cells (DPCs and PDLCs, respectively) was designed using exogenous bone morphogenetic protein 2 (BMP2). DPCs and PDLCs showed enhanced alkaline phosphatase (ALP) activity and calcified nodule formation in medium containing dexamethasone, beta-glycerophosphate, and ascorbic acid (osteogenic medium). However, the addition of recombinant human bone morphogenetic protein 2 (rhBMP2) to osteogenic medium remarkably increased ALP activity and in vitro calcification above the increases observed with osteogenic medium alone. rhBMP2 also significantly upregulated the expression of osteocalcin, osteopontin, and dentin matrix protein 1 mRNA in both cell types cultured in osteogenic medium. Finally, we detected prominent bone-like tissue formation in vivo when cells had been exposed to rhBMP2 in osteogenic medium. In contrast, treatments with osteogenic medium or rhBMP2 alone could not induce abundant mineralized tissue formation. We propose here that treatment with rhBMP2 in osteogenic medium can make dental mesenchymal tissues a highly useful source of cells for bone tissue engineering. In addition, both DPCs and PDLCs showed similar and remarkable osteo-inducibility.The original publication is available at www.springerlink.co

Epithelium-poor Odontogenic Fibroma with an Unusual Progress

Odontogenic fibroma (OF) is a relatively rare benign tumor derived from odontogenic ectodermal mesenchymal tissue. It is divided into central (COF) or peripheral OF (POF) based on the affected area. Regarding its pathological features, OF can also be classified as epithelium-rich (WHO type) or epithelium-poor (simple type), depending on the amount of odontogenic epithelium in the tumor. There is limited information available about the latter type because of its low incidence. We report case of simple type COF apparently like POF. A 52- year-old Japanese male was suffering from tenderness at the right posterior maxilla during occlusion with his removable partial denture. The lesion was diagnosed as a simple type OF arising at the edentulous region around the right molar site of the maxilla. A tumor resection was performed, and there was no evidence of recurrence at his 18-month follow-up examination. In addition, we provide a review of the literature with the most up-to-date information about this lesion so that it can be diagnosed correctly

Prediction of outcome of patients with oral squamous cell carcinoma using vascular invasion and the strongly positive expression of vascular endothelial growth factors.

Vascular invasion and lymph node metastasis have been used as histopathological prognosticators of cancers including oral squamous cell carcinoma (OSCC). In addition to metastatic potential via blood vessels, tumor-induced angiogenesis might also be associated with prognosis. However, the efficacy of combined evaluation of vascular invasion and angiogenesis-associated molecules for the prognosis of OSCC remains obscure. This is also the case in lymph node metastasis and lymphovasculogenesis-associated molecules. The aim of this study was to examine factors related to prognosis to improve the accuracy of prognostic prediction of OSCC using vasculogenesis-associated markers. Ninety specimens of patients from 1991 to 2002 with previously untreated OSCC, who underwent either biopsy or surgery, were histopathologically and immunohistochemically analyzed using antibodies for vascular endothelial growth factor (VEGF)-A, VEGF-C, cyclooxygenase (COX)-2 and Midkine. The ninety cases were composed of 72 well-differentiated, 12 moderately differentiated and 6 poorly differentiated OSCC. Efficient models of prognostic prediction were evaluated by extensive statistical analyses. The presence of vascular invasion or lymph node metastasis was confirmed to be significantly associated with poor prognosis in the univariate analysis. Multivariate logic regression analysis suggested that patients with the strongly positive expression of either VEGF-A or VEGF-C had a significant association with poor prognosis even in patients without vascular invasion and in early-stage patients. Neither COX-2 nor Midkine contributed to predict the prognosis of the patients. The strongly positive expression of VEGF-A or VEGF-C was suggested to reinforce the histopathological diagnosis of vascular invasion and improve the accuracy and efficacy of prognostic prediction of OSCC