On the Craw-Ishii conjecture

Craw and Ishii proved that for a finite abelian group G in SL_3(C) every (projective) relative minimal model of C^3/G is isomorphic to the fine moduli space of \theta-stable G-constellations for some GIT parameter \theta. In this article, we conjecture that the same is true for a finite group G in GL_3(C) if a relative minimal model Y of X=C^3/G is smooth. We prove this for some abelian groups.Comment: comments are welcom

Gravity model explained by the radiation model on a population landscape

Understanding the mechanisms behind human mobility patterns is crucial to improve our ability to optimize and predict traffic flows. Two representative mobility models, i.e., radiation and gravity models, have been extensively compared to each other against various empirical data sets, while their fundamental relation is far from being fully understood. In order to study such a relation, we first model the heterogeneous population landscape by generating a fractal geometry of sites and then by assigning to each site a population independently drawn from a power-law distribution. Then the radiation model on this population landscape, which we call the radiation-on-landscape (RoL) model, is compared to the gravity model to derive the distance exponent in the gravity model in terms of the properties of the population landscape, which is confirmed by the numerical simulations. Consequently, we provide a possible explanation for the origin of the distance exponent in terms of the properties of the heterogeneous population landscape, enabling us to better understand mobility patterns constrained by the travel distance.Comment: 14 pages, 4 figure

On the Craw–Ishii Conjecture

於 城崎国際アートセンター(2015年10月20日-10月23日)平成27年度科学研究費補助金 基盤研究(S)(課題番号23224001, 代表 中村 郁), 平成27年度科学研究費補助金 基盤研究(S)(課題番号24224001, 代表 齋藤 政彦), 平成27年度科学研究費補助金 基盤研究(S)(課題番号25220701, 代表 向井 茂), 平成27年度科学研究費補助金 基盤研究(S)(課題番号15H05738, 代表 金銅 茂之)Date : Oct. 19, 2015 (Mon) — Oct. 23, 2015 (Fri). Venue : Kinosaki International Arts Center.The Kinosaki symposium 2015 is partially supported by Grant-in-Aid for Scientific Research (S) 23224001(PI: Iku Nakamura), 24224001(PI: Masa-Hiko Saito), 25220701(PI: Shigeru Mukai), 15H05738(PI: Shigeyuki Kondo)

Hodge ideals and spectrum of isolated hypersurface singularities

We introduce Hodge ideal spectrum for isolated hypersurface singularities to see the difference between the Hodge ideals and the microlocal $V$-filtration modulo the Jacobian ideal. Via the Tjurina subspectrum, we can compare the Hodge ideal spectrum with the Steenbrink spectrum which can be defined by the microlocal $V$-filtration. As a consequence of a formula of Mustata and Popa, these two spectra coincide in the weighted homogeneous case. We prove sufficient conditions for their coincidence and non-coincidence in some non-weighted-homogeneous cases where the defining function is semi-weighted-homogeneous or with non-degenerate Newton boundary in most cases. We also show that the convenience condition can be avoided in a formula of Zhang for the non-degenerate case, and present an example where the Hodge ideals are not weakly decreasing even modulo the Jacobian ideal.Comment: 29 page

Eliciting usage contexts of safety-critical medical devices

This position paper outlines our approach to improve the usage choice of suitable devices in different health care environments (contexts). Safety-critical medical devices are presumed to have undergone a thorough (user-centred) design process to optimize the device for the intended purpose, user group and environment. However, in real-life health care scenarios, actual usage may not reflect the original design parameters. We suggest the identification of further usage contexts for safety-critical medical devices through ethnographic and other studies, to assist better modelling of the challenges of different usage environments. In combination with system and interaction models, these context models can then be used for decision-support in choosing medical devices that are suitable for the intended environment