Holonomic Gradient Descent and its Application to Fisher-Bingham Integral

We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere $S^n$, which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.Comment: 23 pages, 1 figur

Perturbation method for determining the group of invariance of hierarchical models

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in Aoki and Takemura [2008a]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof in Aoki and Takemura [2008a] which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model.Comment: 17pages, no figure

Transcriptional Repression of Cdc25B by IER5 Inhibits the Proliferation of Leukemic Progenitor Cells through NF-YB and p300 in Acute Myeloid Leukemia

The immediately-early response gene 5 (IER5) has been reported to be induced by γ-ray irradiation and to play a role in the induction of cell death caused by radiation. We previously identified IER5 as one of the 2,3,4-tribromo-3-methyl-1-phenylphospholane 1-oxide (TMPP)-induced transcriptional responses in AML cells, using microarrays that encompassed the entire human genome. However, the biochemical pathway and mechanisms of IER5 function in regulation of the cell cycle remain unclear. In this study, we investigated the involvement of IER5 in the cell cycle and in cell proliferation of acute myeloid leukemia (AML) cells. We found that the over-expression of IER5 in AML cell lines and in AML-derived ALDHhi (High Aldehyde Dehydrogenase activity)/CD34+ cells inhibited their proliferation compared to control cells, through induction of G2/M cell cycle arrest and a decrease in Cdc25B expression. Moreover, the over-expression of IER5 reduced colony formation of AML-derived ALDHhi/CD34+ cells due to a decrease in Cdc25B expression. In addition, over-expression of Cdc25B restored TMPP inhibitory effects on colony formation in IER5-suppressed AML-derived ALDHhi/CD34+ cells. Furthermore, the IER5 reduced Cdc25B mRNA expression through direct binding to Cdc25B promoter and mediated its transcriptional attenuation through NF-YB and p300 transcriptinal factors. In summary, we found that transcriptional repression mediated by IER5 regulates Cdc25B expression levels via the release of NF-YB and p300 in AML-derived ALDHhi/CD34+ cells, resulting in inhibition of AML progenitor cell proliferation through modulation of cell cycle. Thus, the induction of IER5 expression represents an attractive target for AML therapy

Hierarchical subspace models for contingency tables

For statistical analysis of multiway contingency tables we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving conditional independence structures in the hierarchical model. We discuss estimation and exacts tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets.Comment: 26 page

Hierarchical subspace models for contingency tables

For the statistical analysis of multiway contingency tables, we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving the localization property of the inference in the hierarchical model. This approach also enables us to evaluate the localization property of a given log-affine model. We discuss estimation and exact tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets.Context specific interaction model Divider Markov bases Split model Uniform association model