Maximum Likelihood Estimation of Log-Concave Densities on Tree Space

Phylogenetic trees are key data objects in biology, and the method of phylogenetic reconstruction has been highly developed. The space of phylogenetic trees is a nonpositively curved metric space. Recently, statistical methods to analyze the set of trees on this space are being developed utilizing this property. Meanwhile, in Euclidean space, the log-concave maximum likelihood method has emerged as a new nonparametric method for probability density estimation. In this paper, we derive a sufficient condition for the existence and uniqueness of the log-concave maximum likelihood estimator on tree space. We also propose an estimation algorithm for one and two dimensions. Since various factors affect the inferred trees, it is difficult to specify the distribution of sample trees. The class of log-concave densities is nonparametric, and yet the estimation can be conducted by the maximum likelihood method without selecting hyperparameters. We compare the estimation performance with a previously developed kernel density estimator numerically. In our examples where the true density is log-concave, we demonstrate that our estimator has a smaller integrated squared error when the sample size is large. We also conduct numerical experiments of clustering using the Expectation-Maximization (EM) algorithm and compare the results with k-means++ clustering using Fr\'echet mean.Comment: 41 pages, 10 figure

インド論理学者が描くパーニニ文法学 : 『ニヤーヤマンジャリー』第六日課の研究

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 丸井 浩, 東京大学教授 斎藤 明, 東京大学准教授 小林 正人, 広島大学教授 小川 英世, 東北大学教授 吉水 清孝University of Tokyo(東京大学

Pulmonary Artery Leiomyosarcoma Diagnosed without Delay

A 63-year-old female presented with abnormal lung shadows but had, apart from this, few symptoms. Computed tomography (CT) revealed multiple nodules and blockage of the pulmonary artery. She was immediately diagnosed with pulmonary artery sarcoma based on a careful differential diagnosis and underwent surgery. Her tumor was pathologically diagnosed as leiomyosarcoma (i.e. intimal sarcoma). Pulmonary artery sarcoma can be easily confounded with thromboembolism in a clinical setting and some cases are diagnosed post mortem only. In our case, clinical prediction scores (Wells score, Geneva score, and revised Geneva score) for the pulmonary embolism showed low probability. Moreover, chest CT showed uncommon findings for pulmonary thromboembolism, as the nodules were too big for thrombi. Because surgical resection can provide the only hope of long-term survival in cases of pulmonary artery sarcoma, clinicians should consider this possibility in the differential diagnosis of pulmonary embolism. Clinical prediction scores and CT findings might help to reach the correct diagnosis of pulmonary artery sarcoma

Primary leiomyoma of the bladder

The case presented is of a 47-year-old patient with an extravesical pedunculated bladder leiomyoma, which was difficult to distinguish from a retroperitoneal tumor. Preoperatively, it was suspected to be a retroperitoneal tumor and a laparotomy with tumor resection was performed. lntraoperatively, the bladder and tumor were connected by a cord-like tissue. A retrospective review of preoperative images revealed that cord-like tissue, identified intraoperatively, was also present. Bladder leiomyomas can grow as extravesical pedunculated tumors. Therefore, when the continuity between the bladder and tumor is only a cord-like object, the finding of continuity is useful to diagnose with bladder leiomyoma

Malignant Mesothelioma in the Thoracic Cavity of a Crj:CD(SD) Rat Characterized by Round Hyalinous Stroma

Spontaneous malignant mesothelioma was found in a 104-week-old male Crj:CD(SD) rat. The tumor was scattered on the surface of the lung, heart, mediastinal pleura and thoracic wall and metastasized to the alveolar septa. Histopathologically, small flattened or cuboidal tumor cells proliferated with stroma, formed almost normal papillary structures and reacted positively to colloidal iron stain and immunohistochemical staining for mesothelin. Round hyalinous stromata were pronounced, which is a characteristic feature, and the possible reason for this is as follows; at first, a small amount of collagen fibers was formed in the center of the clusters of several tumor cells, and then the cell clusters expanded like balloons with an increase in the collagen fibers

Efficient Drug Delivery of Paclitaxel Glycoside: A Novel Solubility Gradient Encapsulation into Liposomes Coupled with Immunoliposomes Preparation

Although the encapsulation of paclitaxel into liposomes has been extensively studied, its significant hydrophobic and uncharged character has generated substantial difficulties concerning its efficient encapsulation into the inner water core of liposomes. We found that a more hydrophilic paclitaxel molecule, 7-glucosyloxyacetylpaclitaxel, retained tubulin polymerization stabilization activity. The hydrophilic nature of 7-glucosyloxyacetylpaclitaxel allowed its efficient encapsulation into the inner water core of liposomes, which was successfully accomplished using a remote loading method with a solubility gradient between 40% ethylene glycol and Cremophor EL/ethanol in PBS. Trastuzumab was then conjugated onto the surface of liposomes as immunoliposomes to selectively target human epidermal growth factor receptor-2 (HER2)-overexpressing cancer cells. In vitro cytotoxicity assays revealed that the immunoliposomes enhanced the toxicity of 7-glucosyloxyacetylpaclitaxel in HER2-overexpressing cancer cells and showed more rapid suppression of cell growth. The immunoliposomes strongly inhibited the tumor growth of HT-29 cells xenografted in nude mice. Notably, mice survived when treated with the immunoliposomes formulation, even when administered at a lethal dose of 7-glucosyloxyacetylpaclitaxel in vivo. This data successfully demonstrates immunoliposomes as a promising candidate for the efficient delivery of paclitaxel glycoside

Genomic view of heavy-ion-induced deletions associated with distribution of essential genes in Arabidopsis thaliana

Heavy-ion beam, a type of ionizing radiation, has been applied to plant breeding as a powerful mutagen and is a promising tool to induce large deletions and chromosomal rearrangements. The effectiveness of heavy-ion irradiation can be explained by linear energy transfer (LET; keV µm-1). Heavy-ion beams with different LET values induce different types and sizes of mutations. It has been suggested that deletion size increases with increasing LET value, and complex chromosomal rearrangements are induced in higher LET radiations. In this study, we mapped heavy-ion beam-induced deletions detected in Arabidopsis mutants to its genome. We revealed that deletion sizes were similar between different LETs (100 to 290 keV μm-1), that their upper limit was affected by the distribution of essential genes, and that the detected chromosomal rearrangements avoid disrupting the essential genes. We also focused on tandemly arrayed genes (TAGs), where two or more homologous genes are adjacent to one another in the genome. Our results suggested that 100 keV µm-1 of LET is enough to disrupt TAGs and that the distribution of essential genes strongly affects the heritability of mutations overlapping them. Our results provide a genomic view of large deletion inductions in the Arabidopsis genome